Processes Library User Manual D Water_Quality_Processes_Technical_Reference_Manual Water Quality Technical Reference

User Manual: Pdf D-Water_Quality_Processes_Technical_Reference_Manual

Open the PDF directly: View PDF PDF.
Page Count: 481

DownloadProcesses Library User Manual D-Water_Quality_Processes_Technical_Reference_Manual D-Water Quality Technical Reference
Open PDF In BrowserView PDF
1D/2D/3D Modelling suite for integral water solutions

DR
AF

T

Delft3D Flexible Mesh Suite

D-Water Quality Processes Library Description

Technical Reference Manual

DR
AF
T

T

DR
AF

Processes Library Description
Detailed description of Processes
Technical Reference Manual

Released for:
Delft3D FM Suite 2018
D-HYDRO Suite 2018
SOBEK Suite 3.7
WAQ Suite 2018

Version: 5.01
SVN Revision: 54328
April 18, 2018

DR
AF

T

Processes Library Description, Technical Reference Manual

Published and printed by:
Deltares
Boussinesqweg 1
2629 HV Delft
P.O. 177
2600 MH Delft
The Netherlands

For sales contact:
telephone: +31 88 335 81 88
fax:
+31 88 335 81 11
e-mail:
software@deltares.nl
www:
https://www.deltares.nl/software

telephone:
fax:
e-mail:
www:

+31 88 335 82 73
+31 88 335 85 82
info@deltares.nl
https://www.deltares.nl

For support contact:
telephone: +31 88 335 81 00
fax:
+31 88 335 81 11
e-mail:
software.support@deltares.nl
www:
https://www.deltares.nl/software

Copyright © 2018 Deltares
All rights reserved. No part of this document may be reproduced in any form by print, photo
print, photo copy, microfilm or any other means, without written permission from the publisher:
Deltares.

Contents

Contents
List of Figures

vii

List of Tables

ix

1 How to find your way in this manual
1.1 Introduction . . . . . . . . . . . . .
1.2 Overview . . . . . . . . . . . . . .
1.3 Processes reference tables . . . . .
1.4 What’s new? . . . . . . . . . . . .
1.5 Backward compatibility . . . . . . .
1.6 Modelling water and sediment layers
1.6.1 Usage notes . . . . . . . .

.
.
.
.
.
.
.

1
1
1
3
4
6
7
7

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

9
10
20
24
26
29
31
32
32
33
33
34
41
44
44
44
45

3 Nutrients
3.1 Nitrification . . . . . . .
3.2 Calculation of NH3 . . .
3.3 Denitrification . . . . . .
3.4 Adsorption of phosphate
3.5 Formation of vivianite . .
3.6 Formation of apatite . . .
3.7 Dissolution of opal silicate

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

47
48
54
57
63
71
75
78

4 Primary producers
4.1 Introduction to primary production . . . . . . . . . . . . . .
4.2 Growth and mortality of algae (BLOOM) . . . . . . . . . .
4.3 Bottom fixation of BLOOM algae types . . . . . . . . . . .
4.4 Settling of phytoplankton . . . . . . . . . . . . . . . . . .
4.5 Production and mortality of algae (DYNAMO) . . . . . . . .
4.6 Computation of the phytoplankton composition (DYNAMO) .
4.7 Production and mortality of benthic diatoms S1/2 (DYNAMO)
4.8 Mortality and re-growth of terrestrial vegetation (VEGMOD) .

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

81
82
83
102
104
107
116
119
125

DR
AF

T

2 Oxygen and BOD
2.1 Reaeration, the air-water exchange of DO . . . .
2.2 Dam reaeration, SOBEK only . . . . . . . . . .
2.3 Saturation concentration of DO . . . . . . . . .
2.4 Diurnal variation of DO . . . . . . . . . . . . .
2.5 Calculation of daily minimal DO concentration .
2.6 Calculation of actual DO concentration . . . . .
2.7 BOD, COD and SOD decomposition . . . . . .
2.7.1 Chemical oxygen demand . . . . . . .
2.7.2 Biochemical oxygen demand . . . . . .
2.7.3 Measurements and relations . . . . . .
2.7.4 Accuracy . . . . . . . . . . . . . . . .
2.8 Sediment oxygen demand . . . . . . . . . . .
2.9 Production of substances: TEWOR, SOBEK only
2.9.1 Coliform bacteria – listing of processes .
2.9.2 TEWOR-production fluxes . . . . . . .
2.9.3 Process TEWOR: Oxydation of BOD . .

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

.
.
.
.
.
.
.

5 Macrophytes
137
5.1 Framework of the macrophyte module . . . . . . . . . . . . . . . . . . . . . 138
5.1.1 Relation macrophyte module and other DELWAQ processes . . . . . 138

Deltares

iii

Processes Library Description, Technical Reference Manual

5.4

5.5
5.6
5.7

T

5.3

DR
AF

5.2

5.1.2 Growth forms . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 Plant parts . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.4 Usage note . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.5 Different macrophyte growth forms . . . . . . . . . . . . . . .
Growth of submerged and emerged biomass of macrophytes . . . . . .
5.2.1 Nutrient limitation . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Uptake of carbon, nitrogen and phosphorus from rhizomes . . .
5.2.3 Daylength limitation . . . . . . . . . . . . . . . . . . . . . . .
5.2.4 Temperature limitation . . . . . . . . . . . . . . . . . . . . .
5.2.5 Decay of emerged and submerged biomass . . . . . . . . . .
5.2.5.1 Hints for use . . . . . . . . . . . . . . . . . . . . .
5.2.6 Growth of the rhizomes/root system . . . . . . . . . . . . . . .
5.2.7 Formation of particulate organic carbon . . . . . . . . . . . . .
5.2.8 Uptake of nitrogen and phosphorus from sediment . . . . . . .
5.2.8.1 Hints for use . . . . . . . . . . . . . . . . . . . . .
5.2.9 Uptake of nitrogen and phosphorus from water . . . . . . . . .
5.2.10 Oxygen production and consumption . . . . . . . . . . . . . .
5.2.11 Net growth of emerged and submerged vegetation and rhizomes
Maximum biomass per macrophyte species . . . . . . . . . . . . . . .
5.3.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Hints for use . . . . . . . . . . . . . . . . . . . . . . . . . .
Grazing and harvesting . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Grazing . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 Hints for use . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.3 Harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . .
Light limitation for macrophytes . . . . . . . . . . . . . . . . . . . . .
Vegetation coverage . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . .
Vertical distribution of submerged macrophytes . . . . . . . . . . . . .
5.7.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.1.1 Linear distribution (SwDisSMii=1) . . . . . . . . . . .
5.7.1.2 Exponential distribution (SwDisSMii=2) . . . . . . . .
5.7.2 Hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 Light regime
6.1 Light intensity in the water column . . .
6.2 Extinction coefficient of the water column
6.3 Variable solar radiation during the day . .
6.4 Computation of day length . . . . . . .
6.5 Computation of Secchi depth . . . . . .

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

7 Primary consumers and higher trophic levels
7.1 Grazing by zooplankton and zoobenthos (CONSBL)
7.2 Grazing by zooplankton and zoobenthos (DEBGRZ)
8 Organic matter (detritus)
8.1 Decomposition of detritus . . . . . . . . . . .
8.2 Consumption of electron-acceptors . . . . . .
8.3 Settling of detritus . . . . . . . . . . . . . . .
8.4 Mineralization of detritus in the sediment (S1/2)

.
.
.
.

.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

139
140
140
140
144
145
145
146
147
148
148
148
149
150
150
151
151
152
153
153
153
155
155
156
156
158
159
159
161
161
161
163
164

.
.
.
.
.

.
.
.
.
.

.
.
.
.
.

165
166
170
180
183
185

187
. . . . . . . . . . . . . 188
. . . . . . . . . . . . . 199

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

217
218
228
241
245

9 Inorganic substances and pH
249
9.1 Air-water exchange of CO2 . . . . . . . . . . . . . . . . . . . . . . . . . . 250
9.2 Saturation concentration of CO2 . . . . . . . . . . . . . . . . . . . . . . . 255
9.3 Calculation of the pH and the carbonate speciation . . . . . . . . . . . . . . 258

iv

Deltares

Contents

9.4
9.5
9.6
9.7
9.8
9.9
9.10
9.11
9.12
9.13
9.14
9.15
9.16

Volatilisation of methane . . . . . . . . . . .
Saturation concentration of methane . . . . .
Ebullition of methane . . . . . . . . . . . . .
Oxidation of methane . . . . . . . . . . . . .
Oxidation of sulfide . . . . . . . . . . . . . .
Precipitation and dissolution of sulfide . . . . .
Speciation of dissolved sulfide . . . . . . . .
Precipitation, dissolution and conversion of iron
Reduction of iron by sulfides . . . . . . . . .
Oxidation of iron sulfides . . . . . . . . . . .
Oxidation of dissolved iron . . . . . . . . . .
Speciation of dissolved iron . . . . . . . . . .
Conversion salinity and chloride process . . .

.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.

T

10 Organic micropollutants
10.1 Partitioning of organic micropollutants . . . . . . . . .
10.2 Calculation of organic matter . . . . . . . . . . . . .
10.3 Dissolution of organic micropollutants . . . . . . . . .
10.4 Overall degradation . . . . . . . . . . . . . . . . . .
10.5 Redox status . . . . . . . . . . . . . . . . . . . . .
10.6 Volatilisation . . . . . . . . . . . . . . . . . . . . .
10.7 Transport coefficients . . . . . . . . . . . . . . . . .
10.8 Settling of micropollutants . . . . . . . . . . . . . . .
10.9 Sediment-water exchange of dissolved micropollutants
10.10 General contaminants . . . . . . . . . . . . . . . . .

.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

DR
AF

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.

269
274
276
278
282
285
288
292
301
304
307
310
315

.
.
.
.
.
.
.
.
.
.

317
. 318
. 326
. 328
. 330
. 335
. 337
. 343
. 347
. 351
. 355

11 Heavy metals
357
11.1 Partitioning of heavy metals . . . . . . . . . . . . . . . . . . . . . . . . . . 358
11.2 Reprofunctions for partition coefficients . . . . . . . . . . . . . . . . . . . . 371
12 Bacterial pollutants
12.1 Mortality of coliform bacteria

375
. . . . . . . . . . . . . . . . . . . . . . . . . 376

13 Sediment and mass transport
13.1 Settling of sediment . . . . . . . . . . . . . . . . .
13.2 Calculation of settling fluxes of suspended matter . .
13.3 Transport in sediment for layered sediment . . . . .
13.4 Transport in sediment and resuspension (S1/2) . . .
13.5 Calculation of horizontal flow velocity . . . . . . . .
13.6 Calculation of the Chézy coefficient . . . . . . . . .
13.7 Waves . . . . . . . . . . . . . . . . . . . . . . .
13.8 Calculation of wind fetch and wave initial depth . . .
13.9 Calculation of bottom shear stress . . . . . . . . .
13.10 Computation of horizontal dispersion . . . . . . . .
13.11 Computation of horizontal dispersion (one-dimension)
13.12 Allocation of dispersion from segment to exchange .
13.13 Conversion of segment variable to exchange variable
13.14 Conversion of exchange variable to segment variable

.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.

379
380
386
389
395
405
407
409
411
413
416
417
418
419
420

14 Temperature
421
14.1 Calculation of water temperature . . . . . . . . . . . . . . . . . . . . . . . 422
14.2 Calculation of temperature for flats run dry . . . . . . . . . . . . . . . . . . 424
15 Various auxiliary processes
15.1 Computation of aggregate substances

Deltares

427
. . . . . . . . . . . . . . . . . . . . 428

v

Processes Library Description, Technical Reference Manual

15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9

Computation of the sediment composition (S1/2) . . .
Allocation of diffusive and atmospheric loads . . . . .
Calculation of the depth of water column or water layer
Calculation of horizontal surface area . . . . . . . . .
Calculation of gradients . . . . . . . . . . . . . . . .
Calculation of residence time . . . . . . . . . . . . .
Calculation of age of water . . . . . . . . . . . . . .
Inspecting the attributes . . . . . . . . . . . . . . . .

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.

432
437
438
439
440
441
442
443

16 Deprecated processes descriptions
445
16.1 Growth and mortality of algae (MONALG) . . . . . . . . . . . . . . . . . . . 446
455

DR
AF

T

References

vi

Deltares

List of Figures

List of Figures

2.2
2.3
2.4

2.5
2.6

3.1
3.2

3.4

4.1
4.2
4.3

4.4

4.5

4.6

5.1
5.2
5.3
5.4
5.5
5.6
5.7

6.1

Deltares

. 19
. 27
. 38

. 39
. 39
. 40

Figure 1 Default pragmatic oxygen limitation function for nitrification (O2FuncNit,
option 0). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Default pragmatic oxygen inhibition function for denitrification (O2Func, option
0). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Variation of the equilibrium concentration AAP (eqAAP) as a function of PO4
and the maximum adsorption capacity (MaxPO4AAP). . . . . . . . . . . . .
Variation of the equilibrium concentration of AAP (eqAAP) as a function of PO4
and the partition coefficient of PO4 (KdPO4AAP). . . . . . . . . . . . . . . .

DR
AF

3.3

The reaeration rate RCRear (=klrear20 20/H) as a function of water depth, flow
velocity and/or wind velocity for various options SWRear for the mass transfer
coefficient klrear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The distribution of gross primary production over a day . . . . . . . . . . .
A typical oxygen demand curve . . . . . . . . . . . . . . . . . . . . . . .
The relation between the amount of oxidizable carbonaceous material [mgC/l],
the amount of oxygen consumed in the stabilisation of this organic material
after 5 days and after ultimate time . . . . . . . . . . . . . . . . . . . . .
Default and optional oxygen functions for decay of CBOD (O2FuncBOD) . .
Optional function for the calculation of the first order rate constant for BOD and
NBOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

T

2.1

Example of the salinity dependent mortality function . . . . . . . . . . . . .
Primary production rate of algae species i as a function of temperature and
radiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Limitation function for radiation (f rad_i) for algae species i as a function of
radiation (Is,RAD) at different temperature ranging from 5 to 25 ◦ C. . . . . .
Interactions between the compartments of a vegetation cohort (left side, green)
and the detritus fractions POC1–5/DOC in the model (particulate fractions
brown, dissolved fraction blue). Similar schemes apply to PON1–5/DON,
POP1–5/DOP and POS1–5/DOS. . . . . . . . . . . . . . . . . . . . . . . .
The growth curve of a vegetation cohort (y -axis) as a function of it’s age is a
function of 4-parameters: minimum biomass (MIN), maximum target biomass
(MAX), cohort age where 50 % of maximum biomass is achieved (b) and a
factor indicating how ‘smooth’ the growth curve is (s). . . . . . . . . . . . . .
The effect of shape constant Fs(F ) on the distribution of vegetation biomass
above the sediment (a) and vegetation biomass in the sediment (b). The symbols used are explained in the text (T = Ht ). . . . . . . . . . . . . . . . . .
Interactions between the nutrient cycles and the life cycle of macrophytes. . .
The different macrophytes growth forms that can be modeled with the Macrophyte Module. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The abbreviations for the parts of the vegetation that are used in the equations.
The light intensity under water – explanation of the variables in the light intensity functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Definition of the quantities used for determining the linear vertical distribution. .
Definition of the quantities used for determining the exponential vertical distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Examples of the exponential vertical distribution for three values of the shape
parameter F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53
62
70
70
89
115
115

134

134

135
138
139
140
160
162
163
164

Day length calculated by the module DAYL for the latitudes 10 ◦ , 52.1◦ , 65◦ and
75◦ . The latitude of 52.1◦ refers to De Bilt, The Netherlands . . . . . . . . . . 184

vii

Processes Library Description, Technical Reference Manual

8.1
8.2

When an algae module is included. . . . . . . . . . . . . . . . . . . . . . . 220
When the terrestrial vegetation module is included. . . . . . . . . . . . . . . 220

10.1 Liquid-air exchange rate (kvol) for a very volatile pollutant

. . . . . . . . . . 342

13.1 Sedimentation velocity as a function of total suspended solid concentration
solely . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
13.2 Sedimentation velocity (VSed) as a function of salinity solely (effect of flocculation and density not included). . . . . . . . . . . . . . . . . . . . . . . . . 385
. . . . . . . . . . . . . 451

DR
AF

T

16.1 Example of the salinity dependent mortality function

viii

Deltares

List of Tables

List of Tables
Definitions of the parameters in the above equations for REAROXY . . . . .
Factor ’b’ (characteristic structure) for various structures. . . . . . . . . . .
Definitions of the parameters in the above equations for REAROXY . . . . .
Definitions of the parameters in the above equations for REAROXY . . . . .
Definitions of the parameters in the equations for SATUROXY . . . . . . . .
Definitions of the parameters in the above equations for VAROXY . . . . . .
Definition of the parameters in the equations and the mode input for OXYMIN
Definitions of the parameters in the above equations for POSOXY . . . . . .
Typical values for oxygen demanding waste waters (values in [mgO2 /l]) . . .
SOBEK-WQ processes for coliform bacteria. . . . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for PROD_TEWOR. . .
Definitions of the parameters in the above equations for DBOD_TEWOR. . .

3.1

Definitions of the parameters in the above equations for NITRIF_NH4. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . .
Definitions of the input parameters in the formulations for NH3FREE. . . . .
Definitions of the parameters in the above equations for DENWAT_NO3. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for DENSED_NO3. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for ADSPO4AAP. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for VIVIANITE. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for APATITE. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for DISSI. Volume units
refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . . .
b

w

DR
AF

3.2
3.3

T

2.1
2.2
2.3
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11

3.4
3.5
3.6
3.7
3.8

b

4.1
4.2
4.3
4.4

4.5

b

w

b

w

b

w

b

w

b

w

w

.
.
.
.
.
.
.
.
.
.
.
.

17
22
22
23
25
28
30
31
32
44
44
45

. 52
. 56
. 61
. 62
. 69
. 74
. 77
. 80

Definitions of the input parameters in the formulations for BLOOM. . . . . . . 98
Definitions of the output parameters for BLOOM. . . . . . . . . . . . . . . . 101
Definitions of the input parameters in the above equations for SED(i), SEDPHBLO and SEDPHDYN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Definitions of the input parameters in the above equations for GROMRT_(i),
TF_(i), NL(i), DL_(i), RAD_(i), PPRLIM, NUTUPT_ALG and NUTREL_ALG.
(i) = Green or Gree for green algae (input names maximum 10 letters
long!), and (i) = Diat for diatoms. . . . . . . . . . . . . . . . . . . . . . . 114
Definitions of the input parameters in the above equations for PHY_DYN. (i) is
a substance name, Green or Diat. Volume units refer to bulk ( ) or to water
( ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Definitions of the output parameters in the above equations for PHY_DYN.
Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . 118
Definitions of the input parameters in the above equations for GROMRT_DS1,
TF_DIAT , DL_DIAT , RAD_DIAT S1, MRTDIAT_S1, MRTDIAT_S2 and
NRALG_S1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Definitions of the input parameters in the above equations for VBMORT(i),
VB(i)_MRT3W, VB(i)_MRT3S, VBGROWTH(i), VB(i)UPT, VB(i)_UPT3D, VB(i)AVAILN
and VBSTATUS(i). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Definitions of the additional output parameters for VBMORT(i), VB(i)_MRT3W,
VB(i)_MRT3S, VBGROWTH(i), VB(i)UPT, VB(i)_UPT3D, VB(i)AVAILN and VBSTATUS(i). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
b

w

4.6

b

4.7

4.8

4.9

Deltares

w

ix

Processes Library Description, Technical Reference Manual

Computation of the maximum biomass of three macrophyte species as a function of the Habitat Suitability Index. . . . . . . . . . . . . . . . . . . . . . . 154

6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8

Definitions of the input parameters in the formulations for CALCRAD. . . . . .
Definitions of the output parameters for CALCRAD. . . . . . . . . . . . . . .
Definitions of the input parameters in the formulations for CALCRADDAY. . . .
Table IV Definitions of the output parameters for CALCRADDAY. . . . . . . .
Definitions of the input parameters in the formulations for CALCRAD_UV. . . .
Definitions of the output parameters for CALCRAD_UV. . . . . . . . . . . . .
Definitions of the input parameters in the formulations for Extinc_VLG. . . . .
Definitions of the input parameters in the formulations for ExtinaBVLP (ExtinaBVL) for BLOOM algae. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Definitions of the input parameters in the formulations for ExtPhDVL. . . . . .
Definitions of the output parameters for Extinc_VLG, ExtinaBVLP (ExtinaBVL),
ExtPhDVL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Definitions of the input parameters in the formulations for Extinc_UVG. . . . .
Definitions of the input parameters in the formulations for ExtinaBUVP (ExtinaBUV) for BLOOM algae. . . . . . . . . . . . . . . . . . . . . . . . . . .
Definitions of the input parameters in the formulations for ExtPhDUV. . . . . .
Definitions of the output parameters for Extinc_UVG, ExtinaBUVP (ExtinaBUV),
ExtPhDUV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Definitions of the input parameters in the formulations for DAYRAD. . . . . . .
Definitions of the output parameters for DAYRAD. . . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for SECCHI, exclusive of
input parameters for auxiliary process UITZICHT. . . . . . . . . . . . . . . .

6.11
6.12
6.13
6.14
6.15
6.16
6.17

7.1
7.2
7.3
7.4
8.1
8.1
8.1
8.2
8.2
8.3

DR
AF

6.9
6.10

T

5.1

Definitions of the input parameters in the formulations for CONSBL.
Definitions of the output parameters for CONSBL. . . . . . . . . .
Definitions of the input parameters in the formulations for DEBGRZ.
Definitions of the output parameters for DEBGRZ. . . . . . . . . .

8.5

b

9.4
9.5
9.6

x

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

175
175
176
177
178
178
179
182
182
186
196
198
211
216

Definitions of the input parameters in the above equations for DECFAST, DECMEDIUM
and DECSLOW. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . 224
Definitions of the input parameters in the above equations for DECFAST, DECMEDIUM
and DECSLOW. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . 225
Definitions of the input parameters in the above equations for DECFAST, DECMEDIUM
and DECSLOW. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . 226
Definitions of the input parameters in the above equations for DECREFR,
DECDOC and DECPOC5. Volume units refer to bulk ( ) or to water ( ). . . . 226
Definitions of the input parameters in the above equations for DECREFR,
DECDOC and DECPOC5. Volume units refer to bulk ( ) or to water ( ). . . . 227
Definitions of the parameters in the above equations for CONSELAC. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . 238
Definitions of the input parameters in the above equations for SED_(i), SEDN(i)
and SED_CAAP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Definitions of the parameters in the above equations for BMS1_i, BMS2_i,
DESO_AAPS1 and DESO_AAPS2. ) (i) is one of the names of the 7 detritus
components or AAP. (k) indicates sediment layer 1 or 2. Volume units refer to
bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
b

8.4

.
.
.
.

167
168
168
168
168
169
174

b

w

b

w

b

w

b

w

b

w

w

w

Definitions of the parameters in the above equations for REARCO2. . . . . . 254
Definitions of the parameters in the above equations for SATURCO2. . . . . . 257
Processes in D-Water Quality with effects on pH . . . . . . . . . . . . . . . 258

Deltares

List of Tables

9.7

Definitions of the input parameters in the above equations for pH _simp. Vol-

9.8

ume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . 268
Definitions of the output parameters of pH _simp. Volume units refer to bulk
b

( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for VOLATCH4. . . . . .
The efinitions of the parameters in the above equations for SATURCH4. . . . .
Definitions of the parameters in the above equations for EBULCH4. . . . . . .
Definitions of the parameters in the above equations for OXIDCH4. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for OXIDSUD. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for PRECSUL. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . .
Definitions of the input parameters in the above equations for SPECSUD. . . .
Definitions of the input parameters in the above equations for SPECSUDS1/2.
Definitions of the output parameters of SPECSUD and SPECSUDS1/2. . . . .
Definitions of the parameters in the above equations for PRIRON concerning
oxidizing iron. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . .
Definitions of the parameters in the above equations for PRIRON concerning
reducing iron. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . .
Definitions of the parameters in the above equations for PRIRON concerning
reducing iron. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . .
Definitions of the parameters in the above equations for PRIRON concerning
reducing iron. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . .
Definitions of the parameters in the above equations for IRONRED. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for IRONRED. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for SULPHOX. Volume
units refer to bulk ( ) or to water ( ) . . . . . . . . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for SULPHOX. Volume
units refer to bulk ( ) or to water ( ) . . . . . . . . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for IRONOX. Volume units
refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . . . .
Definitions of the input parameters in the above equations for SPECIRON. . .
Definitions of the input parameters in the above equations for SPECIRON. . .
Definitions of the output parameters of SPECIRON. . . . . . . . . . . . . . .
Definitions of the parameters in the above equations for SALINCHLOR. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . .

9.13
9.14
9.15
9.16
9.17
9.18

w

b

w

b

w

b

w

b

w

DR
AF

9.19

T

b

9.9
9.10
9.11
9.12

w

9.19
9.19
9.20

9.20
9.21
9.21
9.22

b

w

b

w

b

w

b

w

b

9.23
9.23
9.24
9.25

b

w

b

w

b

w

w

b

w

10.1 Definitions of the input parameters in the above equations for PARTWK_(i). (i)
is a substance name. Volume units refer to bulk ( ) or to water ( ). . . . . .
10.2 Definitions of the input parameters in the above equations for PARTS1_(i) and
PARTS2_(i). (i) is a substance name. (k) indicates sediment layer 1 or 2.
Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . .
10.3 Definitions of the output parameters for PARTWK_(i). (i) is a substance name.
Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . .
10.3 Definitions of the output parameters for PARTWK_(i). (i) is a substance name.
Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . .
b

Deltares

b

w

b

w

b

w

w

268
273
275
277
281
284
287
290
291
291
298
298
299
300
302
303
305
306
309
313
314
314
316

. 323

. 324
. 324
. 325

xi

Processes Library Description, Technical Reference Manual

10.4 Definitions of the output parameters for PARTS1_(i) and PARTS2_(i). (i) is a
substance name. (k) indicates sediment layer 1 or 2. Volume units refer to
bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
10.5 Definitions of the input parameters in the above equations for MAKOOC, MAKOOCS1
and MAKOOCS2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
10.6 Definitions of the ouput parameters in the above equations for MAKOOC,
MAKOOCS1 and MAKOOCS2. . . . . . . . . . . . . . . . . . . . . . . . . 327
10.7 Definitions of the parameters in the above equations for DISOMP_(i). (i) is a
substance name. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . 329
10.8 Definitions of the parameters in the above equations for LOS_WK_(i). (i) is a
substance name. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
10.9 Definitions of the parameters in the above equations for LOS_S1/2_(i). (i) is a
substance name. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
10.10 Definitions of the parameters in the above equations for SWOXYPARWK. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . 336
10.11 Definitions of the parameters in the above equations. (i) is a substance name. 341
10.12 Definitions of the parameters in the above equations for TRCOEF_(i). (i) is a
substance name. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
10.13 Definitions of the input parameters in the above equations for SED_(i). . . . . 349
10.13 Definitions of the input parameters in the above equations for SED_(i). . . . . 350
10.14 Definitions of the parameters in the above equations for SWEOMP_(i). (i) is a
substance name. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . 353
10.14 Definitions of the parameters in the above equations for SWEOMP_(i). (i) is a
substance name. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . 354
10.15 Definitions of the specific parameters in the above equations for cascade(i) . . 356
b

w

w

DR
AF

b

w

T

b

b

w

b

w

11.1 Definitions of the input parameters in the above equations for PARTWK_(i) in
relation to sorption. (i) is a substance name. Volume units refer to bulk ( ) or
to water ( ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2 Definitions of the input parameters in the above equations for PARTS1_(i) and
PARTS2_(i) in relation to sorption. (i) is a substance name. (k) indicates
sediment layer 1 or 2. Volume units refer to bulk ( ) or to water ( ). . . . . .
11.3 Definitions of the input parameters in the above equations for PARTWK_(i),
PARTS1_(i) and PARTS2_(i) in relation to precipitation. (i) is a substance
name. (k) indicates sediment layer 1 or 2. . . . . . . . . . . . . . . . . . .
11.4 Definitions of the output parameters for PARTWK_(i). (i) is a substance name.
Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . .
11.5 Definitions of the output parameters for PARTS1_(i) and PARTS2_(i). (i) is a
substance name. (k) indicates sediment layer 1 or 2. Volume units refer to
bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.6 Definitions of input parameters in RFPART_(i), (i) is a substance name. . . .
b

w

b

b

b

w

w

w

. 366

. 367

. 368
. 369

. 370
. 374

12.1 Conversion constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
12.2 Definitions of the parameters in the above equations for (i)MORT. . . . . . . . 378
13.1 Definitions of the input parameters in the above equations for SED_(i), S_(i)
and CALVS_(i). (i) is the name of a substance. . . . . . . . . . . . . . . .
13.2 Definitions of the input parameters in the formulations for SUM_SEDIM. (i) is
IM1, IM2 or IM3. (j) is POC1, POC2, POC3 or POC4. . . . . . . . . . . . .
13.3 Definitions of the input parameters in the formulations for SED_SOD. . . . .
13.4 Definitions of the input parameters in the above equations for ADVTRA, DSPTRA and TRASE2_(i) (or TRSE2_(i) or TRSE2(i)). Volume units refer to bulk
( ), water ( ) or solids ( ). . . . . . . . . . . . . . . . . . . . . . . . . .
b

xii

w

s

. 382
. 388
. 388

. 393

Deltares

List of Tables

T

13.5 Definitions of the input parameters in the above equations for S12TRA(i). . .
13.6 Definitions of the input parameters in the above equations for RES_DM. . .
13.7 Definitions of the input parameters in the above equations for BUR_DM. . .
13.8 Definitions of the input parameters in the above equations for DIG_DM. . . .
13.9 Definitions of the input and output parameters for VELOC . . . . . . . . . .
13.10 Definitions of the input and output parameters for CHEZY . . . . . . . . . .
13.11 Definitions of the input and output parameters for WAVE . . . . . . . . . .
13.12 Definitions of the input and output parameters for WDEPTH. (i) runs from 1 to
8. Only the input parameters for (i) is 1 and 2 are required. . . . . . . . . .
13.13 Definitions of the input and output parameters for WFETCH. (i) runs from 1 to
8. Only the input parameters for (i) is 1 and 2 are required. . . . . . . . . .
13.14 Definitions of the input and output parameters for CALTAU . . . . . . . . .
13.15 Definitions of the input and output parameters for HDISPERVEL . . . . . .
13.16 Definitions of the input and output parameters for HORZDISP . . . . . . . .
13.17 Definitions of the input and output parameters for VERTDISP . . . . . . . .

.
.
.
.
.
.
.

401
402
403
403
406
408
410

. 411
.
.
.
.
.

412
415
416
417
418

14.1 Definitions of the parameters in the above equations for TEMPERATUR. . . . 426

DR
AF

15.1 Definitions of the output parameters for COMPOS. (i) is POC1, POC2, POC3
or POC4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.2 Definitions of the input parameters in the above equations for S1_COMP and
S2_COMP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.3 Definitions of the output parameters in the above equations for S1_COMP and
S2_COMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.4 Definitions of the input and output parameters . . . . . . . . . . . . . . . .
16.1 Definitions of the input parameters in the formulations for MONALG.

Deltares

. 431
. 435
. 436
. 443

. . . . . 452

xiii

DR
AF

T

Processes Library Description, Technical Reference Manual

xiv

Deltares

1 How to find your way in this manual
1.1

Introduction
This part of the D-Water Quality manual is called the Technical Reference Manual. It contains an overview of state variables, input parameters and output parameters and a detailed
description of all processes included in the Processes Library for Delft3D and SOBEK. You
should use detailed process descriptions in combination with the Processes Library Configuration Tool (PLCT) in order to connect state variables, input parameters, default values and
output parameters to mathematical formulations.

Implementation
Formulation

Directives for use

References
Parameter Tables

1.2

List of substances or other state variables for which the process is
implemented, with references to other (auxiliary) processes used
Detailed description of mathematical formulations and all process
parameters and coefficients
Definition of the schematisations (1DV, 1DH, 2DV, 2DH, 3D) for which
the process can be used
Tips for use of the process and for the quantification of input parameters
List of referenced literature
Tabulated lists of all input parameters and coefficients, and of output
parameters (not included for some processes)

DR
AF

Direction

T

Each process in the Processes Library is documented separately. Each process description
starts with an introduction containing background and conceptual information, which precedes
the following items:

Overview

This manual provides process descriptions per group of substances. Within each group the
proces descriptions have been ranked according to individual substances and the position in
a processes cycle. Production comes first, and is followed by decomposition and removal.
Additional processes that provide parameters to primary processes immediately follow the
primary processes. Auxiliary processes that basically deliver additional output parameters
take the last position.
Primary processes for a group of substances may affect the substances of another group
as well, because they deliver mass fluxes for these substances. Typical examples are the
processes that concern biomass or dead organic matter. These processes deliver fluxes
for many other substances such as oxygen and nutrients. Auxiliary processes may provide
additional input or output parameters, and do generally not deliver mass fluxes.
The Processes Library of D-Water Quality contains a comprehensive set of substances and
processes, that covers a wide range of water quality parameters. In view of making the water
quality module, D-Water Quality, available as open source modelling software, the Processes
Library has been optimised into one coherent standard set of substances and processes for
Delft3D. Usually only a part of this will be implemented in a specific water quality model. A
selection can be made with Delft3D’s user interface (PLCT). To facilitate the quick selection of
substances and processes for a specific type of model such as a model for eutrophication or a
model for dissolved oxygen Deltares intends to make available predefined sets. However, the
manual is equally applicable to all selections, because the processes formulations are exactly
the same for each selection.
The Processes Libary used for SOBEK still uses its own set of substances and processes,

Deltares

1 of 464

Processes Library Description, Technical Reference Manual

accessible in the form of pre-defined configurations. These configurations contain selections
of substances and processes, on which this manual does not provide information. Parts of this
manual that concern SOBEK only are indicated as such. Deltares intends to merge SOBEK’s
set of substances and processes with the standard set as described in this manual.

T

Present D-Water Quality has two standard options for the modelling of sediment-water interaction, a simplified approach and an advanced approach. The user interface supports only
the simplified ’S1-S2’ approach, for which additional substances represent two sediment layers. This manual includes the S1-S2 specific substances and processes. The comprehensive
’layered sediment’ approach involves adding a sediment grid to the computational grid and
including a sediment specific transport process. This is described in the addition manual
’Sediment Water Interaction’. The substances and processes are the same for water and
sediment in the layered sediment approach as the formulations of the processes are generic.
Processes turn out differently in water and sediment depending on local conditions, such as
the dissolved oxygen concentration. Unless stated otherwise, a process description in this
manual applies to the water column as well as the sediment. Presently the ’layered sediment’
approach only applies to Delft3D.
















DR
AF

The water quality processes are grouped under the following chapters:
Oxygen and BOD (chapter 2)
Nutrients (chapter 3)
Primary producers (chapter 4)
Light regime (chapter 6)
Primary consumers and higher trophic levels (chapter 7)
Organic matter (detritus) (chapter 8)
Inorganic substances and pH (chapter 9)
Organic micropollutants (chapter 10)
Heavy metals (chapter 11)
Bacterial pollutants (chapter 12)
Sediment and mass transport (chapter 13)
Temperature (chapter 14)
Various auxiliary processes (chapter 15)
Deprecated processes descriptions (chapter 16)

Generic mass transport processes are dealt with together with the substances group ”sediment” (chapter 13).
Remarks:
 Two different formats have been used for the process description. The original format
and the improved format (as of 2000). The latter is more elaborate, has a different notation of parameters in formulations and provides tables with input and output parameters,
facilitating the specification of parameter values in the input of models. Process descriptions according to the improved format usually concern the latest and most advanced
versions of the processes. However, some of the process descriptions have not been
updated for a long time, so that with regard to details they may not picture the actual
situation. Process descriptions according to the original format may be incomplete and
do not have the tables for the in- and output parameters.
 This manual may not be entirely complete with regard to substances and processes
available in the Processes Library. Some processes are described in this manual that
are not included in the standard set of processes, and are therefore not accessible in
present D-Water Quality. This concerns the module the module MICROPHYT for microphytobenthos. Some processes are not described in this manual because they have
not been integrated as they are under development such as module DEB for grazers

2 of 464

Deltares

How to find your way in this manual

(shell fish) and a module for aquatic macrophytes. All modules mentioned can be made
available upon request.
 As the water quality module is open source software it also has a facility to modify the
formulations of existing processes or to add new substances and processes. This is
described in ‘Open Processes Library, User Manual’.
Processes reference tables
Each process has a unique name, which is the way to get to the process you are interested
in. The processes and their relation are listed in Table 1.1 to Table 16.1 from the Processes
Library Tables manual (D-WAQ PLT, 2013).
Table 1.1

T

Table 1.1 presents a list of the processes in the library together with the chapter where you
can find the detailed description.
There are two ways to find the unique name of a process:

1 the report file of D-Water Quality <∗.lsp> tells you the name of a process
2 one of the following index-tables:

DR
AF

1.3

Table 2.1

This table is indexed on substance name and lists the associated water quality processes.
When you model a substance find the associated processes in this table and refer to Table
1.1 to find the description of the water quality-processes involved.
Table 3.1 and Table 4.1

These tables are indexed on substance name and lists the associated transport processes.
Table 3.1 lists the transport processes which calculate velocities and Table 4.1 lists the transportprocesses which calculate dispersions. When you model a substance find the associated processes in these tables and refer to Table 1.1 to find the description of the transport-processes
involved.
Table 5.1

This table is indexed on flux name and lists the substances and water quality processes
associated. When you know the name of a flux (e.g. from D-Water Quality 4 post-processing)
you can find in this table the substances which are influenced by this flux and the process
which calculates this flux. Refer to Table 1.1 to find the description of the process involved.
Table 6.1 and Table 7.1
These tables are indexed on respectively velocity and dispersion name and lists the associated substances and transport processes. When you know the name of a velocity or dispersion (e.g. from D-Water Quality post-processing) you can find in this table the substances
which are influenced and the process which calculates the velocity or dispersion. Refer to
Table 1.1 to find the description of the transport process involved.

Deltares

3 of 464

Processes Library Description, Technical Reference Manual

Table 8.1 and Table 9.1
These tables are indexed on respectively segment related and exchange related processinput that can be produced by other processes and lists the process that can calculate the
input-item. When you know the name of a process input item (e.g. from the detailed process
description (Chapters 2 up to 15) or from the D-Water Quality list file <∗.lsp>) find the name
of the process that can calculate this item in this table. Refer to Table 1.1 to find a description of the process involved. You can also ’shop’ through this list to find items worthwhile
presenting.
Table 10.1 and Table 11.1

Table 12.1 and Table 13.1

T

These tables are indexed on respectively segment related and exchange-related process
input that has a default value. When you have the name of a process input item (e.g. from
the detailed process description or from the D-Water Quality list file <∗.lsp>) find the default
value for this item in this table. Refer to Table 1.1to find a description of the process involved.

DR
AF

These tables are indexed on respectively segment related and exchange-related process
input that has no default value and can not be calculated by other processes. When you
have the name of a process input item (e.g. from the detailed process description or from the
D-Water Quality list file <∗.lsp>) find the default value for this item in this table. Refer to
Table 1.1 to find a description of the process involved.
Table 14.1 and Table 15.1

These tables are indexed on respectively segment related and exchange related processoutput that is not used by other processes and lists the process that calculates the output
item. When you have the name of a process output item (e.g. from the detailed process
descriptions or from the D-Water Quality list file <∗.lsp>) find the name of the process that
can calculate this item in this table. Refer to Table 1.1 to find a description of the process
involved. You can also ’shop’ through this list to find items worthwhile presenting.
Table 16.1

This table is indexed on the processes and lists in which configurations of the Processes
Library it is included (only relevant for SOBEK).
1.4

What’s new?

This section gives a concise overview of new features in and restructuring of the Technical
Reference Manual, which concerns the first open source version of D-Water Quality. In this
version, the Processes Library has undergone modifications that resulted in a revised standard set of substances and processes, sofar as Delft3D is concerned. These modifications
have been carried out to remove duplications and redundancies from the Processes Library
and to integrate coherent clusters of smaller processes into larger units, which enhances the
transparency of the Processes Library and reduces the risk of accidentally leaving out relevant processes in a model application. Extensions have been made as well to enlarge the
modelling potential. The changes include:

 The definition of sub-sets of processes, called ”configurations”, has been removed.
 Processes which are not routinely used have been removed.
 The state variables (substances) DetC, DetN, DetP, DetSi, OOC, OON, OOP and OOSi
have been replaced by POC1, PON1, POP1, POC2, PON2, POP2 and Opal. All pro-

4 of 464

Deltares

How to find your way in this manual


















T



DR
AF



cesses dealing with the state variables DetC, DetN, DetP, DetSi, OOC, OON, OOP and
OOSi representing organic matter have been removed.
The processes dealing with the state variables POC1-4, PON1-4, POP1-4 and Opal have
been extended to include the precise formulations previously used for DetX and OOX.
All processes dealing with resuspension, burial and digging for the state variables representing the S1-S2 sediment layers have been integrated in one single process per state
variable called S12TraXXXX, where XXXX equals the state variable name (substance
name). This single process makes use of the supporting processes Res_DM, Bur_DM
and Dig_DM, where DM refers to total sediment dry matter.
The state variables (substances) GreenS1 and GreenS2, representing Green algae after
settling to the bed, have been removed. Green algae that settle are now instantaneously
converted to detritus, just like the present practice with settling of BLOOM algae. Similarly,
Diat algae that settle are now instantaneously converted to detritus.
The state variables DiatS1 and DiatS2 now exclusively represent benthic algae (microphytobenthos), that may grow on the sediment. Settling water Diat algae are no longer
converted into benthic DiatS1 algae, while resuspending benthic DiatS1 and DiatS2 algae
are no longer converted into water Diat algae.
The previous processes Salin and Chloride have been replaced by the new Salinchlor
process.
The process Tau has been renamed to CalTau.
The processes descriptions dealing with the algae module DYNAMO have been regrouped
into two overall process descriptions for the water column and the sediment and one auxiliary process description.
All processes dealing with the extinction of visible light (VL) and ultraviolet light (UV) have
been integrated in two overall processes Extinc_VLG and Extinc_UVG.
The processes calculating aggregated parameters of organic pools (e.g. POC) in water
and sediment have been integrated with the overall composition processes for water and
sediment Compos, S1_Comp and S2_Comp.
The processes calculating aggregated settling fluxes of organic matter have been integrated with the overall aggregated settling fluxes process Sum_Sedim.
A host of new state variables (substances) has been included to extend the modelling
potential of D-Water Quality, particularly relevant for the modelling of sediment-water
interaction modelling and greenhouse gases. This includes state variables VIVP, APATP (phosphate minerals), SO4 (sulfate), SUD, SUP (dissolved and particulate sulfide),
POC5, PON5, POP5 (non-transportable detritus, see below), POS1, POS2, POS3, POS4,
POS5, DOS (particulate and dissolved organic sulfur), FeIIIpa, FeIIIpc, FeIIId, FeS, FeS2,
FeCO3, FeIId (dissolved and particulate iron species) TIC (total inorganic carbon and
alkalinity), CH4 (methane). TIC replaces CO2. State variable EnCoc was added to represent bacterial pollutant Enterococci.
Several new processes have been included to support the modelling of the new state variables. This includes VIVIANITE, APATITE (precipitation of phosphate), CONSELAC (consumption of oxygen, nitrate, iron and sulfate, and the production of methane in the mineralization of organic matter), SPECSUD, OXIDSUD, SULPHOX, SPECSUDS1, SPECSUDS2, PRECSUL (speciation, oxidation and precipitation of sulfide), SPECIRON, IRONOX,
IRONRED, PRIRON (speciation, oxidation, reduction and precipitation of iron) OXIDCH4,
VOLATCH4, EBULCH4 (oxidation, volatilization and ebullition of methane), SPECCARB,
REARCO2, SATURCO2 (speciation and water-atmosphere exchange of dissolved inorganic carbon), and EnCocMRT (mortality of Enterococci).
Process LSEDTRA has been added for the transport processes in sediment for the modeling of sediment-water interaction as based on the comprehensive layered sediment approach.
A new module has been included for the mortality and (re-)growth of terrestrial drowned
vegetation. This concerns additional state variables VBNN, where NN is a number from 01
to 09, and POC5, PON5, POP5, POS5, into which the non-transportable detrital biomass

Deltares

5 of 464

Processes Library Description, Technical Reference Manual

(stems, branches, roots) is released at mortality.
Backward compatibility
The present version of open source D-Water Quality is generally backward compatible with
the previous non open source version. However, there are a few non-backward compatible
items in the Processes Library. With very few exceptions older input files of existing models
are still supported. The input processor  makes the necessary modifications
and reports them in the <∗.lsp> message file. Non-backward compatible items are printed
as warnings with a reference number. These references are listed here.

T

1 void.
2 The concentration of detritus N, P and Si as well as OON, OOP, OOSi in the deep sediment
boundary (layer ”S3”) are now specified directly as a solid phase concentration (FrDetNS3
in gN/gDM, FrDetPS3, FrDetSiS3, FrOONS3, FrOOPS3, FrOOSiS3). In previous versions,
the carbon to X ratio was used (C-NDetCS3, C-PDetCS3, C-SDetCS3, C-NOOCS3, CPOOCS3, C-SOOCS3). If one of the latter constants has been detected in your input
file, please replace by the appropriate new constant. Note: these numbers only have a
meaning if the item SWDigS2 = 1.
3 The concentration of AAP in the deep sediment (layer ”S3”) is now specified directly as a
solid phase concentration (FrAAPS3 in gP/gDM. In previous versions, the concentration
in TIM was used (FrAAPTIMS3). If the latter constant has been detected in your input file,
please replace by the new constant. Note: this number only has a meaning if the item
SWDigS2 = 1.
4 The concentration of metals (As, Cd, Cr, Cu, Hg, Ni, Pb, Va, Zn) in the deep sediment
(layer ”S3”) is now specified directly as a solid phase concentration (e.g. QCdDMS3 in
mg/kgDM). In previous versions, this concentration was specified via the concentrations
in IM1, IM2, IM3, Phyt and POC (e.g. QCdIM1S3, QCdIM2S3, QCdIM3S3, QCdPHYTS3,
QCdPOCS3). If one of the latter constants has been detected in your input file, please
replace by the appropriate new constant. Note: these numbers only have a meaning if the
item SWDigS2 = 1
5 The concentration of organic chemicals (153, Atr, BaP, Diu, Flu, HCB, HCH, Mef, OMP)
in the deep sediment (layer ”S3”) is now specified directly as a solid phase concentration
(e.g. QAtrDMS3 in mg/kgDM). In previous versions, this concentration was specified via
the concentrations in Phyt and POC (e.g. QAtrPHYTS3, QAtrPOCS3). If one of the latter
constants has been detected in your input file, please replace by the appropriate new
constant. Note: these numbers only have a meaning if the item SWDigS2 = 1.
6 Where previously up to two substances represented biogenic silica (DetSi and OOSi),
the Processes Library now uses just one substance (Opal). DELWAQ will automatically
convert DetSi to Opal, and neglect OOSi. Biogenic silica formed within the model domain
as a result of algae mortality will be released as Opal, will dissolve and will be available
for uptake by algae. A problem exists if the user has specified an inflow of biogenic silica
to the model domain in the form of the substance OOSi via boundary conditions and/or
waste loads. This part of the biogenic silica will no longer dissolve, will not be available for
algae and will not count in the output parameter total silica (TotSi). To avoid this problem,
the user has to add the boundary concentrations and waste loads of OOSi to the boundary
concentrations and waste loads of DetSi or Opal.

DR
AF

1.5

6 of 464

Deltares

How to find your way in this manual

1.6

Modelling water and sediment layers
The processes library distinguishes two approaches to modelling the water and sediment
compartments of a water system:

 The simpler approach is the so-called "S1/S2" approach, where an upper layer S1 is

DR
AF

Usage notes

The presence of these two approaches has some consequences for the use of the processes
library:

 To use the layered sediment approach you must define the sediment layers separately



(see the separate manual for this, Deltares (2017)). As there are no substances that are
specific to the sediment anymore, substances like IM 1S1 are not to be used.
 In the process formulations the bulk concentration is used for both the water phase and the
sediment (both approaches). To accommodate for a uniform treatment, however, sometimes the pore water concentration is needed and therefore the porosity has been introduced even for processes that mostly work for the water phase. The convention there
is:



1.6.1

T

assumed to be at the top of the sediment and below it there is a layer S2. The layer S1
directly interacts with the water column and most of the sediment processes are located
in this layer. The layer underneath, S2, is mostly inert and exchanges mass with the first
layer via processes like burial and digging. In the process formulations specific substances
are used to model the S1 and S2 layers. For instance: IM 1 is the first inorganic matter
fraction – the concentration of particulate matter in the water phase. Its counterpart in the
S1 layer is called IM 1S1" and in the S2 layer it is called "IM 1S2".
 The alternative approach is the so-called "layered sediment" approach. With this approach
all substances are present in both the water phase and the sediment layers (where the
user can define the layout of the sediment layers themselves). This enables the library to
treat all segments in the same way and reduces the number of individual substances. But
above all it enables the detailed modelling of processes that take place in the sediment.

The porosity is 1 for the water segments, in case of the layered sediment approach,
and smaller than 1, typically around 0.4, for the sediment segments. In this case the
porosity has to be specified explicitly for the sediment layers.
For the S1/S2 approach the porosity is simply 1, as then the distinction between bulk
and pore-water concentrations is handled in an implicit way. The processes library
provides this value as a default, so you should not specify it yourself.

Deltares

7 of 464

DR
AF

T

Processes Library Description, Technical Reference Manual

8 of 464

Deltares

2 Oxygen and BOD
Contents
2.1

Reaeration, the air-water exchange of DO . . . . . . . . . . . . . . . . . .

2.2

Dam reaeration, SOBEK only . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3

Saturation concentration of DO . . . . . . . . . . . . . . . . . . . . . . . . 24

2.4

Diurnal variation of DO . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.5

Calculation of daily minimal DO concentration . . . . . . . . . . . . . . . . 29

2.6

Calculation of actual DO concentration . . . . . . . . . . . . . . . . . . . . 31

2.8

32

Chemical oxygen demand . . . . . . . . . . . . . . . . . . . . . .

32

2.7.2

Biochemical oxygen demand

. . . . . . . . . . . . . . . . . . . .

33

2.7.3

Measurements and relations . . . . . . . . . . . . . . . . . . . . .

33

2.7.4

Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Deltares

34

Sediment oxygen demand . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Production of substances: TEWOR, SOBEK only . . . . . . . . . . . . . . 44
2.9.1

Coliform bacteria – listing of processes . . . . . . . . . . . . . . . 44

2.9.2

TEWOR-production fluxes . . . . . . . . . . . . . . . . . . . . . . 44

2.9.3

Process TEWOR: Oxydation of BOD . . . . . . . . . . . . . . . .

DR
AF

2.9

BOD, COD and SOD decomposition . . . . . . . . . . . . . . . . . . . . .
2.7.1

T

2.7

10

45

9 of 464

Processes Library Description, Technical Reference Manual

Reaeration, the air-water exchange of DO
PROCESS :

REAROXY

T

Dissolved oxygen (DO) in surface water tends to saturate with respect to the atmospheric
oxygen concentration. However, oxygen production and consumption processes in the water
column counteract saturation, causing a DO-excess or DO-deficit. The resulting super- or
undersaturation leads to reaeration, the exchange of oxygen between the atmosphere and
the water. Reaeration may cause an oxygen flux either way, to the atmosphere or to the water.
The process is enhanced by the difference of the saturation and actual DO concentrations,
and by the difference of the velocities of the water and the overlying air. Since lakes are rather
stagnant, only the windspeed is important as a driving force for lakes. The reaeration rate
tends to saturate for low windspeeds (< 3 m.s−1 ). On the other hand, the stream velocity
may deliver the dominant driving force for rivers. Both forces may be important in estuaries.
Extensive research has been carried out all over the world to describe and quantify reaeration
processes, including the reaeration of natural surface water. Quite a few different models
have been developed. The most generally accepted model is the “film layer” model. This
model assumes the existence of a thin water surface layer, in which a concentration gradient
exists bounded by the saturation concentration at the air-water interface and the water column
average DO concentration. The reaeration rate is characterised by a water transfer coefficient,
which can be considered as the reciprocal of a mass transfer resistance. The resistance in
the overlying gas phase is assumed to be negligibly small.

DR
AF

2.1

Many formulations have been developed and reported for the water transfer coefficient. These
formulations are often empirical, but most have a deterministic background. They contain
the stream velocity or the windspeed or both. Most of the relations are only different with
respect to the coefficients, the powers of the stream velocity and the windspeed in particular.
Reaeration has been implemented in DELWAQ with ten different formulations for the transfer
coefficient. Most of these relations have been copied or derived from scientific publications
(WL | Delft Hydraulics, 1980b, 1978). The first two options are pragmatic simplifications to
accommodate preferences of the individual modeller. All reaeration rates are also dependent
on the temperature according to the same temperature function.
Implementation

Process REAROXY has been implemented in such a way, that it only affects the DO-budget
of the top water layer. An option for the transfer coefficient can be selected by means of input
parameter SWRear (= 0–10, 13). The DO saturation concentration required for the process
REAROXY is calculated by an additional process SATUROXY.
The process has been implemented for substance OXY.
Table 2.1 provides the definitions of the parameters occurring in the formulations.

10 of 464

Deltares

Oxygen and BOD

Formulation
The reaeration rate has been formulated as a linear function of the temperature dependent
mass transfer coefficient in water and the difference between the saturation and actual concentrations of DO as follows:

Rrear = klrear × (Coxs − max(Cox, 0.0))/H

T

klrear = klrear20 × ktrear(T −20)



a × vb
20
2
klrear =
+
d
×
W
Hc
Coxs = f (T, Ccl or SAL)
(delivered by SATUROXY)
max(Cox, 0.0)
f sat = 100 ×
Coxs
with:

coefficients with different values for each reaeration options
chloride concentration [gCl m−3 ]
actual dissolved oxygen concentration [gO2 m−3 ]
saturation dissolved oxygen concentration [gO2 m−3 ]
percentage of saturation [%]
depth of the water column [m]
reaeration transfer coefficient in water [m d−1 ]
reaeration transfer coefficient at reference temperature 20 ◦ C [m d−1 ]
temperature coefficient of the transfer coefficient [-]
reaeration rate [gO2 m−3 d−1 ]
salinity [kg m−3 ]
temperature [◦ C]
flow velocity [m s−1 ]
wind speed at 10 m height [m s−1 ]

DR
AF

a, b, c, d
Ccl
Cox
Coxs
f sat
H
klrear
klrear20
ktrear
Rrear
SAL
T
v
W

Notice that the reaeration rate is always calculated on the basis of a positive dissolved oxygen concentration, whereas OXY may have negative values. Negative oxygen equivalents
represent reduced substances.
Depending on the reaeration option, the transfer coefficient is dependent on either the flow
velocity or the wind speed, or dependent on both. With respect to temperature dependency
option SWRear = 10 is an exception. The respective formulation is not dependent on temperature according the above equations, but has its own temperature dependency on the basis
of the Schmidt number. Information on the coefficients a–d and the applicability is provided
below for each of the options.

SWRear = 0
The transfer coefficient is simplified to a constant, multiplied with the water depth H, using the
transfer coefficient as input parameter. So klrear20 is to be provided as a value in [d−1 ] in
stead of in [m d−1 ]! Consequently, the coefficients are:

a = klrear20 × H,

b = 0.0,

c = 0.0,

d = 0.0

SWRear = 1

Deltares

11 of 464

Processes Library Description, Technical Reference Manual

The transfer coefficient is simplified to a constant, using the transfer coefficient as input parameter. Consequently, the coefficients are:

a = klrear20 /H,

b = 0.0,

c = 0.0,

d = 0.0

SWRear = 2
The coefficients according to Churchill et al. (1962) are:

a = 5.026,

b = 0.969,

c = 0.673,

d = 0.0

T

The relation is valid for rivers, and therefore independent of wind speed.

SWRear = 3

DR
AF

The coefficients according to O’ Connor and Dobbins (1956) are:

a = 3.863,

b = 0.5,

c = 0.5,

d = 0.0

The relation is valid for rivers, and therefore independent of wind speed.

SWRear = 4

The coefficients are the same as for option SWRear = 3 according to O’ Connor and Dobbins (1956), but coefficient a can be scaled using the transfer coefficient as input parameter.
Consequently, the coefficients are:

a = 3.863 × klrear20 ,

b = 0.5,

c = 0.5,

d = 0.0

The relation is valid for rivers, and therefore independent of wind speed.

SWRear = 5

The coefficients according to Owens et al. (1964) are:

a = 5.322,

b = 0.67,

c = 0.85,

d = 0.0

The relation is valid for rivers, and therefore independent of wind speed.

SWRear = 6
The coefficients according to Langbein and Durum (1967) are:

a = 11.23,

b = 1.0,

c = 0.33,

d = 0.0

The relation is valid for rivers, and therefore independent of wind speed.

12 of 464

Deltares

Oxygen and BOD

SWRear = 7
The relation is according to O’ Connor and Dobbins (1956) and Banks and Herrera (1977) as
reported by WL | Delft Hydraulics (1980b), but the coefficients have been modified according
WL | Delft Hydraulics (1978); d = 0.3-0.6) and later WL | Delft Hydraulics modelling studies for
Dutch lakes. Consequently, the coefficients are:

a = 3.863,

b = 0.5,

c = 0.5,

d = 0.065 × klrear20

The relation is valid for rivers, lakes, seas and estuaries.

The option is presently void and should not be used.

DR
AF

SWRear = 9

T

SWRear = 8

The relation is according to Banks and Herrera (1977) as reported by WL | Delft Hydraulics
(1980b), but the coefficients have been modified according to WL | Delft Hydraulics (1978);
d = 0.03–0.06) and later modelling studies for Dutch lakes WL | Delft Hydraulics (1992c).
Consequently, the coefficients are:

a = 0.3,

b = 0.0,

c = 0.0,

d = 0.028 × klrear20

The relation is valid for lakes and seas, and therefore independent of flow velocity. The relation
takes into account that the mass transfer coefficient saturates at a lower boundary for low wind
velocities (W < 3 m s−1 ).

SWRear = 10

The relation according to Wanninkhof (1992) deviates from the previous relations with respect
to temperature dependency, that is not included according to the above Arrhenius equation
for klrear. The temperature dependency enters the relation in a scaling factor on the basis of
the Schmidt number. Coefficient d had to be scaled from cm h−1 to m d−1 . Consequently,
the coefficients are:

a = 0.0,

b = 0.0,

c = 0.0,

d = 0.0744 × f sc

−0.5
Sc
f sc =
Sc20
Sc = d1 − d2 × T + d3 × T 2 − d4 × T 3


with:

d1–4
f sc
Sc
Sc20
T
Deltares

coefficients
scaling factor for the Schmidt number [-]
Schmidt number at the ambient temperature [g m−3 ]
Schmidt number at reference temperature 20 ◦ C [d−1 ]
temperature [◦ C]

13 of 464

Processes Library Description, Technical Reference Manual

The relation is valid for lakes and seas, and therefore independent of flow velocity.
The Schmidt number is the ratio of the kinematic viscosity of water (ν ) and the molecular
diffusion coefficient of oxygen in water (D). The appropriate constants to compute the Schmidt
number in both seawater and fresh water are given in the table below.
Water system

d1

d2

d3

d4

Sea water Salinity > 5 kg m−3

1953.4

128.0

3.9918

0.050091

Fresh water Salinity ≤ 5 kg m−3

1800.6

120.1

3.7818

0.047608

T

SWRear = 12 (SOBEK-only)

DR
AF

This relation is a hybrid combination of SWRear = 3 (O’ Connor and Dobbins, 1956) and
SWRear = 5 (Owens et al., 1964). This hybride formulation is developed for urban water
management in The Netherlands. More information concerning the derivation of this hybrid
relation can be found in Stowa (2002).
(O’ Connor and Dobbins, 1956):

a = 3.93 , b = 0.5 , c = 0.5 , d = 0.0 if



v<

3.93 0.35
H
5.32

6

(2.1)

(Owens et al., 1964):

a = 5.32 , b = 0.67 , c = 0.85 , d = 0.0 if



v<

3.93 0.35
H
5.32

6

klrear20 = max(klrearmin , klrear20 )
with:

(2.2)

(2.3)

klrearmin minimum water transfer coefficient for oxygen [m.d−1 ]
The relation is valid for rivers, and therefore independent of windspeed.

SWRear = 13
The relation according to Guérin (2006); Guérin et al. (2007) deviates strongly from the previous relations, with respect to wind dependency, with respect to an additional forcing parameter, namely rainfall, and with respect to temperature dependency. The latter is not included
according to the above Arrhenius equation for klrear. Like the relation described for option 10,

14 of 464

Deltares

Oxygen and BOD

the temperature dependency enters the relation in a scaling factor on the basis of the Schmidt
number. The relation for transfer coefficient is:



klrear = a × exp b1 × W b2 + c1 × P c2 × f sc
−0.67

Sc
f sc =
Sc20
Sc = d1 − d2 × T + d3 × T 2 − d4 × T 3
with:
coefficients
transfer coefficient in water [m d−1 ]
precipitation, e.g. rainfall [mm h−1 ]
Schmidt number at the ambient temperature [g m−3 ]
Schmidt number at reference temperature 20 ◦ C [d−1 ]
temperature [◦ C]
windspeed at 10 m height [m s−1 ]

T

a, b, c, d
klrear
P
Sc
Sc20
T
W

a

DR
AF

The relation is valid for (tropical) lakes and therefore independent of stream velocity. The
general coefficients have the following input names and values:
b1

b2

c1

c2

CoefAOXY

CoefB1OXY

CoefB2OXY

CoefC1OXY

CoefC2OXY

1.660

0.26

1.0

0.66

1.0

The Schmidt number is the ratio of the kinematic viscosity of water (ν ) and the molecular
diffusion coefficient of oxygen in water. The appropriate constants to compute the Schmidt
number for fresh water are given in the table below (Guérin, 2006):
d1

d2

d3

d4

CoefD1OXY

CoefD2OXY

CoefD3OXY

CoefD4OXY

1800.06

120.10

3.7818

0.047608

Directives for use
 Options SWRear = 0, 1, 4, 7, 9 provide the user with the possibility to scale the mass
transfer coefficient KLRear. All other options contain fixed coefficients.
 When using option SWRear = 0 the user should be aware that the mass transfer coefficient KLRear has the unusual dimension d−1 . Since high values of KLRear may cause
numerical instabilities, the maximum KLRear value is limited to 1.0 day−1 .
 When using option SWRear = 1 the user should be aware that the mass transfer coefficient
KLRear has the standard dimension m d−1 .
 When using options SWRear = 4, 7 or 9 you should be aware that the input parameter
KLRear is used as a dimensionless scaling factor. The default value of KLRear is 1.0 in
order to guarantee that scaling is not carried out when not explicitly wanted.
 The dependencies of klrear20 /H on v, W and H for options SWRear = 2, 3, 5, 6, 7 are
presented in Figure 2.1.
 The coefficients a–c2 are input parameters for option SWRear=13 only. The default values
are those for option 13.

Deltares

15 of 464

Processes Library Description, Technical Reference Manual

30

SWRear = 2
25

R C R e a r(1 /d )

20

15

10

0
0

1

2

3

4
Veloc (m/s)

Depth=1m

Depth=2m

Depth=4m

30

5

6

Depth=8m

8

7

Depth=15m

DR
AF

SWRear = 3

T

5

25

R C R e a r (1 /d )

20

15

10

5

0

0

1

2

3

4

5

6

7

8

Veloc (m/s)

Depth=1m

Depth=2m

Depth=4m

Depth=8m

Depth=15m

 The coefficients d1−4 are input parameters for options SWRear = 10, 13. The default
values are the freshwater values, which are the same for both options.

16 of 464

Deltares

Oxygen and BOD

Table 2.1: Definitions of the parameters in the above equations for REAROXY

Name in
in/output

Definition

Units

Cox
Coxs

OXY
SaturOXY

concentration of dissolved oxygen
saturation concentration dissolved oxygen
from SATUROXY

gO2 m−3
gO2 m−3

a
b1
b2
c1
c2

CoefAOXY
CoefB1OXY
CoefB2OXY
CoefC1OXY
CoefC2OXY

coefficients for option 13 only

-

d1
d2
d3
d4

CoefD1OXY
CoefD2OXY
CoefD3OXY
CoefD4OXY

coefficients for options 10 and 13

–
–

scaling factor for the Schmidt number
percentage oxygen saturation

%

Depth

depth of the water layer

m

klrear20
kltemp

KLRear
TCRear

water transfer coefficient for oxygen1)
temperature coefficient for reaeration

m d−1
-

P

rain

rainfall

mm −1

Rrear

–

reaeration rate

gO2
d−1

SAL

Salinity

salinity

kg m−3

Sc

–

Schmidt number for dissolved oxygen in water

-

SWRear

SWRear

switch for selection of options for transfer
coefficient

-

T

Temp

temperature

◦

v
W

Velocity
VWind

flow velocity
wind speed at 10 m height

m s−1
m s−1

H

1)

DR
AF

fcs
fsat

T

Name in
formulas1)

-

m−3

C

See directives for use concerning the dimension of KLRear.

Deltares

17 of 464

Processes Library Description, Technical Reference Manual

30
SWRear = 5

25

R C R e a r (1 /d )

20

15

T

10

5

0
1

2

3

4

5

6

DR
AF

0

7

8

Veloc (m/s)

Depth=1m

30

Depth=2m

Depth=4m

Depth=8m

Depth=15m

SWRear = 6

25

R C R e a r (1 /d )

20

15

10

5

0
0

1

2

3

4

5

6

7

8

Veloc (m/s)
Depth=1m

18 of 464

Depth=2m

Depth=4m

Depth=8m

Depth=15m

Depth=30m

Deltares

7

SWRear=7
Depth = 5m

DR
AF

6

T

Oxygen and BOD

R C R e a r (1 /d )

5

4

3

2

1

0

0

2

4

6

8

10

12

14

16

18

20

Vwind

Veloc=0.25 m/s

Series2

Veloc=1.0m/s

Veloc=2.5m/s

Veloc=5m/s

Veloc=10m/s

Figure 2.1: The reaeration rate RCRear (=klrear20 20/H) as a function of water depth, flow
velocity and/or wind velocity for various options SWRear for the mass transfer
coefficient klrear

Deltares

19 of 464

Processes Library Description, Technical Reference Manual

Dam reaeration, SOBEK only
PROCESS :

DAMREAR

Water quality downstream of weirs improves as a result of reaeration. From this interest a lot
of research on dam reaeration has been carried out in the United States and England in the
sixties. Dam reaeration occurs because of an more intensive contact between air and water
as a result of energy loss of the weir. The largest percentage change of the dissolved oxygen
concentration occurs at the base of the weir (Gameson, 1957).

T

In the past reaeration at weirs and dams was described as a function of the difference of
water levels up- and downstream of the structure. In formulations that are more commonly
applicable other factors are taken into account as well. These are for example: temperature
of the water, water quality, discharge over the structure, water depth behind the structure and
characteristics of the structure, such as size, shape and construction material.
Implementation

Process damrear has been implemented in such a way, that it only affects the DO-budget of
the top water layer. An option for the deficit ratio can be selected by means of input parameter SWdrear (= 0/1). The DO saturation concentration required for the process damrear is
calculated by an additional process SATUROXY.

DR
AF

2.2

The process has been implemented for substance OXY.

Table 2.3 provides the definitions of the parameters occurring in the formulations.
Formulation

The amount of oxygen needed to reach a concentration Cox downstream of the weir is formulated as:

Rdrear =
with:

Rdrear
Cox
∆t

Cox − Coxt−1
∆t

(2.4)

oxygen reaeration rate as a result of dam reaeration [gO2 .m−3 .d−1 ]
oxygen concentration [gO2 .m−3 ]
timestep [d]

Almost all publications about dam aeration assume that the upstream oxygen deficit at a weir
is partly neutralised as a result of dam aeration. Cox is determined as a function of the
saturation concentration, the upstream concentration and the oxygen deficit ratio:

Cox =

1
(Coxs(f drear − 1) + Coxup)
f drear

(2.5)

with:

f draer
Coxs
Coxup

oxygen deficit ratio [−]
oxygen saturation concentration [gO2 .m−3 ]
oxygen concentration upstream of weir [gO2 .m−3 ]

Dam reaeration is always calculated on the basis of a positive dissolved oxygen concentration, whereas OXY may have negative values. Negative oxygen values equivalents represent
reduced substances.

20 of 464

Deltares

Oxygen and BOD

Notice that the reaeration rate is always calculated on the basis of a positive dissolved oxygen concentration, whereas OXY may have negative values. Negative oxygen equivalents
represent reduced substances.
There are different options to calculate dam reaeration. Gameson developed a much quoted
empirical formulation for the oxygen deficit ratio (SWdrear = 0). This formulation does not
contain discharge over the structure and water depth behind the structure, while both parameters are both considered to be important. The formulation by Nakasone (SWdrear = 1) is
a possible alternative which does take both parameters into account (Nakasone, 1975). A
hybrid combination of both formulations is also available via SWdrear =1 (Stowa, 2002). In
the latter case some coefficients get different values.

T

SWdrear = 0

f drear = 1.0 + 0.38 a b ∆h (1 − 0.11 ∆h) (1 + 0.046 T )
with:

water quality factor [−]
characteristic structure [−]
difference of water levels up- and downstream of the structure (hup − hdown )
[m]
water level upstream of structure [m]
water level downstream of structure [m]
water temperature [◦ C]

DR
AF

a
b
∆h

hup
hdown
T

(2.6)

SWdrear = 1
Hybrid formulation for the oxygen deficit ratio of Gameson and Nakasone. If a and b are zero
the oxygen deficit ratio according to Nakasone is calculated.

f drear = 1 + (f drearn − 1) a b (1 + 0.02(T − 20))
!

0.62
3600
Q
f drearn = exp 0.0675 ∆h1.28
H 0.439
L

with:

f drearn
Q
L
H

(2.7)
(2.8)

oxygen deficit ratio according to Nakasone [−]
discharge over structure [m3 s−1 ]
width of crest structure [m]
water depth [m]

The water quality factor is related to the BOD concentration:


a = min 1.80,

1.90
Cbod0.44


(2.9)

with:

Cbod

biological oxygen demand [gO2 m−3 ]

Butts T. A and Evans (1983) studied reaeration at 54 small dams and en weirs in Illinois and
determined the dam reaeration coefficient b (characteristic structure) for each structure. The
structures could be subdivided into 9 categories with typical values for b (see Table 2.2). The
b-values that were found vary from 1.05 for a sharp-crested straight slope face to 0.6 for round
broad-crested straight slope face.

Deltares

21 of 464

Processes Library Description, Technical Reference Manual

Table 2.2: Factor ’b’ (characteristic structure) for various structures.

b

flat broad-crested regular step

0.70

flat broad-crested irregular step

0.80

flat broad-crested vertical face

0.80

flat broad-crested straight slope face

0.90

flat broad-crested curved face

0.75

round broad-crested straight slope face

0.60

sharp-crested straight slope face

1.05

sharp-crested vertical face

T

weir type

0.80

DR
AF

sluice gates with submerged discharge

0.05

Directives for use

 factor b (structure characteristic) is equal to the discharge coefficient Ce in the module
Channel Flow of SOBEK Rural.

 In order to use the Nakasone formulation the following coefficient values should be used:
SW dRear = 1, Cbod = 1, b = 1/1.8, T = 20.
Table 2.3: Definitions of the parameters in the above equations for REAROXY

Name in
formulas1)

Name in
input

Definition

Units

a

−

water quality factor

-

Coef bi

dam reaeration coefficient of structure i

-

CBOD5

biological oxygen demand

gO2 .m−3

b
Cbod

Cox
Coxs
Coxup

OXY
concentration of dissolved oxygen
SaturOXY saturation conc. dissolved oxygen from saturoxy
OXY
oxygen concentration upstream of weir

gO2 .m−3
gO2 .m−3
gO2 m−3

f drear
f drearn

-

-

hup
hdown

W tLvLSti Water level upstream of structure i (according to
W tLvRSti definition in schematisation)
Water level downstream of structure i (according

oxygen deficit ratio
oxygen deficit ratio according to Nakasone

m
m

to definition in schematisation)

H

Depth

depth of the top water layer

m

L

W idthsti

width of crest of structure i

m

22 of 464

Deltares

Oxygen and BOD

Table 2.3: Definitions of the parameters in the above equations for REAROXY

Name in
formulas1)

Name in
input

Definition

Units

Q

DischSti

discharge over structure i

m3 s−1

Rdrear

-

oxygen reaeration rate as a result of dam aeration

gO2 .m−3 d−1

∆t

Delt

timestep

d

T

T emp

temperature

◦

DR
AF

T

C

Deltares

23 of 464

Processes Library Description, Technical Reference Manual

Saturation concentration of DO
PROCESS :

SATUROXY

The reaeration of oxygen proceeds proportional to the difference of the saturation and actual
dissolved DO concentrations. The saturation concentration of DO is primarily a function of
water temperature and salinity. The air pressure also affects the saturation concentration, but
this effect is minor and can be taken into account in the temperature dependency.

T

The calculation of the saturation concentration has been implemented with two alternative
formulations. Such formulations have been described by Weiss (1970); Fair et al. (1968);
Truesdale et al. (1955) and WL | Delft Hydraulics (1978).
Implementation

Process SATUROXY calculates the DO saturation concentration in water at ambient temperature and salinity required for the process REAROXY. The process has been implemented
with two options for the formulations of the saturation concentration, that can be selected by
means of input parameter SWSatOxy (=1, 2).

DR
AF

2.3

The process has been implemented for substance OXY.

Table 2.4 provides the definitions of the parameters occurring in the formulations.
Formulation

The saturation concentration (SaturOxy ) has been formulated as the following functions of the
temperature and the salinity.
For SWSatOxy = 1:

2

3

Coxs = a − b T + (c T ) − (d T )





Ccl
1−
m

For SWSatOxy = 2:




b
32 000
2
Coxs = exp a +
+ c ln(Tf ) + d Tf + SAL (m + n Tf + o Tf )
Tf
22 400
(2.10)


Tf =

T + 273
100


(2.11)

with:

a, b, c, d, m, n, o coefficients with different values for the two formulations
Ccl
chloride concentration [gCl m−3 ]
Coxs
saturation dissolved oxygen concentration [gO2 m−3 ]
T
water temperature [◦ C]
Tf
temperature function [-]
24 of 464

Deltares

Oxygen and BOD

salinity [kg m−3 ]

SAL

The coefficients in both formulations are fixed. The values are presented in the table below.
SWSatOxy

a

b

c

d

m

n

o

1

14.652

0.41022

0.089392

0.042685

105

-

-

2

-173.4292

249.6339

143.3483

-21.8492

-0.033096

0.014259

-0.0017

SAL = 1.805 × Cl / 1 000.
Additional references

DR
AF

WL | Delft Hydraulics (1980b)

T

Directives for use
 The chloride concentration Cl can either be imposed by you or simulated with the model.
The salinity can be estimated from the chloride concentration with:

Table 2.4: Definitions of the parameters in the equations for SATUROXY

Name in
formulas

Name in
input

Definition

Units

Coxs
Ccl

SaturOXY
Cl

saturation concentration of oxygen in water
chloride concentration

gO2 m−3
gCl m−3

SAL
SWSatOxy

Salinity
SWSatOxy

salinity
switch for selection options for saturation
equation

kg m−3
-

T
Tf

Temp
–

water temperature
temperature function

◦

Deltares

C

-

25 of 464

Processes Library Description, Technical Reference Manual

Diurnal variation of DO
PROCESS :

VAROXY

T

The phytoplankton models implemented in DELWAQ are subjected to daily averaged forcing
functions. In particular, this is reflected by the choice of the input parameters for the subsurface light intensity model: the daily averaged solar radiation and the day length. However,
in reality the gross primary production of phytoplankton is constrained to daytime. The same
goes for the associated production of oxygen. On the contrary, the respiration process consumes oxygen all 24 hours of the day. The combination of gross production and respiration
causes a rather strong diurnal variation of the dissolved oxygen concentration (DO). The process VAROXY modifies the daily DO-production by algae in such a way, that it is spread out
over the period of daylight (day length) only.
Implementation

Process VAROXY can only be used in combination with the algae module BLOOM. This process produces the net primary production flux dPrProdOxy and the respiration flux fRespTot.
The module D40BLO has the option parameter SWOxyProd for activation of the process
VAROXY. For SWOxyProd = 1 process VAROXY will be activated and the respiration flux will
be used to calculate the gross production flux distribution over the day length. The respiration
flux will be ignored for the DO-budget, when SWOxyProd has any other value.

DR
AF

2.4

Process VAROXY has been implemented for substance OXY.

Table 2.5 provides the definitions of the parameters occurring in the formulations.
Formulation

The net daily primary production and the respiration are added to obtain the gross production
flux:
For SWOxyProd = 1: (diurnal variation)

Rgpa =
with:

F np
F rsp
H
Rgpa

F np + F rsp
H

net primary production flux [gC m−2 d−1 ]
respiration flux [gC m−2 d−1 ]
depth of the water column [m]
daily average gross primary production rate [gC m−3 d−1 ]

The distribution of the gross primary production over the day is shown in Figure 2.2. The
shape of the production curve depends on day length DL and the times t1 and t2 which
define the period of the maximum production during a day Rgpmax . The value of Rgpmax is
calculated at the constraint that the integral of the production curve over 24 hours equals the
daily averaged primary production Rgpa . This results in:

Rgpmax =

48 × Rgpa
t2 − t1 + (DL × 24)

with:

26 of 464

Deltares

Oxygen and BOD

0

1 2 -D L x1 2

t1

T

o xygen
p ro d .
(g/m 3 /d )
R gp
m ax

t2
12
tim e (h )

1 2 + D L x1 2

24

DR
AF

Figure 2.2: The distribution of gross primary production over a day

DL
Rgpmax
t1
t2

day length, fraction of a day [-]
maximal gross primary production rate during a day [gC m−3 d−1 ]
time at which the maximal production is reached [h]
time at which the production starts to fade [h]

The net primary production as a function of the time in a day then follows from:


F rsp


−


H



Rgpmax
F rsp


(t − (12 − 12 DL)) −


H

 (t1 − (12 − 12 DL))
F rsp
Rnp = Rpgmax −

H


Rgpmax
F rsp


Rpgmax −
(t − t2 ) −



((12 + 12 DL) − t2 )
H


 F rsp

−
H

with:

Rnp
t

for t ≤ (12 − 12 DL)
for (12 − 12 DL) < t < t1
for t1 ≤ t ≤ t2
for t2 < t < (12 + DL 12)
for t ≥ (12 + 12 DL)

net primary production (or respiration) rate during a day [gC m−3 d−1 ]
actual time in a day [hr]

For SWOxyProd = 0: (no diurnal variation)

Rnp = 0.0
The conversion from the carbon fluxes of gross production and respiration into oxygen fluxes
involves the multiplication of these fluxes with 2.67 gO2 /gC as defined in the stoichiometric
matrix for the calculation of mass balances in DELWAQ.

Deltares

27 of 464

Processes Library Description, Technical Reference Manual

Table 2.5: Definitions of the parameters in the above equations for VAROXY

Name in
in/output

Definition

Units

DL

DayL

day length, fraction of a day

-

F np
F rsp

fPPtot
fResptot

net primary production flux
respiration flux

gC m−2 d−1
gC m−2 d−1

H

Depth

thickness of the computational cell

m

SW OxyP rod SWOxyProd

switch for the option to activate process
VAROXY

-

Rnp

–

gC m−3 d−1

Rgpa

–

Rgpmax

–

net primary production (or respiration)
rate during a day
average gross primary production rate
during a day
maximal gross primary production rate
during a day

Itime

DELWAQ time

scu

T1MXPP

time at which the maximal production is
reached
time at which the production starts to fade
ratio between a day and system clock
units (86400)
time at the start of the simulation

h

time in a day
time at which the maximal production is
reached
time at which the production starts to fade

h
h

t1
t2
–
–

t
t1
t2

DR
AF

t

T

Name in
formulas

T2MXPP
AuxSys
Refhour

Time
T1MXPP
T2MXPP

gC m−3 d−1
gC m−3 d−1

h
s d−1
h

h

The actual time in a day is derived from system time, the time step and the start time of the
simulation.
Directives for use
 The times of beginning and ending of the maximal primary production period on a day
must satisfy the following constraints: t2 < (12 + 12 DL) and t1 > (12 − 12 DL).
 The actual time in a day is available as output parameter ActualTime.

28 of 464

Deltares

Oxygen and BOD

Calculation of daily minimal DO concentration
PROCESS :

OXYMIN

The phytoplankton models implemented are subject to daily averaged forcing functions. This
is reflected in particular by the choice of the input parameters for the subsurface light intensity
model: the daily averaged solar radiation and the day length. However, in reality the gross primary production of phytoplankton and the associated production of oxygen are constrained to
daytime. In contrast, respiration consumes oxygen all 24 hours of the day. The combination of
gross production and respiration can cause a strong diurnal variation of the dissolved oxygen
concentration (DO). The process OXYMIN computes the minimal DO-concentration that may
occur during the day, when daily averaged forcing is used.

T

The actual minimal DO-concentration can be calculated with a mass balance on the basis
of actual process rates. When dealing with daily average values, one has to settle for an
estimate. Such an estimate can be made, either by neglecting all other processes but primary
production and respiration, or by assuming that these other processes (mainly reaeration)
exactly compensate for the DO-concentration change resulting from gross production and
respiration on a daily basis. The truth lies in between these extremes. Whether option 1 or
option 2 results in the lowest DO-minimum depends on production being larger or smaller
than respiration. Since one does not want to overestimate DO-minima, the various options for
estimation need to be combined in such a way that underestimation is prevented.

DR
AF

2.5

Implementation

Process OXYMIN can only be used in combination with the algae module DYNAMO, consisting of various production, respiration and mortality processes. The module delivers the
net primary production fluxes and the respiration fluxes for two algae species (diatoms and
non-diatoms, referred to as ‘greens’).
Process OXYMIN makes use of the substance OXY and calculates the minimum DO concentration that occurs during a 24-hour day (output parameter OXYMIN).
Table 2.6 provides the definitions of the parameters occurring in the formulations.
Formulation

When neglecting all processes but gross primary production and respiration, the minimal dissolved oxygen concentration in a day follows from half the DO-decrease during the night:

Coxmin1 = Cox − 0.5 × 2.67 × Rrsp × (1 − DL)
2
X
Rrsp =
(krspi × Calgi )
i=1

with:

Calg
algae biomass [gC m−3 ]
Cox
average dissolved oxygen concentration [gO2 m−3 ]
Coxmin1 minimal dissolved oxygen concentration in a day for estimation method 1 [gO2
DL
krsp
Rrsp
Deltares

m−3 ]
day length, fraction of a day [-]
algae respiration rate constant [d−1 ]
total algae respiration rate [gC m−3 d−1 ]

29 of 464

Processes Library Description, Technical Reference Manual

Table 2.6: Definition of the parameters in the equations and the mode input for OXYMIN

Name in
formulas

Name in
in/output

Definition

Units

Calg1
Calg2
Cox
Coxmin

Green
Diat
OXY
OXYMIN

biomass of Green algae
biomass of Diatoms
average dissolved oxygen concentration
minimal dissolved oxygen concentration in a
day

gC m−3
gC m−3
gO2 m−3
gO2 m−3

DL

DayL

day length, fraction of a day

-

kgp1

RcGroGreen

d−1

kgp2
krsp1
krsp2

gross primary prod. rate constant of Green algae
RcGroDiat
gross primary prod. rate constant of Diatoms
RcRespGreen algae respiration rate constant of Green algae
RcRespDiat
algae respiration rate constant of Diatoms

Rgp

–

gC m−3
d−1
gC m−3
d−1

i

T

total gross primary production rate

DR
AF

Rrsp

d−1
d−1
d−1

–

total algae respiration rate

index for algae species (1-2)

When assuming that the other processes, reaeration in particular, compensate net production
on a daily basis, the minimal dissolved oxygen concentration in a day follows from half the
maximal DO-difference between day and night:

Coxmin2 = Cox − 0.5 × 2.67 × Rgp × (1 − DL)
2
X
Rgp =
(kgpi × Calgi )
i=1

with:

Coxmin2 minimal dissolved oxygen concentration in a day for estimation method 2 [gO2
kgp
Rgp

m−3 ]
gross primary production rate constant [d−1 ]
total net primary production rate [gC m−3 d−1 ]

In order to avoid overestimation of the DO-minimum, the minimal value is of both estimates is
used in the model:

Coxmin = min (Coxmin1 , Coxmin2 )
Directives for use
 The process OXYMIN is used for presentation purposes only. The concentrations of the
substance OXY and the parameter OXYMIN are both available for presentations.

30 of 464

Deltares

Oxygen and BOD

Table 2.7: Definitions of the parameters in the above equations for POSOXY

Name in
in/output

Definition

Units

Cox

OXY

equivalent dissolved oxygen concentration

gO2 m−3

DO

–

positive dissolved oxygen concentration

gO2 m−3

Calculation of actual DO concentration
POSOXY

T

PROCESS :

DELWAQ allows negative dissolved oxygen concentrations (DO). Decomposition of dead organic matter continues, when DO has become depleted using other substances such as nitrate and sulfate as electron donors. A correct oxygen balance requires that these reduced
substances produced at the anaerobic decomposition are taken into account. However, as
not all reduced substances (for example sulfate) are included in DELWAQ, the reduced substances are includeed instead as negative oxygen equivalents. As it may be undesirable
to show negative concentrations in the presentation of DO model results, process POSOXY
determines the actual DO concentration, effectively setting negative concentrations to zero.

DR
AF

2.6

Name in
formulas

Implementation

Process POSOXY makes use of the substance OXY and generates the output parameter DO.
Table 2.7 provides the definitions of the parameters occurring in the formulations.
Formulation

The actual dissolved oxygen concentration follows from:

DO = max (Cox, 0.0)

with:

DO
Cox

actual dissolved oxygen concentration [gO2 m−3 ]
equivalent dissolved oxygen concentration [gO2 m−3 ]

Directives for use
 The process POSOXY is used for presentation purposes only. The concentration of the
substance OXY and the parameter DO are both available for output.

Deltares

31 of 464

Processes Library Description, Technical Reference Manual

Table 2.8: Typical values for oxygen demanding waste waters (values in [mgO2 /l])

Source

CBOD5

CBODu

NBODu

Municipal waste (untreated)

100-400

220
(120-580)

220

170
(40-500)

220

-

Separate urban runoff (untreated)

19
(2-80)

-

-

Background natural water (excl. algae and detritus)

0

Background of natural water (incl.
algae and detritus)

2-3

sewer

overflow

(un-

2-3

T

Combined
treated)

COD

10

2.7

DR
AF

Data from Thomann and Mueller (1987).
Explanation: CBOD5 = 5-day CBOD; CBODu = ultimate CBOD

BOD, COD and SOD decomposition

PROCESS :

BODCOD

Organic matter in natural waters includes a great variety of organic compounds usually present
in minute concentrations, many of which elude direct isolation and identification. Collective parameters such as chemical oxygen demand (COD), biochemical oxygen demand (BOD) and
total organic carbon (TOC) or dissolved organic carbon (DOC), are therefore often used to
estimate the quantity of organic matter. Although often used they lack physiological meaning. The rates of microbial growth and the overall use of organic matter in multi-substrate
media depend in a complex way on the activities of a great variety of different enzymes and
on various mechanisms by which these activities are interrelated.
Discharges of wastes (municipal or industrial) and sewer overflows are principal inputs of
oxygen demanding wastes. These discharges cause a chemical oxygen demand (COD), a
carbonaceous bio-chemical oxygen demand (CBOD) and a nitrogenous biochemical oxygen
demand (NBOD). CBOD represents the oxygen demanding equivalent of the complex carbonaceous material present in waste. Typical values for different waters are presented in
Table 2.8.
2.7.1

Chemical oxygen demand
The chemical oxygen demand is a test that determines the organic matter content both in
wastewater and natural waters. The oxygen equivalent of the organic matter that can be
oxidized is measured using a strong chemical oxidizing agent in an acidic medium. Two
chemicals are used: potassium dichromate (referred to as Cr-method) and potassium permanganate (referred to as Mn-method). The efficiency of the Cr-method is approximately
90 % whereas the Mn-method only yields around 50 % of the oxidizable carbon. COD cannot
be measured accurately in samples containing more than 2 g l−1 Cl. There is no fixed relation
between the results obtained with the Mn and Cr-method.

32 of 464

Deltares

Oxygen and BOD

2.7.2

Biochemical oxygen demand
Biochemical oxygen demand is the sum of carbonaceous and nitrogenous oxygen demand.
This oxygen demand is determined by standard methods that measure the oxygen consumption of a filtered sample during a laboratory incubation within a period of time (usually 5-days
at 20 ◦ C in the dark). To obtain meaningful results the samples must be diluted in such a way
that adequate nutrients and oxygen will be available during the incubation (Standard methods: APHA (1989)). A typical oxygen demand curve is presented in Figure 2.3. The CBOD is
usually exerted first because of the time lag in the growth of the autotrophic nitrifying bacteria.

DR
AF

T

The heterotrophic carbonaceous oxidizing organisms are usually abundantly present in natural and sewage systems. The nitrifying bacteria convert ammonia to nitrate, a reaction that
demands a lot of oxygen. These bacteria can be eliminated by pre-treatment with inhibitory
agents, so that only the CBOD is measured. NBOD can then be obtained by the difference between BOD measurements in treated and untreated samples. Degradation of organic matter
during BOD measurements is a complex reaction of sequential oxidation steps which finally
results in CO2 and H2 O. Simplification to first order kinetics is used frequently. Fresh organic
matter is more susceptible to biochemical oxidation than older material. This preferential digestion causes residual material after treatment (either natural or anthropogenic) to be more
resistant to further treatment (biochemical oxidation).
Figure 2.4 illustrates the relation between the amount of oxidizable carbonaceous material
[gC m−3 ] and the amount of oxygen consumed in the stabilisation of this organic material as
a function of time. Note that it is assumed that 2.67 mg O2 are used to oxidize 1 mg of carbon.
The ratio between CBOD5 and CBODu depends on the decay rate of the organic material:
BOD5/BODu = (1 − exp(−5 × RcBodC)). The higher the decay rate the more the
ratio will reach unity. From the BOD5/BODu ratio the decay rate (called bottle-decay
rate) can be derived. The decomposition rate in rivers differs from the decomposition rate in
laboratory bottles (Hydroscience, 1971 referenced within Thomann and Mueller (1987)). But
information is scarce. Theoretically one would expect the decay rate to depend on the degree
of treatment, significant trends were however not found (Hydroqual, 1983 referenced within
Thomann and Mueller (1987)). BOD5/BODu ratios reported in this study range from 0.8
for untreated to 0.3 for activated sludge.
2.7.3

Measurements and relations

Conversion of total BOD (TBOD) to CBOD can be tricky when nitrifying bacteria are present.
During decomposition of organic material (proteins, urea) nitrogen can be liberated and subsequently be oxidized. Total BOD5 is often equal to CBOD5, due to the timelag of nitrifying
bacteria: reproduction time of nitrifying bacteria is low (one day) compared to that of heterotrophic bacteria (hours). Nitrifying bacteria are present in soil but also in wastewaters and
therefore in natural waters receiving wastewater. Industrial discharges (e.g. paper mills) are
usually deficient in any nitrogen forms in which case TBOD can be used as CBOD.
The temperature dependence of bacteria mediated reactions is considerable. An often used
value for the temperature coefficient is 1.04. For low temperatures however (below 20 ◦ C)
higher values up to 1.13 are suggested by Schroepfer et al. (1964) (referenced within Thomann
and Mueller (1987)).
Empirical relations between water depth and or flow and the decay rate of BODC exist, for
instance:

rate(20◦ C) = 0.3 Depth−0.434

Deltares

[d−1 ] for depths < 2.5 m.

(2.12)

33 of 464

Processes Library Description, Technical Reference Manual

For deeper water bodies the authors assume 0.33 m d−1 .
Accuracy
The BOD-test is a test in which much can go wrong: adequate bacterial seed is required,
no toxic wastes are allowed, nitrifying bacteria should be considered and the dilution of the
sample should be adequate. There is no standard against which the accuracy of the BODtest can be measured. Inter laboratory precision on a glucose-glutamic acid mixture gave
a standard deviation of 15 % (average level 175 mg l−1 ). At lower values of BOD the error
strongly increases for BOD values below 10 mg l−1 .
Implementation

T

All substances in this chapter are expressed as oxygen demand, so no direct connection with
the carbon-cycle of phytoplankton is considered. DELWAQ considers two pools of CBOD
with different decay rates (0.3 and 0.15 d−1 ). These two pools can e.g. be used to keep
track of waste from two different sources (with different treatment before entering the surface
water). For NBOD and COD, one pool for each is implemented. Each pool (CBOD, CBOD_2,
NBOD and COD) is characterized by a rate constant for decay, a coefficient for temperature
dependence and a dependency of the ambient oxygen concentration.

DR
AF

2.7.4

Because for each pool different types of measurements exist, DELWAQ accepts two different measurements for each pool. For the biochemical pools CBOD, CBOD_2 and NBOD the
standard measurement after 5 days as well as the measurement after ultimate time are accepted. For the chemical pool COD the Cr-method as well as the Mn-method are accepted.
Thus waste loads measured by different methods do not have to be converted to one standard
before they are entered into DELWAQ.
DELWAQ keeps track of the decay of each individual substance accepted by the system
(CBOD5, CBODu, CBOD5_2, CBODu_2, COD_Cr, COD_Mn. NBOD5 and NBODu). The
effects that individual decay fluxes cause on the oxygen balance are considered for the group
as a whole (only one oxygen consumption flux, dOXYCODBOD, is calculated). The same
aggregation is applied to the sediment (a description is given in documentation for the process
Sediment Oxygen Demand, sod). For aggregation purposes, the biochemical substances
are added to BOD5 and the chemical substances to COD (both parameters available for
output). When using default settings (see also the Directives for use) the oxygen demand of
detritus and part of the algae are added to these BOD and COD parameters (assuming that
measurements of BOD and COD have been made in unfiltered samples and did therefore
include the effect of algae and detritus).
You should be careful converting measurements to DELWAQ substances. There is a danger
of ’double counting’ the effect on the oxygen balance in the following situations:

 when one measurement of carbonaceous BOD is divided over the two BOD pools (CBOD
and CBOD_2) the sum should equal 100% of the original measurement;

 when different measurements of one wasteload are added, they both affect the oxygen
balance (e.g. when both COD_Cr and COD_Mn are measured, only one should be supplied as a wasteload). Measurements of BOD and COD of one wasteload may be added
simultaneously; only one (chosen by you) will affect the oxygen balance;
 when measurements of oxygen demand include algae and detritus and simultaneously
algae are modelled, their contribution to the oxygen demand is added to the BOD and
COD pools.
The decay of biochemical as well as chemical oxygen demanding substances are modelled as

34 of 464

Deltares

Oxygen and BOD

a first order process. If the water temperature drops below a critical value the decay is reduced
to zero. The first order flux is corrected for water temperature and oxygen concentration.
Below a critical oxygen concentration the oxygen function becomes equal to a user-defined
level (default 0.3) while for above optimal oxygen concentration these functions have a value
of 1.0. Linear interpolation of the oxygen functions is the default for intermediate oxygen
concentrations. A higher order interpolation for intermediate values may also be applied.
One option is implemented for the calculation of the first order rate constant (correction by
means of an ’aging function’). In this option the rate constant is made a function of the ratio
between COD and BOD. This option is based on the fact that the COD/BOD ratio increases
with the age of the decaying material. Of course both COD and BOD must be supplied for all
boundaries and wasteloads to use this option in a meaningful way.

T

This process is implemented for CBOD5, CBODu, CBOD5_2, CBODu_2, COD_Cr, COD_Mn,
NBOD5 and NBODu.
Formulation

DR
AF

Substance aggregation:

−1
BODu = CBODu + CBODu_2 + CBOD5 × 1 − e−5×RcBOD
+

−1
+CBOD5_2 × 1 − e−5×RcBOD_2


BOD5 = CBODu × 1 − e−5×RcBOD + CBODu_2 × 1 − e−5×RcBOD_2 +
+CBOD5 + CBOD5_2
COD_Cr
COD_M n
+
COD =
Ef f COD_Cr Ef f COD_M n
−1
N BOD = N BODu + N BOD5 × 1 − e−5×RcBODN
BODu_P HY T = P HY T × AlgF rBOD × OXCCF
BOD5_P HY T = BODu_P HY T × BOD5/uP HY T
BODu_P OC = P OC × P OCF rBOD × OXCCF
BOD5_P OC = BODu_P OC × BOD5/ inf P O
BOD5 = BOD5 + BOD5_P OC + BOD5_P HY T
BODu = BODu + BODu_P OC + BODu_P HY T
Oxygen function for all biological oxygen demand:

OXY = max(OXY, 0)
O2F uncBOD = 1

for (OXY ) ≥ OOXBOD then

O2F uncBOD = CF LBOD
for (OXY ) ≤ COXBOD then


O2F uncBOD = (1 − CF LBOD) ×

Deltares

(OXY ) − COXBOD
OOXBOD − COXBOD

10CurvBOD
+ CF LBOD

35 of 464

Processes Library Description, Technical Reference Manual

Functions for calculation of rate constant (’aging function’):

AgeIndx =

COD
BOD5

(2.13)

for AgeIndx ≤ LAgeIndx:

AgeF un = U AgeF un

(2.14)

for LAge < AgeIndx < LAgeIndx:

AgeF un = (U AgeF un−LAgeF un)×exp −

for AgeIndx ≥ LAgeIndx:

DR
AF

AgeF un = LAgeF un

AgeIndx − LAgeIndx
U AgeIndx

2 !
+LAgeF un

T



(2.15)

(2.16)

Decay fluxes:

dCBOD5 = RcBOD × (CBOD5) × T cBODT emp−20 × O2F uncBOD × AgeF un

dCBODu = RcBOD × (CBODu) × T cBODT emp−20 × O2F uncBOD × AgeF un
dN BOD5 = RcBODN × (N BOD5) × T cBODT emp−20 × O2F uncBOD × AgeF un
dN BODu = RcBODN × (N BODu) × T cBODT emp−20 × OF uncBOD × AgeF un
dCBOD5_2 = RcBOD_2 × (CBOD5_2) × T cBOD_2T emp−20 × O2F uncBOD × AgeF un
dCBODu_2 = RcBOD_2 × (CBODu_2) × T cBOD_2T emp−20 × O2F uncBOD × AgeF un
dCOD_Cr = RcCOD × (COD_Cr) × T cCODT emp−20

dCOD_M n = RcCOD × (COD_M n) × T cCODT emp−20
Oxygen demand:

SWOxyDem = 0: BOD determining (default)

dOxyBODCOD = dCBOD5+dCBOD5_2+dCBODu+dCBODu_2+dN BOD5+dN BODu
SWOxyDem = 1: COD determining (option)

dOxyBODCOD = dCOD_Cr + dCOD_M n
SWOxyDem = 2: BOD ∧ COD determining (option)

dOxyBODCOD = dBOD5 + dCBOD5_2 + dCBODu + dCBODu_2+
+dN BOD5 + dN BODu + dCOD_Cr + dCOD_M n
where:

36 of 464

Deltares

Oxygen and BOD

DR
AF

BODu

carbonaceous BOD (first pool) at 5 days [gO2 m−3 ]
carbonaceous BOD (second pool) at 5 days [gO2 m−3 ]
carbonaceous BOD (first pool) ultimate [gO2 m−3 ]
carbonaceous BOD (second pool) ultimate [gO2 m−3 ]
scaling function for decay rates [-]
ratio of CBOD5 and COD [-]
total phytoplankton concentration [gC m−3 d−1 ]
fraction of algae that contribute to BOD [-]
calculated carbonaceous BOD at ultimate from PHYT [gO2 m−3 ]
ratio BOD5 to BOD_ultimate for PHYT [-]
calculated carbonaceous BOD at 5 days from PHYT [gO2 m−3 ]
total particulate organic carbon concentration [gC m−3 d−1 ]
fraction of POC that contribute to BOD [-]
calculated carbonaceous BOD at ultimate from POC [gO2 m−3 ]
ratio BOD5 to BOD_ultimate for POC [-]
calculated carbonaceous BOD at 5 days from POC [gO2 m−3 ]
calculated carbonaceous BOD at 5 days (incl. PHYT and POC) [gO2
m−3 ]
calculated carbonaceous BOD at ultimate (incl. PHYT and POC)
[gO2 m−3 ]
calculated chemical oxygen demand days [gO2 m−3 ]
COD concentration by the Cr-method [gO2 m−3 ]
COD concentration by the Mn-method [gO2 m−3 ]
critical oxygen concentration: [g m−3 ]
value of the oxygen function for oxygen levels below the critical oxygen concentration [-]
factor that determines the curvature [-] between COXBOD and OOXBOD (-1 < CurvBOD < 0)
decay flux of CBOD5 [gO2 m−3 d−1 ]
decay flux of CBOD5_2 [gO2 m−3 d−1 ]
decay flux of COD_Cr [gO2 m−3 d−1 ]
decay flux of CBODu [gO2 m−3 d−1 ]
decay flux of CBODu_2 [gO2 m−3 d−1 ]
decay flux of COD_Mn [gO2 m−3 d−1 ]
decay flux of NBOD5 [gO2 m−3 d−1 ]
decay flux of NBODu [gO2 m−3 d−1 ]
oxygen consumption flux of BOD and COD species [gO2 m−3 d−1 ]
efficiency of the Cr_method [-]
efficiency of the Mn_method [-]
lower value of age function [-]
lower value of age index [-]
calculated nitrogenous BOD at ultimate [gO2 m−3 ]
nitrogenous BOD after 5 days [gO2 m−3 ]
nitrogenous BOD ultimate [gO2 m−3 ]
oxygen function for decay of CBOD [-]
oxygen to carbon ratio
optimum oxygen concentration: above this value the oxygen function
becomes 1.0 [gO2 m−3 ]
oxygen concentration [gO2 m−3 ]
reaction rate BOD (first pool) at 20 ◦ C [d−1 ]
reaction rate BOD_2 (second pool) at 20 ◦ C [d−1 ]
reaction rate BODN (second pool) at 20 ◦ C [d−1 ]
reaction rate COD (first pool) at 20 ◦ C [d−1 ]
switch that determines the oxygen consuming substance (0: BOD;

T

CBOD5
CBOD5_2
CBODu
CBODu_2
AgeF un
AgeIndx
P HY T
AlgF rBOD
BODu_P HY T
BOD5/uP hyt
BOD5_P HY T
P OC
P OCF rBOD
BODu_P OC
BOD5/inf P O
BOD5_P OC
BOD5

COD
COD_Cr
COD_M n
COXBOD
CF LBOD
CurvBOD

dCBOD5
dCBOD5_2
dCOD_Cr
dCBODu
dCBODu_2
dCOD_M n
dN BOD5
dN BODu
dOxyBODCOD
Ef f COD_Cr
Ef f COD_M n
LAgeF un
LAgeIndx
N BOD
N BOD5
N BODu
O2F unc
OXCCF
OOXBOD
OXY
RcBOD
RcBOD_2
RcBODN
RcCOD
SW OxyDem

Deltares

37 of 464

DR
AF

T

Processes Library Description, Technical Reference Manual

Figure 2.3: A typical oxygen demand curve

T cBOD
T cBOD_2
T cCOD
T emp
U AgeF un
U AgeIndx

1: COD; 2: COD+BOD) [-]
temperature coefficient BOD [-]
temperature coefficient BOD (second pool)[-]
temperature coefficient COD [-]
water temperature [◦ C]
upper value of age function [-]
upper value of age index [-]

Directives for use
 To change the aging function from its default value (1.0) to the shape presented in Figure 2.6, change the value LAgeFun to 0.15.
 Disable the contribution of algae and detritus when filtered measurements of BOD are
used as input. An easy way is to set AlgFRBOD and POCFrBOD to 0.
 The optimal oxygen concentration must be higher than the critical oxygen concentration
(see Figure 2.5).
 By choosing a low (or negative) value for the optimal oxygen concentration, the oxygen
function will have a value of 1.0 and thus not hamper the first order flux.
 By choosing a positive value for the minimum oxygen function level the oxygen function
can have a user-defined value at oxygen concentrations below the critical oxygen concentration. This results in mineralisation of BODC when no oxygen is present (note that
DELWAQ allows a negative oxygen concentration).
 The aging function (AgeFun) has a default value of 1.0. Adjust the value of LAgeFun to
get functions as pictured in Figure 2.6.
Additional references
Metcalf and Eddy (1991), Stumm and Morgan (1987)

38 of 464

Deltares

DR
AF

T

Oxygen and BOD

Figure 2.4: The relation between the amount of oxidizable carbonaceous material
[mgC/l], the amount of oxygen consumed in the stabilisation of this organic
material after 5 days and after ultimate time

1.1

1

0.9

O x y g e n fu n c tio n B O D (-)

0.8
0.7
0.6
0.5
0.4

CurvBOD = 0

0.3

CurvBOD = 0.5

CFLBOD
0.2
OOXBOD

COXBOD

CurvBOD = -0.3

0.1
0
0

1

2

3

4

5

Oxygen concentration (mg/l)

Figure 2.5: Default and optional oxygen functions for decay of CBOD (O2FuncBOD)

Deltares

39 of 464

DR
AF

T

Processes Library Description, Technical Reference Manual

Figure 2.6: Optional function for the calculation of the first order rate constant for BOD
and NBOD

40 of 464

Deltares

Oxygen and BOD

Sediment oxygen demand
PROCESS :

SEDOXYDEM

This process scales a user-defined sediment oxygen demand flux fSOD [gO2 m−2 d−1 ] to the
dimensions required by DELWAQ. This parameter represents the sediment oxygen demand,
as measured in the field. It is also possible to model a model substance SOD [gO2 ], which
equals the sum of BOD and COD components that accumulate in the sediment due to sedimentation. SOD represents the potential oxygen demand by BOD and COD components in
the sediment. The actual flux is calculated according to the equations listed below.

T

Note that sediment oxygen demand is additional to the oxygen consumption caused by the
oxidation of organic matter in the sediment (decay of substances DetCS1, DetCS2, OOCS1,
OOCS2).
DELWAQ assumes that all mineralisation processes in the sediment lead to an instantaneous
consumption of oxygen in the water column. In reality, mineralisation only causes a direct
depletion of oxygen in the aerobic top layer of the sediment. The oxygen penetration depth in
sediments is usually a few millimetres, or less.

DR
AF

2.8

Below the aerobic zone, reducing components, such as methane and hydrogen sulfide are
formed. These components will be transported upwards by diffusion. In the aerobic zone,
these components will react rapidly (instantaneously in the model) with oxygen. However,
at relatively high mineralisation rates a part of the methane may disappear from the water
column as gas bubbles, and not contribute to the sediment oxygen demand.
It is possible to introduce a methane-bubble correction term in DELWAQ, by specifying the
appropriate value of constant (SwCH4bub) in the model input. The correction term accounts
for the fraction of mineralized organic matter in the sediment that disappears as methane
bubbles. The correction term is calculated by an algorithm, based on ?.
Implementation

The process is implemented for DELWAQ substances oxygen (OXY) and sediment oxygen
demand (SOD).
Formulations

If SwCH4bub 6= 1:

f SOD RcSOD × T cSODT emp−20 × SOD
dSOD =
+
depth
V olume

if OXY < COXSOD
0
OXY −COXSOD
O2f unc = OOXSOD−COXSOD

1
if OXY > OOXSOD
dOxSOD = dSOD



× O2f unc

where

f SOD
SOD
Deltares

user-specified sediment oxygen demand [gO2 m−2 d−1 ]
BOD/COD components, accumulated in sediment [gO2 ]

41 of 464

Processes Library Description, Technical Reference Manual

RcSOD
T cSOD
depth
V olume
dSOD
dOxSOD
O2f unc
OXY
COXSOD
OOXSOD

decay rate of SOD in sediment [d−1 ]
temperature coefficient SOD decay [-]
depth of a DELWAQ segment [m]
volume of a DELWAQ segment [m3 ]
decay of SOD (DELWAQ flux) [gO2 m−3 d−1 ]
oxygen consumption (DELWAQ flux) [gO2 m−3 d−1 ]
oxygen function for decay of SOD [-]
oxygen concentration in surface water [gO2 m−3 ]
critical oxygen concentration for SOD decay [gO2 m−3 ]
optimal oxygen concentration for SOD decay [gO2 m−3 ]

If SwCH4bub = 1:

T

DELWAQ treats the methane bubble module as a black box. Reference is made to DiToro et
al. (1990) for theoretical backgrounds on this algorithm. As well the oxygen demand by SOD
(if modelled) as the oxygen consumption through the mineralisation of DetC and OOC in the
sediment are corrected. The latter equals:

where:

DR
AF

dOxM inSed = 2.67×(dM inDetCS1+dM inDetCS2+dM inOOCS1+dM inOOCS2)

dOxM inSed

dM inDetCS1
dM inDetCS2
dM inOOCCS1
dM inOOCCS2

oxygen consumption by mineralisation of DetC and OOC in sediment
[gO2 m−3 d−1 ]
mineralisation of DetC in sediment layer 1 [gC m−3 d−1 ]
mineralisation of DetC in sediment layer 2 [gC m−3 d−1 ]
mineralisation of OOC in sediment layer 1 [gC m−3 d−1 ]
mineralisation of OOC in sediment layer 2 [gC m−3 d−1 ]

The methane module computes the flux of methane, escaping from the water column to the
atmosphere. The flux is a function of dSOD + dOxM inSed.

F lCH4

methane bubble flux [gO2 m−2 d−1 ]

Additional output parameter:

dCH4

bubble flux expressed in DELWAQ units (= F lCH4/depth) [gO2 m−3 d−1 ]

Also the oxygen consumption by the sediment (fSOD*) is computed by the algorithm, fSOD*
includes dOxMinSed! Because the contribution of dOxMinSed to the mass balance of oxygen
is accounted for already by the mineralisation processes it has to be substracted from the
sediment oxygen demand flux. A part of the methane does not escape to the atmosphere, but
dissolves in the water column (DifCH4bub, DifCH4dis) where it is oxidized rapidly, causing no
additional oxygen consumption.
The resulting DELWAQ flux for oxygen equals:

dOxSOD =

f SOD∗ + Dif CH4bub + Dif CH4dis
− dOxM inSed
Depth

where:

f SOD∗
Dif CH4bub
Dif CH4dis

42 of 464

calculated total oxygen consumption in sediment [gO2 m−2 d−1 ]
oxygen consumption by CH4 dissolving from bubbles [gO2 m−2 d−1 ]
oxygen consumption by CH4 diffusing from sediment towards water
column [gO2 m−2 d−1 ]

Deltares

Oxygen and BOD

DR
AF

T

Remarks:
 The methane bubble formulation was developed for a single layer water column (1D,
2DH). If it is used in a multi-layer application (1DV, 2DV, 3D) an error is introduced
because DifCH4bub is entirely assigned to the bottom layer in stead of the total water
column. This means an overestimation of the oxygen consumption in the bottom layer.
Still, FlCH4 will be computed correctly since the total depth (TotalDepth) is used in the
methane bubble module.
 Field measurements of SOD represent the actual oxygen consumption of the sediment,
and should not be corrected for methane bubble formation. Hence, do not use fSOD in
combination with the methane bubble correction.
 The (escaping) methane bubble production dCH4 is a fraction of the mineralisation of
SOD + the mineralisation of DetC and OOC. It is possible that dCH4 exceeds dSOD,
for instance when you want to correct the oxygen consumption by DetC and OOC in the
sediment, but does not want to use SOD.
 If dCH4 > dSOD, dOxSod will become negative, which means that it becomes a positive contribution to the mass balance of oxygen. In that case, dOxSod acts as a correction term for the oxygen consumption by DetC and/or OOC in the sediment.
Directives for use
 The constant SwCH4bub must be specified in the model input if you want to use the SOD
module.
 If organic carbon in the sediment is modelled (DetCS1, OOCS1) oxygen from the water column is consumed during mineralisation. Take this sediment oxygen demand into
account when using substance SOD.
 If switched on, the methane-bubble correction will also compensate for the oxygen consumption by DetCS1 etc.
 Usually, the DELWAQ substance SOD is only applied in studies which focus on oxygen
problems, and where only measurements of (N)BOD and COD are available in stead of
accurate measurements of particulate organic matter, phytoplankton etc.
 SOD is not a real bottom substance like IM1S1, DetCS1 etc, because all settled BOD
species are lumped into this parameter. No distinction is made between SOD in the first
or second sediment layer. It is not accounted for in the sediment composition routines,
and it cannot be resuspended. Once settled it can only disappear by decay.
 In the current DELWAQ version the substance SOD and all BOD and COD species are
expressed as oxygen equivalents.
 In earlier versions only one BOD related substance was distinguished, it was expressed as
carbon (BODC, [gC m−3 ]). Substance BODC may still be used, but will not be converted
to SOD once sedimented.
Additional references

Thomann and Mueller (1987), Smits and Van der Molen (1993), DiToro (1986)

Deltares

43 of 464

Processes Library Description, Technical Reference Manual

2.9
2.9.1

Production of substances: TEWOR, SOBEK only
Coliform bacteria – listing of processes
Table 2.9: SOBEK-WQ processes for coliform bacteria.

Process description

Process name

TEWOR Production Fluxes

PROD_TEWOR

Mortality of coli bacteria

(i)MRT1)

1)

T

TEWOR-production fluxes

PROCESS :

PROD_TEWOR

Production fluxes have been introduced for the TEWOR-module in SOBEK (Stowa, 2002).
This module is used for water quality modelling of urban waters. The production fluxes can
represent certain processes in the water column, for instance algae growth, that are not modelled explicitly.

DR
AF

2.9.2

(i) ∈ {ECOLI, FCOLI or TCOLI}.

Implementation

The process has been implemented for substances CBOD5, CBOD5_2, CBOD5_3, COD_Cr,
OXY, DetN, NH4, NO3, Ecoli.
Table 2.10 provides the definitions of the parameters occurring in the formulations.
Formulation

The TEWOR-production fluxes are formulated as zeroth order fluxes.

Rtewori = f tewori
with:

(2.17)

Rtewori TEWOR production flux (g i.m−3 )
f tewori TEWOR production flux (g i.m−3 )
Directives for use

 The production fluxes were introduced for usage in the TEWOR subset. The fluxes can
also be used in other applications.
Table 2.10: Definitions of the parameters in the above equations for PROD_TEWOR.

Name in
formulas

Name in
input

Definition

Units

Rtewori

dTEWORi

TEWOR production flux

g.m−3

ftewori

fTEWORi

TEWOR production flux

g.m−3

44 of 464

Deltares

Oxygen and BOD

Process TEWOR: Oxydation of BOD
PROCESS :

DBOD_TEWOR

This module is an alternative process for the oxidation or mineralization of BOD that was
introduced for the TEWOR-module in SOBEK (Stowa, 2002). This module is used for water
quality modelling of urban waters. The prevailing process for the mineralization of BOD or
COD in SOBEK-WQ is BODCOD.
Implementation
The process has been implemented for substances CBOD5, CBOD5_2 and CBOD5_3.

T

Table 2.11 provides the definitions of the parameters occurring in the formulations.
Formulation

The oxidation flux of BOD5 is a function of the BOD5 concentration and is limited by the
oxygen concentration.

DR
AF

2.9.3

Rmini = kmini × C5i ×

Cox
Ksox + Cox

(2.18)

The oxygen demand is a function of the ultimate BOD concentration, because the actual
oxygen demand will be higher than the oxygen demand measured at 5 days.

Rox =

X
i

with:

C5i
Cox
kmini
Ksox

Rmini
1 − exp(−5kmini )

(2.19)

carbonaceous BOD (pool i) at 5 days [g O2 m−3 ]
dissolved oxygen [g O2 m−3 ]
oxidation reaction rate BOD (pool i) [d−1 ]
half saturation constant for oxygen limitation on oxidation of BOD [g O2 m−3 ]

Directives for use

 This process was introduced for usage in the TEWOR subset, but it can also be used in
other applications.

Table 2.11: Definitions of the parameters in the above equations for DBOD_TEWOR.

Name in
formulas

Name in
input

Definition

Units

C5i

CBOD5_i

carbonaceous BOD (pool i) at 5 days

g O2 m−3

Cox

OXY

dissolved oxygen

g O2 m−3

Cui

CBODu_i

carbonaceous BOD (pool i) ultimate

g O2 m−3

kmini

RCBOD_i

oxidation reaction rate BOD (pool i)

d−1

Ksox

KMOX

half saturation constant for oxygen limitation
on oxidation of BOD

g O2 m−3

Deltares

45 of 464

DR
AF

T

Processes Library Description, Technical Reference Manual

46 of 464

Deltares

3 Nutrients
Contents
3.1

Nitrification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

3.2

Calculation of NH3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.3

Denitrification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

3.4

Adsorption of phosphate . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

3.5

Formation of vivianite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.6

Formation of apatite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.7

Dissolution of opal silicate . . . . . . . . . . . . . . . . . . . . . . . . . .

DR
AF

T

78

Deltares

47 of 464

Processes Library Description, Technical Reference Manual

Nitrification
PROCESS :

NITRIF_NH4

Nitrification is the microbial, stepwise oxidation of ammonium (and toxic ammonia) into nitrate,
which requires the presence of oxygen. Several intermediate oxidation products are formed,
but the final step from nitrite to nitrate is considered rate limiting. The accumulation of the
intermediate products including toxic nitrite (NO−
2 ) is negligible in systems with residence
times longer than a few days.

T

Nitrification is highly sensitive to temperature. In contrast with the decomposition of detritus,
which may proceed at a slow but measurable rate below 4◦ C, nitrification nearly comes to a
halt at this temperature. This is connected with the fact that only a rather small number of
specialised bacteria species are capable of nitrification. The decomposition of organic matter
is performed by a very large number of species, including species that are adapted to low
temperature environments.
Nitrifiers are predominantly sessile bacteria, that need readily available organic substrates.
This implies that nitrification proceeds most actively at and in the oxidising top sediment layer.

DR
AF

3.1

Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

Process NITRIF_NH4 has been implemented in a generic way, meaning that it can be applied
both to water layers and sediment layers. The formation of intermediate products such as
nitrite is not considered. Two options are available with respect to the formulation of the rate
of nitrification. An option can be selected with parameter SW V nN it.
The process has been implemented for the following substances:

 NH4, NO3 and OXY.

Table 3.1 provides the definitions of the parameters occurring in the formulations.
Formulation

Nitrification can be described as a number of consecutive chemical reactions. The overall
reaction equation is:

N H4+ + 2O2 + H2 O

=⇒

N O3− + 2H3 O+

Nitrification ultimately removes ammonium (ammonia) and oxygen from the water phase and
produces nitrate. The process requires 4.57 gO2 gN−1 .
The formulation according to Michaelis-Menten kinetics (SWVnNit = 1.0)
Nitrification is modelled as the sum of a zeroth order process and a process according to
Michaelis-Menten kinetics Smits and Van Beek (2013). The rate of the last contribution is
limited by the availability of ammonium and dissolved oxygen, and is also a function of the
temperature.

48 of 464

Deltares

Nutrients

T

The zeroth order rate may have different values for the sediment and the water column, and
serves several purposes. It is used to account for the collapse of the process rate at low
temperatures. When the water temperature drops below a critical value, the zeroth order
rate takes over. However, the zeroth order rate is set to zero, when the dissolved oxygen
concentration drops below a critical value. The critical value in sediment layers should be
equal to 0.0, whereas the critical dissolved oxygen concentration in the water column can be
assigned a negative value. In that case, the zeroth order nitrification rate takes over from
the Michelis-Menten process for the water column, when dissolved oxygen gets depleted
and the temperature is still above the critical value. (Simulated DO can have a negative
concentration, representing the DO-equivalent of reduced substances!) This feature in the
nitrification formulations allows the occurrence of nitrification in a water column, in which the
average dissolved oxygen concentration is zero or even negative. In this way it can be taken
into account that the water column may not be homogeneously mixed in reality, and a surface
layer with positive oxygen concentrations persists.
The nitrification rate is formulated as follows to accommodate the above features:


Rnit = k0nit + knit ×

Cam
Ksam × φ + Cam

knit = 0.0
k0nit = 0.0
k0nit = k0temp
k0nit = k0ox
k0nit = 0.0

with:



×

Cox
Ksox × φ + Cox

DR
AF

knit = knit20 × ktnit(T −20)



Cam
Cox
Coxc
knit
ktnit
k0nit
k0ox
k0temp
Ksox
Ksam
T
Tc
φ

or Cox ≤ 0.0

if T < Tc

if T < Tc



Cox > 0.0
if T ≥ Tc and Cox ≤ 0.0
if Cox ≤ Coxc × φ
and

ammonium concentration [gN.m−3 ]
b

dissolved oxygen concentration ≥ 0.0 [g.m−3 ]
b

critical dissolved oxygen concentration [g.m−3 ]
Michaelis-Menten nitrification rate [gN.m−3 d−1 ]
w

b

temperature coefficient for nitrification [-]
zeroth order nitrification rate [gN.m−3 d−1 ]
b

zeroth order nitrif. rate at negative average DO concentrations [gN.m−3 d−1 ]

zeroth order nitrification rate at low temperatures [gN.m−3 d−1 ]

b

b

half saturation constant for dissolved oxygen limitation [g.m−3 ]
half saturation constant for ammonium limitation [gN.m−3 ]
temperature [◦ C]
critical temperature for nitrification [◦ C]
porosity [-]
w

w

An important feature of MM-kinetics is that the process rate saturates at high concentrations
of the substrate. The formulation turns into a first order kinetic process, when the ambient
substrate concentration becomes small compared to the half saturation constant.
The formulation according to pragmatic kinetics (SWVnNit = 0.0)
Nitrification is modelled as the sum of a zeroth and a first order process. If the water temperature drops below a critical value, only the zeroth order flux remains. The first order flux is

Deltares

49 of 464

Processes Library Description, Technical Reference Manual

corrected for water temperature and oxygen concentration. Below a critical oxygen concentration the oxygen function for nitrification becomes equal to a user defined level (default zero),
whereas for above an optimal oxygen concentration this function has a value of 1.0. Linear interpolation of the oxygen function is the default option for intermediate oxygen concentrations.
A higher order interpolation for intermediate values may also be applied.
The nitrification rate is formulated as follows to accommodate the above features:

Rnit = k0nit + f ox × k1nit × Cam

k1nit20 × ktnit(T −20)
k1nit =
0.0
if T < Tc
with:

T

ammonium concentration [gN m−3 ]
the oxygen limitation function [-]
first order nitrification rate [d−1 ]
temperature coefficient for nitrification [-]
zeroth order nitrification rate [gN m−3 d−1 ]
temperature [◦ C]
critical temperature for nitrification [◦ C]
w

w

DR
AF

Cam
f ox
k1nit
ktnit
k0nit
T
Tc

The oxygen limitation function reads:



f oxmin
f ox = (1 − f oxmin) ×

1.0
with:

a
Cox
Coxo
Coxc
f oxmin

if Cox ≤ Coxc

 a
Cox−Coxc 10
Coxo−Coxc

+ f oxmin if Coxc < Cox < Coxo
if Cox ≥ Coxo

curvature coefficient [-]
dissolved oxygen concentration ≥ 0.0 [g m−3 ]
optimal dissolved oxygen concentration [g m−3 ]
critical dissolved oxygen concentration [g m−3 ]
minimal value of the oxygen limitation function [-]
w

w

w

The pragmatic oxygen limitation function for default parameter values is depicted in Figure 3.1.
SOBEK The formulation according to TEWOR (SWVnNit = 2.0)

Nitrification is modelled as a process according to Monod kinetics. The rate of the process is a
function of the ammonium concentration and is limited by the availability of dissolved oxygen.
The nitrification rate is formulated as follows to accommodate the above features:


Rnit = knit × Cam ×

Cox
Ksox + Cox


(3.1)

with:

Cam
Cox
knit
Ksox
50 of 464

ammonium concentration [gN.m−3 ]
b

dissolved oxygen concentration ≥ 0.0 [g.m−3 ]
First order nitrification rate [gN.m−3 .d−1 ]

b

b

half saturation constant for dissolved oxygen limitation [g.m−3 ]
w

Deltares

Nutrients

An important feature of Monod-kinetics is that the process rate saturates at high concentrations of the substrate. The formulation turns into a first order kinetic process, when the
ambient substrate concentration becomes small compared to the half saturation constant.

DR
AF

Concerning option SW V nN it1.0:

T

Directives for use
 Formulation option SW V nN it = 0.0 is the default option for historical reasons.
 Care must be taken that the zeroth order reaction rates are given values, that are in
proportion with the MM-kinetics or first-order kinetics. They should not deliver more than
20 % of the total rate at T = 20 ◦ C, and average ammonium and DO concentrations.
Using zeroth order kinetics may cause negative ammonium concentrations, when the timestep is too large!
 The critical temperature for nitrification CT N it is approximately 4 ◦ C.
 The rate RcN it20 will generally be much higher in the top sediment layer than in the
overlying water. This is due to the sessile nature of nitrifiers. When the sediment is not
explicitly modelled, one should take the nitrifying capacity of the sediment into account in
the nitrification rate for the water column.

 For a start, the zeroth order rates Rc0N itT and Rc0N itOx and the critical DO concentration CoxN it can be set to zero. The zeroth order rate for negative DO concentrations
may not be relevant. If needed, the zeroth order rate for low temperatures can be quantified in establishing a good balance between summer and winter nitrification rates.
 The critical oxygen concentration should not be given negative values for sediment layers.
 Often nitrification has been modelled as a first-order (linear) process with respect to the
ammonium concentration. The MM-kinetics can be made to behave like a first order process by assigning a value to KsAmN it that is high compared to the ambient ammonium
concentrations. By enlarging RcN it20 concurrently approximately the same rates can be
obtained as for first order kinetics.
Concerning option SW V nN it0.0:

 The use of the curvature coefficient CurvN it of the oxygen limitation function is described in WL | Delft Hydraulics (1994a). Linear interpolation between COXN it and
OOXN it occurs, when CurvN it is equal to 0.0, whereas the value -1 establishes
maximal curvature.

 The optimal oxygen concentration OOXN it must be higher than the critical oxygen concentration COXN it (see Figure 3.1).
 The limitation function can be made inactive by choosing a low value for the optimal oxygen concentration OOXN it (e.g. a negative value).
 By choosing a positive minimal value of the oxygen limitation function CF LN it the limitation will have a user defined value at oxygen concentrations below the critical oxygen
concentration. This may result in nitrification when the average dissolved oxygen concentration is negative.
Additional references
DiToro (2001), Smits and Van der Molen (1993), WL | Delft Hydraulics (1997c), Vanderborght
et al. (1977)

Deltares

51 of 464

Processes Library Description, Technical Reference Manual

Table 3.1: Definitions of the parameters in the above equations for NITRIF_NH4. Volume
units refer to bulk ( ) or to water ( ).
b

w

Name in input

Definition

Units

a

CurvN it

curvature coefficient for the oxygen lim. function

-

Cam
Cox
Coxc
Coxo

N H4
OXY
CoxN it
OoxN it

ammonium concentration

gN m−3

dissolved oxygen concentration

g m−3

critical DO concentration for nitrification
optimal DO concentration for nitrification

g m−3
g m−3

f oxmin

CF LN it

minimal value of the oxygen limitation function

-

knit20
k1nit20
ktnit
k0ox
k0temp

RcN it20
RcN it
T cN it
Rc0N itOx
Rc0N itT

MM- nitrification reaction rate at 20 ◦ C

gN m−3 d−1

first order nitrification rate at 20 ◦ C
temperature coefficient for nitrification
zeroth order nitrification rate at negative DO

d−1
gN m−3 d−1

zeroth order nitrification rate at low temperatures
zeroth order nitrification rate

gN m−3 d−1

gN m−3

KsOxN it

half saturation constant for ammonium limitation
half saturation constant for DO limitation

–

nitrification rate

gN m−3 d−1

Ksox
Rnit
-

T
Tc

DR
AF

k0nit
Ksam

T

Name in
formulas

φ

Znit
KsAmN it

b

b

w

w

b

b

b

gN m−3 d−1
b

w

g m−3
w

b

SW V nN it

switch for selection of the process formulations (pragmatic kinetics = 0.0, MM-kinetics =
1.0)

-

T emp
CT N it

temperature
critical temperature for nitrification

◦

P OROS

porosity

m3 m−3

◦

C
C

w

b

52 of 464

Deltares

T

Nutrients

DR
AF

Nitrification)as)function)of)oxygen)concentration
1

OOXNIT

0.8
0.6
0.4
0.2

COXNIT

0

0

2

4
6
Dissolved)oxygen)(g/m3)

8

10

Figure 3.1: Figure 1 Default pragmatic oxygen limitation function for nitrification
(O2FuncNit, option 0).

Deltares

53 of 464

Processes Library Description, Technical Reference Manual

Calculation of NH3
PROCESS :

NH3 FREE

In rivers, estuaries and coastal seas near densely populated areas high loads of BOD and
nutrients may cause conditions which favour high levels of unionised ammonia, especially in
warm climates (Millero, 1995). Unionised, or free ammonia (NH3 ) is toxic to fish.
NH3 is the product of the dissociation of the ammonium (NH+
4 ) ion:
+
NH+
4 ⇒ NH3 + H

K0 =

aNH3 aH+
aNH+
4

where:

T

The reaction is characterised by the equilibrium constant K :

DR
AF

3.2

activity of species i [mol l−1 ]

ai

Rearranging this equation and taking logarithms (pH = − 10 log(aH + )) results in:

log

aNH3
aNH+

!

= log K 0 + pH

4

Because DELWAQ computes concentrations rather than activities, a corrected equilibrium
constant is introduced:

K = K0
where:

γi
K

γNH+
4

γNH3

activity coefficient of species i [-]
equilibrium constant [mol l−1 ], after correction for activities

Note that K is a function of the ionic strength of the solution (which determines gi ). Thus, K
depends on salinity! Combination of the previous two equations yields:

log

(NH3 )
= logK + pH
(NH+
4)

This equation shows the relation between the ratio of unionised and ionised ammonia and the
equilibrium constant. The equilibrium constant of this reaction depends strongly on temperature, increasing temperature favours the dissociation of NH+
4 (Millero, 1995).
In DELWAQ, totalN H4 is modelled as substance NH4, which is the sum of NH+
4 and NH3 .
The concentration of NH3 is derived from the above equation and total NH4 according to:

[NH3 ] =

[NH3 ]
+
[NH4 ]

× (totalN H4 )
1 + [NH+3 ]
[NH4 ]

54 of 464

Deltares

Nutrients

There are two options for calculating unionised ammonia. In the first option, the temperature
dependency of K is computed in a semi-empirical way with a reprofunction for the dissociation
constant, based upon the Netherlands’ water quality standards which tabulate the maximum
allowed total NH4 concentration that yields a certain level of unionised ammonia, at different
pH and T. In the second option, the value of the dissociation constant is calculated with a
reprofunction dependent on salinity and temperature according to Millero (1995).
Implementation
The process has been implemented for the following substance:

 NH4

T

The process calculates additional substance NH3 (g.m3 ), and is active in all types of computational elements.
Tabel 3.2 provides the definitions of the input parameters occurring in the formulations.

DR
AF

Formulation

The process is formulated as follows:

If NH3_Sw = 1 then

m3
1
×
l
M
log K = a + b × T
10logK+pH
× (totalN H4 )
(NH3 ) =
1 + 10logK+pH
l
N H3 = (NH3 ) × M × 3
m
(NH3 )
f rN H3 =
(totalN H4 )

(totalN H4 ) = N H4 ×

If NH3_Sw = 2 then

ln K = −6285.33/(T + 273.15) + 0.0001635 × (T + 273.15) − 0.25444
√
+ (0.46532 − 123.7184/(T + 273.15)) × Sal
+ (−0.01992 + 3.17556/(T + 273.15)) × Sal

ρ = (1000.0 + 0.7 × Sal/(1.0 − Sal/1000.0) − 0.0061 × (T − 4.0)2 )/1000.0
m3
1
(N H 4 ) = N H4 ×
×
l
M ×ρ
10−pH
(N H 3 ) = (N H 4 )/(1 +
)
K
l
N H3 = (N H 3 ) × M × ρ × 3
m
Deltares

55 of 464

Processes Library Description, Technical Reference Manual

where:
option parameter for calculation method [-]
concentration of ammonia [gN m−3 ]
molar concentration of ammonia [mol l−1 ] or [mol kg−1 H2 O]
concentration of ammonium (DELWAQ substance) [gN m−3 ]
molar concentration of ammonium [mol l−1 ] or [mol kg−1 H2 O]
coefficient a of reprofunction 1 [-]
coefficient b of reprofunction 1 [K−1 ]
fraction NH3 of NH4 [-]
dissociation constant [mol l−1 ] or [mol kg−1 H2 O]
atomic weight of nitrogen (= 14) [g mol−1 ]
pH [-]
salinity [g kg−1 ]
water temperature [◦ C]
density of water [kg l−1 ]

T

NH3_Sw
NH3
(NH3 )
NH4
(NH4 )
a
b
frNH3
K
M
pH
Sal
T

ρ

DR
AF

[m3 ] and [l] are the volume units (conversions between the standard volume unit in DELWAQ
and the unit usually used in chemistry).
Directives for use
 Do not change the defaults of KN H3rf 1a and KN H3rf 1a.

Table 3.2: Definitions of the input parameters in the formulations for NH3FREE.

Name in
formulas

Name in input

Definition

Units

N H4

N H4

ammonium concentration

gN m−3

N H3_Sw N H3_Sw

option for calculation method (1=reprofunction
1; 2=Millero)

-

a
b

KN H3rf 1a
KN H3rf 1b

coefficient a of reprofunction 1
coefficient b of reprofunction 1

K−1

pH

acidity

-

Salinity

salinity

psu

T emp

temperature

◦

pH
Sal
T

56 of 464

C

Deltares

Nutrients

Denitrification
PROCESS :

DENWAT_NO3 AND DENSED_NO3

Denitrification is the microbial, stepwise reduction of nitrate into elemental nitrogen, which
requires the absence of oxygen. The nitrogen produced may escape into the atmosphere.
Denitrifiers use nitrate in stead of oxygen to oxidise organic matter. Several intermediate
reduction products are formed, but the first step from nitrate to a nitrite is rate limiting. The
accumulation of the intermediate products including toxic nitrite and various toxic nitrogen
oxides is negligible in systems with residence times longer than a few days. The formation of
intermediate products such as nitrite is not considered in the model.

T

Denitrification is highly sensitive to temperature. In contrast with the decomposition of detritus,
which may proceed at a slow but measurable rate below 4 ◦ C, denitrification nearly comes to
a halt at this temperature. This is connected with the fact that only a rather small number
of specialised bacteria species are capable of denitrification. The decomposition of organic
matter is performed by a very large number of species, including species that are adapted to
low temperature environments.

DR
AF

3.3

Denitrifiers are predominantly sessile bacteria, that need readily available organic substrates
and that can only actively survive in an anoxic environment. This implies that denitrification
usually only proceeds in the lower part of the oxidising top sediment layer. It has been claimed,
however, that denitrification may also be carried out in the water column by highly specialised
bacteria, in anoxic pockets of suspended particles.
Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

Process DENWAT_NO3 has been implemented in a generic way, meaning that it can be applied both to water layers and sediment layers. Process DENSED_NO3 is to be used in
addition to DENWAT_NO3 only when the sediment is simulated according to the S1/2 option.
When sediment layers are not simulated explicitly, this process takes care that denitrification
in the sediment always proceeds, leading to the removal of nitrate from the water column. The
alternative for denitrification by processes DENWAT_NO3and DENSED_NO3 is the denitrification by process CONSELAC (Consumption of electron acceptors), in which nitrate is one
of the electron acceptors for the oxidation of organic detritus. When the "‘layered sediment"’
option is used CONSELAC should be used in stead of DENSED_NO3 and DENWAT_NO3.
Two options are available with respect to the formulation of the rate of nitrification. An option
can be selected with parameter SW V nDen.
The processes have been implemented for the following substances:

 NO3 and OXY.
Tables 3.3 and 3.4 provide the definitions of the parameters occurring in the formulations.
Formulation
Denitrification can be described as a number of consecutive chemical reactions. The overall
reaction equation is:

4N O3− + 4H3 O+ =⇒ 2N2 + 5O2 + 6H2 O
Deltares

57 of 464

Processes Library Description, Technical Reference Manual

Denitrification ultimately removes nitrate from the water phase and produces elemental nitrogen. The process delivers 2.86 gO2 gN−1 . The oxygen in nitrate used to oxidise organic
matter is accounted for in the model using this stochiometric constant. The actual quantity of
dissolved oxygen consumed for organic matter oxidation is therefore equal to the total oxygen
demand minus the part delivered by nitrate.
The formulation according to Michaelis-Menten kinetics (SWVnDen = 1.0)
Denitrification is modelled as the sum of a zeroth order process and a process according to
Michaelis-Menten kinetics. The rate of the latter contribution is a function of the nitrate concentration, the dissolved oxygen concentration and the temperature. The Michealis-Menten
kinetic factor for dissolved oxygen is formulated as an inhibition factor. The denitrification rate
has not been made proportional to the detritus concentration, since detritus is (almost) always
abundantly present.

DR
AF

T

The zeroth order rate may have different values for the sediment and the water column, and
serves several purposes. It is used to account for the collapse of the process rate at low
temperatures. When the water temperature drops below a critical value, the zeroth order rate
takes over. The zeroth order and Michealis-Menten rates are both set to zero, when the dissolved oxygen concentration rises above a critical value, and consequently, the environment is
completely oxic. When the temperature is still above the critical temperature, the zeroth order
denitrification rate may be assigned a substantially higher value than at low temperature. This
feature in the denitrification formulations allows the occurrence of substantial denitrification
in a water column or sediment layer, in which the average dissolved oxygen concentration is
positive but below the critical concentration. In this way it can be taken into account that:

 the water column may not be homogeneously mixed in reality, and that near the sediment
an oxygen depleted water layer persists; and

 denitrification can occur in a sediment environment that is oxic on the average, but does
contain anoxic pockets at the same time.

The denitrification rate is formulated as follows to accommodate the above features:



Rden = k0den + kden ×



f ox =

1.0 −
1.0

Cox
Ksox×φ+Cox

Cni
Ksni × φ + Cni



× f ox

if Cox ≥ 0.0
if Cox < 0.0

kden = kden20 × ktden(T −20)
kden = 0.0
k0den = 0.0
k0den = k0temp
k0den = k0ox
k0den = 0.0

if T < T c or Cox ≥ Coxc × φ

T < T c and Cox < Coxc × φ
if T ≥ T c and Cox < Coxc × φ
if Cox ≥ Coxc × φ
if

with:

Cni
Cox

nitrate concentration [gN m−3 ]
b

dissolved oxygen concentration ≥ 0.0 [g m−3 ]
b

58 of 464

Deltares

Nutrients

critical dissolved oxygen concentration [g m−3 ]
oxygen inhibition function [-]
Michaelis-Menten denitrification rate [gN m−3 d−1 ]
w

b

temperature coefficient for denitrification [-]
zeroth order denitrification rate [gN m−3 d−1 ]
b

zeroth order denitrification rate at moderate DO concentrations [gN m−3 d−1 ]
zeroth order denitrification rate at low temperatures [gN m−3 d−1 ]

b

b

half saturation constant for nitrate limitation [gN m−3 ]
half saturation constant for dissolved oxygen inhibition [g m−3 ]
temperature [◦ C]
critical temperature for denitrification [◦ C]
porosity [-]
w

w

T

Coxc
f ox
kden
ktden
k0den
k0ox
k0temp
Ksni
Ksox
T
Tc
φ

The oxygen inhibition function needs to be set to 1.0 at negative DO concentrations to avoid
the function obtaining values higher than 1.0. (Simulated DO can have a negative concentration, representing the DO-equivalent of reduced substances!)

DR
AF

The formulation according to pragmatic kinetics (SWVnDen = 0.0)
Denitrification is modelled as the sum of a zeroth and a first order process. If the water
temperature drops below a critical value, only the zeroth order flux remains. The first order
flux is corrected for water temperature and oxygen concentration. Above a critical oxygen
concentration the oxygen function for denitrification becomes equal to zero, whereas for below
an optimal oxygen concentration this function has a value of 1.0. Linear interpolation of the
oxygen functions is the default option for intermediate oxygen concentrations. A higher order
interpolation for intermediate values may also be applied.
The denitrification rate is formulated as follows to accommodate the above features:

Rden = k0den + f ox × k1den × Cni

0.0
if T < Tc
k1den =
20
(T −20)
k1den × ktden

with:

Cni
f ox
k1den
ktden
k0den
T
Tc

nitrate concentration [gN m−3 ]
the oxygen inhibition function [-]
first order denitrification rate [d−1 ]
temperature coefficient for denitrification [-]
zeroth order denitrification rate [gN m−3 d−1 ]
temperature [◦ C]
critical temperature for denitrification [◦ C]
w

w

The oxygen inhibition function reads:



1.0


if Cox ≤ Coxo
Coxc − Cox
if Coxo < Cox < Coxc
f ox =
Coxc − Coxo + (ea − e) (Cox − Coxo)



0.0
if Cox ≥ Coxc
with:

a
Cox
Coxo
Deltares

curvature coefficient [-]
dissolved oxygen concentration ≥ 0.0 [g m−3 ]
optimal dissolved oxygen concentration [g m−3 ]
w

w

59 of 464

Processes Library Description, Technical Reference Manual

critical dissolved oxygen concentration [g m−3 ]

Coxc

w

The pragmatic oxygen inibition function for default parameter values is depicted in Figure 3.2.
The above formulations for options 1 and 0 represent process DENWAT_NO3. Process
DENSED_NO3 has been formulated in a much more simplified way with first-order kinetics
with respect to the nitrate concentration. The deeper sediment is essentially reducing, leading
to maximal denitrification in the sediment proportional to the nitrate concentration in the water
column. DO inhibition has therefore been removed from the formulations. Only one zeroth order rate is used, the one associated with the critical temperature. The first-order reaction rate
has to be provided in m.d-1, the zeroth order rate in [g.m−2 d−1 ]. The resulting denitrification
rate is divided by the depth of the water column H in order to obtain the rate in [g.m−3 d−1 ].

DR
AF

T

Directives for use
 Formulation option SW V nDen = 0.0 is the default option for historical reasons.
 Care must be taken that the zeroth order reaction rates are given values, that are in
proportion with the first-order kinetics. They should not deliver more than 20% of the
total rate at T=20 ◦ C, and moderate nitrate and DO concentrations. Using zeroth order
kinetics may cause negative nitrate concentrations, when the time-step is too large!
 The critical temperature for denitrification CT Den is approximately 4 ◦ C.
 If denitrification actually occurs in the water column at all, the rate RcDen20 will generally
be much higher in the top sediment layer than in the overlying water. This is due to the
sessile nature of nitrifiers. When the sediment is not explicitly modelled, one should take
the denitrifying capacity of the sediment into account in process DENSED_NO3.
Concerning option SW V nDen1.0:

 For a start, the zeroth order rates Rc0DenT and Rc0DenOx and the critical DO concentration CoxDen can be set to zero. In a next step the zeroth order rate for low temperatures can be quantified in establishing a good balance between summer and winter
nitrification rates. The zeroth order rate for moderate DO concentrations may not be relevant for the current case.
 The critical oxygen concentration should not be given a value higher than 2 g m−3 for
physical reasons. A higher value might nevertheless be required to take the occurrence
of denitrification in an inhomogeneous water column into account properly.
 Often denitrification has been modelled as a first-order (linear) process with respect to the
nitrate concentration. The MM-kinetics can be made to behave like a first order process by
assigning a value to KsN iDen that is high compared to the ambient nitrate concentrations. By enlarging RcDen20 concurrently approximately the same rates can be obtained
as for first order kinetics.
w

Concerning option SW V nDen0.0:

 Linear interpolation occurs for the oxygen inhibition function between COXDen and
OOXDen, when curvature coefficient Curvat is equal to 1.0. Maximal curvature is
established, when Curvat is equal to 4.0
 The optimal oxygen concentration OOXDen must be smaller than the critical oxygen
concentration COXDen (see Figure 3.2).
 The limitation function can be made inactive by choosing a high value for the optimal
oxygen concentration OOXDen.

60 of 464

Deltares

Nutrients

Additional references
DiToro (2001), Smits and Van der Molen (1993), WL | Delft Hydraulics (1997c), Vanderborght
et al. (1977)
Table 3.3: Definitions of the parameters in the above equations for DENWAT_NO3. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in input

Definition

Units

a

Curvat

curvature coefficient for the oxygen inhib. function

-

Cni
Cox
Coxc
Coxo

N O3
OXY
CoxDen
OoxDen

nitrate concentration

gN m−3

dissolved oxygen concentration

g m−3

optimal DO concentration for denitrification
critical DO concentration for denitrification

g m−3
g m−3

kden20
k1den20
ktden
k0ox

RcDen20
RcDenW at
T cDenW at
Rc0DenOx

MM- denitrification reaction rate at 20 ◦ C

gN m−3 d−1

first order denitrification reaction rate at 20 ◦ C
temperature coefficient for denitrification
zeroth order denitrification rate at moderate
DO
zeroth order denitrification rate at low temperatures
zeroth order denitrification rate

d−1
gN m−3 d−1

half saturation constant for nitrate limitation
half saturation constant for DO inhibition

gN m−3
g m−3

denitrification rate

gN m−3 d−1

Rc0DenT

k0den
Ksni
Ksox

ZDenW at
KsN iDen
KsOxDen

Rden

–

T
Tc
φ

T

DR
AF

k0temp

-

b

Deltares

b

w

w

b

b

gN m−3 d−1
b

gN m−3 d−1
b

w

w

b

SW V nDen

switch for selection of the process formulations
(pragmatic kinetics = 0.0, MM-kinetics = 1.0)

-

T emp
CT Den

temperature
critical temperature for denitrification

◦

P OROS

porosity

m3 m−3

◦

C
C

w

b

61 of 464

Processes Library Description, Technical Reference Manual

Table 3.4: Definitions of the parameters in the above equations for DENSED_NO3. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in input

Definition

Units

Cni

N O3

nitrate concentration in the overlying water
layer

gN m−3
b

Depth

depth of the overlying water layer

m

kden20
ktden
k0temp

RcDenSed
T cDenSed
Rc0DenSed

first-order denitrification reaction rate
temperature coefficient for denitrification
zeroth order denitrification rate

m d−1
gN m−2

Rden

–

denitrification rate

gN m−3 d−1

DR
AF

T
Tc

T

H

T emp
CT Den

◦

temperature
critical temperature for denitrification

◦

b

C
C

DenitrificationOasOfunctionOofOoxygenOconcentration

1

OOXDEN

0.8
0.6
0.4
0.2

COXDEN
0

0

2

4
6
DissolvedOoxygenO(g/m3)

8

10

Figure 3.2: Default pragmatic oxygen inhibition function for denitrification (O2Func, option
0).

62 of 464

Deltares

Nutrients

Adsorption of phosphate
PROCESS :

ADSPO4AAP

Dissolved phosphate, mainly present as ortho-phosphate (mainly present as H2 PO−
4 ), adsorbs onto suspended sediment, in particular to the iron(III)oxyhydroxides in sediment particles. Other adsorbing components are aluminium hydroxides and silicates, manganese oxides and organic matter. The fine sediment fraction (< 0.63 µm), containing more than 90 %
of these components present in suspended sediment, basically accounts for the adsorption
capacity of sediment.

T

The adsorption of phosphate onto sediment particles is highly pH dependent, since phosphate
competes with OH− for the adsorption sites. The adsorption decreases with increasing pH,
which implies that alkalinity producing primary production by algae stimulates desorption,
which in turn may stimulate primary production.
Moreover, the adsorption process is relatively weakly dependent on temperature and ionic
strength (salinity). The effect of the latter has not been quantified very well and has therefore
been ignored in the model formulations.

DR
AF

3.4

The adsorption of phosphate is also very sensitive to low dissolved oxygen concentrations.
Iron(III) gets chemically reduced into iron(II), when dissolved oxygen has been depleted and
the decomposition of detritus continues at anaerobic conditions. As a result, initially, iron(II)
dissolves together with adsorbed substances, among which phosphate. Iron(II) will precipitate
as sulfide and/or carbonate, the phosphate repartitions between the solution and the sediment
particles, according to the decreased adsorption capacity.
The oxygen concentration dependency of the adsorption process has an enormous impact
on the sorption of phosphate in the sediment. The sorption capacity of the oxidising top layer
of the sediment is large, since oxidised iron(III) tends to accumulate in this layer. However,
the sorption capacity of the reducing lower sediment layer is much smaller, since most of the
iron may be present in its chemically reduced iron(II)-form. When the oxidising layer collapses
due to intensified decomposition of organic matter, the phosphate release of the sediment into
the overlying water may suddenly increase an order of magnitude. Consequently, linking the
adsorption of phosphate to the presence of dissolved oxygen allows application of the same
formulations to both the water column and the sediment.
Adsorption is fast and desorption of recently adsorbed phosphate is somewhat slower. Nevertheless, equilibrium is usually established within a few hours. Although process rates are
high, the adsorption process has been formulated kinetically for pragmatic reasons. One reason is that this approach delivers the sorption flux. The present formulations, however, do
not allow taking into account very slow desorption of phosphate from for instance river borne
sediment/soil particles, that contain internally bound phosphate. The solid phase diffusion of
phosphate proceeds very slow in such particles.
Volume units refer to bulk ( ) or to water ( ).
b

Deltares

w

63 of 464

Processes Library Description, Technical Reference Manual

Implementation
Three different sets of formulations have been implemented in process ADSPO4AAP, from
which a selection can be made using switch SW AdsP . The oxygen concentration dependent option SW AdsP = 2 is fully generic, meaning that it can be applied both to water
layers and sediment layers. The adsorption of phosphate in the sediment is not considered,
when phosphate in the sediment is modeled as a number of ‘inactive’ substances.
The process has been implemented for the following substances:

 dissolved PO4 and adsorbed AAP.

T

Table 3.5 provides the definitions of the parameters occurring in the formulations. The concentrations of adsorbing inorganic matter (Cim1−3 ) and the dissolved oxygen concentration
(Cox) can be either calculated by the model or imposed on the model via the input.

DR
AF

In case the S1-S2 option is applied for the sediment, slow desorption from AAPS1 and AAPS2
can be taken into account by processes DESO_AAPS1 and DESO_AAPS2 (see the formulations in section 8.4, Mineralization of detritus in the sediment (S1/2)).
Formulation

The three options regarding the formulation of the adsorption of phosphate to sediment particles range from ultimately simplified to rather complex pH- and DO dependent adsorption.
The adsorption capacity of (suspended) inorganic sediment can be calculated in two different ways. The selection is made with switch parameter SW V nAdsP . The default version
(SW V nAdsP =0.0) calculates the adsorption capacity from the total iron fraction in (suspended) inorganic sediment, whereas version (SW V nAdsP =1.0) calculates the adsorption
capacity from the individual inorganic matter concentrations IM1−3 and pertinent iron fractions. For the eye of the user the versions are only different with respect to the names of
several input parameters, see Table 3.5 and the directives for use.
Simplified equilibrium partitioning (SWAdsP = 0)
Instantaneous reversible equilibrium sorption is assumed. The adsorbed phosphate is quantified as a constant fraction of the total inorganic phosphate concentration, which implies a
constant ratio between the dissolved and adsorbed phosphate concentrations:

Kdph =
where:

Cphae
Cphde
Kdph

Cphde
Cphae

equilibrium adsorbed phosphate concentration [gP m−3 ]
b

equilibrium dissolved phosphate concentration [gP m−3 ]
b

distribution coefficient [-]

Consequently, adsorption in this formulation is not proportional to the sorption capacity of
sediment.
The equilibrium adsorbed concentration follows from:

Cphae + Cphde = Cpha + Cphd
Cphae =

64 of 464

Cpha + Cphd
1 + Kdph
Deltares

Nutrients

where:

Cpha
Cphd

the adsorbed phosphate concentration after the previous time-step [gP m−3 ]
b

the dissolved phosphate concentration after the previous time-step [gP m−3 ]
b

The sorption rate is calculated as:

Rsorp =

Cphae − Cpha
∆t

where:

∆t

Simplified Langmuir adsorption (SWAdsP = 1)

T

computational time-step [d]

The adsorption equilibrium can be considered as a chemical equilibrium described with the
following simplified reaction equation:

DR
AF

ADS + P ⇔ ADSP

The kinetics of the reaction saturate with respect to the amount of adsorption sites (e.q. the
adsorption capacity), which according to Langmuir can be taken into account with the following
equilibrium equation:

Kads =

Cphae × φ
Cphde × Cadse

where:

Cadse
Cphae
Cphde
Kads
φ

equilibrium concentration of free adsorption sites in P equivalents [gP m−3 ]
b

equilibrium adsorbed phosphate concentration [gP m−3 ]
b

equilibrium dissolved phosphate concentration [gP m−3 ]
b

adsorption equilibrium constant [m3 gP−1 ]
porosity [-]

The free adsorbent is a fraction of the total adsorbent concentration. This fraction becomes
infinitely small at an abundance of phosphate, which prevents the further increase of the concentration of adsorbed phosphate (see Fig. 3.3 and 3.4). The total adsorbent concentration
Cadst is proportional to the suspended sediment concentration. The proportionality factor is
defined as the fraction reactive iron in suspended sediment:

Cadst = f cap ×

3
X

(f f ei × Cimi )

i=1

f imi = (f f ei × Cimi )/

3
X

(f f ei × Cimi )

i=1

where:

Cadst
Cimi
f imi
Deltares

total concentration of adsorption sites [gP m−3 ]
b

concentration of inorganic matter fractions i=1, 2, 3 [gDW.m−3 ]
b

fraction of adsorbed phosphate bound to inorganic matter fractions i=1, 2, 3 [-]

65 of 464

Processes Library Description, Technical Reference Manual

phosphate adsorption capacity of inorganic matter [gP gFe−1 ]
fraction reactive iron(III) in inorganic matter fractions i=1, 2, 3 [gFe gDW−1 ]

f cap
f f ei

The fractions f imi are available as output parameters to be used for the calculation of the
settling of adsorbed phosphate connected with the settling of the inorganic matter fractions.
The equilibrium concentrations can be approximated with:

Cphae + Cphde = Cpha + Cphd
Cadse = Cads = Cadst − Cpha

(3.2)
(3.3)

where:
the concentration of free ads. sites after the previous time-step [gP m−3 ]

Cads
Cpha
Cphd
e

b

T

the adsorbed phosphate concentration after the previous time-step [gP m−3 ]
b

the dissolved phosphate concentration after the previous time-step [gP m−3 ]
index for the chemical equilibrium value
b

DR
AF

The above equations result in the following equation for the equilibrium adsorbed phosphate
concentration:


Cphae = (Cpha + Cphd)/ 1 +

φ
Kads × Cads



if Cads < 0.0 then Cphae = 0.9 × (31 000 × φ) × Cadst

The above correction applies to a situation where imposed initial AAP would be larger than
the adsorption capacity.
Considering (potentially) slow kinetics delivers for the sorption rate:

Rsorp = ksorp × (Cphae − Cpha)
where:

ksorp
Rsorp

sorption reaction rate [d−1 ]
adsorption or desorption rate [gP m−3 d−1 ]
b

Comprehensive Langmuir adsorption (SWAdsP = 2)

A more comprehensive description of the Langmuir adsorption equilibrium must include the
dependency of the pH and the temperature with concentrations on a molar basis (Smits and
Van Beek (2013)):

ADS(OH)a + P ⇔ ADSP + a × OH
Kads =

Cphae × OH a
Cphde × Cadse

Kads = Kads20 × ktads(T −20)
OH = 10−(14−pH)
where:

a
66 of 464

stochiometric reaction constant [-]

Deltares

Nutrients

Cadse
Cphae
Cphde
Kads
ktads
OH
pH
e

equilibrium concentration of free adsorption sites [molFe l−1 ]
equilibrium adsorbed phosphate concentration [molP l−1 ]
equilibrium dissolved phosphate concentration [molP l−1 ]
adsorption equilibrium constant [(mol l−1 )a−1 ]
temperature coefficient for adsorption [-]
molar hydroxyl concentration [mol l−1 ]
acidity [-]
index for the chemical equilibrium value
w

w

w

w

Cadst = f cor ×

3
X

(f f ei × Cimi ) ×

i=1

T

The free adsorbent is a fraction of the total adsorbent concentration. The total adsorbent
concentration Cadst is proportional to the actual adsorption capacity of suspended sediment,
which is coupled to the reactive iron(III) fraction, and the concentration suspended sediment.
The actual adsorption capacity depends on the redox status of the total reactive iron fraction.
Consequently, the total adsorbent concentration follows from:

1
56, 000 × φ

if Cox ≥ Coxc × φ

DR
AF

f cor = 1.0
f cor = f f eox

if Cox < Coxc × φ

f imi = (f f ei × Cimi )/

3
X

(f f ei × Cimi )

i=1

where:

Cadst
Cimi
Cox
Coxc
f cor
f imi
f f ei
f f eox
φ

total molar concentration of adsorption sites [molFe l−1 ]
concentration of inorganic matter fractions i=1,2,3 [gDW m−3 ]
w

dissolved oxygen concentration [g m−3 ]

b

b

critical dissolved oxygen concentration [g m−3 ]
correction factor for the oxidised iron(III) fraction [-]
fraction of adsorbed phosphate bound to inorganic matter fractions i=1, 2, 3 [-]
fraction of reactive iron in inorganic matter fractions i=1,2,3 [gFe gDW−1 ]
fraction of oxidised iron(III) in the reactive iron fraction [-]
porosity [-]
w

The fractions f imi are available as output parameters to be used for the calculation of the
settling of adsorbed phosphate connected with the settling of the inorganic matter fractions.
The equilibrium concentrations can be approximated with:

Cphae + Cphde =

(Cpha + Cphd)
31 000 × φ

Cadse = Cads = Cadst −

Cpha
31 000 × φ

where:

Cads
Cpha
Cphd
e
Deltares

the concentration of free ads. sites after the previous time-step [molFe l−1 ]
the adsorbed phosphate concentration after the previous time-step [gP m−3 ]
w

b

the dissolved phosphate concentration after the previous time-step [gP m−3 ]
index for chemical equilibrium value
b

67 of 464

Processes Library Description, Technical Reference Manual

The above equations result in the following equation for the equilibrium adsorbed phosphate
concentration:

Cphae =

(Cpha + Cphd)

OH a
31 000 × φ × 1 + Kads×Cads

Considering (potentially) slow kinetics delivers for the sorption rate:

Rsorp = ksorp × (31 000 × φ × Cphae − Cpha)
where:

ksorp

sorption reaction rate [d−1 ]

T

A positive value of the adsorption flux Rsorp represents adsorption of P O4, a negative value
represents desorption of P O4.

DR
AF

Directives for use
 Version SW V nAdsP = 0.0 uses RcAdsP gem as input name for the sorption rate in
the case of formulation option SW AdsP = 2.
Version SW V nAdsP = 0.0 uses fr_Fe as input name for the fraction of reactive iron in
inorganic matter in the cases of formulation options SW AdsP = 1 and 2.
 When using formulation option SW AdsP = 0, an indicative value for KdP O4AAP is
0.5.
 Using data of Stumm and Morgan (1996) , it can be deduced that KadsP _20 and
a_OH − P O4 may be approximately equal to respectively 3.8 (mole l−1 )a−1 and 0.2.
These values relate to the sorption of ortho-phosphate onto α − F eOOH (goethite)
within a pH range of 6 to 9, approximately at a temperature of 20 ◦ C. Amorphous iron
coating of sediment may have a much higher adsorption constant (≈1000).
 When dissolved oxygen (OXY ) is not simulated, OXY must be imposed as the actual
concentration times porosity for option 2 (SW AdsP = 2). This is necessary, because
the formulations are based on simulated OXY , which is calculated internally as bulk
concentration. The critical concentration CrOXY , however, is to be imposed as the
actual concentration in (pore) water.
 When simulating the “inactive” substances in the sediment AAP S1 and AAP S2, the
sorption process only affects AAP in the water column. However, slow desorption in the
sediment can be taken into account with processes DESO_AAPS1 and DESO_AAPS2.
 AAP is also affected by settling and resuspension. The settling of AAP is coupled
to the settling of inorganic matter fractions IM 1 − 3, the fine inorganic matter fraction
IM 1 in particular since AAP is predominantly adsorbed to IM 1. When IM 1 − 3 are
not modelled explicitly but imposed, the settling velocity of AAP should be equal to the
settling velocity of the fine inorganic matter fraction IM 1.
 The phosphorus fractions F P IM 1, F P IM 2 and F P IM 3 (= f imi ) in the inorganic
matter fractions are output parameters, that are used to correct the settling flux for differences in the settling velocities of IM 1 − 3. The fractions add up to 1.
 The iron fraction in (suspended) sediment bound in redox stable minerals such as clay is
not part of the reactive iron fraction. The reactive iron fraction is probably smaller than
the redox sensitive iron fraction, because a part of this fraction is not available for surface
reactions such as sorption.
Additional references
WL | Delft Hydraulics (1992a), WL | Delft Hydraulics (1997c)

68 of 464

Deltares

Nutrients

Table 3.5: Definitions of the parameters in the above equations for ADSPO4AAP. Volume
units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in input

Definition

a

a_OH − P O4

stochiometric
dependency

Cimi
Cox
Coxc
Cpha
Cphd
f cap
f imi

IM i
OXY
Cc_oxP sor
AAP
P O4
M axP O4AAP

conc. of inorg. matter fractions i = 1,2,3

gDW m−3

dissolved oxygen concentration

g m−3

critical DO concentration for iron reduction
adsorbed phosphate concentration

g m−3
gP m−3

dissolved phosphate concentration

gP m−3
gP gFe−1
-

f f ei

f r_F eIM i

„

f r_F e

phosphate adsorp. capacity of inorg. matter
fraction ads. phosphate in inorg. matter fr. i =
1,2,3
fraction react. iron in inorg. fr. i=1,2,3
(SW V nAdsP =1)
fraction reactive iron in inorg.
matter
(SW V nAdsP =0)
fraction oxidised iron(III) in the reactive iron
fraction

reaction

constant

f f eox

f r_F eox

Kdph

KdP O4AAP

for

pH-

-

b

T

b

DR
AF

–

Units

w

b

b

gFe gDW−1
gFe gDW
-

distribution coefficient (SW AdsP = 0; see
directives!)
KdP O4AAP
adsorption eq. constant (SW AdsP = 1)
KadsP _20
molar adsorption equil. const. (SW AdsP =
2; see directives!)
RCAdP O4AAP sorption reaction rate (SW V nAdsP = 1)
RcAdsP gem
sorption reaction rate (SW V nAdsP = 0)
T CKadsP
temperature coefficient for adsorption

-

OH
pH

–

pH

hydroxyl concentration
acidity

mol l−1
-

Rsorp

–

sorption rate

g m−3 d−1

Kpads
Kads20
ksorp
„

ktads

m3 gP−1
(mol l−1 )a−1
d−1
d−1
-

b

SW AdsP SW AdsP
SW V nAdsP

switch for selection of the formulation options
switch for selection of the original (= 0.0) or the
advanced (= 1.0) formulations

-

T

T emp

temperature

◦

φ

P OROS

porosity

m3 m−3

C

w

b

∆t

Deltares

Delt

computational time-step

d

69 of 464

Processes Library Description, Technical Reference Manual

Equilibrium concentration of AAP as function of phosphate
TSS = 50 g/m3, partition coefficient = 0.1 m3/gDM
(gP/m3)
0.6
0.5
0.4
0.3

capacity = 0.001
capacity = 0.005
capacity = 0.01

0.1

0

0.2

0.4
0.6
Phosphate concentration (gP/m3)

0.8

1

DR
AF

0

T

0.2

Figure 3.3: Variation of the equilibrium concentration AAP (eqAAP) as a function of PO4
and the maximum adsorption capacity (MaxPO4AAP).

Equilibrium concentration of AAP as function of phosphate
TSS = 50 g/m3, capacity = 0.005 gP/m3

(gP/m3)
0.6
0.5
0.4
0.3
0.2

partition coefficient = 0.02
partition coefficient = 0.1
partition coefficient = 1.0

0.1
0

0

0.2

0.4
0.6
Phosphate concentration (gP/m3)

0.8

1

Figure 3.4: Variation of the equilibrium concentration of AAP (eqAAP) as a function of
PO4 and the partition coefficient of PO4 (KdPO4AAP).

70 of 464

Deltares

Nutrients

Formation of vivianite
PROCESS :

VIVIANITE

At reducing conditions phosphate may precipitate with iron(II) as vivianite (iron(II) phosphate:
Fe3 [PO4 ]2 ). Vivianite is thermodynamically unstable at oxidising conditions. At the presence
of dissolved oxygen iron(II) in vivianite is oxidised into iron(III), resulting in the subsequent dissolution of vivianite, the precipitation of iron(III)oxyhydroxides and the adsorption of phosphate
to these minerals.

T

The precipitation of vivianite only occurs in a supersaturated solution at the absence of dissolved oxygen, and actually when also nitrate has depleted. These conditions usually only
occur in the reducing sediment, just below an oxidising top layer. Precipitation is not only
temperature dependent, but also pH dependent due to the acid-base equilibria to which both
dissolved phosphate and iron are subjected. However, in a simplified approach the pH dependency may be ignored, since the pH is rather constant in the sediment.
Vivianite is transported to the oxidising top layer mainly by bioturbation. Oxidative dissolution
of vivianite follows, a process the kinetics of which are not straight forward. The oxidation with
dissolved oxygen seems to be a temperature dependent surface reaction mainly, due to the
low solubility and slow dissolution of the mineral. The pH-dependency of the surface reaction
seems to be rather weak and is therefore ignored.

DR
AF

3.5

Literature regarding sediment diagenesis as well as modelling exploits have provided indications for the formation of other stable phosphate minerals, hardly sensitive to the redox
conditions. Such stable minerals most probably are apatite like calcium phosphate minerals.
Another explanation for slow remobilisation of phosphate might be found in rather permanent
inclusion of phosphate in various oxyhydroxides.
Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

Process VIVIANITE has been implemented in a generic way, meaning that it can be applied
both to water layers and sediment layers. The precipitation of phosphate in the sediment is not
considered, when phosphate in the sediment is modeled as a number of ‘inactive’ substances.
The process has been implemented for the following substances:

 dissolved PO4 and VIVP.

Table 3.6 provides the definitions of the parameters occurring in the formulations. The dissolved oxygen concentration (Cox) can be either calculated by DELWAQ or imposed to DELWAQ via the input.

Deltares

71 of 464

Processes Library Description, Technical Reference Manual

Formulation
The precipitation and dissolution equilibrium of vivianite can be described with the following
simplified reaction equation:

3 Fe2+ + 2 PO3−
4 ⇔ Fe3 (PO4 )2
The precipitation rate is formulated with first-order kinetics, with the difference between the actual dissolved phosphate concentration and the equilibrium dissolved concentration as driving
force (Smits and Van Beek (2013)):

Rprc =

f rp × kprc × ( Cphd
− Cphde) × φ
φ
0.0
if Rprc < 0.0

kprc = kprc20 × ktprc(T −20)


with:

1.0
if Cox < Coxc × φ
f rp = 0.0 if Cox ≥ Coxc × φ

DR
AF

f rp =

T



Cox
Coxc
Cphd
Cphde
f rp
kprc
ktprc
Rprc
T
φ

dissolved oxygen concentration [g m−3 ]
b

critical dissolved oxygen concentration [g m−3 ]
dissolved phosphate concentration [gP m−3 ]
w

b

equilibrium dissolved phosphate concentration [gP m−3 ]
switch concerning the redox conditions for precipitation [-]
precipitation reaction rate [d−1 ]
temperature coefficient for precipitation [-]
rate of precipitation [g m−3 d−1 ]
w

temperature [◦ C]
porosity [-]

b

The dissolution of vivianite is probably characterised by two steps: a) the oxidation of dissolved Fe2+ , and b) the dissolution of vivianite at a very low Fe2+ concentration. The first
depends on the dissolved oxygen concentration, the latter on the quantity of vivianite present.
(However, the main driving force of the dissolution process might be the difference of the
“equilibrium” Fe2+ concentration near the vivianite crystals and the average very low dissolved Fe2+ concentration.) The dissolution rate can be formulated pragmatically as follows:


f rd × ksol × Cphpr ×
Rsol =
0.0

Cox
φ

if Rsol < 0.0

ksol = ksol20 × ktsol(T −20)

f rp =

1.0
if Cox < Coxc × φ
f rp = 0.0 if Cox ≥ Coxc × φ

with:

Cphpr
f rd
ksol
72 of 464

precipitated phosphate concentration [gP m−3 ]
b

switch concerning the redox conditions for dissolution [-]
−1
dissolution reaction rate [m3 gO−1
2 d ]
w

Deltares

Nutrients

ktsol
Rsol

temperature coefficient for dissolution [-]
rate of dissolution [g m−3 d−1 ]
b

The dissolution process must stop at the depletion of vivianite. Therefore, the dissolution flux
is made equal to half the concentration of vivianite V IV P divided with timestep ∆t, when
the flux as calculated with the above formulation is larger than V IV P/∆t.

w

DR
AF

T

Directives for use
 The formation of stable mineral “apatite” can also be included in the model. As an alternative, the user may ignore this substance and provide a (very) slow dissolution rate in the
input for process VIVIANITE.
 The equilibrium dissolved phosphate concentration follows from the solubility product of
vivianite, the dissolved Fe(II) concentration and the pH. Solubility products determined
in the laboratory tend to underestimate the equilibrium concentration, since the mineral
in natural sediment has lower stability due to the formation of amorphous, impure and
coated vivianite. For similar reasons the actual reaction rates of precipitation and dissolution may deviate substantially from experimentally determined values. The following
values are representative for fresh water sediments: EqV IV DisP = 0.05 gP m−3 ,
−1
RcP recP 20 = 0.8 d−1 , RcDissP 20 = 0.005 m3 gO−1
2 d .
 When DO is not simulated, OXY must be imposed as the actual concentration times
porosity for option 2 (SW AdsP = 2). This is necessary, because the formulations are
based on simulated DO, which is calculated internally as bulk concentration. The critical
concentration CrOXY , however, is to be imposed as the actual concentration in (pore)
water. CrOXY is also used for the adsorption process ADSPO4AAP.
 When simulating the “inactive” substances in the sediment AAP S1 and AAP S2, the
precipitation process only affects P O4 and V IV P in the water column. V IV P settles
and ends up in AAP S1 and AAP S2.
Additional references

Santschi et al. (1990), Smits and Van der Molen (1993), Stumm and Morgan (1996), WL |
Delft Hydraulics (1997c)

Deltares

73 of 464

Processes Library Description, Technical Reference Manual

Table 3.6: Definitions of the parameters in the above equations for VIVIANITE. Volume
units refer to bulk ( ) or to water ( ).
w

T

b

Name in input

Definition

Cox
Coxc
Cphd
Cphde
Cphpr
f rd

OXY
Cc_oxP sor
P O4
EqV IV DisP
V IV P

dissolved oxygen concentration

g m−3

critical DO concentration for iron reduction
dissolved phosphate concentration

g m−3
gP m−3

equilibrium dissolved phosphate concentration
precipitated vivianite phosphate concentration

gP m−3
gP m−3

–

-

f rp

–

switch concerning redox conditions for dissolution
switch concerning redox conditions for precipitation

RcP recP 20
T cP recipP
RcDissP 20
T cDissolP

vivianite precipitation reaction rate
temperature coefficient for precipitation
vivianite dissolution reaction rate
temperature coefficient for dissolution

d−1
−1
m3 gO−1
2 d
-

–

vivianite precipitation rate

g m−3 d−1

–

vivianite dissolution rate

g m−3 d−1

T emp

temperature

◦

Delt

timestep

d

P OROS

porosity

m3 m−3

kprc20
ktprc
ksol20
ktsol
Rprc
Rsol
T
∆t
φ

DR
AF

Name in
formulas

74 of 464

Units

b

w

b

w

b

-

w

b

b

C

w

b

Deltares

Nutrients

Formation of apatite
PROCESS :

APATITE

T

Phosphate may precipitate in various minerals that are stable under both oxidizing and reducing conditions. In literature regarding sediment diagenesis and sediment modelling, indications can be found for the formation of such stable minerals. As contrasting with vivianite that
is only stable under reducing conditions, the identity of these stable minerals has not been
determined unequivocally. The formation of pure calcium apatite in sediment may not be
very likely due to the high pH required (calcium phosphate: Ca3[PO4]2); stable at pH>8.5).
However, the co-precipitation of phosphate with several carbonates and sulfides and even the
rather permanent inclusion of phosphate in various oxyhydroxides seem certainly possible,
also at a pH of 7. Such a co-precipitation might be induced by the adsorption of phosphate
on the surface of calcite-like minerals. For pragmatic reasons the stable phosphate minerals
are named “apatite” in this documentation.
The precipitation of “apatite” only occurs in a supersaturated solution. Apatite is primarily
formed in deeper sediment layers. It is exchanged among the sediment layers by means
of bioturbation. Since supersaturation may not occur near the sediment-water interface, the
apatite formed in deeper layers may dissolve slowly in the top sediment layer. The actual
rate of the dissolution will be highly dependent on the dissolution of co-precipitated calcite-like
minerals. Usually, these minerals do not dissolve significantly. Dissolution may then proceed
very slowly by means of solid matter and surface diffusion of phosphate ions.

DR
AF

3.6

Precipitation is not only temperature dependent, but also pH dependent due to the acid-base
equilibria to which both dissolved phosphate and calcite-like minerals are subjected. However,
in a simplified approach the pH dependency may be ignored, since the pH is rather constant
in the sediment.
Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

Process APATITE has been implemented in a generic way, meaning that it can be applied
both to water layers and sediment layers. The precipitation of phosphate in the sediment
is not considered, when phosphate in the sediment is modeled as a number of ‘inactive’
substances.
The process has been implemented for the following substances:

 dissolved PO4 and APATP.

Table 3.7 provides the definitions of the parameters occurring in the formulations.
Formulation
Even when co-precipitating with calcite, the precipitation and dissolution equilibrium of apatite
can be described with the following simplified reaction equation:

3 Ca2+ + 2 PO3−
4

⇔

Ca3 (PO4 )2

The calcium concentration is usually very constant in sediment pore water. Therefore, the
precipitation rate is formulated with first-order kinetics, with the difference between the actual dissolved phosphate concentration and the equilibrium dissolved concentration as driving

Deltares

75 of 464

Processes Library Description, Technical Reference Manual

force. In order to allow better control over the precipitation of apatite relative to the precipitation of vivianite the precipitation rate is formulated as follows (Smits and Van Beek (2013)):


Rprc = f rr × kprc ×
Rprc = 0.0


Cphd
− Cphde × φ
φ

if Rprc < 0.0

kprc = kprc × ktprc(T −20)
20

with:
dissolved phosphate concentration [gP m−3 ]
b

equilibrium dissolved phosphate concentration [gP m−3 ]
ratio of the apatite and vivianite precipitation reaction rates [-]
precipitation reaction rate [d−1 ]
temperature coefficient for precipitation [-]
rate of precipitation [g m−3 d−1 ]
temperature [◦ C]
porosity [-]

T

w

b

DR
AF

Cphd
Cphde
f rr
kprc
ktprc
Rprc
T
φ

The dissolution of apatite is driven by undersaturation in the pore water. The rate is dependent
on the extent of undersaturation as well as the concentration of apatite. The dissolution rate
is formulated pragmatically according to second-order kinetics as follows:



Cphd
Rsol = ksol × Cphpr × Cphde −
φ
Rsol = 0.0
if Rsol < 0.0
20
ksol = ksol × ktsol(T −20)
with:

Cphpr
ksol
ktsol
Rsol

precipitated phosphate concentration [gP m−3 ]
dissolution reaction rate [m3 gP−1 d−1 ]
temperature coefficient for dissolution [-]
rate of dissolution [g m−3 d−1 ]

b

w

b

The dissolution process must stop at the depletion of apatite. Therefore, the dissolution flux
is made equal to half the concentration of apatite AP AT P divided with timestep ∆t, when
the flux as calculated with the above formulation is larger than AP AT P/∆t.
Directives for use
 The formation of vivianite should be included in the model too.
 The equilibrium dissolved phosphate concentration would follow from the solubility product of the mineral formed. Solubility products determined in the laboratory tend to underestimate the equilibrium concentration, since the mineral in natural sediment has lower
stability due to the formation of amorphous, impure, co-precipitated and coated apatite.
For similar reasons the actual reaction rates of precipitation and dissolution may deviate
substantially from experimentally determined values. Since the identity of the phosphate
mineral is poorly known, the equilibrium concentration and the reaction rates are typically
calibration parameters. However, a good starting point can be found in equalising the
equilibrium concentrations and the precipitation rates for vivianite and apatite, implying
that RatAP andV P = 1.0. For a start the dissolution rate may be set at zero.

76 of 464

Deltares

Nutrients

 When simulating the “inactive” substances in the sediment AAP S1 and AAP S2, the
precipitation process only affects P O4 and APATP in the water column. AP AT P settles
and ends up in AAP S1 and AAP S2.
Additional references
Santschi et al. (1990), Stumm and Morgan (1996), WL | Delft Hydraulics (1994b)
Table 3.7: Definitions of the parameters in the above equations for APATITE. Volume units
refer to bulk ( ) or to water ( ).
b

w

Name in
input

Cphd
Cphde

P O4
dissolved phosphate concentration
EqAP AT DisP equilibrium dissolved phosphate con-

Cphpr

centration
precipitated “apatite” phosphate concentration

Units

DR
AF

f rr

AP AT P

Definition

gP m−3

T

Name in
formulas

RatAP andV P ratio of the apatite and vivianite precipi-

b

gP m−3
w

gP m−3
b

-

kprc20
ktprc
ksol20
ktsol

RcP recP 20
T cP recipP
RcDisAP 20
T cDissolP

tation rates
vivianite precipitation reaction rate
temperature coefficient for precipitation
apatite dissolution reaction rate
temperature coefficient for dissolution

Rprc
Rsol

–

apatite precipitation rate

g m−3 d−1

–

apatite dissolution rate

g m−3 d−1

T
∆t
φ

Deltares

d1
m3 gP−1 d−1
w

b

b

T emp

temperature

◦

Delt

timestep

d

P OROS

porosity

m3 .m−3

C

w

b

77 of 464

Processes Library Description, Technical Reference Manual

Dissolution of opal silicate
PROCESS :

DISSI

Opal silicate is produced by diatoms, that strengthen their cell walls with silicate skeletons.
When diatom cells have died, the skeleton remains start to dissolve and settle on the sediment. The physical-chemical dissolution process continues in the sediment, since pore water
is generally undersaturated with respect to opal silicate. However, the process is retarded
strongly due to the adsorption of various substances such as metal ions (Fe, Al, Mn) onto
the silicate frustules and due to coating of these frustules with iron and manganese minerals.
Consequently, opal silicate is rather abundantly present in most sediments.

T

Dissolved silicate may adsorb onto iron and aluminium oxyhydroxides and silicates, and may
also precipitate in extremely stable silicate minerals. However, adsorption is rather weak and
reversible. Precipitation proceeds extremely slow. Both types of processes are rather poorly
understood, and have been ignored in the model for all these reasons.
Volume units refer to bulk ( ) or to water ( ).
b

w

DR
AF

3.7

Implementation

Process DISSI has been implemented in a generic way, meaning that it can be applied both
to water layers and sediment layers. When silicate in the sediment is modeled as a number
of ‘inactive’ substances DET SiS1/2 and OOSiS1/2, the dissolution of opal silicate in the
sediment is formulated as simple first-order decomposition processes BMS1/2_(i) linked up
with the decomposition of detritus.
The process has been implemented for the following substances:

 dissolved Si and Opal.

Table 3.8 provides the definitions of the parameters occurring in the formulations.
Formulation

The dissolution of opal silicate is formulated according to second-order (e.g. double first-order)
or first-order kinetics. In the case of second-order kinetics the concentration of opal silicate
and the difference between the actual dissolved silicate concentration and the equilibrium
dissolved concentration determine the dissolution rate.
For option SW DisSi = 0.0 the dissolution rate is formulated according to second order
kinetics (Smits and Van Beek (2013)):

Rsol = ksol × Csip × (Cside −

Csid
)
φ

where:

Csid
Cside
Csip
ksol
φ
78 of 464

dissolved silicate concentration [gSi m−3 ]
b

equilibrium dissolved silicate concentration [gSi m−3 ]
opal silicate concentration [gSi m−3 ]
w

b

dissolution reaction rate [m3 gSi−1 d−1 ]
porosity [-]
w

Deltares

Nutrients

For option SW DisSi = 1.0 the dissolution rate is formulated according to first order kinetics:

Rsol = ksol × Csip
where:

ksol

dissolution reaction rate [d−1 ]

In both cases the rate is dependent on temperature:

ksol = ksol20 × ktsol(T −20)
where:
dissolution reaction rate [m3 gSi−1 d−1 or d−1 ]
temperature coefficient for dissolution [-]
temperature [◦ C]
w

T

ksol
ktsol
T

DR
AF

Directives for use
 The type of kinetics to be applied is selected with option parameter SW Dissi (=0.0 for
second order kinetics, =1.0 for first order kinetics).
 The equilibrium dissolved silicate concentration follows from the solubility product of opal
silicate and the pH. Solubility products determined in the laboratory tend to overestimate
the equilibrium concentration, since the mineral in natural sediment has higher stability
due to the formation of impuraties and coatings. For similar reasons the actual reaction
rates of dissolution may deviate substantially from experimentally determined values. The
following values are representative for fresh water sediments: EqDisSi = 10 gSi m−3 ,
RcDisSi20 = 0.09 d−1 .
 When simulating “inactive” substances in the sediment, the dissolution process only affects Si and Opal in the water column. Opal settles and ends up in DET SiS1 (and
DET SiS2), subjected to first-order decomposition.
w

Additional references

Berner (1974), DiToro (2001), Schink and Guinasso (1978), Smits and Van der Molen (1993),
Stumm and Morgan (1996), Vanderborght et al. (1977), WL | Delft Hydraulics (1997c)

Deltares

79 of 464

T

Processes Library Description, Technical Reference Manual

Table 3.8: Definitions of the parameters in the above equations for DISSI. Volume units
refer to bulk ( ) or to water ( ).
b

w

Name in input

Definition

Csid
Cside
Csip

Si
Ceq _DisSi
Opal

dissolved silicate concentration

gSi m−3

equilibrium dissolved silicate concentration
opal silicate concentration

gSi m−3
gSi m−3

T cDisSi

second order dissolution reaction rate, or first
order dissolution rate
temperature coefficient for dissolution

m gSi−1 d−1
d−1
-

-

dissolution rate

g m−3 d−1

ksol

20

ktsol
Rsol

DR
AF

Name in
formulas

RcDisSi20

Units

b

w

b

3

w

b

SW Dissi SW Dissi

option (=0.0 for second order, =1.0 for first order)

-

T

T emp

temperature

◦

P OROS

porosity

m3 m−3

φ

80 of 464

C

w

b

Deltares

4 Primary producers
Contents
Introduction to primary production . . . . . . . . . . . . . . . . . . . . . .

82

4.2

Growth and mortality of algae (BLOOM) . . . . . . . . . . . . . . . . . . . 83

4.3

Bottom fixation of BLOOM algae types . . . . . . . . . . . . . . . . . . . . 102

4.4

Settling of phytoplankton . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.5

Production and mortality of algae (DYNAMO) . . . . . . . . . . . . . . . . 107

4.6

Computation of the phytoplankton composition (DYNAMO) . . . . . . . . . 116

4.7

Production and mortality of benthic diatoms S1/2 (DYNAMO) . . . . . . . . 119

4.8

Mortality and re-growth of terrestrial vegetation (VEGMOD) . . . . . . . . . 125

DR
AF

T

4.1

Deltares

81 of 464

Processes Library Description, Technical Reference Manual

Introduction to primary production
Within the processes library there are two distinct approaches to model primary production,
that is, the growth and decay of phytoplankton. The first approach, called BLOOM, allows the
user to model several groups of algae and types within these groups. While it is a very flexible
method, it requires some understanding of the physiology of algae and the ecosystem that is
being modelled. The second approach, called DYNAMO, is limited to two algal groups, "green
algae" and "diatoms". As it is simpler, it may be easier to use (less coefficients with which to
describe the properties of the algae, for instance). This simplicity also has a disadvantage, as
the results will in general be less good than with a properly set up model using the BLOOM
approach.

T

The two approaches are mutually exclusive: either use BLOOM or use DYNAMO, not both.
This also holds, to a certain degree, to the input parameters. The parameters specific to
algae have different names for the two approaches, but the environmental conditions, such as
nutrient concentrations and irradiation, are described by the same parameters. For irradiation
this requires some attention:

 The irradiation at the surface is always given as the total irradiation (correction for the

DR
AF





photoactive fraction is done internally) in [W.m−2 ].
 As BLOOM is based on the concept of optimising the biomass, its time step is typically
24 hours, you can use 12 and 6 hour time steps as well. The time step should be long
enough to make sure that an equilibrium can be achieved. This has three consequences:



4.1

The irradiance for BLOOM has to be given as a daily average, not as hourly or even
more frequent values.
BLOOM is usually called only once every few time steps of D-Water Quality itself. This
is arranged via the parameter TimMultBl.
As the algae in BLOOM "see" an average amount of irradiation as they are transported
over the vertical by mixing processes, the light intensity at the current location is not
entirely representative for calculating the growth within the allotted time step. To account for this a special process is used, VTRANS. This has a parameter PeriodVTRA
which controls the details. For most if not all situations, this parameter should be set
to 24 hours.

 In contrast, the DYNAMO approach can handle irradiation time series at arbitrarily short
intervals.

82 of 464

Deltares

Primary producers

Growth and mortality of algae (BLOOM)
PROCESS :

BLOOM, BLOOM_P, U LVAFIX , U LVAFIX _P, P HY _B LO, P HY _B LO _P, D EPAVE ,
V TRANS , DAY L ENGTH

Algae are subject to gross primary production, respiration, excretion, mortality, grazing, resuspension and settling. Net growth (biomass increase) is the result. Net primary production
is defined as the gross primary production minus respiration. The phytoplankton module
BLOOM includes specific formulations for these processes with the exception of excretion,
grazing, resuspension and settling. Excretion is ignored. Grazing, resuspension and settling are similar for other phytoplankton modules in DELWAQ, and are therefore dealt with in
separate process descriptions.

T

BLOOM considers different algae species groups. These groups may be defined as diatoms,
green algae, bluegreen algae, flagellates, dinoflagellates, Phaeocystis, Ulva, etc. Diatoms
differ from other species among other things by their dependency on dissolved silicon for
growth. However, each group may be defined as being any other individual species. Each
algae species (group) has several types, that are adapted to specific environments to cope
with limiting resources. The types have different properties with respect to nutrient stoichiometry, chlorophyll content and process rates. Depending on which growth factor is currently
limiting, the best adapted type of each group is selected. The relevant factors are nitrogen,
phosphorus, silicon, carbon and energy (light), meaning that biomass stoichiometry depends
on the availability of these factors. This mechanism enables BLOOM to describe phenotypical
adaptation of algae under different growth conditions. BLOOM can simulate 30 algae species
types (10 species × 3 types) at maximum. The default parameter values for several phytoplankton groups and types that have been modelled before can be read from a database with
Delft3D.

DR
AF

4.2

BLOOM uses the technique of linear programming to calculate the optimum distribution of
biomass over all algae types. The competition between the species is determined by the ratio
of the resource requirement and the nett growth rate. Mathematically this is equivalent to
maximizing the net growth rate of the total of all types. For a description of the use of this
technique in bloom the user is referred to Los (2009); DBS (1991); BLOOM UM (1985). The
solution of the optimisation is bound by several constraints: the available nutrient resources,
the available amount of energy, the maximum growth rate and the maximum mortality rate.
BLOOM allows to account for mixotrophy and nitrogen fixation, by modification of the nutrient
constraints. The amount of available nutrients for mixotrophic algae comprises both inorganic
and organic nutrients. Nitrogen fixing algae are able to convert elementary nitrogen (dissolved
N2 ) into organic nitrogen.
The energy constraint concerns the energy obtained from ambient light intensity. It is expressed as the maximal extinction by phytoplankton where the light intensity is reduced due
to self-shading, to a level where the growth rate equals the respiration rate. The relation between the growth rate and light intensity is determined by the light response curve. The light
response curve is defined by the user as a table of growth efficiencies at different light intensities. It can be read from a database with Delft3D for the species that have been modelled
and calibrated before with BLOOM. The light response curve can be derived from laboratory
experiments. Light inhibition has not been included yet in the existing light response curves.
The processes growth, respiration and mortality are part of the constraints used in the optimisation technique. The process rates are corrected for temperature dependency before being
used in the optimisation. Mortality is also corrected for salinity stress.

Deltares

83 of 464

Processes Library Description, Technical Reference Manual

DELWAQ determines the concentrations of substances from the transport and the process
rates. Therefore the BLOOM process should calculate process rates for DELWAQ instead of
an optimum species composition. These rates are therefore calculated from the change of
biomass divided by the time step.
BLOOM has its own time step within the computational procedure of DELWAQ. Usually,
BLOOM’s time step is bigger than DELWAQ’s time step used for the modelling of mass transport and the other water quality processes. A bigger time step reduces the computation time
needed for a simulation. Using a bigger time step requires that the average water depth over
BLOOM’s time step is determined in view of light limitation. Therefore the process DEPAVE
should be activated, calculating the average water depth during each BLOOM time step. This
is particularly relevant for cases where the water depth varies significantly during a BLOOM
time step such as tidal simulations.

T

A macro algae species like U lva or other macrophyte species can be included in BLOOM.
This species may both be suspended in the water column and attached to the sediment. The
process of resuspension of U lva is simulated with the process UlvaFix.

DR
AF

The algae processes affect a number of other DELWAQ substances apart from the algae
biomass concentrations [gC m−3 ]. Growth involves the uptake of inorganic nutrients [gN/P/Si/S/C
m−3 ] and the production of dissolved oxygen [gO2 m−3 ], and affects alkalinity (pH). Preferential uptake of ammonium over nitrate is included in the model. Mortality produces detritus
[gC/N/P m−3 ] and opal silicate [gSi m−3 ]. The process rates for these substances are derived
from the algae process rates by multiplication with the appropriate stoichiometric constants.
These ratios reflect the chemical composition of the biomass of algae types.
All rates in BLOOM are daily averaged. The dissolved oxygen concentration is calculated
on a daily average basis unless process VAROXY is included in the model. This process
deduces the daily varying dissolved oxygen production rate from the daily average net primary
production rate. The process VAROXY is described elsewhere in this manual.
Implementation

The algae module BLOOM can simulate maximally 30 algae species types. BLOOM has been
implemented for the following substances:

 BLOOMALG01 – BLOOMALG30,
 POC1, PON1, POP1, POS1, POC2, PON2, POP2, POS2, Opal,
 NH4, NO3, PO4, Si, SO4 SUD, OXY, TIC and ALKA.

The module BLOOM is generic and can be applied for water as well sediment layers, although
the algae in sediment layers have no primary production and are subject to mortality. It can
also be used in combination with the sediment option S1/S2.
Process BLOOM (plus BLOOM_P) has auxiliary processes UlVAFIX (plus ULVAFIX_P), PHY_BLO
(plus PHY_BLO_P), DEPAVE, VTRANS and DAYLENGTH. ULVAFIX adds specific parameters for the ”inactive” algae species Ulva. PHY_BLO generates additional output for BLOOM,
the overall organic carbon (PHYT), dry matter (ALGDM) and nutrients concentrations (ALGN,
ALGP, ALGSi) and the chlorophyll-a concentration (Chlfa). DEPAVE determines the average
water depth that algae experience during a time step, which is relevant for tidal water systems.
VTRANS produces ”tracers” that allow for the determination of average light intensity for algae
as resulting from vertical mixing.
Table 4.1 and Table 4.2 provide the definitions of the parameters occurring in the user-

84 of 464

Deltares

Primary producers

defined input and output. BLOOM requires an additional input file  containing tabulated data describing the relation between the daily averaged light intensity in the
water column and the production efficiency for the species groups in the model. This file
can be automatically generated with the PLCT. For simulations with BLOOM also the files:
 and  need to be available in the work directory.
Formulation

1
2
3
4

the nutrient constraints;
the energy constraints;
the growth constraints; and
the mortality constraints.

T

In the first four sections formulations are presented for the constraints for growth as included in
the optimisation technique (linear programming). This technique delivers the algae biomasses
of all species groups and types at the end of a time step by means of solving a set of linear
equations and constraints, thereby maximising the total net growth. The constraints are:

DR
AF

The rates of growth, production, respiration and mortality are derived from the change of the
algae biomasses over a time step. The following sections deal with the formulations for these
rates and constraints, and specific additional output. The final sections describe the process
of resuspension of Ulva (or other macrophytes) called Ulvafix, and the process DEPAVE, that
calculates the averaged depth during a BLOOM time step.
Nutrient constraints

The solution of the linear programming method for the calculation of biomasses of autotrophic
algae should satisfy the following set of nutrient balances:

Ctnutk = Cnutk +

n
X

(anutk,i × Calgi ) − Cnutck

i=1

with:

anutk,i

Calgi
Cnutk
Cnutck
Ctnutk
i
k
n

stoichiometric constant of nutrient k originating from dissolved inorganic nutrient over organic carbon in algae biomass [gN/P/Si gC−1 ], an, aph or asi
algae biomass concentration [gC m−3 ]
concentration of dissolved inorganic nutrient k [gN/P/Si m−3 ]
threshold concentration of dissolved inorganic nutrient k [gN/P/Si m−3 ]
concentration of total available nutrient k [gN/P/Si m−3 ]
index for algae species type [-]
index for nutrients, 1 = nitrogen, 2 = phosphorus, 3 = silicon, 4 = carbon [-]
number of algae species types, equal to 15 [-]

Additional requirements are that Calgi ≥ 0.0 and Cnutk ≥ 0.0. The total available nutrient
concentration includes the total dissolved inorganic nutrients and nutrients in phytoplankton.
The dissolved nitrogen concentration is the sum of the concentrations of ammonium and
nitrate. The threshold concentration is the dissolved nutrient concentration below which algae
are no longer able to withdraw this nutrient from the ambient water. The threshold is ignored
for total dissolved inorganic carbon (TIC).
Some algae (especially dinoflagellates) are able to use detritus as an additional food source,
when resources of dissolved nutrients are low. For these so-called mixotrophic algae the
nutrient constraints are modified in a way that more nutrients are available to these algae.

Deltares

85 of 464

Processes Library Description, Technical Reference Manual

Extra constraints are added for the nutrients detritus nitrogen and detritus phosphorus. The
dissolved nutrient constraints are modified as follows:
n
X

Cdet2k = Cdet1k +

(adk,i × Calgi )

i=1

Ctnutk = Cnutk +

n
X

((anutk,i − adk,i ) × Calgi ) − Cnutck

i=1

with:

Cdet1k
Cdet2k
k

stoichiometric constant of a nutrient originating from detritus over org. carbon in
algae biomass [gN/P gC−1 ], adn, adph or adsi
concentration of a detritus nutrient at t1 , the beginning of a time step [gN/P
mS−3 ]
concentration of a detritus nutrient at t2 , the end of a time step [gN/P m−3 ]
index for nutrients, 1 = nitrogen, 2 = phosphorus [-]

T

adk,i

DR
AF

Note that these formulations are equivalent to the formulations for autotrophic algae when the
stochiometric constants adk,i obtain the value zero.
Some other algae are able to use elementary nitrogen (N2 ) dissolved in the water as a nutrient
source. This is established in the constraint in a similar way. Extra nutrient constraints are
added to describe the uptake of N2 by nitrogen fixative algae:

Cen2 = Cen1 +

n
X

(aeni × Calgi )

i=1

Ctnut1 = Cnut1 +

n
X

((anut1,i − aeni ) × Calgi ) − Cnutc1

i=1

with:

aeni
Cen1
Cen2

stoichiometric constant of nitrogen orig. from el. nitrogen in algae biomass
[gN gC−1 ]
concentration of elementary nitrogen at t1 , the beginning of a time step [gN m−3 ]
concentration of elementary nitrogen at t2 , the end of a time step [gN m−3 ]

The concentration of dissolved elementary nitrogen is assumed never to be limiting, so both
concentrations are infinite. Notice that these formulations reduce to the formulations for autotrophic algae when the stoichiometric constants aeni obtain the value zero.
The limitation of phytoplankton by total dissolved inorganic carbon is only included in BLOOM’s
optimisation algorithm, when option parameter SwTICdummy has a value 10.0 or higher
(default value = 0.0). Alternatively, carbon limitation can be taken into account for BLOOM
in a simplified way by scaling of the overall growth rates with a simple limitation factor. This
factor, a multiplier on the growth rate, increases linear from zero at TIC = 0.0 to 1.0 at TIC =
KCO2. The factor is equal to 1.0 for higher TIC.
Sulfur is not a constraint, because it has been included in BLOOM only in the form of the
sulfur stored in biomass, assuming that sulfate is always amply available. Sulfate is just taken
up proportional to biomass produced and is released from algae biomass on the basis of a
constant species independent stoichiometric ratio set at 0.0175 gS/gC.

86 of 464

Deltares

Primary producers

Energy constraints (light)
Energy in light (solar radiation) becomes limiting through self shading when the total extinction
exceeds the maximum at which growth is just balanced by respiration and mortality. For each
type a specific value of the total extinction coefficient eamaxi exists, at which this is the case.
On the other hand the total extinction coefficient cannot be smaller than a certain extinction
coefficient eamini , which is equal to the background extinction coefficient augmented with
a small contribution by the minimum algae concentation. Hence the extinction coefficient
must satisfy the following condition as an additional constraint for the solution of the linear
programming method for the calculation of biomasses of algae:

eat =

n
X

(eai × Calgi )

eamini ≤ eat ≤ eamaxi
eamini = eatmini − eb
eamaxi = eatmaxi − eb
with:

DR
AF

eb = et − eat

T

i=1

eai
eat
eb
et
eamini

eatmini
eamaxi
eatmaxI

specific extinction coefficient of an algae species type [m2 gC−1 ]
total extinction coefficient of all algae [m−1 ]
extinction by other substances than algae [m−1 ]
total extinction coefficient [m−1 ]
minimum extinction coefficient of algae i connected with background extinction
[m−1 ]
minimum total extinction coefficient connected with background extinction [m−1 ]
maximum extinction coefficient of algae i needed to avoid self shading [m−1 ]
maximum total extinction coefficient needed to avoid self shading of algae i
[m−1 ]

At a certain critical level of self shading the respective algae species is no longer able to have
net growth. The maximally allowed extinction coefficient eatmaxi for algae species type i is
determined as the extinction where the light intensity allows for a gross production rate that
exactly compensates for the mortality and respiration rates. Gross production is formulated
as a potential specific rate multiplied with a light efficiency factor. This factor Ef is a function
of the light intensity, the amount of available light (0.0 ≤ Ef ≤ 1.0) The critical efficiency at
which no net growth or mortality occurs follows from:

Efc i =

krspi + kmrti
kgpi

with:

Ef
Efc i
kgpi
kmrt i
krsp i

light efficiency factor [-]
critical light efficiency factor [-]
specific growth rate [d−1 ]
specific mortality rate [d−1 ]
specific maintenance respiration rate [d−1 ]

Once the critical efficiency factor is known, the pertinent critical light intensity (the total available amount of light) can be obtained from the efficiency versus photosynthic light intensity
table in input file . The maximum extinction coefficient eatmaxi is calculated from this critical light intensity and the light intensity at the top of a water compartment

Deltares

87 of 464

Processes Library Description, Technical Reference Manual

(layer) which must be provided as a daily average intensity. The calculation uses the depth
integrated law of Lambert-Beer, which can be described with the following exact solution:

Iai =

(1 − f r) × f pa × Itop × (1 − exp (−eatmaxi × Ha))
eatmaxi × Ha

Iai = f (Ef ci )
with:

f pa
fr
Ha
Iai
Itop
z

T

fraction of photosinthetically active light in visible light, = 0.45 [-]
fraction of visible light reflected at the water surface [-]
timestep average depth of a water compartment or water layer [m]
critical depth average intensity of photosynthetic light [W m−2 ]
visible light intensity at the top of a water compartment/layer [W m−2 ]
depth [m]

The fraction of visible light reflected at the water surface f r is approximately 0.1 depending
on the time in a year. Both fr and fpa are allocated fixed values in BLOOM.

DR
AF

The maximal extinction coefficient is found via transformation of the integral.

The specific rates of growth, maintenance respiration and mortality are formulated as functions of temperature:

kgpi = kpgi0 × ktpgiT
kgpi = kpgi0 × (T − ktpgi )
kgpi ≥ 0.0

T F P M xAlg(i) = 1.0
for T F P M xAlg(i) = 0.0
for

krspi = krsp0i × ktrspTi

kmrti = kmrt0i × ktmrtTi
kmrti = kmrt0i
kmrti = kmrt0i × (T − 25)
with:

kgp0
ktgp

kmrt0
ktmrt
krsp0
ktrsp
T

for all algae except macro algae (Ulva)
for Ulva when T < 25.0

for Ulva when T ≥ 25.0

growth rate at 0 ◦ C [d−1 ], or per degree centigrade [◦ C−1 d−1 ]
temperature coefficient for growth [-], or temperature at which kgp0 is equal to
zero
specific mortality rate at 0 ◦ C or at temperatures < 25 ◦ C [d−1 ], or per degree
centigrade at temperatures > 25 ◦ C [◦ C−1 d−1 ]
temperature coefficient for mortality [-]
specific maintenance respiration rate at 0 ◦ C [d−1 ]
temperature coefficient for maintenance respiration [-]
water temperature [◦ C]

Growth respiration is not modelled explicitly but is included in the growth rate.
Algal mortality is caused by temperature dependent natural mortality, salinity stress mortality,
and grazing by consumers. The last process is either thought to be part of the overall mortality
rate imposed or modelled explicitly apart from BLOOM. The modelling of grazers is described
elsewhere in this manual. Salinity driven mortality is described with a sigmoidal function of
chlorinity (NIOO/CEMO, 1993)

kmrt0i =

88 of 464

m2i − m1i
+ m1i
1 + exp (b1i × (Ccl − b2i ))
Deltares

T

Primary producers

with:

DR
AF

Figure 4.1: Example of the salinity dependent mortality function. m1 = 0.08 d−1 ; m2 =
0.16 d−1 ; b2 = 11000 (equivalent with 20 ppt salinity) [gCl m−3 ]; b1 = 0.001
and 0.002 m3 gCl−1 .

b1i
b2i
m1i
m2i
Ccl

coefficient 1 of salinity stress function [g−1 .m3 ]
coefficient 2 of salinity stress function [g.m−3 ]
rate coefficient 1 of salinity stress function [d−1 ]
rate coefficient 2 of salinity stress function [d−1 ]
chloride concentration [g m−3 ]

m1 and m2 are the end members of the above function, meaning that the function obtains
the value m1 at high Ccl, and the value m2 for low Ccl. The mortality rate increases with
decreasing chloride concentration, when m2 is larger than m1. This situation which applies
to marine algae is depicted in the example of Figure 4.1. The mortality rate increases with
increasing chloride concentration, when m1 is larger than m2. This situation applies to fresh
water algae.
Growth constraints

The maximum biomass of a species can also be limited by the maximum growth under the
given environmental conditions. The maximum increase of the biomass is determined by:
1 the initial biomass; and
2 the net growth rate.
To simplify the formulation a single growth constraint for all types (i) within each species (j )
is considered by the model. The maximum growth rate of the energy limited type (E-type)
is used as maximum growth rate of the species. Furthermore, since rapidly growing species
have a low mortality rate, the mortality is ignored in the computation of the growth constraint.
The growth constraint for species j applying to all types of this species is computed as:

Calgmaxi = Calg1i × exp ((kgpi × Efi − krspi ) × ∆tb)

Deltares

89 of 464

Processes Library Description, Technical Reference Manual

Calgmaxj =

m
X

Calgmaxi

i=l


Calgmaxj =
m
X

Calgmaxj
0

if Calgmaxj ≥ Calgcj
if Calgmaxj < Calgcj

(Calg2i ) ≤ Calgmaxj

i=l

∆tb = f t × ∆t
with:

Calg1
Calg2
ft
Ef
kgp
krsp
∆t
∆tb
j
i
l
m

timestep [gC m−3 ]
threshold biomass concentration of an algae species at time t1 , the beginning
of a timestep [gC m−3 ]
biomass concentration of algae species j at time t1 [gC m−3 ]
biomass concentration of algae species j at time t2 [gC m−3 ]
ratio of the BLOOM timestep and the DELWAQ timestep ≥ 1.0 [-]
light efficiency factor [-]
potential specific growth rate of the fastest growing type of an algae species
[d−1 ]
specific maintenance respiration rate of the fastest growing type of an algae
species [d−1 ]
time step in DELWAQ [d]
time interval, the time step in BLOOM [d]
index for algae species [-]
index for algae species type [-]
index of the first algae type for species j [-]
index of the last algae type for species j , = l−1+ number of types species j−
1 [-]

DR
AF

Calgc

T

Calgmax maximum concentration of an algae species or type at time t2 , the end of a

For each species a minimum level Calgc is defined in the model. If the actual biomass is
lower, this threshold level is used instead. This enables the growth of a new species when the
conditions become favourable to this species.
The production efficiency factor Ef is determined from the table in the input file “bloominp.frm”
using the actual visible light intensity corrected with fpa and (1 − fr ). The average light
intensity Ia within a water layer is derived from the light intensity at the top of this layer
as calculated according to the above integrated attenuation function of Lamber-Beer using
the actual total extinction coefficient et. Itop is delivered by process CalcRad, described
elsewhere in this manual.
Mortality constraints
As in the case of growth the mortality of each algae species is also constrained within the
model to prevent a complete removal within a single time step. The minimum biomass value
of a species is obtained when there is no production, but only mortality. This minimum biomass
depends on:
1 the initial biomass; and
2 the mortality rate.

90 of 464

Deltares

Primary producers

This minimum value is computed for each individual algae type i, but the model takes the
summation of all types within a species. This way the maximum possible mortality cannot
be exceeded, but transitions between types remain possible. Thus the following equation is
included:

Calgmini = Calg1i × e(−kmrti ×∆tb)
Calgminj =

m
X

(Calgmini )

i=l

m
X

if Calgminj ≥ Calgcj
if Calgminj < Calgcj

(Calg2i ) ≥ Calgminj

i=l

with:

T


Calgminj
Calgminj =
0

Calgmin minimum concentration of an algae species type at time t2 , the end of a time

DR
AF

step [gC m−3 ]
biomass concentration of an algae species type at time t1 [gC m−3 ]
biomass concentration of an algae species type at time t2 [gC m−3 ]
specific mortality rate of an algae species type [d−1 ]

Calg1
Calg2
kmrt

Since mortality is computed according to a negative exponential function, the minimum biomass
level is always positive, in other words a species can never disappear completely. For numerical reasons, however, a base level is included in the model as indicated in relation to the
growth constraints.
Growth, production, mortality and respiration rates

The algae processes lead to the production of algae biomass (C, N, P, Si, S), detritus (C, N,
P, S), opal silicate and dissolved oxygen, and to the consumption of nutrients (N, P, Si, C, S).
In case of mixotrophic algae there is also the consumption of detritus. Nitrogen fixative algae
have an additional nitrogen uptake from elementary nitrogen. DELWAQ requires the rates of
all processes that affect the mass balances in the model, which renders the nitrogen fixation
rates per se superfluous. The rates are deduced from the changes of the algae biomasses
over a time step. The mass balances for algae types are based on the following growth,
respiration and mortality rates:

Calg2i − Calg1i
∆tb
= Rgri × (ani + adni + aeni )
= Rgri × (aphi + adphi )
= Rgri × asii
= Rgri + Rrspi + Rmrti
= Rgpi − Rrspi
(Calg2i + Calg1i )
= krspi ×
2
(Calg2i + Calg1i )
= kmrti ×
2

Rgri =

Rgron,i
Rgrop,i
Rgrosi,i
Rgpi
Rnpi
Rrspi
Rmrti
with:

Deltares

91 of 464

Processes Library Description, Technical Reference Manual

algae biomass concentration at t1 , the beginning of a time step [gC m−3 ]
algae biomass concentration at t2 , the end of a time step [gC m−3 ]
specific respiration rate [d−1 ]
specific mortality rate [d−1 ]
gross primary production rate [gC.m−3 d−1 ]
growth rate for organic carbon [gC.m−3 d−1 ]
growth rate for organic nitrogen [gN m−3 .d−1 ]
growth rate for organic phosphorus [gP m−3 d−1 ]
growth rate for ”organic” silicate [gSi m−3 d−1 ]
mortality rate [gC m−3 d−1 ]
net primary production rate [gC m−3 d−1 ]
respiration rate [gC m−3 d−1 ]
time interval, the time step in BLOOM [d]
index for species group 1-4 [-]

T

Calg1i
Calg2i
krsp
kmrt
Rgp
Rgr
Rgron
Rgrop
Rgrosi
Rmrt
Rnp
Rrsp
∆tb
i

The consumption rate for inorganic carbon is equal to the algae biomass growth rate Rgr .
The consumption and production rates for dissolved oxygen, nutrients and detritus for each
algae species type are derived from the above rates as follows:

ani
ani + adni





DR
AF



Rprdox,i =

× Rnpi + Rauti

× aoxi

Rcnsam,i = Rnpi × ani × f am

Rcnsni,i = Rnpi × ani × (1 − f am)
Rcnsph,i = Rnpi × aphi
Rcnssi,i = Rnpi × asii
Rcnss,i = Rnpi × asi

Rf ixi = Rnpi × aeni

Rcnsoc1,i = Rnpi ×

adni
ani + adni



Rcnson1,i = Rnpi × adni

Rcnsop1,i = Rnpi × adphi
Rauti = f auti × Rmrti

Rautam,i = Rauti × ani

Rautph,i = Rauti × aphi
Rautsi,i = Rauti × asii
Rauts,i = Rauti × asi

Rprdoc1,i = Rmrti × (1 − f auti ) × f deti
Rprdon1,i = Rmrti × ani × (1 − f auti ) × f deti
Rprdop1,i = Rmrti × aphi × (1 − f auti ) × f deti
Rprdosi1,i = Rmrti × asii × (1 − f auti ) × f deti
Rprdos1,i = Rmrti × asi × (1 − f auti ) × f deti
Rprdoc2,i = Rmrti × (1 − f auti ) × (1 − f deti )
Rprdon2,i = Rmrti × ani × (1 − f auti ) × (1 − f deti )
92 of 464

Deltares

Primary producers

Rprdop2,i = Rmrti × aphi × (1 − f auti ) × (1 − f deti )
Rprdosi2,i = Rmrti × asii × (1 − f auti ) × (1 − f deti )
Rprdos2,i = Rmrti × asi × (1 − f auti ) × (1 − f deti )
with:

an
adn
aph
adph

DR
AF

aox
asi
as
f am
f det
f aut
Raut
Rautam
Rautph
Rautsi
Rauts
Rcnsam
Rcnsni
Rcnsph
Rcnssi
Rcnss
Rcnsoc1
Rcnson1
Rcnsoph1
Rf ix
Rprdox
Rprdoc1
Rprdon1
Rprdop1
Rprdosi1
Rprdos1
Rprdoc2
Rprdon2
Rprdop2

stoichiometric constant of nitrogen originating from elementary nitrogen in algae
biomass [gN gC−1 ]
stoichiometric constant for ammonium/nitrate over carbon in algae biomass [gN
gC−1 ]
stoichiometric constant for detritus nitrogen over carbon in algae biomass [gN
gC−1 ]
stoichiometric constant for phosphate over carbon in algae biomass [gP gC−1 ]
stoichiometric constant for detritus phosphorus over carbon in algae biomass
[gP gC−1 ]
stoichiometric constant for oxygen over carbon in algae biomass [gO2 gC−1 ]
stoichiometric constant for silicon over carbon in algae biomass [gSi gC−1 ]
stoichiometric constant for sulfur over carbon in algae biomass [gS.gC−1 ]
fraction of ammonium in the consumed nitrogen nutrients [-]
fraction of dead algae biomass allocated to fast decomposing detritus [-]
fraction of dead algae biomass autolysed [-]
autolysis rate for dead algae biomass (organic carbon) [gC m−3 d−1 ]
autolysis rate for ammonium [gN m−3 d−1 ]
autolysis rate for phosphate [gP m−3 d−1 ]
autolysis rate for silicate [gSi m−3 d−1 ]
autolysis rate for sulfide [gS m−3 d−1 ]
consumption rate for ammonium [gN m−3 d−1 ]
consumption rate for nitrate [gN m−3 d−1 ]
consumption rate for phosphate [gP m−3 d−1 ]
consumption rate for silicate [gSi m−3 d−1 ]
consumption rate for sulfate [gS m−3 d−1 ]
consumption rate for detritus carbon [gC m−3 d−1 ]
consumption rate for detritus nitrogen [gN m−3 d−1 ]
consumption rate for detritus phosphorus [gP m−3 d−1 ]
nitrogen fixation (consumption) rate [gN m−3 d−1 ]
net production rate for dissolved oxygen [gO2 m−3 d−1 ]
production rate for fast decomposing detritus carbon POC1 [gC m−3 d−1 ]
production rate for fast decomposing detritus nitrogen PON1 [gN m−3 d−1 ]
production rate for fast decomposing detritus phosphorus POP1 [gP m−3 d−1 ]
production rate for particulate soluble silicate OPAL [gSi m−3 d−1 ]
production rate for fast decomposing detritus sulfur POS1 [gS m−3 d−1 ]
production rate for slowly decomposing detritus carbon POC2 [gC m−3 d−1 ]
production rate for slowly decomposing detritus nitrogen PON2 [gN m−3 d−1 ]
production rate for slowly decomposing detritus phosphorus POP2 [gP m−3
d−1 ]
production rate for particulate soluble silicate OPAL [gSi m−3 d−1 ]
production rate for slowly decomposing detritus sulfur POS2 [gS m−3 d−1 ]

T

aen

Rprdosi2
Rprdos2

The stoichiometric constants for oxygen and sulfur over carbon aoxi and asi are not input
parameters. In the model for all algae species they are fixed and equal to 2.67 and 0.0175,
respectively.
The overall production and consumption rates required for DELWAQ are derived simply by
adding up the above rates for all algae species types.

Deltares

93 of 464

Processes Library Description, Technical Reference Manual

The fraction of ammonium in nitrogen nutrients consumed f am simply follows from the total
demand for the nitrogen nutrients and the current ammonium and nitrate concentrations. If
the demand is not covered by ammonium alone, the model allocates the additional demand
to nitrate.
Output
BLOOM delivers some additional output parameters, such as the overall concentrations of
algae biomass, indicators for the active limiting factors, and the rates of total net primary
production, respiration and nitrogen fixation. The algae biomass concentrations expressed in
various units are:
n
X

Calgt =

(Calgi )

Cadm =

n
X

(admi × Calgi )

i=1
n
X

(achfi × Calgi )

DR
AF

Cchf = 1000 ×

T

i=1

i=1

n
X

Can =

((ani + adni + aeni ) × Calgi )

i=1

n
X

Caph =

((aphi + adphi ) × Calgi )

i=1

Casi =

n
X

(asii × Calgi )

i=1

with:

achf
adm
Calgt
Can
Caph
Casi
Cadm
Cchf

stoch. constant for chlorophyll-a over carbon in algae biomass [gChf gC−1 ]
stoch. constant for dry matter over carbon in algae biomass [gDM gC−1 ]
total algae biomass concentration [gC m−3 ]
total concentration of nitrogen in algae biomass [gN m−3 ]
total concentration of phosphorus in algae biomass [gP m−3 ]
total concentration of silicon in algae biomass [gSi m−3 ]
total algae biomass concentration on a dry matter basis [gDM m−3 ]
total chlorophyll-a concentration [mgChf m−3 ]

The limiting factors concern inorganic and detrital nitrogen, inorganic and detrital phosphorus,
dissolved silicon, dissolved inorganic carbon, energy (light), growth and mortality. The active
factors for each timestep are delivered by the optimisation method.
The rates of total net primary production, mortality and nitrogen fixation are:

Rnpt =


n 
X
Rnpi
i=1

Rrspt =


n 
X
Rrspi
i=1

94 of 464

H

H

Deltares

Primary producers

Rf ixt =


n 
X
Rf ixi
H

i=1

with:

Rf ixt
Rrspt
Rnptt

total nitrogen fixation rate [gN m−2 d−1 ]
total algal maintenance respiration rate [gC m−2 d−1 ]
total algal primary production rate [gC m−2 d−1 ]

If the option parameter SwBloomOut is set to 1.0, and the option ‘DUMP’ is selected in
the file bloomip.d09, the model writes information on the bloom-calculations to the additional
output file “bloominp.dbg”.

T

Process UlvaFix

DR
AF

Macro algae such as U lva and similarly behaving macrophytes which can be described with
BLOOM may both be suspended in the water column and attached to the sediment. Two
states are distinguished for such a species, one suspended type and one attached type.
These different states are modelled as different species groups. The two states form a pair
in the sense that biomass can be transferred from the attached type to the suspended state
and vise versa WL | Delft Hydraulics (1998). This “resuspension” or “detachment” process is
due to elevated water flow velocity, and requires the sediment shear stress caused by water
flow. The shear stress can be imposed on the model as a time series or calculated from
the flow field ( a velocity array), which is described elsewhere in this manual. “Resettling” or
“reattachment” to the sediment occurs at the decrease of shear stress.
The characteristics of the pair of types will be identical, except for an additional model parameter SDM ixAlg(i) that indicates the position of the algae in the water column. This
parameter has the default value of 1.0 for the suspended type, meaning that the algae are
mixed over the complete water column. For the attached type, SDM ixAlg(i) has a small
negative value, for example -0.25, meaning that the algae are mixed over the lower 25 % of the
water column. The calculation of the energy constraint for this algae type takes into account
that the attached type “observes” the light intensity in the lower part of the water column.
The parameter F ixAlg(i) defines for each algae type, whether it belongs to a pair of attached and suspended types. At the default value of 0.0 an algae type is considered a normal
suspended algae species. If the parameter obtains a positive value (1.0, 2.0, etc.), it is the
suspended type of a pair. For the attached type of this pair F ixAlg(i) must have the same
but negative value.
Based on the ratio of the actual shear stress and a critical shear stress the fraction of the
algae biomass which is attached to the sediment is calculated as follows:

f at = af −

τ
τc

0.0 ≤ f at ≤ 1.0
with:

af
Calgi
Calg − j
f at
τ
τc

Deltares

attachment affinity coefficient [-]
biomass concentration of the suspended algae species type [gC m−3 ]
biomass concentration of the attached algae species type [gC m−3 ]
target fraction of attached algae type [-]
shear stress at the sediment water interface [Pa]
critical shear stress for resuspension [Pa]

95 of 464

Processes Library Description, Technical Reference Manual

The resuspension and settling rates for algae biomass are then calculated in such a way, that
the concentrations of suspended and attached algae will tend to agree with the calculated
target distribution:
Calgj
:
Calgi

if f at ≥

Rresj =

((1.0 − f at) × (Calgi + Calgj )) − Calgi
∆t

Rresi = −Rresj

Rseti =

Calgj − (f at × (Calgi + Calgj ))
∆t

Rresj = −Rseti
Rresj
Rsetj
Rresi
Rseti
∆tb

DR
AF

with:

T

Calgj
:
Calgi

if f at <

resuspension rate of the attached algae species j [gC m−3 d−1 ]
settling rate of the attached algae species j [gC m−3 d−1 ]
resuspension rate of the suspended algae species i [gC m−3 d−1 ]
settling rate of the suspended algae species i [gC m−3 d−1 ]
time interval, the timestep in BLOOM [d]

In case macro algae attached to sediment are included in the model BLOOM produces additional output in the form of the fraction of biomass attached to the sediment and the algae
biomasses per m2 (derived from the concentrations and the water depth).
Process: DEPAVE

When BLOOM’s time step is bigger than DELWAQ’s time step the average depth for BLOOM
should be calculated using the process DEPAVE. DEPAVE calculates a running average of
the DEPTH within a BLOOM timestep according to:

Hant =
with:

ft
nt
Ha
Hant
Hnt

(nt − 1) × Hant−1 + Hnt
nt

for nt ≤ f t

ratio of the BLOOM time step and the DELWAQ time step ≥ 1.0 [-]
counter for number of DELWAQ time steps made in current BLOOM time step
[-]
average water depth for the current BLOOM time step [m]
running average water depth at DELWAQ time step nt in the current BLOOM
time step [m]
water depth at DELWAQ time step nt [m]

The depth averaging is activated or deactivated according to the value of option parameter
SWDepAve in the process DEPAVE.

96 of 464

Deltares

Primary producers

DR
AF

T

Directives for use
 The variable TimMultBl is a multiplication factor for the transport time step, that enables bloom to use a bigger time step then the transport. With the process decomposition
method also for the other water quality processes a larger time step than the transport
time step can be used. bloom was set up to calculate algae processes on a daily (average) scale. Suitable time steps for bloom are in the range of 6 hours to 2 days. The value
of TimMultBl should be an integer, not less than one. When the time step of bloom is
larger than the time step of the water quality processes, nutrient levels rise between the
bloom time steps and drop when a bloom computation is performed. Output should therefore only be generated at time steps where a bloom computation has been performed. At
times teps in between the nutrient levels are not accurate.
 The bloom module will only be used if the name bloomalg01 is specified in the delwaq
input. N.B. the rate constants for growth, mortality and maintenance respiration must be
supplied for a standard temperature of 0 ◦ C, instead of 20 ◦ C as in the other delwaq
modules.
 The flux of algae mortality to slowly decomposing detritus is calculated as the total mortality flux, minus the autolysis and the flux to fast decomposing detritus. If slowly decomposing detritus (P OC2) is not modelled, the sum of FrAutAlg(i) and FrDetAlg(i) should
equal to 1.0 for each algae type. In no case the sum should exceed one.
 The specific extinction of bloom-algae can not be set equal to zero, or the calculation will
stop with the error message that the model cannot divide by zero.
 Mixotrophic nitrogen and phosphorus algae types can be defined by providing a positive
value for the coefficients XNCRAlg(i) and XPCRAlg(i) respectively. These coefficients must be equal to 0.0 for autotrophic algae. The sum of the stoichiometric constants
NCRAlg(i) and XNCRAlg(i), or PCRAlg(i) and XPCRAlg(i), of the mixotrophic
algae types should be equal to the real overall stoichiometric constant for nitrogen, or
phosphorus. The distribution of the nutrients regarding their origin, that is the ratio of both
constants, should be chosen in such a way, that a realistic amount of nutrients in detritus
is consumed by the mixotrophic type. It is very well possible, that the results will not show
high biomass for the mixotrophic type, even if the nutrients become completely depleted.
Other types of the same group may be more efficient in the use of the nutrients, once they
have been made available by the mixotrophic types. The production of the mixotrophic
types can be calculated by division of the nutrient uptake by the prescribed stoichiometry
(XNCRAlg(i) and XPCRAlg(i)).
 It is possible to describe nitrogen fixation by algae types by providing a positive value
for the coefficient FNCRAlg(i). These coefficients must be equal to 0.0 for autotrophic
and mixotrophic algae. Again the sum of the stoichiometric constants NCRAlg(i) and
FNCRAlg(i) of the nitrogen fixative algae types should be equal to the real overall stoichiometric constant for nitrogen. Nitrogen fixation is not limited by the availability of the nutrient (N2), but by the fixation capacity of the algae. Therefore, the values of FNCRAlg(i)
and PPMaxAlg(i) should be chosen in such a way, that a realistic nitrogen fixation rate
will be used. Furthermore, the primary production rate PPMaxAlg(i) will be lower than
for the autotrophic types, because nitrogen fixation costs more energy than the uptake
of dissolved nutrients. Maximum nitrogen fixation is in the order of 25 kgN ha−1 y−1
∼ 0.006 8 gN m−2 d−1 (Ross, 1995). If PPMaxAlg(i) is set to be 0.1 1/d (after temperature correction) on average during the growing season, the depth is 2.0 meters and
the biomass of the nitrogen fixing group is 10 gC m−3 , then the maximum realistic value
of FNCRAlg(i) can be calculated as 0.006 8 / (10 × 0.1 × 2) = 0.0034 gN gC−1 .
 Changes in salinity can induce extra algae mortality. Marine algae suffer from extra mortality when they are exposed to fresh water and vice versa, fresh water algae die in a
marine environment. The effect in bloom depends on the relative magnitudes of coefficients MND(i)m1 and MND(i)m2. The salinity effect on mortality can be inactivated
by allocating the same value to MND(i)m1 and MND(i)m2.
 The current implementation of BLOOM allows for only one macro algae of macrophyte

Deltares

97 of 464

Processes Library Description, Technical Reference Manual








T



DR
AF



species, whereas in parameter naming U lva was taken as a reference. With the default
value of 2.0 for FixGrad the target attached fraction f at is equal to 1.0, when shear
stress Tau is less than TauCrUlva , and equql to 0.0 when Tau is more than two times
TauCrUlva . This can be modified by changing the value of FixGrad .
When (macro) algae from the bottom are resuspended their biomass is converted to the algae type with the corresponding positive value of the parameter FixAlg(i). So the biomass
of the type with the value of FixAlg(i) = -1.0 is converted to the type with the value of
FixAlg(i) = +1.0.
Biomass of the algae species attached to the sediment (one of a pair) is expressed in [gC
m−2 ], since this state variable is modelled as an “inactive” substance.
Usually the observed light intensity, also indicated as irradiation or solar radiation, is expressed in [J cm−2 week−1 ]. Notice that the light intensity has to be provided in [W m−2 ].
Always make sure that the light input (observed solar radiation) is consistent with the
light related parameters of BLOOM. This concerns the use of either visible light or the
photosynthetic fraction of visible light. BLOOM assumes total visible light observed just
above the water surface. It carries out corrections for the fraction of photosynthetically
active light (45 %) and reflection (approximately 10 % depending on the point of time in a
year). The input incident light time series should have been corrected for cloudiness.
Carbon limitation can be taken account according to options, through the advanced BLOOM
optimisation approach and through the simplified growth scaling approach. For the advanced approach the input parameter SwTICdummy (default value = 0.0) needs to be
allocated a value of 10.0 or higher. The limitation parameter KCO2 of the simplified approach has a default value of 0.0, implying no limitation by carbon, which must not be
modified when applying the advanced approach. When using the simplified approach, an
appropriate value of KCO2 for limitation is 1.0 gC.m3 .
The sulfur content of algae will only be taken into account automatically, when SO4,
SU D, P OS1 and P OS2 are actually modelled.

Additional references

Van der Molen et al. (1994a), WL | Delft Hydraulics (1992c), BLOOM UM (1985), DBS (1994),
DBS (1991), Los (2009)
Table 4.1: Definitions of the input parameters in the formulations for BLOOM.

Name in
formulas

Name in input

Calgi
Cam
Ccl
Cni
Cph
Csi
Cnutc1

BLOOM ALG(i)biomass concentration of algae species type i
N H4
ammonium concentration
Cl
chloride concentration
N O3
nitrate concentration
P O4
phosphate concentration
Si
dissolved inorganic silicate concentration
T hrAlgN H4 threshold concentration for uptake of ammo-

Cnutc2
Cnutc3

T hrAlgN O3
T hrAlgP O4

Cnutc4

T hrAlgSi
P ON 1
or
DetN

–

Definition

Units

nium
threshold concentration for uptake of nitrate
threshold concentration for uptake of phosphorus
threshold concentration for uptake of silicate
concentration of nitrogen in fast decomp. detritus

gC m−3
gN m−3
gCl m−3
gN m−3
gP m−3
gSi m−3
gN m−3
gN m−3
gP m−3
gSi m−3
gN m−3

continued on next page

98 of 464

Deltares

Primary producers

Table 4.1 – continued from previous page
Definition

Units

concentration of phosphorus in fast decomp.
detritus
species identification number of types

gP m−3

–

P OP 1
or
DetP
SpecAlg(i)3

achfi

ChlaCAlg(i)

gChf gC−1

admi

DM CF Alg(i)

ani

N CRAlg(i)

adni

XN CRAlg(i)

aeni

F N CRAlg(i)

aphi

P CRAlg(i)

adphi

XP CRAlg(i)

asii

SCRAlg(i)

algae type spec. stoch. const. chlorophyll
over carbon
algae type spec. stoch. const. dry matter over
carbon
algae type spec. stoch. const. nutr. nitrogen /
carbon
algae type spec. stoch. const. detr. nitrogen /
carbon
algae type spec. stoch. const. elem. nitrogen
/ carbon
algae type spec. stoch. const. nutr. phos. /
carbon
algae type spec. stoch. const. detr. phos. /
carbon
algae type spec. stoch. const. for silicon over
carbon
algae type spec. rate coefficient 1 of salinity
stress
algae type spec. rate coefficient 2 of salinity
stress
algae type spec. coefficient 1 of salinity stress
function
algae type spec. coefficient 2 of salinity stress
function
algae species type specific extinction coefficient

m1i

M ort0Alg(i)

m2i

M ort2Alg(i)

b1i

M rtB1Alg(i)

b2i
eai

T

Name in input

DR
AF

Name in
formulas
–

M rtB2Alg(i)
ExtV lAlg(i)

-

gDM gC−1
gN gC−1
gN gC−1
gN gC−1
gP gC−1
gP gC−1
gSi gC−1
d−1
d−1
g−1 .m3
g m−3
m2 gC−1

KCO2

KCO2

limitation constant for carbon

gC m3

f auti
f deti

F rAutAlg(i)
F rDetAlg(i)

fraction of dead algae biomass autolised
fr. of dead algae biomass allocated to fast dec.
detritus

-

–

SDM ixAlg(i) distribution of an algae type over the water col-

-

umn
identifier for pairs of algae types attaching to
sediment (0 =not applying, > 0 = suspended,
< 0 = attached)

–

F ixAlg(i)

–

SwBloomOut option for specific BLOOM output (0 = no, 1 =

-

–

yes)
option for calc. oxygen conc. (0 = daily av., 1
= daily var.)

-

SW OxyP rod2

-

continued on next page

Deltares

99 of 464

Processes Library Description, Technical Reference Manual

Table 4.1 – continued from previous page
Name in input

Definition

Units

SW DepAve

option depth aver. over BLOOM timestep (0 =
off, 1 = on)

-

H
Ha
V

Depth
BloomDepth
V olume

depth of a water compartment or water layer
average depth during a BLOOM timestep
volume of a water compartment or water layer

m
m
m3

DL
et
eat
Itop

DayL
ExtV l4
ExtV lP hyt4
Rad

daylength, fraction of a day
total extinction coefficient of visible light
extinction coefficient of all agae species types
light intensity at top of layer or compartment

m−1
m−1
W m−2

kgp0i

P P M axAlg(i) algae type spec. pot. gross primary prod. rate

ktgpi

T cP M xAlg(i) algae type spec. temperature coeff. for pri-

◦

at 0 C

krsp0i

DR
AF

mary prod.

–

T F P M xAlg(i) option temperature dep. of prod. (0 = linear, 1
M RespAlg(i)

ktmrti

M rtExAlg(i)
T cM rtAlg(i)

ktrspi

T cRspAlg(i)

–

T
af
τ
τc
ft
∆t
1

T

Name in
formulas
–

= exp.)
algae type spec. maintenance respiration rate
at 0 ◦ C
algae type spec. extra rapid mortality rate
algae type spec. temperature coefficient for
mortality
algae type spec. temperature coef. for maint.
resp.

d−1
- or ◦ C
d−1
d−1 ◦ C−1
-

T emp

water temperature

◦

F ixGrad
T au
T auCrU lva

attachment affinity coefficient
shear stress at the sediment water interface
critical shear stress for resuspension

Pa
Pa

T imM ultBl

ratio of the BLOOM timestep and the DELWAQ timestep
time interval, that is the DELWAQ timestep

-

Delt

C

d

(i) indicates algae species types 01-15. Biomass of algae species attached to the sediment
is expressed in [gC.m−2 ].
2

For SW OXY P rod = 1.0 process VAROXY is used to calculated the daily varying dissolved oxygen concentration (see description elsewhere in the manual).
3

The species identification number needs to be an integer that is equal for all types that belong
to the same species.
4

These parameters are calculated by processes ExtinaBVL and Extinc_VL.

100 of 464

Deltares

Primary producers

Table 4.2: Definitions of the output parameters for BLOOM.

Name in output1

Definition

Units

Calgti
Cdmi

P hyt
AlgDM

gC m−3
gDM m−3

Cchfi
Cani

Chlf a
AlgN

Caphi

AlgP

Casii

AlgSi

total algae biomass concentration
total algae biomass conc. on a dry matter basis
total chlorophyll-a concentration
total concentration of nitrogen in algae
biomass
total concentration of phosphorus in algae
biomass
total concentration of silicon in algae biomass

–
–
–
–
–
–
–
–

DR
AF

–

Limit N it
or Lim_IN
Lim_DetN
Lim_F ixN
Limit P ho
or Lim_IP
Lim_DetP
Limit Sil
or Lim_Si
Limit E
or Lim_light
Lim_inhib
Limit Gro
or

–

T

Name in
formulas

Lim_GALG
Limit M or
or

mgChf m−3
gN m−3
gP m−3
gSi m−3

indicator for limitation by inorganic nitrogen

-

indicator for limitation by detrital nitrogen
indicator for limitation by nitrogen fixation
indicator for limitation by inorganic phosphorus

-

indicator for limitation by detrital phosphorus
indicator for limitation by silicon

-

indicator for limitation by energy (light)

-

indicator for limitation by photo inhibition
indicator for limitation by growth
can be split into species specific Lim_G(i)

-

indicator for limitation by mortality
can be split into species specific Lim_M (i)

-

Lim_M ALG

Rnpt
Rrspt
Rf ixt

f P P tot
f Resptot
f F ixN U pt

total net primary production
total maintenance respiration
total uptake of nitrogen by fixation

gC m−2 d−1
gC m−2 d−1
gN m−2 d−1

–
–

RcP P Alg(i)
RcM rtAlg(i)

algae type specific net primary production rate
algae type specific net primary mortality rate

d−1
d−1

–
–

f rF ixedAlg
fraction of algae fixed to the sediment bed
BLALG(i)m2 algae type specific biomass per m2

1

gC m−2

(i) indicates the algae species types that are used.

Deltares

101 of 464

Processes Library Description, Technical Reference Manual

Bottom fixation of BLOOM algae types
PROCESS :

U LVA FIX

T

Some macrophytes which can be described with BLOOM, can occur both suspended and
fixed to the bottom. An example of such a macrophyte is ulva. Such macrophytes can be
modelled by BLOOM by defining for each algae type two types: one fixed and one suspended.
The characteristics of the two types will be identical, except for the parameter indicating the
relative mixing depth, SDMixAlgi. This parameter has the default value of 1.0 for the suspended type, meaning that the algae are mixed over the complete water column. For the fixed
type, this parameter has a small negative value, e.g. -0.25, meaning that the algae are mixed
over the lower 25 % of the water column. The flow field should be supplied in a velocity array,
which has been made inactive for the fixed algae types. The exchange of algae between the
fixed and suspended state depends on the bottom shear stress.
Implementation

The parameter FixAlgi defines for each algae type, whether it is part of a combination of fixed
and suspended types or not. If FixAlgi has the default value of 0, this type is omitted from
the further analysis. If the value of FixAlgi is a positive number, it is the suspended type of a
combination. For the fixed type of the combination the value of FixAlgj should be the same
number, but negative.

DR
AF

4.3

Based on comparison of the actual shear stress with the critical shear stress the fraction of the
total concentration which is fixed to the bottom is calculated. The fluxes are then calculated in
such a way, that the concentrations of suspended and fixed algae will be in accordance with
the calculated fraction.
This process is implemented for all BLOOM algae types. The current maximum number of
BLOOM algae types is 15.
i = 1 to 15, suspended type
j = 1 to 15, fixed type forming a pair with i
Formulation

The fraction of the total concentration, which is fixed to the bottom is calculated from the ratio
between the actual and the critical bottom shear stress:

f rF ixedAlg = F ixGrad −

T au
with f rF ixedAlg = [0, 1]
T auCrU lva

The flux for the suspended type is then calculated as:

dResSedi = ((1 − f rF ixedAlg) × (BloomAlgi + BloomAlgj) − BloomAlgi)/Delt
And for the fixed type as:

dResSedj = (f rF ixedAlgae × (BloomAlgi + BloomAlgj) − BloomAlgj)/Delt

102 of 464

Deltares

Primary producers

Directives for use
 For a complete description of the application of DELWAQ for the analysis of ulva see the
documentation of project number T2162, regarding Venice Lagoon (WL | Delft Hydraulics,
1998).

DR
AF

T

With the default value of 2.0 for FixGrad the fraction fixed is 1.0 when Tau is less than TauCrUlva and 0.0 when Tau is more than two times TauCrUlva. This can be modified by changing
the value of FixGrad.

Deltares

103 of 464

Processes Library Description, Technical Reference Manual

Settling of phytoplankton
PROCESS :

SED( I ), SEDPHBLO, SEDPHDYN, CALVS( I )

Live algae biomass settles on the sediment. The biomass components (C,N,P,Si,S) become
parts of algae biomass or detritus in the sediment. The fate of settled biomass depends on
the option for sediment modelling. The destinations in the sediment are:
1 the biomasses of the same algae species Xi as in the water column when sediment layers
are actually simulated (layered sediment approach); or
2 DET(C,N,P,Si)S1 and OO(C,N,P,Si)S1 for the S1/2 approach (sulfur is not covered for
S1/2).

T

When the S1/2 approach is followed phytoplankton biomass is allocated to the sediment detritus pools as follows:

DETCS1
Algae C

OOCS1

DR
AF

4.4

settling

Water

Sediment

For DYNAMO algae biomass only settles in DETC/N/P/Si/S1.
Implementation

Processes SEDALG and SEDPHBLO have been implemented for the BLOOM substances:

 BLOOMALG01-BLOOMALG30.

Processes SEDDIAT, SED_GRE and SEDPHDYN have been implemented for the DYNAMO
substances:

 Diat and Green

Processes SED(i) deliver the settling rates of individual algae species biomass (C). Process
SEDPHBLO delivers the settling rates of total algae biomass (C) and the nutrients in algae
biomass (C,N,P,Si,S), for which BLOOM provides the stochiometric ratios. Process SEDPHDYN delivers the settling rate of total algae biomass (C) and calculates the settling rates of
the nutrients in algae biomass (C,N,P,Si) for DYNAMO using input parameters for the stochiometric ratios.
Processes CALVSALG may be used to modify the input settling velocity of BLOOM algae
for shear stress and/or flocculation, which requires alternative input parameters V 0Sed(i).
Processes CALVS_Diat and CALVSGreen do the same for DYNAMO algae.
Internally in DELWAQ, the above processes for BLOOM set up the same processes for the
individual algae species, using species specific settling velocities.
Table 4.3 provides the definitions of the input parameters occurring in the formulations.

104 of 464

Deltares

Primary producers

Formulation
The settling rate of the organic carbon components is described as the sum of zero-order
and first-order kinetics. The settling rates are zero, when the shear stress exceeds a certain
critical value, or when the water depth is smaller than a certain critical depth Krone (1962).
The rates are calculated according to:

Rseti = f taui ×

F seti
H

if H < Hmin F seti = 0.0
else

F set0i = F set0i + si × Cxi
if τ = −1.0 f tau = 1.0
else

DR
AF




τ
f taui = max 0.0, 1 −
τ ci

T



0 Cxi × H
F seti = min F seti ,
∆t

where:

Cx
F set0
F set
f tau
H
Hmin
Rset
s
τ
τc
∆t
i

concentration of the biomass of an algae species [gC m−3 ]
zero-order settling flux of an algae species [gC m−2 d−1 ]
settling flux of an algae species [gC m−2 d−1 ]
shearstress limitation function [-]
depth of the water column [m]
minimal depth of the water column for resuspension [m]
settling rate of an algae species [gC m−3 d−1 ]
settling velocity of an algae species [m d−1 ]
shearstress [Pa]
critical shearstress for settling of an algae species [Pa]
timestep in DELWAQ [d]
index for algae species (i)

The settling of organic nutrients in algae biomass is coupled to the settling of organic carbon
in algae biomass as follows:

Rsnj,i = f sj,i × Rseti

where:

f sj,i
Rsnj,i
i
j

stochiometric ratio of nutrient j in algae species i [gX gC−1 ]
settling rate of nutrient j in algae species i [gX m−3 d−1 ]
index for algae species (i)
index for nutrient (j)

Directives for use
 T au can be simulated with process CALTAU. If not simulated or imposed Tau will have
the default value -1.0, which implies that settling is not affected by the shear stress. For
specific input parameters, see the process description of CALTAU.
 Settling does not occur, when Depth is smaller than minimal depth M inDepth for settling, which has a default value of 0.1 m. When desired M inDepth may be given a
different value.

Deltares

105 of 464

Processes Library Description, Technical Reference Manual

 The settling fluxes f SedAlg (gDM m−2 .d−1 ) and f SedP hyt (gC m−2 .d−1 ) are available
as additional output parameters.
Table 4.3: Definitions of the input parameters in the above equations for SED(i), SEDPHBLO and SEDPHDYN.

Name in
input

Definition

Cx1i

BLOOM (i)1 concentration of biomass of algae species i,
or (i)1
for BLOOM or DYNAMO

gC m−3

F set0I

ZSed(i)

zero-order settling flux of algae species i

gC m−2 d−1

f sj,i

N CR(i)
P CR(i)
SCR(i)
SuCr(i)

stoch.
stoch.
stoch.
stoch.

ratio N in algae species i for BLOOM
ratio P in algae species i for BLOOM
ratio Si in algae species i for BLOOM
ratio S in algae species i for BLOOM

gN gC−1
gP gC−1
gSi gC−1
gS gC−1

N Crat(i)
P Crat(i)
SCrat(i)
SuCrat(i)

stoch.
stoch.
stoch.
stoch.

ratio N in algae species i for DYNAMO
ratio P in algae species i for DYNAMO
ratio Si in algae species i for DYNAMO
ratio S in algae species i for DYNAMO

gN gC−1
gP gC−1
gSi gC−1
gS gC−1

Depth
M inDepth

depth of the overlying water compartment
minimal water depth for settling and resuspension

m
m

V Sed(i)

input or calc. settling velocity algae species i

m d−1

V 0Sed(i)

basic settling velocity of algae species i

m d−1

T au
T aucS(i)

shear stress
critical shear stress for settling of algae
species i

Pa
Pa

Delt

timestep in DELWAQ

d

H
Hmin
si

DR
AF

or

Units

T

Name in
formulas

or

τ
τ ci
∆t
1

) (i) is equal to one of the algae species names, BLOOM specific names connected to ALG0130, or Diat and Green.

106 of 464

Deltares

Primary producers

Production and mortality of algae (DYNAMO)
PROCESS :

GROMRT_( I ), TF_( I ), NL( I ), DL_( I ), RAD_( I ), PPRLIM, NUTUPT_ALG,
NUTREL_ALG

The primary production of algae is limited by nutrient availability, light and temperature. Mortality is a function of temperature and salinity. DYNAMO applies so-called Monod kinetics for
the growth of algae biomass, and for the competition of two species, green algae and diatoms.
Implementation

 Diat and Green
 NH4, NO3, PO4 and Si

T

Processes GROMRT_(i), TF_(i), NL(i), DL_(i), RAD_(i), PPRLIM, NUTUPT_ALG and NUTREL_ALG have been implemented for the following substances:

Table 4.4 provides the definitions of the input parameters occurring in the formulations.

DR
AF

4.5

Formulation

The production and mortality of algae biomass (organic carbon)
The primary production rate is formulated as follows:

Rnpi = knpi × Calgi
knpi = kgpi − krspi
kgpi = f dli × f radi × f nuti × f tpi × kpp20
i
(T −20)

f tpi = ktpi

where:

Calg
f dl
f nut
f rad
f tp
kgp
knp
kpp20
krsp
ktp
Rnp
T
i

Deltares

concentration of algae biomass [gC m−3 ]
daylength limitation function [-]
nutrient limitation function [-]
light limitation function [-]
production temperature function [-]
gross primary production rate constant [d−1 ]
net primary production rate constant [d−1 ]
potential maximum production rate constant at 20 ◦ C [d−1 ]
total respiration rate constant [d−1 ]
temperature constant for production [-]
net primary production rate [gC m−3 d−1 ]
water temperature [◦ C]
index for algae species

107 of 464

Processes Library Description, Technical Reference Manual

The limitation function for nutrients is given by:

f nuti = M in(f ni , f pi , f sii )
Cnn
f ni =
Cnn + Ksni
Cph
f pi =
Cph + Kspi
Csi
f sii =
Csi + Kssii
Cni
Cnn = Cam +
f ani
concentration of ammonium [gN m−3 ]
concentration of nitrate [gN m−3 ]
concentration of preferred nutrient nitrogen [gN m−3 ]
concentration of dissolved phosphate [gP m−3 ]
concentration of dissolved silicate [gSi m−3 ]
preference of ammonium over nitrate [-]
nutrient limitation function [-]
nitrogen limitation function [-]
phosphorus limitation function [-]
silicon limitation function [-]
half saturation constant for nutrient nitrogen [gN m−3 ]
half saturation constant for phosphate [gP m−3 ]
half saturation constant for silicate [gSi m−3 ]
index for algae species

DR
AF

Cam
Cni
Cnn
Cph
Csi
f an
f nut
fn
fp
f si
Ksn
Ksp
Kssi
i

T

where:

The limitation functions for daylength and light are given by:

min(DL, DLoi )
DLoi
if (Is/Ioi ) ≥ 1.0 and (Ib/Ioi ) ≥ 1.0 then f radi = 1.0
if (Is/Ioi ) ≥ 1.0 and (Ib/Ioi ) < 1.0 then

f dli =

1 + ln(Is/Ioi ) − (Is/Ioi ) × e(−et×H)
et × H
if (Is/Ioi ) < 1.0 then
f radi =

Is
1 − e(−et×H)
f radi =
×
Ioi
et × H
20
Ioi = f tpi × Ioi
Ibi = Isi × e(−et×H)
where:

DL
DLo
et
f dl
f rad
f tp

108 of 464

daylength, fraction of a day [-]
optimal daylength [d]
total extinction coefficient [m−1 ]
daylength limitation function [-]
light limitation function [-]
production temperature function [-]

Deltares

Primary producers

H
Io
Io20
Ib
Is
i

water depth [m]
optimal light intensity [W m−2 ]
optimal light intensity [W m−2 ]
light intensity at the bottom [W m−2 ]
light intensity at water surface [W m−2 ]
index for algae species

Note that the value of Io_i is corrected for temperature. This results in a dependency of f radi
of Is as presented in Figure 4.3 (Harris, 1986). This means that at a constant value for light
intensity, the light limitation is less important at lower temperatures. The above formulations
do not consider the availability of nutrients. However, primary production can not larger than
the available quantities of nutrients allow for. The primary production rate is corrected for
available nutrients as follows:

DR
AF

T

max(Cni + Cam, 0.0) max(Cph, 0.0)
,
)
an1 × ∆t
ap1 × ∆t
max(Cni + Cam, 0.0) max(Cph, 0.0) max(Csi, 0.0)
Rnpmax,2 = min(
,
,
)
an2 × ∆t
ap2 × ∆t
asi2 × ∆t
Rnpmax = max(Rnpmax,1 , Rnpmax,2 )
Rnp = max(Rnp1 , Rnp2 )
if Rnp > Rnpmax then
Rnpmax
Rnpc,2 = min(
× Rnp2 , Rnpmax,2 )
Rnp
Rnpc,1 = Rnpmax − Rnpc,2
∆Rnp2 = Rnpc,2 − Rnp2
∆Rnp1 = Rnpc,1 − Rnp1
Rnpmax,1 = min(

else

Rnpc,1 = Rnp1 and Rnpc,2 = Rnp2
∆Rnpc,1 = 0.0 and ∆Rnpc,2 = 0.0

where:

an
ap
asi
Cam
Cni
Cph
Csi
Rnp
∆Rnp
∆t
c
max
1
2

stoichiometric constant for N over C in algae biomass [gN gC−1 ]
stoichiometric constant for P over C in algae biomass [gP gC−1 ]
stoichiometric constant for Si over C in algae biomass [gSi gC−1 ]
concentration of ammonium [gN m−3 ]
concentration of nitrate [gN m−3 ]
concentration of dissolved phosphate [gP m−3 ]
concentration of dissolved silicate [gSi m−3 ]
total or partial net primary production rate [gC m−3 d−1 ]
correction of the net primary production rate [gC m−3 d−1 ]
computational timestep [d]
index for corrected net primary production
index for maximum net primary production
index for green algae
index for diatoms

The respiration rate is formulated as follows:

krspi = f gri × kgpi + f tmi × (1 − f gri ) × kmri20
where:

Deltares

109 of 464

Processes Library Description, Technical Reference Manual

f gr
f tm
kmr20
krsp
i

growth respiration factor [-]
mortality temperature function [-]
maintenance respiration constant at 20 ◦ C [d−1 ]
total respiration rate constant [d−1 ]
index for algae species

The mortality rate is formulated as follows:

Rmrti = f tmi × kmrt20
i × M ax((Calgi − Calgmini ), 0.0)
(T −20)

f tmi = ktmi
20
if S < Smini then kmrt20
i = kmrtmin,i
else
20
kmrt20
i = kmrtmin,i +

T

20
if S > Smaxi then kmrt20
i = kmrtmax,i

(S − Smini )
20
× (kmrt20
max,i − kmrtmin,i )
(Smaxi − Smini )

where:

concentration of algae biomass [gC m−3 ]
minimum concentration of algae biomass [gC m−3 ]
mortality temperature function [-]
mortality rate constant at 20 ◦ C [d−1 ]
minimum mortality rate constant at 20 ◦ C [d−1 ]
maximum mortality rate constant at 20 ◦ C [d−1 ]
temperature constant for mortality [-]
mortality rate [gC m−3 d−1 ]
ambient salinity [psu] or [g kg−1 ]
salinity limit for minimum mortality [psu] or [g kg−1 ]
salinity limit for maximum mortality [psu] or [g kg−1 ]
water temperature [◦ C]
index for algae species

DR
AF

Calg
Calgmin
f tm
kmrt20
kmrt20
min
kmrt20
max
ktm
Rmrt
S
Smin
Smax
T
i

Uptake and release of nutrients

Nutrients are taken up (consumed) proportional to net primary production as follows:

Ruami = f ram ×

n=2
X

(ani × Rnpc,i )

i

Runii = (1 − f ram) ×

n=2
X

(ani × Rnpc,i )

i

Rupi =
Rusii =

n=2
X
i
n=2
X

(api × Rnpc,i )
(asii × Rnpc,i )

i

where:

an
ap

110 of 464

stoichiometric constant for N over C in algae biomass [gN gC−1 ]
stoichiometric constant for P over C in algae biomass [gP gC−1 ]

Deltares

Primary producers

asi
f ram
Ruam
Runi
Rup
Rusi
Rnp
c
i

stoichiometric constant for Si over C in algae biomass [gSi gC−1 ]
fraction of N consumed as ammonium [-]
ammonium uptake rate [gN m−3 d−1 ]
nitrate uptake rate [gN m−3 d−1 ]
phosphate uptake rate [gP m−3 d−1 ]
silicate uptake rate [gSi m−3 d−1 ]
net primary production rate [gC m−3 d−1 ]
index for corrected net primary production
index for algae species

Algae prefer ammonium over nitrate. The fraction of N consumed as ammonium follows from:

f ram =

Cam
Cam + Cni

else
n=2
X
Run =
(ani × Rnpc,i )

DR
AF

i

T

if Cam < Camc then

if (Cam − Camc ) ≥ (Run × ∆t) then f ram = 1.0

if (Cam − Camc ) < (Run × ∆t) then

f ram =

(Cam − Camc ) + (Camc /(Camc + Cni)) × (Run × ∆t − Cam + Camc )
Run × ∆t

where:

an
Cam
Camc
Cni
f ram
Rnp
Run
∆t
c
i

stoichiometric constant for N over C in algae biomass [gN gC−1 ]
concentration of ammonium [gN m−3 ]
critical concentration of ammonium [gN m−3 ]
concentration of nitrate [gN m−3 ]
fraction of N consumed as ammonium [-]
net primary production rate [gC m−3 d−1 ]
required nitrogen uptake in a timestep [gC m−3 d−1 ]
computational timestep [d]
index for corrected net primary production
index for algae species

The mortality flux is divided among three pools: dissolved inorganic substances (autolysis),
fast decomposing detritus and medium slow decomposing detritus. Organic carbon and nutri-

Deltares

111 of 464

Processes Library Description, Technical Reference Manual

ents are released proportional to mortality as follows:

Ran = f rai ×
Rap = f rai ×
Rasi = f rai ×

n=2
X
i
n=2
X
i
n=2
X

(ani × Rmrti )
(api × Rmrti )
(asii × Rmrti )

i
n=2

n=2
X
Rmn1 = f rpoc1 ×
(ani × Rmrti )

(api × Rmrti )

DR
AF

Rmp1 = f rpoc1 ×

i
n=2
X

T

X
f rpoc1
×
(Rmrti )
Rmc1 =
(1 − f rai )
i

Rmsi1 = f rpoc1 ×

i
n=2
X

(asii × Rmrti )

i

n=2

X
f rpoc1
)×
(Rmrti )
Rmc2 = (1 −
(1 − f rai )
i
Rmn2 = (1 − f rpoc1 − f rai ) ×

n=2
X

(ani × Rmrti )

i

Rmp2 = (1 − f rpoc1 − f rai ) ×

n=2
X

(api × Rmrti )

i

Rmsi2 = (1 − f rpoc1 − f rai ) ×

n=2
X

(asii × Rmrti )

i

where:

an
ap
asi
f ra
f rpoc1
Ran
Rap
Rasi
Rmc1
Rmc2
Rmn1
Rmn2
Rmp1
Rmp2
Rmsi1
Rmsi2

112 of 464

stoichiometric constant for N over C in algae biomass [gN gC−1 ]
stoichiometric constant for P over C in algae biomass [gP gC−1 ]
stoichiometric constant for Si over C in algae biomass [gSi gC−1 ]
fraction released by autolysis [-]
fraction released to detritus POC/N/P1 or OPAL [-]
nitrogen NH4 release due to autolysis [gN m−3 d−1 ]
dissolved phosphate PO4 release due to autolysis [gP m−3 d−1 ]
dissolved silicate Si release due to autolysis [gSi m−3 d−1 ]
detritus C release to POC1 due to mortality [gC m−3 d−1 ]
detritus C release to POC2 due to mortality [gC m−3 d−1 ]
detritus N release to PON1 due to mortality [gN m−3 d−1 ]
detritus N release to PON2 due to mortality [gN m−3 d−1 ]
detritus P release to POP1 due to mortality [gP m−3 d−1 ]
detritus P release to POP2 due to mortality [gP m−3 d−1 ]
silicate release to OPAL due to mortality [gSi m−3 d−1 ]
silicate release to OPAL due to mortality [gSi m−3 d−1 ]

Deltares

Primary producers

Rmrt
i

mortality rate [gC m−3 d−1 ]
index for algae species

DR
AF

T

Directives for use
 Because the limitation function for radiation (f radi ) depends on temperature, the product
of kgpi depends differently on temperature than might be expected at first sight. The
temperature dependency conform to literature (Harris, 1986) is presented in Figure 4.2.
 The value of SalM 2 should be greater than the value of SalM 1. If SalM 1 = −1
then the procedure described above is not applied. In that case the mortality rate equals
M ort0(i).
 Always make sure that the radiation input is coherent with the saturated radiation. Undepleted solar radiation ranges from 100 to 500 W m−2 at altitudes around 50◦ North/South.
At other altitudes these values must be corrected. However, these values should be corrected for e.g. clouds and the wavelength spectrum (0.45 is a frequently used value).

Deltares

113 of 464

Processes Library Description, Technical Reference Manual

Table 4.4: Definitions of the input parameters in the above equations for GROMRT_(i),
TF_(i), NL(i), DL_(i), RAD_(i), PPRLIM, NUTUPT_ALG and
NUTREL_ALG. (i) = Green or Gree for green algae (input names
maximum 10 letters long!), and (i) = Diat for diatoms.

Units

Calgi
(i)
Calgmini M in(i)

concentration algae biomass (i)
minimum conc. algae species (i)

gC m−3
gC m−3

ani
api
asii

N CRat(i)
P CRat(i)
SCRat(i)

stoich. constant N over C in algae (i)
stoich. constant P over C in algae (i)
stoich. constant Si over C in algae (i)

gN gC−1
gN gC−1
gN gC−1

Cam
Camc
Cni
Cph
Csi

N H4
N H4Crit
N O3
P O4
Si

concentration of ammonium
critical conc. of ammonium for uptake
concentration of nitrate
concentration of dissolved phosphate
concentration of dissolved silicate

gN m−3
gN m−3
gN m−3
gP m−3
gSi m−3

DayL
OptDL(i)

daylength, fraction of a day
optimal daylength for algae species (i)

-

ExtV L

total extinction coefficient

m−1

f ani
f gri
f rai
f rpoc1

P rf N H4(i)
GResp(i)
F rAut(i)
F rDet(i)

pref. ammonium over nitrate for algae (i)
growth respiration factor for algae (i)
fraction released by autolysis for algae (i)
fraction released to detritus POC/N/P1 or
OPAL for algae (i)

-

H

Depth

water depth

m

Rad
RadSat(i)

light intensity at water surface
optimal light int. at 20 ◦ C for algae (i)

W m−2
W m−2

kmri20
kmrt20
min,i
kmrt20
max,i
kpp20
i
ktmi
ktpi

M Resp(i)
M ort0(i)
M ortS(i)
P P M ax(i)
T CDec(i)
T CGro(i)

maint. resp. const. at 20 ◦ C of algae (i)
min. mort. constant at 20 ◦ C of algae (i)
max. mort. constant at 20 ◦ C of algae (i)
max. prod. constant at 20 ◦ C of algae (i)
temp. constant for mortality of algae (i)
temp. constant for production of algae (i)

d−1
d−1
d−1
d−1
-

Ksni
Kspi
Kssii

KmDIN (i)
KmP (i)
KmSi(i)

half satur. const. nitrogen for algae (i)
half satur. const. phosphate for algae (i)
half satur. const. silicate for algae (i)

gN m−3
gP m−3
gSi m−3

S
Smini
Smaxi

Salinity
SalM 1(i)
SalM 2(i)

salinity
salinity limit for Mort0 of algae (i)
salinity limit for MortS of algae (i)

psu
psu
psu

T

T emp

water temperature

◦

∆t

Delt

computational timestep

d

et

Is
Io20
i

T

Definition

DL
DLoi

Name in
input

DR
AF

Name in
formulas

114 of 464

C

Deltares

Primary producers

Primary production as function of light intensity
(1/d)
4

3

1

temperature = 5C
temperature = 15C
temperature = 25C

0

10

20
30
40
Intensity (PAR; W/m2)

50

60

DR
AF

0

T

2

Figure 4.2: Primary production rate of algae species i as a function of temperature and
radiation.

Radiation limitation as function of light intensity

1

0.8
0.6
0.4
0.2

0

temperature = 5C
temperature = 15C
temperature = 25C

0

10

20
30
40
Intensity (PAR; W/m2)

50

60

Figure 4.3: Limitation function for radiation (f rad_i) for algae species i as a function of
radiation (Is,RAD) at different temperature ranging from 5 to 25 ◦ C.

Deltares

115 of 464

Processes Library Description, Technical Reference Manual

Computation of the phytoplankton composition (DYNAMO)
PROCESS :

PHY_DYN

Process PHY_DYN computes the total concentrations of the nutrients in biomass from the
contributions of individual algae species. Additionally the processes deliver the total concentration of algae biomass expressed in various units among which chlorophyll-a. The concentrations of nutrients in algae biomass are used to calculate the concentrations of a number of
aggregate substances with auxiliary process COMPOS.
Volume units refer to bulk ( ) or to water ( ).
b

T

Implementation

w

PHY_DYN has been implemented for the following substances:

 Diat and Green

The process does not directly influence state variables, since they do not generate mass
fluxes.

DR
AF

4.6

Tables 4.5–4.6 provide the definitions of the input and output parameters occurring in the
formulations.
Formulation

The total concentrations of algae biomass components follow from:

Calgt1 =
Calgt2 =

n
X

i=1
n
X

Calgi

(f dmi × Calgi )

i=1

Calgn =

Calgp =

n
X

i=1
n
X

(ani × Calgi )
(api × Calgi )

i=1

Calgsi =

n
X

(asii × Calgi )

i=1

Cchf =

n
X

(achfi × Calgi )

i=1

where:

achlf
an
ap
asi
Calg

stochiometric ratio of chlorophyll-a in organic matter [mgChf gC−1 ]
stochiometric ratio of nitrogen in organic matter [gN gC−1 ]
stochiometric ratio of phosphorus in organic matter [gP gC−1 ]
stochiometric ratio of silicate in organic matter [gSi gC−1 ]
concentration of biomass of algae species i [gC m−3 ]
b

116 of 464

Deltares

Primary producers

concentration of organic nitrogen in algae biomass [gC m−3 ]
b

concentration of organic phosphorus in algae biomass [gC m−3 ]
b

concentration of silicate in algae biomass [gC m−3 ]
total concentration of algae biomass [gC m−3 ]

b

b

total concentration of algae biomass [gDM m−3 ]
concentration of chlorophyll-a [mgChf m−3 ]

b

b

dry matter conversion factor [gDM gC−1 ]
index for algae species [-]
number of algae species, 6 for MONALG and GEMMPB, 2 for DYNAMO [-]

T

Calgn
Calgp
Calgsi
Calgt1
Calgt2
Cchl
f dm
i
n

DR
AF

Table 4.5: Definitions of the input parameters in the above equations for PHY_DYN. (i) is
a substance name, Green or Diat. Volume units refer to bulk ( ) or to water
( ).
b

w

Name in
formulas

Name in input1

Definition

Units

ani

N crat(i)

stochiometric ratio of nitrogen in algae
species (i)
stochiometric ratio of phosphorus in algae species (i)
stochiometric ratio of silicate in algae
species (i)
stochiometric ratio of chlorophyll-a in
green algae
stochiometric ratio of chlorophyll-a in diatoms

gN gC−1

concentration
species (i)

gC m−3

api
asii

P Crat(i)
SCrat(i)

achf1

GrT oChl

achf2

DiT oChl

Calgi

(i)

of

biomass

in

algae

f dmi

DM CF (i)

n

N AlgDynamo number of algae species in DYNAMO, de-

dry matter conversion factor for algae
species (i)

gP gC−1
gSi gC−1
gChl gC−1
gChl gC−1

b

gDM gC−1
-

fault=2, this should not be changed

Deltares

117 of 464

Processes Library Description, Technical Reference Manual

Table 4.6: Definitions of the output parameters in the above equations for PHY_DYN. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in input1

Definition

Units

Calgt1
Calgt2

P hyt
AlgDM

total algae biomass carbon concentration

gC m−3

total algae biomass dry matter concentration
concentration of organic nitrogen in algae
biomass
concentration of organic phosphorus in
algae biomass
concentration of silicate in algae biomass

gDM m−3

AlgN

Calgp

AlgP
AlgSi
Chlf a

gN m−3
b

gP m−3
b

gSi m−3
b

chlorophyll-a concentration

mgChf m−3
b

DR
AF

Calgsi
Cchf

b

T

Calgn

b

118 of 464

Deltares

Primary producers

Production and mortality of benthic diatoms S1/2 (DYNAMO)
PROCESS :

GROMRT_DS1, TF_DIAT, DL_DIATS1, RAD_DIATS1, MRTDIAT_S1,
MRTDIAT_S2, NRALG_S1

The primary production of algae in the sediment e.g. microphytobenthos is implemented for
benthic diatoms in sediment layer S1. Mortality of the diatoms occurs in layers S1 and S2.
Implementation

 DiatS1
 NH4, NO3, PO4 and Si

T

Processes GROMRT_DS1, TF_DIAT, DL_DIATS1, RAD_DIATS1, MRTDIAT_S1, MRTDIAT_S2
and NRALG_S1 have been implemented for the following substances:

These processes have been implemented for benthic diatoms according to the S1/2 approach
for the sediment, and can not be used for the layered sediment approach. The processes
affect the upper sediment layer S1, with one exception. The mortality process MRTDIAT_S2
affects layer S2.

DR
AF

4.7

The mineralisation rate for detrital nutrients are delivered by processes BMS1_DetN, BMS1_DetP
and BMS1_DetSi.
Table 4.7 provides the definitions of the input parameters occurring in the formulations.
Formulation

The production and mortality of diatom biomass (organic carbon)
The primary production rate is formulated as follows:

knp × M alg
A×H
knp = kgp − krsp
kgp = f dl × f rad × f nut × f tp × kpp20

Rnp =

f tp = ktp(T −20)

where:

A
f dl
f nut
f rad
f tp
H
kgp
knp
kpp20
krsp
ktp
M alg
Rnp
Deltares

surface area [m2 ]
daylength limitation function [-]
nutrient limitation function [-]
light limitation function [-]
production temperature function [-]
water depth [m]
gross primary production rate constant [d−1 ]
net primary production rate constant [d−1 ]
potential maximum production rate constant at 20 ◦ C [d−1 ]
total respiration rate constant [d−1 ]
temperature constant for production [-]
quantity of diatom biomass [gC]
net primary production rate [gC m−3 d−1 ]

119 of 464

Processes Library Description, Technical Reference Manual

water temperature [◦ C]

T

The limitation function for nutrients is given by:

f nut = M in(f n, f p, f si, 1.0)
(RmnS1 × (1 − f rnb) + (Cnn/(Cnn + Ksn)) × (Cnn/∆t)) × A × H
fn =
an × kpn × M alg
(RmpS1 + (Cph/(Cph + Ksp)) × (Cph/∆t)) × A × H
fp =
ap × kpn × M alg
(RmsiS1 + (Csi/(Csi + Kssi)) × (Csi/∆t)) × A × H
f si =
asi × kpn × M alg
Cnn = Cam + Cni
surface area [m2 ]
stoichiometric constant for N over C in diatom biomass [gN gC−1 ]
stoichiometric constant for P over C in diatom biomass [gP gC−1 ]
stoichiometric constant for Si over C in diatom biomass [gSi gC−1 ]
concentration of ammonium [gN m−3 ]
concentration of nitrate [gN m−3 ]
concentration of nutrient nitrogen [gN m−3 ]
concentration of dissolved phosphate [gP m−3 ]
concentration of dissolved silicate [gSi m−3 ]
nutrient limitation function [-]
nitrogen limitation function [-]
phosphorus limitation function [-]
silicon limitation function [-]
fraction of mineralisation rate N allocated to bacteria in sediment [-]
water depth [m]
half saturation constant for nutrient nitrogen [gN m−3 ]
half saturation constant for phosphate [gP m−3 ]
half saturation constant for silicate [gSi m−3 ]
quantity of diatom biomass [gC]
mineralisation rate for DETNS1 [gN m−3 d−1 ]
mineralisation rate for DETPS1 [gP m−3 d−1 ]
mineralisation rate for DETSiS1 [gSi m−3 d−1 ]

DR
AF

A
an
ap
asi
Cam
Cni
Cnn
Cph
Csi
f nut
fn
fp
f si
f rnb
H
Ksn
Ksp
Kssi
M alg
RmnS1
RmpS1
RmsiS1

T

where:

The limitation functions for daylength and light are given by:

min(DL, DLo)
 DLo
1.0 if (Is/Io) ≥ 1.0
f rad = Ib

if (Ib/Io) < 1.0
Io
f dl =

where:

DL
DLo
f dl
f rad
Io
Ib
120 of 464

daylength, fraction of a day [-]
optimal daylength [-]
daylength limitation function [-]
light limitation function [-]
optimal light intensity [W m−2 ]
light intensity at the bottom [W m−2 ]

Deltares

Primary producers

The above formulations do consider the availability of nutrients, and the uptake of nutrients
beyond availability is prevented.
The respiration rate is formulated as follows:

krsp = f gr × kgp + f tm × (1 − f gr) × kmr20
where:

f gr
f tm
kmr20
krsp

growth respiration factor [-]
mortality temperature function [-]
maintenance respiration constant at 20 ◦ C [d−1 ]
total respiration rate constant [d−1 ]

f tm × kmrt20 × M alg
A×H
(T −20)
f tm = ktm

DR
AF

Rmrt =

T

The mortality rate is formulated as follows:

where:

A
f tm
H
kmrt20
ktm
M alg
Rmrt
T

surface area [m2 ]
mortality temperature function [-]
water depth [m]
mortality rate constant at 20 ◦ C [d−1 ]
temperature constant for mortality [-]
quantity of diatom biomass [gC]
mortality rate [gC m−3 d−1 ]
water temperature [◦ C]

Uptake and release of nutrients

Algae in the sediment primarily consume dissolved nutrients released by the mineralisation of
detritus in the sediment. It is assumed that algae are able to take up all nutrients released. Uptake from the water column occurs when the mineralisation flux is not large enough to sustain
maximal production. Ammonium from the water column is consumed until the concentration
drops below a critical low concentration. Then nitrate is consumed too. The nutrients are
taken up (consumed) proportional to net primary production as follows:

Ruam = f ram × Run
Runi = (1 − f ram) × Run
RunS1 = M in(an × Rnp, (1 − f rnb) × Rmn1 )
Run = M ax((an × Rnp − RunS1 ), 0.0)
RupS1 = M in(ap × Rnp, RmpS1 )
Rup = M ax((ap × Rnp − RupS1 ), 0.0)
RusiS1 = M in(asi × Rnp, RmsiS1 )
Rusi = M ax((asi × Rnp − RusiS1 ), 0.0)

where:

an
ap
Deltares

stoichiometric constant for N over C in algae biomass [gN gC−1 ]
stoichiometric constant for P over C in algae biomass [gP gC−1 ]

121 of 464

Processes Library Description, Technical Reference Manual

stoichiometric constant for Si over C in algae biomass [gSi gC−1 ]
fraction of N consumed as ammonium [-]
fraction of mineralisation rate N allocated to bacteria in sediment [-]
ammonium uptake rate from the water column [gN m−3 d−1 ]
nitrate uptake rate from the water column [gN m−3 d−1 ]
nitrogen uptake rate from the water column [gN m−3 d−1 ]
nitrogen uptake rate from mineralisation DETNS1 [gN m−3 d−1 ]
phosphate uptake rate from the water column [gP m−3 d−1 ]
phosphate uptake rate from mineralisation DETPS1 [gP m−3 d−1 ]
silicate uptake rate from the water column [gSi m−3 d−1 ]
silicate uptake rate from mineralisation DETSiS1 [gSi m−3 d−1 ]
mineralisation rate for DETNS1 [gN m−3 d−1 ]
mineralisation rate for DETPS1 [gP m−3 d−1 ]
mineralisation rate for DETSiS1 [gSi m−3 d−1 ]
net primary production rate [gC m−3 d−1 ]

T

asi
f ram
f rnb
Ruam
Runi
Run
RunS1
Rup
RupS1
Rusi
RusiS1
RmnS1
RmpS1
RmsiS1
Rnp

Algae prefer ammonium over nitrate. The fraction of N consumed as ammonium follows from:

Cam
Cnn
if (Run × ∆t) ≤ (Cam − Camc ) then f ram = 1.0
else
(Cam − Camc ) + (Camc /(Camc + Cni)) × (Run × ∆t − Cam + Camc )
f ram =
Run × ∆t

where:

DR
AF

if Cam < Camc then f ram =

an
Cam
Camc
Cni
Cnn
f ram
Rnp
Run
∆t

stoichiometric constant for N over C in diatom biomass [gN gC−1 ]
concentration of ammonium [gN m−3 ]
critical concentration of ammonium [gN m−3 ]
concentration of nitrate [gN m−3 ]
concentration of nutrient nitrogen DIN [gN m−3 ]
fraction of N consumed as ammonium [-]
net primary production rate [gC m−3 d−1 ]
nitrogen uptake rate from the water column [gC m−3 d−1 ]
computational timestep [d]

The mortality flux is divided among three pools: dissolved inorganic substances (autolysis) in
the water column, fast decomposing detritus and slow decomposing detritus in the sediment

122 of 464

Deltares

Primary producers

(layer S1). Organic carbon and nutrients are released proportional to mortality as follows:

DR
AF

where:

T

Ran = f ra × an × Rmrt
Rap = f ra × ap × Rmrt
Rasi = f ra × asiRmrt
f rdet1
Rmc1 =
× Rmrt
(1 − f ra)
Rmn1 = f rdet1 × an × Rmrt
Rmp1 = f rdet1 × ap × Rmrt
Rmsi1 = f rdet1 × asi × Rmrt
f rdet1
) × Rmrt
Rmc2 = (1 −
(1 − f ra)
Rmn2 = (1 − f rdet1 − f ra) × an × Rmrt
Rmp2 = (1 − f rdet1 − f ra) × ap × Rmrt
Rmsi2 = (1 − f rdet1 − f ra) × asi × Rmrt

an
ap
asi
f ra
f rdet1
Ran
Rap
Rasi
Rmc1
Rmc2
Rmn1
Rmn2
Rmp1
Rmp2
Rmsi1
Rmsi2
Rmrt

stoichiometric constant for N over C in algae biomass [gN gC−1 ]
stoichiometric constant for P over C in algae biomass [gP gC−1 ]
stoichiometric constant for Si over C in algae biomass [gSi gC−1 ]
fraction released by autolysis [-]
fraction released to detritus DetXS1 [-]
nitrogen NH4 release due to autolysis [gN m−3 d−1 ]
dissolved phosphate PO4 release due to autolysis [gP m−3 d−1 ]
dissolved silicate Si release due to autolysis [gSi m−3 d−1 ]
detritus C release to DetCS1 due to mortality [gC m−3 d−1 ]
detritus C release to OOCS1 due to mortality [gC m−3 d−1 ]
detritus N release to DetNS1 due to mortality [gN m−3 d−1 ]
detritus N release to OONS1 due to mortality [gN m−3 d−1 ]
detritus P release to DetPS1 due to mortality [gP m−3 d−1 ]
detritus P release to OOPS1 due to mortality [gP m−3 d−1 ]
silicate release to DetSiS1 due to mortality [gSi m−3 d−1 ]
silicate release to OOSiS1 due to mortality [gSi m−3 d−1 ]
mortality rate [gC m−3 d−1 ]

Directives for use
 The nutrient-carbon ratios for diatoms in the sediment are the same as for diatoms in the
water column.

Deltares

123 of 464

Processes Library Description, Technical Reference Manual

Table 4.7: Definitions of the input parameters in the above equations for GROMRT_DS1,
TF_DIAT , DL_DIAT , RAD_DIAT S1, MRTDIAT_S1, MRTDIAT_S2 and
NRALG_S1.

Name in
input

Definition

Units

M alg

DiatS1

quantity of benthic diatom biomass

gC m−3

A

Surf

surface area

m2

an
ap
asi

N CRatDiat
P CRatDiat
SCRatDiat

stoich. const. N over C in diatom biomass
stoich. const. P over C in diatom biomass
stoich. const. Si over C in diatom biomass

gN gC−1
gN gC−1
gN gC−1

Cam
Camc
Cni
Cph
Csi

N H4
N H4Crit
N O3
P O4
Si

concentration of ammonium
critical conc. of ammonium for uptake
concentration of nitrate
concentration of dissolved phosphate
concentration of dissolved silicate

gN m−3
gN m−3
gN m−3
gP m−3
gSi m−3

DayL
OptDLDiaS1

daylength, fraction of a day
optimal daylength for benthic diatoms

-

GRespDiaS1
F rAutDiatS
F rDetDiatS
F rM inS1Bac

growth respiration factor
fraction released by autolysis
fraction released to detritus DetC/N/P/SiS1
frac. min. N allocated to sediment bacteria

-

Depth

water depth

m

Rad
RadSatDiS1

light intensity at water surface
optimal light intensity for benthic diatoms

W m−2
W m−2

kmr20
kmrt20
kpp20
ktm
ktp

M RespDiaS1
M rtSedDiat
P P M axDiaS1
T CDecDiat
T CGroDiat

maint. resp. const. at 20 ◦ C of diatoms
mortality constant at 20 ◦ C of diatoms
max. prod. constant at 20 ◦ C of diatoms
temp. constant for mortality of diatoms
temp. constant for production of diatoms

d−1
d−1
d−1
-

Ksn
Ksp
Kssi

KmDIN DiaS1 half satur. const. nitrogen for diatoms
KmP DiatS1 half satur. const. phosphate for diatoms
KmSiDiatS1 half satur. const. silicate for diatoms

gN m−3
gP m−3
gSi m−3

RmnS 1
RmpS 1
RmsiS 1

dM inDetN S1
dM inDetP S1
dM inDetSiS

mineralisation rate for DETNS1
mineralisation rate for DETPS1
mineralisation rate for DETSiS1

gN m−3 d−1
gP m−3 d−1
gSi m−3 d−1

T

T emp

water temperature

◦

∆t

Delt

computational timestep

d

f gr
f ra
f rdet1
f rnb
H
Ib
Io

DR
AF

DL
DLo

T

Name in
formulas

124 of 464

C

Deltares

Primary producers

Mortality and re-growth of terrestrial vegetation (VEGMOD)
PROCESSES :

VBM ORT ( I ), VB( I )_M RT 3W, VB( I )_M RT 3S, VBGROWTH( I ), VB( I )U PT,
VB( I )_U PT 3D, V B( I ) AVAIL N, VBS TATUS ( I )

T

The vegetation sub-model simulates the effects of the drowning and re-growth of vegetation
in water systems such as (man-made) reservoirs on water quality. The design of the module is generic to allow for a comprehensive processes content, but only the most essential
formulations for growth and mortality have been included. Starting from a standing stock of
biomasses for a number of vegetation cohorts (types, species, etc.), mortality due to inundation leads to the allocation of organic matter (C, N, P, S) to the POX1–3 and POX5 fractions
in water and sediment. Re-growth in areas ran dry may lead to the building up of a standing
stock of new vegetation biomass, the nutrients for which are withdrawn from the sediment.
A cohort is treated as a homogeneous entity in the model in terms of variables (state variable,
coefficients and mass fluxes). The number of vegetation cohorts in the model is limited to a
maximum 9. Various cohorts may be present in the same model grid cell. The total biomasses
of the cohorts are modelled as inactive substances expressed in grams carbon per m2 . These
not transported state variables only exist in the lower water layer. Additional output parameters provide total biomass for each cohort expressed in tonnes C per ha. The concurrent
organic nutrients (nitrogen, phosphorus, sulfur) in vegetation biomass are not modelled as
state variables, but as quantities derived from the carbon state variables using stoichiometric
ratio’s.

DR
AF

4.8

Each cohort of vegetation consists of the following above-ground and below-ground compartments: 1) stems, 2) foliage, 3) branches, 4) roots, 5) fine roots. The fractions of biomass
of these compartments for each vegetation cohort imposed as allocation factors are used to
calculate the fluxes of biomass turned over into the various detritus pools in the layers of the
water column and the sediment (Figure 4.4). Nutrients are stored in the compartments in
agreement with compartment specific stoichiometric constants.
Mortality starts after a lag time following inundation and proceeds according to a first-order
decay of living biomass. Foliage and fine roots are allocated to the detritus pools in the water
and sediment layers according to vegetation height and rooting depth.
Growth is calculated from a predefined growth curve, and will stop once a certain target
biomass is achieved (Figure 4.5). Growth may be limited by the quantities of nutrients available in the sediment according to rooting depth. Nitrogen is taken from ammonium (NH4,
preferred) and nitrate (NO3), phosphorus from dissolved and adsorbed phosphate (PO4,
preferred, and AAP), and sulfur from sulfate (SO4, preferred) and dissolved sulfide (SUD).
Carbon is taken up from the atmosphere. For each vegetation cohort (re-)growth may be prevented or allowed by means of two “option” parameters. In this way it can be manipulated that
initially present types do not (re-)grow.
Implementation
The processes of vegetation module VEGMOD have been implemented for the following substances:

 VB01, VB02, VB03, VB04, VB05, VB06, VB07, VB08, VB09
 POC1, PON1, POP1, POS1, POC2, PON2, POP2, POS2, POC3, PON3, POP3, POS3,
POC5, PON5, POP5, POS5

 NH4, NO3, PO4, AAP, SO4, SUD

Deltares

125 of 464

Processes Library Description, Technical Reference Manual

Processes VBMORT(i) calculate the mortality rates and the detritus release rates. Processes
VB(i)_MRT3W and VB(i)_MRT3S distribute the release rates among water and sediment layers. Processes VBGROWTH(i) calculates the growth rates as based on available nutrients in
the sediment. Processes VB(i)AVAILN determine the available quantities of the nutrients (N,
P, S), whereas processes VB(i)UPT and VB(i)_UPT3D calculate the nutrient uptake rates for
the sediment layers. Processes VBSTATUS(i) keep record of the inundation time, and set the
option parameters for growth and mortality (SWVB(i)Gro and SWVB(i)Mrt). (i) is the number
of a vegetation cohort (01–09).
Table 4.8 provides the definitions of the input parameters occurring in the formulations, and
Table 4.9 provides the output parameters.

T

Formulation
(Re-)Growth

DR
AF

The growth curve of a vegetation cohort is defined by 4 parameters; minimum biomass, maximum target biomass, cohort age where 50 % of maximum biomass is achieved and a factor for
the shape of the growth curve (Figure 4.5). The “target” attainable biomass is thus a function
of the age of the vegetation cohort. The actual biomass growth in each time step of the simulation is determined from the “target” attainable biomass for the current age and the actual
biomass. The calculation of growth starts with determination of the total attainable biomass
of each vegetation cohort as resulting from the growth curve:

M vega,i =
where:

ag
aghb
M vega
M vegmax
M vegmin
sf
i

(M vegmin,i − M vegmax,i )
+ M vegmax,i
1 + exp (sfi × (agi − aghb,i )/aghb,i )

age of vegetation [d]
age of vegetation when half of attainable biomass is reached [d]
attainable biomass in all compartments [gC.m−2 ]
maximum biomass in all compartments [gC.m−2 ]
minimum biomass in all compartments [gC.m−2 ]
shape factor of the growth function [-]
index for vegetation cohorts (1–9)

The initial vegetation biomass at the start of the simulation (t = 0) is computed from the
amount of vegetation biomass dry matter per ha. Optionally, a percentage of surface coverage
may be used in the calculation of initial biomass according to:

Mveg i = fa i × M veg0 ,i /dmci
where:

dmc
fa
M veg
M veg0

dry matter carbon ratio [gDM.gC−1 ]
percentage of area coverage [%]
actual biomass in all compartments [gC.m−2 ]
initial biomass in all compartments [tDM.ha−1 ]

If growth takes place (SWVB(i)Gro = 1.0), the potential (or target) growth rate of biomass per
vegetation cohort results from:

Rgrp,i = (M vega,i − M vegi )/∆t
where:

126 of 464

Deltares

Primary producers

Rgrp
∆t

potential growth rate of biomass in all compartments [gC.m−2 .d−1 ]
computational time step [d]

In a final step the growth is corrected for nutrient limitation. In case of nutrient limitation, the
above potential growth rates Rgr p,i are reduced to actual growth rates Rgr i in proportion with
the available quantity of the growth limiting nutrient. These actual growth rates are calculated
from the potential growth rates multiplied with the ratio of the available quantity of the most
limiting nutrient and the quantity of this nutrient needed to sustain the potential growth rates
(NutLimVB (i )).

T

When inundation occurs, the vegetation stops growing (SWVB (i)Gro = 0.0), and the vegetation age remains constant at the current age until inundation is over. When vegetation
growth is limited by a shortage of nutrients, vegetation growth and age are reduced accordingly. Initial age is calculated from the initial biomass using the formulation of the growth curve.
Age is reset to zero if the vegetation dies (see below).
Uptake of nutrients

DR
AF

Nutrients (N, P and S) are taken up by vegetation from the sediment within rooting depth,
whereas carbon is taken up from the atmosphere. The total uptake rates are computed using
vegetation cohort and biomass compartment specific carbon to nutrient ratios. The total uptake rates are distributed among the sediment layers within rooting depth proportional to the
quantities of the nutrients available in the layers (grid cells). The nutrient uptake rates result
from:

Ruplin = f nln × Rgri ×

5
X

(f bij /vnlij ) /H

j=1

Rupt,l =

9
nr
X
X
i=1

!

(Rupiln )

n=1

where:

fb
fn
H
Rgr
Rup
Rupt
vn
l
i
j
n

fraction of biomass in a compartment [-]
fraction of total available nutrient in a layer [-]
sediment layer thickness [-]
growth rate of biomass in all compartments [gC.m−2 .d−1 ]
uptake rate of nutrients in all compartments [gN/P/S.m−3 .d−1 ]
total uptake rate of nutrients in all compartments [gN/P/S.m−3 .d−1 ]
carbon nutrient ratio in vegetation biomass [gC.gN/P/S−1 ]
index for nutrient (1=nitrogen, 2=phosphorus, 3=sulfur)
index for vegetation cohorts (1–9)
index for biomass compartments (1=stem, 2=foliage, 3=branches, 4=roots, 5=fine
roots)
index for a sediment layer (nr = number of layer within rooting depth)

The quantities of available nutrients are derived the nutrient concentrations (Cam, Cni, Cph,
Cap, Csu, Csud) in the sediment layers within rooting depth. When not enough nutrient is
available to sustain potential growth, the growth rates have been reduced proportionally (see
above). In order to avoid numerical errors when all available nutrient would be depleted the
maximum fraction of the available nutrients that can be taken up in a time step can be made
smaller than 1.0 by means of input parameter VBFrMaxU.

Deltares

127 of 464

Processes Library Description, Technical Reference Manual

Mortality and detritus release
The onset of mortality from the start of the simulation can be imposed optionally, using option
parameter IniVB(i)Dec=1.0. If the duration of inundation exceeds a lag time defined as the
critical number of subsequent days with inundation, the vegetation cohorts in the inundated
area will start to die:

if SwEmersion = 0 .0 then ti = ti + ∆t else ti = 0 .0
if ti > ti c,i then ag i = 0 .0 and SwVB i Mrt = 0 .0
where:

T

ag
age of biomass [d]
ti
inundation period, the number of successive days of inundation [d]
tic
critical inundation period, the mortality lag time [d]
SwEmersion switch for inundation (0 = yes, 1 = no)
SwV B i M rt switch for mortality (0 = yes, 1 = no)
∆t
computational time step [d]
i
index for vegetation cohorts (1–9)

DR
AF

The lag time for mortality due to inundation is input to the model and not a function of local
conditions such as the dissolved oxygen concentration. The duration of inundation prior to the
simulation start time ti0 can be imposed.
Mortality results in the decrease of vegetation biomass and the transfer of vegetation biomass
to the particulate detritus fractions. Detritus from foliage, stems and branches goes to water
layers, detritus from fine roots and roots to sediment layers. The detritus release rates for each
sediment grid cell are computed using vegetation cohort and biomass compartment specific
carbon to nutrient ratios and the fraction of biomass allocated to a water or sediment layer.
This fraction is derived from vegetation height and rooting depth and the fractions of biomass
allocated to each of the five biomass compartments (see below). The mortality rate of the
vegetation biomass and the release rates of organic nutrients follow from:

Rmrti = kmrti × M vegi
Rmrdklij = f hi × f dkij × f bij × Rmrti /(vnlij × H)
where:

fb
fd
fh
H
kmrt
M veg
Rmrd
Rmrt
vn
k
l
i
j

fraction of biomass in a compartment [-]
fraction of biomass released into a specific detritus fraction [-]
fraction of biomass in a layer [-]
water layer or sediment layer thickness [-]
mortality rate constant [d−1 ]
actual biomass in all compartments [gC.m−2 ]
release rate of detritus [gC/N/P/S.m−3 .d−1 ]
mortality rate of biomass [gC.m−2 .d−1 ]
carbon nutrient ratio in vegetation biomass [gC.gC/N/P/S−1 ]
index for detritus fraction (1 = POX1, 2 = POX2, 3 = POX3, 5 = POX5)
index for carbon and nutrient (0 = carbon, 1 = nitrogen, 2 = phosphorus, 3 =
sulfur)
index for vegetation cohorts (1–9)
index for biomass compartments (1 = stem, 2 = foliage, 3 = branches, 4 = roots,
5 = fine roots)

The fractions fd for foliage and fine roots to POX1–3 are derived from input parameters. The
fractions fd for stems, branches and large roots to POX5 are equal to 1.0.

128 of 464

Deltares

Primary producers

Vertical distribution of the detritus release rates
In order to obtain vertical distributions of the detritus release rates, the biomass compartments
of each vegetation cohort are distributed virtually among the layers (grid cells) in each watersediment column. A distinction is made between the compartments in above-ground biomass
(foliage, branches, stems) and the compartments in below-ground biomass (roots, fine roots).
Above-ground biomass of each cohort has a vegetation height. Below-ground biomass of
each cohort has a rooting depth. Based on these parameters, the number of water layers and
sediment layers involved in the distribution are determined. Water layers above vegetation
height and sediment layers below rooting depth have zero biomass, and therefore zero detritus
release.

Fs i =

T

The distribution is determined from the total above-ground or the total below-ground biomass
per m2 using a distribution shape constant. The total above-ground and total below-ground
biomass is derived from the total biomass of a vegetation cohort and the biomass fractions in
the five compartments. The shape constant is given by:

Cveg i (z max ,i )
Mveg p,i /Hmax ,i



DR
AF

where:

Fs
shape constant for vertical distribution of biomass [-]
Cveg(zmax ) above-ground or under-ground biomass at zmax [gC.m−3 ]
M vegp
above-ground or under-ground biomass [gC.m−2 ]
Hmax
vegetation height (positive) or rooting depth (negative) [m]
zmax
water depth (positive) at vegetation height or sediment (negative) depth at rooti

ing depth [m]
index for vegetation cohorts (1–9)

The value of shape constant Fs varies from 0 to 2. When Fs = 0 the biomass Cveg is zero
at zmax, when Fs = 1 biomass Cveg is homogeneously distributed (constant over depth),
and when Fs = 2 biomass Cveg is zero at the sediment. For values of Fs between 0 and 1
biomass decreases towards vegetation height or rooting depth. For Fs -values between 1 and
2 the biomass decreases towards the sediment. The effects of F on the distribution appear
from Figure 4.6.
A linear distribution function is formulated using two constants, a and b. Both are fixed when
F is fixed because the integral of the biomass distribution must equal the total biomass. The
vertical distribution within the water column or the sediment column follows from:

Cveg i (z) = ai × z +b i
Mveg p,i
(2 − 2 × Fs i )
×
ai =
Hmax ,i
(Ht −z max ,i )
Mveg p,i
(Fs i × (zmax ,i +H t )−2 × zmax ,i )
bi =
×
Hmax ,i
(Ht −z max ,i )

The biomass fraction fh i in a layer n between zn and zn+1 follows from:

Z

zn+1

(Cvegi (z)/M vegi ) dz =
zn


A 2
zn+1 − zn2 + B (zn+1 − zn )
2

R zn+1
(Cveg i (z )/Mveg i ) dz
fh i = Rzznmax ,i
(Cveg i (z )/Mveg i ) dz
zn

Deltares

if zn > zmax ,i
if zn ≤ zmax ,i

129 of 464

Processes Library Description, Technical Reference Manual

with:

Z

zn+1

(Cvegi (z)/M vegi ) dz =
zn


A 2
zn+1 − zn2 + B (zn+1 − zn )
2

where:
above-ground or under-ground biomass at water or sediment depth z [gC.m−3 ]
fraction of biomass in a water or sediment layer [-]
total water depth or total sediment depth [m]
biomass in all compartments [gC.m−2 ]
above-ground or under-ground biomass [gC.m−2 ]
water depth (positive) or sediment depth (negative) at bottom of a layer [m]
index for vegetation cohorts (1–9)

For Fs = 1 the integral reduces to:

M vegp,i (zn+1 − zn )
×
M vegi
Hmax ,i

if zn > zmax ,i

DR
AF

f hi =

T

Cveg(z)
fh
Ht
M veg
M vegp
z
i

f hi =

M vegp,i (zmax ,i − zn )
×
M vegi
Hmax ,i

if zn < zmax ,i and

zn+1 > zmax ,i

Directives for use
1 Two options are available for the input of initial vegetation biomasses. For SwIniVB(i)=1.0
the model expects percentual coverage and initial biomass in tDM.ha−1 for each vegetation type. For SwIniVB(i)=0.0 the model expects biomasses in tDM.ha−1 for each
vegetation type for each grid cell.
2 The input for initial biomasses may be generated as a GIS map representing each model
grid cell, for instance based on a satellite image.
3 The option for the vertical distribution of biomass and detritus fluxes SWDisVB(i) overlaps the distribution shape factor FfacVB(i). If FfacVB(i)=1.0 SWDisVB(i) must equal 1.0
as well. The linear and exponential distributions (SWDisVB(i)=2.0 or 3.0) are not fully
implemented.
4 The option parameter IniVB(i)Dec can be used to impose mortality from the start of the
simulation. Default value 0.0 implies “no” mortality, value 1.0 causes mortality from the
start.
5 The maximum fraction of the available nutrients that can be taken up in a time step VBFrMaxU (<1.0) has a default value of 0.5. To avoid too strong nutrient limitation its value
can be increased, but one should verify that this does not cause numerical errors.
Table 4.8: Definitions of the input parameters in the above equations for VBMORT(i),
VB(i)_MRT3W, VB(i)_MRT3S, VBGROWTH(i), VB(i)UPT, VB(i)_UPT3D,
VB(i)AVAILN and VBSTATUS(i).

Name in
formulas1

Name in
input1

Definition

Units

aghb , i

HlfAgeVb(i)

age of veg. when half of attainable biomass
is reached

d

Cam
Cni
Cph

NH4
NO3
PO4

concentration of ammonium
concentration of nitrate
concentration of dissolved phosphate

gN.m−3
gN.m−3
gP.m−3

130 of 464

Deltares

Primary producers

Name in
input1
AAP
SO4
SUD

Definition

Units

concentration of adsorbed phosphate
concentration of sulfate
concentration of dissolved sulfide

gP.m−3
gS.m−3
gS.m−3

dmci

DMcfVB(i)

dry matter carbon ratio

gDM.gC−1

fai
fbij

IniCovVB(i)
F1VB(i)
F2VB(i)
F3VB(i)
F4VB(i)
F5VB(i)
FfolPOC1
FfolPOC2
FfrootPOC1
FfrootPOC2

percentage of area coverage
fraction of biomass in compartment 1 (stems)
fraction of biomass in comp. 2 (foliage)
fraction of biomass in comp. 3 (branches)
fraction of biomass in comp. 4 (roots)
fraction of biomass in comp. 5 (fine roots)
biomass fraction 2 (foliage) to detr. POX1
biomass fraction 2 (foliage) to detr. POX2
biomass fraction 2 (fine roots) to detr. POX1
biomass fraction 2 (fine roots) to detr. POX2

%
-

Fs

DR
AF

fd1i2
fd2i2
fd1i5
fd2i5

T

Name in
formulas1
Cap
Csu
Csud

FfacVB(i)

shape constant for vertical distr. of biomass

-

H
Hmax
Hmax
Ht
z
z
-

Depth
VegHeVB(i)
RootDeVB(i)
TotalDepth
LocalDepth
LocSedDept
Surf
Volume

water layer or sediment layer thickness
vegetation height (positive)
rooting depth (negative)
total water depth or total sediment depth
depth to the bottom of a water layer
depth to the bottom of a sediment layer
surface area of a grid cell
volume of a grid cell

m
m
m
m
m
m
m−2
m−3

kmrti

RcMrtVB(i)

mortality rate constant

d−1

Mveg
Mveg0
Mvegmax,i
Mvegmin,i

VB(i)
IniVB(i)
MaxVB(i)
MinVB(i)

vegetation biomass in all five compartments
initial biomass in all five compartments
maximum biomass in all five compartments
minimum biomass in all five compartments

gC.m−2
tDM.ha−1
gC.m−2
gC.m−2

sfi

SfVB(i)

shape factor of the growth function

-

SWEmersion
SWDisVB(i)
SwIniVB(i)
IniVB(i)Dec
SwRegrVB(i)

SWEmersion
SWDisVB(i)
SwIniVB(i)
IniVB(i)Dec
SwRegrVB(i)

switch for inundation (0 = yes, 1 = no)
option vert. distr. (1=const., 2=linear, 3=exp.)
option init. biomass (0=biomass,1=coverage)
option mort. at start of simul. (0=no, 1=yes)
option for re-growth (0=no, 1=yes)

-

VBFrMaxU

VBFrMaxU

max. fr. of nutrients taken up in a time step

-

vn1ij

CNF1VB(i)
CNF2VB(i)
CNF3VB(i)
CNF4VB(i)
CNF5VB(i)
CPF1VB(i)

carbon nitrogen ratio in comp. 1 (stems)
carbon nitrogen ratio in comp. 2 (foliage)
carbon nitrogen ratio in comp. 3 (branches)
carbon nitrogen ratio in comp. 4 (roots)
carbon nitrogen ratio in comp. 5 (fine roots)
carbon phosphorus ratio in comp. 1 (stems)

gC.gN−1
gC.gN−1
gC.gN−1
gC.gN−1
gC.gN−1
gC.gP−1

vn2ij

Deltares

131 of 464

Processes Library Description, Technical Reference Manual

Name in
input1
CPF2VB(i)
CPF3VB(i)
CPF4VB(i)
CPF5VB(i)
CSF1VB(i)
CSF2VB(i)
CSF3VB(i)
CSF4VB(i)
CSF5VB(i)

Definition

Units

carbon phosphorus ratio in comp. 2 (foliage)
carbon phos. ratio in comp. 3 (branches)
carbon phosphorus ratio in comp. 4 (roots)
carbon phos. ratio in comp. 5 (fine roots)
carbon sulfur ratio in comp. 1 (stems)
carbon sulfur ratio in comp. 2 (foliage)
carbon sulfur ratio in comp. 3 (branches)
carbon sulfur ratio in comp. 4 (roots)
carbon sulfur ratio in comp. 5 (fine roots)

gC.gP−1
gC.gP−1
gC.gP−1
gC.gP−1
gC.gS−1
gC.gS−1
gC.gS−1
gC.gS−1
gC.gS−1

tic,i
ti0,i

CrnsfVB(i)
Initnsfd

critical inundation period, mortality lag time
inundation period prior to sim. start time

d
d

∆t

Delt

computational time step

d

vn3ij

T

Name in
formulas1

1)

DR
AF

i=1–9 or (i)=01–09 is the vegetation cohort number; j=1–5 is the biomass compartment
number.

Table 4.9: Definitions of the additional output parameters for VBMORT(i), VB(i)_MRT3W,
VB(i)_MRT3S, VBGROWTH(i), VB(i)UPT, VB(i)_UPT3D, VB(i)AVAILN and VBSTATUS(i).

Name in
formulas1

Name in
output1

Definition2

Units

tii

AgeVB(i)

age of vegetation biomass

d

fNVB(i)UP
fPVB(i)UP
fSVB(i)UP
fN1VB(i)UPy
fN2VB(i)UPy
fP1VB(i)UPy
fP2VB(i)UPy
fS1VB(i)UPy
fS2VB(i)UPy

N vegetation uptake flux
P vegetation uptake flux
S vegetation uptake flux
ammonium N vegetation uptake flux
nitrate N vegetation uptake flux
dissolved phosphate P vegetation uptake flux
adsorbed phosphate P vegetation uptake flux
sulfate S vegetation uptake flux
dissolved sulfide S vegetation uptake flux

gN.m−2 .d−1
gP.m−2 .d−1
gS.m−2 .d−1
gN.m−2 .d−1
gN.m−2 .d−1
gP.m−2 .d−1
gP.m−2 .d−1
gS.m−2 .d−1
gS.m−2 .d−1

fC1VB(i)P5
fN1VB(i)P5
fP1VB(i)P5
fS1VB(i)P5
fC2VB(i)P1
fN2VB(i)P1
fP2VB(i)P1
fS2VB(i)P1
fC2VB(i)P2
fN2VB(i)P2
fP2VB(i)P2
fS2VB(i)P2
fC2VB(i)P3

C flux from biomass comp. 1 to detritus POC5
N flux from biomass comp. 1 to detritus POC5
P flux from biomass comp. 1 to detritus POC5
S flux from biomass comp. 1 to detritus POC5
C flux from biomass comp. 2 to detritus POC1
N flux from biomass comp. 2 to detritus POC1
P flux from biomass comp. 2 to detritus POC1
S flux from biomass comp. 2 to detritus POC1
C flux from biomass comp. 2 to detritus POC2
N flux from biomass comp. 2 to detritus POC2
P flux from biomass comp. 2 to detritus POC2
S flux from biomass comp. 2 to detritus POC2
C flux from biomass comp. 2 to detritus POC3

gC.m−3 .d−1
gN.m−3 .d−1
gP.m−3 .d−1
gS.m−3 .d−1
gC.m−2 .d−1
gN.m−2 .d−1
gP.m−2 .d−1
gS.m−2 .d−1
gC.m−2 .d−1
gN.m−2 .d−1
gP.m−2 .d−1
gS.m−2 .d−1
gC.m−2 .d−1

-

-

132 of 464

Deltares

Primary producers

Definition2

Units

N flux from biomass comp. 2 to detritus POC3
P flux from biomass comp. 2 to detritus POC3
S flux from biomass comp. 2 to detritus POC3
C flux from biomass comp. 3 to detritus POC5
N flux from biomass comp. 3 to detritus POC5
P flux from biomass comp. 3 to detritus POC5
S flux from biomass comp. 3 to detritus POC5
C flux from biomass comp. 4 to detritus POC5
N flux from biomass comp. 4 to detritus POC5
P flux from biomass comp. 4 to detritus POC5
S flux from biomass comp. 4 to detritus POC5
C flux from biomass comp. 5 to detritus POC1
N flux from biomass comp. 5 to detritus POC1
P flux from biomass comp. 5 to detritus POC1
S flux from biomass comp. 5 to detritus POC1
C flux from biomass comp. 5 to detritus POC2
N flux from biomass comp. 5 to detritus POC2
P flux from biomass comp. 5 to detritus POC2
S flux from biomass comp. 5 to detritus POC2
C flux from biomass comp. 5 to detritus POC3
N flux from biomass comp. 5 to detritus POC3
P flux from biomass comp. 5 to detritus POC3
S flux from biomass comp. 5 to detritus POC3

gN.m−2 .d−1
gP.m−2 .d−1
gS.m−2 .d−1
gC.m−3 .d−1
gN.m−3 .d−1
gP.m−3 .d−1
gS.m−3 .d−1
gC.m−3 .d−1
gN.m−3 .d−1
gP.m−3 .d−1
gS.m−3 .d−1
gC.m−2 .d−1
gN.m−2 .d−1
gP.m−2 .d−1
gS.m−2 .d−1
gC.m−2 .d−1
gN.m−2 .d−1
gP.m−2 .d−1
gS.m−2 .d−1
gC.m−2 .d−1
gN.m−2 .d−1
gP.m−2 .d−1
gS.m−2 .d−1

Rgri

fVB(i)

actual vegetation biomass growth rate

gC.m−2 .d−1

NutLimVB(i)

NutLimVB(i)

nutrient limitation factor for growth (≤ 1.0)

-

-

VB(i)ha
VB(i)Aha

vegetation biomass density
attainable vegetation biomass density

tC.ha−1
tC.ha−1

VB(i)Navail
VB(i)Pavail
VB(i)Savail

available nutrient N within rooting depth
available nutrient P within rooting depth
available nutrient S within rooting depth

gN.m−2
gP.m−2
gS.m−2

DR
AF

-

T

Name in
output1
fN2VB(i)P3
fP2VB(i)P3
fS2VB(i)P3
fC3VB(i)P5
fN3VB(i)P5
fP3VB(i)P5
fS3VB(i)P5
fC4VB(i)P5
fN4VB(i)P5
fP4VB(i)P5
fS4VB(i)P5
fC5VB(i)P1
fN5VB(i)P1
fP5VB(i)P1
fS5VB(i)P1
fC5VB(i)P2
fN5VB(i)P2
fP5VB(i)P2
fS5VB(i)P2
fC5VB(i)P3
fN5VB(i)P3
fP5VB(i)P3
fS5VB(i)P3

Name in
formulas1

SWVB(i)Gro
SWVB(i)Mrt

SWVB(i)Dec switch continuation mortality (0 = no, 1 = yes)
SWVB(i)Gro switch for growth (0 = no, 1 = yes)
SWVB(i)Mrt switch for mortality (0 = no, 1 = yes)

-

1)

(i)=01–09 is the vegetation cohort number; j=1–5 is the biomass compartment number.
Vegetation biomass compartments are 1=stems, 2=foliage, 3=branches, 4=roots and
5=fine roots.
2)

Deltares

133 of 464

DR
AF

T

Processes Library Description, Technical Reference Manual

Figure 4.4: Interactions between the compartments of a vegetation cohort (left side,
green) and the detritus fractions POC1–5/DOC in the model (particulate
fractions brown, dissolved fraction blue). Similar schemes apply to PON1–
5/DON, POP1–5/DOP and POS1–5/DOS.

Figure 4.5: The growth curve of a vegetation cohort (y -axis) as a function of it’s age is a
function of 4-parameters: minimum biomass (MIN), maximum target biomass
(MAX), cohort age where 50 % of maximum biomass is achieved (b) and a
factor indicating how ‘smooth’ the growth curve is (s).

134 of 464

Deltares

Primary producers

(a)

(b)

DR
AF

T

Figure 4.6: The effect of shape constant Fs(F ) on the distribution of vegetation biomass
above the sediment (a) and vegetation biomass in the sediment (b). The
symbols used are explained in the text (T = Ht ).

Deltares

135 of 464

DR
AF

T

Processes Library Description, Technical Reference Manual

136 of 464

Deltares

5 Macrophytes
Contents
5.1.1

Relation macrophyte module and other DELWAQ processes . . . . 138

5.1.2

Growth forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

5.1.3

Plant parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

5.1.4

Usage note . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

5.1.5

Different macrophyte growth forms

. . . . . . . . . . . . . . . . . 140

Growth of submerged and emerged biomass of macrophytes . . . . . . . . 144
5.2.1

Nutrient limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

5.2.2

Uptake of carbon, nitrogen and phosphorus from rhizomes . . . . . 145

5.2.3

Daylength limitation

5.2.4

Temperature limitation . . . . . . . . . . . . . . . . . . . . . . . . 147

5.2.5

Decay of emerged and submerged biomass

5.2.6

Growth of the rhizomes/root system . . . . . . . . . . . . . . . . . 148

5.2.7

Formation of particulate organic carbon . . . . . . . . . . . . . . . 149

5.2.8

Uptake of nitrogen and phosphorus from sediment . . . . . . . . . 150

5.2.9

Uptake of nitrogen and phosphorus from water . . . . . . . . . . . 151

. . . . . . . . . . . . . . . . . . . . . . . . . 146
. . . . . . . . . . . . 148

DR
AF

5.2

Framework of the macrophyte module . . . . . . . . . . . . . . . . . . . . 138

T

5.1

5.2.10 Oxygen production and consumption . . . . . . . . . . . . . . . . 151
5.2.11 Net growth of emerged and submerged vegetation and rhizomes . 152

5.3

5.4

5.5
5.6

Maximum biomass per macrophyte species . . . . . . . . . . . . . . . . . 153

5.3.1

Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

5.3.2

Hints for use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

Grazing and harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

5.4.1

Grazing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

5.4.2

Hints for use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

5.4.3

Harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

Light limitation for macrophytes . . . . . . . . . . . . . . . . . . . . . . . . 158
Vegetation coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

5.6.1

5.7

Deltares

Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Vertical distribution of submerged macrophytes . . . . . . . . . . . . . . . 161

5.7.1

Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

5.7.2

Hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

137 of 464

DR
AF

T

Processes Library Description, Technical Reference Manual

Figure 5.1: Interactions between the nutrient cycles and the life cycle of macrophytes.

5.1
5.1.1

Framework of the macrophyte module

Relation macrophyte module and other DELWAQ processes

Many processes are acknowledged to be of importance to the development of macrophytes
and their interaction with the environment:









Light climate
Sedimentation and resuspension
Nutrient dynamics
Oxygen and carbon cycles
Diurnal processes
Food web structures
Chemical processes within the root zone

Figure 5.1 gives an overview of the most important fluxes that exist within and between macrophytes and their abiotic surroundings. It also indicates which relevant processes are already
included in D-Water Quality and which fluxes (and processes within macrophytes/ macrophyte stands) are newly included in the D-Water Quality macrophyte module. The internal
processes of transport between different functional parts of macrophytes (being emerged,
submerged and root sections of the plant) play an important role too. The development of
biomass is directly linked to the fluxes between the macrophyte stands and the open water
plus sediment as modelled in D-Water Quality (e.g. nutrient uptake for growth, uptake of CO2 ).

138 of 464

Deltares

Macrophytes

Growth forms

T

In the Macrophytes Module macrophytes can be described based on their growth forms by
selecting to include sections of the plants: emerged, submerged and root sections. Five
growth forms have been selected as examples (Figure 5.2). For each category a few species
growing in Western Europe are given as examples.

Figure 5.2: The different macrophytes growth forms that can be modeled with the Macrophyte Module.

DR
AF

5.1.2

The different macrophytes growth forms that can be modeled with the Macrophyte Module.
1 Helophytes like the common reed Phragmites australis, the cattail or Typhaceae family
and the arrowhead Sagittaria saggittifolia.
2 Eloidids: The submerged angiosperms like the sago pondweed Potamogeton pectinatus,
the common waterweed Elodea canadensis and the Eurasian water-milfoil Myriophyllum
spicatum.
3 Charids: The submerged macro-algae like the stoneworts Chara sp. Chara sp. can also
be modeled with the BLOOMmodule, which models the phytoplankton production in DWater Quality). The coefficients concerning this species are also given separately from
the other submerged species.
4 Lemnids: The emerged, non-rooted species like the lesser duckweed Lemna minor, the
star duckweed Lemna gibba and the water fern Azolla filiculoides.
5 The emerged rooted species like the Nympheaceae family: the white water lily Nymphea
alba, the spatter-dock Nuphar lutea and the yellow floating-heart Nymphoides peltata.
The distinction between emerged and submerged macrophytes is especially important because they have different interactions with water quality processes. The major changes concern the nutrient uptake strategies, the dependence on light availability and the sedimentation/erosion processes (Calow and Petss, 1992; ?; Scheffer, 1998). Emerged sections of
macrophytes can fully cover the water surface and thereby block light penetration and aeration, though oxygen is still released of course into the water via photosynthesis. Submerged
macrophytes on the other hand, are strongly dependent on the light climate and growth is
limited through shading. They too can shade lower parts, but influence on aeration processes
is not modelled. During their life cycle or seasons some plants may change strategy from
submerged to emerged (e.g. Nympheaceae). Thus, a good understanding of the life cycle is
essential when they are to be included in the macrophyte modelling.
Note that the emerged, non-rooted species can also be affected by drift due to winds. This
process is not included in the macrophyte module.

Deltares

139 of 464

T

Processes Library Description, Technical Reference Manual

5.1.3

DR
AF

Figure 5.3: The abbreviations for the parts of the vegetation that are used in the equations.

Plant parts

In the formulas a single species i can consist of emerged parts and/or submerged parts and/or
root-rhizome parts. The emerged part is indicated by EMi , the submerged part by SMi and
the root-rhizome by RHi . Please note that EMi , SMi and RHi refer to the same species i.
This is illustrated in Figure 5.3. The submerged section SMi can be subdivided over multiple
layers in case of a vertically differentiated model (see ??).
5.1.4

Usage note

There can be a strong variation in some of the coeffcients (when adopting those from literature) due to local settings. Especially the coefficient values concern the macrophytes nutrients
uptake and release, the life span and the macrophytes density are prone to local variation. We
recommend appropriate validation of the module for each new application.
5.1.5

Different macrophyte growth forms

This section provides a detailed description of the various forms in which aquatic macrophytes
can grow.

140 of 464

Deltares

Macrophytes

Emerged macrophytes
Emerged macrophytes take up nutrients from the roots and the rhizome exclusively (?). They
contribute to removing some important quantities of nutrients from the sediment, because of
that they are often called helophytes filters. Nevertheless some researchers suspect that they
are not directly taking up nutrients, but that the epiphytic community that they often shelter
is responsible for it. Because of these properties, emerged plants are often grown and harvested in the area of Waste Water Treatment Plants (WWTP) in order to remove the excess
of nutrients. But the nutrients are translocated from shoots and leaves to rhizome and roots
during autumn, so the harvesting is only efficient if done before this translocation (?). The
decomposition of the organic matter, and especially of the rhizome (*), which contains a lot
of carbohydrates reserves, is slow for the emerged plant since they have tissue resistance to
microbiological attacks (?).

DR
AF

T

As their growth is not limited by light extinction, they can reach some very dense stands stage.
Their rhizome, stems, and leaves also contribute to the limitation of the wave and wind impact
and therefore to the stabilization of the sediment in the area where they grow; emerged plants
are also acting as a sediment trap (?). Moreover those plants are also a source of feeding
and a refuge for a lot of bird species.
Water type and habitat: shoreline or even wet ground, out of water of marshy shores; marshes,
ponds, lakes, ditches, streams and estuaries with running or standing waters.
Submerged macrophytes

In general submerged macrophytes take up most of the nutrients from the rhizome and roots
system and little directly from the water (??). It has been demonstrated that in the case
of Myriophyllum exalbescens there is an uptake by the leaves but that the foliar uptake of
Phosphorus goes much faster when the concentration in the water increases (?). The mineralization of the organic matter is quite fast since the roots of the submerged plants are finer
compared to the emerged plants, and don’t have a storage system like the emerged plants.
Their growth can be limited by light availability even in shallow lakes. On the other hand their
roots, leaves and stems contributes to the increase of the resistance to the water flow and
consequently to the increase of sedimentation of suspended particles. The result is the maintenance of water transparency, a factor which itself influences the probability of colonization
by submerged macrophytes. The increase of sedimentation concern notably the nutrients
associated with particles: therefore nutrients are buried in the sediment layer faster and consequently the amount of nutrients in the water remains lower than in more open deep water
bodies.
Many submerged plants like the pondweeds are a very important source of food for the wildlife.
Water type: alkaline fresh to brackish, running or standing water (for Potamogeton sp.)
Habitat: usually found entirely underwater. Can grow from shallow water to depths greater
than ten meters in case of very clear water.

Deltares

141 of 464

Processes Library Description, Technical Reference Manual

Submerged macroalgae

T

The plant-like macroalgae like the Characeae family do not have a real root system and take
up more nitrogen from the water than from the sediment, (?) and there are indications that the
water nutrient concentration can be lowered widely by their presence. In certain cases they
seem to improve the water transparency significantly, especially because they are stabilizing
the sediment and therefore limiting its resuspension (see section II.2.B. on submerged plants).
They grow faster than the submerged plants. Besides, Characeae have the peculiarity to
disperse by detaching from the substrate and emerging above water with the current. In the
already existing BLOOM module (*) of Delwaq, Chara sp. is modeled in this particular growth
form whereas in the macrophyte module, Chara sp. is modeled as an emerged "rooted" plant
at which a very small root biomass is attributed, since in the reality the root system is very
reduced and it tends to lie on or just above the sediment. Chara sp. will be included in the
submerged plant category in the Macrophyte module, but since it possesses some special
features and coefficient, the set of coefficient has been defined properly in the table 8 in
section II.3.C.

DR
AF

Water type: Fresh to brackish hard water.
Habitat: They are found from shallow water to very deep areas in clear water. Their presence
is generally a sign of good ’health’ of the ecosystem.
Emerging non-rooted macrophytes

Emerging non rooted macrophytes, like duckweeds, take up nutrients from the water column
and are also able to transform the diazote directly from the atmosphere. They usually grow
in rather nutrient-rich waters and can remove a lot of nutrients from the water during their
growth that they release during the decay phase. These plants can grow and reproduce very
quickly when the environmental conditions are adequate, and they have a very short life span
(*) compared to the other macrophytes: the Lemnids can decompose to 50 % of the original
biomass within 10 to 20 days (?).
As their name indicates, the emerging-non-rooted plants are laying in the surface of the water
and consequently can block the light up to 99 percent. They might over compete with the submerged plant, but they are more often found on the shore, in between other macrophytes. In
the model they are not considered to be light-limited, even if in the reality they can sometimes
be seen forming layers on top of each other and consequently auto-competing for the light,
which is necessary for the photosynthesis.
The emergent non-rooted plants are an important source of feeding for the water fowls.
Water type: Still and slow moving waters in many nutrient-rich freshwater.
Habitat: Often found along the shoreline. Sometimes form extensive green mats on the water
surface.

142 of 464

Deltares

Macrophytes

Emerged and submerged-rooted macrophytes
Emergent-rooted macrophytes take up most of the nutrients from the sediment by the rhizome
and roots system which is very developed.
They block the light penetration in the water by multiplication on top of the water column, so
that no submerged species are able to grow below these plants since no photosynthesis is
possible in absence of light. The Nympheaceae can sometimes grow on top of each other
and auto-compete for light, but they are not limited by light availability in the model. [TODO:
Rudy’s remark]

T

The seeds constitute a direct food source for birds like waterfowls and the leaves for mammals
like beavers, muskrats, porcupines and deer and provides spawning habitat for fishes (Aquatic
Plant Identification Manual for Washington’s Freshwater Plants, year?).
Water type: shallow, still or slowly moving water in ponds, lakes, swamps, rivers, canals and
ditches.
Habitat: They often form a band along the shallow lake in rich organic sediment.

DR
AF

Emerging submerged non-rooted macrophytes

These plants have emerged parts, while their root system is in the water, but there are exceptions since for example the water soldier (Stratiotes aloides) has a submerged phase in winter
and is only ermergent in summer (see beginning of section II.2.). It requires specific conditions like peat soil and large humic layer, which could correspond to a filling-up stage of the
water body. Moreover the life cycle is rather complex since the shoots formed by vegetative
reproduction sink on the ground in winter and float again in early summer (?). Other classifications like the one from ?, adapted from ? put this category in the emergent unattached
growth form.
Water type and Habitat: stagnant water with organic sediment.

Deltares

143 of 464

Processes Library Description, Technical Reference Manual

Growth of submerged and emerged biomass of macrophytes
PROCESS :

M ACRO P HYTI

The growth rate is calculated via the following formula:
If EMi < M axEMi

T

The start of the growing season depends on the water temperature and the light climate
under water. The growth function differs for emerged and submerged vegetation. In both
cases the potential growth is limited by several factors: light climate, nutrient availability, water
temperature. The growth of submerged macrophytes can stop at a certain maximum due to
light limitation by means of self shading (?). The growth of submerged macrophytes will stop
when a maximum amount of biomass is reached. In order to get a quick start at the beginning
of the growing season, the growth of submerged macrophytes depends on the sum of the
submerged biomass at the beginning of the growing season and the biomass stored in the
rhizomes.

GrowthEMi =(EMi + RHi ) × M axGrowthEMi × LimLightEMi
× LimT EMi × LimAgeEMi
Else

DR
AF

5.2

(5.1)

GrowthEMi = 0
If SMi < M axSMi

GrowthSMi =(SMi + RHi ) × M axGrowthSMi × LimLightSMi
× LimT SMi × LimAgeSMi
Else

GrowthSMi = 0
where:

SMi
GrowthSMi
MaxGrowthSMi
LimLightSMi
LimTSMi
EMi
GrowthEMi
MaxEMi
MaxGrowthEMi
LimNutEMi
LimTEMi

Biomass of submerged (SM) species i
Growth of SM species i
Potential growth rate of SM species i
Light limitation factor SM species i
Temperature limitation factor SM species i
Biomass of emerged species (EM) i
Growth of EM species i
Maximum biomass of EM species i
Potential growth rate of EM species i
Nutrient limitation factor EM species i
Temperature limitation factor EM species i

[g C·m−2 ]
[g C·m−2 ·d−1 ]
[d−1 ]
[-]
[-]
[g C·m−2 ]
[g C·m−2 ·d−1 ]
[g C·m−2 ]
[d−1 ]
[-]
[-]

The limitation factors are explained in the following subsections.

144 of 464

Deltares

Macrophytes

5.2.1

Nutrient limitation
The growth of emerged non-rooted vegetation, such as duck weeds (e.g. Lemna spp.) can
be limited by low dissolved nitrogen and phosphorus concentrations in surface water (?). The
growth of rooted vegetation is not limited by nutrients, for the Dutch shallow eutrophic lakes
situation (REF). For aquatic macroalgae such as Chara and other species uptaking nutrients
predominantly from the water column nutrients can become limiting, although in naturally
eutrophic systems such as the Netherlands this is not very likely (REF). The limitation function
computed on the basis of a half saturation concentration.

N H4
(5.2)
N H4 + N H4hsEMi
N O3
LimN O3EMi =
N O3 + N O3hsEMi
P O4
LimP O4EMi =
P O4 + N O3hsEMi
LimN utEMi = min(LimP O4EMi , max(LimN H4EMi , LimN O3EMi ))

T

LimN H4EMi =

DR
AF

where:
NH4
NH4hsEMi
LimNH4EMi
NO3
NO3hsEMi
LimNO3EMi
PO4
PO4hsEMi
LimPO4EMi
LimNutEMi
5.2.2

Ammonia concentration
Half saturation concentration NH4 for growth of EM species i
Ammonium limitation factor for EM species i
Nitrate concentration
Half saturation concentration NO3 for growth of EM species i
Nitrate limitation factor for EM species i
Ortho-phosphorus concentration
Half saturation concentration PO4 for growth EMi
Phosphorus limitation factor for EM species i
Nutrient limitation factor for EM species i

[g N·m−3 ]
[g N·m−3 ]
[-]
[g N·m−3 ]
[g N·m−3 ]
[-]
[g P·m−3 ]
[g N·m−3 ]
[-]
[-]

Uptake of carbon, nitrogen and phosphorus from rhizomes

The energy stored in the rhizome/root system in the form of glucose (carbon) is the first
source for the growth of submerged vegetation in early spring. When the nitrogen in the
rhizomes is exhausted, the vegetation will switch to the uptake of nutrients via the roots (see
also Subsection 5.2.8). Uptake is regarded as negative translocation. The uptake of carbon
and nutrients from the rhizome continues until a certain minimum biomass has been reached.
The total uptake of nutrients from the sediment by all modelled macrophyte types is then used
for calculating the nutrient content of the sediment.
If (GrowthEMi + GrowthSMi ) × dt < (RHi − RHmini )

CtranslocRHtoEMi =GrowthEMi
CtranslocRHtoSMi =GrowthSMi

(5.3)

Else

CtranslocRHtoEMi =0
CtranslocRHtoSMi =0
If (GrowthEMi × N CratEMi + GrowthSMi × N CrateSMi ) × dt < (N RHi −

N RHmini )
N translocRHtoEMi =GrowthEMi × N CratEMi
N translocRHtoSMi =GrowthSMi × N CratSMi

Deltares

(5.4)

145 of 464

Processes Library Description, Technical Reference Manual

Else

N translocRHtoEMi =0
N translocRHtoSMi =0
If (GrowthEMi × P CratEMi + GrowthSMi × P CrateSMi ) × dt < (P RHi −

P RHmini )
P translocRHtoEMi =GrowthEMi × P CratEMi
P translocRHtoSMi =GrowthSMi × P CratSMi

(5.5)

P translocRHtoEMi =0
P translocRHtoSMi =0
where:

5.2.3

Rhizome species i
Critical biomass of RH species i
Timestep of computation
Translocation of C from RH to EM species i
Translocation of C from RH to SM species i
Nitrogen content of rhizome
Critical nitrogen content of RH species i
Translocation of N from RH to EM species i
Translocation of N from RH to SM species i
Nitrogen-carbon ratio of EM species i
Nitrogen-carbon ratio of SM species i
Phosphorus content of RH species i
Critical phosphorus content of RH species i
Translocation of P from RH to EM species i
Translocation of P from RH to SM species i
Phosphorus-carbon ratio of EM species i
Phosphorus-carbon ratio of SM species i

[g C·m−2 ]
[g C·m−2 ]
[d]
[g C·m−2 ·d−1 ]
[g C·m−2 ·d−1 ]
[g N·m−2 ]
[g N·m−2 ]
[g N·m−2 ·d−1 ]
[g N·m−2 ·d−1 ]
[g N·g C−1 ]
[g N·g C−1 ]
[g P·m−2 ]
[g P·m−2 ]
[g P·m−2 ·d−1 ]
[g P·m−2 ·d−1 ]
[g P·g C−1 ]
[g P·g C−1 ]

DR
AF

RHi
RHmini
dt
CtranslocRHtoEMi
CtranslocRHtoSMi
NRHi
NRHmini
NtranslocRHtoEMi
NtranslocRHtoSMi
NCratEMi
NCratSMi
PRHi
PRHmini
PtranslocRHtoEMi
PtranslocRHtoSMi
PCratEMi
PCratSMi

T

Else

Daylength limitation

The daylength function for macrophytes differs from the method that is applied for algae. The
daylength limitation function for macrophytes becomes zero below a certain threshold value:
If DL < M inDLEMi

LimDLEMi = 0

(5.6)

If M inDLEMi < DL < OptDLEMi

LimDLEMi =

DL − M inDLEMi
OptDLEMi − M inDLEMi

(5.7)

If DL > OptDLEMi

LimDLEMi = 1

(5.8)

The daylength limitation functions are the same for submerged macrophytes:

146 of 464

Deltares

Macrophytes

If DL < M inDLSMi

LimDLSMi = 0

(5.9)

If M inDLSMi < DL < OptDLSMi

LimDLSMi =

DL − M inDLSMi
OptDLSMi − M inDLSMi

(5.10)

If DL > OptDLSMi

LimDLSMi = 1

5.2.4

[d]
[-]
[-]
[d]
[d]
[d]
[d]

T

Daylength
Daylength limitation factor for EM species i
Daylength limitation factor for SM species i
Optimum daylength for EM species i
Optimum daylength for SM species i
Minimum daylength for EM species i
Minimum daylength for SM species i

DR
AF

DL
LimDLEMi
LimDLSMi
where: OptDLEMi
OptDLSMi
MinDLEMi
MinDLSMi

(5.11)

Temperature limitation

Growth rates increase when the water temperature exceeds 20 ◦ C and decreases when the
water temperature drops below 20 ◦ C. Below a certain critical temperature, the growth stops
altogether.
If T > T critEMi

LimT EMi = KT 20 EMiT −20

Else

LimT EMi = 0

(5.12)

If T > T critSMi

LimT SMi = KT 20 SMiT −20

Else

LimT SMi = 0

(5.13)

where:
T
TcritEMi
LimTEMi
KT 20 EMi
TcritSMi
LimTEMi
KT20 SMi

Deltares

Temperature
Critical temperature for growth EM species i
Temperature limitation factor for EM species i
Temperature coefficient for EM species i
Critical temperature for growth SM species i
Temperature limitation factor for SM species i
Temperature coefficient for SM species i

[◦ C]
[◦ C]
[-]
[-]
[◦ C]
[-]
[-]

147 of 464

Processes Library Description, Technical Reference Manual

5.2.5

Decay of emerged and submerged biomass
The decay of emerged and submerged biomass occurs during the autumn and winter. The
decay flux is temperature dependent. The decay is limited to the autumn and winter, the
process is regulated by the daylength function that is also used for the growth process.

DecayEMi =K1DecayEMi × EMi × (1 − LimDLEMi ) × KDecayT 20 EMiT −20
DecaySMi =K1DecaySMi × SMi × (1 − LimDLSMi ) × KDecayT 20 SMiT −20
(5.14)
where:

5.2.6

[g C ·m−2 ·d−1 ]
[d−1 ]
[-]
[d−1 ]
[d−1 ]
[-]

Hints for use
 A sudden collaps of the vegetation can be modelled by means of a high first order decay
rate during a short period of time.
 Some plants remain present over wintertime. This can be modelled by means of a low
decay rate.

DR
AF

5.2.5.1

Decay of emerged part of species i (EMi )
First order autumn decay constant of EMi
Temperature constant for decay of EMi
Decay of submerged part of species i (SMi )
First order autumn decay constant of SMi
Temperature constant for decay of SMi

T

DecayEMi
K1decayEMi
KDecayT 20 EMi
DecaySMi
K1decaySMi
KDecayT 20 SMi

Growth of the rhizomes/root system

The below-ground biomass of macrophytes consists of organs for uptake of nutrients from
the soil (root) and in some cases also storage organs (rhizomes). In plants where both primary roots and rhizomes are present the biomass of the rhizomes will be relatively large.
Part of the decaying vegetation becomes dead organic matter and part of the carbon and
nutrients is stored in the rhizomes. The rhizome/root system has its own nitrogen-carbon ratios and phosphorus-carbon ratios. The rhizome/root system grows predominantly during the
late summer and autumn in case the macrophyte stores nutrients in the below-ground system (REF) and translocated these from above-ground systems to below-ground systems. All
carbon related substances are produced in the above-ground system, and translocation from
these to the rhizome/root system is modelled as follows.
For emerged vegetation:

CtranslocEM toRHi =DecayEMi × F rEM toRHi
N translocEM toRHi =CtranslocEM toRHi × min(N CRatRHi , N CRatEMi )
P translocEM toRHi =CtranslocEM toRHi × min(P CRatRHi , P CRatEMi )
(5.15)
For submerged vegetation:

CtranslocSM toRHi =DecaySMi × F rSM toRHi
N translocSM toRHi =CtranslocSM toRHi × min(N CRatRHi , N CRatSMi )
P translocSM toRHi =CtranslocSM toRHi × min(P CRatRHi , P CRatSMi )
(5.16)
In the current model implementation, the rhizome/root system will not decay. Instead, the
fraction of the decaying emerged and submerged biomass that is not translocated to the
rhizome/root system (FrEMtoRHi ) is converted into organic matter (POC).

148 of 464

Deltares

Macrophytes

In the above formulae:

Formation of particulate organic carbon

D-Water Quality has two different routines for the fractioning and decay of organic material.
The first method is the DetC-OOC approach. The second approach is the POC-approach that
is illustrated in ??. This is the approach taken in the macrophytes module.

DR
AF

5.2.7

Translocation of C from EM to RH species i [g C·m−2 d−1 ]
Fraction of EM that becomes RH species i [-)
Translocation of N from EMi to RHi [g N·m−2 d−1 ]
Nitrogen-carbon ratio of RH species i [g N·g C−1 ]
Nitrogen-carbon ratio of EM species i [g N·g C−1 ]
Translocation of P from EMi to rhizomes [g P·m−2 d−1 ]
Phosphorus-carbon ratio of EM species i [g P·g C−1 ]
Phosphorus-carbon ratio of EM species i [g P·g C−1 ]
Translocation of C from EM to RH species i [g C·m−2 d−1 ]
Fraction of SM that becomes RH species i [-]
Translocation of N from EMi to RHi [g N·m−2 d−1 ]
Nitrogen-carbon ratio of EM species i [g N·g C−1 ]
Translocation of P from EMi to rhizomes [g P·m−2 d−1 ]
Phosphorus-carbon ratio of EM species i [g P·g C−1 ]

T

CtranslocEMtoRHi
FrEMtoRHi
NtranslocEMtoRHi
NCratRHi
NCratEMi
PtranslocEMi
PCratRHi
PCratEMi
CtranslocSMtoRHi
FrSMtoRHi
NtranslocSMtoRHi
NCratSMi
PtranslocSMi
PCratSMi

When the emerged and submerged vegetation starts to die in autumn, some of the carbon
and nutrients are stored in the rhizomes while the remaining part becomes particulate organic
matter, distributed over three different fractions (see ??). The ratio of the three particulate
organic carbon fractions is a user-defined parameter. The following equation is a recalculation
of the fractions in order to guarantee mass conservation in the computations:

F rP OCxEMi =

F rP OCxEMi
F rP OC1EMi + F rP OC2EMi + F rP OC3EMi

(5.17)

(x = 1, 2 or 3) and equivalently for the submerged biomass (SMi ).
The production of particulate organic carbon is calculated by:

P rodP OCxEMi =(DecayEMi − CtranslocEM toRHi ) × F rP OCxEMi +
(DecaySMi − CtranslocSM toRHi ) × F rP OCxSMi
(5.18)

The production of particulate organic nitrogen amnd phosphorus is calculated by:

P rodP ON xEMi =(DecayEMi × N CratEMi − N translocEM toRHi ) × F rP OCxEMi +
(DecaySMi × N CratEMi − N translocSM toRHi ) × F rP OCxSMi
P rodP OP xEMi =(DecayEMi × P CratEMi − P translocEM toRHi ) × F rP OCxEMi +
(DecaySMi × P CratEMi − P translocSM toRHi ) × F rP OCxSMi
(5.19)
where:

Deltares

149 of 464

Processes Library Description, Technical Reference Manual

5.2.8

[g C·m−3 ]
[g C·m−3 ]
[g C·m−3 ]
[-]
[-]
[-]
[-]
[-]
[-]
[g C·m−2 ·d−1 ]
[g C·m−2 ·d−1 ]
[g C·m−2 ·d−1 ]
[g N·m−3 ]
[g N·m−3 ]
[g N·m−3 ]
[g N·m−2 ·d−1 ]
[g N·m−2 ·d−1 ]
[g N·m−2 ·d−1 ]
[g P·m−3 ]
[g P·m−3 ]
[g P·m−3 ]
[g P·m−2 ·d−1 ]
[g P·m−2 ·d−1 ]
[g P·m−2 ·d−1 ]

T

Particulate organic carbon, fraction 1
Particulate organic carbon, fraction 2
Particulate organic carbon, fraction 3
Fraction of decaying EMi that becomes POC1
Fraction of decaying EMi that becomes POC2
Fraction of decaying EMi that becomes POC3
Fraction of decaying SMi that becomes POC1
Fraction of decaying SMi that becomes POC2
Fraction of decaying SMi that becomes POC3
POC1 production from decaying vegetation i
POC2 production from decaying vegetation i
POC3 production from decaying vegetation i
Particulate organic nitrogen, fraction 1
Particulate organic nitrogen, fraction 2
Particulate organic nitrogen, fraction 3
PON1 production from decaying vegetation i
PON2 production from decaying vegetation i
PON3 production from decaying vegetation i
Particulate organic phosphorus, fraction 1
Particulate organic phosphorus, fraction 2
Particulate organic phosphorus, fraction 3
POP1 production from decaying vegetation i
POP2 production from decaying vegetation i
POP3 production from decaying vegetation i

DR
AF

POC1
POC2
POC3
FrPOC1EMi
FrPOC2EMi i
FrPOC3EMi i
FrPOC1SMi i
FrPOC2SMi i
FrPOC3SMi i
ProdPOC1i i
ProdPOC2i i
ProdPOC3i i
PON1
PON2
PON3
ProdPON1i i
ProdPON2i i
ProdPON3i i
POP1
POP2
POP3
ProdPOP1i i
ProdPOP2i i
ProdPOP3i i

Uptake of nitrogen and phosphorus from sediment

The phosphorus in the rhizomes is the first source for the growth of submerged vegetation.
When the phosphorus in the rhizomes is exhausted, the vegetation will switch to the uptake
of phosphorus via the roots.

N uptakesediment =GrowthEMi × N CratEMi − N translocRHtoEMi +
GrowthSMi × N CratSMi − N translocRHtoSMi
P uptakesediment =GrowthEMi × P CratEMi − P translocRHtoEMi +
GrowthSMi × P CratSMi − P translocRHtoSMi
where:

Nuptakesediment
Puptakesediment
5.2.8.1

Uptake of nitrogen from the sediment
Uptake of phosphorus from the sediment

(5.20)

[g N·m−2 ]
[g P·m−2 ]

Hints for use
The sediment should contain enough nutrients to support the growth of macrophytes. In this
model, the growth of macrophytes is NOT limited by a lack of nutrients in the sediment.
The release of dissolved nutrients depends on the decay of organic matter, containing nitrogen
and phosphorus. On the long run, the amount of organic matter in the sediment depends on
the production of organic matter in the lake. It is therefore possible that the nutrient pool in the
sediment is exhausted by the macrophytes.

150 of 464

Deltares

Macrophytes

5.2.9

Uptake of nitrogen and phosphorus from water
TODO(??): revise this section - it is incomplete!

TODO

Nitrogen can only be taken up from the water by the emerged non-rooted vegetation. The
growth of emerged vegetation is limited at low phosphorus and nitrogen concentrations. The
following equations describe the uptake of nutrients on the basis of the growth rate and the
nutrient-carbon ratios. At low nutrient concentrations the growth will be limited.
If N H4 < N H4critEMi

F rN H4EMi =

N H4
N H4 + N O3

F rN H4EMi = 1

T

Else
(5.21)

DR
AF

N H4uptakeEMi =GRowthEMi × N CratEMi × F rN H4EMi
N O3uptakeEMi =GRowthEMi × N CratEMi × (1 − F rN H4EMi )
P O4uptakeEMi =GRowthEMi × P CratEMi
(5.22)

where:

NH4critEMi
NH4uptakeEMi
NO3uptakeEMi
PO4uptakeEMi
FrNH4EMi
5.2.10

Critical NH4 concentration for uptake by EMi
Ammonium uptake by emerged vegetation
Nitrate uptake by emerged vegetation
Ortho-phosphorus uptake by emerged vegetation
Fraction of NH4 in total nitrogen uptake

[g N·m−2 ·d−1 ]
[g N·m−2 ·d−1 ]
[g N·m−2 ·d−1 ]
[g P·m−2 ·d−1 ]
[-]

Oxygen production and consumption

When macrophytes grow, they produce oxygen during the production of biomass. The stoichiometric ratio between O2 production [g O2 ] and CO2 uptake g C] is 2.67 ().
The assumption is made, that the oxygen produced by emerged macrophytes escapes to the
atmosphere immediately. The oxygen that is produced by submerged macrophytes dissolves
in the water:

O2productionSMi = 2.67 × CuptakeSMi

(5.23)

Since respiration is not modelled explicitly, the consumption of oxygen in water in the macrophyte model is limited to the oxygen that is involved in the decay of organic matter.

Deltares

151 of 464

Processes Library Description, Technical Reference Manual

Net growth of emerged and submerged vegetation and rhizomes
All the growth and loss processes together give the net growth of the three parts of the vegetation:

T

EMi
=GrowthEMi − GrazeEMi − HarvestEMi − DecayEMi
dt
SMi
=GrowthSMi − GrazeSMi − HarvestSMi − DecaySMi
dt
RHi
=CtranslocEM toRHi + CtranslocSM toRHi − CtranslocRHtoEMi
dt
CtranslocRHtoSMi − GrazeRHi
N RHi
=N translocEM toRHi + N translocSM toRHi − N translocRHtoEMi
dt
N translocRHtoSMi − GrazeN RHi
P RHi
=P translocEM toRHi + P translocSM toRHi − P translocRHtoEMi
dt
P translocRHtoSMi − GrazeP RHi
(5.24)

DR
AF

5.2.11

In these formulae grazing and harvesting terms have been included (see Section 5.4).

152 of 464

Deltares

Macrophytes

5.3

Maximum biomass per macrophyte species
PROCESS :

M AX M ACRO

5.3.1

Implementation

T

With so-called Habitat Suitability Indices (HSI) the occurrence of a particular growth form at a
certain location can be indicated. The HSI’s should vary between 0 and 1, in which 0 implies
that the habitat is not suitable for the species, and 1 implies that the habitat is very suitable
(optimal) for the species. It can be computed in the dedicated software tool HABITAT for
instance. When the HSI equals 1 for a particular growth form, this growth form can reach its
potential biomass. When the HSI equals 1 for several growth forms, the maximum biomass
for each growth form is computed by weighing the HSI by the total index for all species.

The maximum biomass for each growth form and for each species is calculated as follows:
If

P

i

HSIi > 0:

DR
AF

HSIi × P otEMi
P
i HSIi
HSIi × P otSMi
P
M axSMi =
i HSIi

M axEMi =

Else

(5.25)

M axEMi = 0
M axSMi = 0

where:

EMi
HSIi
i
MaxEMi
PotEMi
SMi
MaxSMi
PotSMi
5.3.2

Emerged biomass of macrophyte species i
Habitat Suitability Index for species i
Subscript for species
Maximum biomass for EM species i
Potential biomass for EM species i
Submerged biomass of macrophyte species i
Maximum biomass for SM species i
Potential biomass for SM species i

[g C · m−2 ]
[-]
[-]
[g C · m−2 ]
[g C · m−2 ]
[g C · m−2 ]
[g C · m−2 ]
[g C · m−2 ]

Hints for use

The competition between macrophyte species is not modelled as such. The species composition is fully determined by the user defined Habitat Suitability Indices. Table 5.1 shows some
examples.

Deltares

153 of 464

T

Processes Library Description, Technical Reference Manual

DR
AF

Table 5.1: Computation of the maximum biomass of three macrophyte species as a function of the Habitat Suitability Index.

example 1

example 2

example 3

example 4

154 of 464

parameter
HSI
PotEM
MaxEM
parameter
HSI
PotEM
MaxEM
parameter
HSI
PotEM
MaxEM
parameter
HSI
PotEM
MaxEM

Name
Habitat Suitability Index
Potential biomass
Maximum biomass
Name
Habitat Suitability Index
Potential biomass
Maximum biomass
Name
Habitat Suitability Index
Potential biomass
Maximum biomass
Name
Habitat Suitability Index
Potential biomass
Maximum biomass

units
[-]
g/m2
g/m2
units
[-]
g/m2
g/m2
units
[-]
g/m2
g/m2
units
[-]
g/m2
g/m2

species 1
1
1000
1000
species 1
1
1000
333
species 1
0.2
1000
200
species 1
0.2
500
100

species 2
0
1000
0
species 2
1
1000
333
species 2
0.3
1000
300
species 2
0.3
1000
300

species 3
0
1000
0
species 3
1
1000
333
species 3
0.5
1000
500
species 3
0.5
250
125

Deltares

Macrophytes

5.4

Grazing and harvesting
PROCESS :

GRZMAC II AND HRVMAC II

Grazing by birds and fishes, and mowing of vegetation as a management option both create
a decrease in the biomass of macrophytes. The characteristics of the grazing/moving depend
not only on the species but also on the season. The model contains both a zero order and
a first order flux for harvesting and grazing. The first order grazing/harvesting depends on
the amount of vegetation. The grazing and harvesting slows down when the macrophytes
are gone. The zero order grazing flux is independend of the amount of vegetation, until all
vegetation has gone.

T

In general one can define a process coefficient as a global value that is valid for the entire
model, or as a local value for specific location. The global value can either be constant or
varying in time.
Grazing and harvesting during a certain period of time can be defined by several methods:

DR
AF

 As a time varying, first order grazing/harvesting pressure. Every day a certain portion of
the vegetation is being eaten until the vegetation is gone.

 As a time varying, zero order grazing/harvesting function. During a certain episode, the
birds eat a constant amount of vegetation.

 Depth of vegetation: for some species of birds e.g. Bewick Swans the grazing is limited by
the depth of the lake. Feeding on the tubers of Potamogeton pectinatus, these birds need
to be able to reach the bottom without diving down (< 0.4 m) ?.
Both fluxes can also be defined locally, but not varying in time.
5.4.1

Grazing

Birds can exert a constant or a first order grazing pressure on the vegetation. The vegetation
is removed from the lake, until all vegetation has been eaten. Grazing stops, when the amount
of vegetation that could be eaten within one time step, exceeds the amount vegetation that is
available. Birds can eat the emerged and submerged vegetation, as well as the rhizomes of
for instance P. pectinatus ?.
If EMi > (K0GrazeEMi + K1GrazeEMi × EMi ) × dt:

GrazeEMi = K0GrazeEMi + K1GrazeEMi × EMi

Else

(5.26)

GrazeEMi = 0
If SMi > (K0GrazeSMi + K1GrazeSMi × SMi ) × dt:

GrazeSMi = K0GrazeSMi + K1GrazeSMi × SMi

(5.27)

Else

GrazeSMi = 0

Deltares

155 of 464

Processes Library Description, Technical Reference Manual

If RHi > (K0GrazeRHi + K1GrazeRHi × RHi ) × dt:

GrazeRHi = K0GrazeRHi + K1GrazeRHi × RHi
N HRi
GrazeN RHi = GrazeRHi ×
RHi
P HRi
GrazeP RHi = GrazeRHi ×
RHi

(5.28)

Else

GrazeRHi = 0
GrazeN RHi = 0
GrazeP RHi = 0

5.4.2

Grazing of EM species i
Zero order grazing constant of EM species i
First order grazing constant o fEM species i
time step of the simulation
Grazing of SM species i
Zero order grazing constant of SM species i
First order grazing constant of SM species i
Rhizome species i
Grazing of RH species i
Zero order grazing of RH species i
First order grazing constant of RH species i
Grazing of RH species i, nitrogen component
Grazing of RH species I, phosphorus component

[g C·m−2 ·d−1 ]
[g C·m−2 ·d−1 ]
[d−1 ]
[d]
[g C·m−2 ·d−1 ]
[g C·m−2 ·d−1 ]
[d−1 ]
[g C·m−2 ]
[g C·m−2 ·d−1 ]
[g C·m−2 ·d−1 ]
[d−1 ]
[g N·m−2 ·d−1 ]
[g P·m−2 ·d−1 ]

DR
AF

GrazeEMi
K0GrazeEMi
K1GrazeEMi
dt
GrazeSMi
K0GrazeSMi
K1GrazeSMi
RHi
GrazeRHi
K0GrazeRHi
K1GrazeRHi
GrazeNRHi
GrazePRHi

T

where:

Hints for use

The grazing can be estimated on the basis of the number of birds, the period during which
they are eating somewhere, the area of the lake and the amount of macrophytes each bird
eats. An example equation for the estimation of the grazing pressure for emerged vegetation
could look like:

K0GrazeEMi =
where:

birds
fooddemand
area

birds × f ooddemand
area

Number of birds in the colony
Amount of vegetation per bird per day
Lake area where the colony of birds is feeding

(5.29)

[-]
[g C·d·−1]
[m2 ]

The grazing of submerged vegetation by birds is limited to a maximum depth. If this is the
case, the grazing function can be applied locally in the shallow areas in the model schematisation.
5.4.3

Harvesting
Harvesting can be used as a management practise to reduce nuicance biomass (e.g. to improve recreational values) or to remove nutrients from the system. Both emerged and submerged vegetation can be removed from the water system. The harvesting can be modelled

156 of 464

Deltares

Macrophytes

as a constant and /or a first order flux. The modelled harvesting stops, when all vegetation is
removed from the lake.
IF EMi > (K0HarvestEMi + K1HarvestEMi × EMi ) × dt:

HarvestEMi = K0HarvestEMi + K1HarvestEMi × EMi
ELSE

HarvestEMi = 0
IF SMi > (K0HarvestSMi + K1HarvestSMi × SMi ) × dt:

ELSE

HarvestSMi = 0

DR
AF

where:

T

HarvestSMi = K0HarvestSMi + K1HarvestSMi × SMi

K0HarvestEMi
K1HarvestEMi
dt
HarvestEMi
K0HarvestSMi
K1HarvestSMi
HarvestSMi

Deltares

Zero order harvesting of emerged vegetation
First order harvesting constants of emerged vegetation
Time step of computation
Harvesting of emerged vegetation
Zero order harvesting of submerged vegetation
First order harvesting constant of submerged vegetation
Harvesting of submerged vegetation

[g C·m−2 ·d−1 ]
[d−1 ]
[d]
[g C·m−2 ·d−1 ]
[g C·m−2 ·d−1 ]
[d−1 ]
[g C·m−2 ·d−1 ]

157 of 464

Processes Library Description, Technical Reference Manual

Light limitation for macrophytes
PROCESS :

R AD _SM II

For the submerged parts of the macrophytes the light limitation is determined from the light
intensity at the tip of the submerged parts.
Implementation
The limitation (f rad) is expressed as the ratio between the light intensity at the tip and the
satuaration light intensity:

where:

f rad
Itop
Isatii

Itop
)
Isatii

(5.30)

T

f rad = min(1,

light limitation factor
light intensity at the tip of the submerged part
light intensity at which saturation occurs for submerged macrophyte ii

DR
AF

5.5

158 of 464

[-]
[-]
[-]

Deltares

Macrophytes

5.6

Vegetation coverage
PROCESS :

C OVERAGE

When a water body is covered by emerged macrophytes, the reaeration with oxygen and
the light intensity in the water are decreased. The parameter f cov for the coverage of the
surface water is an existing model coefficient, that is already used in the computation of the
reaeration flux. On the basis of the model for emerged macrophytes, the coverage can be
computed. The coverage with emerged macrophytes is assumed to be 100 % when the
actual emerged biomass reaches the maximum emerged biomass. The parameter is used in
the model equations for light intensity near the water surface.

T

Implementation

The growth of submerged vegetation can be limited by the underwater light climate. This
depends on the dissolved and suspended matter in the water (both organic and inorganic)
? as well as on the shading due to emerged vegetation that covers the surface of the water.
The growth of emerged vegetation is not limited by light in this model, although several authors report that selfshading can occur. In the light extinction function in D-Water Quality, the
coverage by emerged vegetation is included via the following function:

DR
AF

5.6.1

Itop1 = Is × (1 − f cov)

(5.31)

where:
Itop1
Is
fcov

light intensity at the surface of the water layer (layer 1)
light intensity at the water surface
fraction of the water surface covered by vegetation

[W·m−2 ]
[W·m−2 ]
[-]

The light intensity of the subsequent layers is computed according by the process CalcRad,
see also Figure 5.4:

Itopn =Ibotn−1

Ibotn =Itopn × e

−ExvV ln ×Hn

(5.32)
(5.33)

where:

ExtVLn
Itop
Ibot
H
n

extinction of visible light in layer n
light intensity at the top of a water layer
light intensity at the bottom of a water layer
thickness of the water layer, zn−1 − zn
index for water layers

[m−1 ]
[W·m−2 ]
[W·m−2 ]
[m]
[-]

When there is only one water layer (compartment), the depth is equal to the water depth.
In the case that sediment layers are actually modelled the light intensities at the top and the
bottom of these layers are calculated in a slightly modified way:

Ibotn =a × Itopn × e−ExvV ln ×Hn

(5.34)

where:

a amplification factor by scattering by sediment particles [-]

Deltares

159 of 464

DR
AF

T

Processes Library Description, Technical Reference Manual

Figure 5.4: The light intensity under water – explanation of the variables in the light intensity functions.

The coverage f cov is calculated via:

f cov =

X
i

where:

CoverageEMi
CoverageSMi
fcov
EMi
SMi
MaxEMi
MaxSMi

160 of 464

EMi
M axEMi

Coverage with emerged vegetation
Coverage with submerged vegetation
Total coverage on the basis of all emerged species
Actual biomass emerged vegetation
Actual biomass submerged vegetation
Maximum biomass emerged vegetation
Maximum biomass submerged vegetation

(5.35)

[-]
[-]
[-]
[g·m−2 ]
[g·m−2 ]
[g·m−2 ]
[g·m−2 ]

Deltares

Macrophytes

5.7

Vertical distribution of submerged macrophytes
PROCESS :

MACDIS II

The actual location of the submerged biomass in the water column is species specific. Some
species are evenly distributed over the water column, where others tend to concentrate in the
top layers.

5.7.1

T

The macrophytes biomass is administratively located in the bottom water layer. If the model
is layered (1Dv, 2Dv, 3D), the biomass is distributed over the vertical layers to provide input
for the modules that require such a distribution, in particular the vertical distribution of light
extinction.
Implementation

This process is implemented for different types of macrophytes, indicated by "ii" throughout
this document.

DR
AF

The vertical distribution of the macrophyte biomass is calculated from the following input items
(for submerged macrophyte species ii):
Id in process

Symbol used

Description

Depth
TotalDepth
LocalDepth
SMii
SwDisSMii
HmaxSMii
FfacSMii

D
T
L
MT

depth of segment, layer thickness [m]
total depth water column [m]
depth from water surface to bottom of segment [m]
submerged macrophyte biomass in water column [gC/m2 ]
type of macrophyte shape function (1: linear, 2: exponential)
maximum height of macrohyte [m]
parameter F in shape function [-]

Hmax
F

Figure 5.5 provides an overview of the geometrical quantities used in the calculation. Note
that the vertical co-ordinate z is defined in a downward direction, with a value of zero at the
water surface.
The vertical distribution of the submerged macrophytes m(z) (in g/m3 ) is represented either
by a linear or by an exponential function.
5.7.1.1

Linear distribution (SwDisSMii=1)

The shape function is defined by means of one dimensionless parameter F with a value
ranging from 0 to 2. For F = 0, the biomass approaches zero at the top of the plant, for
F = 1 the biomass is distributed homogeneously and for F = 2, the biomass approaches
zero near the bed. Values between 0 and 1 result in a decreasing biomass from bottom to
top. Values between 1 and 2 result in an increasing biomass from bottom to top.
The biomass distribution m(z) can be expressed by means of two constants A and B , which
are formulated in terms of the total biomass MT and the shape parameter F :

Deltares

161 of 464

T

Processes Library Description, Technical Reference Manual

DR
AF

Figure 5.5: Definition of the quantities used for determining the linear vertical distribution.

m(z) = Az + B
MT 2 − 2F
A=
Hmax T − zm
MT F (zm + T ) − 2zm
B=
Hmax
T − zm

(5.36)

It is easy to derive that for F = 1, A = 0 and B = MT /Hmax .

Consequently, the algorithm to calculate the biomass in a layer from z = Z1 to z = Z2
proceeds as follows:
If zm > z2 (layer above top of plant): M12 = 0

If zm < z1 (layer entirely below top of plant): M12 =
Else (top of plant inside layer): M12 =

R Z2

Zm

R Z2
Z1

m(z)dz

m(z)dz

By integrating the mass distribution function we can derive the biomass in the layer, e.g.:

Z

Z2

m(z)dz =
Z1

A 2
(Z − Z12 ) + B(Z2 − Z1 )
2 2

(5.37)

The module calculates the following output items for submerged macrophyte species ii:
FrBmSMii
BmLaySMii

Fraction of the macrophyte biomass in present layer [-]
Macrophyte biomass density in present layer [gC/m3 ]

The fraction of the biomass in a layer from z = Z1 to z = Z2 is calculated as M12 /MT .

162 of 464

Deltares

T

Macrophytes

5.7.1.2

DR
AF

Figure 5.6: Definition of the quantities used for determining the exponential vertical distribution.

Exponential distribution (SwDisSMii=2)

The exponential shape function is defined on an inverse vertical co-ordinate z’, which is defined as (see also Figure 5.7):

z0 = T − z

(5.38)

The value of z 0 equals 0 at the bottom and it equals Hmax at the tip of the plant.
The mass distribution function is defined as follows:


0
m(z 0 ) = A · eF z /Hmax − 1

(5.39)

The shape function is defined by means of one parameter F . The constant A is determined
by requiring that the integrated mass equals the total mass MT . A value of F approaching
0 defines a linear distribution. Increasing values of F define a stronger and stronger concentration of the biomass near the plant tip (see ??). The value of A can be determined as:

A=

Hmax

M
 T

eF −1
F


−1

(5.40)

Consequently, the algorithm to calculate the biomass in a layer from z 0 = Z10 to z 0 = Z20
proceeds as follows:
If Z10 > Hmax (layer above top of plant): M12 = 0
If Z20 < Hmax (layer entirely below top of plant): M12 =
Else (top of plant inside layer): M12 =

Deltares

R Hmax
Z10

R Z20
Z10

m(z 0 )dz 0

m(z 0 )dz 0

163 of 464

Processes Library Description, Technical Reference Manual

(a) F = 0.001

(b) F = 5

(c) F = 20

Figure 5.7: Examples of the exponential vertical distribution for three values of the shape
parameter F .

Z

Z20

5.7.2

Hints

0
0


eF Z2 /Hmax − eF Z1 /Hmax
m(z 0 )dz 0 = A · Hmax
− (Z20 − Z10 )
F

(5.41)

DR
AF

Z10

T

By integrating the mass distribution function we can derive the biomass in the layer, e.g.:

The module uses a work array ("IBotSeg") which is filled during the first call. This work array contains the segment number of the bottom segment that lies beneath each segment
not located in the bottom layer. This tells each segment where the biomass in the segment
administratively resides, as biomass can only exist in the bottom segment but is ’distributed’
vertically in a post-processing step. Note that in a 2Dh or 1D model this work array is trivial;
every segment is the bottom segment of the whole water column.
For an exponential biomass distribution, the value of F can range from a small positive number to infinite. The table below provides the share of the biomass of the plant present in the
upper 10 % of the plant height, as a function of F :

F
0.1
2
4
6
8
10
15
20
25
30

Share of biomass in top 10%
19
26
36
46
55
63
78
87
93
96

The maximum allowable value for F is 50 – this is a numerical limitation, because otherwise
the numbers could become too large.
TODO

TODO(??): Is the sentence below true indeed?
In the present implementation, the overall biomasses are calculated as g/m2 .

164 of 464

Deltares

6 Light regime
Contents
Light intensity in the water column . . . . . . . . . . . . . . . . . . . . . . 166

6.2

Extinction coefficient of the water column . . . . . . . . . . . . . . . . . . 170

6.3

Variable solar radiation during the day . . . . . . . . . . . . . . . . . . . . 180

6.4

Computation of day length . . . . . . . . . . . . . . . . . . . . . . . . . . 183

6.5

Computation of Secchi depth . . . . . . . . . . . . . . . . . . . . . . . . . 185

DR
AF

T

6.1

Deltares

165 of 464

Processes Library Description, Technical Reference Manual

Light intensity in the water column
PROCESS :

C ALC R AD, C ALC R AD DAY, C ALC R AD _ UV

Due to extinction the light intensity in the water column is reduced compared to the intensity
at the water surface. The light intensity is an exponential attenuation function of depth times
the total extinction coefficient according to the law of Lambert-Beer. This holds for visible light
as well as UV light, but with different extinction coefficients. Total visible light or photoactive
radiation (PAR) is used to determine the growth rates of phytoplankton, microphytobenthos
and submerged macrophytes. UV light is used to determine the mortality rate of bacterial
pollutants.

Implementation

T

The total extinction coefficient is calculated by processes Extinc_VLG and Extinc_UVG and
contains contributions of algae biomass, particulate organic detritus, dissolved organic matter,
suspended inorganic matter, submerged macrophytes and water itself.

Processes CALCRAD and CALCRADDAY deliver the intensity of total visible light (solar radiation) at the top and the bottom of the water and sediment layers in the model. Process
CALCRAD_UV does the same for UV light. CALCRAD and CALCRAD_UV may deliver the
daily average light intensity as well as the actual light intensity as it varies over the day. CALCRADDAY produces the actual light intensity as it varies over the day from daily average input,
and needs to be combined with additional process DAYRAD. All processes use the same light
intensity at the water surface as input. All processes have been implemented in a generic
way, meaning that they apply to water layers as well as sediment layers.

DR
AF

6.1

Table 6.1 to Table 6.6 provide the definitions of the parameters occurring in the user-defined
input and output parameters.
Formulation

The light intensities at the top or bottom of a water layer or compartment follow from:

Itop1 = Is
Itopi = Iboti−1

Iboti = Itopi × e(−eti ×Hi )
with:

et
H
Is
Itop
Ibot
i

total extinction coefficient [m−1 ]
thickness of the water layer [m]
light intensity at the water surface, just below the surface [W.m−2 ]
light intensity at the top of a water layer [W.m−2 ]
light intensity at the bottom of a water layer [W.m−2 ]
index for water layer [-]

When there is only one water layer (compartment) the depth is equal to water depth.
In the case that sediment layers are actually modelled the light intensities at the top and the
bottom of these layers are calculated in a slightly modified way:

Iboti = a × Itopi × e(−eti ×Hi )
with:

166 of 464

Deltares

Light regime

a
H
Itop
Ibot
i

amplification factor due to scattering by sediment particles [-]
thickness of a sediment layer [m]
light intensity at the top of a sediment layer [W.m−2 ]
light intensity at the bottom of a sediment layer [W.m−2 ]
index for sediment layer [-]

Itop at the sediment-water interface is equal to Ibot of the lower water layer.

DR
AF

T

Directives for use
 The light intensity at the water surface RadSurf is the total visible light intensity (solar
radiation) or the photosynthetic active light intensity corrected for reflection.
 Rad_U V is derived from RadSurf , when process CALCRAD_UV is active. Alternatively it can be imposed as input parameter, but this is only applicable for a model with one
water layer. Process BACMORT converts Rad_U V into UV light intensity.
 Unattenuated solar radiation as visible light yields 100–500 W.m-2 at latitudes around 50◦ .
Always make sure that the light input (observed solar radiation) is consistent with the light
related parameters of the primary producer modules used. If data are expressed in units
PAR (photosynthetic active radiation), and the model is based on total visible light, the
PAR data need to be converted by dividing with 0.45 (the photosynthetic fraction of the
visible wavelength spectrum). The radiation data should be corrected for cloudiness and
sometimes also for reflection (approximately 10 %).
 Phytoplankton module BLOOM uses the daily average radiation. In its standard setting it
uses total visible light and carries out corrections for both reflection and photo-synthetic
fraction. DYNAMO may use the daily average radiation or the actual radiation varying over
the day. The latter is delivered by process DAYRAD, which is used in addition to process
CALCRADDAY. This process is used in stead of or in parallel with process CALCRAD.
Additional references

WL | Delft Hydraulics (1991a)

Table 6.1: Definitions of the input parameters in the formulations for CALCRAD.

Name in
formulas

Name in
input

Definition

Units

a

a_enh

amplification factor due to scattering by
sed. particles

-

ExtV l

total extinction coefficient of vivible light

m−1

Radsurf

light intensity at water surface

W.m−2

Depth

thickness of a water or sediment layer

m

et
Is
z1

Deltares

167 of 464

Processes Library Description, Technical Reference Manual

Table 6.2: Definitions of the output parameters for CALCRAD.

Name in
formulas

Name in
output

Definition

Units

Itop

Rad

W.m−2

Ibot

RadBot

light intensity at the top of a water or sediment layer
light intensity at the bottom of a water or
sediment layer

W.m−2

Table 6.3: Definitions of the input parameters in the formulations for CALCRADDAY.

Name in
output

Definition

a

a_enh

amplification factor due to scattering by
sed. particles

-

et

ExtVl

total extinction coefficient of visible light

m−1

H

DR
AF

Is

Units

T

Name in
formulas

DayRadsurf

light intensity at the water surface

W.m−2

Depth

thickness of a water or sediment layer

m

Table 6.4: Table IV Definitions of the output parameters for CALCRADDAY.

Name in
formulas

Name in
output

Definition

Units

Itop

DayRad

light intensity at the top of a water or sediment layer
light intensity at the bottom of a water or
sediment layer

W.m−2

Ibot

DayRadBot

W.m−2

Table 6.5: Definitions of the input parameters in the formulations for CALCRAD_UV.

Name in
formulas

Name in
output

Definition

Units

a

a_enh

amplification factor due to scattering by
sed. particles

-

et

ExtUv

total extinction coefficient of UV light

m−1

Is

Radsurf

light intensity at the water surface

W.m−2

H

Depth

thickness of a water or sediment layer

m

168 of 464

Deltares

Light regime

Table 6.6: Definitions of the output parameters for CALCRAD_UV.

Name in
formulas

Name in
output

Definition

Units

Itop

Rad_Uv 1

W.m−2

Ibot

RadBot_Uv 1

light intensity at the top of a water or sediment layer
light intensity at the bottom of a water or
sediment layer

Total visible light or PAR as based on UV extinction!

DR
AF

T

1

W.m−2

Deltares

169 of 464

Processes Library Description, Technical Reference Manual

Extinction coefficient of the water column
PROCESS :

E XTINC _VLG, E XTINA BVLP (E XTINA BVL), E XT P H DVL, E XTINC _UVG,
E XTINA BUVP (E XTINA BUV), E XT P H DUV

Primary producers like algae use a certain fraction of the visible light for assimilation. The
various algae modules account for this fraction in light limitation functions and light production
efficiency functions. These functions use the intensity of visible light as an input parameter.

T

Due to extinction the light intensity in the water column is reduced compared to the intensity at the water surface. The light intensity is an exponential attenuation function of depth
times the extinction coefficient according to the law of Lambert-Beer. All light absorbing substances in particulate or dissolved form contribute to the extinction coefficent in a linear way.
This includes algae biomass, suspended and dissolved organic matter (detritus), suspended
inorganic matter, water itself and all remaining dissolved substances.
Most of the substances that contribute to the extinction coefficient can be modelled. The
contributions of these substances are calculated on the basis of concentrations and specific extinction coefficients. Water and the remaining substances contribute in the form of a
background extinction coefficient. Dissolved fulvic and humic acids may be modelled as substances DOC or accounted for in the background extinction coefficient, or in a salinity related
extinction coefficient.

DR
AF

6.2

Dominant contributions to the extinction are different for saline and fresh water. Among other
things, in fresh water a relatively large contribution may be delivered by dissolved fulvic and
humic acids, whereas saline water as a rule contains very small quantities of these substances. This is due to photochemical oxidation of these substances and long residence time.
It is also conceivable that marine suspended matter has a specific extinction coefficient that
is different from the coefficient of riverine suspended sediment. Where river water is mixed
with saline water in estuaries, the background extinction changes from a relatively high value
in the river to a low value in the sea. The opposite applies to salinity. It has been shown that
the background extinction coefficient in estuaries can be described empirically as a function
of salinity Rijkswaterstaat/RIKZ (1991). Such a relation has been incorporated in process
Extinc_VLG.
Apart of the processes for the extinction coefficient of visible light similar processes are available for the extinction coefficient of UV-light, which is relevant for the modelling of bacterial
pollutants.
Processes Extinc_VLG and Extinc_UVG may apply an alternative advanced submodel of the
extinction coefficient called UITZICHT. This submodel takes the optical properties of a water
column into account. Given the advanced features of UITZICHT this module is not (yet)
described in this manual. The user is referred to Rijkswaterstaat/RIKZ (1990) for background
and details.
Implementation
The total extinction coefficient of visible light for the water column is delivered by three processes the names of which depend on the algae module selected. Process Extinc_VLG
provides the total extinction coefficient of visible light, for which ExtinaBVLP (ExtinaBVL) or
ExtPhDVL deliver the partial phytoplankton biomass extinction coefficient for BLOOM or for
DYNAMO. Processes Extinc_UVG, ExtinaBUVP (ExtinaBUV), ExtPhDUV provide similar co-

170 of 464

Deltares

Light regime

efficients for UV light. The processes do not deliver process rates and, therefore, do not affect
mass balances.
Processes ExtinaBVLP (ExtinaBVL) and ExtinaBUVP (ExtinaBUV) have been implemented
for the BLOOM algae:

 BLOOMALG01 - BLOOMALG30.
Processes ExtPhDVL and ExtPhDUV have been implemented for the DYNAMO algae:

 Diat and Green.

T

Processes Extinc_VLG and Extinc_UVG add the partial extinction coefficients, and have been
implemented for substances:

 IM1, IM2, IM3, POC1, POC2, POC3, POC4, DOC and Salinity.

DR
AF

The auxiliary process UITZICHT is incorporated in this process, but it is inactivated unless
specific input is provided.
All processes have been implemented in a generic way and therefore cover water as well
sediment layers.
Table 6.7 to Table 6.10 provide the definitions of the input parameters and the output parameters for visible light. Table 6.11 to Table 6.14 provide the same for UV light.
Formulation

Two methods are available to compute the total and partial extinction coefficients.
For SW _U itz = 0.0 (UITZICHT not applied) the total extinction coefficient of visible light or
UV light is calculated as the sum of seven partial extinction coeffcients:

et = eat + emt + ept + edt + est + eot + eb

where:

eat
eb
edt
ept
emt
est
eot
et

partial extinction coefficient of algae biomass [m−1 ]
background extinction coefficient [m−1 ]
partial extinction coefficient of dissolved organic matter [m−1 ]
partial extinction coefficient of particulate detritus [m−1 ]
partial extinction coefficient of macrophytes [m−1 ]
partial extinction coefficient of suspended inorganic matter [m−1 ]
partial extinction coefficient of other substances as a function of salinity [m−1 ]
partial extinction coefficient [m−1 ]

The background extinction coefficient and the partial extinction coefficient of macrophytes are

Deltares

171 of 464

Processes Library Description, Technical Reference Manual

input parameters. The other contributions are determined according to:

eat =
ept =

n
X
i=1
m
X

(eai × Calgi )
(epj × Cpocj )

j=1

edt = ed × Cdoc
3
X
est =
(esk × Cimk )
k=1

where:

biomass concentration of algae species group i [gC.m−3 ]
concentration of detritus component j [gC.m−3 ]
concentration of suspended inorganic matter fraction k [gC.m−3 ]
specific extinction coefficient of an algae species type [m2 .gC−1 ]
specific extinction coefficient of dissolved organic carbon [m2 .gC−1 ]
spec. ext. coefficient of other substances based on relative salinity [m−1 ]
specific extinction coefficient of a particulate detritus component [m2.gC-1]
spec. ext. coefficient of a suspended inorganic matter fraction [m2 .gDM−1 ]
actual salinity ([g.kg−1 ] ≈ [g.l−1 ])
maximal salinity ([g.kg−1 ] ≈ [g.l−1 ])
index for algae species [-]
index for detritus components [-]
index for suspended inorganic matter fractions [-]
number for algae species, =30 for BLOOM, = 2 for DYNAMO [-]
number of detritus components, =4 for POX [-]

DR
AF

Calgi
Cdetj
Cimk
ea
ed
eo
ep
es
SAL
SALmax
i
j
k
n
m

T

eot = eo × (1 − SAL/SALmax)

Besides to the total extinction coefficient the processes deliver the partial extinction coefficients of algae biomass, particulate detritus, dissolved organic matter and suspended inorganic matter.
For SW _U itz = 1.0 the auxiliary process UITZICHT (Rijkswaterstaat, 1990) is applied for
the calculation of the extinction coefficients based on a background extinction and the concentrations of (in)organic suspended matter, chlorophyll and dissolved organic matter (fulvic
and humic acids).
Directives for use
 BLOOM corrects the visible light intensity (irradiation) for the fraction light that can be
used by algae (45 %). Often available irradiation data are expressed in [J.cm−2 .week−1 ]
(PAR or TotalRAD). Notice that irradiation has to be provided in [W.m−2 ]. To convert PAR
(J.cm−2 .week−1 ), multiply with 0.016534 and 1/0.45. To convert TotalRAD (J.cm−2 .week−1 ),
only multiply with 0.016534 .
 The user must make sure that the form of the regression equation used for eot meets the
formulation in the model. An indicative equation provided by Rijkswaterstaat/RIKZ (1991)
for the Eastern Scheldt in the Netherlands is 0.005×(19.4−SAL/1.8) at a background
extinction coefficient of 0.06 (version corrected in 2002). This function is equivalent to
0.079 × (1.0 − SAL/SALmax). If salinity dependent extinction is applied, make sure
there is no double counting due to simulated DOC.

172 of 464

Deltares

Light regime

 UITZICHT is applied when SW _U itz = 1.0. In that case a number of additional input
parameters are needed.

 For the application of the extinction processes for UV light make shure that the light in-

DR
AF

T

tensity is calculated as UV light, and specify the specific extinction coefficients for UV
light.

Deltares

173 of 464

Processes Library Description, Technical Reference Manual

Table 6.7: Definitions of the input parameters in the formulations for Extinc_VLG.

Name in
input

Definition

Units

Cim1
Cim2
Cim3
Cpoc1
Cpoc2
Cpoc3
Cpoc4
Cdoc
SAL

IM 1
IM 2
IM 3
P OC1
P OC2
P OC3
P OC4
DOC
Salinity

conc. of inorg. susp. matter fraction 1
conc. of inorg. susp. matter fraction 2
conc. of inorg. susp. matter fraction 3
concentration of fast dec. part. detritus
conc. of medium dec. part. detritus
concentration of slow dec. part. detritus
concentration of refractory part. detritus
concentration of dissolved organic carbon
actual salinity

gDM.m−3
gDM.m−3
gDM.m−3
gC.m−3
gC.m−3
gC.m−3
gC.m−3
gC.m−3
psu(g.kg−1 )

eat
eb
ep1
ep2
ep3
ep4
ed
emt
eo

ExtV lP hyt
ExtV lBak
ExtV lP OC1
ExtV lP OC2
ExtV lP OC3
ExtV lP OC4
ExtV lDOC
ExtV lM acro
ExtV lSal0

partial ext. coeff. of algae biomass
background extinction coefficient
specific ext. coefficient of detritus POC1
specific ext. coefficient of detritus POC2
specific ext. coefficient of detritus POC3
specific ext. coefficient of detritus POC4
specific ext. coeff. of diss. detritus DOC
partial ext. coefficient of macrophytes
spec. ext. coeff. other subst. based on rel.
salinity
spec. ext. coefficient of inorg. matter IM1
spec. ext. coefficient of inorg. matter IM2
spec. ext. coefficient of inorg. matter IM3

m−1
m−1
m2 .gC−1
m2 .gC−1
m2 .gC−1
m2 .gC−1
m2 .gC−1
m−1
m−1

SALmax SalExt0

maximal salinity

psu(g.kg−1 )

SW _U itz Sw_U itz 1

option parameter: if 0.0 no UITZICHT (default), if 1.0 UITZICHT is applied
diepte Z1
diepte Z2
correctiefactor
coeff. C3 absorp. by glowing dried matter
and detritus
coeff. C1 atten. by glowing dried matter
and detritus
coeff. C2 atten. by glowing dried matter
and detritus
constant for the spectre
constant for calc. of the visibility depth
angle of incidence of solar radiation
dry matter conversion factor for detritus

-

–
–
–
–
–

DR
AF

es1
es2
es3

ExtV lIM 1
ExtV lIM 2
ExtV lIM 3

U itzDEP T 11
U itzDEP T 21
U itzCorCH 1
U itzC _Det1
U itzC _GL11

–

U itzC _GL21

–
–
–
–

U itzHelHM 1
U itzT au1
U itzAngle1
DM CF DetC 1

1

T

Name in
formulas

m2 .gDM−1
m2 .gDM−1
m2 .gDM−1

m
m
nm−1
◦

gDM.gC−1

Only concern alternative calculation method according to UITZICHT.

174 of 464

Deltares

Light regime

Table 6.8: Definitions of the input parameters in the formulations for ExtinaBVLP (ExtinaBVL) for BLOOM algae.

Name in
formulas

Name in
input1

Definition

Units

Calgi

BLOOM ALG(i) biomass concentration of algae species

gC.m−3

type i

ExtV lAlg(i)

algae species type specific extinction coefficient

m2 .gC−1

n
–

N AlgBloom2
SW _f ixin_y 2

-

–

V olume3

–

F ixAlg(i)3

number of algae species groups = 30
indicator for algae species attached to the
sediment = 1
volume of water compartment or sediment
layer
identifier for pairs of algae types attaching
to sediment (0 = not applying, > 0 = suspended, < 0 = attached)

DR
AF

1

T

eai

m3
-

(i) indicates algae species types 1–30.
Default values are fixed and must not be changed because they refer to additional input
F ixAlg(i).
3
Parameters are added for conversion of biomass of algae attached to the sediment from
[gC.m−2 ] to [gC.m−3 ].
2

Table 6.9: Definitions of the input parameters in the formulations for ExtPhDVL.

Name in
formulas

Name in
input

Definition

Units

Calg1
Calg2

Diat
Green

biomass concentration of diatoms
biomass concentration of green algae

gC.m−3
gC.m−3

ea1
ea2

ExtV lDiat
EXtV lGreen

specific ext. coefficient for diatoms
specific ext. coefficient for green algae

m2 .gC−1
m2 .gC−1

–

N AlgDynamo1
SW _f ixin_y1

-

–

V olume

number of algae species groups = 2
indicator for algae species attached to the
sediment = 0
volume of water compartment or sediment
layer

n

1

m3

The default values are fixed and must not be changed!

Deltares

175 of 464

DR
AF

T

Processes Library Description, Technical Reference Manual

Table 6.10: Definitions of the output parameters for Extinc_VLG, ExtinaBVLP (ExtinaBVL), ExtPhDVL.

Name in
formulas

Name in
output1

Definition

Units

eat
edt
ept
est
et

ExtV lP hyt
ExtV lODS
ExtV lOSS
ExtV lISS
ExtV l

partial ext. coefficient of algae biomass
partial ext. coeff. of dissolved org. matter
partial ext. coefficient of part. detritus
partial ext. coeff. of susp. inorg. matter
total extinction coefficient

m−1
m−1
m−1
m−1
m−1

1

Notice that the partial extinction coefficients ExtV lBak and ExtV lM acro are input parameters

176 of 464

Deltares

Light regime

Table 6.11: Definitions of the input parameters in the formulations for Extinc_UVG.

Name in
input

Definition

Units

Cim1
Cim2
Cim3
Cpoc1
Cpoc2
Cpoc3
Cpoc4
Cdoc
SAL

IM 1
IM 2
IM 3
P OC1
P OC2
P OC3
P OC4
DOC
Salinity

conc. of inorg. susp. matter fraction 1
conc. of inorg. susp. matter fraction 2
conc. of inorg. susp. matter fraction 3
concentration of fast dec. part. detritus
conc. of medium dec. part. detritus
concentration of slow dec. part. detritus
concentration of refractory part. detritus
concentration of dissolved organic carbon
actual salinity

gDM.m−3
gDM.m−3
gDM.m−3
gC.m−3
gC.m−3
gC.m−3
gC.m−3
gC.m−3
psu(g.kg−1 )

eat
eb
ep1
ep2
ep3
ep4
ed
emt
eo

ExtU vP hyt
ExtU vBak
ExtU vP OC1
ExtU vP OC2
ExtU vP OC3
ExtU vP OC4
ExtU vDOC
ExtU vM acro
ExtU vSal0

m−1
m−1
m2 .gC−1
m2 .gC−1
m2 .gC−1
m2 .gC−1
m2 .gC−1
m−1
m−1

es1
es2
es3

ExtU vIM 1
ExtU vIM 2
ExtU vIM 3

partial ext. coeff. of algae biomass
background extinction coefficient
specific ext. coefficient of detritus POC1
specific ext. coefficient of detritus POC2
specific ext. coefficient of detritus POC3
specific ext. coefficient of detritus POC4
specific ext. coeff. of diss. detritus DOC
partial ext. coefficient of macrophytes
spec. ext. coeff. other subst. based on rel.
salinity
spec. ext. coefficient of inorg. matter IM1
spec. ext. coefficient of inorg. matter IM2
spec. ext. coefficient of inorg. matter IM3

SALmax SalExt0

maximal salinity

psu(g.kg−1 )

SW _U itz Sw_U itz 1

option parameter: if 0.0 no UITZICHT (default), if 1.0 UITZICHT is applied
diepte Z1
diepte Z2
correctiefactor
coeff. C3 absorp. by glowing dried matter
and detritus
coeff. C1 atten. by glowing dried matter
and detritus
coeff. C2 atten. by glowing dried matter
and detritus
constant for the spectre
constant for calc. of the visibility depth
angle of incidence of solar radiation
dry matter conversion factor for detritus

-

–

DR
AF

–
–
–
–

U itzDEP T 11
U itzDEP T 21
U itzCorCH 1
U itzC _Det1
U itzC _GL11

–

U itzC _GL21

–
–
–
–

U itzHelHM 1
U itzT au1
U itzAngle1
DM CF DetC 1

1

T

Name in
formulas

m2 .gDM−1
m2 .gDM−1
m2 .gDM−1

m
m
nm−1
◦

gDM.gC−1

Only concern alternative calculation method according to UITZICHT.

Deltares

177 of 464

Processes Library Description, Technical Reference Manual

Table 6.12: Definitions of the input parameters in the formulations for ExtinaBUVP (ExtinaBUV) for BLOOM algae.

Name in
formulas

Name in
input1

Definition

Units

Calgi

BLOOM ALG(i) biomass concentration of algae species

gC.m−3

type i

ExtU vAlg(i)

algae species type specific extinction coefficient

m2 .gC−1

n
–

N AlgBloom2
SW _f ixin_y 2

-

–

V olume3

–

F ixAlg(i)3

number of algae species groups = 30
indicator for algae species attached to the
sediment = 1
volume of water compartment or sediment
layer
identifier for pairs of algae types attaching
to sediment (0 = not applying, > 0 = suspended, < 0 = attached)

DR
AF

1

T

eai

m3
-

(i) indicates algae species types 1–30.
Default values are fixed and must not be changed because they refer to additional input
F ixAlg(i).
3
Parameters are added for conversion of biomass of algae attached to the sediment from
[gC.m−2 ] to [gC.m−3 ].
2

Table 6.13: Definitions of the input parameters in the formulations for ExtPhDUV.

Name in
formulas

Name in
input

Definition

Units

Calg1
Calg2

Diat
Green

biomass concentration of diatoms
biomass concentration of green algae

gC.m−3
gC.m−3

ExtU vDiat
EXtU vGreen

specific ext. coefficient for diatoms
specific ext. coefficient for green algae

m2 .gC−1
m2 .gC−1

–

N AlgDynamo1
SW _f ixin_y1

-

–

V olume

number of algae species groups = 2
indicator for algae species attached to the
sediment = 0
volume of water compartment or sediment
layer

ea1
ea2
n

1

m3

The default values are fixed and must not be changed!

178 of 464

Deltares

DR
AF

T

Light regime

Table 6.14: Definitions of the output parameters for Extinc_UVG, ExtinaBUVP (ExtinaBUV), ExtPhDUV.

Name in
formulas

Name in
output1

Definition

Units

eat
edt
ept
est
et

ExtU vP hyt
ExtU vODS
ExtU vOSS
ExtU vISS
ExtU v

partial ext. coefficient of algae biomass
partial ext. coeff. of dissolved org. matter
partial ext. coefficient of part. detritus
partial ext. coeff. of susp. inorg. matter
total extinction coefficient

m−1
m−1
m−1
m−1
m−1

1

Notice that the partial extinction coefficients ExtU vBak and ExtU vM acro are input parameters

Deltares

179 of 464

Processes Library Description, Technical Reference Manual

Variable solar radiation during the day
PROCESS :

DAYRAD

Implementation

T

The light intensity during the day varies due to the different angles of the sun in relation to
the earth surface, which depends on latitude as well as season. This module calculates light
intensity (solar radiance, irradiance) at any moment during the day, as a function of latitude on
earth, the average intensity over the day, the time of the day, and day of the year. The variation
of light intensity during the day is relevant for the simulation of both primary producers and
bacterial pollutants. For microphytobenthos, depending for their light supply on the period
that a tidal flat is emerged, the light intensity during the emersion period is very relevant for
their primary production. For coli bacteria the decay rates are so high and influenced by light
intensity, that the variation of solar irradiance during the day can have a significant impact on
the concentration patterns.

Process DAYRAD calculates the light intensity at any moment during the day. It is used in
combination with process CALCRADDAY, that provides light intensities at the top and the
bottom of water and sediment layers for daily varying light intensity. Currently, DAYRAD can
not be used for the simulation of bacterial pollutants.

DR
AF

6.3

Table 6.15 and Table 6.16 provide the definition of the input and output parameters.
Formulation

The formulations used to calculate the solar intensity are based on the constant radiance from
the sun (1367 W m−2 ) and the angle between the sun and the earth surface. The resulting
solar irradiance can be corrected for measured daily averaged irradiance, or for cloudiness.
The following formulations are used for the calculation of the maximum solar irradiance at time
t at day d and latitude φ:

Et =
where:

I0 R̄2
(sin δ sin φ + cos δ cos φ cos ω)
π R2

δ = 0.006918−
0.399921 × cos(1 × η × d)−
0.006758 × cos(2 × η × d)−
0.002697 × cos(3 × η × d)+
0.070257 × sin(1 × η × d)+
0.000907 × sin(2 × η × d)+
0.001480 × sin(3 × η × d)
η=

2π
366

R̄2
= 1 + 0.033 cos(ηd)
R2
π
ω = |12 − h| ×
12
and:

180 of 464

Deltares

Light regime

maximum solar irradiance at time t [W.m−2 ]
sun constant = 1367 [W.m−2 ]
day of the year (1-366; 1 = 1 January, 365 = 31 December) [d]
relative difference of distance earth-sun compared to average distance [-]
angle between sun and earth surface at specific day [rad]
angle between sun and earth surface at hour h [rad]
hour of the day [h]
latitude [rad]

Et
I0
d
R̄2
R2

δ
ω
h
φ

The parameters above are calculated from the input parameters as follows:

d=

IT IM E
− Ref day
86400



h = IT IM E − int(Ref day) × 86400 −
Latitude
× 2π
360

DR
AF

φ=

Ref time
3600

T



where:

IT IM E
Latitude
Ref Day
Ref time

DELWAQ time [scu]
latitude of area of interest [degrees]
day at start of the simulation [d]
time at the start of the simulation [h]

The maximum solar irradiance at any time during the day is corrected for the effects of clouds
and extinction in the atmosphere with measured data of the daily averaged light intensity.
The calculated function of irradiance over the day is scaled with the ratio between maximum
solar irradiance and measured light intensity. This requires the maximum solar irradiance
expressed as the total irradiance over the day. Integration of the formulation for Et above for
a day results in the following expression for the maximum average irradiance over the day Ed
[W.m−2 ].

Ed =

I0 R̄2
× 2 × (ω0 sin δ sin φ + cos δ cos φ sin ω0 )
π
R

where:

ω0 = arccos(−tgδ × tgφ)

Correction of the maximum irradiance at time t (Et [W m−2 ]) for cloudiness and atmospheric
absorption by using the measured average light intensity (Radsurf [W m−2 ]) is formulated
as follows:

Dayrad = Et ×

Radsurf
Ed

Directives for use
 The light intensity at the water surface RadSurf is the total visible light intensity (solar
radiation) or the photosynthetic active light intensity (PAR). See section Light intensity in
the water column for more information.

Deltares

181 of 464

Processes Library Description, Technical Reference Manual

References
Velds (1992)
Table 6.15: Definitions of the input parameters in the formulations for DAYRAD.

Name in
formulas

Name in
output

Definition

Units

Radsurf

RadSurf

daily average observed light intensity at
water surface

W.m−2

Latitude
Ref day

Latitude
Ref day

thickness of a water or sediment layer
time at the start of the simulation

degrees
-

T

Table 6.16: Definitions of the output parameters for DAYRAD.

Name in
output

Definition

DayRad

DayRadSurf

actual light intensity at water surface as
varying over the day

DR
AF

Name in
formulas

182 of 464

Units
W.m−2

Deltares

Light regime

Computation of day length
PROCESS :

DAYLENGTH

This module calculates the length of a day (sunrise to sunset) as a function of latitude on
earth. As an example, of the results for four different latitudes are shown in Figure 6.1.
Implementation
The process is only implemented for DayL

T

Formulation

E = 0.01721420632
Declin = 0.006918−
0.399921 × cos(1 × E × DayN r)−
0.006758 × cos(2 × E × DayN r)−
0.002697 × cos(3 × E × DayN r)+
0.070257 × sin(1 × E × DayN r)+
0.000907 × sin(2 × E × DayN r)+
0.001480 × sin(3 × E × DayN r)
−0.01454389765 − sin(Declin) × sin(LatRad)
T mp =
cos(Declin) × cos(LatRad)

DR
AF

6.4

If T mp > 1.0

DayL = 0.0

(6.1)

If T mp < −1.0

Else

DayL = 1.0

(6.2)

DayL = 7.639437268 × arccos(T mp)/24

(6.3)

ITIME
Latitude
LatRad
DayNr
RefDay
DayL
Tmp

Deltares

DELWAQ time [scu]
latitude of area of interest [degr]
latitude of area of interest [rad]
number of the day for the calculation of the day length (1=1 January, 365 = 31
December) [-]
day at start of the simulation [d]
daylength (fraction of a day - sunrise to sunset) [-]
temporarily variable for calculation [d]

183 of 464

Processes Library Description, Technical Reference Manual

Day length as function of time of year
(d)
1

0.75

0.5

0.25

0

50

100

150
200
day number

250

=
=
=
=

300

75
65
52.1
10

350

T

0

latitude
latitude
latitude
latitude

DR
AF

Figure 6.1: Day length calculated by the module DAYL for the latitudes 10 ◦ , 52.1◦ ,
65◦ and 75◦ . The latitude of 52.1◦ refers to De Bilt, The Netherlands

Directives for use
 The reference date and time for a DELWAQ calculation is not necessarily the first of January. At the start of a DELWAQ calculation the default day number calculated by the
module DAYL equals 0 (based on variable ITIME which equals 0.0 at that time). The reference day (input item RefDay) enables you to tell the day length module the actual day
number at the start of a calculation. E.g. when a run starts at the first of April, the variable
RefDay should be set to 91.
Additional references
Velds (1992)

184 of 464

Deltares

Light regime

Computation of Secchi depth
PROCESS :

SECCHI

The Secchi depth is a measure for the transparency of water, and is measured with a Secchi
disk. The transparency depends on the extinction of visible light in the water column. The
euphotic zone for algae is approximately 2.5 times the Secchi depth.

Implementation

T

Process SECCHI may apply an alternative advanced sub-model of the extinction coefficient
called UITZICHT. This sub-model takes the optical properties of a water column into account.
Given the advanced features of UITZICHT this module is not (yet) described in this manual.
The user is referred to (Rijkswaterstaat/RIKZ, 1990) for background and details.

The auxiliary process SECCHI has been implemented for the following substances:

 IM1, IM2, IM3, POC1, POC2, POC3, POC4.

DR
AF

6.5

Table 6.17 provides the definitions of the parameters occurring in the formulations.
Formulation

Two methods are available to compute the Secchi depth.

For SW _U itz = 0.0 (UITZICHT not applied) the Poole-Atkins relation is applied:

SD =

apa
et

where:

apa
et
SD

Poole-Atkins constant (1.7-1.9) [-]
total extinction coefficient [m−1 ]
Secchi depth [m]

For SW _U itz = 1.0 the auxiliary process UITZICHT is applied for the calculation of the Secchi depth based on a background extinction and the concentrations of (in)organic suspended
matter, chlorophyll and dissolved organic matter (fulvic and humic acids).
Directives for use
 The concentrations of IM 1, IM 2, IM 3, P OC1, P OC2, P OC3 and P OC4 are only
used if auxiliary process UITZICHT is applied for the calculation of the total extinction
coefficient.
 UITZICHT is applied when SW _U itz = 1.0. In that case a number of additional input parameters are needed, among which ExtV LODS (partial extinction coefficient dissolved
organic matter) calculated by process ExtincV LG and Chlf a calculated by the active
phytoplankton module.

Deltares

185 of 464

DR
AF

T

Processes Library Description, Technical Reference Manual

Table 6.17: Definitions of the parameters in the above equations for SECCHI, exclusive
of input parameters for auxiliary process UITZICHT.

Name in
formulas

Name in
input

Definition

Units

apa

P AConstant

Poole-Atkins constant

-

ExtV l

total extinction coefficient

m−1

option parameter: if 0.0 no UITZICHT (default), if 1.0 UITZICHT is applied

-

et

SW _U itz Sw_U itz

186 of 464

Deltares

7 Primary consumers and higher trophic levels
Contents
7.1

Grazing by zooplankton and zoobenthos (CONSBL) . . . . . . . . . . . . . 188

7.2

Grazing by zooplankton and zoobenthos (DEBGRZ)

DR
AF

T

. . . . . . . . . . . . 199

Deltares

187 of 464

Processes Library Description, Technical Reference Manual

Grazing by zooplankton and zoobenthos (CONSBL)
PROCESS :

CONSBL

The consumption of algae and detritus by zooplankton and zoobenthos is called grazing.
Grazers have a certain preference with respect to the components of their food, meaning that
they consume certain algae species rather than other algae species, and rather phytoplankton
than detritus. The four nutrient components in the model (organic carbon, nitrogen, phosphorus and silicon), are all required for grazers. The consumption process involves ingestion
(uptake) and digestion of food components, egestion of detritus, excretion of nutrients, and
growth and respiration. Grazer biomass eventually returns to detritus due to mortality. Net
biomass growth or decline and net detritus mineralisation are the results of grazing.

T

The grazing module uses a so-called ‘forcing function’ approach. The user needs to specify
the biomass development of filterfeeders (benthic and zooplankton) over the year. Based
on this biomass the grazing rate on phytoplankton and detritus is simulated. The simulation
takes into account the filtration, assimilation, respiration, mortality and excretion by the filter
feeders. Whenever the nutrient availability is insufficient to sustain the specified biomass
development, the filterfeeder biomass in the model is corrected. A lower biomass, that can be
sustained, is assumed in the model in that case. Inorganic nutrients and detritus are released
by the filterfeeders, due to excretion, respiration and mortality. For pelagic filterfeeders these
substances are released to the water column. For benthic filterfeeders the detritus is released
to the sediment.

DR
AF

7.1

CONSBL can be applied for up to five types of grazers, which may be species groups or
individual species of zooplankton and zoobenthos. An important difference between the two
species groups is that zoobenthos is only active in the lower water layer. The egestion of
digested algae and detritus by grazers in the form of faecal pellets implies the production of
detritus. This detritus may be released in the water column or added to the sediment detritus
pool. The last option can be effectuated in the model for all zoobenthos groups.
Due to respiration nutrients (N/P/Si) are released into the water column. The effect of respiration on the dissolved oxygen budget is ignored in the model.
The process formulations of CONSBL have been described in more detail by WL | Delft Hydraulics (1990, 1992c); Van der Molen et al. (1994b).
The advantage of a forcing function over a dynamic grazing model is that the grazer biomass
is controlled. Even state-of-the-art dynamic simulation of grazers is still subject to problems of
stability and limited accurateness. However, imposing forcing functions demands for reliable
and rather frequently measured grazer biomass data.
Implementation
Process CONSBL has been implemented for maximally five species groups of grazers. The
input and output parameter names of the first group refer to zooplankton. The names of
the parameters of the second group concern zoobenthos, and more specifically mussel type
grazers. The other three groups have generic names. However, the names have only been
selected in this way for easy recognition of simulated grazer species groups. The formulations
are equal for the five groups, which means that the user eventually defines the nature of each
grazer group.
Pelagic and benthic grazers are modelled in the same way. The only differences between

188 of 464

Deltares

Primary consumers and higher trophic levels

pelagic and benthic grazers are the unit and the fate of produced detritus. Zooplankton
biomass needs to be imposed in [g m−3 ], whereas zoobenthos biomass must to be provided
in [g m−2 ]. The selection is made using option parameter (i)U nitSW S . Selection of [g m−2 ]
implies that the grazer biomass in water layers without sediment surface is made equal to zero.
The parameter (i)F rDetBot determines whether detritus produced by the grazers is released into the water column ((i)F rDetBot = 0) or to the sediment ((i)F rDetBot = 1).
CONSBL has been formulated in a generic way and can be applied for water as well as
sediment layers (layered sediment). It can also be used in combination with the sediment
option S1/2. Detritus produced by grazers is deposited in the water column or in DETCS1
(etc.).

for BLOOM,

T

CONSBL has been implemented for the following substances:

 ALGC, ALGN, ALGP, ALGSi, BLOOMALG01-BLOOMALG30, POC1, PON1, POP1, OPAL,
DETCS1, DETNS1, DETPS1, DETSiS1, NH4, NO3, PO4, Si, OXY, TIC and ALKA

DR
AF

for DYNAMO,

 GREEN, DIAT, POC1, PON1, POP1, OPAL, DETCS1, DETNS1, DETPS1, DETSiS1,
NH4, NO3, PO4, Si, OXY, TIC and ALKA
Sulfur is not considered by CONSBL.

Table 7.1 and Table 7.2 provide the definitions of the parameters occurring in the user-defined
input and output.
Formulation

The mass fluxes caused by grazing are calculated taking the following steps:
1 conversion of the biomass forcing function input to the desired units;
2 adjustment (if necessary) of the imposed grazer biomass according growth and mortality
constraints;
3 calculation of the consumption rates for detritus and algae;
4 calculation of the rates of food assimilation and detritus production;
5 correction of the assimilation rates for respiration;
6 adjustment of the grazer biomass;
7 calculation of the detritus production rates according to the food availability constraints;
8 evaluation of the total conversion rates as additional output parameters; and
9 evaluation of the grazer biomass concentrations as additional output parameters.
The next sections deal with each of these steps.
1. Conversion of units
The forcing function formulations are based on the imposed grazer biomass expressed in
[gC m−3 ]. However, benthic grazer biomass is usually expressed in [gC m−2 ]. The input
to the model contains option parameters (i)U nitSW , with which the grazer biomass unit
can be selected for each grazer species group. When (i)U nitSW = 0.0 the model assumes that biomass concentrations provided in the input are expressed in [gC m−3 ]. When
(i)U nitSW = 1.0 the model assumes that biomass concentrations provided in the input
are expressed in [gC m−2 ]. In that case the concentrations are converted to [gC m−3 ] by

Deltares

189 of 464

Processes Library Description, Technical Reference Manual

means of divison by the water depth H .
2. Adjustment of grazer biomass according to growth and mortality constraints
The imposed grazer biomasses are adjusted according to growth and mortality constraints
in a step by step way. The grazer biomass at the end of a timestep (t2 ) is diminished when
the maximal growth rate does not support the imposed biomass increase with respect to the
biomass at the beginning of a timestep (t1 ). The grazer biomass at t2 is augmented when the
maximal natural mortality rate does not allow the imposed biomass decrease with respect to
the biomass at t1 . The grazer biomass in the next timestep is adjusted accordingly as follows:
when Cgri2i ≥ Cgr1i ,

Cgr2i = Cgrci
Cgr2i = Cgri2i

if Cgri2i > Cgrci
if Cgri2i ≤ Cgrci

DR
AF

kgri = kgri20 × ektgri ×(T −20)

T

Cgrci = Cgr1i × (1 + kgri × ∆t)

when Cgri2i < Cgr1i ,

Cgrci = Cgr1i × (1 − kmrti × ∆t)
Cgr2i = Cgrci
Cgr2i = Cgri2i

if Cgri2i < Cgrci

if Cgri2i ≥ Cgrci

ktgri ×(T −20)
kmrti = kmrt20
i ×e

with:

Cgr1i
Cgr2i
Cgrci
Cgri2i
kgr
kgr20
ktgr
kmrt
kmrt20
ktmrt
T
∆t
i

grazer biomass concentration at t1 [ gC m−3 ]
grazer biomass concentration at t2 [ gC m−3 ]
grazer biomass concentration constraint at t2 [ gC m−3 ]
imposed grazer biomass concentration at t2 [ gC m−3 ]
maximal growth rate [d−1 ]
maximal growth rate at 20 ◦ C [d−1 ]
temperature coefficient of growth [-]
maximal natural mortality rate [d−1 ]
maximal natural mortality rate at 20 ◦ C [d−1 ]
temperature coefficient of mortality [-]
water temperature [◦ C]
timestep [d]
index for grazer species group 1-5 [-]

3. Consumption rates
The consumption rate of the grazers is limited by the filtration rate at low food availability and
by the uptake rate at high food availability. The filtration rate and the uptake rate are equal
at a certain food concentration Cf dci. The total food availability is defined as the sum of
the concentrations of detritus and phytoplankton groups, adjusted by a preference factor for
each food source. The preference factor accounts for the suitability of the food source for the

190 of 464

Deltares

Primary consumers and higher trophic levels

grazers. Certain phytoplankton species and detritus fractions are more difficult to filtrate and
digest for the grazers than others.

Cf di = f dpri × Cdet1 +

m
X

(f apri × Calgj )

j=1

with:
biomass concentration of algae species group j [ gC m−3 ]
food concentration available to grazer species group i [ gC m−3 ]
detritus organic carbon concentration [ gC m−3 ]
preference of a grazer species group i for detritus [-]
preference of a grazer species group i for algae species group j [-]
number of algae groups, different for (BLOOM) and (DYNAMO) [-]
index for grazer species groups (at most 5) [-]
index for algae species groups (depends on whether BLOOM is used or DYNAMO) [-]

T

Calgj
Cf di
Cdet1
f dpri
f apri,j
m
i
j

DR
AF

The maximal filtration rate and the maximal uptake rate are defined as:

kf ili = Cgr1i × ksf ili ×

Cf di
Ksf di + Cf di

ksf ili = ksf ili20 × ektf ili ×(T −20)
kupi =

Cgr1i × kmupi
Cf di

ktupi ×(T −20)
kmupi = kmup20
i ×e

with:

kf il
ksf il
ksf il20
ktf il
kup
kmup
kmup2 0
ktup
Ksf d
i

filtration rate [d−1 ]
maximal specific filtration rate [m3 gC−1 d−1 ]
maximal specific filtration rate at 20 ◦ C [m3 gC−1 d−1 ]
temperature coefficient for filtration [-]
uptake rate [d−1 ]
maximal uptake rate [d−1 ]
maximal uptake rate at 20 ◦ C [d−1 ]
temperature coefficient for uptake [-]
half saturation constant for uptake [gC m−3 ]
index for grazer species groups 1–5 [-]

The consumption of detritus and algae biomass by grazing is derived from the maximum
uptake rate when the available food concentration is equal or larger than a certain critical
amount. This amount is the biomass cencentration for which the filtration rate and the maximal
uptake rate are equal:

Cf dci =

kmupi Ksf di + Cf di
×
ksf ili
Cf di

with:

Cf dci

Deltares

critical concentration of food for grazer group i [gC m−3 ]

191 of 464

Processes Library Description, Technical Reference Manual

The consumption process rate is equal to either the filtration or the uptake rate according to:

kcnsi = kf ili
kcnsi = kupi

Cf di < Cf dci
if Cf di ≥ Cf dci
if

with:
consumption process rate of grazer group i [d−1 ]

kcnsi

So far, all rates are referring to organic carbon as a nutrient to grazers. Since the nutrient stochiometry of food is also important to grazers, the nutrient fluxes connected with grazing have
to be taken into account in the model. The consumption rates for the nutrient components of
detritus and the biomass of an algae species for a grazer group are:

T

Rdcns1k,i = f dpri × kcnsi × Cdetk

with:

DR
AF

Racnsk,i,j = f apri,j × kcnsi × anutk,j × Calgj

anutk,j
Cdetk
f dpri
f apri,j
Racnsk,i,j
Rdcns1k,i
i
j
k

stochiometric const. of nutr. k over org. carbon in algae j [gC/N/P/Si gC−1 ]
detritus concentration for nutrient k [gC/N/P/Si m−3 ]
preference of a grazer species group i for detritus [-]
preference of a grazer species group i for algae species group j [-]
cons. rate of grazer group i for nutrient k in algae j [gC/N/P/Si m−3 d−1 ]
gross cons. rate of grazer group i for nutrient k in detritus [gC/N/P/Si m−3 d−1 ]
index for grazer species groups 1–5 [-]
index for algae species groups 1–15 (BLOOM) or 1–2 (DYNAMO) [-]
index for nutrients, 1 = carbon, 2 = nitrogen, 3 = phosphorus, 4 = silicon [-]

4. Assimilation and production of detritus
Consumed food is either assimilated into grazer biomass, respired or egested as detritus
(fecal pellets). For benthic grazers part of the egested detritus is deposited at the sediment
and is therefore added to the sediment detritus pool. If respiration is ignored the total rates
of food assimilation, net detritus consumption and sediment detritus production caused by
grazing are as follows:

Ras1k,i = (1 − f deti ) × Rdcns1k,i +

m
X

((1 − f algi,j ) × Racnsk,i,j )

j=1

Rdcns2k,i

m
X
= (1 − f deti )×Rdcns1k,i +
((1 − f algi,j × (1 − f sedi )) × Racnsk,i,j )
j=1

Rsdpr1k,i = f deti × f sedi × Rdcns1k,i +

m
X

(f algi,j × f sedi × Racnsk,i,j )

j=1

with:

f algi,j
f deti
f sedi
Ras1k,i

egested fraction of algae j consumed by grazer i, = 1-yield [-]
egested fraction of detritus consumed by grazer i, = 1-yield [-]
fraction of detritus egested by grazer i added to the sediment detritus pool [-]
total food assimilation rate for nutrient k for grazer group i [gC/N/P/Si m−3 d−1 ]

192 of 464

Deltares

Primary consumers and higher trophic levels

Rdcns2k,i net cons. rate of grazer group i for nutrient k in detritus [gC/N/P/Si m−3 d−1 ]
Rsdpr1k,i total nutrient k in detr. prod. at the sediment for all grazers [gC/N/P/Si m−3 d−1 ]
5. Assimilation corrected for respiration (nutrient excretion)
The food assimilation rates as calculated above are available for the growth of the grazer
biomass. However, the actual assimilation of specific organic nutrients may be lower because
of the difference in the nutrient stochiometries of grazers, algae and detritus. The most limiting
nutrient determines the actual assimilation rates for all nutrients. The remaining portions of
the other nutrients are egested as detritus in addition to the detritus production calculated
above.

T

Moreover, due to growth respiration and maintenance respiration part of the assimilated
biomass is converted back into inorganic nutrients. In order to calculate the nett assimilation rate the gross assimilation rate needs to be corrected for respiration.
The actual assimilation rates and the respiration rates follow from:

Ras21,i = min (Ras1k,i /bnutk,i )
k=1−4

DR
AF

Rrsp1k,i = bnutk,i × f rsp1i × Ras21,i
Rrsp2k,i = bnutk,i × krsp2i × Cgr1i
Rrspk,i = Rrsp1k,i + Rrsp2k,i
Ras3k,i = Ras2k,i − Rrspk,i

ktrsp1i ×(T −20)
f rsp1i = f rsp120
i ×e
ktrsp2i ×(T −20)
krsp2i = krsp220
i ×e

with:

bnutk,i
Cgr1i
f rsp1i
f rsp120
i
ktrsp1
krsp2i
krsp220
i
ktrsp2
Rrspk,i
Rrsp1k,i
Rrsp2k,i
Ras2k,i
Ras3k,i

stochiometric const. of nutr. k over org. carbon in grazer i [gC/N/P/Si gC−1 ]
grazer biomass concentration at t1 [gC m−3 ]
growth respiration fraction [-]
growth respiration fraction at 20 ◦ C [-]
temperature coefficient for growth respiration [-]
maintenance respiration rate [d−1 ]
maintenance respiration rate at 20 ◦ C [d−1 ]
temperature coefficient for maintenance respiration [-]
total respiration rate for nutrient k and grazer i [gC/N/P/Si m−3 d−1 ]
growth respiration rate for nutrient k and grazer i [gC/N/P/Si m−3 d−1 ]
maintenance respiration rate for nutrient k and grazer i [gC/N/P/Si m−3 d−1 ]
actual nutrient k in food ass. rate for grazer group i [gC/N/P/Si m−3 d−1 ],
actual nutrient k in food ass. rate for grazer group i [gC/N/P/Si m−3 d−1 ], diminished with growth respiration

6. Correction of grazer biomass for the food constraint
Grazers can not assimilate more food than is available. The food that is available to a grazer
group on a daily basis is equal to Ras31,i . Consequently, the net growth rate of a grazer
group should not exceed the actual food assimilation rate. If the imposed grazer biomass at
t2 is larger than supported by food assimilation, it must be diminished in order to meet the
food constraint. The corrected grazer biomass Cgr2ci follows from:

Rgr1i =

Deltares

(Cgr2i − Cgr1i × (1 − krsp2i × ∆t))
∆t
193 of 464

Processes Library Description, Technical Reference Manual

if Rgr1i > Ras31,i ,

Cgr2ci = Cgr1i × (1 − krsp2i × ∆t) + Ras31,i × ∆t
Rgri = Ras31,i
if Rgr1i ≤ Ras31,i ,

Cgr2ci = Cgr2i
Rgri = Rgr1i
with:

T

grazer biomass concentration at t1 [ gC m−3 ]
grazer biomass concentration at t2 [ gC m−3 ]
corrected grazer biomass concentration at t2 [ gC m−3 ]
actual growth rate for grazer group i [ gC m−3 d−1 ]
imposed growth rate for grazer group i [ gC m−3 d−1 ]
timestep [d]

DR
AF

Cgr1i
Cgr2i
Cgr2ci
Rgri
Rgr1i
∆t

Notice that Rgri is negative in the case of net mortality within a timestep at the decrease of
grazer biomass.
7. Correction of detritus consumption and production rates for the food constraint
The total rates of food assimilation, net detritus consumption and sediment detritus production
caused by grazer group i calculated above need to be corrected for changes in grazer biomass
resulting from the food constraint. In case of mortality the grazer biomass decrease needs to
be added to the detritus production rates. The corrected rates are:

Rask,i = bnutk,i × Rgri

Rdcnsk,i = Rdcns2k,i + (1 − f sedi ) × (Ras3k,i − Rask,i )
Rsdprk,i = Rsdpr2k,i + f sedi × (Ras3k,i − Rask,i )
with:

Rask,i
nutrient k in food assimilation rate for grazer group i [gC/N/P/Si m−3 d−1 ],
Rdcnsk,i net cons. rate of grazer group i for nutrient k in detritus [gC/N/P/Si m−3 d−1 ]
Rsdprk,i nutrient k in detr. prod. at the sediment for grazer i [gC/N/P/Si m−3 d−1 ]
Notice that these relations hold even in case of mortality within a timestep. Rask,i is negative
in that case and adds up to the detritus rates.
8. Total algae, detritus and inorganic nutrient conversion rates
The total rates of algae consumption, net detritus consumption, sediment detritus production
and inorganic nutrient excretion caused by grazing are:

Racnsk,j =

n
X

(Racnsk,i,j )

i=1

Rtacnsk =

m
X

(Racnsk,j )

j=1

194 of 464

Deltares

Primary consumers and higher trophic levels

Rtask =

n
X

(Rask,i )

i=1

Rtdcnsk =

n
X

(Rdcnsk,i )

i=1

Rtsdprk =

n
X

(Rsdprk,i )

i=1

Rtrspk =

n
X

(Rrspk,i )

i=1

total consumption rate for nutrient k in algae group j [gC/N/P/Si m−3 d−1 ]
total consumption rate for nutrient k in algae [gC/N/P/Si m−3 d−1 ]
total food assimilation rate for nutrient k [gC/N/P/Si m−3 d−1 ]
total consumption rate for nutrient k in detritus [gC/N/P/Si m−3 d−1 ]
total release rate for inorganic nutrient k by respiration [gC/N/P/Si m−3 d−1 ]
total nutrient k in detr. prod. at the sediment for all grazers [gC/N/P/Si m−3 d−1 ]
number of grazer species groups (5; [-])
number of algae species groups (2 for DYNAMO or 15 for BLOOM; [-])
index for grazer species groups [-]
index for algae species groups [-]
index for nutients, 1 = carbon, 2 = nitrogen, 3 = phosphorus, 4 = silicon [-]

DR
AF

Racnsk,j
Rtacnsk
Rtask
Rtdcnsk
Rtrspk
Rtsdprk
n
m
i
j
k

T

with:

9. Grazer biomass concentrations
CONSBL delivers some additional output parameters in the form of the biomass concentrations of the grazer species groups per volume of (sediment overlying) water. The output
values of these parameters may deviate from the imposed biomass time series because of
two reasons. The biomass may have been adjusted as described above in order to obey the
growth, mortality and food constraints. The other reason is connected with interpolation over
time. The output biomasses are input biomasses for t1 at the beginning of the next timestep:

Cgr1i = Cgr2ci /f si

with:

f si

scaling factor for the biomass of grazer group i [-]

The scaling factor f si may be used to scale the grazer biomass up or down for calibration
purposes. When the grazer has been indicated as zoobenthos group with option parameter
(i)U nitSw, the biomass is expressed in [ gC m−2 ] by means of multiplication with water
depth H .
Directives for use
 The proces rates in connection with grazing have a temperature basis of 20 oC. That
means that input values have to be corrected when provided for another temperature
basis.
 The user needs to make a decision about how to route produced detritus in the model
using the input parameters (i)F rDetBot. When (i)F rDetBot = 0.0 all detritus by
grazers will be allocated to the sediment overlying water compartment (layer). All produced detritus will be added to the sediment detritus pools when (i)F rDetBot = 1.0.

Deltares

195 of 464

Processes Library Description, Technical Reference Manual

 Grazers in CONSBL consume algae biomass and detritus from the water column only in
the case of the S1-S2 option for the sediment.

 The constraints imposed on grazer biomass in relation to maximal growth or maximal

T

mortality imply that the first adjustment of the input biomass affects the next adjustment,
and so forth. When composing the input biomass time series the user should be aware
of this step by step adjustment of the grazer biomasses. When differences between the
imposed and adjusted time series turn out to be large or systematic, the user may want to
revise the input time series in order to ensure realistic calculations of grazing pressure on
algae by the model.
 The food preference parameters (i)ALGP R(j) and (i)DET P R are to be considered
weigth factors, that must always be smaller than or equal to 1.0 the default value.
 The scaling factors (i)GRZM L may be used to scale the grazer biomass up or down
for calibration purposes. The factors have the default value 1.0.
 SwDetT yp needs to be equal to 1.0 (default) as it refers to an option for detritus substances input that does no longer exist.
Additional references

DR
AF

WL | Delft Hydraulics (1997c), Scholten and Van der Tol (1994),

Table 7.1: Definitions of the input parameters in the formulations for CONSBL.

Name in
formulas

Name in input

Definition

anut2,1

N CratGreen green algae spec. stoch. constant nitro-

anut2,2

N CratDiat

anut2,j

N CRAlg(j)

anut3,1

P CratGreen

anut3,2

P CratDiat

anut3,j

P CRAlg(j)

anut4,1

SCratGreen

anut4,2

SCratDiat

anut4,j

SCRAlg(j)

Cgri21
Cgri22

Zooplank
M ussel

Cgri23
Cgri24
Cgri25
Calg1

Grazer3
Grazer4
Grazer5
Green

gen over carbon
diatoms spec. stoch. constant nitrogen
over carbon
BLOOM algae group spec. stoch. const.
nitr. over carb.
green algae spec. stoch. constant phos.
over carbon
diatoms spec. stoch. constant phosphorus over carbon
BLOOM algae group spec. stoch. const.
phos. over carb.
green algae spec. stoch. constant silicon
over carbon
diatoms spec. stoch. constant silicon over
carbon
BLOOM algae group spec. stoch. const.
sil. over carb.
biomass concentration of zooplankton
biomass concentration of mussel type
zoobenthos
biomass concentration of grazer type 3
biomass concentration of grazer type 4
biomass concentration of grazer type 5
biomass concentration of green algae
(DYNAMO)

Units
gN gC−1
gN gC−1
gN gC−1
gP gC−1
gP gC−1
gP gC−1
gSi gC−1
gSi gC−1
gSi gC−1
gC m−3 or −2
gC m−3 or −2
gC m−3 or −2
gC m−3 or −2
gC m−3 or −2
gC m−3

continued on next page

196 of 464

Deltares

Primary consumers and higher trophic levels

Table 7.1 – continued from previous page
Name in
formulas

Name in input

Calg2

Diat

Definition

Units
gC m−3

Cdet1
Cdet2
Cdet3
Cdet4

biomass concentration of diatoms (DYNAMO)
BLOOMALG(j )biomass concentration of a BLOOM algae group
P OC1
detritus organic carbon concentration
P ON 1
detritus nitrogen concentration
P OP 1
detritus phosphorus concentration
Opal
opal silicate concentration

H

Depth

depth of a water compartment (layer)

m

–

(i)U nitSW

group spec. option for biomass unit (1=g
m−2 , 0=g m−3 )

-

T

T emp

water temperature

◦

gC m−3
gC m−3
gN m−3
gP m−3
gSi m−3

T

DR
AF

Calgj

C

V olume

volume of a water comp. (layer) or sediment layer

m3

DELT

time interval,
timestep

d

bnut1,i

(i)GRZST C

bnut2,i

(i)GRZST N

bnut3,i

(i)GRZST P

bnut4,i

(i)GRZST Si

stoch. constant for carbon over carbon in
grazer i
stoch. constant for nitrogen over carbon
in grazer i
stoch. constant for phosphorus over carbon in grazer i
stoch. constant for silicon over carbon in
grazer i

f apri,1

(i)ALGP RGrn preference of grazer i for green algae

V
∆t

f apri,2
f apri,j
f dpri
f algi,1
f algi,2
f algi,j
f deti
f sedi

that is the DELWAQ

(DYNAMO)
(i)ALGP RDiatpreference of grazer i for diatoms (DYNAMO)
(i)ALGP R(j) preference of grazer i for BLOOM algae
group j
(i)DET P R
preference of grazer i for detritus
(i)ALGF F Grn egested fraction of green algae consumed by grazer i
(i)ALGF F Diategested fraction of diatoms consumed by
grazer i
(i)ALGF F (j) egested fraction of algae j consumed by
grazer i
(i)DET F F
egested fraction of detritus consumed by
grazer i
(i)F rDetBot fr. of produced detr. by grazer i to sediment detr. pool

gC gC−1
gN gC−1
gP gC−1
gSi gC−1
-

continued on next page

Deltares

197 of 464

Processes Library Description, Technical Reference Manual

Table 7.1 – continued from previous page
Name in
formulas

Name in input

Definition

Units

f si

(i)GRZM L

scaling factor for the biomass of grazer i

-

f rsp120
i

(i)GRZRE

-

kgri20
kmup20
i,k
kmrt20
i

(i)GRZGM
(i)GRZRM
(i)GRZM M

krsp220
i

(i)GRZSE

Ksf di

(i)GRZM O

ksf ili20

(i)GRZF M

ktf il

(i)T M P F M

growth respiration fraction for grazer i at
20 ◦ C
maximal growth rate of grazer i at 20 ◦ C
maximal uptake rate of grazer i at 20 ◦ C
maximal mortality rate of grazer i at 20
◦
C
maintenance respiration rate for grazer i
at 20 ◦ C
half saturation constant for food uptake
by grazer i
maximal specific filtration rate of grazer i
at 20 ◦ C
temperature coefficient of filtration for
grazer i
temperature coefficient of growth for
grazer i
temperature coefficient of mortality for
grazer i
temperature coeff. of growth respiration
for grazer i
temperature coeff. of maintenance resp.
for grazer i
temperature coefficient of uptake for
grazer i

ktmrt

(i)T M P GM

(i)T M P M M

ktrsp1

(i)T M P RE

ktrsp2

(i)T M P SE

ktup

(i)T M P RM

1

d−1

T

DR
AF

ktgr

d−1
d−1
d−1

gC m−3+
m3 gC−1 d−1
◦ −1

C

◦ −1

C

◦ −1

C

◦ −1

C

◦ −1

C

◦

C-1

(i) indicates grazer species groups 1–5, respectively Z for zooplankton, M for mussel type zoobenthos, G3, G4 and G5 for user defined groups.
2
(j) indicates BLOOM algae species groups 1–30.

Table 7.2: Definitions of the output parameters for CONSBL.

Name in
formulas

Name in output

Definition

Units

Cgr11
Cgr12

CZooplank
CM ussel

biomass concentration of zooplankton
biomass concentration of mussel type
zoobenthos
biomass concentration of grazer type 3
biomass concentration of grazer type 4
biomass concentration of grazer type 5

gC m−3 or −2
gC m−3 or −2

Cgr13
Cgr14
Cgr15

198 of 464

CGrazer3
CGrazer4
CGrazer5

gC m−3 or −2
gC m−3 or −2
gC m−3 or −2

Deltares

Primary consumers and higher trophic levels

Grazing by zooplankton and zoobenthos (DEBGRZ)
PROCESS :

DEBGRZ

The consumption of algae and detritus by zooplankton and zoobenthos is called grazing.
Grazer related processes are filtration, ingestion, and digestion of food components, (pseudo)faeces
production and respiration, as well as growth and mortality.

T

The grazer module DEBGRZ simulates grazing using a fully dynamic approach, which contrasts with the semi-dynamic approach of the CONSBL routine. The grazing module is based
on the Dynamic Energy Budget (DEB) theory. DEB-theory is a modelling framework based on
first principles and simple physiology-based rules that describe the uptake and use of energy
and nutrients and the consequences for physiological organization throughout an organism’s
life cycle ?Kooijman2010). DEB models are generic models of organism growth, and can be
used for basically any species or life stage. The aspect that makes DEB framework unique
and separates it from more traditional "net production" models, is its compartmented energy
storage or reserve dynamics.
The DEBGRZ module is originally set up for (passive) shellfish, but can also be used for
other benthic or suspended filter feeders as well as for (active) pelagic filter feeders, but note
that the organisms are described by multiple state variables such that the exchange of active
organisms between grid cells may lead to changes in the ratios of their state variables.

DR
AF

7.2

Implementation

The module allows for maximally 5 different grazer populations or cohorts, which may belong to different species (groups), and which may be simulated separately or simultaneously.
Physiological parameter settings determine which species (group) is simulated. Option parameter SWBen specifies whether the grazers are pelagic (i.e. passively transported by the
water, SWBEN=0), benthic (fixed to the bottom, SWBEN=1), or suspended (fixed to some
structure at any vertical position in the water column, SWBEN=2). Parameter FrDetBot determines whether dead material is released into the water column (FrDetBot = 0) or ends up in
the sediment (FrDetBot = 1). Parameter SFSusp determines whether (or to what extent) the
grazers are deposit feeders or filterfeeders. Finally, the option parameter SwV1 determines
whether the simulated grazers represent a cohort (i.e. a group of equal individuals with individual sizes that increase over time, SwV1=0) or to a (simplified) population (i.e. a group of
different individuals with an overall size distribution that is constant over time, SwV1=1).
Cohorts ((i)_SwV 1 = 1) are described by four state variables:
1
2
3
4

total structural biomass ((i)_V ),
total energy biomass ((i)_E ),
total gonadal biomass ((i)_R), and
the number of individuals ((i)_N ).

For simplified populations ((i)_SwV 1 = 0) the number of individuals becomes a derived
variable instead of a state variable, such that only three state variables remain. For pelagic
(active) grazers, initial values for all state variables need to be specified in units per volume
[m−3 ], whereas for benthic or suspended grazers the initial values must be provided in units
per surface area [m−2 ]. Note that the initial length of organisms in cohorts is defined by the
combination of structural volume and number of individuals.
By default the first grazer corresponds to a simplified population of mussels (Mussel), the sec-

Deltares

199 of 464

Processes Library Description, Technical Reference Manual

ond to a simplified population of mesozooplankton (Zoopl), and the three remaining grazers to
cohorts of small, medium, and large shellfish (Grazer3, Grazer4, Grazer5). Note that Grazer3
and Grazer4 have been configured to represent sedentary organisms and Grazer5 has been
configured to represent organisms that are transported along with the water flow.
DEBGRZ can be used in combination with any of the sediment options, being stand-alone,
S1/2 and S1 in combination with SWITCH or GEMSED. It is necessary to select the detritus
substances using option parameter SwDetTyp. DetX is selected for SwDetTyp = 0:0, POX for
SwDetTyp = 1:0.
DEBGRZ has been implemented for the following substances:
for BLOOM,

T

 ALGC, ALGN, ALGP, ALGSi, BLOOMALG01-BLOOMALG30, POC1, PON1, POP1, OPAL,
DETCS1, DETNS1, DETPS1, DETSiS1, NH4, NO3, PO4, Si, OXY, TIC and ALKA
for DYNAMO,

DR
AF

 GREEN, DIAT, POC1, PON1, POP1, OPAL, DETCS1, DETNS1, DETPS1, DETSiS1,
NH4, NO3, PO4, Si, OXY, TIC and ALKA
Sulfur is not considered by DEBGRZ.

Table 7.3 and Table 7.4 provide the definitions of the parameters occurring in the user-defined
input and output.
Formulation

The mass fluxes caused by grazing are described in the following sections:
1 Individual dynamics
1.1
1.2
1.3
1.4
1.5

Filtration, ingestion, and assimilation
Growth and maintenance
Maturity and reproduction
Respiration
Temperature dependency

2 From individuals to populations
2.1
2.2
2.3
2.4
2.5

Standard approach: isomorphs
Simplified approach: V1-morphs
Total grazer rates of change
Total algae, detritus and inorganic nutrient rates of change
Total grazer biomass and other derived variables;

1. Individual dynamics
Although the DEBGRZ module calculates state variables that refer to the total population or
cohort, the heart of the code is based on DEB theory (?) which is formulated at the individual level. Some additions have been made to the standard DEB equations to incorporate
filterfeeding-specific aspects. These additions are not new but have been included before in
other shellfish modelling studies using DEB ???.
1.1 Filtration, uptake and assimilation

200 of 464

Deltares

Primary consumers and higher trophic levels

Shellfish are filter feeders for whom the relation between food uptake and food density can be
described by a Holling Type II response curve ? that is adjusted for the negative influence of
inorganic matter in the filtration capacity of bivalves ?. The negative effect of inorganic matter
can be compensated for by higher food concentrations (competitive inhibition):

fi =

Cf di
Ksf d0i + Cf di

in which

Ksf d0i


= Ksf di

Ctim
1+
Kstimi



with:

Kstimi
i

T

food concentration available to grazer i [gC m−3 ]
concentration of inorganic matter [ g m−3 ]
scaled functional response of grazer i [-]
half saturation constant for food uptake by grazer i [ gC m−3 ]
half saturation constant for food uptake by grazer i adjusted for the negative
influence of inorganic matter [ gC m−3 ]
half saturation constant for the negative effect of inorganic matter on food uptake
[gC m−3 ]
index for grazer species groups 1–5 [-]

DR
AF

Cf di
Ctim
fi
Ksf di
Ksf d0i

The food concentration available to grazer i is the summed concentration of all edible particles. Some particles are too small and pass through the filtering apparatus, which (passive)
selection mechanism is implemented in the model by a preference coefficient for each of the
food components:
m
X
Cf di = f dpri × Cdet1 +
(f apri × Calgj )
j=1

with:

Cf di
Calgj
Cdet1
f dpri
f apri,j
m
i
j

food concentration available to grazer species group i [ gC m−3 ]
biomass concentration of algae species group j [ gC m−3 ]
detritus organic carbon concentration [ gC m−3 ]
preference of a grazer species group i for detritus [-]
preference of grazer type i for algae type j [-]
number of algae groups, different for (BLOOM) and (DYNAMO) [-]
index for grazer species groups (at most 5) [-]
index for algae species groups (depends on whether BLOOM is used or DYNAMO) [-]

According to the DEB theory, the energy ingestion rate is defined as:
2

3
P upte = kuptm20
i × fi × Vi × kTi

with:

fi
scaled functional response of grazer type i [-]
kuptm20
maximum surface-area-specific ingestion rate of grazer i at 20 ◦ C [J cm−2 d−1 ]
i
kTi
Arrhenius rate of change of chemical reaction processes due to temperature
P uptei
Deltares

(see section 1.5) [-]
energy ingestion rate [J ind−1 d−1 ]

201 of 464

Processes Library Description, Technical Reference Manual

structural biovolume of an individual grazer of type i [cm3 ind−1 ]

Vi

In the DEBGRZ module the carbon uptake rates are derived from the energy ingestion rate
by means of the energy-to-carbon conversion factor cec. Also, they are increased by the
indigestible fractions of algae f alg and detritus f det. These indigestible fractions do not
contribute to the ingested energy since they are assumed to be low in energy, but they do
contribute to the amount of ingested carbon. Hence, these fractions implicitly define the carbon specific energy content of each food component.

P uptdi,j = P uptei ×

ceci
(1 − f deti )

P uptai,j = P uptei ×

ceci
(1 − f algi,j )

energy to carbon conversion factor [ gC J−1 ]
egested fraction of detritus consumed by grazer i [-]
egested fraction of algae j consumed by grazer i [-]
energy ingestion rate of grazer i [J ind−1 d−1 ]
uptake rate of detritus for grazer i [gC ind−1 d−1 ]
uptake rate of algal species j for grazer i [gC ind− d−1 ]

DR
AF

ceci
f deti
f algi,j
P uptei
P uptdi
P uptai,j

T

with:

Filtration rates are derived from the carbon uptake rates by increasing them by pseudofaeces losses. These losses stem from active selection, which is incorporated in the module by
means of the ingestion-efficiency coefficient κI . This coefficient defines the fraction of the
filtered food that is actually ingested, while the remaining part (1 − f ie) is excreted as pseudofaeces. Although pseudofaeces and faeces may have different characteristics with respect
to sedimentation and mineralization, these differences are not (yet) taken into account in this
module, and both products end up in the same detritus pool. But note that the stoichiometry
of detritus will vary according to its constituents, and that its mineralisation rate depends on
this stoichiometry.

P f ildi,j = P uptdi,j /κI,i

P f ilai,j = P uptai,j /κI,i

P f ildnk,i = P f ildi × Cdetk /Cdet1
P f ilank,i,j = P f ilak,i × anutk,j
P f ilnk,i = P f ildnk,i +

m
X

(P f ilank,i,j )

j=1

with:

anutk,j
Cdetk
κI,i
P f ildi
P f ilai,j
P f ildnk,i
P f ilank,i
P f ilnk,i

202 of 464

stoichiometric constant of algal species j for nutrient k [ gC/gN/gP/gSi gC−1 ]
detritus organic carbon concentration [gC m−3 ]
ingestion efficiency coefficient of grazer i [-]
filtration rate of detritus for grazer i [gC ind−1 d−1 ]
filtration rate of algal species j for grazer i [gC ind− d−1 ]
filtration rate of nutrient k from detritus for grazer i [gC ind− d−1 ]
filtration rate of nutrient k from algal species j for grazer i [gC ind−1 d−1 ]
filtration rate of nutrient k for grazer i [gC ind−1 d−1 ]

Deltares

Primary consumers and higher trophic levels

Assimilation rates are determined from the filtration rates through correction for the faecal
fractions and ingestion efficiencies. In addition, assimilation rates are corrected for the differences in the nutrient stochiometries of grazers, algae and detritus: the most limiting nutrient
determines the actual assimilation rates for all nutrients. The remaining portions of the other
nutrients are egested as detritus, as are the indigestible fractions. Optionally, an additional
and constant efficiency loss can be included by means of the assimilation-efficiency coefficient
κA :

P a1k=1,i = ×κI,i ×κA,i × (1 − f deti ) × P f ildnk,i +

m
X

!
((1 − f algi,j ) × κI,i × P f ilank,i,j )

j=1

×P f ildnk,i +

!

T

P a1k=2−4,i = κI,i × κA,i

m
X

(P f ilank,i,j )

j=1

P a2k,i = min (P a1k,i /bnutk,i )
k=1−4

with:

DR
AF

P defk,i = P uptnk,i − P a2k,i

stoch. constant for nutrient k over carbon in grazer i [gC/gN/gP/gSi gC−1 ]
egested fraction of detritus consumed by grazer i [-]
egested fraction of algae j consumed by grazer i [-]
ingestion efficiency coefficient of grazer i [-]
assimilation efficiency coefficient of grazer i [-]
potential assimilation rate of nutrient k [gC/gN/gP/gSi ind−1 d−1 ]
actual assimilation rate of nutrient k [J ind−1 d−1 ]
faeces production rate of nutrient k [gC/gN/gP/gSi ind−1 d−1 ]

bnutk,i
f deti
f algi,j
κI,i
κA,i
P a1k,i
P a2k,i
P defk,i

1.2 Growth and maintenance
Assimilated energy is incorporated into a reserve pool from which it is mobilized and then used
for maintenance, growth, development and reproduction. The catabolic or energy mobilization
rate is defined as follows:

P ci =
with:

2
κA,i × kuptm20
Ei /Vi
i × kTi × kegi
×
× Vi 3 + kpmi × Vi × kTi
κi × Ei /Vi + kegi
kemi

κA,i
κ
kegi
kemi
kuptm20
i
kpm20
i
kTi
P ci
Vi
Ei

Deltares

assimilation efficiency coefficient of grazer i [-]
fraction of mobilized energy to growth and maintenance of grazer i [-]
volume-specific costs for growth of grazer i [J cm−3 ]
maximum energy density of grazer i [ J cm−3 ]
maximum surface area-specific ingestion rate of grazer i at 20 ◦ C [J cm2 d−1 ]
volumetric costs of maintenance for grazer i at 20 ◦ C [J cm−3 d−1 ]
Arrhenius rate of change of chemical reaction processes due to temperature
(see section 1.5)[-]
energy mobilization rate of grazer i [J ind−1 d−1 ]
structural biovolume of individual grazer of type i [cm3 ind−1 ]
energy reserves of individual grazer of type i [ J cm−3 ]

203 of 464

Processes Library Description, Technical Reference Manual

A constant fraction κ of the mobilized energy is allocated to growth and maintenance. The
maintenance rate is determined by the structural volume and the volume specific maintenance
costs. The remaining energy flux will be used for growth. When the energy required for
maintenance is higher than the energy available for growth and maintenance, maintenance is
paid from structural volume. This will require additional overhead costs which we assume to
be proportional to those required for growth, and will result in shrinking of the organism.

P mi = kpmi × Vi × kTi
P gi = (κi × P ci − P mi )
if P gi > 0,

if P gi ≤ 0,

P vi = (1 + (1 − κG,i )) × P gi

in which:

DR
AF

P mi = P mi + abs((1 − κG,i ) × P gi )
cvci
kegi × ceci

κG,i =
with:

ceci
cvci
κi
κG,i
kegi
kpmi
kTi
P gi
P mi
P ci
P vi
Vi

T

P vi = κG,i × P gi

conversion coefficient from energy to carbon of grazer i [ gC J−1 ]
conversion coefficient from volume to carbon of grazer i [gC cm−3 ]
fraction of mobilized energy to growth and maintenance [-]
growth efficiency [-]
volume specific costs for growth of grazer i [J cm−3 ]
volumetric costs of maintenance for grazer i at 20 ◦ C [J cm−3 d−1 ]
Arrhenius rate of change of chemical reaction processes due to temperature for
grazer i [-]
energy flux to growth of grazer i [J ind−1 d−1 ]
maintenance rate of grazer i [J ind−1 d−1 ]
energy mobilization flux of grazer i [J ind−1 d−1 ]
growth rate of structural biovolume of grazer i [cm3 ind−1 d−1 ]
structural biovolume of individual grazer of type i [cm3 ind−1 ]

1.3 Maturity and reproduction
The fraction (1 − κ) of the mobilized energy P c goes to maturation, maturity maintenance,
and reproduction. These fluxes differ between adults and juveniles. The transition of juvenile to adult occurs at a fixed volume V p. For juveniles, the maturity maintenance costs
are proportional to their actual structural volume, while for adults they are proportional to the
volme at puberty. Juveniles use all of the remaining energy for development of reproductive
organs and regulation systems. When juveniles have too little energy available for development and/or maturity maintenance, these processes simply stop without further consequence.
Adults, which do not have to invest in development anymore, use the remaining energy flux
P r for production of gonadal tissue R. When adults have too little energy available for maturity maintenance, gonadal tissue will be used instead. This will entail overhead costs that are
proportional to those for production of gonads.

P jji =

204 of 464

1 − κi
× kpmi × Vi × f juvi × kTi
κi
Deltares

Primary consumers and higher trophic levels

1 − κi
× kpmi × V pi × f adulti × kTi
κi
P rji = (1 − κi )P ci × f juvi − P jji

P jai =

P rai = (1 − κi )P ci × f adulti − P jai
if P rai > 0,

P ri = κR,i × P rai
if P rai ≤ 0,

P ri = (1 + (1 − κR,i )) ∗ P rai

T

P jai = P jai + abs((1 − κR,i ) ∗ P rai )
with:

adult fraction of cohort/population of grazer type i [-]
juvenile fraction of cohort/population of grazer type i [-]
fraction of mobilized energy to growth and maintenance [-]
reproduction efficiency [-]
volumetric costs of maintenance for grazer i at 20 ◦ C [ J cm−3 d−1 ]
maturity maintenance flux of juvenile grazers of type i [J ind−1 d−1 ]
maturity maintenance flux of adult grazers of type i [J ind−1 d−1 ]
maturity development flux of juvenile grazers of type i [J ind−1 d−1 ]
energy flux to reproduction of adult grazers of type i [J ind−1 d−1 ]
gonadal production rate of adult grazers of type i [J ind−1 d−1 ]
energy mobilization flux of grazer type i [J ind−1 d−1 ]
structural biovolume of individual grazer of type i [cm3 ind−1 ]
biovolume at start of reproductive age for individual grazer of type i [cm3 ind−1 ]

DR
AF

f adult
f juvi
κi
κR,i
kpm20
i
P jji
P jai
P rji
P rai
P ri
P ci
Vi
V pi

Spawning events occur when enough energy has been allocated into the gonads (GSI >
GSIupr) and when the water temperature is above a threshold value (T > T spm). Gonads
are released from the buffer at a certain rate per day kspri until the temperature drops below
the threshold value or the GSI drops below an lower threshold value GSIlwr .

P spwi = kspri × Ri + κR,i × max(P rai , 0.)

where:

GSIi =

with:

ceci
cvci
f adult
κR,i
kspri
P rai
GSIi
Vi
Ei
Ri
P spwi
Deltares

ceci × Ri
cvci × f adult × Vi + ceci × f adulti × Ei + ceci × Ri

conversion coefficient from energy to carbon of grazer i [gC J−1 ]
conversion coefficient from volume to carbon of grazer i [gC cm−3 ]
adult fraction of population [-]
fraction of reproduction flux to gonadal tissue [-]
gonadal release rate at spawning for grazer i [d−1 ]
energy flux to reproduction of adult grazers of type i [J ind−1 d−1 ]
gonadal somatic index of grazer type i [-]
structural biovolume of individual grazer of type i [cm3 ind−1 ]
energy reserves of individual grazer of type i [J ind−1 ]
gonadal reserves of individual grazer of type i[J ind−1 ]
spawning rate of grazer type i [J ind−1 d−1 ]

205 of 464

Processes Library Description, Technical Reference Manual

1.4 Respiration
Respiration is the sum of the maintenance rate, maturation flux, development flux, and overhead costs for reproduction and growth:

P resi = P mi +P jji +P jai +P rji +(1−κG,i )×max(P gi , 0.)+(1−κR,i )×max(P rai , 0.)
with

κG,i
κR,i
P rji
P mi
P jai
P jji
P resi

T

growth efficiency [-]
reproduction efficiency [-]
development flux of grazer type i [J ind−1 d−1 ]
maintenance rate of grazer type i [J ind−1 d−1 ]
maturation flux of grazer type i [J ind−1 d−1 ]
energy flux to maturity maintenance of grazer type i [J ind−1 d−1 ]
respiration rate of grazer type i [J ind−1 d−1 ]

1.5 Temperature dependency It is assumed that all physiological rates are affected by temperature in the same way. This temperature effect is based on an Arrhenius type relation,
which describes the rates at ambient temperature T as follows:


)× 1+e

T al
T ali
− Tl i
T ref +273
i

1+e

with:

kTi
T
T aref
T ai
T ahi
T ali
T li
T hi





+e

T ahi
T ahi
− T ref +273
T hi

DR
AF

kT = e(

T ai
T ai
− T +273
T ref +273



T ali
T al
− Tl i
T +273
i





+e

T ahi
T ahi
− T +273
T hi





Arrhenius rate of change of chemical reaction processes due to temperature [-]
water temperature [◦ C]
reference temperature (set to 20◦ C) [◦ C]
Arrhenius temperature for grazer i [K]
Arrhenius temperature for rate of decrease at upper boundary for grazer i [K]
Arrhenius temperature for rate of decrease at lower boundary for grazer i [K]
Lower temperature boundary for grazer i [K]
Upper temperature boundary for grazer i [K]

2. From individuals to populations The equations above apply to growth and reproduction
of individual organisms. The DEBGRZ module provides two approaches to scale up the
equations to the population level.
2.1 Default approach: isomorphs The default, and most straightforward, approach to scale
up the individual dynamics to the population level is by grouping the individuals into various
age classes (cohorts). Each cohort consists of a number of equal individuals following the
same growth trajectory. The total number of individuals in a cohort is included as an additional
state variable. This number is the resultant of its rates of change: the recruitment rate and the
mortality rate.
Recruitment is not included as a dynamic process but can be included by (manual) initialization of a new cohort. Mortality is implemented as a first order decrease of the number
of individuals in the cohort. A distinction is made between natural mortality and harvesting,
where harvesting does not depend on temperature and harvested material will leave the system, while natural mortality does depend on temperature and will end up in the local detritus
pool. Both mortality rates may be made dependable on the size of the individuals by setting
kmrt1B and kmrt2B unequal 0:

kmrt1i = kmrt11,20
× Liklmrt1i × kTi
i
i
kmrt2i = kmrt21i × Lklmrt2
i

206 of 464

Deltares

Primary consumers and higher trophic levels

in which:
1/3

Li = V i

/kshpi

with
mortality rate [ d−1 ]
harvesting rate [ d−1 ]
reference mortality rate of grazer i for individuals of 1 cm at 20 [d−1 ]
reference harvesting rate of grazer i for individuals of 1cm [ d−1 ]
length dependency coefficient of mortality rate [-]
length dependency coefficient of harvesting rate [-]
shape coefficient for grazer i [-]
Arrhenius rate of change of chemical reaction processes due to temperature [-]
individual length of grazer i [cm]
structural biovolume of individual grazer of type i [cm3 ind−1 ]

T

kmrt1i
kmrt2i
kmrt11,20
i
kmrt21i
klmrt1i
klmrt2i
kshpi
kTi
Li
Vi

Note that in this approach starvation will lead to a decrease in the structural volume, but not
to enhanced mortality. Starvation occurs when the growth rate P g becomes negative.

DR
AF

2.2 Simplified approach: V1-morphs
An alternative, simplified, approach to scale up the individual growth model to the population
level is available in the DEBGRZ module. In this approach the difference between individuals
and the population is eliminated, and the population is considered as a whole. This approach
requires some additional assumptions, but requires less state variables, which makes the
model easier to initialize, calibrate and/or analyse. This makes it specifically suitable when
only little information is available about the population size- or age distribution, or when the
model objective is system-oriented rather than grazer-oriented.
implementation and consequences of the V1-morph approach:

 The alternative approach is implemented by modeling the organisms as so-called "V1-










morphs". V1-morphs are a specific class of shape-changing organisms that have a constant surface-to-volume ratio (Kooijman 2000). The corresponding assumption is that the
size distribution of the population remains constant.
A surface-to-volume ratio is achieved by making the body size L an input parameter instead of an output parameter (L = Lref ). Note that reference length Lref erpresents
the average length (weighted by structural body volume) and thus characterizes the population size composition, which makes it an important parameter affecting the physiological
behaviour of the whole population.
As a result of the constant size Lref , the structural body volume per individual V becomes
constant as well (V = (Lref /kshp)3 ). Note that individual energy reserves E and
gonads R will remain dynamic state variables that may vary over time.
Also, the number of individuals is no longer a dynamic state variable but can now be
derived from the total structural biomass Cgrv divided by the individual length V and is
provided as output variable: Cgrn = Cgrv/V = Cgrv/(Lref × kshp)3 .
For V1-morphs, starvation (P g ≤ 0) will lead to a decrease in the number of individuals
Cgrn, and thus to an increased mortality (while for isomorphs, it leads to shrinking of the
individual structural body volume).
In the V1-morph approach, recruitment can be implemented by a first order increase.
Hence, mortality and recruitment may be combined into one net (mortality) rate. Underlying assumption is that the larvae prefer settling at locations where conspecifics are already
present.
Reproduction related processes depend on a critical volume V p at which the transition
from juvenile to adult occurs. For V1-morphs, it is assumed that a fraction Vp/(Vp+Vref) of

Deltares

207 of 464

Processes Library Description, Technical Reference Manual

the population consists of juveniles, while the remaining fraction consists of adults. This
fraction depends on the reference size relative to the critical volume as follows:

Vp
V p + V ref
f juvi = 0
f juvi = 1
f adulti = 1 − f juvi

if SwV 1 = 1

f juvi =

(SwV 1 = 0andVi > Vp )
if (SwV 1 = 0andVi ≤ Vp )
if

Rgrvi = ceci × P vi × Cgrni

DR
AF

Rgrei = ceci × (P a2i − P ci ) × Cgrni

T

2.3 Total grazer rates
The total mass fluxes for the whole cohort or population are calculated by multiplying the
individual energy fluxes by the number of individuals in the cohort or population and converting
them to mass fluxes. Note that isomorphs only grow in terms of their individual size, while V1morphs only grow with respect to their number of individuals. This results in the following
rates of change for each of the state variables of grazer i:

Rgrri = ceci × P ri × Cgrni

Rgrni =0
Rgrni =ceci × (P vi /Vi ) × Cgrni

if SwV 1 = 0
if SwV 1 = 1

Rmrvi = cvci × (kmrt1i + kmrt2i ) × Vi × Cgrni

Rmrei = cvci × (kmrt1i + kmrt2i ) × Ei × Cgrni

Rmrri = cvci × (kmrt1i + kmrt2i ) × Ri × Cgrni
Rmrni = (kmrt1i + kmrt2i ) × Cgrni
with

Cgrni
ceci
cvci
kmrt1i
kmrt2i
P a2k,i
P ci
P vi
P ri
Rgrvi
Rgrei
Rgrri
Rgrni
Rmrvi
Rmrei
Rmrri
Rmrni
Vi
Ei

208 of 464

number of individuals of grazer type i [ # m−3 ] or [−2 ]
conversion coefficient from energy to carbon of grazer i [gC J−1 ]
conversion coefficient from volume to carbon of grazer i [gC cm−3 ]
mortality rate of grazer type i [ d−1 ]
harvesting rate of grazer type i [ d−1 ]
actual assimilation rate of nutrient k for grazer type i [J ind−1 d−1 ]
energy mobilization flux of grazer type i [J ind−1 d−1 ]
growth rate of structural biovolume of grazer type i [cm3 d−1 ]
gonadal production rate of adult grazers of type i [J ind−1 d−1 ]
total growth rate of structural volume of grazer i
total growth rate of energy reserves of grazer i
total growth rate of structural volume of grazer i
total increase rate of number of individuals due to growth of grazer i
total decrease rate of structural volume due to growth of grazer i [d−1 ]
total decrease rate of energy reserves due to mortality of grazer i [d−1 ]
total decrease rate of gonadal reserves due to mortality of grazer i [d−1 ]
total decrease rate of number of individuals due to mortality of grazer i [d−1 ]
structural biovolume of individual grazer of type i [cm3 ind−1 ]
energy reserves of individual grazer of type i [J ind−1 ]

Deltares

Primary consumers and higher trophic levels

gonadal reserves of individual grazer of type i [J ind−1 ]

Ri

2.4 Total algae, detritus and inorganic nutrient rates of change
Uptake rate for each of the algal species and detritus are:

Racnsk,j = P uptdnk,i × Cgrni
Rdcnsk,j = P uptank,i,j × Cgrni
with

T

Cgrni
number of individuals of grazer type i [ # m−3 or −2 ]
P uptdnk,i uptake rate of nutrient k from detritus for grazer i [gC ind− d−1 ]
P uptank,i uptake rate of nutrient k from algal species j for grazer i [gC ind−1 d−1 ]
Racnsk,j total consumption rate for nutrient k in algae group j [gC/N/P/Si m−3 d−1 ]
Rdcnsk,j total consumption rate for nutrient k in detritus [gC/N/P/Si m−3 d−1 ]
i
index for grazer species groups [-]
j
index for algae species groups [-]
k
index for nutients, 1 = carbon, 2 = nitrogen, 3 = phosphorus, 4 = silicon [-]

DR
AF

The detritus production rates for each of the nutrients are the sum of the natural mortality
fluxes from the three body compartments (structural volume, energy reserves and gonads)
and the spawning flux (survival of spawned eggs is assumed to be negligible). The fraction
f sus determines to what extend the material ends up in the detritus in the water column or
in the sediment. Spawned material, and (pseudo)faeces end up in the pelagic detritus pool,
while respired nutrients end up as ammonia and phosphate:

Rmrti,k = (Rmrvi + Rmrei + Rmrri ) × f susi × bnutk,i
Rmrts1i,k = (Rmrvi + Rmrei + Rmrri ) × f sedi × bnutk,i
Rresi,k = ceci × P resi × Cgrni × bnutk,i
Rdefi,k = ceci × P defi,k × Cgrni

Rspwi,k = ceci × P spwi × Cgrni × bnutk,i

The release rate for inorganic nutrients by respiration is as follows:

Rresi,k = ceci × P resi,k × Cgrni

with

bnutk,i
Cgrni
ceci
P resi
P spwi
P defk,i
Rresi,k
Rspwi,k
Rdefk,i
i
j
k
Deltares

stoch. constant for nutrient k over carbon in grazer i [gC/gN/gP/gSi gC−1 ]
number of individuals of grazer type i [ # m−3 ] or [−2 ]
conversion coefficient from energy to carbon of grazer i [gC J−1 ]
respiration rate of grazer type i [J ind−1 d−1 ]
spawning rate of grazer type i [J ind−1 d−1 ]
defaecation rate of nutrient k [gC/gN/gP/gSi ind−1 d−1 ]
release rate of inorganic nutrient k by respiration [gC/N/P/Si m−3 d−1 ]
detritus production of nutrient k by spawning [J ind−1 d−1 ]
detritus production rate of nutrient k by defaecation [gC/gN/gP/gSi ind−1 d−1 ]
index for grazer species groups [-]
index for algae species groups [-]
index for nutients, 1 = carbon, 2 = nitrogen, 3 = phosphorus, 4 = silicon [-]

209 of 464

Processes Library Description, Technical Reference Manual

2.5 Total grazer biomass and other derived variables
The total carbon biomass, ash-free dry weight and wet weight of the population or cohort are
defined as follows:

Cgrci = (ceci × (Ei + Ri ) + cvci × Vi ) × Cgrni
Cgrdi = Ccgri /cawci
Cgwri = Ccgri /cwwci
with:

T

Total number of individuals of grazer i [ # m−3 ] or [−2 ]
Total carbon biomass of grazers [ gC ]
Total ash free dry weight of zooplankton [ gAFDW ]
Total wet weight of zooplankton [ gWW ]
conversion coefficient from energy to carbon of grazer i [gC J−1 ]
conversion coefficient from volume to carbon of grazer i [gC cm−3 ]
conversion coefficient from ash free dry weight to carbon for grazer i [gC gAFDW−1 ]
conversion coefficient from wet weight to carbon for grazer i [gC gWW−1 ]
structural biovolume of individual grazer of type i [cm3 ind−1 ]
energy reserves of individual grazer of type i [J ind−1 ]
gonadal reserves of individual grazer of type i [J ind−1 ]

DR
AF

Cgrni
Cgrci
Cgrdi
Cgrwi
ceci
cvci
cdwci
cwwci
Vi
Ei
Ri

Individual length may be derived from the individual structural volume and the shape coefficient as follows:
1/3

Li = V i
with

kshpi
Li
Vi

/kshpi

shape coefficient of grazer type i [-]
length of individual grazer of type i [cm]
structural biovolume of individual grazer of type i [cm3 ind−1 ]

The scaled energy density is a measure for the condition of the organisms, which can be expressed as the energy density relative to the maximum energy density. Similarly, the gonadalsomatic index is a measure for the reproductive state of the organism, and is defined as the
ratio of the gonadal biomass over the total biomass:

Esi = Ei /(Vi × kemi )
GSIi =

ceci × Ri
cvci × f adult × Vi + ceci × f adulti × Ei + ceci × Ri

with:

f adult
GSIi
ceci
cvci
kemi
Esi
Vi
Ei
Ri

210 of 464

adult fraction of population of grazer i [-]
Gonadal Somatic Index of grazer type i [J ind−1 ]
conversion coefficient from energy to carbon of grazer i [gC J−1 ]
conversion coefficient from volume to carbon of grazer i [gC cm−3 ]
maximum energy density for grazer i [J cm−3 ]
scaled energy density of grazer i [-]
structural biovolume of individual grazer of type i [cm3 ind−1 ]
energy reserves of individual grazer of type i [J ind−1 ]
gonadal reserves of individual grazer of type i [J ind−1 ]

Deltares

Primary consumers and higher trophic levels

T

Directives for use
 The proces rates in connection with grazing have a temperature basis of 20 oC. That
means that input values have to be corrected when provided for another temperature
basis.
 Parameter values for a range of species can be found on the "add my pet" page at
http://www.bio.vu.nl/thb/ → DEB → Laboratory. If parameter values are not
available for a certain species, this page also contains instructions on how to construct a
new (and consistent) set of parameter values.
 The initial length of isomporphs is determined from the inital carbon biomass and number
of individuals.
 Benthic and suspended grazers (SwBen>0) are fixed to a specific vertical location in the
water column. Therefore, they may not be present in all vertical layers. In this case,
any output (both state and derived variables) that is aggregated over a monitoring area,
should be multiplied by the number of layers included in the monitoring area. Output
values in single segment locations do not have to be corrected. Note that this correction
is necessary for all passive substances.
Additional references

DR
AF

Bacher, C., and Gangnery, A. 2006 Use of dynamic energy budget and individual based
models to simulate the dynamics of cultivated oyster populations. J. Sea Res. 56,140-155.
Holling C.S. 1959. Some characteristics of simple types of predation and parasitism. Can.
Entomol., 91:385-398.
Kooijman S. A. L. M. 2006. Pseudo-faeces production in bivalves. J. Sea Research, 56:103106.
Kooijman, S.A.L.M. 2010. Dynamic Energy Budget theory for metabolic organization. Cambridge University Press, Great Britain (3rd edition). ISBN 9780521131919.
Pouvreau, S., Bourles, Y., Lefevre, S., Gangnery, A., Alunno-Bruscia, M. 2006 Application of a
dynamic energy budget model to the Pacific oyster, Crassostrea gigas, reared under various
environmental conditions. J. Sea Res. 56, 156-167.
Rosland, R., Strand, O., Alunno-Bruscia, M., Bacher, C., Strohmeier, T. 2009 Applying Dynamic Energy Budget (DEB) theory to simulate growth and bio-energetics of blue mussels
under low seston conditions. J. Sea Res. 62, 49-61.
Van der Veer H.W., Cardoso, J.F.M.F., van der Meer, J. 2006. The estimation of DEB parameters for various Northeast Atlantic bivalve species. J. Sea Res. 56, 107-124.
Table 7.3: Definitions of the input parameters in the formulations for DEBGRZ.

Name in
formulas

Name in input

anut2,1

N CratGreen green algae spec. stoch. constant nitro-

gN gC−1

anut2,2

gen over carbon
diatoms spec. stoch. constant nitrogen
over carbon

gN gC−1

N CratDiat

Definition

Units

continued on next page

Deltares

211 of 464

Processes Library Description, Technical Reference Manual

Table 7.3 – continued from previous page
Name in
formulas

Name in input

Definition

Units

anut2,j

N CRAlg(j)

gN gC−1

anut3,1

P CratGreen

anut3,2

P CratDiat

anut3,j

P CRAlg(j)

anut4,1

SCratGreen

anut4,2

SCratDiat

anut4,j

SCRAlg(j)

BLOOM algae group spec. stoch. const.
nitr. over carb.
green algae spec. stoch. constant phos.
over carbon
diatoms spec. stoch. constant phosphorus over carbon
BLOOM algae group spec. stoch. const.
phos. over carb.
green algae spec. stoch. constant silicon
over carbon
diatoms spec. stoch. constant silicon over
carbon
BLOOM algae group spec. stoch. const.
sil. over carb.

Cgrv1

ZooplV

structural biomass concentration of zooplankton
energy reserve biomass concentration of
zooplankton
gonadal biomass concentration of zooplankton
number of individuals (density) of zooplankton
structural biomass concentration of mussel
energy reserve biomass concentration of
mussel
gonadal biomass concentration of mussel
number of individuals (density) of mussel
structural biomass concentration of
grazer type 3
energy reserve biomass concentration of
grazer type 3
gonadal biomass concentration of grazer
type 3
number of individuals (density) of grazer
type 3
structural biomass concentration of
grazer type 4
energy reserve biomass concentration of
grazer type 4
gonadal biomass concentration of grazer
type 4
number of individuals (density) of grazer
type 4

gC m−3 or −2

Cgrr1
Cgrn1
Cgrv2
Cgre2
Cgrr2
Cgrn2
Cgrv3
Cgre3
Cgrr3
Cgrn3

ZooplE

ZooplR

ZooplN

M usselV

M usselE

M usselR

M usselN
Grazer3V

Grazer3E

Grazer3R

Grazer3N

Cgrv4

Grazer4V

Cgre4

Grazer4E

Cgrr4

Grazer4R

Cgrn4

Grazer4N

gP gC−1
gP gC−1
gSi gC−1

T

DR
AF

Cgre1

gP gC−1

gSi gC−1
gSi gC−1

gC m−3 or −2
gC m−3 or −2
# m−3 or −2
gC m−3 or −2
gC m−3 or −2
gC m−3 or −2
# m−3 or −2
gC m−3 or −2
gC m−3 or −2
gC m−3 or −2
# m−3 or −2
gC m−3 or −2
gC m−3 or −2
gC m−3 or −2
# m−3 or −2

continued on next page

212 of 464

Deltares

Primary consumers and higher trophic levels

Table 7.3 – continued from previous page
Name in
formulas

Name in input

Cgrv5

Grazer5V

Definition

Units
gC m−3 or −2

Cdet1
Cdet2
Cdet3
Cdet4
Ctim

structural biomass concentration of
grazer type 5
Grazer5E
energy reserve biomass concentration of
grazer type 5
Grazer5R
gonadal biomass concentration of grazer
type 5
Grazer5N
number of individuals (density) of grazer
type 5
Green
biomass concentration of green algae
(DYNAMO)
Diat
biomass concentration of diatoms (DYNAMO)
BLOOMALG(j )biomass concentration of a BLOOM algae group
P OC1
detritus organic carbon concentration
P ON 1
detritus nitrogen concentration
P OP 1
detritus phosphorus concentration
Opal
opal silicate concentration
Opal
concentration of inorganic matter

H

Depth

depth of a water compartment (layer)

m

(i)U nitSW

-

(i)_SwV 1

group spec. option for biomass unit (1=g
m−2 , 0=g m−3 )
group spec. option for upscaling (0=isomorphs(cohort), 1=V1morphs (population))

T emp

water temperature

◦

bnut1,i

(i)_T C

gC gC−1

bnut2,i

(i)_T N

bnut3,i

(i)_T P

bnut4,i

(i)_T Si

stoch. constant for carbon over carbon in
grazer i
stoch. constant for nitrogen over carbon
in grazer i
stoch. constant for phosphorus over carbon in grazer i
stoch. constant for silicon over carbon in
grazer i

f apri,1

(i)_ALGP RGrnpreference of grazer i for green algae

Cgrr5
Cgrn5
Calg1
Calg2

–
–

T

DR
AF

Calgj

f apri,2
f apri,j
f dpri
f algi,1

gC m−3 or −2
gC m−3 or −2
# m−3 or −2
gC m−3

T

Cgre5

(DYNAMO)
(i)_ALGP RDiat
preference of grazer i for diatoms (DYNAMO)
(i)_ALGP R(j) preference of grazer i for BLOOM algae
group j
(i)_DET P R preference of grazer i for detritus
(i)_ALGF F Grnegested fraction of green algae consumed by grazer i

gC m−3
gC m−3
gC m−3
gN m−3
gP m−3
gSi m−3
g m−3

-

C

gN gC−1
gP gC−1
gSi gC−1
-

continued on next page

Deltares

213 of 464

Processes Library Description, Technical Reference Manual

Table 7.3 – continued from previous page
Name in
formulas

Name in input

f algi,2

(i)_ALGF F Diat
egested fraction of diatoms consumed by
grazer i
(i)_ALGF F (j) egested fraction of algae j consumed by
grazer i
(i)_DET F F egested fraction of detritus consumed by
grazer i
(i)_F rDetBot fr. of mortality flux of grazer i to sediment

f algi,j
f deti
f sedi

Definition

Units

κi

(i)_kappa

f susi

i

ceci
cvci
cdwci

(i)_kappaR
(i)_cEC

(i)_cV C

(i)_cDW C

-

fr. of mobilized energy to growth and
maintenance of grazer i
fr. of reproduction flux to gonadal tissue
of grazer i

-

conversion coefficient from energy to carbon biomass of grazer i
conversion coefficient from volume to carbon biomass of grazer i
conversion coefficient from carbon
biomass to ash free dry weight for grazer

gC J−1

DR
AF

κR,i

-

T

κI,i
κA,i

detr. pool
(i)_F rDetBot fr. of mortality flux of grazer i to sediment
detr. pool
(i)_kappaI
fr. of filtered food ingested by grazer i
(i)_kappaA
fr. of ingested food assimilated by grazer

-

-

gC cm−3
gC gAFDW−1

i

cwwci

(i)_cW W C

GSIupri

(i)_GSIupr

GSIlwri

(i)_GSIlwr

kegi

(i)_EG

conversion coefficient from carbon
biomass to wet weight for grazer i
energy threshold to start spawning for
grazer i
energy threshold to stop spawning for
grazer i
volume-specific costs for growth of grazer

gC gWW−1
J cm−3

i

kemi
kuptm20
i

(i)_EM
(i)_JXm

kmrt11,20
(i)_rM or
i
kmrt21i

(i)_rHrv

klmrt1i

(i)_cM or

klmrt2i

(i)_cHrv

kpm20
i

(i)_P M

maximum energy density of grazer i
maximum surface-area-specific ingestion
rate of grazer i at 20 ◦ C
reference mortality rate of grazer i for individuals of 1cm at 20 ◦ C
reference harvesting rate of grazer i for
individuals of 1cm
length dependency coefficient for mortality rate of grazer i
length dependency coefficient for harvesting rate of grazer i
volumetric costs of maintenance for
grazer i at 20 ◦ C

J cm−3
J cm2 d−1
d−1
d−1
J cm−3 d−1

continued on next page

214 of 464

Deltares

Primary consumers and higher trophic levels

Table 7.3 – continued from previous page
Name in
formulas

Name in input

kspri

(i)_Rspw

Kstimi
Lrefi
T ai
T ali

T li
T hi

T spmi
V pi
1

gonadal release rate at spawning for
grazer i
(i)_Shape
shape coefficient for grazer i
(i)_Xk
half saturation constant for food uptake
by grazer i
(i)_Y k
half saturation constant for the negative
effect of inorganic matter on food uptake
by grazer i
(i)_Lref
reference length of individual grazer of
type i (only for V1morphs)
(i)_T a
Arrhenius temperature for grazer i
(i)_T al
Arrhenius temperature for rate of decrease at upper boundary for grazer i
(i)_T ah
Arrhenius temperature for rate of decrease at lower boundary for grazer i
(i)_T l
Lower temperature boundary of tolerance
range for grazer i
(i)_T h
Upper temperature boundary of tolerance
range for grazer i
(i)_M inST mp minimum spawning temperature for
grazer i
(i)_V p
biovolume at start of reproductive age for
grazer i

DR
AF

T ahi

Units
d−1
gC m−3
gC m−3

cm

T

kshpi
Ksf di

Definition

K
K
K
K
K
K

cm3 ind−1

(i) indicates grazer species groups 1–5, respectively Z for zooplankton, M for mussel type zoobenthos, G3, G4 and G5 for user defined groups.
2
(j) indicates BLOOM algae species groups 1–30.

Deltares

215 of 464

T

Processes Library Description, Technical Reference Manual

Table 7.4: Definitions of the output parameters for DEBGRZ.

Name in
formulas

Name in output

Li
Esi

(i)_L
(i)_Escaled

Ei
Ri
Cgrci
Cgrdi
Cgrwi
Cgrci
Cgrdi
Cgrwi

216 of 464

Units

Individual length of grazer i
Scaled energy density, which is a measure for the condition of the organism
(i)_GSI
Gonadal Somatic Index of grazer type i
(i)_V ind
Structural biovolume of individual grazer
of type i
(i)_Eind
Energy reserves of individual grazer of
type i
(i)_Rind
Gonadal reserves of individual grazer of
type i
(i)_T otBiomassTotal carbon biomass concentration of
grazer type i
(i)_T otAF DW Total ash free dry weight concentration of
grazer type i

cm
-

(i)_T otW W

Wet weight concentration of grazer i

gWW m−3 or −2

(i)_Biomass
(i)_AF DW

Total carbon biomass of grazer i
Total ash free dry weight of grazer i

gC
gAFDW

(i)_W W

Total wet weight of grazer i

gWW

DR
AF

GSIi
Vi

Definition

cm3 ind−1
J ind−1
J ind−1
gC m−3 or −2
gAFDW
m−3 or −2

Deltares

8 Organic matter (detritus)
Contents
Decomposition of detritus . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

8.2

Consumption of electron-acceptors . . . . . . . . . . . . . . . . . . . . . . 228

8.3

Settling of detritus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

8.4

Mineralization of detritus in the sediment (S1/2) . . . . . . . . . . . . . . . 245

DR
AF

T

8.1

Deltares

217 of 464

Processes Library Description, Technical Reference Manual

Decomposition of detritus
PROCESS :

DECFAST, DECMEDIUM, DECSLOW, DECREFR, DECDOC AND
DECPOC5

T

Being natural dead organic matter, detritus is produced when algae and higher plants die off.
Detritus may also arise from organic matter present in discharged wastewater. The microbial
decomposition of detritus into its basic inorganic components such as carbon dioxide, ammonium, phosphate and sulfide is called mineralization. During the decomposition process the
organic matter is gradually converted into material that is more resistant to microbial breakdown. In other words, the decomposition rate decreases at the increase of the age of detritus.
This is caused by both the difference in degradability of the numerous chemical components
in detritus and the (bio)chemical conversion of readily degradable components into less readily degradable components. Eventually, refractory organic matter results, that is subjected to
very slow decomposition. Humic matter may not be decomposed at all, when stored under
chemically reducing conditions. The decomposition of humic matter only continues significantly when exposed to oxygen, especially when solar radiation is available to speed up the
process by means of photo-oxidation.

DR
AF

8.1

The slowing down of the decomposition process over time can be modelled by means of the
distinction of several detritus fractions, each having a different decomposition rate. The resulting model will show a decreasing overall decomposition rate, when no new detritus is added
to the initial detritus pools. Adding “fresh” detritus brings along the question how this detritus
must be allocated to the existing detritus pools. This can be done by i) distributing the fresh
detritus among the detritus fractions according to fixed ratios, and/or by ii) converting a more
readily degradable fraction into a more refractory fraction proportional to the decomposition
rates.A combination of these options has been implemented in the model. The fresh detritus
from algae is added to both the fast and medium slow decomposing detritus fractions according to fixed ratios. The fresh detritus from submerged and emerging terrestrial vegetation is
added to all detritus fractions according to user defined ratios. However, all organic matter in
stems (incl. branches) and roots is by definition allocated to one and the same organic “detritus” fraction, that has been included in DELWAQ specifically for this purpose. The detritus
from waste water can be allocated to the organic fractions via the loads.
Detritus consists of both particulate and dissolved components. The dissolved components
can be allocated to two categories:
1 highly degradable dissolved substances, such as amino acids and sugars, and
2 highly refractory dissolved substances such as humic and fulvic acids.
Category 1 is taken into account in the model by means of the autolysis of fresh detritus,
which is implemented in connection with the algae mortality process (detritus production).
Autolysis leads to the instantaneous release of inorganic nutrients present in autolysed algal
biomass. Category 2 demands for the definition of a refractory dissolved detritus fraction,
being produced from particulate detritus.
The decomposition rates depend on the availability of nutrients (N, P), as well as on the redox conditions. Both aspects are connected with the needs and the efficiency of bacteria
in performing the decomposition process. The availability of nutrients can be taken into account by interpolating the decomposition rate between a maximal value and a minimal value
proportional to the nutrient contents of the detritus.
The redox-dependency is caused by the fact that the energy gain of decomposition (oxidation)

218 of 464

Deltares

Organic matter (detritus)

decreases going from aerobic decomposition, to denitrification, to sulfate reduction and finally
to methanogenesis. In principle, these processes are mutually exclusive. Only one of them
may occur at the same time and the same place. Consequently, the decomposition rate has
been made a function of the presence of the various electron acceptors, dissolved oxygen
and nitrate in particular.

T

Carbon, nitrogen, phosphorus and sulfur in detritus are considered as separate state variables in the model (sulfur can be ignored). The mineralization of organic nitrogen and organic
phosphorus is fast, compared to the mineralization of organic carbon, when the organic matter is rich in these nutrients. During the decomposition process detritus becomes less rich in
nutrients, until eventually the minimal nutrients contents of refractory organic matter (humic
matter) have been established. In order to take this preferential nutrient stripping into account, the decomposition rates of organic nitrogen, phosphorus and sulfur have been made a
function of the nutrient stochiometry of refractory detritus.

DR
AF

The rate of mineralization is also a function of the temperature. Decomposition rates tend to
decrease progressively at temperatures below 4 ◦ C. Because the decomposition of organic
matter is performed by a very large number of species, including species that are adapted to
low temperature environments, the effect is not nearly as strong as in the case of nitrification.
The present model ignores the “near-freezing” effect, which means that imposing a discontinuity at a critically low temperature is not possible when using the processes described here.
Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

Processes DECFST, DECMEDIUM, DECSLOW, DECREFR, DECPOC5 and DECDOC for the
decomposition of organic matter have been implemented in a generic way, meaning that they
can be applied both to water layers and sediment layers. The processes can also be used
in combination with one of the other options for mineralization in the sediment (BMS1_i and
BMS2_i).
The processes have been implemented for the following substances:

 POC1, PON1, POP1, POS1, POC2, PON2, POP2, POS2, POC3, PON3, POP3, POS3,
POC4, PON4, POP4, POS4, POC5, PON5, POP5, POS5, DOC, DON, DOP, DOS, NH4,
PO4 and SUD.
POC/N/P/S5 must be defined as inactive substances (= substances that are not transported),
and should be used for stem and root ”detritus” from vegetation only. As opposed to all other
conversion processes, the decomposition of POC5 continues in grid cells when running dry.
Table 8.1 and Table 8.2 provide the definitions of the input parameters occurring in the formulations.

Deltares

219 of 464

Processes Library Description, Technical Reference Manual

Formulation
The biochemical decomposition of dead organic matter (detritus) is described here as the mineralization and conversion of five particulate fractions and the mineralization of one dissolved
fraction. Each mineralization flux for the particulate fractions has one or two proportional
conversion fluxes. The overall decomposition (loss) flux of the fractions is the sum of the mineralization and the conversion fluxes. The fractions are produced, converted and mineralized
according to the following schemes:
POC1 + O 2

CO2 + DOC + O 2

CO2

POC2 + O 2

CO2 + DOC + O 2

CO2

POC3 + O 2

CO2 + DOC + O 2

DR
AF

T

Algae C, waste C

POC4 + O 2

CO2

CO2

Figure 8.1: When an algae module is included.

POC1 + O 2

CO2 + DOC + O 2

CO2

POC2 + O 2

CO2 + DOC + O 2

CO2

POC3 + O 2

CO2 + DOC + O 2

CO2

POC4 + O 2

CO2

POC5 + O 2

CO2 + DOC + O 2

Vegtation C

CO2

Figure 8.2: When the terrestrial vegetation module is included.

The first scheme (Figure 8.1) applies when an algae module is included in a model. The
second scheme (Figure 8.2) concerns the situation when the terrestrial vegetation module is
included. Both schemes apply when both algae and vegetation are in the model.
POC1 is the fast decomposing detritus fraction, POC2 the medium slow decomposing fraction
POC3 the slow decomposing fraction, and POC4 the particulate refractory fraction. DOC
represents dissolved refractory organic matter. POC5 contains the organic matter in stems

220 of 464

Deltares

Organic matter (detritus)

and roots that may be subjected to (very) slow decomposition. POC5 should only be included
in a model when the vegetation module is used.
At the absence of (sufficient) oxygen, nitrate and sulfate, not only CO2 (carbon dioxide) but
also CH4 (methane) will be produced. The consumption fluxes of the electron-acceptors OXY,
NO3 and SO4, and the production fluxes of CO2 and CH4 are generated by another process,
called CONSELAC
The schemes represent carbon, but is similarly applicable to nitrogen, phosphorus and sulfur,
for which the mineralization products are ammonium (NH4), phosphate (PO4) and sulfide
(SUD).

DR
AF

T

Mineralization
Mineralization has been formulated as a first-order kinetic process. The first-order mineralization rate is a function of limiting factors related to the electron acceptor used, the preferential
stripping of nutrients, and the nutrient availability for bacteria. Two options are available. One
option concerns a comprehensive approach with nutrient stripping. The other option does not
explicitly consider nutrient stripping (Smits and Van Beek (2013)). However, a difference in
the mineralization of the nutrients relative to carbon can be established by using different rate
constants for C, N and P.
For the comprehensive approach the formulations are as follows (SW OM Dec=0.0):

Rminj,i = f el × f accj,i × kmini × Cxj,i
(T −20)
kmini = kmin20
i × ktmin

where:

Cx

f acc
f el
kmin
kmin20
ktmin
Rmin
T
i
j

organic carbon, nitrogen, phosphorus or sulfur concentration ([gC/N/P/S m−3 ];
x is oc, on, op or os)
acceleration factor for nutrient stripping [-]
limiting factor for electron acceptors [-]
first-order mineralization rate [d−1 ]
first-order mineralization rate at 20 ◦ C [d−1 ]
temperature coefficient for mineralization [-]
mineral. rate for organic carbon, nitrogen, phosphorus or sulfur [gC/N/P/S m−3 .d−1 ]
temperature [◦ C]
index for the organic matter fraction (1–5; see scheme above)
index for the nutrient (1–4, that is C, N, P and S)
b

b

The mineralization rate of a specific detritus fraction has a maximal and a minimal value. The
first-order rate is a linear function of the nutrient (N, P) availability according to:
if

Coni/Coci > ani,max and Copi/Coci > api,max
20
kmin20
i = kmini,max

if Coni/Coci < ani,min

or

Copi/Coci < api,min

20
kmin20
i = kmini,min

else
20
20
20
kmin20
i = kmini,min + f nuti × kmini,max − kmini,min

Deltares



221 of 464

Processes Library Description, Technical Reference Manual


f nuti = min

((Coni /Coci ) − ani,min ) ((Copi /Coci ) − api,min )
,
ani,max − ani,min
api,max − api,min



(if ani,max = ani,min or api,max = api,min then f nuti = 0.5!)
where:
stochiometric constant of nitrogen in organic matter [gN gC−1 ]
stochiometric constant of phosphorus in organic matter [gP gC−1 ]

an
ap
Coc
Con
Cop
f nut
i
max
min

organic carbon concentration [gC m−3 ]
organic nitrogen concentration [gN m−3 ]
organic phosphorus concentration [gP m−3 ]
limiting factor for nutrient availability [-]
index for the organic matter fraction (1–5; see scheme above)
index for the maximal value, the upper limit
index for the minimal value, the lower limit
b

b

T

b

DR
AF

The limiting factor for electron acceptors is simply a constant, the value of which depends on
the presence of dissolved oxygen and nitrate:


1.0
f el = bni

bsu
where:

bni
bsu

Cox > 0.0
Cox < 0.0 and Cni > 0.1
if Cox < 0.0 and Cni < 0.1

if

if

attenuation constant in case nitrate is the prevailing electron acceptor [-]
attenuation constant in case sulfate or carbon monoxide is the prevailing electron acceptor [-]

The acceleration factor for nutrient stripping is proportional to the relative difference of the
actual nutrient composition and the stochiometric constant of refractory detritus:

f accj,i = 1.0 +
with:

ar

((Cxj,i /Coci ) − arj )
arj

stochiometric constant of nitrogen, phosphorus or sulfur in refractory [gN/P/S
gC−1 ]

Notice that the acceleration factor is 1.0 for the carbon detritus components.
In principal, the above formulations concern each of the 24 organic carbon, nitrogen, phosphorus and sulfur detritus components. However, in the model the acceleration factor facc
and the nutrient related variability of the first-order mineralization rate are ignored for the refractory fractions POC/N/P/S4 and DOC/N/P/S. Consequently, the processes DECREFR and
DECDOC do not contain the process parameters connected with these aspects.
The decomposition of POC5 continues in above-ground grid cells when these run dry. The
decomposition rate is a function of the temperature of the air and the sediment, an additional
input parameter NatTemp, different from the temperature of water. All decomposition products
except CO2 accumulate in these cells during a dry period. The production of CO2 as well as
the consumption of oxygen (OXY) continue in process DECPOC5 (in stead of in process
CONSELAC), and pertinent fluxes are calculated in order to maintain full mass balances for

222 of 464

Deltares

Organic matter (detritus)

these substances. However, oxygen (OXY) is obtained from the atmosphere, and carbon
dioxide is released into it. Therefore, additional inverse fluxes of CO2 and OXY are generated
by process DECPOC5 to prevent the change of concentrations during a dry period as well as
the impacts of such concentration changes on water quality when the water returns.
The alternative approach (SW OM Dec=1.0) uses the same formulations for the dependencies of nutrient availability, electron acceptor dominance and temperature. The acceleration
factors for nutrient stripping are set equal to 1.0. The first-order mineralization rates for fast,
medium and slow decomposing organic carbon (POC1-3), nitrogen (PON1-3) and phosphorus (POP1-3) are different. This requires two additional sets of input parameters. The maximal
and minimal rates for organic sulfur are the same as for organic carbon.

DR
AF

Rconj,i = bi × Rminj,i /f accj,i

T

Conversion
The production of a less readily degradable detritus fraction from a more readily degradable
fraction is supposed to be proportional to the mineralization rate. The rationale behind this
hypothesis is that bacterial activity is driving the conversion process. Chemical reactions
are highly dependent on the presence of all kinds of intermediate decomposition products.
Consequently, the conversion rate has been linked to the mineralization rate according to the
following formulation, which is the same for both mineralization options: :

where:

b

Rcon

constant fraction of detritus C component i converted into detritus C component
i + 1 relative to and in addition to mineralization [-]
conversion rate for particulate organic carbon, nitrogen, phosphorus or sulfur to
slower particulate or dissolved fractions [gC/N/P/S m−3 .d−1 ]
b

Notice that the fractions b are equal for organic carbon, nitrogen, phosphorus and sulfur. The
mineralization rate of organic carbon is taken as the reference rate, which implies the need
for correction of the mineralization rate for nitrogen, phosphorus and sulfur for acceleration
(nutrient stripping).
For POC5, just like decomposition, conversion continues when a grid cell runs dry.
Directives for use
 The simulation of the consumption of dissolved oxygen (substance OXY) resulting from
the decomposition of organic matter requires that process CONSELAC (Consumption of
electron-acceptors) is included in the model! This also holds for taking into account denitrification, sulfate reduction, iron(III) reduction and methanogenesis. As an alternative
when sediment-water interaction is simulated according to the S1/2 option, denitrification
can be taken into account by means of processes DENSED_NO3 and/or DENWAT_NO3.
 Option SW OM Dec=0.0 (default) for the comprehensive approach with nutrient stripping based on the input mineralization rate for organic carbon. Option SW OM Dec=1.0
does not use the formulation for nutrient stripping but has different mineralization rates for
POC1/2, PON1/2 and POP1/2. Consequently, two additional sets of input decomposition
rates are required for N and P. The names of the mineralization rates of POC1-5 and DOC
have changed after the introduction of separate mineralization rates of PON1-5, DON,
POP1-5 and DOP. When using the new names for the mineralization rates of POC1-5 and
DOC (as in the tables below), for option SW OM Dec=1.0 it is necessary to also allocate
input values to the mineralization rates of PON1-5, DON, POP1-5 and DOP. The rates for
POC1-5 and DOC will also be used for POS1-5 and DOS.
 For a start, the first-order mineralisation rates ky_YdcX20 for POX1−5 and DOX can be
set to 0.15, 0.05, 0.005, 0.00001, 0,00001 and 0.001 d−1 respectively, the maximal and

Deltares

223 of 464

Processes Library Description, Technical Reference Manual







T



DR
AF



minimal values being the same. The attenuation constants for electron acceptors bni
and bsu can be set at 1.0. When using option SW OM Dec=0.0, the stochiometric constants for refractory detritus a_dNpr, a_dPpr and a_dSpr can be set at 0.05 gN.gC−1 ,
0.005 gP.gC−1 and 0.005 gS.gC−1 . The conversion fractions b_poc1poc2, b_poc2poc3
and b_poc3poc4 can be set at 1.0, conversion fractions b_poc1doc, b_poc2doc and
b_poc3doc at 0.025, and the additional conversion fractions for POC5 b_poc5poc4 and
b_poc5doc at 0.0. Redfield ratios (C106 N16 P1 S1 ) and 40 % lower values may be used for
the maximal and minimal values of the remaining stochiometric constants.
Not all POX1-5 and DOX substances need to be included in a model, but the substances
need to form a logical coherent decomposition scheme. The most simple scheme contains
POX1 only. Extensions subsequently add POX2 and/or DOC, POX3 and POX4. POX5 can
be added independently. The default values of b_poc1poc2, b_poc2poc3 and b_poc3poc4
are 1.0, and the default value of b_poc5poc4 is 0.4. The default value of b_poc1doc is
0.0, the default values of b_poc2doc and b_poc3doc are 0.025, and the default value of
b_poc5doc is 0.04. If some of the POX2-4 and DOC substances are not included in the
model, the conversion fractions that would deliver a production flux for one of the missing
substances need to be allocated the value 0.0.
In case an upper limit of a stochiometric constant is set equal to its lower limit (for instance
aud N f = ald N f or aud P f = ald P f .), then the process routine might set the pertinent
mineralization rate at the average of the maximal and minimal rates to prevent dividing by
zero. In this case it is recommended to also allocate the same value to the maximal rate
and the minimal rate in order to avoid misinterpretation.
Loads of organic matter may be allocated to each of the detritus fractions. The user must
make a choice on the basis of the origin and the history of the organic loads. For instance,
dead algae biomass and raw domestic waste may be allocated to the fast (mainly) and
medium slow decomposing detritus fractions. Treated domestic waste to the medium
slow and slow decomposing fractions, terrestrial organic matter to the slow decomposing
fraction, and dissolved organic (humic) matter to the dissolved refractory fraction.
When the terrestrial vegetation module is included in a model, detritus fractions for vegetation biomass can be specified by the user. Stem and root biomass will be allocated
to POC/N/P/S5. In connection with the vegetation module these substances must be defined as inactive substances. When the vegetation module is not used, there is no need
to include POC/N/P/S5 in the model.
The algae module and/or the terrestrial vegetation module can be used with or without
POS1-5 and DOS.

Additional references

DiToro (2001), Smits and Van der Molen (1993), Westrich and Berner (1984), WL | Delft
Hydraulics (1997c), WL | Delft Hydraulics (1980a)
Table 8.1: Definitions of the input parameters in the above equations for DECFAST,
DECMEDIUM and DECSLOW. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas1

Name in input

Definition

Units

ani,max
„
„
ani,min
„
„
api,max

au_dN f
au_dN m
au_dN s
al_dN f
al_dN m
al_dN s
au_dP f

max. st. constant N in fast dec. detritus
max. st. const. N in medium slow detr.
max. st. constant N in slow dec. detritus
min. st. constant N in fast dec. detritus
min. st. const. N in medium slow detr.
min. st. constant N in slow dec. detritus
max. st. constant P in fast dec. detritus

gN.gC−1
gN.gC−1
gN.gC−1
gN.gC−1
gN.gC−1
gN.gC−1
gP.gC−1

224 of 464

Deltares

Organic matter (detritus)

Table 8.1: Definitions of the input parameters in the above equations for DECFAST,
DECMEDIUM and DECSLOW. Volume units refer to bulk ( ) or to water ( ).
b

Definition

Units

au_dP m
au_dP s
al_dP f
al_dP m
al_dP s
a_dN pr
a_dP pr
a_dSpr
b_poc1poc2
b_poc2poc3
b_poc2doc
b_poc3poc4
b_poc3doc
b_ni
b_su

max. st. const. P in medium slow detr.
max. st. constant P in slow dec. detritus
min. st. const. P in fast dec. detritus
min. st. const. P in medium slow detr.
min. st. constant P in slow dec. detritus
stoch. constant N in refractory detritus
stoch. constant P in refractory detritus
stoch. constant S in refractory detritusitus
conv. fraction fast detr. into medium detr.
conv. fraction medium detr. into slow detr.
conv. fr. medium detr. into diss. refr. detr.
conv. fr. slow detr. into part. refr. detr.
conv. fr. slow detr. into diss. refr. detr.
atten. const. for nitrate as el. acceptor
atten. const. for sulfate as el. acceptor

gP.gC−1
gP.gC−1
gP.gC−1
gP.gC−1
gP.gC−1
gN.gC−1
gP.gC−1
gS.gC−1
-

P OC1
P OC2
P OC3
P ON 1
P ON 2
P ON 3
P OP 1
P OP 2

conc. organic carbon in fast detritus

gC.m−3

conc. organic phosphorus in medium detritus

gP.m

P OP 3
P OP 1
P OP 2
P OP 3
OXY
N O3

conc. organic phosphorus in slow detritus

gP.m−3

concentration of nitrate

gN m

f accj,i

–

-

f el
f nuti

–
–

accel. factors nutrient strip. for six detritus
components
limiting factor for electron acceptors
limiting factors for nutrient availability

kmin20
i,max
„

ku_dF dcC20 max. min. rate fast detr-C at 20 ◦ C
ku_dM dcC20 max. min. rate medium detr-C detr. at 20

bni
bsu

Coci
„
„

Coni
„
„

Copi
„
„

Cosi
„
„
Cox
Cni

T

Name in input

DR
AF

Name in
formulas1
„
„
api,min
„
„
arj
„
„
bi
„
„
„
„

w

conc. organic carbon in medium detritus
conc. organic carbon in slow detritus

b

−3

gC.m

b

−3

gC.m

b

−3

conc. organic nitrogen in fast detritus

gN.m

conc. organic nitrogen in medium detritus

gN.m−3

conc. organic nitrogen in slow detritus
conc. organic phosphorus in fast detritus

conc. organic sulfur in fast detritus

conc. organic sulfur in medium detritus
conc. organic sulfur in slow detritus
concentration of dissolved oxygen

b

b

−3

gN.m

b

−3

gP.m

b

−3
b

b

gS.m

−3

gS.m

−3

gS.m

−3

b

b

b

gO2 m

−3
b

−3
b

d−1
d−1

◦

„
kmin20
i,min
„
„

Deltares

ku_dSdcC20
kl_dF dcC20
kl_dM dcC20
kl_dSdcC20

C
max. min. rate slow detr-C at 20 ◦ C
min. min. rate fast detr-C at 20 ◦ C
min. min. rate medium detr-C at 20 ◦ C
min. min. rate slow detr-C at 20 ◦ C

d−1
d−1
d−1
d−1

225 of 464

Processes Library Description, Technical Reference Manual

Table 8.1: Definitions of the input parameters in the above equations for DECFAST,
DECMEDIUM and DECSLOW. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in input

Definition

Units

kT _dec

temperature coefficient for mineralization

-

kmin20
i,max
„
„
kmin20
i,min
„
„

ku_dF dcN 20
ku_dM dcN 20
ku_dSdcN 20
kl_dF dcN 20
kl_dM dcN 20
kl_dSdcN 20

max. min. rate fast detr-N at 20 ◦ C
max. min. rate medium detr-N at 20 ◦ C
max. min. rate slow detr-N at 20 ◦ C
min. min. rate fast detr-N at 20 ◦ C
min. min. rate medium detr-N at 20 ◦ C
min. min. rate slow detr-N at 20 ◦ C

d−1
d−1
d−1
d−1
d−1
d−1

kmin20
i,max
„
„
kmin20
i,min
„
„

ku_dF dcP 20
ku_dM dcP 20
ku_dSdcP 20
kl_dF dcP 20
kl_dM dcP 20
kl_dSdcP 20

max. min. rate fast detr-P at 20 ◦ C
max. min. rate medium detr-P at 20 ◦ C
max. min. rate slow detr-P at 20 ◦ C
min. min. rate fast detr-P at 20 ◦ C
min. min. rate medium detr-P at 20 ◦ C
min. min. rate slow detr-P at 20 ◦ C

d−1
d−1
d−1
d−1
d−1
d−1

SW OM DecSW OM Dec

option (0.0 = nutrient stripping; 1.0 = different rates)

-

T
T

temperature of water
temperature of air and sediment when
ran dry

◦

DR
AF

1

T

Name in
formulas1
ktmin

T emp
N atT emp

◦

C
C

j = C, N, P or S; i = POC1, POC2 or POC3.

Table 8.2: Definitions of the input parameters in the above equations for DECREFR, DECDOC and DECPOC5. Volume units refer to bulk ( ) or to water ( ).
b

Name in
formulas1

Name in input

ani,max

au_dN P OC5 max. stoch. constant N in stem/root

ani,min
api,max

al_dN P OC5
au_dP P OC5

api,min
arj
bi

al_dP P OC5
a_dN pr
a_dP pr
a_dSpr
b_poc5poc4

„

b_poc5doc

bni

b_ni

bsu

b_su

„
„

226 of 464

Definition

POC5
min. stoch. constant N in stem/root POC5
max. stoch. constant P in stem/root
POC5
min. stoch. constant P in stem/root POC5
stoch. constant N in refr. detritus
stoch. constant P in refr. detritus
stoch. constant S in refr. detritus
conv. fraction stem/root POC5 into part.
refr. detr.
conv. fraction stem/root POC5 into diss.
refr. detr.
attenuation constant for nitrate as electron acceptor
attenuation constant for sulfate as electron acceptor

w

Units
gN.gC−1
gN.gC−1
gP.gC−1
gP.gC−1
gN.gC−1
gP.gC−1
gS.gC−1
-

Deltares

Organic matter (detritus)

Table 8.2: Definitions of the input parameters in the above equations for DECREFR, DECDOC and DECPOC5. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas1

Name in input

Definition

Units

Coci

conc. organic C in part. refr. detritus

gC.m−3

conc. organic C in stems and roots

gC.m−3

Cox
Cni

P OC4
P OC5
DOC
P ON 4
P ON 5
DON
P OP 4
P OP 5
DOP
P OP 4
P OP 5
DOP
OXY
N O3

concentration of nitrate

gN.m

f el

-

limiting factor for electron acceptors

-

ktmin

k _dprdcC20
ku_P 5dcC20
kl_P 5dcC20
k _DOCdcC20
kT _dec

min. rate part. refractory detr. at 20 ◦ C
max. min. rate stem/root POC5 at 20 ◦ C
min. min. rate stem/root POC5 at 20 ◦ C
min. rate diss. refractory detr. at 20 ◦ C
temperature coefficient for mineralisation

d−1
d−1
d−1
-

T
T

T emp
N atT emp

temperature
temperature of air and sediment when
ran dry

◦

„

Coni
„
„

Copi
„
„

Cosi
„

kmin20
i
„
„
„

1

conc. organic N in part. refr. detritus
conc. organic N in stems and roots
conc. organic N in diss. refr. detritus
conc. organic P in part. refr. detritus
conc. organic P in stems and roots

conc. organic P in diss. refr. detritus

b

−3

gN.m

b

−3

gN.m

b

−3

gN.m

b

−3

gP.m

b

−3

gP.m

b

−3

gP.m

b

−3

gS.m

conc. organic S in stems and roots

gS.m−3

conc. organic S in diss. refr. detritus
concentration of dissolved oxygen

b

gC.m

conc. organic S in part. refr. detritus

DR
AF

„

conc. organic C in diss. refr. detritus

b

−3

T

„

gS.m

b

b

−3
b

gO2 .m

−3
b

−3

◦

b

C
C

j = C, N, P or S; i = POC4, POC5 or DOC.

Deltares

227 of 464

Processes Library Description, Technical Reference Manual

Consumption of electron-acceptors
PROCESS :

CONSELAC








oxygen consumption;
denitrification;
manganese reduction;
iron reduction;
sulfate reduction; and
methanogenesis.

T

The microbial decomposition (mineralisation, oxidation) of organic matter into carbon dioxide
involves the consumption (reduction) of electron acceptors. These substances are used by
different species of bacteria in a specific order in agreement with the thermodynamic potentials of the reduction processes (Santschi et al., 1990; DiToro, 2001). The electron acceptors
are used in the following sequence: dissolved oxygen, nitrate, manganese(IV), iron(III), sulfate and carbon monoxide. The last substance as well as the electron donor hydrogen are
derived from organic matter itself as intermediate products in methanogenesis, whereas the final products are more or less equal amounts of carbon dioxide and methane. The subsequent
redox processes are indicated as:

DR
AF

8.2

In principal the thermodynamically more favourable reduction process excludes the less favourable process, provided that the more favourable electron acceptor is available. When an
electron acceptor is not sufficiently supplied from an external source it will eventually become
depleted. Therefore, oxygen consumption, denitrification and sulfate reduction are mutually
exclusive to a large extent. However, denitrification may also be carried out in the water column at aerobic conditions by highly specialised bacteria (aerobic denitrification). After depletion of the respective electron acceptors methanogenesis takes over as a final possibility for
bacteria to utilise organic matter for energy and growth. The reduction of manganese and iron
are excluded by oxygen consumption and denitrification, but may concur with sulfate reduction
and methanogenesis due to slow kinetics. Consequently, one would expect the occurrence
of the various reduction processes in distinct stages in time, or in distinct water or sediment
layers. However, due to spatial heterogeneity various processes may be active at the same
time in the same compartment. In other words: Compartments may show substantial overlap
with respect to the reduction processes.
The electron acceptors that can be considered in DELWAQ currently are dissolved oxygen, nitrate, iron(III), sulfate and organic matter, which replaces carbon monoxide as the actual electron acceptor. Methane as the product of organic matter decomposition by means of methanogenesis included in DELWAQ too. The production of reducing iron(II), sulfide, methane has
implications for the dissolved oxygen budget. It is possible to exclude nitrate, iron(III), sulfate
or methane from simulations. The reduction of manganese is ignored, as it can be considered
implicit in sulfate and iron reduction.
Denitrification, iron reduction, sulfate reduction and methanogenesis are relatively sensitive to
low temperature. In contrast with the aerobic decomposition of detritus, which may proceed
at a slow but measurable rate below 4 ◦ C, the other processes nearly come to a halt below
this temperature. This may be connected with the fact that only a rather small number of
specialised bacteria species are capable of one of these processes. As contrasted with this
the decomposition of organic matter is performed by a very large number of species, including
species that are adapted to low temperature environments.
Denitrifiers, iron reducers, sulfate reducers and methanogens are predominantly sessile bac-

228 of 464

Deltares

Organic matter (detritus)

teria, that need readily available organic substrates and that can only actively survive in an
anoxic environment. This implies that denitrification usually only proceeds in the lower part of
the oxidising top sediment layer. The reducing substance may be organic matter but also ammonium (anaerobic ammonium oxidation; annamox). Denitrification may also be carried out
in the water column at aerobic conditions by highly specialised bacteria or in anoxic pockets
of suspended particles. Sulfate and iron reduction and even more so methanogenesis usually
only occur in the deeper parts of sediment. However, all these may proceed in completely
anoxic water layers in deep stratified water systems.

T

The consumption (reduction) rates depend on electron acceptor availability (limitation) as well
as on inhibition by the next more favourable process. The overall consumption of electron
acceptors is dependent of the organic matter decomposition flux. The fractional contributions
of the electron acceptors are deduced on the basis of the relative abundance of electron
acceptors, taking into account both limitation and inhibition. These fractions add up to one,
and are used to calculate the organic matter mineralisation fluxes connected with dissolved
oxygen consumption, denitrification, iron reduction, sulfate reduction and methanogenesis.
DELWAQ converts these fluxes into the concurrent consumption fluxes for DO, nitrate, iron(III)
and sulfate, and into the concurrent methane production flux.

DR
AF

Dead organic matter in natural water, also called detritus, is a complicated mixture of substances that vary greatly with respect to chemical structure. Therefore, the microbial decomposition (oxidation) of detritus is described considering various fractions of organic matter,
each having its own decomposition rate. The decomposition of the organic fractions is described elsewhere for processes DECFAST, DECMEDIUM, DECSLOW, DECREFR, DECPOC5
and DECDOC. These processes are based on first-order kinetics regarding the concentration
of organic matter. The total organic matter decomposition flux is calculated in CONSELAC as
the sum of the fluxes for the four organic matter fractions.
Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

Process CONSELAC is generic in the sense that it is applied to both water layers and sediment layers, when sediment layers are simulated as compartments. However, it can also be
used for the water column only in combination with one of the other options for mineralisation
in the sediment (BMS1/2_i).
Process DENSED_NO3 is to be used in addition to CONSELAC only when the sediment is
simulated according to the S1/S2 option. When sediment layers are not simulated explicitly,
this process takes care that denitrification in the sediment proceeds anyhow, and ultimately
causes the removal of nitrate from the water column.
Process CONSELAC has been implemented for the following substances:

 OXY, NO3, FeIIIpa, FeIId, SO4, SUD and CH4,
in connection with the following organic substances:

 POC1, POC2, POC3, POC4, POC5 and DOC.
The oxygen consumed is stored in TIC or CO2. The nitrate reduced is removed from the model
as elementary nitrogen is not simulated. The iron reduced is withdrawn from the amorphous
fraction of the particulate oxidizing iron FeIIIp, and added to the dissolved reducing iron FeIId.

Deltares

229 of 464

Processes Library Description, Technical Reference Manual

The sulfate reduced is added to dissolved sulfide SUD. Table 8.3 provides the definitions of
the parameters occurring in the formulations.
Formulation
The relative contributions of the electron acceptors in the microbial decomposition of organic
matter are formulated on the basis of limitation and inhibition terms according to MichaelisMenten kinetics (Smits and Van Beek (2013)).
Consumption of oxygen
The consumption of oxygen at the aerobic decomposition of organic matter can be described
with the following simplified reaction equation:

T

O2 + CH2 O =⇒ CO2 + H2 O

DR
AF

For simplicity it is assumed that organic matter is represented by the molecular stochiometry
of glucose, whereas in reality organic matter may be richer in hydrogen. In this example
2.667 gram of oxygen is consumed for every gram of carbon oxidised. The consumption
of oxygen is limited by the availability of dissolved oxygen. This process is not inhibited by
any other electron acceptor. However, the decomposition of organic matter is temperature
dependent. Since the temperature dependency of the consumption of the electron acceptors
is different to a certain extent for each of the electron acceptors, it is necessary to consider
this in the contributions of the electron-acceptors. The contribution of dissolved oxygen in the
mineralisation of organic matter is proportional to:
20

f ox
where:

Cox
f ox20
Ksox
φ



=

Cox
Ksox × φ + Cox



dissolved oxygen concentration [g.m−3 ]
b

unscaled relative contr. of oxygen consumption in mineralisation at 20 ◦ C [-]
half saturation constant for dissolved oxygen limitation [gO2 m−3 ]
porosity [-]
w

The relative contribution is the following function of temperature:

f ox = f ox20 × ktoxc(T −20)
where:

f ox
ktoxc
T

unscaled relative contribution of oxygen consumption in mineralisation [-]
temperature coefficient for oxygen consumption [-]
temperature [◦ C]

Denitrification
Denitrification can be described as a number of consecutive chemical reactions in which oxygen is made available for the oxidation of organic matter. Several intermediate reduction
products are formed, but the first step from nitrate to a nitrite is rate limiting. The accumulation of the intermediate products including toxic nitrite and various toxic nitrogen oxides is
generally negligible. The overall reaction equation is:

4N O3− + 4H3 O+ + 5CH2 O =⇒ 2N2 + 5CO2 + 11H2 O
Denitrification ultimately removes nitrate from the water phase and produces elemental nitrogen that may escape into the atmosphere. The process delivers 2.86 gO2 gN−1 , instantly consumed for the oxidation of organic matter. Consequently, the process consumes 0.933 gram N

230 of 464

Deltares

Organic matter (detritus)

per gram C. Denitrification is limited by the availability of nitrate. It is inhibited by dissolved
oxygen. The contribution of nitrate in the mineralisation of organic matter is proportional to:
20

f ni


=

Cni
Ksni × φ + Cni




× 1−

Cox
Ksoxi × φ + Cox



where:

Cni
f ni20
Ksni
Ksoxi

nitrate concentration [gN m−3 ]
b

unscaled relative contribution of denitrification in mineralisation at 20 ◦ C [-]
half saturation constant for nitrate limitation [gN m−3 ]
half saturation constant for dissolved oxygen inhibition [gO2 .m−3 ]
w

w

f ni = f ct × f ni20 × ktden(T −20)
f ct = 1.0
f ct = f den

T ≥ Tc
if T < Tc

if

DR
AF

where:

T

The relative contribution of denitrification needs to be adjusted for (low) temperature:

f ct
f den
f ni
ktden
T
Tc

reduction factor for temperatures below critical temperature [-]
reduction factor for denitrification below critical temperature [-]
unscaled relative contribution of denitrification in mineralisation [-]
temperature coefficient for denitrification [-]
temperature [◦ C]
critically low temperature for specific bacterial activity [◦ C]

Imposing of a higher temperature coefficient than the coefficient for aerobic detritus composition leads to reduction of the relative contribution of denitrification. Below the critical temperature, the contribution of denitrification may be reduced further to a low background level,
when f den receives a value smaller than 1.0. The second reduction implies a discontinuity
at the critical temperature.
Because denitrification is not to occur when dissolved oxygen is present in significant quantity,
it is necessary to exclude denitrification if DO exceeds a certain critical level:

f ni = 0.0

if

Cox ≥ Coxc1 × φ

where:

Coxc1

critical dissolved oxygen conc. for inhibition of denitrification [g m−3 ]
b

Iron reduction
Iron reduction is assumed to take place on the surface of iron minerals, the amorphous fraction
Fe(OH)3 or FeOOH, which leads to the following reaction equation:

4F e(OH)3 a + CH2 O ⇒ 4F eIId + CO2 + 3H2 O + 8OH −
The resulting dissolved reducing iron may largely precipitate with sulfide. The process delivers
0.143 gO2 .gFe−1 , instantly consumed for the oxidation of organic matter. Consequently, the
process consumes 18.67 gram Fe per gram C. Iron reduction is limited by the availability of
the amorphous fraction of particulate oxidizing iron. It is inhibited by both nitrate and dissolved
oxygen. However, it is reasonable to assume that nitrate is present in substantial quantities at

Deltares

231 of 464

Processes Library Description, Technical Reference Manual

the significant presence of dissolved oxygen. Therefore, the relative contribution of iron in the
mineralisation of organic matter is proportional to:
20

ffe


=

Cf ea
Ksf e × φ + Cf ea




× 1−

Cni
Ksnif ei × φ + Cni



where:

Cf ea
f f e20
Ksf e
Ksnif ei

amorphous oxidizing iron concentration [gFe.m−3 ]
b

unscaled relative contrib. of iron reduction in mineralisation at 20 ◦ C [-]
half saturation constant for iron limitation [gFe.m−3 ]
half saturation constant for nitrate inhibition of iron reduction [gN.m−3 ]
w

w

T

The relative contribution of iron reduction is adjusted for (low) temperatures in the same way
as in the case of denitrification:

where:

f ird
ffe
ktird

DR
AF

f f e = f ct × f f e20 × ktird(T −20)
f ct = 1.0
if T ≥ T c
f ct = f ird
if T < T c

reduction factor for iron reduction below critical temperature [-]
unscaled relative contribution of iron reduction in mineralisation [-]
temperature coefficient for iron reduction [-]

Because iron reduction is not to occur when dissolved oxygen is present in significant quantity,
it is necessary to exclude iron reduction if DO exceeds a certain critical level:

f f e = 0.0
where:

if Cox ≥ Coxc2 × ϕ

= critical dissolved oxygen conc. for inhibition of iron reduction (g.m−3 b)

Coxc2

Sulfate reduction
Sulfate reduction is also carried out in a number of consecutive steps in which oxygen is made
available for the oxidation of organic matter. The overall reaction equation is:

SO4−2 + 2CH2 O =⇒ S −2 + 2CO2 + 2H2 O

Sulfate reduction removes sulfate and ultimately produces sulfide, which may largely precipitate with iron(II). The process delivers 2 gO2 gS−1 , instantly consumed for the oxidation of
organic matter. Consequently, the process consumes 1.333 gram S per gram C. Sulfate reduction is limited by the availability of sulfate. It is inhibited by both nitrate and dissolved
oxygen, but not by oxidizing iron due to the slow kinetics of iron reduction. However, it is
reasonable to assume that nitrate is present in substantial quantities at the significant presence of dissolved oxygen. Therefore, the relative contribution of sulfate in the mineralisation
of organic matter is proportional to:
20

f su


=

Csu
Kssu × φ + Csu




× 1−

Cni
Ksnisui × φ + Cni



with:

232 of 464

Deltares

Organic matter (detritus)

Csu
f su20
Kssu
Ksnisui

sulfate concentration [gS m−3 ]
b

unscaled relative contrib. of sulfate reduction in mineralisation at 20 ◦ C [-]
half saturation constant for sulfate limitation [gS m−3 ]
half saturation constant for nitrate inhibition of sulfate reduction [gN m−3 ]
w

w

The relative contribution of sulfate reduction is adjusted for (low) temperatures in the same
way as in the case of denitrification:

f su = f ct × f su20 × ktsrd(T −20)
f ct = 1.0
f ct = f srd

if T ≥ Tc

T < Tc

if

where:

f srd
f su
ktsrd

T

reduction factor for sulfate reduction below critical temperature [-]
unscaled relative contribution of sulfate reduction in mineralisation [-]
temperature coefficient for sulfate reduction [-]

DR
AF

Because sulfate reduction is not to occur when dissolved oxygen is present in significant
quantity, it is necessary to exclude sulfate reduction if DO exceeds a certain critical level:

f su = 0.0

if Cox ≥ Coxc3 × φ

where:

critical dissolved oxygen conc. for inhibition of sulfate reduction [g.m−3 ]

Coxc3

b

Methanogenesis
Organic matter will be decomposed by bacteria into carbon dioxide and methane when all
other electron acceptors have been depleted. The production of these substances takes place
in several intermediate steps, in which carbon monoxide and hydrogen feature. Assuming the
glucose molecular stochiometry for organic matter the overall reaction equation is:

2CH2 O =⇒ CO2 + CH4

Methane dissolves until saturation, after which methane may be stored and removed as gass
bubbles (ebullition). Methanogenesis does not deliver dissolved oxygen, and is only limited by
the availability of organic matter. The process is inhibited by the availability of sulfate, nitrate
and dissolved oxygen, but not by oxidizing iron due to the slow kinetics of iron reduction.
However, it is reasonable to assume that sulfate is present in substantial quantities at the
significant presence of dissolved oxygen or nitrate. Therefore, the relative contribution of
sulfate in the mineralisation of organic matter is proportional to:
20

f ch4



=

Csu
1−
Kssui × φ + Csu



where:

f ch420
Kssui

unscaled relative contribution of methanogenesis in mineralisation at 20 ◦ C [-]
half saturation constant for sulfate inhibition [gS m−3 ]
w

The relative contribution of methanogenesis is adjusted for low temperatures in the same way
as in the case of denitrification:

f ch4 = f ct × f ch420 × ktmet(T −20)
f ct = 1.0
f ct = f met

Deltares

if T ≥ Tc
if T < Tc

233 of 464

Processes Library Description, Technical Reference Manual

where:

f ch4
f met
ktmet

unscaled relative contribution of methanogenesis in mineralisation [-]
reduction factor for methanogenesis below critical temperature [-]
temperature coefficient for methanogenesis [-]

Because methanogenesis is not to occur when dissolved oxygen or nitrate are present in
significant quantities, it is necessary to exclude methanogenesis if DO or nitrate exceeds a
certain critical level:

f ch4 = 0.0

if Cox ≥ Coxc4 × φ or

Cni ≥ Cnic × φ

where:
critical dissolved oxygen conc. for inhibition of methanogenesis [g m−3 ]
critical nitrate conc. for inhibition of methanogenesis [gN m−3 ]
w

w

T

Coxc4
Cnic

DR
AF

Corrections for negative concentrations
Notice that negative concentrations would cause incorrect relative contributions. DELWAQ
checks on negative concentrations anyway and equals them effectively to zero, but only locally
in process CONSELAC.
The scaled relative contributions
The scaled contributions of the five reduction processes to the decomposition of organic matter now follow from the requirement that the sum of these contributions equals one:

f ox
f ox + f ni + f f e + f su + f ch4
f ni
f rni =
f ox + f ni + f f e + f su + f ch4
ffe
f rf e =
f ox + f ni + f f e + f su + f ch4
f su
f rsu =
f ox + f ni + f f e + f su + f ch4
f rch4 = 1 − f rox − f rni − f f e − f rsu
f rox =

where:

f rox
f rni
f rf e
f rsu
f rch4

scaled contribution of dissolved oxygen consumption [-]
scaled contribution of denitrification [-]
scaled contribution of iron reduction [-]
scaled contribution of sulfate reduction [-]
scaled contribution of methanogenesis [-]

The total mineralisation flux
The total flux of the decomposition (mineralisation) of organic matter Rtmin is equal to the
sum of the mineralisation fluxes of the six fractions:

Rtmin = Rmin1 + Rmin2 + Rmin3 + Rmin4 + Rmin5 + Rmin6
where:

Rmin1

mineralisation flux for organic carbon in the fast decomposing detritus fraction
POC1 [gC m−3 d−1 ]

Rmin2

mineralisation flux for organic carbon in the slowly decomposing detritus fraction
POC2 [gC m−3 d−1 ]

b

b

234 of 464

Deltares

Organic matter (detritus)

Rmin3

mineralisation flux for organic carbon in the very slowly decomposing detritus
fraction POC3 [gC m−3 d−1 ]

Rmin4

mineralisation flux for organic carbon in the particulate refractory detritus fraction POC4 [gC m−3 d−1 ]

Rmin5

mineralisation flux for organic carbon in dead stems and roots of vegetation
detritus fraction POC5 [gC m−3 d−1 ]

Rmin6

mineralisation flux for organic carbon in the dissolved refractory detritus fraction
DOC [gC m−3 d−1 ]

Rtmin

total mineralisation flux for organic carbon [gC m−3 d−1 ]

b

b

b

b

b

Oxygen consumption
The mineralisation flux connected to oxygen consumption follows from:



0.5 × Cox
f rox × Rtmin × 2.67 × ∆t

DR
AF

f rox0 =



T

Cox
Rcns = min f rox × Rtmin, 0.5 ×
2.67 × ∆t

where:

f rox0
Rcns
∆t

corrected scaled relative contribution of oxygen consumption [-]
mineralisation flux connected to oxygen consumption [gC m−3 d−1 ]
b

the timestep of DELWAQ [days]

Since the oxygen consumption rate is only proportional to the concentration of organic matter
and not to the concentration of dissolved oxygen, it is possible that negative dissolved oxygen
concentrations arise. This happens when the stock of dissolved oxygen is too small to satisfy
the demand. A negative concentration leads to f rox = 0.0 as described before. Negative
oxygen concentrations will therefore remain small and they will soon be eliminated by means
of diffusion of oxygen. Negative oxygen concentrations are acceptable in DELWAQ, because
they can be perceived as the negative oxygen equivalents of reduced substances such as
iron(II) and manganese(II). However, in order to reduce negative concentrations as much as
possible, a correction is carried out by means of limiting the oxygen consumption rate to 50 %
of the stock of oxygen divided by the timestep, when the stock is too small to satisfy the
demand.
Denitrification
The mineralisation flux connected to denitrification cannot be coupled to the total mineralisation flux in the same straightforward way as in the case of oxygen consumption. As explained above negative nitrate concentrations might arise. A negative concentration leads to
f rni = 0.0 as described above. However, negative nitrate concentrations are conceptually
unacceptable. A correction is therefore carried out by means of limiting the denitrification rate
to 90 % of the stock of nitrate divided by the timestep, when the stock is too small to satisfy
the demand. The mineralisation flux and the corrected contribution are calculated as follows:



Cni
Rden = min f rni × Rtmin, 0.9 ×
0.933 × ∆t
f rni0 =



0.9 × Cni
f rni × Rtmin × 0.933 × ∆t

where:

Cni

nitrate concentration [gN.m−3 ]
b

Deltares

235 of 464

Processes Library Description, Technical Reference Manual

f rni0
Rden
∆t

corrected scaled relative contribution of denitrification [-]
mineralisation flux connected to denitrification [gC.m−3 d−1 ]
b

the timestep of DELWAQ [days]

Iron reduction
The mineralisation flux connected to iron reduction needs a similar correction as made for
denitrification, when the stock of oxidizing iron is too small to satisfy the demand. The mineralisation flux and the corrected contribution are calculated as follows:


Rird = min f rf e × Rtmin , 0.9 ×



0.9 × Cf ea
f rf e × Rtmin × 18.67 × ∆t

T

f rf e0 =

Cf ea
18.67 × ∆t

where:

Cf ea
f rf e0
Rird

amorphous oxidizing iron concentration [gFem-3 ]
corrected scaled relative contribution of iron reduction [-]
b

mineralisation flux connected to iron reduction [gC m-3 d-1]

DR
AF

b

Sulfate reduction
The mineralisation flux connected to sulfate reduction needs a similar correction as made for
denitrification, when the stock of sulfate is too small to satisfy the demand. The mineralisation
flux and the corrected contribution are calculated as follows:


Rsrd = min f rsu × Rtmin, 0.9 ×
f rsu0 =
where:

Csu
f rsu0
Rsrd

Csu
1.33 × ∆t



0.9 × Csu
f rsu × Rtmin × 1.33 × ∆t

sulfate concentration [gS m−3 ]
b

corrected scaled relative contribution of sulfate reduction [-]
mineralisation flux connected to sulfate reduction [gC m−3 d−1 ]
b

Methanogenesis
A limitation of the methanogenesis flux is not needed because the stock of electron acceptor
(organic matter) is always large enough. The mineralisation flux connected to methanogenesis follows from:

Rmet = am × f rch4 × Rtmin
where:

am
Rmet

fraction of organic C actually turned into methane [-]
mineralisation flux connected to methanogenesis [gC m−3 d−1 ]
b

The coefficient am is in fact a stochiometric constant of the decomposition reaction. By default
this constant has a value of 0.5, assuming that the composition of organic matter is CH2O on
average. Half of carbon ends up in methane, the other half in carbon dioxide.
Correction of oxygen consumption and methanogenesis
When one or more of the contributions of oxygen consumption, denitrification, iron reduction and sulfate reduction have changed due to limited stocks, the contribution of the other
processes need to be corrected too. This is achieved by

236 of 464

Deltares

Organic matter (detritus)

 shifting the required decrease of the fraction of denitrification to the fraction of oxygen
consumption

 if also necessary, the required decrease of the fraction of oxygen consumption to the
fraction of sulfate reduction

 if also necessary, the required decrease of the fraction of iron consumption to the fraction
of sulfate reduction

 and if also necessary, the required decrease of the fraction of sulfate reduction to the
fraction of methanogenesis.
The corrected contribution of methanogenesis follows from:

f rch40 = 1 − f rox0 − f rni0 − f rf e0 − f rsu0
f rch40

T

where:
corrected scaled relative contribution of methanogenesis [-]

DR
AF

Directives for use
 Indicative values for the limitation constants are: KsOxCon = 1.0 gO2 m−3 , KsN iDen =
0.25 gN m−3 , KsF eRed = 100 000.0 gFe m3 , KsSuRed = 2.0 gS m−3 .
Indicative values for the inhibition constants are: KsOxDenInh = 1.0 gO2 m−3 ,
KsN iIReInh = 0.2 gN m−3 , KsN iSReInh = 0.2 gN m3 , KsSuM etInh =
1.0 gS m−3 .
 The half saturation constants may have different values for the sediment and the water
column, reflecting differences as to the abundance and activity of specific bacteria species.
Raising a limitation constant leads to a smaller contribution of the specific process. Raising
an inhibition constant leads to a larger contribution.
 The half saturation constants in the limitation and inhibition functions determine the actually occurring spatial overlap of processes. Denitrification, iron reduction, sulfate reduction
and methanogenesis are virtually excluded from the water column when the values of the
inhibition constants of these processes are decreased to 10% of the indicative values.
 The half saturation constants for inhibition in the water column may also be used to account for the consequences of inhomogeneity in the water column. Denitrification, iron
reduction, sulfate reduction and even methanogenesis may occur in the lower part of the
water column due to oxygen depletion near the sediment. The average dissolved oxygen
concentration can still be clearly positive, which may lead to the underestimation of three
of the reduction processes. The user could then decide to schematise the water column
with several layers (compartments). As an alternative he may decide to raise the values
of the half saturation constants for inhibition.
 A similar reasoning goes for the concentration gradients that may occur in organic matter
rich suspended particles. Denitrification in the particles can be accounted for by raising the
oxygen inhibition constant to about 2 gO2 m−3 , which is an appropriate value for physical
reasons.
 The temperature coefficients are connected to the temperature coefficient of the decomposition of organic matter. Default values are: T cOxCon = 1.07, T cDen = 1.07,
T cIRed = 1.07, T cSRed = 1.07, T cM et = 1.07.
 The adjustment of the relative contributions of denitrification, iron reduction, sulfate reduction and methanogenesis for (low) temperature is based on retardation of consumption of the respective electron acceptors compared to the aerobic decomposition of detritus (retardation factors < 1.0). The critically low temperature CT BactAc is 2–4 ◦ C.
In case sediment temperature is set equal to water temperature, one wants some enhancement in stead of retardation because generally sediment temperature is higher than
water temperature in winter time. Enhancement factors RedF acDen, RedF acIRed,
RedF acSRed, RedF acM et can be 1.25.
w

w

w

w

w

w

w

w

w

Deltares

237 of 464

Processes Library Description, Technical Reference Manual

 The critical concentrations for inhibition of denitrification, iron reduction, sulfate reduction
and methanogenesis should have low values. Recommended values are: CoxDenInh =
1.0 in water column, and = 5.0 in sediment, CoxIRedInh = 0.05, CoxSRedInh =
0.05, CoxM etInh = 0.02, CniM etInb = 0.05.
 Assuming CH2O as a measure for the chemical structure of organic matter the default
stochiometric coefficients in the processes matrix of DELWAQ are:
The amount of oxygen consumed per amount of carbon is 2.667 gO2 gC−1 .
The amount of nitrate consumed per amount of carbon is 0.932 gN gC−1 .
The amount of iron consumed per amount of carbon is 18.67 gFe.gC−1 .
The amount of sulfate consumed per amount of carbon is 1.333 gS gC−1 .
The amount of methane produced per amount of carbon is 0.5 gC gC−1 .

 The corrected scaled relative contributions of dissolved oxygen consumption, denitrifica-

DR
AF

T

tion, iron reduction, sulfate reduction and methanogenesis are available as the following
output parameters: F rOxCon, F rN itDen, F rF eRed, F rSulRed, F rM etGen.
 Coeffcient F rM etGeCH4 is 0.5 by default. If the user would modify its value, he should
realize that all oxygen and carbon dioxide fluxes have been quantified assuming that the
basic composition of organic matter is CH2 O. He should modify these fluxes too.
Additional references

Boudreau (1996), DiToro (2001), Luff and Moll (2004), Santschi et al. (1990), Smits and
Van der Molen (1993), Soetaert et al. (1996), Vanderborght et al. (1977), Wang and Cappellen (1996), WL | Delft Hydraulics (2002), Wijsman et al. (2001)
Table 8.3: Definitions of the parameters in the above equations for CONSELAC. Volume
units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in input

Definition

Units

Cox
Cni
Cf ea

OXY
N O3
F eIIIpa

dissolved oxygen concentration

gO2 m−3

nitrate concentration

gN m−3

particulate amorphous oxidizing iron concentration
sulfate concentration

gFe m−3

critical diss. oxygen conc. inhibition of
denitrific.
critical diss. oxygen conc. inhibition of
iron red.
critical diss. oxygen conc. inhibition of
sulfate red.
critical diss. oxygen conc. inhib. of
methanogenesis
critical nitrate conc. inhibition of methanogenesis

gO2 m−3

unscaled rel. contr. of oxygen cons. in
mineralisation
unscaled rel. contr. of denitrif. in mineralisation

-

Csu
Coxc1
Coxc2
Coxc3

SO4
CoxDenInh

CoxIRedInh

CoxSRedInh

Coxc4

CoxM etInh

Cnic

CniM etInb

f ox

-

f ni

-

b

b

b

gS m−3
b

w

gO2 m−3
w

gO2 m−3
w

gO2 m−3
w

gN m−3
w

-

continued on next page

238 of 464

Deltares

Organic matter (detritus)

Table 8.3 – continued from previous page
Name in
formulas

Name in input

Definition

Units

ffe

-

-

f su

-

f ch4

-

f rox

-

f rni
f rf e
f rsu

-

f rch4c

-

unscaled rel. contr. of iron red in mineralisation
unscaled rel. contr. of sulfate red. in mineralisation
unscaled rel. contr. of methanog. in mineralisation
scaled rel. contr. of dissolved oxygen
consumption
scaled rel. contribution of denitrification
scaled rel. contribution of iron reduction
scaled rel. contribution of sulfate reduction
scaled rel. contribution of methanogenesis

f ct

-

reduction factor for temp. below critical
temperature
reduction factor for denitr. below critical
temperature
reduction factor for iron red. below critical
temperature
reduction factor for sulfate red. below critical temperature
reduction factor for methanog. below critical temperature

-

temperature coefficient for oxygen consumption
temperature coefficient for denitrification
temperature coefficient for iron reduction
temperature coefficient for sulfate reduction
temperature coefficient for methanogenesis

-

RedF acDen

f ird

RedF acIRed

f srd

RedF acSRed

f met

RedF acM et

ktoxc

T cOxCon

ktden
ktird
ktsrd

T cDen
T cIred
T cSRed

ktmet

T cM et

Ksox

KsOxCon

Ksni

Ksf e
Kssu
Ksoxi
Ksnif ei
Ksnisui

-

T

DR
AF

f den

-

half saturation constant for oxygen limitation
KsN iDen
half saturation constant for nitrate limitation
KsF iRed
half saturation constant for iron limitation
KsSuRed
half saturation constant for sulfate limitation
KsOxDenInh half sat. const. for DO inhibition of denitrification
KsN iIRdInh half sat. const. for nitrate inhib. of iron
reduction
KsN iSRdInh half sat. const. for nitrate inhib. of sulfate
reduction

-

-

gO2 m−3
w

gN m−3
w

gFe m−3
gS m−3
w

w

gO2 m−3
w

gN m−3
w

gN m−3
w

continued on next page

Deltares

239 of 464

Processes Library Description, Technical Reference Manual

Table 8.3 – continued from previous page
Name in
formulas

Name in input

Definition

Units

Kssui

KsSuM etInh half sat. const. for sulfate inhib. of

gS m−3
w

methanogenesis

Rcns
Rden

gC m−3 d−1

f _M inP OC1 mineralisation flux for organic carbon in

gC m−3 d−1

b

gC m−3 d−1
b

gC m−3 d−1
b

-

the fast decomposing detritus fraction
POC1
f _M inP OC2 mineralisation flux for organic carbon in
the slowly decomposing detritus fraction
POC2
f _M inP OC3 mineralisation flux for organic carbon in
the very slowly decomposing detritus
fraction POC3
f _M inP OC4 mineralisation flux for organic carbon in
the particulate refractory detritus fraction
POC4
f _M inP OC5 mineralisation flux for organic carbon in
dead stems and roots, detritus fraction
POC5
f _M inDOC mineralisation flux for organic carbon in
the dissolved refractory detritus fraction
DOC
F rM etGeCH4 fraction of organic C converted into
methane (CH4)

DR
AF

Rmin2
Rmin3
Rmin4
Rmin5
Rmin6

φ

b

T

-

Rmin1

∆t

mineralisation flux connected to sulfate
reduction
mineralisation
flux
connected
to
methanogenesis

-

Rmet

T
Tc

gC m−3 d−1

-

Rird
Rsrd

am

mineralisation flux connected to oxygen
consumption
mineralisation flux connected to denitrification
mineralisation flux connected to iron red

-

gC m−3 d−1
b

b

gC m−3 d−1
b

gC m−3 d−1
b

gC m−3 d−1
b

gC m−3 d−1
b

gC m−3 d−1
b

-

T emp
CT BactAc

temperature
critically low temp. for specific bacterial
activity

◦

Delt

computational time-step

d

P OROS

porosity

m3 m−3

◦

C
C

w

b

240 of 464

Deltares

Organic matter (detritus)

Settling of detritus
PROCESSES :

SED_( I ), SEDN( I ), SED_CAAP, CALVS( I ), COMPOS

The particulate organic matter components also indicated as detritus settle on the sediment.
After settling these substances become part of the sediment detritus pools, depending on the
way of modelling the detritus and the sediment. The detritus pools in the sediment are:
1 DET(C,N,P)S1/2 and OO(C,N,P)S1/2 for the S1/S2 approach
2 POC/N/P/S1-4, the same substances when sediment layers are simulated explicitly

T

For POX combined with the S1/2 approach the organic matter fractions are allocated to the
sediment detritus pools as follows:
POC1

DETCS1

DETCS2

POC2

OOCS1

OOCS2

Algae C

DR
AF

8.3

OOCS2

OOCS1

POC4

mortality

OOCS2

OOCS1

POC3

settling

Water

burial

Sediment

The decomposition rate constants of DETCS1/2 and OOCS1/2 should be lower than those for
POC1 and POC2 taking into account that the sediment contains more refractory detritus.
Similar schemes apply to organic nitrogen (PON) and organic phosphorus (POP). For organic
sulfur (POS) no provision has been made for option S1/2. The inorganic nutrients adsorbed
phosphate (AAP), vivianite phosphate (VIVP), apatite phosphate (APATP) and opal silicate
(OPAL) settle respectively into AAPS1 and DETSiS1 for S1/2.
Implementation

Processes SED_(i) have been implemented for the following substances:

 POC1, POC2, POC3, POC4, AAP, VIVP, APATP, OPAL, DETCS1, OOCS1, AAPS1 and
DETSIS1
Processes SED_CAAP (independent settling) and SED_AAP (settling coupled to IM1/2/3) can
be selected for AAP.
Process SEDN(i = POC1, POC2, POC3, POC4) has been implemented for the following
substances:

 PON1, PON2, PON3, PON4, POP1, POP2, POP3, POP4, POS1, POS2, POS3, POS4,
DETNS1, DETPS1, OONS1, and OOPS1.

Deltares

241 of 464

Processes Library Description, Technical Reference Manual

Processes SEDN(i) deliver the settling rates of organic nutrients (i) relative to organic carbon
components (i). Process COMPOS provides the stochiometric ratios f s of the organic nutrients (N,P,S) for this. Process SED_AAP is used for settling coupled to IM1/2/3. Alternative
process SED_CAAP can be selected for independent settling.
Processes CALVS(i) may be used to modify the input settling velocity for shear stress and/or
flocculation, which requires alternative input parameters V 0Sed(i).
Table 8.4 provides the definitions of the input parameters occurring in the formulations.
Formulation

F seti
H

DR
AF

Rseti = f taui ×

T

The settling rates of the organic carbon components and the particulate inorganic nutrient
components are described as the sum of zero-order and first-order kinetics. The rates are
zero, when the shear stress exceeds a certain critical value, or when the water depth is smaller
than a certain critical depth Krone (1962). The rates are calculated according to:

if H < Hmin F seti = 0.0
else



0 Cxi × H
F seti = min F seti ,
∆t
0
F seti = F set0i + si × Cxi

if τ = −1.0 f tau = 1.0
else




τ
f taui = max 0.0, 1 −
τ ci

where:

Cx
F set0
F set
f tau
H
Hmin
Rset
s
τ
τc
∆t
i

242 of 464

concentration of a substance [gC/P/Si m−3 ]
zero-order settling flux of a substance [gC/P/Si m−2 d−1 ]
settling flux of a substance [gC/P/Si m−2 d−1 ]
shear stress limitation function [-]
depth of the water column [m]
minimal depth of the water column for resuspension [m]
settling rate of a substance [gC/P/Si m−3 d−1 ]
settling velocity of a substance [m d−1 ]
shear stress [Pa]
critical shear stress for settling of a substance [Pa]
timestep in DELWAQ [d]
index for substance (i), POC1, POC2, POC3, POC4, AAP, VIVP, APATP, OPAL.

Deltares

Organic matter (detritus)

The settling of organic nutrients is coupled to the settling of organic carbon as follows:

Rsnj,i =

Rseti
f sj,i

where:
stochiometric ratios carbon over nutrient j in detritus component i [gC gX−1 ]
settling rate of nutrient j in organic detritus component i [gX m−3 d−1 ]
index for organic carbon component (i); POC1, POC2, POC3, POC4
index for organic nutrient (j ); PON1/2/3/4, POP1/2/3/4 and POS1/2/3/4

T

f sj,i
Rsnj,i
i
j

DR
AF

Directives for use
 T au can be simulated with process CALTAU. If not simulated or imposed Tau will have
the default value -1.0, which implies that settling is not affected by the shear stress. For
specific input parameters, see the process description of CALTAU.
 Settling does not occur, when Depth is smaller than minimal depth M inDepth for settling, which has a default value of 0.1 m. When desired M inDepth may be given a
different value.
 The primary settling fluxes f Sed(i) delivered by processes SED_(i), and the additional
settling fluxes f Sed(j) delivered by processes SEDNPOC1, SEDNPOC2, SEDNPOC3
and SEDNPOC4 are available as additional output parameters.
Table 8.4: Definitions of the input parameters in the above equations for SED_(i), SEDN(i)
and SED_CAAP.

Name in
formulas

Name in
input

Definition

Units

Cx1i

(i)1

concentration of substance (i)

gC/P/Si m−3

F set0i

ZSed(i)

zero-order settling flux of substance (i)

gC/P/Si m−2 d−1

f sj,i

C−N P OC12
C − N P OC2
C − N P OC3
C − N P OC4
C − P P OC1
C − P P OC2
C − P P OC3
C − P P OC4
C − SP OC1
C − SP OC2
C − SP OC3
C − SP OC4

stoch. ratio C and N in POC1
stoch. ratio C and N in POC2
stoch. ratio C and N in POC3
stoch. ratio C and N in POC4
stoch. ratio C and P in POC1
stoch. ratio C and P in POC2
stoch. ratio C and P in POC3
stoch. ratio C and P in POC4
stoch. ratio C and S in POC1
stoch. ratio C and S in POC2
stoch. ratio C and S in POC3
stoch. ratio C and S in POC4

gC gN−1
gC gN−1
gC gN−1
gC gN−1
gC gN−1
gC gP−1
gC gP−1
gC gP−1
gC gS−1
gC gS−1
gC gS−1
gC gS−1

H

Depth

depth of the water column,
thickness of water layer

m
continued on next page

Deltares

243 of 464

Processes Library Description, Technical Reference Manual

Table 8.4 – continued from previous page
Name in
input

Definition

Units

Hmin

M inDepth

minimal water depth for settling
and resuspension

m

si

V SedP OC
V SedIM
V SedAAP
V SedV IV P
V SedAP AT P
V SedOP AL

settling velocity of POC
settling velocity of inorg. matter
settling velocity of AAP
settling velocity of VIVP
settling velocity of APATP
settling velocity of OPAL

m d−1
m d−1
m d−1
m d−1
m d−1
m d−1

τ
τ ci

T au
T aucS(i)

shear stress
critical shear stress for settling
of substance (I )

Pa
Pa

∆t

Delt

timestep in DELWAQ

d

1

T

Name in
formulas

DR
AF

) Substances are POC1, POC2, POC3, POC4, AAP, VIVP, APATP and OPAL. Additional
substances (j ) for output are PON1, PON2, PON3, PON4, POP1, POP2, POP3, POP4,
POS1, POS2, POS3 and POS4.
2
) All stochiometric ratios are delivered by process COMPOS.

244 of 464

Deltares

Organic matter (detritus)

Mineralization of detritus in the sediment (S1/2)
PROCESS :

BMS1/2_i

Detritus is produced when algae and higher plants die off. The microbial decomposition of
detritus into its basic inorganic components such as carbon dioxide, ammonium and phosphate is called mineralization. The mineralization starts in the water column, where (most
of) the detritus is produced. The process continues at and in the sediment after settling of
detritus particles at the sediment. This process specifically deals with the mineralization in
the sediment according to simplified formulations. Various factors that limit the mineralization
rates are ignored here. The decomposition in the water column, formulated with much more
process detail is described elsewhere in this manual.

T

During the decomposition process the organic matter is gradually converted into material
that is more resistant to microbial breakdown. This phenomenon is ignored in the simplified
approach of mineralization in the sediment. Two detritus fractions are considered, the slow
decomposing detritus fraction (DET C/N/P/SiS1/2) and the refractory detritus fraction
(OOC/N/P S1/2). In the sediment the latter pool is not produced from the former pool.
Both settle from the water column. The fast decomposing detritus fraction (P OC/N/P 1) and
OPAL settle into the former pool, whereas the other fractions (P OC/N/P 2, P OC/N/P 3,
P OC/N/P 3) settle into the latter pool. Carbon, nitrogen, phosphorus and silicate in detritus
are considered as separate state variables in the model. Opal silicate in the sediment is dealt
with as a detritus component. For the water column a specific dissolution process has been
implemented.

DR
AF

8.4

In addition to mineralization the desorption of phosphate can be taken into account. The adsorbed phosphate in the water column AAP settles into AAP S1 The sorption in water and
sediment formulated with much more process detail is described elsewhere in this manual.
The rates of mineralization and desorption are also a function of the temperature. The rates
tend to decrease progressively at temperatures below 4 ◦ C. Since the decomposition of organic matter is performed by a very large number of species, including species that are
adapted to low temperature environments, the effect is not nearly as strong as in the case
of nitrification. This ”near-freezing” effect can be taken into account in the sediment by means
of imposing a discontinuity at a critically low temperature.
Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

Processes BMS1_i , BMS2_i , DESO_AAPS1 and DESO_AAPS2 deal with so-called ”inactive
substances”. (i) refers to the name of one of the detrital substances mentioned below. In the
model these substances are as if present in the water column, but they are not subjected
to transport by advection and dispersion. The resulting mineralization fluxes are input to the
water column.
Processes BMS1_i and BMS2_i have been implemented for the following substances:

 OXY, NH4, PO4 and Si
 DETCS1, DETNS1, DETPS1, DETSiS1, DETCS2, DETNS2, DETPS2, DETSiS2, OOCS1,
OONS1, OOPS1, OOSiS1, OOCS2, OONS2, OOPS2 and OOSiS2.
Processes DESO_AAPS1 and DESO_AAPS2 have been implemented for the following sub-

Deltares

245 of 464

Processes Library Description, Technical Reference Manual

stances:

 PO4, AAPS1 and AAPS2
Table 8.5 provides the definitions of the parameters occurring in the formulations.
Formulation
The mineralization of all detritus components and the desorption of phosphate has been formulated as the sum of a first-order kinetic process and a zero-order kinetic process. The
first-order process is only active when the temperature exceeds a critical temperature. Consequently, the formulations are as follows:

Rmini,k =

k0mini,k
H
k0mini,k
H

+

kmini,k ×M xi,k
V

if T < T c
(T −20)

kmini,k = kmin20
i,k × ktmini

DR
AF

where:

Mx

if T ≥ T c

T

(

k0min
kmin
kmin20
ktmin
Rmin

quantity of organic carbon, nitrogen, phosphorus or silicate ([gC/N/P/Si]; x is oc,
on, op, osi or aap)
zero-order mineralization or desorption rate [gC/N/P/Si m−2 d−1 ]
first-order mineralization or desorption rate [d−1 ]
first-order mineralization or desorption rate at 20 ◦ C [d−1 ]
temperature coefficient for mineralization or desorption [-]
mineral. rate org. carbon, nitrogen, phosphorus or silicate, or desorption rate of
phosphate [gC/N/P/Si m−3 d−1 ]
temperature [◦ C]
critical temperature [◦ C]
index for the detritus component
index for sediment layers S1 and S2
b

T
Tc
i
k

Directives for use
 For a start, the first-order mineralization rates RcDetXS1 and RcOOXS1 can be set to
0.01 and 0.001 d−1 , the zero-order mineralization rates ZM inDetXS1 and ZminOOXS1
to 0.0 gX m−2 d−1 and the critical temperature CT M in to 0.0 ◦ C. If used at all, 4 ◦ C
seems an appropriate choice for the critical temperature. It is possible (and very much
justifiable) to provide lower mineralization rates to the S2 sediment layer than to the S1
layer.
 Calibration of the rates should lead to a more or less stable amount of detritus in the sediment, provided that the input of detritus into the sediment does not substantially change
from one year to the next. That is to say, the amounts of detritus at the end of a simulated
year should be more or less equal to the initial amounts.
Additional references
Smits and Van der Molen (1993), Westrich and Berner (1984), WL | Delft Hydraulics (1980a)

246 of 464

Deltares

Organic matter (detritus)

Table 8.5: Definitions of the parameters in the above equations for BMS1_i, BMS2_i,
DESO_AAPS1 and DESO_AAPS2. ) (i) is one of the names of the 7 detritus components or AAP. (k) indicates sediment layer 1 or 2. Volume units refer
to bulk ( ) or to water ( ).
b

w

Name in input

Definition

Units

M xi

(i)S(k)

quantity of slow decomposing detritus carbon,
nitrogen, phosphorus, silicate, or refractory detritus carbon, nitrogen, phosphorus, silicate, or
desorbing phosphate

gC/N/P/Si

H

Depth

depth of overlying water segment

m

kmin20
i
ktmini
ktmini
k0mini

Rc(i)S(k)
T cBM (i)
T cAAP S(k)
ZM in(i)S(k)

first-order mineralisation or desorption rate
temperature coefficient for mineralization
temperature coefficient for desorption
zero-order mineralization or desorption rate

d−1
gX m−2

V
1

b

T emp
temperature
CT M in
critical temperature for mineralization
CT M inAAP S critical temperature for desorption

◦

V olume

m3

DR
AF

T
Tc
Tc

T

Name in
formulas1

volume of overlying water segment

C
C
◦
C
◦

) i = one of the 7 detritus components or AAP.

Deltares

247 of 464

DR
AF

T

Processes Library Description, Technical Reference Manual

248 of 464

Deltares

9 Inorganic substances and pH
Contents
9.1

Air-water exchange of CO2 . . . . . . . . . . . . . . . . . . . . . . . . . . 250

9.2

Saturation concentration of CO2 . . . . . . . . . . . . . . . . . . . . . . . 255

9.3

Calculation of the pH and the carbonate speciation . . . . . . . . . . . . . 258

9.4

Volatilisation of methane . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

9.5

Saturation concentration of methane . . . . . . . . . . . . . . . . . . . . . 274

9.6

Ebullition of methane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

9.7

Oxidation of methane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

9.8

Oxidation of sulfide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

9.9

Precipitation and dissolution of sulfide . . . . . . . . . . . . . . . . . . . . 285

T

9.10 Speciation of dissolved sulfide . . . . . . . . . . . . . . . . . . . . . . . . 288
9.11 Precipitation, dissolution and conversion of iron . . . . . . . . . . . . . . . 292
9.12 Reduction of iron by sulfides . . . . . . . . . . . . . . . . . . . . . . . . . 301
9.13 Oxidation of iron sulfides . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
9.14 Oxidation of dissolved iron . . . . . . . . . . . . . . . . . . . . . . . . . . 307

DR
AF

9.15 Speciation of dissolved iron . . . . . . . . . . . . . . . . . . . . . . . . . . 310
9.16 Conversion salinity and chloride process . . . . . . . . . . . . . . . . . . . 315

Deltares

249 of 464

Processes Library Description, Technical Reference Manual

Air-water exchange of CO2
PROCESS :

REARCO2

Carbon dioxide (CO2 ) in surface water tends to saturate with respect to the atmospheric carbon dioxide concentration. However, carbon dioxide production and consumption processes
in the water column counteract saturation, causing a CO2 -excess or CO2 -deficit. Furthermore,
the CO2 concentration is dependent on the pH:
CO2 + H2 O

⇔

H2 CO3 + H2 O

⇔

+
HCO−
3 + H3 O + H2 O

⇔

+
CO2−
3 + 2 H3 O

T

The resulting super- or undersaturation leads to reaeration, the exchange of carbon dioxide
between the atmosphere and the water. Reaeration may cause a carbon dioxide flux either
way, to the atmosphere or to the water. The process is enhanced by the difference of the
saturation and actual CO2 concentrations, and by the difference of the flow velocities of the
water and the overlying air. Since lakes are rather stagnant, only the windspeed is important
as a driving force for lakes. The reaeration rate tends to saturate for low windspeeds (< 3 m
s−1 ). On the other hand, the stream velocity may deliver the dominant driving force for rivers.
Both forces may be important in estuaries.

DR
AF

9.1

Extensive research has been carried out all over the world to describe and quantify reaeration processes for dissolved oxygen (DO), including the reaeration of natural surface water.
Quite a number of models have been developed. The most generally accepted model is the
“film layer” model. This model assumes the existence of a thin water surface layer, in which
a concentration gradient exists bounded by the saturation concentration at the air-water interface and the water column average CO2 concentration. The reaeration rate is characterised
by a water transfer coefficient, which can be considered as the reciprocal of a mass transfer
resistance. The resistance in the overlying gas phase is assumed to be negligibly small.
Many formulations have been developed and reported for the water transfer coefficient, mostly
in connection with the reaeration of DO (WL | Delft Hydraulics, 1980b). These formulations are
often empirical, but most have a deterministic background. They contain the stream velocity
or the windspeed or both. Most of the relations are only different with respect to the coefficients, the powers of the stream velocity and the windspeed in particular. Reaeration has
been implemented in DELWAQ with four different formulations for the transfer coefficient. The
first two options are pragmatic simplifications to accommodate preferences of the individual
modeller. The other two relations have been copied or derived from scientific publications. All
reaeration rates are also dependent on the temperature according to the same temperature
function.
Implementation
Process REARCO2 has been implemented in such a way, that it only affects the CO2 -budget
of the top water layer. An option for the transfer coefficient can be selected by means of
input parameter SW RearCO2 (= 0, 1, 4, 11, 13). The other options concern DO. The
saturation concentration required for the process REARCO2 is calculated by an additional
process SATURCO2.
The process has been implemented for substance CO2 .
Table 9.4 provides the definitions of the parameters occurring in the formulations.

250 of 464

Deltares

Inorganic substances and pH

Formulation
The reaeration rate has been formulated as a linear function of the temperature dependent
mass transfer coefficient in water and the difference between the saturation and actual concentrations of CO2 as follows:

Rrear = klrear × [Cco2s − max(Cco2, 0.0)] /H
klrear = klrear20 × ktrear(T −20)



a × vb
2
20
+
d
×
W
klrear =
Hc
Cco2s = f (T, Ccl or SAL)
(delivered by SATURCO2)
max(Cco2, 0.0)
f sat = 100 ×
Cco2s
coefficients with different values for eleven reaeration options
chloride concentration [gCl m−3 ]
actual carbon dioxide concentration [gCO2 m−3 ]
saturation carbon dioxide concentration [gCO2 m−3 ]
percentage of saturation [%]
depth of the water column [m]
reaeration transfer coefficient in water [d−1 ]
reaeration transfer coefficient at reference temperature 20 ◦ C [d−1 ]
temperature coefficient of the transfer coefficient [-]
reaeration rate [gCO2 m−3 d−1 ]
salinity [kg m−3 , ppt]
temperature [◦ C]
stream velocity [m s−1 ]
windspeed at 10 m height [m s−1 ]

DR
AF

a, b, c, d
Ccl
Cco2
Cco2s
f sat
H
klrear
klrear20
ktrear
Rrear
SAL
T
v
W

T

with:

Notice that the reaeration rate is always calculated on the basis of a positive carbon dioxide
concentration. Although not realistic, CO2 may have negative values in the model due to the
consumption of CO2 by phytoplankton. This may happen only at exceptional conditions.
Depending on the reaeration option, the transfer coefficient is only dependent on the stream
velocity or the windspeed. With respect to temperature dependency option SW Rear =
11 is an exception. The respective formulation is not dependent on temperature according
the above equations, but has its own temperature dependency on the basis of the Schmidt
number. Information on the coefficients a − d and the applicability is provided below for each
of the options.

SW RearCO2 = 0
The transfer coefficient is simplified to a constant, multiplied with the water depth H , using
the transfer coefficient as input parameter. So klrear 20 is to be provided as a value in
d−1 in stead of in m d−1 Consequently, the coefficients are:

a = klrear20 × H,

b = 0.969,

c = 0.5,

d = 0.0

SW RearCO2 = 1
The transfer coefficient is simplified to a constant, using the transfer coefficient as input
parameter. Consequently, the coefficients are:

a = klrear20 ,
Deltares

b = 0.969,

c = 0.5,

d = 0.0
251 of 464

Processes Library Description, Technical Reference Manual

SW RearCO2 = 4
The coefficients are according to (O’ Connor and Dobbins, 1956) for DO, but coefficient
a can be scaled for CO2 using the transfer coefficient as input parameter. Consequently,
the coefficients are:

a = klrear20 × 3.863,

b = 0.5,

c = 0.5,

d = 0.0

The relation is valid for rivers, and therefore independent of windspeed.

SW RearCO2 = 11

a = F (T ),

b = 0.0,

c = 0.0,

T

The relation according to Wanninkhof (1992) deviates from the previous relations with
respect to temperature dependency, that is not included according to the above Arrhenius
equation for klrear . The temperature dependency enters the relation in a scaling factor
on the basis of the Schmidt number. Coefficient d had to be scaled from cm h−1 to m d−1 .
Consequently, the coefficients are:

d = 0.0744 × f sc

with:

DR
AF

F (T ) = 2.5 × (0.5246 + 0.016256 × T + 0.00049946 × T 2 )
−0.5

Sc
f sc =
Sc20
Sc = d1 − d2 × T + d3 × T 2 − d4 × T 3

d1−4
f sc
Sc
Sc20
T

coefficients
scaling factor for the Schmidt number [-]
Schmidt number at the ambient temperature [m d−1 ]
Schmidt number at reference temperature 20 ◦ C [m d−1 ]
temperature [◦ C]
The relation is valid for lakes and seas, and therefore independent of stream velocity.
The Schmidt number is the ratio of the kinematic viscosity of water (ν ) and the molecular
diffusion coefficient of oxygen in water (D ). The appropriate constants to compute the
Schmidt number in both seawater and fresh water are given in the table below.
Water system

d1

d2

d3

d4

Sea water, Salinity > 1 kg m−3

2073.1

125.62

3.6276

0.043219

Fresh water, Salinity ≤ 1 kg m−3

1911.1

118.11

3.4527

0.041320

SW RearCO2 = 13
The relation according to Guérin (2006); Guérin et al. (2007) deviates strongly from the
previous relations, with respect to wind dependency, with respect to an additional forcing
parameter, namely rainfall, and with respect to temperature dependency. The latter is not
included according to the above Arrhenius equation for klrear. Like the relation described
for option 10, the temperature dependency enters the relation in a scaling factor on the

252 of 464

Deltares

Inorganic substances and pH

basis of the Schmidt number. The relation for transfer coefficient is:



klrear = a × exp b1 × W b2 + c1 × P c2 × f sc

−0.67
Sc
f sc =
Sc20
Sc = d1 − d2 × T + d3 × T 2 − d4 × T 3

(9.1)
(9.2)
(9.3)

with:

a, b, c, d
klrear
P
Sc
Sc20
T
W

DR
AF

T

coefficients
transfer coefficient in water [m.d−1 ]
precipitation, e.g. rainfall [mm.h−1 ]
Schmidt number at the ambient temperature [g.m−3 ]
Schmidt number at reference temperature 20 ◦ C [d−1 ]
temperature [◦ C]
windspeed at 10 m height [m.s−1 ]
The relation is valid for (tropical) lakes and therefore independent of stream velocity. The
general coefficients have the following input names and values:
a

b1

b2

c1

c2

CoefACO2

CoefB1CO2

CoefB2 CO2

CoefC1CO2

CoefC2CO2

1.660

0.26

1.0

0.66

1.0

The Schmidt number is the ratio of the kinematic viscosity of water (ν ) and the molecular
diffusion coefficient of oxygen in water. The appropriate constants to compute the Schmidt
number for fresh water are given in the table below (Guérin, 2006):
d1

d2

d3

d4

CoefD1CO2

CoefD2 CO2

CoefD3 CO2

CoefD4 CO2

1911.1

118.11

3.4527

0.04132

Directives for use
 Options SW RearCO2 = 0, 1, 4 provide the user with the possibility to scale the mass
transfer coefficient KLRearCO2. The options contain fixed coefficients.
 When using option SW RearCO2 = 0 the user should be aware that the mass transfer coefficient KLRearCO2 has the unusual dimension d−1 . Since high values of
KLRear may cause numerical instabilities, the maximum KLRearCO2 value is limited
to 1.0 d−1 .
 When using option SW RearCO2 = 4 the user should be aware that the input parameter KLRearCO2 is used as a dimensionless scaling factor. The default value of
KLRearCO2 is 1.0 in order to guarantee that scaling is not carried out when not explicitly wanted.
 The coefficients a–c2 are input parameters for option SW RearCO2 = 13 only. The
default values are those for option 13.
 The coefficients d1–4 are input parameters for options SW RearCO2 = 11, 13. The
default values are the freshwater values, which are the same for both options.

Deltares

253 of 464

Processes Library Description, Technical Reference Manual

Table 9.4: Definitions of the parameters in the above equations for REARCO2.

Name in input

Definition

Units

Cco2
Cco2s

DisCO2
SaturCO2

concentration of carbon dioxide
saturation conc. of carbon dioxide
from SATURCO2

gCO2 m−3
gCO2 m−3

a
b1
b2
c1
c2

Coef ACO2
Coef B1CO2
Coef B2CO2
Coef C1CO2
Coef C2CO2

coefficients for option 13 only

-

d1
d2
d3
d4

Coef D1CO2
Coef D2CO2
Coef D3CO2
Coef D4CO2

coefficients for option 11 and 13

-

f cs

–

scaling factor for the Schmidt number
percentage carbon dioxide saturation

-

depth of the top water layer

m

H

DR
AF

f sat

T

Name in formulas1

klrear20

–

Depth

KLRearCO2 water transfer coefficient for carbon

%

m d−1

kltemp

T CRearCO2

dioxide1
temperature coefficient for reaeration

P

rain

Rainfall

mm h−1

–

reaeration rate for carbon dioxide

gCO2
d−1

Salinity

salinity

kg m−3

–

Schmidt number for carbon dioxide
in water

-

SW RearCO2 SW RearCO2 switch for selection of options for

-

Rrear
SAL
Sc

-

m−3

transfer coefficient

T

T emp

temperature

◦

v
W

V elocity
V W ind

stream velocity
windspeed at 10 m height

m s−1
m s−1

1

C

KLRearCO2 is a dimensionless scaling factor for option 4.

254 of 464

Deltares

Inorganic substances and pH

Saturation concentration of CO2
PROCESS :

SATURCO2

The reaeration of carbon dioxide proceeds proportional to the difference of the saturation
CO2 concentration and the actual dissolved CO2 concentration. The saturation concentration
of CO2 is primarily a function of the partial atmospheric CO2 pressure, the water temperature
and the salinity. However, the partial atmospheric CO2 pressure is assumed to be constant.

T

The calculation of the saturation concentration in DELWAQ is performed as a separate process, which has been implemented with two alternative formulations. Such formulations have
been described by Weiss (1974) and Stumm and Morgan (1981).
Implementation

Process SATURCO2 delivers the CO2 saturation concentration in water required for the process REARCO2. The process has been implemented with two options for the formulations of the saturation concentration, which can be selected by means of input parameter
SW SatCO2 (= 1 − 2).

DR
AF

9.2

The process has been implemented in connection with substance CO2 . Table 9.5 provides
the definitions of the parameters occurring in the formulations.
Formulation

The saturation concentration (SaturCO2) has been formulated as the following functions of
the temperature and the salinity.
For SW SatCO2 = 1 (Stumm and Morgan, 1981):

f ac = 10−f temp

f temp = a −

b
− c × (T + 273) + f cl × (d − m × (T + 273))
(T + 273)

f cl = n + o × Ccl + p × Ccl2

For SW SatCO2 = 2 (Weiss, 1974):




b
2
f ac = exp a +
+ c × ln(T f ) + SAL × m + n × T f + o × T f
Tf


T + 273
Tf =
100

For both options:

Cco2s = P co2 × f ac × 44 × 1000
with:

a, b, c, d

Deltares

coefficients with different values for the two formulations

255 of 464

Processes Library Description, Technical Reference Manual

m, n, o, p
Ccl
Cco2s
f ac
f cl
f temp
P co2
T
Tf
SAL

chloride concentration [gCl m−3 ]
saturation carbon dioxide concentration in water [gCO2 m−3 ]
factor for temperature and salinity dependency
function for chloride concentration dependency
function for temperature dependency
atmospheric carbon dioxide pressure [atm]
temperature [◦ C]
temperature function [◦ C]
salinity [kg m−3 , ppt]

The coefficients in both formulations are fixed. The values are presented in the table below.
b

SW SatOxy = 1

14.0184

2385.73

SW SatOxy = 2

-58.0931

90.5069

Option

c

d

T

a

0.015264

0.28569

22.2940

-

DR
AF

Option

m

n

o

p

SW SatOxy = 1

0.6167×10−5

0.00147

0.3592×10−4

0.68×10−10

SW SatOxy = 2

0.027766

-0.025888

0.0050578

-

Directives for use
 The chloride concentration Cl can either be imposed by the user or simulated with the
model. The salinity can be estimated from the chloride concentration with:

SAL = 1.805 × Cl/1000

 A representative value for the atmospheric carbon dioxide pressure P AP CO2 is 3.162×10−4 atm.

256 of 464

Deltares

T

Inorganic substances and pH

Table 9.5: Definitions of the parameters in the above equations for SATURCO2.

Name in
input

Cco2s

–

Ccl

Cl

f ac

Definition

DR
AF

Name in
formulas

saturation concentration of carbon dioxide in water
chloride concentration

gCO2 m−3

-

gCl m−3

f temp

–

factor for temperature and salinity dependency
unction for chloride concentration dependency
function for temperature dependency

P co2

P AP CO2

atmospheric carbon dioxide pressure

atm

SAL

Salinity

salinity

kg m−3

f cl

–

Units

–

SW SatCO2 SW SatCO2 switch for selection options for saturation

-

-

equation

T
Tf

Deltares

T emp
–

temperature
temperature function

◦

C

-

257 of 464

Processes Library Description, Technical Reference Manual

Calculation of the pH and the carbonate speciation
PROCESS : P H_ SIMP

2−
The pH, the carbonate speciation (CO2 , pCO2 , H2 CO3 , HCO−
3 and CO3 ) and the saturation
states of calcium carbonate (calcite and aragonite) in the water column and the sediment bed
can be calculated from the alkalinity (Alka; gHCO3 m−3 ) and the total dissolved inorganic
carbon concentration (TIC; gC m−3 ). Salinity (g kg−1 ) and temperature (◦ C) are necessary
inputs.

T

The dissolved [CO2 ] concentration is more than two orders of magnitude higher than the
concentration of carbonic acid [H2 CO3 ]. Consequently, the sum of the concentrations of these
species [CO∗2 ] is practically identical to the concentration of [CO2 ], and thus TIC is defined as:
−

2
TIC = [CO∗2 ] + [HCO−
3 ] + [CO3 ]

The equilibrium in the carbonate system is dependent of temperature, salinity and pressure.
The relative proportions of total inorganic carbon species control the pH in natural waters.

DR
AF

9.3

Alkalinity is defined as carbonate, borate and water alkalinity, the dissociation constants of
which are calculated from salinity and temperature. The [H+ ] concentration is derived from
the alkalinity equation and is used to calculate pH:
−

−
2
−
+
ALKA =[HCO−
3 ] + 2[CO3 ] +[B(OH)4 ] + [OH ] - [H ]

In process pH_simp two sets of equilibrium constants are used, one for fresh water and one
for saline water. The sets only differ in the way to calculate the first (K 1 ) and the second
dissociation constant of carbonic acid (K 2 ). The appropriate set is selected by the model
depending on salinity.
The pH is measured on the ‘total pH scale’ (pHT ):
pHT = − 10 log([H + ] + [HSO4− ])

>

− 10 log([H + ]) = pH

−
Not the free [H+ ] is measured but [H+ ]T (=[H+ ] + [HSO−
4 ]). In fresh water [HSO4 ] is negligible,
but through the abundance of sulfate it is significant in seawater. Because in this model the
pH is calculated from [H+ ] only, the calculated pH slightly underestimates the pH measured
in seawater.

A number of processes influence the pH of the water. For example, mineralisation of organic
carbon produces CO2 (an acid) and thus lowers the pH. On the other hand denitrification
consumes H+ , raising the pH. All processes in DELWAQ that can change pH are taken into
account. Table 9.6 gives a general summary of all processes that have a pH effect.
Table 9.6: Processes in D-Water Quality with effects on pH

process description

equivalent chemical reaction

stoichiometry

reaeration of CO2

CO2 (g) + H2 O ↔ H2 CO3 ∗(aq)

TIC +0.273 a )
continued on next page

258 of 464

Deltares

Inorganic substances and pH

Table 9.6 – continued from previous page
equivalent chemical reaction

stoichiometry

primary production

CO2 + H2 O → CH2 O + O2

TIC -1.000
H2O -1.500
Corg +1.000
OXY +2.670

mineralisation
organic C

CH2 O + O2 → CO2 + H2 O

TIC +1.000
H2O +1.500
Corg -1.000
OXY -2.670

of

+
NO−
3 +H →

1
2

N2 + 1 14 O2 +

1
2

NO3 -1.000 b )
ALKA +4.357
OXY +2.857
H2O +0.643

H2 O

DR
AF

denitrification

T

process description

nitrification

−
+
NH+
4 + 2 O2 ↔ NO3 + 2 H + H2 O

NH4 -1.000
OXY -4.571
NO3 +1.000
ALKA -8.714
H2O +1.286

Uptake of ammonia c )

+
NH+
4 → (NH3 )org + H

NH4 -1.000
Norg +1.000
ALKA -4.357

Uptake of phosphate c )

+
H2 PO−
4 + H → (H3 PO4 )org

PO4 -1.000
Porg +1.000
ALKA 1.968

Uptake of nitrate

+
NO−
3 + H + H2 O → (NH3 )org + 2 O2

NO3 -1.000
ALKA +4.357
H2O -1.286
Norg +1.000
OXY -4.571

Atmospheric deposition of nitrate

HNO3 → H+ + NO−
3

NO3 +1.000
H+ +0.071
ALKA -4.357

Atmospheric
deposition
ammonium

−
NH3 + H2 O → NH+
4 + OH

NH4 +1.000
ALKA +4.357

of

Atmospheric deposition of sulfate

−

H2 SO4 → 2H+ + SO24

SO4 +1.000
H+ +0.143
ALKA -8.714
continued on next page

Deltares

259 of 464

Processes Library Description, Technical Reference Manual

Table 9.6 – continued from previous page
process descrip- equivalent chemical reaction
stoichiometry
tion
a
The CO2 flux in D-Water Quality has units gCO2 m−3 d−1 and is converted to gC
m−3 d−1 .
b
Denitrification in the sediment is thought to be a sink for nitrate. No alkalinity, oxygen
and water are added to the water column
c
Mineralisation reactions are the reverse of the uptake reactions

Implementation

 TIC, Alka and Salinity

T

Process pH_simp has been implemented for the following substances:

DR
AF

Although process pH_simp has been formulated in a generic way, the calculation of the pH
should be applied to water layers only. Concentrations are corrected for porosity (input parameter POROS) to allow for application to sediment layers, but buffering of the pH by minerals like
calcite is not considered. Process pH_simp can be used for a model with ”layered sediment”
because the lapse of the pH and pH dependent processes can be avoided by constraining the
pH within a user defined range. pH_simp cannot be used for pH and carbonate speciation in
the sediment, when substances are modelled as ’inactive’ substances according to the S1/2
approach.
Two versions for the calculation of pH are available. The original version 2 is selected with
option parameter SwpH = 0.0 (default value), and applies to water with low salinity (< 5
psu). The other version 1 is selected with option parameter SwpH = 1.0, and is suitable for
fresh as well as saline water. Apart from the pH both versions calculate the concentrations
and the fractions of the carbonate species. Version 2 includes the calculation of DisH2CO3
and F rH2CO3d, whereas this is not done by version 1 because this species is assumed
included in DisCO2.
Instead of simulating the pH, it can be imposed on a model. If process pH _simp is activated
to calculate the carbonate speciation with the formulations of version 2, this is done for option
SwpH = -1.0. The carbonate speciation computed by pH_simp can be used by process
PRIRON for the formation of iron(II) carbonate. The dissolved carbon dioxide concentration
DisCO2 computed by pH_simp can be used for process REARCO2 to calculate the CO2
exchange flux between atmosphere and water.
Table 9.7 provides the definitions of the input parameters in the formulations and Table 9.8
provides the output parameters.

260 of 464

Deltares

Inorganic substances and pH

Formulation
Version 2 (SwpH = 1.0)
The hydrolysis reactions of carbonate and borate and the self-ionization of water proceed
according to the following reaction equations:
CO2 (g) ⇔ CO2 (aq)
CO2 (aq) + H2 O ⇔ H2 CO3
+
CO2 (aq) + H2 O ⇔ HCO−
3 +H
−

+
B(OH)3 + H2 O ⇔ B(OH)−
4 +H

H2 O ⇔ OH− + H+

T

+
2
HCO−
3 ⇔ CO3 + H

DR
AF

As the concentration of H2 CO3 is negligible compared to CO2 (aq), and therefore the dissociation constants for carbonic acid do not differentiate between these substances, it is common
to combine the second and the third reaction, and to allocate an acidity constant to the combined reaction based on CO2 , which is the sum of H2 CO3 and CO2 (aq). Consequently, the
chemical equilibria are described with:

[CO2 ]
pCO2
[H + ][HCO3− ]
K1 =
[CO2 ]
+
[H ][CO32− ]
K2 =
[HCO3− ]
[H + ][B(OH)−
4]
KB =
[B(OH)3 ]
+
KW = [H ][OH − ]
K0 =

where:

K0
K1
K2
KB
KW

solubility constant of carbon dioxide in water [mol kg−1 atm−1 ]
first dissociation constant of carbonic acid [mol kg−1 solution]
second dissociation constant of carbonic acid [mol kg−1 solution]
dissociation constant of boric acid [mol kg−1 solution]
dissociation constant of water [mol2 kg−2 solution]

The equilibrium constants are functions of the absolute temperature and the salinity. The
absolute temperature is defined as:

Tabs = T + 273.15
where:

T
Tabs

ambient water temperature [◦ C]
absolute temperature [K]

Because the model calculates bulk salinity, it is corrected for porosity as follows:

S = Salinity/ϕ
Deltares

261 of 464

Processes Library Description, Technical Reference Manual

where:
salinity of the water phase [g kg−1 water]
porosity [-]

S
ϕ

The following K1 and K2 formulations from Roy (1993) were determined in artificial water
and for total pH scale.
For Salinity (S) < 5 g kg−1 (psu):

K1 = eln K1

T

ln K1 = 290.9097 − 14554.21/Tabs − 45.0575 × ln(Tabs )+
(−228.39774 + 9714.36839/Tabs + 34.485796 × ln(Tabs )) × S 0.5 +
(54.20871 − 2310.48919/Tabs − 8.19515 × ln(Tabs )) × S+
(−3.969101 + 170.22169/Tabs + 0.603627 × ln(Tabs )) × S 1.5 −
0.00258768 × S 2 + ln(1 − S × 0.001005)

DR
AF

ln K2 = 207.6548 − 11843.79/Tabs − 33.6485 × ln(Tabs )+
(−167.69908 + 6551.35253/Tabs + 25.928788 × ln(Tabs )) × S 0.5
(39.75854 − 1566.13883/Tabs − 6.171951 × ln(Tabs )) × S+
(−2.892532 + 116.270079/Tabs + 0.45788501 × ln(Tabs )) × S 1.5 −
0.00613142 × S 2 + ln(1 − S × 0.001005)
K2 = eln K2

For Salinity (S) < 45 and ≥ 5 g kg−1 (psu):

ln K1 = 2.83655 − 2307.1266/Tabs − 1.5529413 × ln(Tabs )+
(−0.20760841 − 4.0484/Tabs ) × S 0.5 + 0.08468345 × S
− 0.00654208 × S 1.5 + ln(1 − 0.001005 × S)
K1 = eln K1

ln K2 = −9.226508 − 3351.6106/Tabs − 0.2005743 × ln(Tabs )+
(−0.106901773 − 23.9722/Tabs ) × S 0.5 + 0.1130822 × S
− 0.00846934 × S 1.5 + ln(1 − 0.001005 × S)
K2 = eln K2
For all values of salinity:

ln K0 = −60.2409 + 93.4517/(Tabs /100) − 23.3585 × ln(Tabs /100)+
S × (0.023517 − 0.023656 × (Tabs /100) + 0.000447036 × (Tabs /100)2 )
K0 = eln K0

262 of 464

Deltares

Inorganic substances and pH

ln KB = (−8966.90 − 2890.53 × S 0.5 − 77.942 × S + 1.728 × S 1.5 − 0.0996 × S 2 )/Tabs
+ 148.0248 + 137.1942 × S 2 + 1.62142 × S+
(−24.4344 − 25.085 × S 0.5 − 0.2474 × S) × ln(Tabs ) + 0.053105 × S 0.5 × Tabs
KB = eln KB
ln KW = 148.96502 − 13847.26/Tabs − 23.6521 × ln(Tabs )+
(118.67/Tabs − 5.977 + 1.0495 × ln(Tabs )) × S 0.5 − 0.01615 × S
KW = eln KW

DR
AF

KCal = eln KCal

T

ln KCal = −171.9065 − 0.077993 × Tabs + 2839.319/Tabs + 71.595 × ln(Tabs )+
(−0.77712 + 0.0028426 × Tabs + 178.34/Tabs ) × S 0.5 −
0.07711 × S + 0.0041249 × S 1.5

ln KArg = −171.9065 − 0.077993 × Tabs + 2903.293/Tabs + 71.595 × ln(Tabs )+
(−0.068393 + 0.0017276 × Tabs + 88.135/Tabs ) × S 0.5 −
0.10018 × S + 0.0059415 × S 1.5
KArg = eln KArg

where:

S
KCal
KArg

salinity in the water phase [g kg−1 water or psu]
solubility constant of calcite [mol2 kg−2 solution]
solubility constant of aragonite [mol2 kg−2 solution]

Apart from the definition of total dissolved inorganic carbon (TIC) and alkalinity (Alka) as the
sums of their components, the following formulations are needed to solve the above equilibrium and to calculate the saturation states of calcite and aragonite:


ρw = 1000. + 0.7 × S/(1 − S/1000.) − 0.0061 × (T − 4.0)2 /1000
T ICM = mtmm × (T IC/(M W C × ρw × m3tl × ϕ))
AlkaM = mtmm × (Alka/(M W HCO3 × ρw × m3tl × ϕ))
B = mtmm × 0.000416 × (S/35)
2+
[Ca ] = mtmm × 0.01028 × (S/35)

where:

mtmm conversion factor for mol to mmol (103 ) [mmol mol−1 ]
m3tl
conversion factor for m3 to litre (103 ) [l m−3 ]
MW C
molar weight of carbon (12) [g mol−1 ]
M W HCO3 molar weight of the bicarbonate ion (61) [g mol−1 ]
ρw
density of water [kg l−1 ]
T IC
total dissolved inorganic carbon concentration [gC m−3 ]
T ICM molar total dissolved inorganic carbon concentration [mmolC kg−1 ]
Alka
alkalinity [gHCO3 m−3 ]
AlkaM molar alkalinity [mmolHCO3 kg−1 ]
B
molar total boric acid concentration [mmol kg−1 ]
Deltares

263 of 464

Processes Library Description, Technical Reference Manual

molar calcium ion concentration [mmol kg−1 ]
porosity [-]

Ca2+
ϕ

The equilibrium equations can now be substituted in the component sums resulting in:

T ICM × (K 1 × [H + ] + 2 × K 1 × K 2 )/([H + ]2 + K 1 × [H + ] + K 1 × K 2 )+
B × K B /([H + ] + K B ) + K W /[H + ] − [H + ] − AlkaM = 0
From this quintic polynomial equation in [H + ] the following outputs are generated:

pH = − 10 log[H + ]

DR
AF

T

CO2 = mtmm × m3tl × M W CO2 × ρw × T ICM ×
[H + ]2 /([H + ]2 + K 1 × [H + ] + K 1 × K 2 )
pCO2w = F CO2/(exp(atpa × (BV + 2 × D)/(R × Tabs )))
F CO2 = atma × CO2M/K 0
2
3
BV = (−1636.75 + 12.0408 × Tabs − 0.0327957 × Tabs
+ 3.16528 × 10−5 × Tabs
)/m3tcm3
D = (57.7 − 0.118 × Tabs )/m3tcm3
HCO3 = M W C × ρw × m3tl × ϕ×
(T ICM × K 1 × [H + ])/(([H + ]2 + K 1 × [H + ] + K 1 × K 2 ) × mtmm)
CO3 = M W C × ρw × m3tl × ϕ×
(T ICM × K 1 × K 2 )/(([H + ]2 + K 1 × [H + ] + K 1 × K 2 ) × mtmm)
BOH4 = M W B × ρw × m3tl × ϕ × B/(([H + ] + K B ) × mtmm)
ΩCal = Ca2+ × CO3/(KCal × M W C × ρw × m3tl × mmtm × ϕ)
ΩArg = Ca2+ × CO3/(KArg × M W C × ρw × m3tl × mmtm × ϕ)
where:

atma
conversion factor for atmosphere to microatmosphere (106 ) [µatm atm−1 ]
atpa
conversion factor for atmosphere to pascal (101325) [Pa atm−1 ]
cm3tm3 conversion factor for cm3 to m3 (106 ) [cm3 m−3 ]
BV
virial coefficient of carbon dioxide in air [m3 mol−1 ]
D
virial coefficient of pure carbon dioxide [m3 mol−1 ]
+
H
proton activity [mol kg−1 solution]
MW B
molar weight of boron (10.8) [g mol−1 ]
M W CO2 molar weight of carbon dioxide (44) [g mol−1 ]
R
ideal gas constant [m3 Pa K−1 mol−1 ]
CO2
dissolved carbon dioxide concentration [gCO2 m−3 ]
CO2M molar dissolved carbon dioxide concentration [mmolCO2 kg−1 ]
F CO2
fugacity of carbon dioxide concentration [µatm−1 ]
pCO2w partial pressure of carbon dioxide in water [µatm−1 ]
−
CO3
dissolved carbonate CO32 concentration [gC m−3 ]
HCO3 dissolved bicarbonate HCO3 − concentration [gC m−3 ]
BOH4 dissolved borate B(OH)4 − concentration [gB m−3 ]
ΩCal
saturation state of calcite [-]
ΩArg
saturation state of aragonite [-]

264 of 464

Deltares

Inorganic substances and pH

If the pH is larger than pH _max, it is made equal to pH _max. If the pH is smaller than
pH _min, it is made equal to pH _min.
Finally, the fractions (gC gC−1 or mol mol−1 ) of the carbon dioxide and the carbonate species
of total dissolved inorganic carbon (TIC) are calculated as follows:

HCO3
T IC
CO3
f c3 =
T IC
f c0 = 1 − f c2 − f c3

f c2 =

fraction CO 2 of TIC [−]
fraction HCO 3 − of TIC [−]
−
fraction CO 3 2 of TIC [−]

f c0
f c2
f c3

DR
AF

Version 1 (SwpH = 0.0)

T

where:

The original version 1 uses only the formulations for K1 and K2 valid for salinity < 5 psu. Boric
acid is not considered. The equilibrium equations substituted in the component sums result
in:

Alka × [H + ]2 /K 1 + (Alka − T IC) × [H + ] + K 2 × (Alka − 2 × T IC) = 0

This quadratic equation in [H + ]2 delivers two roots, the feasible one of which is used to
calculate the pH.
Version 1 calculates the carbonate species differently. The hydrolysis reactions of carbonate
proceed according to the following reaction equations:
CO2(aq) + H2 O ⇔ H2 CO3

H2 CO3 + H2 O ⇔ HCO3 − + H3 O+
HCO3 − + H2 O ⇔ CO3 2− + H3 O+

It is common to combine the first and the second reaction, and to allocate an acidity constant
to the combined reaction based on H2 CO3 ∗ , the sum of true H2 CO3 and CO2 (aq). Consequently, the chemical equilibria are described with:

Ccd0
Ccd1
Ccd2 × H +
Kc1 =
(Ccd0 + Ccd1 )
Ccd3 × H +
Kc2 =
Ccd2
Ccdt = Ccd0 + Ccd1 + Ccd2 + Ccd3
Kc0 =

where:

Ccd0
Ccd1
Deltares

dissolved carbon dioxide [mol.l−1 ]
dissolved H2 CO3 [mol.l−1 ]

265 of 464

Processes Library Description, Technical Reference Manual

dissolved HCO3 − [mol.l−1 ]
dissolved CO3 2− [mol.l−1 ]
total dissolved inorganic carbon [mol.l−1 ]
proton concentration [mol.l−1 ]
hydrolysis (equilibrium,) constant for CO2 [-]
acidity (equilibrium, hydrolysis) constant for H2 CO3 ∗ [mol.l−1 ]
acidity (equilibrium, hydrolysis) constant for HCO3 − [mol.l−1 ]

Ccd2
Ccd3
Ccdt
H+
Kc0
Kc1
Kc2

The proton concentration H+ and the stability constants follow from:

H + = 10−pH
Kc0 = 650.0
Kc1 = 10lKc1

where:

pH
S
T
T abs

DR
AF

T

Kc2 = 10lKc2
lKc1 = −3404.71/T abs − 0.032786 × T abs + 14.712 + 0.19178 × (0.543 × S)0.333
lKc2 = −2902.39/T abs − 0.02379 × T abs + 6.471 + 0.4693 × (0.543 × S)0.333
T abs = T + 273.15

acidity [-]
salinity [psu]
temperature [◦ C]
absolute temperature [K]

Salinity replaces chlorinity in the above formulations derived from Stumm and Morgan (1981)
based on 19 ‰ chlorinity agreeing with 35 psu (‰) salinity.
The concentration of the relevant carbonate species in solution can now be calculated from:

Ccdt =

Ctic
12 000 × ϕ

1
Ccdt
×
(1 + Kc1 /H + + (Kc1 × Kc2 )/(H + )2 ) (1 + Kc0 )
Ccd0 = Kc0 × Ccd1
Kc1 × (Kc0 + 1) × Ccd1
Ccd2 =
H+
Ccd3 = Ccdt − Ccd0 − Ccd1 − Ccd2
Ccd1 =

if due to rounding off the resulting Ccd3 ≤ 0.0

Ccd3 =

Kc2 × Ccd2
H+

where:

Ctic
ϕ

total dissolved inorganic carbon (gC.m−3 )
porosity
b

The constant 12 000 concerns the conversion from gC.m−3 to mol.l−1 . This constant is also
used to convert the above molar concentrations back into gC.m−3 for the carbonate species.
A constant 44 000 is used to convert the molar concentration of dissolved carbon dioxide into
gCO2 .m−3 .

266 of 464

Deltares

Inorganic substances and pH

The pertinent carbonate fractions (mol mol−1 or g g−1 ) follow from:

Ccd0
Ccdt
Ccd1
f c1 =
Ccdt
Ccd2
f c2 =
Ccdt
f c3 = 1 − f c0 − f c1 − f c2
f c0 =

if due to rounding off the resulting f c3 ≤ 0.0

Ccd3
Ccdt

where:
fraction CO 2 of TIC [−]
fraction H 2 CO 3 of TIC [−]
fraction HCO 3 − of TIC [−]
−
fraction CO 3 2 of TIC [−]

DR
AF

f c0
f c1
f c2
f c3

T

f c3 =

The saturation states of calcite and aragonite are not calculated.

Directives for use
 Two versions for the calculation of pH are available. The original version 1 is selected
with option parameter SwpH = 0.0 (default value). Former process SPECCARB for the
calculation of the concentrations and the fractions of the carbonate species needed for
processes REARCO2 and PRIRON was integrated into the pH_Simp process. Version
2 is selected with option parameter SwpH = 1.0, and has its own formulations for the
calculation of the carbonate species.
 Version 1 is suitable for water with a salinity < 5 psu.
 With the input parameters for process pH_Simp, pH _min and pH _max, the pH can
be constrained within a certain user defined range. This is required for the sediment
bed in the "layered sediment" approach, because the pH calculation does not account for
buffering of the pH by minerals like calcite. Reasonable values for the lower and upper pH
for the bed sediment are 6.5 and 7.5.
 pH_Simp can be used to calculate the pH as described above, or the pH can be imposed
as a function of time and space with option SwpH = -1.0. When the pH is imposed,
pH_Simp calculates the concentrations and the fractions of the carbonate species process
according to Version 1.
 Version 1 includes the calculation of DisH2CO3 and F rH2CO3d, whereas this is not
done by version 2 because this species is assumed included in DisCO2.
 Dissociation constants are calculated internally and cannot be modified through input parameters.
 The CO2 concentration in water needed for the exchange of carbon dioxide between water
and atmosphere (process REARCO2) is delivered by pH_Simp as DisCO2.
−
 The fraction of carbonate CO3 2 concentration in water needed for the formation of Fe(II)CO3
(process PRIRON) is delivered by pH_Simp as F rCO3dis.
Additional references
Millero (1995), Roy (1993), Millero (1982), Mucci (1983), Dickson (1990), Dickson and Goyet
(1994), Zeebe and Wolf-Gladrow (2001)

Deltares

267 of 464

Processes Library Description, Technical Reference Manual

Table 9.7: Definitions of the input parameters in the above equations for pH _simp. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in
Input

Definition

Units

SwpH

SwpH

option parameter for formulations
(0.0 = old version; 1.0 = new version)

-

Alka
T IC

Alka
T IC

alkalinity
total dissolved inorganic carbon concentration

gHCO3 m−3
gC.m−3
b

pH
pH _max
pH _min

imposed pH, acidity
maximum pH
minimum pH

-

S
T

Salinity
T EM P

salinity
ambient water temperature

psu
◦
C

DR
AF

T

pH
pH _max
pH _min

ϕ

b

P OROS

porosity

b

-

Table 9.8: Definitions of the output parameters of pH _simp. Volume units refer to bulk
( ) or to water ( ).
b

w

Name in
formulas

Name in
Input

Definition

Units

pH

pH

simulated pH, acidity

-

CO2
or
Ccd0
HCO3 or
Ccd1
CO3
or
Ccd2
H2CO3 or
Ccd3

DisCO2

concentration of dissolved CO2

gCO2 .m−3

f c0
f c1
f c2
f c3

F rCO2dis
F rH2CO3d
F rHCO3dis
F rCO3dis

fraction of dissolved carbon dioxide
fraction of dissolved H2 CO3
fraction of dissolved HCO3 −
fraction of dissolved CO3 2−

gC gC−1
gC gC−1
gC gC−1
gC gC−1

BOH4

dissolved borate B(OH)4 − concentration
partial pressure of carbon dioxide in
water

gB m−3

saturation state of calcite
saturation state of aragonite

-

BOH4

DisHCO3
DisCO3

DisH2CO3

pCO2w

pCO2water

ΩCal
ΩArg

SatCal
SatArg

268 of 464

concentration of dissolved HCO3 −
concentration of dissolved CO3 2−

concentration of dissolved H2 CO3

b

gC.m−3
b

gC.m−3
b

gC.m−3
b

b

µatm−1

Deltares

Inorganic substances and pH

Volatilisation of methane
PROCESS :

VOLATCH4

Methane (CH4 ) in surface water tends to escape to the atmosphere, because its partial atmospheric pressure is extremely low. Volatisation is enhanced by the difference of the CH4
saturation concentration and the actual CH4 concentration, and by the difference of the velocities of the water and the overlying air. The saturation concentration is approximately zero.

T

Since lakes are rather stagnant, only the windspeed is important as a driving force for lakes.
The volatilisation rate tends to saturate for low windspeeds (< 3 m s−1 ). On the other hand,
the stream velocity may deliver the dominant driving force for rivers. Both forces may be
important in estuaries.
The rate of methane volatilisation is described in the same way as the reaeration of dissolved
oxygen (DO). Only those formulations can be applied that may be valid for methane too. A
scaling factor is available to scale methane volatilisation relation relative to reaeration.
Extensive research has been carried out all over the world to describe and quantify reaeration
processes for DO, including the reaeration of natural surface water. Quite a few different
models have been developed. The most generally accepted model is the ‘film layer’ model.
This model assumes the existence of a thin water surface layer, in which a concentration
gradient exists bounded by the saturation concentration at the air-water interface and the
water column average DO concentration. The reaeration rate is characterised by a water
transfer coefficient, which can be considered as the reciprocal of a mass transfer resistance.
The resistance in the overlying gas phase is assumed to be negligibly small.

DR
AF

9.4

Many formulations have been developed and reported for the water transfer coefficient, mostly
in connection with the reaeration of DO, WL | Delft Hydraulics (1980b). These formulations are
often empirical, but most have a deterministic background. They contain the stream velocity
or the windspeed or both. Most of the relations are only different with respect to the coefficients, the powers of the stream velocity and the windspeed in particular. Volatisation has
been implemented in DELWAQ with four different formulations for the transfer coefficient. The
first two options are pragmatic simplications to accommodate preferences of the individual
modeller. The other two relations have been copied or derived from scientific publications. All
reaeration rates are also dependent on the temperature according to the same temperature
function.
Implementation

Process VOLATCH4 has been implemented in such a way, that it only affects the CH4 -budget
of the top water layer. An option for the transfer coefficient can be selected by means of input
parameter SW V olCH4 (= 0, 1, 4, 9, 13). The other options concern only DO or CO2. The
saturation concentration required for the process VOLATCH4 is calculated by an additional
process SATURCH4.
The process has been implemented for substance CH4 .
Table 9.9 provides the definitions of the parameters occurring in the formulations.

Deltares

269 of 464

Processes Library Description, Technical Reference Manual

Formulation
The volatilisation rate has been formulated as a reaeration rate. This rate is a linear function
of the temperature dependent mass transfer coefficient in water and the difference between
the saturation and actual concentrations of CH4 as follows:

Rvol = klvol × [Cch4s − max(Cch4, 0.0)] /H

T

klvol = klvol20 × ktvol(T −20)



a × vb
20
+ d × W2
klvol =
c
H
Cch4s = f (T, P ch4)
(delivered by SATURCH4)
max(Cch4, 0.0)
f sat = 100 ×
Cch4s
with:

coefficients with different values for eleven reaeration options
actual dissolved methane concentration [gC m−3 ]
saturation methane concentration [gC m−3 ]
percentage of saturation [%]
depth of the water column [m]
transfer coefficient in water [m d−1 ]
transfer coefficient at reference temperature 20 ◦ C [m d−1 ]
temperature coefficient of the transfer coefficient [-]
partial atmospheric methane pressure [gC m−3 ]
volatilisation rate [gC m−3 d−1 ]
temperature [◦ C]
stream velocity [m.s−1 ]
windspeed at 10 m height [m.s−1 ]

DR
AF

a, b, c, d
Cch4
Cch4s
f sat
H
klvol
klvol20
ktvol
P ch4
Rvol
T
v
W

Notice that the volatilisation rate is always calculated on the basis of a positive methane
concentration. Allthough technically possible, negative concentrations of methane should not
occur in the model.
Depending on the volatilisation option, the transfer coefficient is only dependent on the stream
velocity or the windspeed. Information on the coefficients a−d and the applicability is provided
below for each of the options.

SWVolCH4 = 0

The transfer coefficient is simplified to a constant, multiplied with the water depth H , using
the transfer coefficient as input parameter. So klvol 20 is to be provided as a value in [d−1 ]
instead of [m d−1 ] Consequently, the coefficients are:

a = klvol20 × H,

b = 0.0,

c = 0.0,

d = 0.0

SWVolCH4 = 1
The transfer coefficient is simplified to a constant, using the transfer coefficient as input parameter. Consequently, the coefficients are:

a = klvol20 ,
270 of 464

b = 0.0,

c = 0.0,

d = 0.0
Deltares

Inorganic substances and pH

SWVolCH4 = 4
The coefficients are according to O’ Connor and Dobbins (1956) for DO, but coefficient a
can be scaled for CH4 using the transfer coefficient as input parameter. Consequently, the
coefficients are:

a = klvol20 × 3.863,

b = 0.5,

c = 0.5,

d = 0.0

The relation is valid for rivers, and therefore independent of windspeed.

SWVolCH4 = 9

b = 0.0,

c = 0.0,

d = klvol20 × 0.028

DR
AF

a = 0.3,

T

The relation for DO is according to Banks and Herrera (1977) as reported by WL | Delft
Hydraulics (1980b), but the coefficients have been modified according to WL | Delft Hydraulics
(1978); (d = 0.03 − 0.06) and later modelling studies for Dutch lakes (WL | Delft Hydraulics,
1992c). Coefficient d can be scaled for CH4 using the transfer coefficient as input parameter.
Consequently, the coefficients are:

The relation is valid for lakes and seas, and therefore independent of stream velocity. The
relation takes into account that the mass transfer coefficient saturates at a lower boundary for
low wind velocities (W < 3 m s−1 ).

SWVolCH4 = 13

The relation according to Guérin (2006); Guérin et al. (2007) deviates strongly from the previous relations, with respect to wind dependency, with respect to an additional forcing parameter, namely rainfall, and with respect to temperature dependency. The latter is not included
according to the above Arrhenius equation for klrear. The temperature dependency enters
the relation in a scaling factor on the basis of the Schmidt number. The relation for transfer
coefficient is:



klrear = a × exp b1 × W b2 + c1 × P c2 × f sc

−0.67
Sc
f sc =
Sc20
Sc = d1 − d2 × T + d3 × T 2 − d4 × T 3

with:

a, b, c, d
klrear
P
Sc
Sc20
T
W

coefficients
transfer coefficient in water [m.d−1 ]
precipitation, e.g. rainfall [mm.h−1 ]
Schmidt number at the ambient temperature [g.m−3 ]
Schmidt number at reference temperature 20 ◦ C [d−1 ]
temperature [◦ C]
windspeed at 10 m height [m.s−1 ]

The relation is valid for (tropical) lakes and therefore independent of stream velocity. The
general coefficients have the following input names and values:

Deltares

271 of 464

Processes Library Description, Technical Reference Manual

a

b1

b2

c1

c2

CoefACH4

CoefB1CH4

CoefB2CH4

CoefC1CH4

CoefC2CH4

1.660

0.26

1.0

0.66

1.0

The Schmidt number is the ratio of the kinematic viscosity of water (ν ) and the molecular
diffusion coefficient of oxygen in water. The appropriate constants to compute the Schmidt
number for fresh water are given in the table below (Guérin, 2006):
d2

d3

d4

CoefD1 CH4

CoefD2 CH4

CoefD3 CH4

CoefD4 CH4

1897.8

114.28

3.2902

T

d1

0.039061

DR
AF

Directives for use
 Options SW V olCH4 = 0, 1, 4, 9 provide the user with the possibility to scale the mass
transfer coefficient KLV olCH4. Other options contain fixed coefficients.
 When using option SW V olCH4 = 0 the user should be aware that the mass transfer
coefficient KLV olCH4 has the unusual dimension d−1 . Since high values of KLV olCH4
may cause numerical instabilities, the maximum KLV olCH4 value is limited to 1.0 day−1 .
 When using option SW V olCH4 = 1 the user should be aware that the mass transfer
coefficient KLV olCH4 has the standard dimension m d−1 .
 When using options SW V olCH4 = 4 or 9 the user should be aware that the input
parameter KLV olCH4 is used as a dimensionless scaling factor. The default value of
KLV olCH4 is 1.0 in order to guarantee that scaling is not carried out when not explicitly
wanted.
 The coefficients a–d4 are input parameters for option SW V olCH4 = 13 only. The
default values are those for option 13.

272 of 464

Deltares

Inorganic substances and pH

Table 9.9: Definitions of the parameters in the above equations for VOLATCH4.

Name in
input

Definition

Units

Cch4
Cch4s

CH4
SaturCH4

concentration of methane
saturation conc. of methane from SATURCH4

gC m−3
gC m−3

a
b1
b2
c1
c2

Coef ACH4
Coef B1CH4
Coef B2CH4
Coef C1CH4
Coef C2CH4

coefficients for option 13 only

DR
AF

d1
d2
d3
d4

T

Name in
formulas1

-

Coef D1CH4 coefficients for option 13 only
Coef D2CH4
Coef D3CH4
Coef D4CH4

-

f cs
f sat

–
–

scaling factor for the Schmidt number
percentage methane saturation

%

H

Depth

depth of the top water layer

m

klvol20
ktvol

KLV olCH4
T CV olCH4

water transfer coefficient for methane1
temperature coefficient for methane
volatilisation

d−1
-

P

Rain

rainfall

mm h−1

–

methane volatilisation rate

gC m−3 d−1

SW V olCH4 SW V olCH4

switch for selection of options for transfer coefficient

-

T

T emp

temperature

◦

V elocity
V W ind

stream velocity
windspeed at 10 m height

m s−1
m s−1

Rvol

v
W
1

C

See directives for use concerning the dimension of KLV olCH4

Deltares

273 of 464

Processes Library Description, Technical Reference Manual

Saturation concentration of methane
PROCESS :

SATURCH4

The volatilization of methane proceeds proportional to the difference of the saturation CH4
concentration and the actual dissolved CH4 concentration. The saturation concentration of
CH4 is primarily a function of water temperature, allthough salinity affects the saturation concentration too.

T

The saturation concentration at the water surface is also proportional to the partial atmospheric CH4 pressure. This pressure is so low that is reasonable to assume that this pressure
is equal to zero. This means that the saturation concentration at the water surface is also
approximately equal to zero.
The calculation of the saturation concentration in DELWAQ is performed as a separate process, the formulation of which has been described by DiToro (2001).
Implementation

DR
AF

9.5

Process SATURCH4 delivers the CH4 saturation concentration in water required for the process REARCH4, referring to the loss of methane to the atmosphere by means of the transfer
of dissolved methane transfer at the water surface.
The process has been implemented for substance CH4 . Table 9.10 provides the definitions of
the parameters occurring in the formulations.
Formulation

The saturation concentration is:

Cch4s = 18.76 × P ch4 × (1.024)(20−T )
where:

Cch4s
P ch4
T

methane saturation concentration at the water surface [gC m−3 ]
atmospheric methane pressure [atm]
temperature [◦ C]

Directives for use
 A representative value for the atmospheric methane pressure AtmP rCH4 is 10− 5 atm.
 The name of the output parameter for the saturation concentration of methane is SaturCH4.

274 of 464

Deltares

DR
AF

T

Inorganic substances and pH

Table 9.10: The efinitions of the parameters in the above equations for SATURCH4.

Name in
formulas

Name in
input

Definition

Units

Cch4s

–

saturation concentration of methane in water

gC m−3

P ch4

AtmP rCH4 atmospheric methane pressure

atm

T

T emp

◦

Deltares

temperature

C

275 of 464

Processes Library Description, Technical Reference Manual

Ebullition of methane
PROCESS :

EBULCH4

T

The ebullition of methane from sediment or deep water layers concerns the loss of methane
that escapes to the atmosphere via gas bubbles. It is assumed that supersaturation does not
occur and that all methane produced in excess of the dissolved saturation concentration is
immediately transferred to gas bubbles. Gas bubbles accumulate in sediment until a certain
maximal part of the volume is taken up by bubbles. Continuation of the methane gas production results in ebullition from this point on. However, the initial phase of gas accumulation
can be ignored. In most cases it is reasonable to assume that the maximal amount of gas
is already present at the start of a simulation. This means that all methane produced after
establishment of the dissolved saturation concentration is lost to the atmosphere.
The saturation concentration of CH4 in sediment pore water or in deep water layers concerns
the equilibrium of water with a more or less pure methane gas phase. The saturation concentration is primarily a function of water pressure (depth) and water temperature, although
salinity will affect the saturation concentration too. This function has been described by DiToro
(2001).

DR
AF

9.6

Implementation

Process EBULCH4 delivers the flux of methane escaping to the atmosphere as gas bubbles.
The process has been implemented for substance CH4.

Table 9.11 provides the definitions of the parameters occurring in the formulations.
Formulation

The methane ebullition flux follows from:


Cch4/φ − Cch4s
if Cch4/φ ≥ Cch4s
Rebu = f ×
∆t


H
Cch4s = 18.76 × 1 +
× (1.024)(20−T )
10


with:

Cch4
Cch4s
f
H
T
∆T
φ

dissolved methane concentration [gC m−3 ]
methane saturation concentration [gC m−3 ]
scaling factor [-]
water depth [m]
temperature [◦ C]
timestep in DELWAQ [day]
porosity [-]

It is obvious that Rebu = 0.0 at undersaturation.

276 of 464

Deltares

Inorganic substances and pH

Directives for use
 The scaling factor f ScEbul can be used to scale the ebullition flux in order to established
the required degree of supersaturation. This factor should not be larger than the default
value 1.0. A value zero will result in no methane escaping at all.
Table 9.11: Definitions of the parameters in the above equations for EBULCH4.

Name in input

Definition

Units

Cch4
Cch4s

CH4
–

dissolved methane concentration
saturation concentration of methane in
water

gC m−3
gC m−3

f

f ScEbul

scaling factor for methane ebullition

-

H

T otalDepth

total depth of the water column

m

Rebu

–

methane ebullition rate

gC m−3 d−1

∆t
φ

DR
AF

T

T

Name in
formulas

Deltares

T emp

temperature

◦

Delt

computational time-step

d

P OROS

porosity

-

C

277 of 464

Processes Library Description, Technical Reference Manual

Oxidation of methane
PROCESS :

OXIDCH4

Dissolved methane does not react in a purely chemical way with dissolved oxygen. However,
methane is oxidised by several families of bacteria species. The microbial oxidation with
oxygen has been confirmed extensively. The oxidation with sulfate has not been so extensively
investigated. For the model, however, it is assumed that both oxidations may proceed, but not
to full extent at the same time because of thermodynamic reasons. Sulfate reduction does not
deliver energy at the (substantial) presence of dissolved oxygen. Therefore, the oxidation with
sulfate only occurs when sulfate is abundant and oxygen is present in very low concentrations.
Such conditions occur in sediment.

T

The microbial oxidation of methane is a function of the concentrations of dissolved methane
and the electron-acceptor. It is also a relatively steep function of the temperature, because
only a rather small number of specialised bacteria species are capable of methane oxidation.
The process may effectively take place at a rather constant, small rate at low temporatures. It
may even come to a halt.

DR
AF

9.7

Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

Process METHOX has been implemented in a generic way, meaning that it can be applied
both to water layers and sediment layers.
The process has been implemented for the following substances:

 CH4, OXY and SO4.

Table 9.12 provides the definitions of the parameters occurring in the formulations.
Formulation

Methane oxidation can be described with the following overall reaction equations:

CH4 + 2O2
CH4 + SO42−

=⇒
=⇒

CO2 + 2H2 O
CO2 + 2H2 S + 2OH −

These processes require 5.33 gO2 gC−1 or 2.67 gS gC−1 .

Methane oxidation is modelled as the sum of a zero-order process and a process according
to Michaelis-Menten kinetics. The rate of the MM-contribution is limited by the availability of
methane and dissolved oxygen or sulfate. It is also a function of the temperature. When the
water temperature drops below a critical value, the zero-order rate takes over. The oxidation
with dissolved oxygen excludes the oxidation with sulfate at DO concentrations exceeding a
certain critical concentration.
Methane oxidation is formulated as follows to accommodate the above features (Smits and

278 of 464

Deltares

Inorganic substances and pH

Van Beek (2013)):


Roxi1 = k0oxi1 + koxi1 ×

Cch4
Ksch4 × φ + Cch4




×



Cox
Ksox × φ + Cox

(T −20)

koxi1 = koxi20
1 × ktoxi1


Roxi2 = k0oxi2 + koxi2 ×

T

koxi1 = 0.0 if T < T c
or Cox ≤ 0.0
or Cox ≤ Coxc × φ
k0oxi1 = 0.0 if Cox > Coxc × φ
or Cox ≤ 0.0

Cch4
Ksch4 × φ + Cch4

(T −20)



×

Csu
Kssu × φ + Csu

DR
AF

koxi2 = koxi20
2 × ktoxi2





koxi2 = 0.0 if T < T c
or Csu ≤ 0.0
or Csu ≤ Csuc × φ
or Cox > Coxc × φ
k0oxi2 = 0.0 if Csu > Csuc × φ
or Csu ≤ 0.0
or Cox > Coxc × φ

with:

Cch4
Cox
Coxc
Csu
Csuc
k0oxi1
k0oxi2
koxi1
ktoxi1
Ksch4
Ksox
koxi2
ktoxi2
Kssu
Roxi1
Roxi2
T
Tc
φ

Deltares

dissolved methane concentration [gC m−3 ]
b

dissolved oxygen concentration [gO2 m−3 ]
b

critical dissolved oxygen concentration for oxidation with sulfate [gO2 m−3 ]
sulfate concentration [gS m−3 ]
w

b

critical sulfate concentration for oxidation with sulfate [gS m−3 ]
zero-order methane oxidation rate for diss. oxygen consumption [gC m−3 d−1 ]
w

b

zero-order methane oxidation rate for sulfate consumption [gC m−3 d−1 ]
b

Michaelis-Menten rate for oxidation with dissolved oxygen [gC m−3 d−1 ]
b

temperature coefficient for oxidation with dissolved oxygen [-]
half saturation constant for methane consumption [gC m−3 ]
half saturation constant for dissolved oxygen consumption [gO2 m−3 ]
Michaelis-Menten rate for oxidation with sulfate [gC m−3 d−1 ]
w

w

b

temperature coefficient for oxidation with sulfate [-]
half saturation constant for sulfate consumption [gS m−3 ]
methane oxidation rate with DO [gC m−3 d−1 ]
w

b

methane oxidation rate with sulfate [gC m−3 d−1 ]
temperature [◦ C]
critical temperature for methane oxidation [◦ C]
porosity [-]
b

279 of 464

Processes Library Description, Technical Reference Manual

Directives for use
 For a start, the zero-order rates Rc0M etOx and Rc0M etSu and the critical concentrations CoxM et and CsuM et can be set to zero. In a next step the zero-order rates for
low temperatures can be quantified in establishing a good balance between summer and
winter oxidation rates.
 Care must be taken that the zero-order reaction rates are given values, that are in proportion with the first-order kinetics. They should not deliver more than 20 % of the total rate
at T = 20 ◦ C, and average methane, DO and sulfate concentrations. Using zero-order
kinetics may cause negative methane concentrations, when the time-step is too large!
 The critical temperature for methane oxidation CT M etOx is approximately 3–4 ◦ C.
 An indicative value for the critical DO concentration CoxM et is 2 gO2 m−3 .
 An indicative value for the temperature coefficients T cM etOx and T cM etSu is 1.07.
 The oxidation with sulfate can simply be excluded from the simulation by setting rates
Rc0M etSu and RcM etSu20 equal to 0.0.
Additional references

T

w

DR
AF

DiToro (2001), WL | Delft Hydraulics (2002), Wijsman et al. (2001)

280 of 464

Deltares

Inorganic substances and pH

Table 9.12: Definitions of the parameters in the above equations for OXIDCH4. Volume
units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in input

Definition

Units

Cch4
Cox
Coxc

CH4
OXY
CoxM et

methane concentration

gC m−3

dissolved oxygen concentration

gO2 m−3

Csuc

CsuM et

Csu

SO4

b

b

koxi20
1

gS m−3
w

gS m−3
b

gC m−3 d−1

–

rate of oxidation of methane with DO

gC m−3 d−1

–

rate of oxidation of methane with sulfate

gC m−3 d−1

T cM etOx

koxi20
2

RcM etSu20

ktoxi2

T cM etSu

Ksch4

KsM et

Ksox

KsOxM et

Kssu

KsSuM et

k0oxi1

Rc0M etOx

Roxi1
Roxi2

w

MM-rate for methane oxidation with DO
at 20 ◦ C
temp. coefficient for methane oxidation
with DO
MM-rate for methane oxid. with sulfate at
20 ◦ C
temp. coefficient for methane oxidation
with sulfate
half saturation constant for methane consumption
half saturation constant for DO consumption
half saturation constant for sulfate consumption
zero-order methane oxid. rate for DO
consumption
zero-order methane oxid. rate for sulfate
cons.

RcM etOx20

ktoxi1

k0oxi2

gO2 m−3

T

DR
AF

critical DO concentration for methane oxidation
critical sulfate concentration for methane
oxidation
sulfate concentration

Rc0M etSu

b

gC m−3 d−1
b

gC m−3
w

gO2 m−3
w

gS m−3
w

gC m−3 d−1
b

gC m−3 d−1
b

b

b

T
Tc

T emp
CT M etOx

temperature
critical temperature for methane oxidation

◦

φ

P OROS

porosity

m3 m−3

◦

C
C

w

b

Deltares

281 of 464

Processes Library Description, Technical Reference Manual

Oxidation of sulfide
PROCESS :

OXIDSUD

T

Sulfide oxidation is established by both a purely chemical reaction and a microbially mediated
process. Both processes are temperature dependent. However, the chemical oxidation is
usually dominant at the significant presence of dissolved oxygen, because it proceeds very
fast. The oxidation can be complete within an hour. The microbial oxidation of sulfide can be
important at low dissolved oxygen concentrations. Specific autotrophic bacteria species are
capable of oxidising sulfide when solar radiation is available as a source of energy. Given the
specific features of sulfide oxidation, this process usually takes place in regions with steep
concentration gradients. Examples are the sediment-water interface and water layers near
the thermocline in a water column.
The chemical oxidation of sulfide is taken as a starting point for the formulation of the oxidation
rate. Although oxidation occurs both in solution as well as on the surface of sulfide minerals,
it is assumed that only dissolved sulfide is available to quick oxidation.
Volume units refer to bulk ( ) or to water ( ).

DR
AF

9.8

b

w

Implementation

Process SULFOX has been implemented in a generic way, meaning that it can be applied
both to water layers and sediment layers.
The process has been implemented for the following substances:

 SUD, SO4 and OXY.

Table 9.13 provides the definitions of the parameters occurring in the formulations.
Formulation

Sulfide oxidation can be described with following overall reaction equation:

H2 S + 2O2 + 2OH −

=⇒

SO42− + 2H2 O

The process requires 2.0 gO2 gS−1 .

Sulfide oxidation is modelled as the sum of a zero order process and a second-order kinetic
process, involving the concentrations of both total dissolved sulfide and dissolved oxygen.
The rate is also a function of the temperature.
The zero-order rate should generally be equal to zero, but it can be used for two different purposes. One purpose is to add a contribution of microbial sulfide oxidation when the dissolved
oxygen concentration falls below a critical level. The other purpose is to have sulfide oxidation in a water column, in which the average dissolved oxygen concentration is zero or even
negative. In this way it can be taken into account that the water column may not be homogeneously mixed in reality, and a surface layer with positive oxygen concentrations persists. The
zero-order rate is set to zero, when the dissolved oxygen concentration is above the critical
concentration, the second-order rate is set to zero when the dissolved oxygen concentration
is negative.

282 of 464

Deltares

Inorganic substances and pH

The sulfate oxidation rate is formulated as follows to accommodate the above features (Smits
and Van Beek (2013)):


Roxi = k0oxi + koxi ×

Csud
φ




×

Cox
φ


×φ

koxi = koxi20 × ktoxi(T −20)
koxi = 0.0

if Cox ≤ 0.0

k0oxi = 0.0

if Cox > Coxc × φ

with:
dissolved oxygen concentration [gO2 m−3 ]
b

T

critical dissolved oxygen concentration [gO2 m−3 ]
total dissolved sulfide concentration [gS m−3 ]
w

b

3
pseudo second-order sulfide oxidation rate [gO−1
2 m d]
temperature coefficient for sulfide oxidation [-]
zero-order sulfide oxidation rate [gS m−3 d−1 ]
w

DR
AF

Cox
Coxc
Csud
koxi
ktoxi
k0oxi
T
φ

temperature [◦ C]
porosity [-]

b

Notice that the porosity occurs three times in the rate equation, whereas only once would
suffice. However, a systematic formulation is preferred in order to make clear how the porosity
affects the rate.
The oxidation process must stop at the depletion of dissolved sulfide. Therefore, the oxidation
flux is made equal to half the concentration of dissolved sulfide SU D divided with timestep
∆t, when the flux as calculated with the above formulation is larger than SU D/∆t.
Directives for use
 The zero-order rate Rc0Sox should always be equal to its default value 0.0, unless it is
really required to have sulfide oxidation going on when the water column average oxygen
concentration is negative.
 Care must be taken that the zero-order reaction rates is given a value, that is in proportion
with the second-order kinetics. They should not deliver more than 20 % of the total rate
at T = 20 ◦ C, and average DO concentrations. Using zero-order kinetics may cause
negative sulfide concentrations, when the time-step is too large!
 The critical dissolved oxygen concentration CoxSUD needs to be 0.0 to accommodate the
use of Rc0Sox for sulfide oxidation in a water column with negative oxygen concentrations.
Additional references
DiToro (2001), Wang and Cappellen (1996), WL | Delft Hydraulics (2002), Wijsman et al.
(2001)

Deltares

283 of 464

T

Processes Library Description, Technical Reference Manual

Table 9.13: Definitions of the parameters in the above equations for OXIDSUD. Volume
units refer to bulk ( ) or to water ( ).
b

Name in input

Cox
Coxc
Csud

OXY
CoxSU D
SU D

∆t
koxi20
ktoxi
k0oxi
Roxi
T
φ

Definition

DR
AF

Name in
formulas

w

284 of 464

Units

dissolved oxygen concentration

gO2 m−3

critical dissolved oxygen concentration
total dissolved sulfide concentration

gO2 m−3
gS m−3

b

w

b

Delt

timestep

d

RcSox20

pseudo second-order sulfide oxidation
rate at 20 ◦ C
temperature coefficient for sulfide oxidation
zero-order sulfide oxidation rate

3 −1
gO−1
2 m d

T cSox

Rc0Sox
–

sulfide oxidation rate

w

gS m−3 d−1
b

gS m−3 d−1
b

T emp

temperature

◦

P OROS

porosity

m3 m−3

C

w

b

Deltares

Inorganic substances and pH

Precipitation and dissolution of sulfide
PROCESS :

PRECSUL

At reducing conditions sulfide resulting from sulfate reduction may precipitate with iron(II) as
rather amorphous iron(II) sulfide. This mineral is thermodynamically unstable at oxidising
conditions. At the presence of dissolved oxygen iron(II) in sulfides is oxidised into iron(III),
sulfide into sulfate, resulting in the subsequent dissolution of the mineral.

T

Not only sulfide but also elementary sulfur is produced at sulfate reduction. Crystalline pyrite
(FeS2 ) is formed from iron(II) sulfide and sulfur, a mineral which can be very stable under
oxidising conditions. However, the formation of pyrite is not considered in the model. It can be
argued that the formation of pyrite being a slow process does not play an important part is the
oxygen budget and sediment diagenesis in the short term. It should nevertheless be noticed,
that ignoring pyrite may cause some overestimation of the sediment oxygen demand.
The precipitation of iron(II) sulfide only occurs at the absence of dissolved oxygen in a solution
supersaturated with respect to free sulfide and iron(II) ions. These conditions usually occur in
the reducing sediment, just below an oxidising top layer. However, sulfide may also precipitate
in the lower part of the water column at lasting stratification. Precipitation is not only temperature dependent, but also pH dependent among other things due to the acid-base equilibria to
which sulfide is subjected. The pH-dependency is taken into account via the calculation of a
pH dependent free sulfide concentration with process SPECSUD.

DR
AF

9.9

The dissolution of iron(II) sulfide occurs when the solution is undersaturated with respect to
sulfide and iron(II). Since the oxidation of these ions with dissolved oxygen proceeds rapid,
it is assumed in the model that oxidation entirely occurs in the solution. This is described
elsewhere for process SULPHOX. Rapid oxidation implies that the dissolved concentrations
of sulfide and iron(II) will be very small at the presence of dissolved oxygen. In other words,
the solution will be strongly undersaturated with respect to iron(II) sulfide. However, in reality
oxidation will also take place at the mineral surface to a certain extent.
Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

Process PRECSUL has been implemented in a generic way, meaning that it can be applied
both to water layers and sediment layers. The precipitation of sulfide in sediment is not considered, when substances in the sediment are modeled as a ‘inactive’ substances (the S1/2
approach).
The process has been implemented for the following substances:

 total dissolved sulfide SUD and particulate sulfide SUP.
The process should only be applied when iron (7 substances) is not simulated. When iron is
simulated, SUP should not be simulated. Process PRIRON will take care of the precipitation
and dissolution of sulfide as iron sulfide in stead of process PRECSUL.
Table 9.14 provides the definitions of the parameters occurring in the formulations. The actual
dissolved free sulfide concentration (Csd) can be delivered by process SPECSUD or imposed
to DELWAQ via the input.

Deltares

285 of 464

Processes Library Description, Technical Reference Manual

Formulation
The precipitation and dissolution equilibrium of iron(II) sulfide can be described with the following simplified reaction equation:

F e2+ + S 2−

⇔

F eS

The precipitation and dissolution rates are formulated with first-order kinetics, with the difference between the actual dissolved free sulfide concentration and the equilibrium dissolved
concentration as driving force (Smits and Van Beek (2013)):
if Csd ≥ Cdse

Rdis = 32 000 × kdis × (Csde − Csd) × φ

if Csd < Cdse

T

Rprc = 32 000 × kprc × (Csd − Csde) × φ

kprc = kprc20 × ktprc(T −20)
kdis = kdis20 × ktdis(T −20)
with:

dissolved free sulfide concentration [mol l−1 ]
equilibrium dissolved free sulfide concentration [mol l−1 ]
dissolution reaction rate [d−1 ]
precipitation rate [d−1 ]
temperature coefficient for dissolution [-]
temperature coefficient for precipitation [-]
rate of dissolution [gS m−3 d−1 ]

DR
AF

Csd
Csde
kdis
kprc
ktdis
ktprc
Rdis
Rprc
T
φ

b

rate of precipitation [gS m−3 d−1 ]
temperature [◦ C]
porosity [-]

b

The constant of 32,000 concerns the conversion of [mol/l] to [gS/m−3 ].

The dissolution process must stop at the depletion of precipitated sulfide. Therefore, the dissolution flux is made equal to half the concentration of precipitated sulfide SU P divided with
timestep ∆t, when the flux as calculated with the above formulation is larger than SU P/∆t.
Notice that the effect of the dissolved iron(II) concentration is ignored. In case iron is simulated
too, the driving force can be formulated on the basis of the solubility product of the dissolved
free sulfide and iron(II) concentrations. However, iron is currently not included in DELWAQ.
Directives for use
 The equilibrium dissolved free sulfide concentration can be calculated with process SULFID using an imposed total dissolved sulfide concentration. However, it is also possible to
impose fixed dissolved free sulfide concentrations by assigning values to DisSW K as
input parameter.
 The equilibrium dissolved free sulfide concentration DisSEqF eS is an input parameter.
Its value can be deduced from the solubility product of iron(II) sulfide and an estimated
dissolved free iron(II) concentration.
 As a start the precipitation and dissolution reaction rates can be given the same value. The
rates must be high enough to establish a near equilibrium at the absence of oxidation. The
dissolution rate should be consistent with the sulfide oxidation rate RcSox20 for process
OXIDSUD.

286 of 464

Deltares

Inorganic substances and pH

 When simulating the substances in the sediment as “inactive” substances (the S1/2 approach) process SULFPR only affects SUD and SUP in the water column. Settled SU P
is then permanently removed from the simulated system.
Additional references
DiToro (2001),
Stumm and Morgan (1996),
Wang and Cappellen (1996),
WL | Delft Hydraulics (2002),
Wijsman et al. (2001)
Table 9.14: Definitions of the parameters in the above equations for PRECSUL. Volume
units refer to bulk ( ) or to water ( ).
w

T

b

Name in input

Definition

Csd
Csde

DisSW K
DisSEqF eS

Csup

SU P

dissolved free sulfide concentration
equilibrium dissolved free sulfide concentration for amorphous iron sulfide
precipitated sulfide concentration

∆t

DR
AF

Name in
formulas

Units
mol l−l
mol l−1
gS m−3
b

Delt

timestep

d

kdis20
ktdis
kprc20
ktprc

RcDisS20
T cDisS
RcP rcS20
T cP rcS

dissolution reaction rate
temperature coefficient for dissolution
precipitation reaction rate
temperature coefficient for precipitation

d−1
d−1
-

Rdis
Rprc

–

dissolution rate

gS m−3 d−1

–

precipitation rate

gS m−3 d−1

T
φ

Deltares

b

b

T emp

temperature

◦

P OROS

porosity

m3 m−3

C

w

b

287 of 464

Processes Library Description, Technical Reference Manual

Speciation of dissolved sulfide
PROCESS :

SPECSUD AND SPECSUDS1/2

Sulfide can only persist in anoxic environment, the reducing enviroment which usually occurs
in the sediment. Being a weak acid sulfide forms two protonised species in solution. These
equilibrium processes are temperature dependent. The pH-dependent speciation affects dissolved metal concentrations as well as total dissolved sulfide concentrations in the reducing
environment. Metal sulfide complexes are formed and only the concentrations of the free
metal ion and the free sulfide ion affect the precipitation and the dissolution of a solid metal
sulfide.

Volume units refer to bulk ( ) or to water ( ).
b

w

T

The computed sulfide speciation is used in processes PARTWK_(i) and PARTS1/S2_(i) to
determine the precipitated and dissolved heavy metal fractions. It is also used for the generic
process PRECSUL to compute the precipitation and dissolution rates concerning iron sulfide.

DR
AF

9.10

Implementation

Process SPECSUD is fully generic, meaning that it can be applied both to water layers and
sediment layers. However, in case the sediment is modeled as a number of ‘inactive’ substances, the processes SPECSUDS1/2 have to be applied next to SPECSUD. In stead of
using these processes, it is also possible to provide the dissolved sulfide species as model
input
The processes have been implemented for the following substances:

 dissolved sulfide species SUD and SUDS1/2.

Table 9.15 and Table 9.16 provide the definitions of the parameters occurring in the formulations. Table 9.17 provides the output parameters.
Formulation

The hydrolysis of hydrogen sulfide proceeds according to the following reaction equations:

H2 S + H2 O
HS − + H2 O

⇔
⇔

HS − + H3 O+
S 2− + H3 O+

The chemical equilibria are described with:

Csd2 × H +
Csd1
Csd3 × H +
Ks2 =
Csd2
Csdt = Csd1 + Csd2 + Csd3
Ks1 =

(9.4)
(9.5)
(9.6)

with:

Csd1
Csd2
288 of 464

concentration of dissolved hydrogen sulfide [mol l−1 ]
concentration of hydrogen sulfide anion [mol l−1 ]

Deltares

Inorganic substances and pH

Csd3
Csdt
H+
Ks1
Ks2

concentration of free dissolved sulfide [mole l−1 ]
concentration of total dissolved sulfide [mol l−1 ]
proton concentration [mol l−1 ]
acidity (dissociation, equilibrium) constant for H2 S [mol l−1 ]
acidity (dissociation, equilibrium) constant for HS− [mol l−1 ]

The proton concentration H + and the temperature dependent equilibrium constants follow
from:

H + = 10−pH
Ks1 = 10−lK11 × kth2s(T −20)
Ks2 = 10−lKs2 × kths(T −20)
temperature coefficient for HS−1 equilibrium [-]
temperature coefficient for H2 S equilibrium [-]
acidity [-]
temperature [◦ C]

DR
AF

kths
kth2s
pH
T

T

where:

The concentration of the relevant sulfide species in solution can now be calculated from:

Csdt =

Csud
32 000 × φ

Csd1 =

/H +

Csdt
+ (Ks1 × Ks2 )/(H + )2 )

(1 + Ks1
Ks1 × Csd1
Csd2 =
H+
Csd3 = Csdt − Csd1 − Csd2

if due to round off the resulting Csd3 ≤ 0.0

Csd3 =

Ks2 × Csd2
H+

where:

Csud
φ

concentration of total dissolved sulfide [gS m−3 ]
b

porosity [-]

The constant 32 000.0 concerns the conversion from gS m−3 to mol l−1 .
The pertinent fractions follow from:

Csd1
Csdt
Csd2
f s2 =
Csdt
f s3 = 1 − f s1 − f s2
f s1 =

if due to rounding off the resulting f s3 = 0.0

f s3 =

Deltares

Csd3
Csdt

289 of 464

Processes Library Description, Technical Reference Manual

 

Directives for use
 The acidity constants for the hydrogen sulfides have to be provided in the input of the
model as logarithmic values ( 10 log)!
 The negative logarithms of the equilibrium constants at 20 ◦ C are:

lKstH2S = −7.1 and lKstHS = −14.0.
An indicative value for total sulfide concentration SU D is 32 mg/l or 10−3 mol l−1 .

 The temperature dependencies are ignored by default temperature coefficients of the acid-

Additional references
Stumm and Morgan (1996)

T

ity constants equal to 1.0. Temperature dependency can be established by modification
of the values of TcKstHS and TcKstH2S.
 Different pH’s and total sulfide concentrations apply to the water column and the various
sediment layers.

Table 9.15: Definitions of the input parameters in the above equations for SPECSUD.

Name in
input

Definition

Csdt
Csud

SUD

concentration of total dissolved sulfide
concentration of total dissolved sulfide

lKs1
lKs2
kth2s
kths
H+
pH
T

ϕ

DR
AF

Name in
formulas

290 of 464

−1

Units

mol l−1
gS.m−3
b

lKstH2S
lKstHS
TcKstH2S
TcKstHS

log acidity constant for H2 S (mol l )
log acidity constant for HS− (mol l−1 )
temperature coefficient for KstH2S
temperature coefficient for KstHS

log(-)
log(-)
-

–
pH

proton concentration
acidity

mol l−1
-

TEMP

ambient temperature

◦

POROS

porosity

m3 w.m−3

C

b

Deltares

Inorganic substances and pH

Table 9.16: Definitions of the input parameters in the above equations for SPECSUDS1/2.

Name in
formulas

Name in
input

Definition

Units

Csdt
Csud

–
SUDS1/2

concentration of total dissolved sulfide
concentration of total dissolved sulfide

mol l−1
gS.m−3
b

−

−1

lKstHS
lKstH2S
TcKstH2S
TcKstHS

log acidity constant for HS (mol l )
log acidity constant for H2 S (mol l−1 )
temperature coefficient for KstH2S
temperature coefficient for KstHS

H+
pH

–
pH

proton concentration
acidity

T

TEMP

ambient temperature (currently not used)

DR
AF

ϕ

PORS1/2

log(-)
log(-)
-

T

lKhs
lKh2 s
kth2s
kths

porosity

mol l−1
◦

C

m3 w.m−3
b

Table 9.17: Definitions of the output parameters of SPECSUD and SPECSUDS1/2.

Name in
formulas

Name in
input

Definition

Units

Csd1
Csd2
Csd3

DisH2SWK
DisHSWK
DisSWK

of dissolved hydrogen sulfide
concentration of hydrogen sulfide anion
concentration of free dissolved sulfide

mol l−1
mol l−1
mol l−1

fs1
fs2
fs3

FrH2Sdis
FrHSdis
FrS2dis

fraction of dissolved hydrogen sulfide
fraction of hydrogen sulfide anion
fraction of free dissolved sulfide

-

Csd1

DisH2SS1

mol l−1

Csd2

DisHSS1

Csd3

DisSS1

concentration of dissolved hydrogen sulfide
in S1
concentration of hydrogen sulfide anion in
S1
concentration of free dissolved sulfide in S1

Csd1

DisH2SS2

mol l−1

Csd2

DisHSS2

Csd3

DisSS2

concentration of dissolved hydrogen sulfide
in S2
concentration of hydrogen sulfide anion in
S2
concentration of free dissolved sulfide in S2

Deltares

mol l−1
mol l−1

mol l−1
mol l−1

291 of 464

Processes Library Description, Technical Reference Manual

Precipitation, dissolution and conversion of iron
PROCESS :

PRIRON

This process considers the precipitation dissolution and conversion of oxidizing and reducing
iron minerals.

T

Particulate oxidizing iron in the model consists of iron(III) oxyhydroxide chemically indicated
with Fe(OH)3 or FeOOH. In the model an amorphous fraction and a crystalline fraction (goethite)
are distinguished respectively substances FeIIIpa and FeIIIpc. The latter fraction reacts much
more slowly due to the additional activation energies needed to add ions to or to detach ions
from its crystal lattice. Due to “aging” the amorphous fraction slowly turns into the crystalline
fraction. The precipitation of Fe3+ adds to the amorphous fraction. Precipitation occurs at
oxidizing conditions when the solution is supersaturated that is when the ion activity product
with regard to OH− overrides the solubility product. Dissolution occurs when the solubility
product overrides the ion activity product usually at reducing conditions (Luff and Moll, 2004;
Wang and Cappellen, 1996; Boudreau, 1996).
Particulate reducing iron in the model consists of rather amorphous iron(II) sulfide rather crystalline pyrite and rather crystalline iron(II) carbonate (siderite) chemically indicated with FeS
FeS2 and FeCO3 . In the model these substances are indicated with Fes FeS2 and FeCO3.
Pyrite reacts much more slowly than iron(II) sulfide due to the additional activation energies
needed to add ions to or to detach ions from its crystal lattice. Siderite is usually also less
reactive than iron(II) sulfide. Precipitation of Fe2+ adds to the FeS whereas FeS2 is formed
from FeS and S. Elementary sulfur is produced at sulfate reduction but is not considered in
the model. For the model it is assumed that FeS reacts with H2 S. Precipitation occurs at
reducing conditions when the solution is supersaturated either with regard to S2− or CO3 2−
that is when the at least one of the ion activity products overrides the pertinent solubility product. Dissolution occurs when the solubility product overrides the ion activity product usually at
oxidizing conditions (Luff and Moll, 2004; Wang and Cappellen, 1996; Boudreau, 1996).

DR
AF

9.11

Iron(II) sulfide and pyrite are thermodynamically unstable at oxidizing conditions. At the presence of dissolved oxygen the sulfide is oxidized into sulfate upon which the dissolved iron(II)
gets oxidized too. The oxidation of the iron(II) in siderite proceeds after dissolution of this
mineral. See process SULPHOX for the oxidation of FeS and FeS2 .
The precipitation of iron(II) sulfide only occurs at the absence of dissolved oxygen which is
usually only the case in reducing sediment just below an oxidizing top layer. However iron(II)
sulfide may also precipitate in the lower part of the water column at lasting stratification.
The precipitation of the iron minerals is not only temperature dependent but also pH dependent. The pH dependency is due to the concentrations of the co-precipitating ions OH− S2−
and CO3 2− are ruled by acid-base equilibria. The pH-dependency with regard to sulfide can
be taken into account via the calculation of the pH dependent concentration of S2− . The pHdependency with regard to carbonate can be taken into account via the calculation of the pH
dependent concentration of CO3 2− .
Implementation
Process PRIRON has been implemented in a generic way meaning that it can be applied both
to water layers and sediment layers. If PRIRON is applied the process PRESUL must not be
used. The precipitation dissolution and conversion of iron in sediment is not considered when
substances in the sediment are modeled as a ‘inactive’ substances (the S1/2 approach).

292 of 464

Deltares

Inorganic substances and pH

The process has been implemented for the following substances:

 FeIIIpa FeIIIpc FeIIId FeS FeS2 FeCO3 FeIId and SUD.

Formulation
Precipitation and dissolution of iron(III)

T

Tables 9.18 and 9.19 provide the definitions of the parameters occurring in the formulations.
The dissolved free iron(III) and iron(II) fractions can be delivered by auxiliary process SPECIRON or imposed on the model as an input parameter. The fraction dissolved free sulfide can
be delivered by auxiliary process SPECSUD or imposed on the model as an input parameter.
The fraction of dissolved free carbonate can be delivered by auxiliary process SPECCARB or
imposed on the model as an input parameter. Either TIC or CO2 must be simulated or imposed for computation of the free carbonate fraction. Option parameter SWTICCO2 indicates
which substance is used.

DR
AF

The precipitation and dissolution equilibrium of amorphous iron(III) oxyhydroxide (FeIIIpa) can
be described with the following simplified reaction equation:
Fe3+ + 3 OH−

⇔

Fe(OH)3

The precipitation and dissolution rates are formulated with approximate kinetics with the difference of the ion activity and solubility products as driving force:


IAP1
−1 ×ϕ
Rpf e3 = kpf e3 ×
Ksp1


IAP1
Rdf e3 = kdf e3 × Cf ea × 1 −
Ksp1
− 3
IAP1 = Cf e3d × (OH )
1
Cf e3d = f f e31 × Cf e3dt ×
56 000 × ϕ
−
−(14−pH)
OH = 10


if IAP 1 ≥ Ksp1
if IAP 1 < Ksp1

Ksp1 = 10lKsp1

Kf e1 = 10lKf e1

kpf e3 = kpf e320 × ktpf e3(T −20)
kdf e3 = kdf e320 × ktdf e3(T −20)

where:

Cf ea
Cf e3dt
Cf e3d
f f e31
IAP 1
Ksp1
kdf e3
kpf e3
ktdf e3
Deltares

particulate amorphous oxidizing iron concentration [gFe.m−3 ]
dissolved oxidizing iron concentration [gFe.m−3 ]

b

b

equilibrium dissolved free iron(III) concentration [mol.l−1 ]
fraction dissolved free iron(III) [-]
ion activity product for Fe(OH)3 [(mol.l−1 )4 ]
solubility product for Fe(OH)3 [(mol.l−1 )4 ]
specific iron(III) dissolution rate [d−1 ]
specific iron(III) precipitation rate [gFe.m−3 .d−1 ]
b

temperature coefficient for iron(III) dissolution [-]

293 of 464

Processes Library Description, Technical Reference Manual

ktpf e3
OH −
pH
Rdf e3
Rpf e3
T
ϕ

temperature coefficient for iron(III) precipitation [-]
hydroxyl concentration [mol.l−1 ]
acidity [-]
rate of amorphous iron(III) dissolution [gFe.m−3 .d−1 ]
b

rate of amorphous iron(III) precipitation [gFe.m−3 .d−1 ]
temperature [◦ C]
porosity [-]

b

The constant of 56 000 concerns the conversion of gFe.m−3 to mol.l−1 .

T

The dissolution process must stop at the depletion of precipitated iron(III). Therefore the dissolution flux is made equal to half the concentration of amorphous precipitated iron(III) Cfea
divided with timestep ∆t when the flux as calculated with the above formulation is larger than
Cfea/∆t.
Aging of iron(III)

DR
AF

The coversion of amorphous iron(III) oxyhydroxide (FeIIIpa) into crystalline iron(III) oxyhydroxide (FeIIIpc) can be described with the following simplified reaction equation:
Fe(OH)3 ⇒ FeOOH + H2 O

The rate of aging is equal to:

Raf e3 = kaf e3 × Cf ea

kaf e3 = kaf e320 × ktaf e3(T −20)
where:

Cf ea
kaf e3
ktaf e3
Raf e3
T

particulate amorphous oxidizing iron concentration [gFe.m−3 ]
specific iron(III) aging rate [d−1 ]
temperature coefficient for iron(III) aging [-]
rate of amorphous iron(III) aging [gFe.m−3 .d−1 ]
temperature [◦ C]

b

b

Precipitation and dissolution of iron(II)

The precipitation of iron(II) minerals in the model includes iron(II) sulfide (FeS) and siderite
(FeCO3 ). The precipitation and dissolution equilibria can be described with the following simplified reaction equations:
Fe2+ + S2− ⇔ FeS

Fe2+ + CO3 2− ⇔ FeCO3
The precipitation and dissolution rates are formulated with approximate kinetics with the difference of the ion activity and solubility products as driving force. The formulations for iron

294 of 464

Deltares

Inorganic substances and pH

sulfide formation are:


IAP2
−1 ×φ
Rpf es = kpf es ×
Ksp2


IAP2
Rdf es = kdf es × Cf es × 1 −
Ksp2
IAP2 = Cf e2d × Csd3
1
Cf e2d = f f e21 × Cf e2dt ×
56 000 × ϕ
1
Csd3 = f s3 × Csdt ×
32 000 × ϕ
lKsp2
Ksp2 = 10


kdf es = kdf es20 × ktdf es(T −20)
where:

iron(II) sulfide concentration [gFe.m−3 ]

DR
AF

Cf es
Cf e2dt
Cf e2d
Csdt
Csd3
f s3
IAP 2
Ksp2
kdf es
kpf es
ktdf es
ktpf es
Rdf es
Rpf es
T
ϕ

if IAP 2 < Ksp2

T

kpf es = kpf es20 × ktpf es(T −20)

if IAP 2 ≥ Ksp2

b

dissolved reducing iron concentration [gFe.m−3 ]
b

equilibrium dissolved free iron(II) concentration [mol.l−1 ]
total dissolved sulfide concentration [gS.m−3 ]
b

dissolved free sulfide concentration [mol.l−l ]
fraction dissolved free sulfide [-]
ion activity product for Fes [mol.l−12 ]
solubility product for Fes [mol.l−12 ]
specific FeS dissolution rate [d−1 ]
specific Fes precipitation rate [gFe.m−3 .d−1 ]
b

temperature coefficient for FeS dissolution [-]
temperature coefficient for FeS precipitation [-]
rate of Fes dissolution [gFe.m−3 .d−1 ]
b

rate of Fes precipitation [gFe.m−3 .d−1 ]
temperature [◦ C]
porosity [-]

b

The constant of 56 000 concerns the conversion of gFe.m−3 to mol.l−1 .

Deltares

295 of 464

Processes Library Description, Technical Reference Manual

The formulations for iron carbonate formation are:


IAP3
−1 ×φ
Rpf eco3 = kpf eco3 ×
Ksp3


IAP3
Rdf eco3 = kdf eco3 × Cf eco3 × 1 −
Ksp3
IAP3 = Cf e2d × Cco3d
1
Cf e2d = f f e21 × Cf e2td ×
56 000 × ϕ
1
Cco3d = f c3 × Ctic ×
12 000 × ϕ
lKsp3
Ksp3 = 10


kdf eco3 = kdf eco320 × ktdf eco3(T −20)
where:

iron(II) carbonate concentration [gFe.m−3 ]

DR
AF

Cf eco3
Cf e2td
Cf e2d
Ctic
Cco3d
f c3
IAP 3
Ksp3
kdf eco3
kpf eco3
ktdf eco3
ktpf eco3
Rdf eco3
Rpf eco3
T
ϕ

if IAP 3 < Ksp3

T

kpf eco3 = kpf eco320 × ktpf eco3(T −20)

if IAP 3 ≥ Ksp3

b

dissolved reducing iron concentration [gFe.m−3 ]
b

equilibrium dissolved free iron(II) concentration [mol.l−1 ]
total dissolved inorganic carbon concentration [gC.m−3 ]
b

total dissolved free carbonate concentration [mol.l−l ]
fraction dissolved free carbonate [-]
ion activity product for FeCO3 [mol.l−12 ]
solubility product for FeCO3 ([mol.l−12 ])
specific FeCO3 dissolution rate [d−1 ]
specific FeCO3 precipitation rate [gFe.m−3 .d−1 ]
b

temperature coefficient for FeCO3 dissolution [-]
temperature coefficient for FeCO3 precipitation [-]
rate of FeCO3 dissolution [gFe.m−3 .d−1 ]
b

rate of FeCO3 precipitation [gFe.m−3 .d−1 ]
temperature [◦ C]
porosity [-]

b

The constant of 12 000 concerns the conversion of gC.m−3 to mol.l−1 .

The dissolution process must stop at the depletion of precipitated FeS or FeCO3 . Therefore
the dissolution fluxes are made equal to half the concentration of mineral concerned Cfes or
Cfeco3 divided with timestep ∆t when the flux as calculated with the above formulation is
larger than Cfes/∆t or Cfeco3/∆t.
The total inorganic carbonate concentration is derived from TIC when SWTICCO2 = 0.0 (default) or from CO2*12/44 when SWTICCO2 = 1.0.
Formation of pyrite
The formation of pyrite (FeS2) can be described with the following simplified reaction equations:
FeS + S ⇒ FeS2

296 of 464

Deltares

Inorganic substances and pH

or
FeS + H2 S ⇒ FeS2 + H2
Nor elemental sulfide nor elemental hydrogen is included in the model consequently the electrons transferred cannot be accounted for. Pragmatically the formation rate is formulated as
follows:

Rpyr = kpyr × Cf es × f s1 × Csdt/ϕ
kpyr = kpyr20 × ktpyr(T −20)
where:
iron(II) sulfide concentration [gFe.m−3 ]
b

T

total dissolved sulfide concentration [gS.m−3 ]
b

fraction dissolved hydrogen sulfide [-]
specific pyrite formation rate (gS−1 .m3 .d−1 )
temperature coefficient for iron(III) aging [-]
rate of pyrite formation [gFe.m−3 .d−1 ]
temperature [◦ C]
porosity [-]

b

DR
AF

Cf es
Csdt
f s1
kpyr
ktpyr
Rpyr
T
ϕ

Directives for use
 The fractions dissolved free iron(II) and iron(III) FrFe2dis and FrFe2dis can be calculated
with process SPECIRON using an imposed or simulated total dissolved iron(II) and iron(III)
concentrations.
 The fraction dissolved free sulfide FrS2dis can be calculated with process SPECSUD
using an imposed or simulated total dissolved sulfide concentration.
 The fraction dissolved free carbonate FrCO3dis can be calculated with process SPECCARB using an imposed or simulated total carbonate concentration. This may be TIC or
CO2. The model will choose the substance according to option parameter SWTICCO2
(0.0 = use TIC; 1.0 = use CO2).
 As a start the precipitation and dissolution reaction rates of a mineral can be given the
same value.
 The solubility products have to be provided in the input of the model as logarithmic values
( 10 log )!!!
 The logarithms of the solubility products at 25 ◦ C and I=0.0 are:
lKspFeOH3 = -38.7 lKspFeS = -18.1 and lKspFeCO3 = -10.7 .
 The temperature dependency of the solubilities is ignored in the model but can be taken
into account by modification of the default solubility products as constants or as time series.
References
DiToro (2001),
Stumm and Morgan (1996),
Wang and Cappellen (1996),
WL | Delft Hydraulics (2002),
Wijsman et al. (2001)

Deltares

297 of 464

Processes Library Description, Technical Reference Manual

Table 9.18: Definitions of the parameters in the above equations for PRIRON concerning
oxidizing iron. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in
Input

Definition

Units

Cfea

FeIIIpa

particulate amorphous oxidizing iron
concentration
dissolved oxidizing iron concentration

gFe.m−3

equilibrium dissolved free iron(III) concentration
fraction dissolved free iron(III)

mol.l−l

b

gFe.m−3

Cfe3dt

FeIIId

Cfe3d

–

ffe31

FrFe3dis

IAP1
lKsp1

–
lKspFeOH3

ion activity product for Fe(OH)3
log solubility product for Fe(OH)3
[mol.l−14 ]

mol.l−14
log(-)

kafe320
kdfe320
kpfe320

RcAgFe320
RcDisFe320
RcPrcFe320

specific iron(III) aging rate at 20 ◦ C
specific iron(III) dissolution rate at 20 ◦ C
specific iron(III) precipitation rate at 20
◦
C
temperature coefficient for iron(III) aging
temperature coefficient for iron(III) dissolution
temperature coefficient for iron(III) precipitation

d−1
d−1
gFe.m−3 .d−1

–
pH

hydroxyl concentration
acidity

mol.l−1
-

–

rate of amorphous iron(III) aging

gFe.m−3 .d−1

–

rate of amorphous iron(III) dissolution

gFe.m−3 .d−1

–

rate of amorphous iron(III) precipitation

gFe.m−3 .d−1

Temp

temperature

◦

Delt

timestep

d

POROS

porosity

m3 .m−3

ktpfe3
OH−
pH
Rafe3
Rdfe3
Rpfe3
T

∆t
ϕ

DR
AF

ktafe3
ktdfe3

T

b

TcAgFe3
TcDisFe3

TcPrcFe3

b

-

b

b

b

C

w

b

Table 9.19: Definitions of the parameters in the above equations for PRIRON concerning
reducing iron. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in
Input

Definition

Units

Cfes

FeS

iron(II) sulfide concentration

gFe.m−3

Cfe2dt

FeIId

total dissolved reducing iron concentration
equilibrium dissolved free iron(II) concentration
fraction dissolved free iron(II)

gFe.m−3

b

Cfe2d

–

ffe21

FrFe2dis

298 of 464

b

mol.l−l
−

Deltares

Inorganic substances and pH

Table 9.19: Definitions of the parameters in the above equations for PRIRON concerning
reducing iron. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas
Csdt

Name in
Input
SUD

Definition

Units

total dissolved sulfide concentration

gS.m−3

Csd3
fs1
fs3
Cfeco3

–
FrH2Sdis
FrS2dis
FeCO3

dissolved free sulfide concentration
fraction dissolved hydrogen sulfide
fraction dissolved free sulfide
iron(II) carbonate concentration

mol.l−l
gFe.m−3

Ctic

TIC or CO2

gC.m−3

b

b

Cco3d

–

total dissolved inorganic carbon concentration
total dissolved sulfide concentration

fc3

FrCO3dis

fraction dissolved free carbonate

mol.l−l

IAP2
lKsp2
IAP3
Ksp3

–
lKspFeS
–
lKspFeCO3

ion activity product for FeS
log solubility product for FeS [mol.l−12 ]
ion activity product for FeCO3
log solubility product for FeCO3
[mol.l−12 ]

[mol.l−12 ]
log(-)
[mol.l−12 ]
log(-)

kpyr20
kdfes20

RcPyrite20
RcDisFeS20

gS−1 .m3 .d−1
d−1

kpfes20

RcPrcFeS20

specific pyrite formation rate at 20 ◦ C
specific iron(II) sulfide dissolution rate at
20 ◦ C
specific iron(II) sulfide precipitation rate
at 20 ◦ C
specific iron(II) carbonate dissolution
rate at 20 ◦ C
specific iron(II) carbonate precipitation
rate at 20 ◦ C
temperature coefficient for pyrite formation
temperature coefficient for iron(II) sulfide
diss.
temperature coefficient for iron(II) sulfide
prec.
temperature coefficient for iron(II) carbonate diss.
temperature coefficient for iron(II) carbonate prec.

RcDisFeC20

kpfeco320

RcPrcFeC20

gCO2 .m−3
b

T

DR
AF

kdfeco320

b

gFe.m−3 .d−1
b

d−1
gFe.m−3 .d−1
b

ktpyr

TcPyrite

-

ktdfes

TcDisFeS

ktpfes

TcPrcFeS

ktdfeco3

TcDisFeCO3

ktpfeco3

TcPrcFeCO3

Rpyr

–

rate of pyrite formation

gFe.m−3 .d−1

Rdfes

–

rate of iron(II) sulfide dissolution

gFe.m−3 .d−1

Rpfes

–

rate of iron(II) sulfide precipitation

gFe.m−3 .d−1

Rdfeco3

–

rate of iron(II) carbonate dissolution

gFe.m−3 .d−1

Rpfeco3

–

rate of iron(II) carbonate precipitation

gFe.m−3 .d−1

-

b

b

b

b

b

SWTICCO2 SWTICCO2

option parameter (0.0 = use TIC; 1.0 =
use CO2)

-

T

temperature

◦

Deltares

Temp

C

299 of 464

Processes Library Description, Technical Reference Manual

Table 9.19: Definitions of the parameters in the above equations for PRIRON concerning
reducing iron. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in
Input

Definition

Units

∆t

Delt

timestep

d

ϕ

POROS

porosity

m3 .m−3
w

DR
AF

T

b

300 of 464

Deltares

Inorganic substances and pH

Reduction of iron by sulfides
PROCESS :

IRONRED

Particulate oxidizing iron in the model consists of iron(III) oxyhydroxide, chemically indicated
with Fe(OH)3 or FeOOH. Particulate oxidizing iron can be reduced abiotically by dissolved sulfides and particulate iron sulfides (Luff and Moll, 2004; Wang and Cappellen, 1996; Boudreau,
1996). The latter reaction is very slow compared to the former reaction. Both reactions produce reducing iron Fe2+ and sulfate. See process CONSELAC for the biotic reduction of
iron.

T

For particulate oxidizing iron two fractions are distinguished in the model, an amorphous fraction and a crystalline fraction (goethite). The amorphous reactive fraction is indicated as
substance FeIIIpa. The less reactive crystalline fraction is indicated as substance FeIIIpc.
The latter fraction reacts much more slowly due to the additional activation energy needed to
detach ions from its crystal lattice.
Implementation

DR
AF

9.12

Process IRONRED has been implemented in a generic way, meaning that it can be applied
both to water layers and sediment layers. It covers all simulated abiotic particulate oxidizing
iron reduction processes and has been implemented for the following substances:

 FeIIIpa, FeIIIpc, FeS, FeIId, SUD and SO4

The reducing iron produced is added to FeIId, the sulfate produced is added to SO4. Table I
provides the definitions of the parameters occurring in the formulations.
Formulation

The following reduction reactions are included in the model:
H2 S + 8 Fe(OH)3 ⇒ 8 Fe2+ + SO4 2− + 6 H2 O + 14 OH−
FeS + 8 Fe(OH)3 ⇒ 9 Fe2+ + SO4 2− + 4 H2 O + 16 OH−

The reduction of iron oxyhydroxide requires 0.0714 gS.gFe−1 in the cases of H2 S and FeS,
and 0.125 gFe.gFe−1 in the case of FeS.
The reduction reactions are formulated according to double first-order kinetics:



Rire1 =
Rire2 =
Rire3 =
Rire4 =


f s1 × Csdt
kire1 × Cf ea ×
×ϕ
ϕ


f s1 × Csdt
kire2 × Cf ec ×
×ϕ
ϕ
kire3 × Cf es × Cf ea
kire4 × Cf es × Cf ec

where:

Cf es
Cf ea

particulate iron sulfide concentration [gFe.m−3 ]
b

particulate amorphous oxidizing iron concentration [gFe.m−3 ]
b

Deltares

301 of 464

Processes Library Description, Technical Reference Manual

particulate crystalline oxidizing iron concentration [gFe.m−3 ]

Cf ec
Csdt
f s1
kire1
kire2
kire3
kire4
Rire1
Rire2
Rire3
Rire4
ϕ

b

total dissolved sulfide [gS.m−3 ]
b

fraction hydrogen sulfide [-]
specific rate of amorphous iron reduction with H2 S [1/(gS.m−3 .d)]
specific rate of crystalline iron reduction with H2 S [1/(gS.m−3 .d)]
specific rate of amorphous iron reduction with FeS [1/(gFe.m−3 .d)]
specific rate of crystalline iron reduction with FeS [1/(gFe.m−3 .d)]
rate of amorphous iron reduction with H2 S [gFe.m−3 .d−1 ]
rate of crystalline iron reduction with H2 S [gFe.m−3 .d−1 ]
rate of amorphous iron reduction with FeS [gFe.m−3 .d]
rate of crystalline iron reduction with FeS [gFe.m−3 .d]
porosity [-]

T

Notice that the porosity occurs two times in some of the rate equations, whereas it does not
affect the rates. However, a systematic formulation is preferred in order to make clear how the
porosity affects kinetics.
The specific reduction rates are temperature dependent according to:

where:

DR
AF

(T −20)
kirei = kire20
i × ktire

kirei 20
ktire
T

specific rate of abiotic particulate iron reduction i at 20 ◦ C [1/(gS.m−3 .d)]
temperature coefficient for abiotic particulate iron reduction [-]
temperature [◦ C]

The reduction process must stop at the depletion of particulate oxidizing iron or hydrogen
sulfide or particulate iron sulfide. Therefore, each of the reduction fluxes is made equal to half
the concentration of amorphous oxidizing iron or crystalline oxidizing iron or hydrogen sulfide
or iron sulfide divided with timestep ∆t, when a flux as calculated with the above formulations
is larger.
Directives for use
 The specific rates for the reduction of amorphous oxidizing iron should have much higher
value than the specific rates for the oxidation of crystalline oxidizing iron.
 The specific rates of reduction with H2 S should be higher than the specific rates of reduction with FeS.
References

Boudreau (1996),
DiToro (2001),
Luff and Moll (2004),
Soetaert et al. (1996),
Wang and Cappellen (1996)

Table 9.20: Definitions of the parameters in the above equations for IRONRED. Volume
units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in
Input

Definition

Units

Cfes

FeS

particulate iron sulfide concentration

gFe.m−3
b

302 of 464

Deltares

Inorganic substances and pH

Table 9.20: Definitions of the parameters in the above equations for IRONRED. Volume
units refer to bulk ( ) or to water ( ).
b

Name in
formulas
Cfea
Cfec
Csdt

Name in
Input
FeIIIpa
FeIIIpc
SUD

w

Definition

Units

particulate amorphous oxidizing iron
concentration
particulate crystalline oxidizing iron concentration
total dissolved sulfide concentration

gFe.m−3
b

gFe.m−3
b

gS.m−3
b

fs1

FrH2Sdis

fraction dissolved hydrogen sulfide (H2 S)

-

kire1 20

RcFeaH2S20

gS−1 .m3 .d−1

kire2 20

RcFecH2S20

kire3 20

RcFeaFeS20

spec. rate of amorphous iron red. with
H2 S at 20 ◦ C
spec. rate of crystalline iron red. with
H2 S at 20 ◦ C
spec. rate of amorphous iron red. with
FeS at 20 ◦ C
spec. rate of crystalline iron red. with
FeS at 20 ◦ C
temperature coeff. for abiotic iron reduction at 20 ◦ C

rate of amorphous iron reduction with
H2 S
rate of crystalline iron reduction with H2 S

gFe.m−3 .d−1

rate of amorphous iron reduction with
FeS
rate of crystalline iron reduction with FeS

gFe.m−3 .d−1

RcFecFeS20

ktire

TcFeRed

Rire1

-

Rire2

-

Rire3

-

Rire4
T

∆t
ϕ

T

DR
AF

kire4 20

Deltares

-

w

gS−1 .m3 .d−1
w

gFe−1 .m3 .d−1
w

gFe−1 .m3 .d−1
w

-

b

gFe.m−3 .d−1
b

b

gFe.m−3 .d−1
b

Temp

temperature

◦

Delt

timestep

d

POROS

porosity

m3 .m−3

C

w

b

303 of 464

Processes Library Description, Technical Reference Manual

Oxidation of iron sulfides
PROCESS :

S ULPH OX

Particulate components FeS and FeS2 are oxidized chemically as well as by microbs using
dissolved oxygen (Luff and Moll (2004), Wang and Cappellen (1996), Wijsman et al. (2001),
Boudreau (1996)). The oxidation of iron sulfides proceeds in two steps. First the sulfide part
is oxidized into sulfate. Secondly, the iron released as Fe2+ is oxidized. The latter process is
taken care of in process IRONOX.
The particulate component FeCO3 is assumed not to be oxidized directly. The iron in this
component is oxidized after dissolution.

T

The oxidation of dissolved sulfide is taken care of in process OXIDSUD.
Implementation

Process SULPHOX has been implemented in a generic way, meaning that it can be applied
both to water layers and sediment layers. It covers all simulated iron sulfide oxidation processes and has been implemented for the following substances:

DR
AF

9.13

 place FeS, FeS2, FeIId, OXY and SO4

The iron from FeS and FeS2 is added to the dissolved reducing iron FeIId. The oxygen consumed is removed from the model as water, which is not simulated. The sulfide oxidized is
added to sulfate. Table I provides the definitions of the parameters occurring in the formulations.
Formulation

The following oxidation reactions are included in the model:
FeS + 2 O2 ⇒ Fe2+ + SO4 2−

2 FeS2 + 7 O2 + 4 OH− ⇒ 2 Fe2+ + 4 SO4 2− + 2 H2 O

The oxidation of iron sulfide requires 1.143 gO2 .gFe−1 or 2.0 gO2 .gS−1 . The oxidation of
pyrite requires 2.0 gO2 .gFe−1 or 1.75 gO2 .gS−1 .
The oxidation reactions are formulated according to double first-order kinetics:


Cox
Rsox1 = ksox1 × Cf es ×
×ϕ
ϕ


Cox
Rsox2 = ksox2 × Cf es2 ×
×ϕ
ϕ


where:

Cf es
Cf es2
Cox
ksox1
304 of 464

iron sulfide concentration [gFe.m−3 ]
pyrite concentration [gFe.m−3 ]

b

b

dissolved oxygen concentration [gO2 .m−3 ]
b

specific rate of iron sulfide oxidation [1/(gO2 .m−3 .d)]

Deltares

Inorganic substances and pH

ksox1
Rsox2
Rsox2
ϕ

specific rate of pyrite oxidation [1/(gO2 .m−3 .d)]
rate of iron sulfide oxidation [gFe.m−3 .d−1 ]
rate of pyrite oxidation [gFe.m−3 .d−1 ]
porosity [-]

Notice that the porosity occurs two times in the rate equation, whereas it does not affect the
rate. However, a systematic formulation is preferred in order to make clear how the porosity
affects kinetics.
The specific oxidation rates are temperature dependent according to:
(T −20)
ksoxi = ksox20
i × ktsox
ksoxi = 0.0

if Cox ≤ 0.0

specific rate of iron sulfide or pyrite oxidation at 20 ◦ C [1/(gO2 .m−3 .d)]
temperature coefficient for iron sulfide oxidation [-]
temperature [◦ C]

DR
AF

ksoxi 20
ktsox
T

T

where:

The oxidation process must stop at the depletion of iron sulfide. Therefore, each of the oxidation fluxes is made equal to half the concentration of the iron sulfide concerned divided with
timestep ∆t, when this flux as calculated with the above formulations is larger than CfeS /∆t
or CfeS2 /∆t.
Directives for use
 The specific rate for the oxidation of pyrite should have a much lower value than the
specific rate for the oxidation of iron sulfide.
References

Boudreau (1996)
DiToro (2001)
Luff and Moll (2004)
Santschi et al. (1990)
Soetaert et al. (1996)
Wang and Cappellen (1996)
WL | Delft Hydraulics (2002)
Wijsman et al. (2001)

Table 9.21: Definitions of the parameters in the above equations for SULPHOX. Volume
units refer to bulk ( ) or to water ( )
b

w

Name in
formulas

Name in
Input

Definition

Units

Cfes

FeS

particulate iron sulfide concentration

gFe.m−3

Cfes2

FeS2

pyrite concentration

gFe.m−3

Cox

OXY

dissolved oxygen concentration

gO2 .m−3

b

b

b

ksox1 20

RcFeSox20

ksox2 20

RcFeS2ox20

Deltares

specific rate of iron sulfide oxidation at
20 ◦ C
specific rate of pyrite oxidation at 20 ◦ C

gO2 −1 .m3 .d−1
w

gO2 −1 .m3 .d−1
w

305 of 464

Processes Library Description, Technical Reference Manual

Table 9.21: Definitions of the parameters in the above equations for SULPHOX. Volume
units refer to bulk ( ) or to water ( )
b

w

Name in
formulas
ktsox

Name in
Input
TcFeSox

Definition

Units

temperature coefficient for iron sulfide
oxidation

-

Rioo1

–

rate of iron sulfide oxidation

gFe.m−3 .d−1

Rioo2

–

rate of pyrite oxidation

gFe.m−3 .d−1

b

b

T

Temp

temperature

◦

∆t

Delt

timestep

d

ϕ

POROS

porosity

T

C

m3 .m−3
w

DR
AF

b

306 of 464

Deltares

Inorganic substances and pH

Oxidation of dissolved iron
PROCESS :

IRONOX

The oxidation of reducing iron components can be abiotic as well as biotic. The dissolved
species Fe2+ , Fe(OH)+ and Fe(OH)2 are primarily oxidized by dissolved oxygen and nitrate
in abiotic chemical processes. Although all three oxidation processes can be described with
the same kinetics, the oxidation rate constants are different (Luff and Moll, 2004; Wang and
Cappellen, 1996; Wijsman et al., 2001; Boudreau, 1996).

Implementation

T

Particulate components FeS and FeS2 are oxidized chemically as well as by microbs using
dissolved oxygen. The oxidation of iron sulfides proceeds in two steps. First the sulfide part
is oxidized into sulfate, which is a separate process and is described for process SULPHOX.
Secondly, the iron released as Fe2+ is oxidized. The particulate component FeCO3 is assumed not to be oxidized directly. The iron in this component is only oxidized after dissolution.

Process IRONOX has been implemented in a generic way, meaning that it can be applied
both to water layers and sediment layers. It covers all simulated iron oxidation processes and
has been implemented for the following substances:

DR
AF

9.14

 FeIId, FeIIId, OXY and NO3

The dissolved reducing iron FeIId oxidized is added to the dissolved oxidizing iron FeIIId. The
dissolved iron fractions can be provided by auxiliary process SPECIRON or imposed on the
model as input parameters. The oxygen and nitrate consumed are removed from the model
as water and elementary nitrogen, which are not simulated. Table I provides the definitions of
the parameters occurring in the formulations.
Formulation

The following oxidation reactions are included in the model:
4 Fe2+ + O2 + 4 H+ ⇒ 4 Fe3+ + 2 H2 O

4 Fe(OH)+ + O2 + 4 H+ ⇒ 4 Fe3+ + 2 H2 O + OH−

4 Fe(OH)2 + O2 + 4 H+ ⇒ 4 Fe3+ + 2 H2 O + 2 OH−

10 Fe2+ + 2 NO3 − + 12 H+ ⇒ 10 Fe3+ + N2 + 6 H2 O

10 Fe(OH)+ + 2 NO3 − + 12 H+ ⇒ 10 Fe3+ + N2 + 6 H2 O + 10 OH−
10 Fe(OH)2 + 2 NO3 − + 12 H+ ⇒ 10 Fe3+ + N2 + 6 H2 O + 20 OH−
The processes require 0.143 gO2 .gFe−1 or 0.05 gN.gFe−1 .

Deltares

307 of 464

Processes Library Description, Technical Reference Manual

The oxidation reactions are formulated according to double first-order kinetics:

 

Cox
Cf eIId
×
×ϕ
Rioo = (kioo1 × f f e1 + kioo2 × f f e2 + kioo3 × f f e3 ) ×
ϕ
ϕ

 

Cf eIId
Cni
Rion = (kion1 × f f e1 + kion2 × f f e2 + kion3 × f f e3 ) ×
×
×ϕ
ϕ
ϕ


where:
total dissolved reducing iron concentration [gFe.m−3 ]
dissolved oxygen concentration [gO2 .m−3 ]
nitrate concentration [gN.m−3 ]

b

b

b

T

fraction Fe2+ (i=1), Fe(OH)+ (i=2) or Fe(OH)2 (i=3) in FeIId [-]
specific rate of iron i oxidation with dissolved oxygen [1/(gO2 .m−3 .d)]
specific rate of iron i oxidation with nitrate [1/(gN.m−3 .d)]
total rate of iron oxidation with oxygen [gFe.m−3 .d−1 ]
total rate of iron oxidation with nitrate [gFe.m−3 .d−1 ]
porosity [-]

DR
AF

Cf eIId
Cox
Cni
f f ei
kiooi
kioni
Rioo
Rion
ϕ

Notice that the porosity occurs three times in the rate equation, whereas only once would
suffice. However, a systematic formulation is preferred in order to make clear how the porosity
affects kinetics.
The specific oxidation rates are temperature dependent according to:
(T −20)
kiooi = kioo20
i × ktiox
kiooi = 0.0
if Cox ≤ 0.0

(T −20)
kioni = kion20
i × ktiox
kioni = 0.0
if Cox ≤ 0.0

where:

kiooi 20
kioni 20
ktiox
T

specific rate of iron i oxidation with oxygen at 20 ◦ C [1/(gO2 .m−3 .d)]
specific rate of iron i oxidation with nitrate at 20 ◦ C [1/(gO2 .m−3 .d)]
temperature coefficient for iron oxidation [-]
temperature [◦ C]

The oxidation process must stop at the depletion of dissolved iron. Therefore, the total oxidation flux (Rioo+Rion) is made equal to half the concentration of dissolved iron divided with
timestep ∆t, when the flux as calculated with the above formulations is larger than FeIId/∆t.
Directives for use
 The specific rates for the oxidation of iron species with oxygen can be given the same
average value.
 The specific rates for the oxidation of iron species with nitrate can be given the same
average value.
References
Boudreau (1996),
DiToro (2001),
Santschi et al. (1990),
Soetaert et al. (1996),

308 of 464

Deltares

Inorganic substances and pH

Wang and Cappellen (1996),
WL | Delft Hydraulics (2002),
Wijsman et al. (2001)
Table 9.22: Definitions of the parameters in the above equations for IRONOX. Volume
units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in
Input

Definition

Units

CfeIId

FeIId

dissolved reducing iron concentration

gFe.m−3

Cox

OXY

dissolved oxygen concentration

gO2 .m−3

Cni

NO3

nitrate concentration

gN.m−3

b

b

b

FrFe2dis
FrFe2OHd
FrFe2OH2d

fraction of Fe2+ in FeIId
fraction of FeOH+ in FeIId
fraction of Fe(OH)2 in FeIId

-

kioo1 20

RcI1oxox20

specific rate of Fe2+ oxidation with oxygen at 20 ◦ C
specific rate of FeOH+ oxid. with oxygen
at 20 ◦ C
specific rate of Fe(OH)2 oxid. with oxygen at 20 ◦ C
specific rate of Fe2+ oxidation with nitrate at 20 ◦ C
specific rate of FeOH+ oxidation with nitrate at 20 ◦ C
specific rate of Fe(OH)2 oxid. with nitrate
at 20 ◦ C
temperature coefficient for iron oxidation

gO2 −1 .m3 .d−1

rate of iron oxidation with dissolved oxygen
rate of iron oxidation with nitrate

gFe.m−3 .d−1

DR
AF

kioo2 20

RcI2oxox20

kioo3 20

RcI3oxox20

kion1 20

RcI1oxni20

kion2 20

RcI2oxni20

kion3 20

RcI3oxni20

ktiox

TcIox

Rioo

-

Rion
T

∆t
ϕ

T

ffe1
ffe2
ffe3

Deltares

-

w

gO2 −1 .m3 .d−1
w

gO2 −1 .m3 .d−1
w

gN−1 .m3 .d−1
w

gN−1 .m3 .d−1
w

gN−1 .m3 .d−1
w

b

gFe.m−3 .d−1
b

Temp

temperature

◦

Delt

timestep

d

POROS

porosity

m3 .m−3

C

w

b

309 of 464

Processes Library Description, Technical Reference Manual

Speciation of dissolved iron
PROCESS :

SPECIRON

Iron ions in solution associate with numerous anions, but under oxidizing conditions the dominant ligand is the hydroxyl ion. Under reducing conditions the sulfide ion may play a role too.
Dissolved organic matter may be important as a ligand when high concentrations of humic
and fulvic acids are present. In the model we only consider the hydrolysis of dissolved iron as
a useful approximation of the free dissolved iron concentration.

Implementation

T

The computed iron speciation is used in processes PRIRON and IRONOX to calculate precipitation/dissolution rates of iron minerals and oxidation rates of dissolved iron(II).

Process SPECIRON is fully generic, meaning that it can be applied both to water layers and
sediment layers. However, this process cannot be used for speciation in the sediment, when
substances are modeled as a number of ‘inactive’ substances according to the S1/2 approach.
The pH needed as input can be either imposed or simulated with process pH_SIMP.

DR
AF

9.15

The processes have been implemented for the following substances:

 FeIIId and FeIId.

The process calculates equilibrium speciation, not the associated mass fluxes. Table I provides the definitions of the parameters occurring in the formulations. Table II provides the
output parameters.
Formulation
Iron(III)

The hydrolysis of dissolved oxidizing iron proceeds according to the following reaction equations:
Fe3+ + 2 H2 O ⇔ FeOH2+ + H3 O+

Fe3+ + 4 H2 O ⇔ Fe(OH)2 + + 2 H3 O+

The chemical equilibria are described with:

Cf e3d2 × H +
Cf e3d1
Cf e3d3 × (H + )2
Kf e32 =
Cf e3d1
Cf e3dt = (Cf e3d1 + Cf e3d2 + Cf e3d3 ) × 56 000 × ϕ
Kf e31 =

where

Cf e3d1
Cf e3d2
Cf e3d3
Cf e3dt

concentration of free dissolved Fe3+ [mol.l−1 ]
concentration of dissolved FeOH2+ [mol.l−1 ]
concentration of dissolved Fe(OH)2 + [mol.l−1 ]
concentration of total dissolved oxidizing iron [gFe.m−3 ]
b

310 of 464

Deltares

Inorganic substances and pH

H+
Kf e31
Kf e32
ϕ

proton concentration [mol.l−1 ]
stability (equilibrium, hydrolysis) constant for FeOH2+ [mol.l−1 ]
stability (equilibrium, hydrolysis) constant for Fe(OH)2 + [mol.l−1 ]
porosity

The constant 56 000 concerns the conversion from gFe.m−3 to mol.l−1 .
The proton concentration H+ and the temperature dependent stability constants follow from:

H + = 10−pH
(T −20)

Kf e31 = 10lKf e31 × ktf e31

(T −20)

Kf e32 = 10lKf e32 × ktf e32

temperature coefficient for FeOH2+ equilibrium [-]
temperature coefficient for Fe(OH)2 + equilibrium [-]
acidity [-]
temperature [◦ C]

DR
AF

ktf e31
ktf e32
pH
T

T

where

The concentration of the relevant iron(III) species in solution can now be calculated from:

Cf e3dt
1
×
+
+
2
(1 + Kf e31 /H + Kf e32 /(H ) ) 56 000 × φ
Kf e31 × Cf e3d1
Cf e3d2 =
H+
Cf e3dt
− Cf e3d1 − Cf e3d2
Cf e3d3 =
56 000 × ϕ

Cf e3d1 =

if due to rounding off the resulting Cfe3d3 < 0.0

Cf e3d3 =

Kf e32 × Cf e3d1
(H + )2

The pertinent fractions follow from:

Cf e3d1
× 56 000 × ϕ
Cf e3dt
Cf e3d2
f f e32 =
× 56 000 × ϕ
Cf e3dt
f f e33 = 1 − f f e31 − f f e32
f f e31 =

if due to rounding off the resulting ffe3 < 0.0

f f e33 =

Cf e3d3
× 56 000 × ϕ
Cf e3dt

Iron(II)
The hydrolysis of dissolved reducing iron proceeds according to the following reaction equations:
Fe2+ + 2 H2 O ⇔ FeOH+ + H3 O+

Deltares

311 of 464

Processes Library Description, Technical Reference Manual

Fe2+ + 4 H2 O ⇔ Fe(OH)2 + 2 H3 O+
The chemical equilibria are described with:

Cf e2d2 × H +
Kf e21 =
Cf e2d1
Cf e2d3 × (H + )2
Kf e22 =
Cf e2d1
Cf e2dt = (Cf e2d1 + Cf e2d2 + Cf e2d3 ) × 56 000 × ϕ
where

T

concentration of free dissolved Fe2+ [mol.l−1 ]
concentration of dissolved FeOH+ [mol.l−1 ]
concentration of dissolved Fe(OH)2 [mol.l−1 ]
concentration of total dissolved reducing iron [gFe.m−3 ]
b

proton concentration [mol.l−1 ]
stability (equilibrium, hydrolysis) constant for FeOH+ [mol.l−1 ]
stability (equilibrium, hydrolysis) constant for Fe(OH)2 + [mol.l−1 ]
porosity

DR
AF

Cf e2d1
Cf e2d2
Cf e2d3
Cf e2dt
H+
Kf e21
Kf e22
ϕ

The constant 56 000 concerns the conversion from gFe.m−3 to mol.l−1 .

The proton concentration H+ and the temperature dependent stability constants follow from:

H + = 10−pH

(T −20)

Kf e21 = 10lKf e21 × ktf e21

(T −20)

Kf e22 = 10lKf e22 × ktf e22
where

ktf e21
ktf e22
pH
T

temperature coefficient for FeOH+ equilibrium [-]
temperature coefficient for Fe(OH)2 equilibrium [-]
acidity [-]
temperature [◦ C]

The concentration of the relevant iron(II) species in solution can now be calculated from:

1
Cf e2dt
×
+
+
2
(1 + Kf e21 /H + Kf e22 /(H ) ) 56 000 × φ
Kf e21 × Cf e2d1
Cf e2d2 =
H+
Cf e2dt
Cf e3d2 =
− Cf e2d1 − Cf e2d2
56 000 × ϕ
Cf e2d1 =

if due to rounding off the resulting Cfe2d3 = 0.0

Cf e2d3 =

312 of 464

Kf e22 × Cf e2d1
(H + )2

Deltares

Inorganic substances and pH

The pertinent fractions follow from:

Cf e2d1
× 56 000 × ϕ
Cf e2dt
Cf e2d2
f f e22 =
× 56 000 × ϕ
Cf e2dt
f f e23 = 1 − f f e21 − f f e22
f f e21 =

if due to rounding off the resulting ffe2 = 0.0

Cf e2d3
× 56 000 × ϕ
Cf e2dt

T

f f e23 =

DR
AF

Directives for use
 The stability constants have to be provided in the input of the model as logarithmic values
( 10 log )!
 The logarithms of the stability constants at 20 ◦ C are:
lKstFe3OH = -3.05 and lKstFe3OH2 = -6.31.
lKstFe2OH = -9.50 and lKstFe2OH2 = -17.0 (?).
 The temperature dependencies are ignored by default temperature coefficients of the stability constants equal to 1.0. Temperature dependency can be established by modification
of the values of TcKFe2OH and TcKFe2OH2.
 The total dissolved oxidizing iron(III) and dissolved reducing iron(II) concentrations are
dependent on pH. An indicative value of iron(III) for pH = 7 is 5.6 10−4 mg/l or 10−8
mol.l−1 . For pH 8 the concentration is five times lower. An indicative value of iron(II) under
reducing conditions is 56 mg/l or 10−3 mole.l−1 .
 Different pH’s and total dissolved iron concentrations apply to the water column and the
various sediment layers.
References

Stumm and Morgan (1996)

Table 9.23: Definitions of the input parameters in the above equations for SPECIRON.

Name in
formulas

Name in
Input

Definition

Units

Cfe3dt

FeIIId

concentration of total dissolved oxidizing
iron(III)
concentration of total dissolved reducing
iron(II)

gFe.m−3

log stability constant for Fe3OH2+
(l.mol−1 )
log stability constant for Fe3OH2 +
(l.mol−1 )
temperature coefficient for KstFe3OH
temperature coefficient for KstFe3OH2

log(-)

Cfe2dt

FeIId

lKfe31

lKstFe3OH

lKfe32

lKstFe3OH2

ktfe31
ktfe32

TcKFe3OH
TcKFe3OH2

lKfe21

lKstFe2OH

lKfe22

lKstFe2OH2

Deltares

log stability
(l.mol−1 )
log stability
(l.mol−1 )

b

gFe.m−3
b

log(-)
-

constant

for

Fe2OH+

log(-)

constant

for

Fe2OH2

log(-)

313 of 464

Processes Library Description, Technical Reference Manual

Table 9.23: Definitions of the input parameters in the above equations for SPECIRON.

Name in
formulas
ktfe21
ktfe22

Name in
Input
TcKFe2OH
TcKFe2OH2

Definition

Units

temperature coefficient for KstFe2OH
temperature coefficient for KstFe2OH2

-

H+
pH

–
pH

proton concentration
acidity

mol.l−1
-

T

Temp

temperature

◦

ϕ

POROS

porosity

m3 .m−3

C

w

T

b

Table 9.24: Definitions of the output parameters of SPECIRON.

Name in
output

Definition

Units

DR
AF

Name in
formulas
Cfe3d1

DisFe3

Cfe3d2

DisFe3OH

Cfe3d3

DisFe3OH2

ffe31
ffe32
ffe33
Cfe2d1

FrFe3dis
FrFe3OHd
FrFe3OH2d
DisFe2

Cfe2d2

DisFe2OH

Cfe2d3

DisFe2OH2

ffe21
ffe22
ffe23

FrFe2dis
FrFe2OHd
FrFe2OH2d

314 of 464

concentration of free dissolved
iron(III)
concentration
of
dissolved
FeOH2+
concentration
of
dissolved
Fe(OH)2 +
fraction of free dissolved iron(III)
fraction of dissolved FeOH2+
fraction of dissolved Fe(OH)2 +
concentration of free dissolved
iron(II)
concentration
of
dissolved
+
FeOH
concentration
of
dissolved
Fe(OH)2
fraction of free dissolved iron(II)
fraction of dissolved FeOH+
fraction of dissolved Fe(OH)2

mol.l−1
mol.l−1
mol.l−1
mol.l−1
mol.l−1
mol.l−1
-

Deltares

Inorganic substances and pH

Conversion salinity and chloride process
PROCESSES :

SALINCHLOR

Salinity is defined as the total solids content of water that results after all carbonates have
been converted to oxides, all bromide and iodide has been replaced by chloride, and all organic matter has been removed by oxidation. It is usually reported as practical salinity units
(psu) which is equivalent to grams per kilogram and parts per thousand (ppt, ‰). Associated
terms are chlorinity and chlorosity. Chlorinity includes chloride, bromide and iodide, and is
reported as grams Cl per kilogram. Chlorosity is chlorinity multiplied by the water density at
20◦ C, and is assumed to be equal to the chloride concentration (gCl.L−1 ). This concentration can be calculated from salinity and vice versa as described below.

S = 0.03 +

T

The empirical relation between salinity and the chloride concentration (chlorosity) used is:

1.805 × Cl
ρw

The chloride concentration is expressed as gCl.m−3 when density is expressed as kg.m−3 .

DR
AF

9.16

Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

Auxiliary process SALINCHLOR has been implemented in a generic way, meaning that it can
be applied both to water layers and sediment layers. The process does not deliver mass
fluxes.
The process has been implemented for the following substances:

 Salinity and Cl.

If Salinity is simulated the process will generate Cl from it. If Cl is simulated the process will
generate Salinity from it. Table 9.25 provides the definitions of the parameters occurring in
the formulations.
Formulation

The conversion of chloride into salinity follows from (SWSalCl = 0.0):

0.7 × Cl
× rscl − 0.0061 × (T − 4.0)2
1000
rscl × Cl
S = S0 +
ρw

ρw = 1000 +

The conversion of salinity into chloride follows from (SWSalCl = 1.0):

700 × S
× rscl − 0.0061 × (T − 4.0)2
(1000 − S)
(S − S0 ) × ρw
Cl =
rscl
ρw = 1000 +

where:

Deltares

315 of 464

Processes Library Description, Technical Reference Manual

chloride concentration (g.m−3 )
ratio of salinity and chloride in water (g.g −1 )
salinity (g.kg −1 ; psu; ppt; ‰)
minimal salinity at zero Cl (g.kg −1 ; psu; ppt; ‰)
temperature (◦ C)
density of water with dissolved salts (kg.m−3 )

Cl
rscl
S
S0
T
ρw

b

b

References
Greenberg et al. (1980)

T

Directives for use
1 The relations described here are best applicable for marine and brackish water. They may
be very inaccurate when applied to fresh water.
2 Option SWSalCl set to be set at 0.0 when Salinity is simulated, SWSalCl needs to be set
at 1.0 when Cl is simulated (default value = 0.0).

Table 9.25: Definitions of the parameters in the above equations for SALINCHLOR. Volume units refer to bulk ( ) or to water ( ).
w

DR
AF

b

Name in
formulas

Name in
input

Definition

Units

Cl
S
S0

Cl
Salinity
–

chloride concentration
salinity
salinity at zero Cl

g.m−3
g.kg−1
g.kg−1

GtCl

ratio of salinity and chloride in water

g.g−1

SW SalCl

SWSalCl

option parameter for simulated substance

–

T

Temp

temperature

◦

–

density of water with dissolved salt

kg.m−3

rscl

ρw

316 of 464

b

C
b

Deltares

10 Organic micropollutants
Contents
10.1 Partitioning of organic micropollutants . . . . . . . . . . . . . . . . . . . . 318
10.2 Calculation of organic matter . . . . . . . . . . . . . . . . . . . . . . . . . 326
10.3 Dissolution of organic micropollutants . . . . . . . . . . . . . . . . . . . . 328
10.4 Overall degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
10.5 Redox status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
10.6 Volatilisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
10.7 Transport coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
10.8 Settling of micropollutants

. . . . . . . . . . . . . . . . . . . . . . . . . . 347

10.9 Sediment-water exchange of dissolved micropollutants . . . . . . . . . . . 351
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

DR
AF

T

10.10 General contaminants

Deltares

317 of 464

Processes Library Description, Technical Reference Manual

Partitioning of organic micropollutants
PROCESS :

PARTWK_i AND PARTS1/2_i

Partitioning is the process in which a substance is distributed among various dissolved and
adsorbed species. Organic micropollutants adsorb to organic matter components, that is
detritus (POC, dead particulate organic matter), dissolved organic matter (DOC) and phytoplankton (PHYT). The partitioning of micropollutants is usually described as an equilibrium
process by means of a linear partition coefficient, based on amounts of organic carbon. The
partition coefficients for the various organic matter components may be different, although the
coefficient for DOC is usually considered proportional to the coefficient for POC.

T

Slow diffusion in solid matter has been acknowledged to take place after fast equilibrium adsorption or prior to fast equilibrium desorption. Therefore, the sorption flux can be calculated
according to equilibrium partitioning or slow sorption by choosing one of the available options.
The model only actually simulates the total concentration (or the total particulate and total
dissolved concentrations) of a micro-pollutant. The partitioning process delivers the dissolved
and adsorbed species as fractions of the total concentration, as well as the sorption flux.

DR
AF

10.1

Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

Processes PARTWK_(i) are generic and can be used for water and sediment compartments.
For the S1/2 option for the sediment processes PARTS1_(i) and PARTS2_(i) can be used.
The substances in the sediment are modeled as ’inactive’ substances. Whereas PARTWK_(i)
needs concentrations (g m−3 ) as input, PARTS1_(i) and PARTS2_(i) require total quantities
per sediment layer (g) as input with only one exception (DOC in g m−3 ). The formulations
are identical for PARTWK_(i) and PARTS1/2_(i) with two exceptions:
w

 the correction of DOC for porosity is not carried out in PARTWK; and
 PARTS1/2 carries out a conversion from concentration units into quantity units and vice
versa, and therefore needs the input of layer thickness and surface area.
The processes have been implemented for the following substances:











OMP, unspecified organic micropollutant
HCH, lindane or hexachlorohexane
HCB, hexachlorobenzene
153, polychlorinated biphenyl (or PCB) 153
BaP, benzo[a]pyrene
Flu, fluoranthene
Diu, diuron
Atr, atrazine
Mef, mefinphos

OMP can be any micro-pollutant. The default values of the input parameters for OMP should
be replaced by values suitable for the particular compound. For instance, PCB52 can be
simulated as OMP (but also as PCB153) by replacing the values of the input parameters by
those for PCB52.

318 of 464

Deltares

Organic micropollutants

The above substance names concern the situation, where equilibrium partitioning is simulated. The simulation of slow sorption requires the use of two simulated substances for each
micro-pollutant in stead of the one simulated substance (total concentration). The names of
these substances are OMP(or other name)-dis and OMP-par. OMP-dis is the total dissolved
concentration, the sum of free dissolved and DOC-adsorbed micro-pollutant. OMP-par is the
total particulate micro-pollutant concentration.
The process formulations are the same for all substances, but default values for properties
are substance specific. The organic micro-pollutants belong to the group 4 substances. The
input parameter OM P Group identifies the group to which a substance belongs, in order
to distinguish them from other groups of substances such as heavy metals, for which other
partitioning formulations are used.

T

The concentrations of detritus (Cpoc), dissolved organic matter (Cdoc) and phytoplankton
(Calg ) can either be calculated by the model or be imposed on the model via its input. In
case of the former Cpoc is generated by processes COMPOS, S1_COMP and S2_COMP.
Calg is generated by processes PHY_BLO (BLOOM) or PHY_DYN (DYNAMO), S1_COMP
and S2_COMP.

DR
AF

Tables 10.1 and 10.2 provide the definitions of the input parameters occurring in the formulations. Tables 10.3 and 10.4 contain the definitions of the output parameters.
Formulation

The fractions of the dissolved and adsorbed species add up to one. Consequently these
fractions as resulting from equilibrium are computed with:

f df =

φ+

Kppoc0

φ
× (Cpoc + Xdoc × Cdoc) + Kpalg 0 × Calg

f doc = (1 − f df ) ×

Kppoc0 × Xdoc × Cdoc
Kppoc0 × (Cpoc + Xdoc × Cdoc) + Kpalg 0 × Calg

Kppoc0 × Cpoc
f poc = (1 − f df ) ×
Kppoc0 × (Cpoc + Xdoc × Cdoc) + Kpalg 0 × Calg
f alg = (1 − f df − f doc − f poc)

where:

Calg/poc/doc

concentration of algae biomass, dead particulate organic matter matter, and dissolved organic matter [gC m−3 ]
fraction of a micropollutant adsorbed to algae, dissolved organic matter, dead particulate organic matter [-]
freely dissolved fraction of a micropollutant [-]
partition coefficient for algae and dead particulate organic matter
[m3 gC−1 ]
adsorption efficiency of DOC relative to POC [-]
porosity ([m3 m−3 ]; equal to 1.0 for the water column)
b

f alg/poc/doc
f df
Kpalg/poc0

w

Xdoc
φ

w

b

For PARTS1_(i) and PARTS2_(i), Cdoc is corrected for porosity considering the fact that
DOC input only in this case is specified as concentrations in pore water:

Cdoc = DOC × φ

Deltares

319 of 464

Processes Library Description, Technical Reference Manual

All substance quantities in the above partitioning equations are converted in case of PARTS1/2
into bulk concentrations by dividing with the volume of the layer (V = Z · A).
The partition coefficients in the above equations expressed in [m3 .gC−1 ] are derived from
the input parameters expressed in [ 10 log(l.kgC−1 )], corrected for temperature:
w

1
1
−
)
(T + 273.15) 293.15
1
1
logKpalg = logKpalg 20 + a × (
−
)
(T + 273.15) 293.15
Kppoc0 = 10logKppoc × 10−6

logKppoc = logKppoc20 + a × (

Kpalg 0 = 10logKpalg × 10−6

a
Kpalg/poc20

temperature coefficient [K]
partition coefficient for algae and dead particulate organic matter at
a temperature of 20 ◦ C [L kgC−1 ]
temperature [◦ C]

DR
AF

T

T

where:

The simulation of slow partitioning is optional. Equilibrium partitioning (option 0) occurs when
the half-life-time of the adsorption process or the desorption process is equal to or smaller
than 0.0. Slow partitioning (option 1) is applied when one of these half-life-times is bigger
than 0.0.

Option 0

When tads and tdes ≤ 0.0, the above equations are applied to calculate the fractions in
equilibrium.

Option 1

When tads or tdes > 0.0, the above equations are also applied to calculate the fractions
in equilibrium. In addition the various micropollutant fractions are corrected for slow sorption
proportional to the difference between the equilibrium fractions and the fractions in the previous time step. No distinction is made regarding the various particulate adsorbents. Average
sorption rates are used for POC and phytoplankton. The calculation using first-order sorption
reaction rates derived from half-life-times proceeds as follows:

f p0 = f poc0 + f alg 0 =

Cmpp0
Cmpt0

f pe = f poc + f alg
if f p < f pe then

ksorp =

ln(2)
tads

ksorp =

ln(2)
tdes

else

320 of 464

Deltares

Organic micropollutants

and

T

f p = f pe − (f pe − f p0 ) × exp(−ksorp × ∆t)
(1 − f p)
f df = f df e ×
(1 − f pe)
(1 − f p)
f doc = f doce ×
(1 − f pe)
fp
f poc = f poce ×
f pe
fp
f alg = f alge ×
f pe
where:

Cmpt/mpp0

DR
AF

total and particulate concentration of micropollutant after the previous time-step [g m−3 ]
fractions of micropollutant adsorbed to algae and dead particulate
organic matter after the previous time step [-]
total particulate micropollutant fraction after the previous time-step,
at the end of the present timestep, and in equilibrium [-]
sorption rate [d−1 ]

f alg/poc0
f p0 /p/pe
ksorp

For both options the sorption rate is calculated as:

Rsorp =

f p × Cmpt0 − Cmpp0
∆t

where:

Rsorp
∆t

sorption rate [g m−3 d−1 ]
b

timestep of DELWAQ [d−1 ]

The calculation of the rate requires division with the volume of the overlying water segment
(V = Z · A) in case of PARTS1_(i) and PARTS2_(i).
The dissolved and particulate micropollutant concentrations and the quality of the particulate
organic fractions follow from:

f df × Cmpt0
φ
f doc × Cmpt0
Cmpdoc =
φ
Cmpd = Cmpdf + Cmpdoc
Cmpp = (f poc + f alg) × Cmpt0
f poc × Cmpt0
Cmppoc =
Cpoc
f alg × Cmpt0
Cmpalg =
Calg
Cmpdf =

Deltares

321 of 464

Processes Library Description, Technical Reference Manual

For PARTS1_(i) and PARTS2_(i) the calculation of the dissolved concentrations also requires
division with the volume of the layer (V).
Output
The process generates output for:

 the various particulate and dissolved micropollutant fractions;
 the total micropollutant concentration, the freely dissolved concentration, the concentration adsorbed to DOC;

 the apparent overall partition coefficient; and
 the micropollutant contents of total suspended solids, detritus and phytoplankton.

Cmpp × 106
Css
Cmppt × 10−3
Kpt =
Cmpd + Cmpdoc

where:

DR
AF

Cmppt =

T

The micro-pollutant content of total suspended solids and the apparent partition coefficient
follow from:

Css
Cmppt
Kpt

the total suspended solids concentration [g m−3 ].
the micropollutant content of total suspended solids [mg kg−1 ].
the apparent overall parttion coefficient [m3 kg−1 ].

The contents of the individual particulate fractions are calculated in a similar way.
Directives for use
 The partition coefficients for phytoplankton and P OC have to be provided in the input
of the model as logarithmic values ( 10 log) of [L kgC−1 ] or [L kgDW−1 ]. If the partition
coefficient is to be temperature dependent its input value concerns reference temperature
20 ◦ C. When temperature coefficient T cKp(i) = 0.0 (default value), this implies a partition
coefficient that is not dependent on temperature.
 The concentrations of DOCS1/2 for the S1/S2 sediment option have to be provided
as pore water concentrations. In all other cases DOC needs to be provided as bulk
concentrations. DOC is calculated as bulk concentration, when simulated with the model.
 The process of aging (internal diffusion in particles) may cause the apparent partition
coefficient to increase over time. The partitioning in the sediment may therefore require a
substantially higher partition coefficient than the partitioning in the water column.
 The formulations do not allow for an irreversibly adsorbed fraction. Such a fraction can
be taken into account implicitly by reducing the load proportionally, or by increasing the
partition coefficients and slowing down of the sorption process, which may be relevant for
sediment compartments in particular.
 Field partition coefficients may not (readily) be available. For many substances the field
partition coefficient can be estimated from the octanol-water partition coefficient according
to log(Kppoc) = a log(Kow) + b (a = 0.8 − 1.0 and b = 0.0 − 0.3; these coefficients
are different for the various types of micropollutants).
 The input parameters SW SedY es/N o and OM P Group always have the same default
value, respectively 1.0/0.0 and 4.0, which must not be changed by the user!
 Slow sorption requires the use of two simulated substances (total particulate and total
dissolved) in stead of the one substance (total concentration), see above! All other input
parameters and output parameters remain the same.

322 of 464

Deltares

Organic micropollutants

Additional references
WL | Delft Hydraulics (1992b), DiToro and Horzempa (1982), Karickhoff et al. (1979), ?, Connolly et al. (2000)
Table 10.1: Definitions of the input parameters in the above equations for PARTWK_(i).
(i) is a substance name. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in input

Definition

Units

-

OM P Group

identifier of group 4 substances (organic
micropollutants)

-

Calg
Cdoc
Cimi
Cpoc

P HY T 1
DOC
IM i
P OCnoa2

phytoplankton concentration

gC m−3

dissolved organic matter concentration

gC m−3

conc. inorg. particulate fractions i=1,2,3

gDW m−3

particulate organic matter concentration
without algae
total micropollutant concentration

gC m−3

total dissolved micropollutant conc.
totsl particulate micropollutant conc.

g m−3
g m−3

total suspended matter concentration

gDW m−3

logKpalg

lKphy(i)

logKppoc lKpoc(i)
a

T

(i)
(i) − dis
(i) − par
SS

DR
AF

Cmpt
Cmpd
Cmpp
Css

b

10 logarithm of part. coeff. for phytoplankton
10 logarithm of part. coeff. for POC

b

b

b

g m−3
b

w

b

b

10

log

10

log

−1

kgC
K

temperature coefficient of partition coefficient

W SedN o3

option for process in water column (default = 0.0)

-

tads
tdes

HLT Ads(i)
HLT Des(i)

half-life-time adsorption process
half-life-time desorption process

d
d

T

T emp

temperature

K

V olume

volume

K

Xdoc

XDOC(i)

adsorption efficiency of DOC relative to
POC

-

φ

P OROS

porosity

m3 m−3

V

(L

)

T cKp(i)

−

(L

kgC−1 )

w

b

∆t

Delt

timestep

d−1

1

) Delivered by processes PHY_BLO (BLOOM) or PHY_DYN (DYNAMO).
) Delivered by process COMPOS.
3
) Default value must not be changed.
2

Deltares

323 of 464

Processes Library Description, Technical Reference Manual

Table 10.2: Definitions of the input parameters in the above equations for PARTS1_(i)
and PARTS2_(i). (i) is a substance name. (k) indicates sediment layer 1 or 2.
Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in input

Definition

Units

A

Surf

surface area

m2

Calg
Cdoc
Cimi

P HY T S(k)1
DOCS(k)
IM iS(k)

gC
gC m−3
gDW

Cpoc
Cmpt
Cmpd
Cmpp
Css

P OCS(k)1
(i)S(k)
(i)S(k) − dis
(i)S(k) − par
DM S(k)1

phytoplankton quantity
dissolved organic matter concentration
quantity inorg. particulate fractions
i=1,2,3
part. organic matter without algae
quantity of total micropollutant
quantity of total diss. org. micro-poll.
quantity of total part. org. micro-poll.
total quantity of total sediment
10 logarithm of part. coeff. for phyt.
10 logarithm of part. coeff. for POC
temperature coefficient of partition coefficient

log(L kgC−1 )
log(L kgC−1 )
K

identifier for processes PARTS1/2

-

SW SedY es2

-

tads
tdes
Xdoc
T
V
Z
φ
∆t
1
2

gC
g
g
g
gDW

T

DR
AF

logKpalg lKphy(i)S(k)
logKppoc lKpoc(i)S(k)
a
T cKp(i)S(k)

w

HLT Ads(i)S(k) half-life-time adsorption process
HLT Des(i)S(k) half-life-time desorption process

d
d

XDOC(i)

adsorption efficiency of DOC relative
to POC

-

T emp

temperature

K

V olume
ActT hS(k)
P ORS(k)
Delt

volume

m−3

thickness of sediment layer
porosity

m
m3 m−3

timestep

d−1

b

w

b

) Delivered by processes S1_COMP and S1_COMP.
) Default value must not be changed.

Table 10.3: Definitions of the output parameters for PARTWK_(i). (i) is a substance name.
Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in input

Definition

Units

Cmpt
Cmpd
Cmpdoc

(i)tot
Dis(i)
Doc(i)

total micropollutant concentration

g m−3

freely dissolved micropollutant conc.
DOC adsorbed micropollutant conc.

g m−3
g m−3

f df

F r(i)Dis

freely diss. micropoll. fraction (not bound
to DOC!)

-

324 of 464

b

w

w

Deltares

Organic micropollutants

Table 10.3: Definitions of the output parameters for PARTWK_(i). (i) is a substance name.
Volume units refer to bulk ( ) or to water ( ).
b

w

Name in input

Definition

Units

f doc
f poc
f alg

F r(i)DOC
F r(i)P OC
F r(i)P HY T

fraction micropollutant adsorbed to DOC
fraction micropollutant adsorbed to POC
fraction micropollutant adsorbed to phytoplankton

-

Kpt

Kd(i)SS

apparent overall partition coefficient for
susp. solids

m3 kgDW−1

-

Q(i)P OC
Q(i)P HY T
Q(i)SS

micropoll. content of particulate detritus
micropoll. content of phyt. biomass
micropollutant content of total suspended solids

g gC−1
g gC−1
mg kgDW−1

Cmppt

T

Name in
formulas

DR
AF

Table 10.4: Definitions of the output parameters for PARTS1_(i) and PARTS2_(i). (i) is a
substance name. (k) indicates sediment layer 1 or 2. Volume units refer to
bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in
input1

Definition

Units

Name in
formulas

Name in input

Definition

Units

Cmpt
Cmpd
Cmpdoc

(i)S(k)tot
Dis(i)S(k)
Doc(i)S(k)

total mass of the micropollutant
freely dissolved micropollutant conc.
DOC adsorbed micropollutant conc.

g
g m−3
g m−3

f df

F r(i)DisS(k) freely diss. micropoll. fraction (not bound

w

w

-

to DOC!)

f doc
f poc
f alg

F r(i)DOCS(k) fraction micropollutant adsorbed to DOC
F r(i)P OCS(k) fraction micropollutant adsorbed to POC
F r(i)P HY T S(k)
fraction micropollutant adsorbed to phy-

-

toplankton

Kpt

Kd(i)DM S(k) apparent overall partition coefficient for

m3 kgDW−1

susp. solids

-

Cmppt

Q(i)P OCS(k) micropollutant content of part. detritus
Q(i)P HY T S(k)micropollutant content of phyt. biomass
Q(i)DM S(k) micropollutant content of total sus-

g gC−1
g gC−1
mg kgDW−1

pended solids

Deltares

325 of 464

Processes Library Description, Technical Reference Manual

Calculation of organic matter
PROCESS :

MAKOOC AND MAKOOCS1/2

When organic matter components are actually simulated or imposed as POC1-4, total POC is
made available as the sum of these components by process COMPOS. In that case processes
MAKOOC, MAKOOCS1 and MAKOOCS2 are not needed.

T

However, when modelling organic micropollutants or heavy metals, organic matter might not
be simulated. The particulate organic matter concentration POC can then be derived from
(suspended) inorganic sediment using processes MAKOOC, MAKOOCS1 and MAKOOCS2.
Inorganic sediment may be simulated, or may be imposed as forcing function.
Implementation

Process MAKOOC has been implemented for the following substances:

 IM1, IM2 and IM3

DR
AF

10.2

Processes MAKOOCS1 and MAKOOCS2 have been implemented for the following substances:

 IM1S1, IM2S1, IM3S1, IM1S2, IM2S2 and IM3S2

Process MAKOOC is generic and can be used for water and sediment layers. Whereas
MAKOOC needs concentrations as input, MAKOOCS1 and MAKOOCS2 require total quantities per sediment layer as input. The formulations for the processes are identical.
Table 10.5 and Table 10.6 provide the definitions of the input and output parameters.
Formulation

The total POC concentration is the sum of the contribution of the three sediment fractions:

Cpoc =

3
X
(f ocsedi ×
i=1

where:

Cim
Cpoc
f ctr
f ocsed
i

Cimi
)
1 − f ocsedi × f ctr

the concentration or quantity of inorganic matter [gDM m−3 or gDM]
b

the concentration or quantity of particulate organic carbon [gC m−3 or gOC]
b

weight conversion factor [gDM gOC−1 ]
content organic carbon in total of sediment fraction [gOC gDM−1 ]
index for sediment component

The conversion factor f ctr enters the equation because the content of organic matter f ocsed
is provided as organic carbon per dry matter total sediment for each fraction. From the converted organic content, the inorganic fraction and the total weight of the sediment in dry weight
is calculated. Then, using the content of organic matter f ocsed again, the Cpoc is calculated
from the total sediment dry weight for each fraction, and summed.
Table 10.5: Definitions of the input parameters in the above equations for MAKOOC,
MAKOOCS1 and MAKOOCS2.

326 of 464

Deltares

Organic micropollutants

Name in
formulas

Name in input

Cimi

IM (i )S (k )

f ctr

f ocsedi

Units

concentration of inorganic particulate
fractions i = 1,2,3
DMCFOOC
weight conversion factor for water column
DMCFOOCS
weight conversion factor for sediment
layers
FCSEDIM (i )S (k c)ontent organic carbon in total of sediment fractions

DW m−3
gDW gC−1
gDW gC−1
gOC gDM−1

) (i) is 1, 2 or 3 for IM1, IM2 or IM3. (k) is 1 or 2 for sediment layer S1 or S2.

T

1

Definition

Table 10.6: Definitions of the ouput parameters in the above equations for MAKOOC,
MAKOOCS1 and MAKOOCS2.

Name in input

Cpoc

P OCnoa

Cpoc

1

Definition

DR
AF

Name in
formulas

P OCS(k)

conc. of total particulate organic carbon
in water (with or without algae biomass!)
quantity of total part.
organic carbon in sediment (with or without algae
biomass!)

Units
gC m−3
b

gC

) (i) is 1, 2 or 3 for IM1, IM2 or IM3. (k) is 1 or 2 for sediment layer S1 or S2.

Deltares

327 of 464

Processes Library Description, Technical Reference Manual

Dissolution of organic micropollutants
PROCESS :

DISOMP_( I )

Organic micropollutants may be discharged into a water system contained in an organic solvent. This applies to for instance PCB containing oil. If not already dispersed into droplets
prior to discharge, dispersion proceeds in the receiving water system. The micropollutant in
the solvent as well as the solvent in the droplets slowly dissolve into water. Dissolution may
be slow compared to the transport of substances, implying that the fate of the micropollutant
is dependent on the slow dissolution.

T

The dissolution of the micropollutant can also be understood as the desorption from organic
matter. In the case that the solvent dissolves much slower in water than the micropollutant
desorption eventually leads to equilibrium concentrations in water and organic solvent. When
the initial concentration of the micropollutant in the solvent is much higher than the equilibrium
concentration, practically all micropollutant dissolves. In the case that the organic solvent dissolves at a similar or higher rate than the micropollutant, the adsorbent disappears eventually
also leading to the dissolution of all micropollutant. For the formulation of the dissolution process it is assumed that conditions for the eventual dissolution of all micropollutant are fulfilled.
Equilibrium sorption with respect to the solvent is ignored.

DR
AF

10.3

In order to take slow dissolution from an organic solvent into account an additional substance
was defined for the micropollutant contained in an organic solvent. After dissolution the micropollutant repartitions among various organic phases also defined in the model.
Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

Process DISOMP_(i) has been implemented for the following substances:

 OMP-ios, OMP, OMP-dis (any micropollutant); and
 153-ios, 153, 153-dis (PCB153).

Substance (i)-ios concerns the micropollutant in organic solvent. Substance (i) concerns the
micropollutant in the other dissolved and particulate phases in the model. The process formulations in the model are generic, as they are similar for all substances. Default values for
process coefficients are substance specific. Consequently, the name (i) has to be added in
the names of pertinent process coefficients.
For the substance name (i) equilibrium partitioning is simulated as based on the total concentration of this substance. For the substance name (i)-dis slow sorption is simulated in
combination with equilibrium partitioning. In that case the micropollutant is simulated with two
substance names, (i)-dis for the total dissolved concentration which is the sum of free dissolved and DOC-adsorbed micropollutant, and (i)-par for the total particulate micropollutant
concentration which is the sum of PHYT-adsorbed and POC-adsorbed micropollutant.
Table 10.7 provides the definitions of the input parameters occurring in the formulations.

328 of 464

Deltares

Organic micropollutants

Formulation
Assuming the eventual dissolution of all micropollutant in a solvent the dissolution is formulated as a first order kinetic process:

Rdis = −kdis × Cios
kdis = kdis20 × ktdis(T −20)
where:
concentration of micropollutant in organic solvent in water [g.m−3 ]
b

dissolution rate constant at 20 ◦ C [d−1 ]
temperature constant for dissolution [-]
dissolution rate [g.m−3 .d−1 ]

T

Cios
kdis20
ktdis
Rdis

The micropollutant dissolved from the organic solvent is allocated to the total micropollutant
(i) or to the dissolved micropollutant (i)-dis.

DR
AF

Directives for use

The dissolution rate constant RcDis(i) should ideally be quantified on the basis of experimental
data. An indicative range for the dissolution rate of PCBs is 0.3 − 1.5 d−1 . An indicative
value for the dissolution rate of PCB153 is 0.7 d−1 (measured for the desorption from natural
organic detritus by means of tenax-extraction keeping a near zero dissolved concentration).
References
None.

Table 10.7: Definitions of the parameters in the above equations for DISOMP_(i). (i) is a
substance name. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in input

Definition

Units

Cios

(i)-ios

micropollutant in organic solvent
concentration

g.m−3
d−1
−
g.m−3 .d−1

kdis20
ktdis

RcDis(i)

T cDis(i)

dissolution rate constant at 20 ◦ C
temperature constant of dissolution

Rdis

−

dissolution rate

Deltares

b

b

329 of 464

Processes Library Description, Technical Reference Manual

Overall degradation
PROCESS :

LOS_WK_i AND LOS_S1/2_i

Organic micropollutants may be decomposed in various ways, either chemical or biochemical
in nature. The rates of degradation processes in water systems are complex functions of
numerous local conditions. Often the individual degradation processes are not well known
or can not be quantified exactly for a given substance. Overall degradation rates, usually
calibrated on concentration data for the water system concerned, are applied in models in
stead.

T

Degradation rates are different for water column, oxidising sediment and reducing sediment
(WL | Delft Hydraulics, 1992b). This module calculates the overall degradation fluxes for each
compartment, taking these differences into account. When formulation option SW V nDegM P
= 1.0 different values can be provided for the rate constants for oxidising and reducing conditions, which are assigned according to the value of the dissolved oxygen concentration. The
appropriate degradation rate is selected using a switch.
The degradation rate is described according to temperature dependent first order kinetics.
Below a critical temperature the flux is set equal to a constant value (zero order constant). By
means of a switch (SW Deg ) the degradation can be made proportional to dissolved fractions
or the total concentration of the micropollutant.

DR
AF

10.4

Implementation

Process LOS_WK_(i) is generic and can be used for water and sediment compartments.
However, when substances in the sediment are modeled as ‘inactive’ substances, processes
LOS_S1/2_(i) are to be used in stead for these ‘inactive’ substances. These processes calculate the overall degradation fluxes for sediment layers S1 and S2. In order to account for different rates at oxidising and reducing conditions, different values can be provided for the rate
constants for S1 and S2. Whereas LOS_WK_(i) needs concentrations as input, processes
LOS_S1/2_(i) require total quantities per sediment layer as input. Moreover, the zeroth-order
degradation rate in LOS_S1/2_(i) is expressed in [g m−2 d−1 ] in stead of [g m−3 d−1 ].
Two options are available with respect to the formulation of the rate of degradation. An option
can be selected with parameter SW V nDegM P . The processes have been implemented
for the following substances:











OMP (unspecified organic micropollutant);
HCH (hexachlorohexane),
HCB (hexachlorobenzene),
153 (PCB 153);
BaP (Benzo[a]pyrene),
Flu (fluoranthene);
Diu (diuron);
Atr (atrazine); and
Mef (mevinphos).

The names (i) of these substances are known to the model, and have to be part of the
relevant input parameters (see tables Table 10.8 and Table 10.9 with parameter definitions).
The processes in the model are generic. They are similar for all substances. Default values
for the properties of the above substances are substance specific.

330 of 464

Deltares

Organic micropollutants

OMP can be any micropollutant. The default values of the input parameters for OMP are
meaningless. For instance, PCB 52 can be simulated as OMP (but also as PCB 153) by
replacing the values of the input parameters by those for PCB 52.
The switch for oxizing or reducing conditions can be delivered by auxiliary process SWOXYPARWK as based on the dissolved oxygen concentration, which can be simulated or imposed
in the input of DELWAQ.
The (freely) dissolved and DOC-bound fractions of a micropollutant are also input to LOS_WK_(i)
and LOS_S1/2_(i). These parameters are calculated with partitioning processes PARTWK_(i)
and PARTS1/2_(i).
Formulation

T

Two different sets of formulations are available. These sets differ with respect to the distinction of oxidising and reducing conditions and the pollutant fractions that are subjected to
degradation.

DR
AF

Formulation with distinction of oxidising and reducing conditions (SWVnDegMP = 1.0)
The degradation rate for a specific compartment is equal to:

Rdeg = k0deg

if

T < Tc

and else equal to:


Rdeg = k0deg + k1deg 20 × ktdeg (T −20) × f rdeg × Cmpt

where:

Cmpt
f rdeg
k0deg
k1deg
ktdeg
Rdeg
T
Tc

total micropollutant concentration [g.m−3 ]
fraction subjected to degradation [-]
zeroth order degradation rate [g.m−3 .d−1 ]
first order degradation rate [d−1 ]
temperature coefficient of degradation [-]
degradation rate [g.m−3 .d−1 ]
temperature [◦ C]
critical temperature for degradation [◦ C]

The first order degradation rate at 20 ◦ C k1deg 20 [d−1 ] depends on the redox conditions
according to:

k1deg

20


kdego20 if SW OXY = 1
=
kdegr20 if SW OXY = 0

where:

k1dego
k1degr

first order degradation rate at oxidising conditions [d−1 ]
first order degradation rate at reducing conditions [d−1 ]

The switch is determined as function of the dissolved oxygen concentration in process SWOXYPARWK.
In case of LOS_S1/2_(i), the zeroth-order degradation rate and the quantity of micropollutant
are divided with the depth of the overlying water segment (H ) and the volume of this segment
respectively (V = H · A), in order to change units into [g m−3 d−1 ] and [g m−3 ]. (After all

Deltares

331 of 464

Processes Library Description, Technical Reference Manual

fluxes have been quantified, they are multiplied with the water volume in order to obtain fluxes
in terms of [g d−1 ]!)
Factor f rdeg is different for various options imposed with SW Deg with respect to the concentration fraction that is subjected to degradation.

Option 0

f rdeg = 1.0

(default)

f rdeg = f df
Option 2

where:

f df
f doc

DR
AF

f rdeg = f df + f doc

T

Option 1

freely dissolved fraction of the micropollutant [-]
DOC-bound fraction of the micropollutant [-]

A situation in which only the particulate fraction is subjected to degradation is very unlikely.
Consequently, such an option has not been implemented.
Formulation without distinction of oxidising and reducing conditions (SWVnDegMP =
0.0)
The degradation rate for a specific compartment is equal to:

Rdeg = k0deg

if T < Tc

and else equal to:


Rdeg = k0deg + k1deg 20 × ktdeg (T −20) × f df × Cmpt
where:

Cmpt
f df
k0deg
k1deg
ktdeg
Rdeg
T
Tc

total micropollutant concentration [g.m−3 ]
freely dissolved fraction of the micropollutant [-]
zeroth order degradation rate [g.m−3 .d−1 ]
first order degradation rate [d−1 ]
temperature coefficient of degradation [-]
degradation rate [g.m−3 .d−1 ]
temperature [◦ C]
critical temperature for degradation [◦ C]

In case of LOS_S1/2_(i), the zeroth-order degradation rate and the quantity of micropollutant
are divided with the depth of the overlying water segment (H ) and the volume of this segment
respectively (V = H · A), in order to change units into [g.m−3 .d−1 ] and [g.m−3 ]. (After all
fluxes have been quantified, they are multiplied with the water volume in order to obtain fluxes
in terms of [g.d−1 ]!)

332 of 464

Deltares

Organic micropollutants

T

Directives for use
 Formulation option SW V nDegM P = 0.0 is the default option for historical reasons.
 Overall degradation may be connected with biodegradation, photolysis and/or hydrolysis.
When photolysis is the dominant process, the degradation rate should reflect either the
time average effects of solar radiation at the water surface and light extinction in the water
column. When hydrolysis is the main degradation process, the rate should be based on
the time average effect of the pH.
 The rates for degradation in sediment are usually much higher than the rates in water,
when mainly biodegradation occurs. The rates for degradation in water are usually much
higher when mainly photolysis occurs.
 The rates for degradation at oxidising conditions can be given equal values to the rates for
degradation at reducing conditions, when degradation of a micropollutant is not sensitive
to the presence of oxygen.
 The default values for all kinetic parameters and option parameters are equal to zero with
two exceptions. The default values of temperature constants T c(i) and T c(i)Sed are
equal to 1.07. The default value of the option parameters SW Deg(i) and SW Deg(i)S1/2
are equal to 1.0.

DR
AF

Additional references
WL | Delft Hydraulics (1993b), Burns (1982)

Table 10.8: Definitions of the parameters in the above equations for LOS_WK_(i). (i) is a
substance name.

Name in
formulas

Name in input

Definition

Units

Cmpt
f rdeg
f df
f doc

(i)

total micropollutant concentration
fraction subjected to degradation
freely dissolved micropollutant fraction
DOC-bound dissolved micropollutant fraction

g m−3
-

switch for selection of one of the options
switch for oxidising and reducing conditions,
computed with SWOXYPARWK
switch for selection of formulations (no redox
dependency = 0.0, with redox dependency =
1.0)

-

g m−3 d−1
d−1

-

F r(i)Dis
F r(i)Doc

SW Deg SW Deg(i)
SW OXY SW W aterCh
-

SW V nDegM P

-

k0deg
kdego20

ZLoss(i)
RcDegO(i)

kdegr20

RcDegR(i)

k1deg 20
ktdeg

Rc(i)
T c(i)

zeroth-order degradation rate
first-order degr. rate at oxid. cond. and at 20
◦
C
first-order degr. rate at red. cond. and at 20
◦
C
first-order degradation rate at 20 ◦ C
temperature constant of degradation

Rdeg

-

overall degradation rate

g m−3 d−1

T
Tc

T emp
CT Loss

ambient temperature
critical temperature for degradation

◦

Deltares

d−1
d−1
-

◦

C
C

333 of 464

Processes Library Description, Technical Reference Manual

Table 10.9: Definitions of the parameters in the above equations for LOS_S1/2_(i). (i) is
a substance name.

Name in input

Definition

H

Depth

depth of overlying water segment

m

Cmtt
f rdeg

(i)S1/2

g
-

f df
f doc

F r(i)DisS1/2
F r(i)DocS1/2

total micropollutant concentration
factor for conc. fraction subjected to
degradation
freely dissolved micropollutant fraction
DOC-bound dissolved micropollutant
fraction

SW Deg(i)S1/2 switch that allows selection of one of the

-

DR
AF

-

Units

T

Name in
formulas

SW Deg

-

options

SW OXY SW P oreChS1/2 switch for oxidising and reducing condi-

SW V nDegM P

k0deg
kdego20

tions computed with SWOXYPARWK
switch for selection of formulations (no
redox dependency = 0.0, with redox dependency = 1.0)

ZLoss(i)S1/2 zeroth-order degradation rate
RcDgO(I)S1/2 first-order degr. rate at oxid. cond. and

-

g m−2 d−1
d−1

k1deg 20
ktdeg

Rc(i)S1/2
T c(i)Sed

at 20 ◦ C
first-order degr. rate at red. cond. and
at 20 ◦ C
first-order degradation rate at 20 ◦ C
temperature constant of degradation

Rdeg

-

overall degradation rate

g.d−1

T emp
CT Loss

ambient temperature
critical temperature for degradation

◦

V olume

volume

m3

kdegr

T
Tc

20

V

334 of 464

RcDgR(i)S1/2

d−1
d−1
-

◦

C
C

Deltares

Organic micropollutants

Redox status
PROCESS :

SWOXYPARWK

The partitioning of heavy metals and the degradation rate of organic micropollutants depend
on the presence of oxidising or reducing conditions. The dissolved oxygen concentration is an
indicator for the prevailing conditions. Because the conditions in (suspended) particles may be
different from those in the surrounding water, anaerobic reduction of adsorbing components
and anaerobic degradation may already occur in these particles at a small but positive ambient
dissolved oxygen concentration. The specific consequences of spatial heterogeneity within
segments are not considered in the present model. It is assumed that the prevailing conditions
are decisive with respect to the dissolved concentrations.

T

This module determines the value of a switch (SW W aterKCh) for oxidising or reducing
conditions, depending on the local dissolved oxygen concentration. The latter maybe simulated or provided as input. The switch is used in processes PARTWK_(i) and DEGMP_(i).
The switch is used for the water phase and the sedment layers if the layered sediment option
is used (Section 1.6). If the S1/S2 approach is used, then two other switches are important
as well: SwP oreChS1 and SW P oreChS2 for respectively the upper, S1, layer and the
lower, S2, layer. It is assumed for this approach that the oxygen concentration in layer S1 is
the same as that for the overlying water and that the oxygen concentration in layer S2 is zero.

DR
AF

10.5

Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

Process SWOXYPARWK is generic and can be used for water and sediment compartments.
When substances in the sediment are modeled as ‘inactive’ substances, SWOXYPARWK
affects both the water compartments and the S1/2 partitioning processes. See Table 10.10
below for definition of the parameters.
Formulation

The prevailing chemical conditions are determined on the basis of a critical dissolved oxygen
concentration. The switch may have one of two values as follows:

SW OXY = 1
SW OXY = 0

with:

Cox
Coxc
φ

if Cox/φ > Coxc

if Cox/φ ≤ Coxc

actual dissolved oxygen concentration [g m−3 ]
b

critical dissolved oxygen concentration [g m−3 ]
porosity (Section 1.6.1) [-]
w

The critical concentration Coxc maybe different for water and sediment compartments, when
this parameter is provided in the input as a segment function. In case of the S1/2 sediment
option, the critical concentration for S1 is the same as for the overlying water compartment.
The value of SW OXY is always 0 for S2, assuming that this layer is a reducing layer by
definition.

Deltares

335 of 464

Processes Library Description, Technical Reference Manual

Directives for use
 The critical dissolved oxygen concentration CoxP art is generally below 2 g m−3 , as can
be learned from growth experiments with fungal pellets with a diameter of about a few
millimetres in a very well mixed medium. Such a value seems applicable to sediment layers. A substantially smaller value could be applied for the water column, but 0.25 g m−3
seems appropriate considering that such an average concentration may imply the presence of rather large anaerobic water masses within a compartment.
Table 10.10: Definitions of the parameters in the above equations for SWOXYPARWK.
Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
input/output

Definition

Units

Cox
Coxc

OXY
CoxPart

dissolved oxygen concentration

g m−3

critical dissolved oxygen concentration

g m−3

φ

POROS

porosity (Section 1.6.1)

-

T

Name in
formulas

DR
AF

b

SWOXY

SWWaterKch switch for oxidising or reducing cond. wa-

SWOXY

SWPoreChS1

SWOXY

SWPoreChS2

336 of 464

ter column
switch for oxidising or reducing cond.
sediment S1
switch for oxidising or reducing cond.
sediment S2

w

-

Deltares

Organic micropollutants

Volatilisation
PROCESS :

VOLAT_i

Transfer of dissolved organic micropollutants from the water column to the atmosphere is
called volatilization. Transfer in the opposite direction is called intake. Both processes may
occur in the model, depending on the direction of the concentration gradient. However, intake
is usually not relevant as the concentration of a micropollutant in the atmosphere is almost
always negligibly small. For this reason the overall process is given the generally accepted
name ‘volatilization’. This process only applies to water segments that are in contact with the
atmosphere. The volatilization rate equals 0 in all other segments.

T

The model formulations for both processes are based on the double film theory for diffusive
transport of a substance across gas-liquid interfaces as described by Liss and Slater (1974).
Further background and literature references can be found in Lyman et al. (1990). According
to the double film theory, the air-water interface consists of two stagnant layers: a gas film and
a liquid film. In steady-state, the flux across the gas film equals the flux across the liquid film.
Both fluxes can be calculated according to a finite difference approximation of Fick’s Law.

DR
AF

10.6

Equilibrium is assumed between the concentrations of the micropollutant at the interface of
the gas film and the liquid film according to Henry’s Law. The concentration of a micropollutant
in the atmosphere is not modelled but can be supplied by the user as boundary condition.
Implementation

The process VOLAT is implemented for the following substances:











OMP (unspecified organic micropollutant),
HCH (hexachlorohexane),
HCB (hexachlorobenzene),
153 (PCB 153),
BaP (Benzo[a]pyrene),
Flu (fluoranthene),
Diu (diuron),
Atr (atrazine) and
Mef (mevinphos).

The names (i) of these substances are known to the model, and have to be part of the relevant
input parameters (see Table 10.11 with parameter definitions). The processes in the model
are generic. They are similar for all substances. Default values for the properties of the above
substances are substance specific.
OMP can be any micropollutant. The default values of the input parameters for OMP are
meaningless. For instance, PCB 52 can be simulated as OMP (but also as PCB153) by
replacing the values of the input parameters by those for PCB 52.
The transfer coefficients kl and kg are inputs to VOLAT. These parameters are calculated with
‘process’ TRCOEF_(i) . The (freely) dissolved fraction of a micropollutant f df concentration
is also input to VOLAT_(i) . This parameter is calculated with partitioning process PARTWK_(i)
.

Deltares

337 of 464

Processes Library Description, Technical Reference Manual

Formulation
The volatilization rate for a specific water segment is equal to:

Rvol =

kvol × (Cd − Cde)
H

with:
freely dissolved micropollutant concentration [g m−3 ]
freely dissolved micropollutant concentration in equilibrium [g m−3 ]
water depth [m]
overall transfer coefficient for volatilization [m d−1 ]
volatilization rate [g m−3 d−1 ]

Cd
Cde
H
kvol
Rvol

T

The dissolved concentrations follow from:

with:

Ct
Cg
f df
He

DR
AF

Cd = f df × Ct
Cg
Cde =
He

total micropollutant concentration [g m−3 ]
micropollutant concentration in the atmosphere [g m−3 ]
freely dissolved micropollutant fraction [-]
dimensionless Henry’s constant at ambient temperature
[(mol m−3 ) (mol m−3 )−1 ]

The overall transfer coefficient kvol consists of contributions for the gas film and the liquid film.
The reciprocals can be interpreted as resistances. Adding these resistances results in:



kvol = 1/
with:

kl
kg

1
1
+
kl (He × kg )



transfer coefficient for the liquid film [m d−1 ]
transfer coefficient for the gas film [m d−1 ]

The dimensionless Henry’s constant He at ambient temperature is derived from Henry’s constant on the basis of partial vapour pressure (Hepr in Pa.m3 .mol−1 ) at reference temperature.
In literature this constant is usually given for reference temperature 20 ◦ C. The following formula is used to calculate the dimensionless Henry’s constant He at ambient temperature:

Ng
× e(a1 +a2 /(T +273.15))
Nl
P
Ng =
Rg × (Tref + 273.15)
a2 = (Tref + 273.15) × (ln (Hemr ) − a1 )
Nl
Hemr = Hepr ×
P
He =

with:

a1
a2
338 of 464

temperature coefficient for volatization entropy [-]
temperature coefficient for volatilization enthalpy [K−1 ]

Deltares

Organic micropollutants

Hemr
Hepr
Ng
Nl
P
Rg
T
Tref

ref. Henry’s constant on the basis of mole fraction
[(molefr gas) (molefr water)−1 ]
ref. Henry’s constant on the basis of vapour pressure [Pa m3 mol−1 ]
number of moles in a m3 gas [m−3 ]
number of moles in a m3 water (55510 m−3 )
atmospheric pressure (1.01×105 Pa)
the gas constant (8.314 Pa m3 mol−1 K−1 )
ambient temperature [◦ C]
reference temperature [◦ C]

T

Coefficient a2 represents the specific enthalpy of volatilization for the micropollutant, divided
by the gas constant (∆H ◦ /Rg ). The coefficient a1 is an input, which can be derived from the
specific entropy of volatilization for the micropollutant, divided by the gas constant (∆S ◦ /Rg ).
Literature sometimes reports data on the thermodynamic property ∆S ◦ (in [kJ mol−1 K−1 ]),
that can be used to calculate Henry’s constant at ambient temperature T . The reference
temperature Tref and the Hepr are also inputs.
The various constants of Henry at a specific temperature are related in the following way:

DR
AF

Pm
= He × R × (Tref + 273.15)
Cd
Ng
P
Hep = Hem × R × (Tref + 273.15) ×
= Hem ×
Nl
Nl
Hep =

−∆H o

Hem = e Rg×(T +273.15) +

with:

He

Hem
Hep
Pm
R
∆H ◦
∆S ◦

∆S o
Rg

dimensionless Henry’s constant on the basis of concentration
[(mol m−3 ) (mol m−3 )−1 ]
Henry’s constant on the basis of mole fraction [(molefr gas).(molefr water)−1 ]
Henry’s constant on the basis of vapour pressure [Pa.m3 mol−1 ]
partial vapour pressure of a micropollutant [Pa]
universal gas constant [Pa.m3 mol−1 K−1 ]
enthalpy of volatilization for a micropollutant [kJ mol−1 ]
entropy of volatilization for a micropollutant [kJ mol−1 K−1 ]







Directives for use
 If no information on the input for a1 (= T F He) is available, a reasonable value is 20. This
value implies a temperature dependence comparable to a Q10 of 5, a five-fold increase of
He if the temperature rises with 10 degrees.
 Henry’s constant Hepr (= HeT ref ) gives some insight into the controlling rate processes. This parameter may range from less than 10−2 to up to 103 Pa m3 mol−1 :
In the range of 10−2 to 1.0 Pa m3 mol−1 the micropollutant volatilizes slowly at a rate
dependent on Hepr . The gas-phase resistance dominates the liquid-phase resistance
by a factor of at least 10. The rate is controlled by slow molecular diffusion through air.
In the range of 1.0 to 102 Pa m3 mol−1 the liquid-phase and the gas-phase resistance
are both important. Volatilization for pollutants in this range is less rapid than for pollutants in a higher range of Hepr , but is still a significant transfer mechanism. Polycyclic
aromatic hydrocarbons (PAH’s) are in this range.
When Hepr is higher than 102 Pa m3 mol−1 , the resistance of the water film dominates
by a factor of at least 10. The transfer is liquid-phase controlled. Most hydrocarbons
are in this range.

Deltares

339 of 464

Processes Library Description, Technical Reference Manual

 Note that the temperature at which a Henry’s constant is measured in the literature Tref
should be used as model input.
Additional references

DR
AF

T

Mackay et al. (1980), Ten Hulscher et al. (1992)

340 of 464

Deltares

Organic micropollutants

Table 10.11: Definitions of the parameters in the above equations. (i) is a substance
name.

Name in
formulas

Name in input

Definition

Units

a1

T F He(i)

-

a2

-

temperature coefficient for volatization
entropy
temperature coefficient for volatilization
enthalpy

Cd
Cde

-

g.m−3
g.m−3

Cg

Atm(i)

-

dissolved micropollutant concentration
freely dissolved micropollutant concentration in equilibrium with the atmosphere
micropollutant concentration in the atmosphere
total micropollutant concentration in the
water
freely dissolved micropollutant fraction

Depth

depth of the upper water segment

m

-

dimensionless Henry’s constant of micropollutant (i) at ambient temperature
[(mol.m−3 ).(mol.m−3 )−1 ]
Henry’s constant of micropoll.
(i)
on the basis of mole fractions at ref.
Temp.[(mfr.Gas).(mfr.water)−1 ]
Henry’s constant of micropollutant (i) on
the basis of vapour pressure at reference
temperature

-

transfer coefficient for a micropollutant
for the liquid film
transfer coefficient for a micropollutant
for the gas film

m.d−1

-

number of moles in a m3 gas
number of moles in a m3 water
atmospheric pressure
universal gas constant

m−3
m−3
Pa
Pa.m3 .mol−1 .K−1

Rvol

-

volatilization rate

g.m−3 .d−1

T
Tref

T emp
T ref (i)

ambient water temperature
reference temperature

◦

f df
H
He

(i)

Hemr

-

Hepr

HeT ref (i)

kl

-

kg
Ng
Nl
P
R

T

DR
AF

Ct

Deltares

-

K−1

g.m−3
g.m−3
-

-

Pa.m3 .mol−1

m.d−1

◦

C
C

341 of 464

Processes Library Description, Technical Reference Manual

(m/d)
100

Volatilisation rate as a function of wind
(SwTrcoef=0)

T

10
1
0.1

DR
AF

0.01

0.001

1

(m/d)
100

2

3

4
5
wind (m/s)

6

7

8

7

8

Volatilisation rate as a function of wind
(SwTrcoef=1)

10

1

0.1

0.01

0.001

1

2

3

4
5
wind (m/s)

6

Figure 10.1: Liquid-air exchange rate (kvol) for a very volatile pollutant: toluene (dashed
lines: Hepr = 660) and a non-volatile pollutant lindane (solid lines: Hepr =
0.48 Pa.m3 .mole−1 ). Values of kl and kg for kvol were calculated using
the two options implemented in process TRCOEF (1: Water flow velocity =
0.5 m s−1 , 2: Water flow velocity = 2.0 m s−1 ).

342 of 464

Deltares

Organic micropollutants

Transport coefficients
PROCESS :

TRCOEF_i

The transfer coefficients kl and kg are used to quantify the exchange of organic micropollutants between water and atmosphere in process VOLAT_i. The process of mass exchange is
also indicated as volatilization. The coefficients relate to the double film theory, according to
which this process has been formulated by Liss and Slater (1974). Two transfer coefficients
have to be determined, kl for the liquid film and kg for the gas film bordering the interface
between water and atmosphere. These coefficients are in fact mass transfer velocities.

T

Numerous empirical relations exist, that describe the transfer coefficients as functions of the
wind speed and/or the water flow velocity (Lyman et al., 1990). Two options have been implemented, for flowing water systems and for stagnant water systems respectively:

 Option 0 is based on the water flow velocity, the wind velocity and the molecular weight of
the pollutant. This method was developed for Henry’s constants ranging from 1 to 102 Pa
m3 mol−1 and for molecular weights exceeding 65 g mol−1 , but will hold for a broader
range as well. The formulations are suitable for water systems, in which flow is caused by
the force of gravity, such as rivers and estuaries.
 Option 1 is based on formulations of O’ Connor (1983) (as used in IMPAQT; IMPAQT UM
(1996)), using wind velocity and the molecular diffusion coefficients of the micropollutant
in gas and water. The formulations were originally developed for stagnant systems, such
as lakes, and therefore do not include the influence of water flow velocity.

DR
AF

10.7

Implementation

The micropollutant specific transfer coefficients kg and kl are input parameters to process
VOLAT_(i). Process TRCOEF_(i) has been implemented for the same substances (i) as
process VOLAT. The names of these substances are known to the model, and have to be part
of the names of the relevant input parameters (see Table 10.11 with parameter definitions
below). Default values for the properties of the above substances are available.
An option can be selected by giving input parameter SW T rCoef value 0 (option 0) or value
1 (option 1).
Formulation
Option 0

This method is suitable for flowing water systems, such as rivers and estuaries. The transfer
coefficients are formulated as the following functions of both the water flow velocity and the
wind speed:

r
kg = 273.15 × (W + v) ×

18
Mw

for W < 1.9 m s−1 :


kl = 5.64 ×

Deltares

v 0.969
H 0.673

r


×

32
Mw

343 of 464

Processes Library Description, Technical Reference Manual

for 1.9 m s−1 ≤ W < 5 m s−1 :


kl = 5.64 ×

v 0.969
H 0.673



v 0.969
H 0.673



r

32
× e(0.526×(W −1.9))
Mw

r


32
× e(0.526×(5.0−1.9)) × 1 + (W − 5.0)0.7
Mw

×

for W ≥ 5 m s−1 :


kl = 5.64 ×

×

with:
molecular weight of the micropollutant [g mol−1 ]
water flow velocity [m s−1 ]
windspeed at 10 meters above water level [m s−1 ]

T

Mw
v
W

Option 1

DR
AF

The water flow velocity v has to be larger than a critical small value (0.001 m s−1 ). When
smaller than the critical value, v is set equal to this value.

This method is suitable for stagnant water systems, such as lakes. The transfer coefficients
are formulated as the following functions of the friction velocity and the Schmidt numbers for
air and water:


kg = 86 400 × 0.001 + 0.0463 ×

u
Sc0.67
g



for u < 0.3 m s−1 :



−6

kl = 86 400 × 10

u2.2
√
+ 0.0144 ×
Scl



for u ≥ 0.3 m s−1 :



−6

kl = 86 400 × 10
with:

Scg
Scl
u

u
+ 0.00341 × √
Scl



Schmidt number for the micropollutant in the atmosphere [-]
Schmidt number for the micropollutant in the water [-]
friction velocity [m.s−1 ]

The friction velocity at the water surface u is a function of the wind speed. The Schmidt
numbers are derived from the viscosity, density and the molecular diffusion coefficient in water
and air, and are corrected for temperature.

u = 0.01 × W ×

p
(6.1 + 0.63 × W )

ηg
ρg × Dg
ηl
Scl = 86 400 ×
ρl × Dl
Scg = 86 400 ×

344 of 464

Deltares

Organic micropollutants

1.293
1 + 0.00367 × T
ρl = 1 000 − 0.088 × T
ρg =

ηg = 10−5 × (1.32 + 0.009 × T )
ηl = 0.001
with:
molecular diffusion coeff. of micropollutant in air [m2 d−1 ]
molecular diffusion coeff. of micropollutant in water [m2 d−1 ]
ambient temperature [◦ C]
density of air [kg m−3 ]
density of water [kg m−3 ]
dynamic viscosity of air [Pa s−1 ]
dynamic viscosity of water [Pa s−1 ]

T

Dg
Dl
T
ρg
ρl
ηg
ηl

DR
AF

Directives for use
 Wind speed and water flow velocity are provided in [m s−1 ], whereas the transfer coefficients are calculated in [m day−1 ]. Differences in time units between the various (input)
parameters have been taken into account in the equations by means of the conversion
number 86 400, the number of seconds in a day.
 Figure 10.1 of process VOLAT_(i) shows the dependency of the windspeed and the water
flow velocity for the overall transfer coefficient for both calculation methods.
Additional references

O’ Connor and St. John (1982)

Deltares

345 of 464

Processes Library Description, Technical Reference Manual

Table 10.12: Definitions of the parameters in the above equations for TRCOEF_(i). (i) is
a substance name.

Name in input

Definition

Units

Dg

GDif (i)

m2 d−1

Dl

LDif (i)

molecular diffusion coeff. of micropol. (i)
in air
molecular diffusion coeff. of micropol. (i)
in water

H

Depth

depth of the upper water segment

m

kg
Mw
option
Scg
Scl
u
v
W
T
ηg
ηl
ρg
ρl

DR
AF

kl

T

Name in
formulas

346 of 464

m2 d−1

transfer coefficient for micropollutant (i)
for the liquid film
transfer coefficient for micropollutant (i)
for the gas film

m d−1

M ol(i)

molecular weight of micropollutant (i)

g mol−1

SW T rCoef

switch that allows selection of one of the
options

-

-

Schmidt number for a micropollutant in
the atmosphere
Schmidt number for a micropollutant in
the water

-

V elocity
V W ind

friction velocity at the water surface
water flow velocity
wind speed at 10 meter above water
level

m s−1
m s−1
m s−1

T emp

ambient water temperature

◦

-

dynamic viscosity of air [Pa s−1 ]
dynamic viscosity of water [Pa s−1 ]
density of air
density of water

kg m−1 .s−1
kg m−1 .s−1
kg m−3
kg m−3

Kl(i)

Kg(i)

-

m d−1

-

C

Deltares

Organic micropollutants

Settling of micropollutants
PROCESS :

SED_(i)

Organic micro-pollutants adsorb to detritus and algae. Heavy metals also adsorb to suspended inorganic matter. The micro-pollutants settle on the sediment together with these
substances. After settling the micro-pollutants become part of the sediment micro-pollutant
pools, depending on the way of modelling the sediment. The micro-pollutant pools in the
sediment are:
1 the same substances (i) when sediment layers are simulated in a generic way; or
2 the connected (i)S1/2 substances for the S1/S2 approach.

T

When the S1/S2 approach is followed, the micropollutants are allocated to the sediment micropollutant pools as follows:

DR
AF

MP =⇒ MPS1 =⇒ MPS2
settling
burial
====== W ater = || = Sediment ======

Process SED_(j) delivers the settling rates of the carrier substances (j). Process SED_(i)
delivers the settling rates of the micropollutants (i). The rates are zero, when the shear stress
exceeds a certain critical value, or when the water depth is smaller than a certain critical
depth. The rates are calculated according to Krone (1962).
Implementation

Process SED_(i) has been implemented for the following substances:

  

heavy metals,

Cd, Cu, Zn, Ni, Hg and Pb (group 1; sulfide forming heavy metals)
Cr (group 2; hydroxide forming metal)
As and Va (group 3; anion forming “metals”)

organic micropollutants,

       

10.8

OMP (unspecified organic micropollutant)
HCH (hexachlorohexane), HCB (hexachlorobenzene)
153 (PCB 153)
BaP (Benzo[a]pyrene), Flu (fluoranthene);
Diu (diuron)
Atr (atrazine)
Mef (mevinphos)
(i)S1 with (i) one of the above names

Processes SED_(i) deliver the settling rates of the above mentioned micro-pollutants (i), for
which processes SED_(j) (IM1-3, POC1-4, ALG01-30, Green, Diat), SUM_SEDIM (POC), and
SEDPHBLO (PHYT; BLOOM) or SEDPHDYN (PHYT; DYNAMO) deliver the settling fluxes of
the carrier substances (j). The individual substances (j) and the pertinent settling parameters
are the additional input parameters required.
Processes PARTWK_(i) provide the concentrations of the micro-pollutants in the carrier substances (IM1, IM2, IM3, POC, PHYT) for this.

Deltares

347 of 464

Processes Library Description, Technical Reference Manual

Table 10.13 provides the definitions of the input parameters occurring in the formulations.
Formulation
The settling of the heavy metals is coupled to the settling of inorganic matter (IM 1/2/3),
particulate particulate organic detritus (P OC ) and algae biomass (P HY T ). The settling of
the organic micro-pollutants is coupled to the settling of particulate organic detritus (P OC )
and algae biomass (P HY T ). The settling rates of all individual carrier substances are generated by process SED_(j) as the sum of zero-order and first-order kinetics. The rates are zero,
when the shear stress exceeds a certain critical value, or when the water depth is smaller
than a certain critical depth Krone (1962). The rates are calculated according to:

F setj
H

if H < Hmin
F setj = 0.0
else

DR
AF



0 Cxj × H
F setj = min F setj ,
∆t
0
F setj = F set0j + sj × Cxj

T

Rsetj = f tauj ×

if τ = −1.0
f tau = 1.0
else





τ
f tauj = max 0.0, 1 −
τ cj

where:

Cx
F set0
F set
f tau
H
Hmin
Rset
s
τ
τc
∆t
j



concentration of a carrier substance ([gDM m−3 ] or [gC m−3 ])
zero-order settling flux of a carrier substance ([gDM m−2 d−1 ] or [gC m−2 d−1 ])
settling flux of a carrier substance ([gDMm−2 d−1 ] or [gC m−2 d−1 ])
shear stress limitation function [-]
depth of the water column [m]
minimum depth of the water column for settling and resuspension [m]
settling rate of a carrier substance ([gDM m−3 d−1 ] or [gC m−3 d−1 ])
settling velocity of a carrier substance [m d−1 ]
shear stress [Pa]
critical shear stress for the settling of a carrier substance [Pa]
timestep in DELWAQ (d)
index for carrier substance (j), IM1, IM2, IM3, POC1, POC2, POC3, POC4,
ALG01-30 (BLOOM) or Green and Diat (DYNAMO)

The settling fluxes of the aggregated carrier substances POC and PHYT are computed as
the sum of the fluxes of the individual detritus components (POC1-4) or the individual algae
species.
The settling of micro-pollutants is coupled to the settling of carrier substances as follows:

Rsmpi,j = f si,j × Rsetj
where:

348 of 464

Deltares

Organic micropollutants

f si,j
Rsetj
Rsmpi,j
i
j

conc. of micro-pollutant i in carrier substance j ([gX gDM−1 ] or [gX gC−1 ])
settling rate carrier substance j ([gDW m−3 d−1 ] or [C m−3 d−1 ])
settling rate of micro-pollutant i in carrier substance j [gX m−3 d−1 ]
index for micro-pollutant (i)
index for carrier substance (j), IM1, IM2, IM3, POC or PHYT

T

Directives for use
 T au can be simulated with process TAU. If not simulated or imposed T au will have the
default value -1.0, which implies that settling is not affected by the shear stress.
 Settling does not occur, when Depth is smaller than minimal depth M inDepth for settling, which has a default value of 0.1 [m]. When desired M inDepth may be given a
different value.
 The settling fluxes f Sed(i) and f Sed(j) are available as additional output parameters.
Table 10.13: Definitions of the input parameters in the above equations for SED_(i).

Name in
input

Definition

DR
AF

Name in
formulas

Cx1j

(j 1 )

F set0j
F setj

ZSed(j)
zero-order sett. flux of carrier subst. (j )
2
f SedIM 1
settling flux of carrier substance IM1
f SedIM 22
settling flux of carrier substance IM2
f SedIM 32
settling flux of carrier substance IM3
2
f SedP HY T settling flux of carrier substance PHYT
f SedP OCnoa2 settling flux of carrier substance POC

concentration of carrier substance (j )

Units
gC/DM m−3
gC/DM.m−2 d−1
gDM m−2 d−1
gDM m−2 d−1
gDM m−2 d−1
gC m−2 d−1
gC m−2 d−1

without algae biomass

f si,j

Q(i)IM 13
Q(i)IM 2
Q(i)IM 3
Q(i)P HY T
Q(i)P OC

metal conc. in inorg. part. fraction IM1
metal conc. in inorg. part. fraction IM2
metal conc. in inorg. part. fraction IM3
micro-pollutant conc. in algae PHYT
micro-pollutant conc. in POC

g gDW−1
g gDW−1
g gDW−1
g gC−1
g gC−1

–
–
–
–

F r(i)IM 13
F r(i)IM 2
F r(i)IM 3
F r(i)P HY T

fraction metal ads. to inorg. IM1
fraction metal ads. to inorg. IM2
fraction metal ads. to inorg. IM3
fraction micro-pollutant ads. to phytoplankton
fraction micro-pollutant ads. to POC

-

–

F r(i)P OC

-

H
Hmin

Depth
M inDepth

depth of the overlying water compartment
minimum water depth for settling and resuspension

m
m

sj

V Sed(j)

settling velocity of carrier substance (j )

m d−1

τ
τ cj

T au
T aucS(j)

shear stress
crit. shear stress for settling of carrier
substance (j )

Pa
Pa

∆t

Delt

timestep in DELWAQ

d

Deltares

349 of 464

Processes Library Description, Technical Reference Manual

Table 10.13: Definitions of the input parameters in the above equations for SED_(i).

Name in
formulas

Name in
input

Definition

Units

1

DR
AF

T

) Carrier substances (j) are IM1, IM2, IM3, POC (POC1-4) and PHYT (ALG01-30
for BLOOM, or Green and Diat for DYNAMO).
2
) Settling fluxes are delivered by processes SED_(j), SUM_SEDIM (POCnoa), and
SEDPHBLO (PHYT – BLOOM) or SEDPHDYN (PHYT – DYNAMO).
3
) Organic micro-pollutants and heavy metals are indicated with (i). All qualities
and fractions are delivered by processes PARTWK_(i). The fractions are needed
for the calculation of vertical mass transport in the water column.

350 of 464

Deltares

Organic micropollutants

Sediment-water exchange of dissolved micropollutants
PROCESSES :

SWEOMP_( I )

Dissolved organic micropollutants may be exchanged between sediment and overlying water by means of a number of advective and dispersive processes. Advective transport arises
from seepage (upwelling or downwelling), that is calcuted from a seepage flow velocity. Dispersive transport arises from diffusion, bio-irrigation and flow induced dispersion. The overall
dispersion coefficient is applied to calculate a dispersion flux proportional to a concentration
gradient across the sediment-water interface.

T

The concentration gradient across the sediment-water interface is affected by sorption in the
top sediment layer. If sorption is slow, dissolved and adsorbed concentrations are not in
equilibrium in this top layer. For organic micropollutants it can be assumed that adsorption is
always fast enough to establish equilibrium. Desorption will generally be much slower though,
meaning that dissolved concentrations are often not in equilibrium.
Seepage, dispersion and sorption interact. Ideally, these processes should be modelled in
a way that takes the effects of interaction into account. However, in the present transport
formulations sorption is ignored, and only the dominant transport process is active.

DR
AF

10.9

Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

Process SWEOMP_(i) has been implemented for the following substances:

 OMP, OMP-dis, OMPS1, OMPS2 (any micropollutant); and
 153, 153-dis, 153S1, 153S2 (PCB153).

Substance (i) concerns the micropollutant in the various dissolved and particulate phases in
the model. The process formulations in the model are generic, as they are similar for all
substances. Default values for process coefficients are substance specific. Consequently, the
name (i) has to be added in the names of pertinent process coefficients.
For the substance name (i) equilibrium partitioning is simulated as based on the total concentration of this substance. For the substance name (i)-dis slow sorption is simulated in
combination with equilibrium partitioning. In that case the micropollutant is simulated with two
substance names, (i)-dis for the total dissolved concentration which is the sum of free dissolved and DOC-adsorbed micropollutant, and (i)-par for the total particulate micropollutant
concentration which is the sum of POC-adsorbed and PHYT-adsorbed micropollutant.
Table 10.14 provides the definitions of the input parameters occurring in the formulations. A
part of the input parameters, namely the dissolved concentrations, is calculated by processes
PARTWK_(i), PARTS1_(i) and PARTS2_(i)

Deltares

351 of 464

Processes Library Description, Technical Reference Manual

Formulation
The advective transport flux at the sediment-water interface due to seepage is formulated as
follows:

Rseep = vseep × Cmpd

Cmpds1 = Cmpdfs1 + Cmpdocs1
Cmpd =
Cmpdw = Cmpdfw + Cmpdocw

if vseep ≥ 0.0
if vseep < 0.0

where:
total dissolved micropollutant concentration [g.m−3 ]
b

DOC-bound dissolved micropollutant concentration [g.m−3 ]
b

−3

freely dissolved micropollutant concentration [g.m
seepage transport flux [g.m−2 .d−1 ]
volumetric seepage velocity [m.d−1 ]
index for the top sediment S1
index for water

]

b

T

Cmpd
Cmpdoc
Cmpdf
Rseep
vseep
s1
w

DR
AF

The advective transport flux between the two sediment layers S1 and S2 due to seepage is
formulated similarly, but the dissolved concentrations apply to the sediment pools:



Cmpd =
where:

s1
s2

Cmpds2 = Cmpdfs2 + Cmpdocs2
Cmpds1 = Cmpdfs1 + Cmpdocs1

if vseep ≥= 0.0
if vseep < 0.0

index for the top sediment S1
index for the deep sediment S2

V seep has a positive value for upwelling, a negative value for downwelling. In the case of
upwelling the dissolved micropollutants concentrations concern the sediment (S1 or S2). For
downwelling the dissolved micropollutants concentrations concern the concentrations in the
overlying water or in the top sediment (S1). These concentrations are delivered by processes
PARTWK_(i), PARTS1_(i) and PARTS2_(i).
The dispersive transport flux at the sediment-water interface due bio-irrigation, flow induced
dispersion and molecular diffusion is formulated as follows:

Rdisp = φs1 × Dsw ×
where:

D
L
Rdisp
ϕ
sw
s1
w

(Cmpds1 − Cmpdw )
Lsw

dispersion coefficient (m2 .d−1 )
mixing length (m)
dispersive transport flux (g.m−2 .d−1 )
porosity of the sediment (-)
index for the sediment-water interface
index for the top sediment S1
index for water

A positive flux results in the transport of micropollutant from the sediment to the overlying water, a negative flux in the transport of micropollutant from the overlying water to the sediment.

352 of 464

Deltares

Organic micropollutants

The dispersive transport flux between the top and deep sediment S1 and S2 is formulated as
follows:

Rdisp = φs2 × Dss ×

(Cmpds2 − Cmpds1 )
Lss

where:

ss
s1
s2

index for the interface of sediment S1 and S2
index for the deep sediment S1
index for the deep sediment S2

A positive flux results in the transport of micropollutant from sediment S1 to sediment S2, a
negative flux in the transport of micropollutant from sediment S2 to sediment S1.

Rseep = 0.0, if |vseep| < ϕ.s1.Dsw /Lsw

DR
AF

Rdisp = 0.0, if |vseep| ≥ ϕ.s1.Dsw /Lsw

T

For the sediment-water interface only the dominant transport process is active in any time
step as follows from:

Both processes are always active for the interface between the two sediment layers.
The seepage and dispersion fluxes are truncated at half the mass of micropollutant stored in
S1 when they are larger than this quantity in order guarantee numerical stability. The fluxes
are larger are converted into rates (g.d-1) by multiplication with the area of the sediment-water
interface. The seepage and dispersion rates are deducted from or added to total micropollutant (i)S1 and (i)S2 in the sediment and total micropollutant (i) in the overlying water. When a
micropollutant is simulated with substances (i)-dis and (i)-par, the fluxes are abstracted from
or allocated to dissolved micropollutant (i)-dis in the overlying water and abstracted from or
allocated to total micropollutant (i)S1 and (i)S2 in the sediment.
Directives for use
1 V Seep has a positive value for upwelling, a negative value for downwelling. It is defined
as the flow velocity of water in sediment multiplied with the porosity.
2 DisCoefSW and DisCoefSS always have positive values. The minimal value of the dispersion coefficients is the molecular diffusion coefficient adjusted for tortuosity. This adjustment can be made by multiplication with ϕ2 (ϕ = porosity).
3 An indicative value forMixLswand MixLss is 0.02 m.
References
None.
Table 10.14: Definitions of the parameters in the above equations for SWEOMP_(i). (i) is
a substance name. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in
input

Definition

Units

Cmpdfw

Dis(i)

g.m−3

Cmpdfs1

Dis(i)S1

freely dissolved micropollutant concentration water
freely dissolved micropollutant conc. in sediment S1

Deltares

g.m−3

w

w

353 of 464

Processes Library Description, Technical Reference Manual

Table 10.14: Definitions of the parameters in the above equations for SWEOMP_(i). (i) is
a substance name. Volume units refer to bulk ( ) or to water ( ).
b

Cmpdfs2

Name in
input
Dis(i)S2

Definition

Units

freely dissolved micropollutant conc. in sediment S2
DOC-bound micropollutant concentration in
water
DOC-bound micropollutant conc. in sediment S1
DOC-bound micropollutant conc. in sediment S2
total dissolved micropollutant concentration
in water

g.m−3

Cmpdocw

Doc(i)

m2 .d−1

VSeep

dispersion coefficient at the sediment-water
interface
dispersion coefficient at the sediment S1/2
interface
mixing length across the sediment-water interface
mixing length across the sediment S1/2 interface
volumetric seepage velocity

-

dispersive transport rate
seepage transport rate

g.m−2 .d−1
g.m−2 .d−1

PORS1
PORS2

porosity of the top sediment S1
porosity of the deep sediment S2

-

Cmpdocs1 Doc(i)S1
Cmpdocs2 Doc(i)S2
(i)-dis

Dsw

DisCoefSW

Dss

DisCoefSS

Lsw
Lss
vseep
Rdisp
Rseep

ϕs1
ϕs2

DR
AF

Cmpd

354 of 464

MixLsw
MixLss

g.m−3
g.m−3
g.m−3
g.m−3

w

w

w

w

w

T

Name in
formulas

w

m2 .d−1
m
m
m.d−1

Deltares

Organic micropollutants

General contaminants
PROCESS :

CASCADE

The process CASCADE allows the user to model a small set of non-specific contaminants.
Currently two types of processes are implemented for these contaminants: first-order decay
and first-order transformation, that is:

 Substance 1, called cascade1, may be subject to decay and may be transformed into any
of the four other substances, cascade2, cascade3, cascade4 and cascade5.

 Similarly, substance cascade2, may be subject to decay and may be transformed into any
of the three substances cascade3, cascade4 and cascade5.
and cascade5.

T

 Substance cascade3, may be subject to decay and may be transformed into cascade4
 Substance cascade4, may be subject to decay and may be transformed into cascade5.
 Substance cascade5, may be subject to decay only.
Thus you can define a cascade of transformation products, such as may be pertinent for
metabolites of pharmaceuticals or a chain of radioactive elements.

DR
AF

10.10

Implementation

Process CASCADE has been implemented for these substances. At a minimum you must
include cascade1, but all others are optional, as are the processes.
Table 10.15 provides the definitions of the input parameters occurring in the formulations.
Formulation

Decay is assumed to be first-order:

dCi
= −di Ci
dt

The transformation process of cascade(i) into cascade(j) (index j larger than index i) is also
assumed to be of first-order:

dCi
= −tij Ci
dt
dCj
= +tij Ci
dt

where:

Ci
Cj
di
tij

concentration of contaminant cascade(i) [g.m−3 ]
concentration of contaminant cascade(j) [g.m−3 ]
decay rate of contaminant cascade(i) [d−1 ]
transformation rate of contaminant cascade(i) into cascade(j)[d−1 ]

The transformations are restricted to substances with a higher index (so cascade2 cannot be
formed from cascade2) to prevent "circular" transformations, but otherwise there are no restrictions. Substance cascade2 may therefore simultaneously be transformed into cascade3,
cascade4 as well as cascade5, similarly for all others.

Deltares

355 of 464

Processes Library Description, Technical Reference Manual

Directives for use
At least cascade1 must be present in the simulation.
As the actual contaminants that are to be modelled using this set of substances may be
very diverse, there is not much guidance possible as to rate coefficients or the actual set of
transformations.
References
This process was inspired by a similar capability in the WASP model from the US EPA.
Table 10.15: Definitions of the specific parameters in the above equations for cascade(i)

Name in input

Definition

C1
C2
C3
C4
C5

cascade1
cascade2
cascade3
cascade4
cascade5

Generic contaminant cascade1
Generic contaminant cascade2
Generic contaminant cascade3
Generic contaminant cascade4
Generic contaminant cascade5

g.m−3
g.m−3
g.m−3
g.m−3
g.m−3

decayc1
decayc2
decayc3
decayc4
decayc5

Decay rate constant for cascade1
Decay rate constant for cascade2
Decay rate constant for cascade3
Decay rate constant for cascade4
Decay rate constant for cascade1

d−1
d−1
d−1
d−1
d−1

trans1to2

Transformation rate constant
cascade1 to cascade2
Transformation rate constant
cascade1 to cascade3
Transformation rate constant
cascade1 to cascade4
Transformation rate constant
cascade1 to cascade5

for

d−1

for

d−1

for

d−1

for

d−1

Transformation rate constant for
cascade2 to cascade3
Transformation rate constant for
cascade2 to cascade4
Transformation rate constant for
cascade2 to cascade5

d−1

Transformation rate constant for
cascade3 to cascade4
Transformation rate constant for
cascade3 to cascade5

d−1

Transformation rate constant for
cascade4 to cascade5

d−1

t12
t13
t14
t15
t23
t24
t25

DR
AF

d1
d2
d3
d4
d5

Units

T

Name in
formulas

trans1to3
trans1to4
trans1to5
trans2to3
trans2to4
trans2to5

t34

trans3to4

t35

trans3to5

t45

trans4to5

356 of 464

.

d−1
d−1

d−1

Deltares

11 Heavy metals
Contents
11.1 Partitioning of heavy metals

. . . . . . . . . . . . . . . . . . . . . . . . . 358

DR
AF

T

11.2 Reprofunctions for partition coefficients . . . . . . . . . . . . . . . . . . . 371

Deltares

357 of 464

Processes Library Description, Technical Reference Manual

Partitioning of heavy metals
PROCESS :

PARTWK_i AND PARTS1/2_i

Partitioning is the process in which a substance is distributed among various dissolved, adsorbed and precipitated species. Heavy metals adsorb to inorganic matter components (IM1–
3, dead organic matter components (particulate detritus POC and dissolved organic matter
DOC) and phytoplankton (PHYT).

T

The partitioning of heavy metals caused by sorption is usually described as an equilibrium
process by means of a linear partition coefficient, based on amounts of dry weight (inorganic
particulate matter) or on amounts of organic carbon. The partition coefficients for the various
inorganic and organic matter components may be different, although the coefficient for DOC
is usually considered proportional to the coefficient for POC. Copper for instance adsorbs
rather strongly to organic components compared to other metals. Arsenic is predominantly
adsorbed on organic components.
The adsorption capacity of inorganic matter mainly depends on the contents of iron oxyhydroxides, aluminium hydroxides, manganese oxide and clays such as illite. Moreover, the adsorption is strongly dependent on the pH, the redox-potential and complexation, and weakly
dependent on temperature. The dependency on redox potential is connected with the reduction of iron and manganese at low redox potential, implying the loss of adsorption capacity especially in sediments. The complexation in solution is metal specific and depends on
the abundance of ligands such as hydroxyl (OH− ), bicarbonate, chloride, sulfide and sulfate.
Complexation is therefore much stronger in the sediment than in the water column. However, the effects of pH and complexation on sorption can be taken into account, when using
so-called repro-functions for the partition coefficient.

DR
AF

11.1

Vanadium and arsenic (not truly one of the heavy metals) show basically different sorption
behaviour compared to the sulfide forming heavy metals like zinc and copper, since they are
present in anionic forms in stead of in cationic form. Arsenic occurs in arsenate, that is As(V),
in an oxidising environment and as dissolved arsenic hydroxide, that is As(III), in a reducing
environment. Chromium is predominantly present as cationic Cr(III) forms, but chromium may
also be present partially in anionic Cr(VI) form, that is as chromate. The adsorption of anions
becomes stronger with decreasing pH, the adsorption of metal cations becomes weaker with
decreasing pH.
Whereas chromium may precipitate as hydroxide both at oxidising and reducing conditions,
arsenic and vanadium do not precipitate due to high solubility. The sulfide forming heavy
metals may precipitate as sulfides at reducing conditions, especially in sediments. The coprecipitation with iron(II) sulfides is likely to occur.
Slow diffusion in solid matter has been acknowledged to take place after fast equilibrium adsorption or prior to fast equilibrium desorption. Therefore, the sorption flux can be calculated
according to equilibrium partitioning or slow sorption by choosing one of the available options.
DELWAQ only actually simulates the total concentration (or the total particulate and total dissolved concentrations) of a heavy metal. The partitioning process delivers the dissolved, the
adsorbed and the precipitated species as fractions of the total concentration, as well as the
aggregate sorption/precipitation flux.
Volume units refer to bulk ( ) or to water ( ).
b

358 of 464

w

Deltares

Heavy metals

Implementation
Processes PARTWK_(i) are generic and can be used for water and sediment compartments.
For the S1/2 option for the sediment processes PARTS1_(i) and PARTS2_(i) can be used.
The substances in the sediment are modeled as ’inactive’ substances. Whereas PARTWK_(i)
needs concentrations g m−3 as input, PARTS1_(i) and PARTS2_(i) require total quantities per
sediment layer (g) as input with only one exception (DOC in g m−3 ). The formulations are
identical for PARTWK_(i), PARTS1_(i), PARTS2_(i) with two exceptions: The substances in
the sediment are modeled as ‘inactive’ substances. Whereas PARTWK_(i) needs concentrations g m−3 as input, PARTS1_(i) and PARTS2_(i) require total quantities per sediment layer
(g) as input with only one exception (DOC in g m−3 ). The formulations are identical for
PARTWK_(i), PARTS1_(i), PARTS2_(i) with two exceptions:
w

w

T

 the correction of DOC for porosity is not carried out in PARTWK_(i); and
 PARTS1_(i) and PARTS2_(i) carry out a conversion from concentration units into quantity
units and vice versa, and therefore need the input of layer thickness and surface area.
The processes have been implemented for the following substances:
Cd, Cu, Zn„ Ni, Hg, Pb (group 1, sulfide forming heavy metals)
Cr (group 2, hydroxide forming metals)
As and Va (group 3, anion forming “metals”)
(i)S1 and (i)S2 with (i) each of the above names

DR
AF






The above substance names concern the situation, where equilibrium partitioning is simulated. The simulation of slow sorption requires the use of two simulated substances for heavy
metal in stead of the one simulated substance (i). The names of these substances are (i)-dis
and (i)-par. (i)-dis is the total dissolved concentration, the sum of free dissolved and DOCadsorbed heavy metal. (i)-par is the total particulate heavy metal concentration.
The process formulations depend on the group that a heavy metals belongs to, and default values for properties are substance specific. The private parameters HM Group1/2/3 identify
the group to which a heavy metal belongs.
The concentrations of inorganic matter (Cim1–3), detritus (Cpoc), dissolved organic matter (Cdoc) and phytoplankton (Calg ) can either be calculated by the model or be imposed
on the model via its input. In case of the former Cpoc is generated by processes COMPOS, S1_COMP and S2_COMP. Calg is generated by processes PHY_BLO (BLOOM) or
PHY_DYN (DYNAMO), S1_COMP and S2_COMP.
Precipitation is dependent on the oxygen concentration. The required dissolved sulfide concentrations can be generated by processes SPECSUD, SPECSUDS1 and SPECSUDS2. Process SWOXYPARWK generates the input parameter SW W aterKCh, that indicates the
oxidising (oxic) or reducing (anoxic) conditions.
Tables 11.1, 11.2 and 11.3 provide the definitions of the input parameters occurring in the
formulations. Tables 11.4 and 11.5 contain the definitions of the output parameters.

Deltares

359 of 464

Processes Library Description, Technical Reference Manual

Formulation
The partitioning of group 1 heavy metals is different for oxidising conditions and for reducing
conditions. The prevailing conditions are defined with switch SW OXY , the value of which
depends on the dissolved oxygen concentration. The value of the switch is determined by
process SWOXYPARWK or can be provided as input parameter.
Oxidising conditions (SWOXY = 1), without precipitation
The fractions of the dissolved and adsorbed species add up to one. Consequently these
fractions as resulting from an equilibrium are computed with:

φ+

P3

0
i=1 (Kpimi

× Cimi ) +

Kppoc0

φ
× (Cpoc + Xdoc × Cdoc) + Kpalg 0 × Calg

T

f df =

for i = 1, 2 and 3:

(1 − f df ) × Kpim0i × Cimi
0
0
0
i=1 (Kpimi × Cimi ) + Kppoc × (Cpoc + Xdoc × Cdoc) + Kpalg × Calg

DR
AF

f imi = P3

(1 − f df ) × Kppoc0 × Xdoc × Cdoc
f doc = P3
0
0
0
i=1 (Kpimi × Cimi ) + Kppoc × (Cpoc + Xdoc × Cdoc) + Kpalg × Calg
(1 − f df ) × Kppoc0 × Cpoc
0
0
0
i=1 (Kpimi × Cimi ) + Kppoc × (Cpoc + Xdoc × Cdoc) + Kpalg × Calg

f poc = P3

f alg = (1 − f df − f im1 − f im2 − f im3 − f doc − f poc)
where:

Calg/poc/doc

concentration of algae biomass, dead particulate organic matter matter, and dissolved organic matter [gC m−3 ]
concentration of inorganic matter fractions i = 1, 2 and 3 [gDW m−3 ]
fraction of micropollutant adsorbed to algae, dead particulate organic
matter dissolved organic matter, [-]
fraction of micropollutant adsorbed to inorganic matter fractions i =
1, 2 and 3 [-]
freely dissolved fraction of a micropollutant [-]
partition coefficient for algae and dead particulate organic matter
[m3 gC−1 ]
partition coefficient for inorganic matter fractions i = 1, 2 and 3 [m3
gDW−1 ]
adsorption efficiency of DOC relative to POC [-]
porosity ([m3 m−3 ]; equal to 1.0 for the water column)
b

Cimi
f alg/poc/doc
f imi

f df
Kpalg/poc0

b

w

Kpim0i
Xdoc
φ

w

w

b

In case of PARTS1_(i) and PARTS2_(i), Cdoc is corrected for porosity considering the fact
that DOC input only in this case is specified as concentrations in pore water:

Cdoc = DOC × φ
All substance quantities in the above partitioning equations are converted in case of PARTS1_(i)
and PARTS2_(i) into bulk concentrations by dividing with the volume of the layer (V = Z · A).

360 of 464

Deltares

Heavy metals

The partition coefficients in the above equations expressed in [m3 gC−1 ] or in [m3 gDW−1 ]
are derived from the input parameters expressed in [m3 kgC−1 ] or [m3 kgDW−1 ]:
w

w

Kpim0i =

Kpimi
1000

w

w

for i = 1, 2 and 3

Kppoc
1000
Kppoc
Kppoc0 =
1000
Kppoc0 =

T

The simulation of slow partitioning is optional. Equilibrium partitioning (option 0) occurs when
the half-life-time of the adsorption process or the desorption process is equal to or smaller
than 0.0. Slow partitioning (option 1) is applied when one of these half-life-times is bigger
than 0.0.

DR
AF

Option 0

When tads and tdes ≤ 0.0, the above equations are applied to calculate the fractions in
equilibrium.

Option 1

When tads or tdes > 0.0, the above equations are also applied to calculate the fractions
in equilibrium. In addition the various metal fractions are corrected for slow sorption proportional to the difference between the equilibrium fractions and the fractions in the previous time
step. No distinction is made regarding the various particulate adsorbents. Average sorption
rates are used for inorganic matter, POC and phytoplankton. The calculation using first-order
sorption reaction rates derived from half-life-times proceeds as follows:

f p0 = f im01 + f im02 + f im03 + f poc0 + f alg 0 =

Chmp0
Chmt0

f pe = f im1 + f im2 + f im3 + f poc + f alg

and

(

ksorp =

ln(2)
tads
ln(2)
tdes

if f p < f pe

if f p ≥ f pe

with

f p = f pe − (f pe − f p0 ) × exp(−ksorp × ∆t)
f df = f df e ×

(1 − f p)
(1 − f pe)

f doc = f doce ×

(1 − f p)
(1 − f pe)

f imi = f imei ×

fp
f pe

Deltares

for

i = 1, 2 and 3

361 of 464

Processes Library Description, Technical Reference Manual

f poc = f poce ×

fp
f pe

f alg = f alge ×

fp
f pe

where:

Chmt/hmp0

total and particulate conc. of metal after the previous time-step [g
m−3 ]
fractions of metal adsorbed to inorganic matter fractions I = 1, 2 or 3
after the previous time step [-]
fractions of metal adsorbed to algae and dead particulate organic
matter after the previous time step [-]
total particulate metal fraction after the previous time-step, at the end
of the present timestep, and in equilibrium [-]
sorption reaction rate [d−1 ]

f imi

f alg/poc0
f p0 /p/pe
ksorp

For both options the sorption rate is calculated as:

where:

f p × Chmt0 − Chmp0
∆t

DR
AF

Rsorp =

T

b

0

Rsorp
∆t

sorption rate [g m−3 d−1 ]
timestep of DELWAQ [d−1 ]
b

The calculation of the rate also requires division with the volume of the volume of the sediment
layer (V= Z.A) in case of PARTS1_(i) and PARTS2_(i).
The dissolved and particulate metal concentrations and the quality of the particulate organic
fractions follow from:

Chmdf =

f df × Chmt0
φ

Chmdoc =

f doc × Chmt0
φ

Chmd = Chmdf + Chmdoc

Chmp = (f im1 + f im2 + f im3 + f poc + f alg) × Chmt0
Chmimi =

f imi × Chmt0
Cpoc

Chmpoc =

f poc × Chmt0
Cpoc

Chmalg =

f alg × Chmt0
Calg

for

i = 1, 2 or 3

For PARTS1_(i) and PARTS2_(i) the calculation of the dissolved concentrations also requires
division with the volume of the layer (V = Z · A).

362 of 464

Deltares

Heavy metals

Oxidising conditions (SWOXY = 1), with precipitation
The above equations need a modification for group 2 metals such as chromium. These metals may precipitate as hydroxide. Consequently the metal fractions have to be corrected for a
precipitated fraction, when the molar ion activity product calculated using the above formulations exceeds the solubility product. A correction factor for precipitation to be applied on the
various sorbed metal fractions can be derived from the ratio of the dissolved concentration in
equilibrium with the metal hydroxide and the dissolved concentration estimated on the basis
of sorption only. The initial estimate of the freely dissolved chromium concentration resulting
form the above equations is indicated with Crdf 0 . The molar freely dissolved concentration
follows from:

Crdf 0 = Chmdf
Crdf 0
M w × 10+3

T

0
=
Crdfm

with:

molar freely dissolved chromium concentration [mol l−1 ]
molecular weight of chromium [g mol−1 ]

DR
AF

0
Crdfm
Mw

The solubility of metal hydroxide is proportional to the free metal ion concentration, which is
derived from equilibrium equations for the three hydroxyl complexes that are formed by the
metal. The equilibrium molar free chromium ion concentration in case of sorption only follows
from:

OH = 10−(14−pH)
0
Crf rm
=

1 + 10logKCr1

0
Crdfm
× OH + 10logKCr2 × OH 2 + 10logKCr3 × OH 3

where:

0
Crf rm
molar free chromium ion concentration [mol l−1 ]
logKCr1/2/3 the three equilibrium constants for hydroxyl complexation of chromium
[ 10 log((l mol−1 )1,2or3 ) ]
OH
the hydroxyl concentration [mol l−1 ]
pH
acidity [-]

The ion activity product based on this concentration and the solubility product are:
0
IAP = Crf rm
× OH 3

SOL = 10logKCrS

where:

logKCrS solubility equilibrium constant for chromium hydroxide [ 10 log(mol l−1 )4 ]
Precipitation occurs only when IAP > SOL. Consequently a correction of the various
chromium fractions is only carried when this condition is met. The correction factor for precipitation is derived from the equilibrium free chromium ion concentration:

Crf rm =

10logKCrS
OH 3

Crdfm = Crf rm × 1 + 10logKCr1 × OH + 10logKCr2 × OH 2 + 10logKCr3 × OH 3



Crdf = Crdfm × M w × 10+3
Deltares

363 of 464

Processes Library Description, Technical Reference Manual

f cor =

Crdf
Crdf 0

Multiplying this correction factor (< 1) with the initially estimated sorbed fractions delivers the
actual fractions. Keeping in mind that all fractions add up to one, the precipated fraction f pr
must be equal to:

f pr = 1 − f cor
The corrected sorbed fractions and concentrations for chromium are:

f df = f df 0 × (1 − f pr)
f imi = f im0i × (1 − f pr)

for

T

f doc = f doc0 × (1 − f pr)
i = 1, 2 or 3

f poc = f poc0 × (1 − f pr)
f alg = f alg 0 × (1 − f pr)

DR
AF

Chmdf = Crdf × (1 − f pr)

Chmdoc = Chmdoc0 × (1 − f pr)
Chmd = Chmd0 × (1 − f pr)

Chmp = (f im1 + f im2 + f im3 + f poc + f alg + f pr) × Chmt0
Chmimi = Chmim0i × (1 − f pr)

for

i = 1, 2 or 3

Chmpoc = Chmpoc0 × (1 − f pr)
Chmalg = Chmalg 0 × (1 − f pr)

The group 2 metals such as chromium have been excluded from slow sorption as a consequence of the correction for precipitation!
Reducing conditions (SWOXY = 0), without precipitation

Group 3 metals do not precipitate at all. Therefore no modification of the partitioning formulations is needed.
Reducing conditions (SWOXY = 0), with precipitation

Group 1 and group 2 metals may precipitate in reducing conditions. The required modification
of the partitioning formulations has already been dealt with above in the case of group 2
metals, as there is no difference regarding the kind of precipitate formed between oxidising
and reducing conditions. Group 1 metals however, the sulfide forming metals, precipitate as
sulfides at reducing conditions and form two sulfide complexes at the same time (MeS0 and
MeHS+ ). The solubility of the metal sulfides is so low, that sorption can be ignored. The
computation starts with calculation of the molar total dissolved metal concentration from the
equilibrium equations for solubility and complexation:

Chmdfm =

1 + 10logKhm1 × Csd + 10logKhm2 × Chsd
10logKhmS × Csd

Chmdf = Chmdfm × M w × 10+3
where:

364 of 464

Deltares

Heavy metals

Chmdfm
Csd
Chsd
logKhm1/2
logKhmS
Mw

molar total dissolved metal concentration [mol l−1 ]
molar dissolved sulfide S 2− concentration [mol l−1 ]
molar dissolved hydrogen sulfide HS − concentration [mol l−1 ]
the two equilibrium constants for sulfide complexation of a metal
[ 10 log(l mol−1 )]
solubility equilibrium constant for metal sulfide [ 10 log((l mol−1 )2 )]
molecular weight of the metal [g mol−1 ]

The molar dissolved sulfide and hydrogen sulfide concentrations are computed in processes
SPECSUD(S1/2), using the pH, the total dissolved sulfide concentration and two equilibrium
constants as input.

f df =

Chmdfm × φ
Chmt0

f pr = 1 − f df

T

The fractions of the dissolved and precipitated species add up to one. Consequently the
various concentrations and fractions are:

DR
AF

f doc = f im1 = f im2 = f im3 = f poc = f alg = 0.0

Chmdoc = Chmim1 = Chmim2 = Chmim3 = Chmpoc = Chmalg = 0.0
Chmd = Chmdf

Chmp = f pr × Chmt0

Output
The process generates output for:

 the various particulate and dissolved heavy metals fractions;
 the total metal concentration, the freely dissolved concentration, the concentration adsorbed to DOC;

 the apparent overall partition coefficient; and
 the metal contents of total suspendid solids, particulate inorganic matter fractions, detritus
and phytoplankton.

The metal content of total suspended solids and the apparent partition coefficient follow from:

Chmp × 10+6
Chmpt =
Css

Kpt =

Chmpt × 10−3
Chmd + Chmdoc

where:

Css
Chmpt
Kpt

the total suspended solids concentration [g m−3 ].
the metal content of total suspended solids [mg kg−1 ].
the apparent overall partition coefficient [m3 kg−1 ].
b

The contents of the individual particulate fractions are calculated in a similar way.

Deltares

365 of 464

Processes Library Description, Technical Reference Manual

Directives for use
 The partition coefficients for inorganic matter fractions, phytoplankton and POC have to
be provided in the input of DELWAQ on the basis of [m−3 kgC−1 ] or [m−3 kgDW−1 ].
 The concentrations of DOCS1/2 for the S1/S2 sediment option have to be provided
as pore water concentrations. In all other cases DOC needs to be provided as bulk
concentrations. DOC is calculated as bulk concentration, when simulated with the model.
 The process of aging (internal diffusion in particles) may cause the apparent partition
coefficient to increase over time. The partitioning in the sediment may therefore require a
substantially higher partition coefficient than the partitioning in the water column.
 The formulations do not allow for an irreversibly adsorbed fraction. Such a fraction can
be taken into account implicitly by reducing the load proportionally, or by increasing the
partition coefficients and slowing down of the sorption process, which may be relevant for
sediment compartments in particular.
 The partition coefficients for inorganic matter should be based on field partition coefficients, since the sorption capacity of sediments may vary substantially among water systems. In case three inorganic sediment fractions are considered one could take the partition coefficient for the finest fraction and derive the coefficient for the other two fractions
by multiplication with the relative clay or iron content.
 The implementation uses several private parameters to indicate the metal group and the
occurrence or absence of precipitation. These parameters should never be changed to
ensure correct operation.
 Slow sorption requires the use of two simulated substances (total particulate and total
dissolved) in stead of the one substance (total concentration), see above! All other input
parameters and output parameters remain the same.
w

DR
AF

T

w

Additional references

WL | Delft Hydraulics (1992b), DiToro and Horzempa (1982), ?, Rai et al. (1989), Schnoor
et al. (1987)
Table 11.1: Definitions of the input parameters in the above equations for PARTWK_(i) in
relation to sorption. (i) is a substance name. Volume units refer to bulk ( ) or
to water ( ).
b

w

Name in
formulas

Name in input

Definition

Units

Calg
Cdoc
Cimi
Cpoc

P HY T 1
DOC
IM i
P OCnoa2

phytoplankton concentration

gC m−3

particulate organic matter concentration
without algae

gC m

Chmt
Chmd
Chmp
Css

(i)
(i) − dis
(i) − par
SS 2

total metal concentration

g m−3

Kpalg

Kd(i)P HY T

Kpimi

Kd(i)IM i

dissolved organic matter conc.

conc. inorg. part. fractions i = 1,2,3

gC m

b

−3
b

gDW m

−3
b

−3
b

b

gm

−3

total particulate metal concentration

gm

−3

total suspended matter concentration

gDW m−3

partition coefficient for phytoplankton
(see directives!)
part. coeff. for inorg. fractions i = 1,2,3

m−3 kgC−1

total dissolved metal concentration

b

b

b

m−3 kgDW−1

continued on next page

366 of 464

Deltares

Heavy metals

Table 11.1 – continued from previous page
Name in
formulas

Name in input

Definition

Units

Kppoc

Kd(i)P OC

partition coefficient for POC

m−3 kgC−1

SW OXY SW W aterKCh3 switch for oxidising or reducing condi-

-

tions

HLT Ads(i)
HLT Des(i)

half-life-time adsorption process
half-life-time desorption process

d
d

Xdoc

XDOC(i)

ads. efficiency of DOC relative to POC

-

V

V olume

volume

m−3

ϕ

P OROS

porosity

∆t

Delt

timestep

2
3
4

m3

b

w

m−3

b

d

DR
AF

1

T

tads
tdes

Delivered by processes PHY_BLO (BLOOM) or PHY_DYN (DYNAMO).
Delivered by process COMPOS.
Can be computed by process SWOXYPARWK.
Default value must not be changed.

Table 11.2: Definitions of the input parameters in the above equations for PARTS1_(i)
and PARTS2_(i) in relation to sorption. (i) is a substance name. (k) indicates
sediment layer 1 or 2. Volume units refer to bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in input

Definition

Units

A

Surf

surface area

m2

Calg
Cdoc
Cimi

P HY T S(k)1
DOCS(k)
IM iS(k)

gC
gC m−3
gDW

Cpoc
Chmt
Chmd
Chmp
Css

P OCS(k)1
(i)S(k)
(i)S(k) − dis
(i)S(k) − par
DM S(k)1

phytoplankton quantity
dissolved organic matter concentration
quantity of inorganic particulate fractions i = 1,2,3
particulate organic matter quantity
quantity total heavy metal
quantity total dissolved heavy metal
quantity total particulate heavy metal
quantity of total sediment

Kpalg

Kd(i)P HY T S(k) partition coeff. for phytoplankton (see

Kpimi
Kppoc

Kd(i)IM iS(k)
Kd(i)P OCS(k)

directives!)
part. coeff. for inorg. fractions i = 1,2,3
part. coeff. for POC (see directives!)

SW OXY SW P oreChS(k)2 switch for oxidising or reducing condi-

w

gC
g
g
g
gDW
m−3 kgC−1
m−3 kgDW−1
m−3 kgC−1
-

tions
continued on next page

Deltares

367 of 464

Processes Library Description, Technical Reference Manual

Table 11.2 – continued from previous page
Name in
formulas

Name in input

tads
tdes

HLT Ads(i)S(k) half-life-time adsorption process
HLT Des(i)S(k) half-life-time desorption process

d
d

Xdoc

XDOC(i)

ads. efficiency of DOC relative to POC

-

V
Z

-

ActT hS(k)

volume
thickness of sediment layer

m−3
m

ϕ

P ORS(k)

porosity

m3

∆t

Delt

timestep

3

Delivered by processes S1_COMP and S1_COMP.
Can be computed by process SWOXYPARWK.
Default value must not be changed.

b

w

m−3

b

T

2

Units

DR
AF

1

Definition

d

Table 11.3: Definitions of the input parameters in the above equations for PARTWK_(i),
PARTS1_(i) and PARTS2_(i) in relation to precipitation. (i) is a substance
name. (k) indicates sediment layer 1 or 2.

Name in
formulas

Name in input

Definition

Units

Chsd

DisHSW K 1)
or DisHSS(k)
DisSW K or
DisSS(k)

molar diss. hydrogen sulfide HS− concentration
molar dissolved sulfide S2− concentration

mol l−1

Csd

logKCr1 logK(i)OH1

mol l−1
10

log(l mol−1 )

10

log((l mol−1 )2 )

10

log((l mol−1 )3 )

10

log((l mol−1 )4 )

10

log(l mol−1 )

10

log(l mol−1 )

10

log((l mol−1 )2 )

logKhmS logK(i)Ss

metal hydroxyl compl. constant
(1xOH; group 2)
metal hydroxyl compl. constant
(2xOH; group 2)
metal hydroxyl compl. constant
(3xOH; group 2)
metal hydroxide solubility constant
(group 2)
metal sulfide S2− complexation constant (group 1)
metal hydr. sulfide HS− compl. constant (group 1)
metal sulfide solubility const. (group 1)

M wi

M olW t(i)

molecular weight of a metal

g mol−1

pH

pH or pHS(k)

acidity

-

logKCr2 logK(i)OH2
logKCr3 logK(i)OH3
logKCrS logK(i)Sol

logKhm1 logK(i)Saq

logKhm2 logK(i)HSaq

1)

The sulfide concentrations can be generated by processes SPECSUD, SPESUDS1 and
SPECSUDS2.

368 of 464

Deltares

Heavy metals

Table 11.4: Definitions of the output parameters for PARTWK_(i). (i) is a substance name.
Volume units refer to bulk ( ) or to water ( ).
w

T

b

Name in output

Definition

Chmt
Chmd
Chmdoc

(i)tot
Dis(i)
Doc(i)

total metal concentration
freely dissolved metal concentration
DOC adsorbed metal concentration

g m−3
g m−3
g m−3

f df

F r(i)Dis

freely dissolved metal fraction (not
bound to DOC!)
fraction metal adsorbed to DOC
fraction metal ads. to inorg. fraction IM1
fraction metal ads. to inorg. fraction IM2
fraction metal ads. to inorg. fraction IM3
fraction metal adsorbed to POC
fraction metal ads. to phytoplankton
fraction metal precipitated

-

DR
AF

Name in
formulas

Units

b

w

w

f doc
f im1
f im2
f im3
f poc
f alg
f pr

F r(i)DOC
F r(i)IM 1
F r(i)IM 2
F r(i)IM 3
F r(i)P OC
F r(i)P HY T
F r(i)Sulf

Kpt

Kd(i)SS

apparent overall partition coefficient for
susp. solids

m3 kgDW−1

-

Q(i)IM 1
Q(i)IM 2
Q(i)IM 3
Q(i)P OC
Q(i)P HY T
Q(i)SS

metal content of inorg. matter fr. IM1
metal content of inorg. matter fr. IM2
metal content of inorg. matter fr. IM3
metal content of particulate detritus
metal content of phytoplankton biomass
metal content of total suspended solids

g gDW−1
g gDW−1
g gDW−1
g gC−1
g gC−1
mg kgDW−1

Chmpt

Deltares

-

369 of 464

Processes Library Description, Technical Reference Manual

Table 11.5: Definitions of the output parameters for PARTS1_(i) and PARTS2_(i). (i) is a
substance name. (k) indicates sediment layer 1 or 2. Volume units refer to
bulk ( ) or to water ( ).
b

w

Name in
formulas

Name in output

Definition

Units

Chmt
Chmd
Chmdoc

(i)S(k)tot
Dis(i)S(k)
Doc(i)S(k)

total metal concentration
freely dissolved metal concentration
DOC adsorbed metal concentration

g m−3
g m−3
g m−3

f df

F r(i)DisS(k)

Kpt
-

w

w

freely dissolved metal fraction (not
bound to DOC!)
F r(i)DOCS(k) fraction metal adsorbed to DOC
F r(i)IM 1S(k) fraction metal ads. to inorg. fraction IM1
F r(i)IM 2S(k) fraction metal ads. to inorg. fraction IM2
F r(i)IM 3S(k) fraction metal ads. to inorg. fraction IM3
F r(i)P OCS(k) fraction metal adsorbed to POC
F r(i)P HY T S(k)fraction metal ads. to phytoplankton
F r(i)Sulf S(k) fraction metal precipitated

-

Kd(i)DM S(k)

apparent overall partition coefficient for
susp. solids

m3 kgDW−1

Q(i)IM 1S(k)1
Q(i)IM 1S(k)
Q(i)IM 1S(k)
Q(i)P OCS(k)
Q(i)P HY T S(k)
Q(i)DM S(k)

metal content of inorg. matter fr. IM1
metal content of inorg. matter fr. IM2
metal content of inorg. matter fr. IM3
metal content of part. detritus
metal content of phytopl. biomass
metal content of total suspended solids

g gDW−1
g gDW−1
g gDW−1
g gC−1
g gC−1
mg kgDW−1

-

T

DR
AF

f doc
f im1
f im2
f im3
f poc
f alg
f pr

b

Chmpt

370 of 464

Deltares

Heavy metals

Reprofunctions for partition coefficients
PROCESS :

RFPART_(i)

The partition coefficient for (heavy) metals is a function of the composition of particulate matter, and therefore varies substantially among surface water systems. Strongly adsorbing components of suspended sediment are iron(III) oxyhydroxides, manganese oxides, aluminium
hydroxide, clays and organic matter. The overall adsorption capacity can be quantified using
the so-called cation exchange capacity (CEC), which can be measured. (These remarks do
not apply to anion forming metals like As!)

T

The partition coefficient is a function of the pH, the alkalinity, the chlorinity (or salinity) and the
concentrations of various anions and macrochemical metal ions. In case of sulfide forming
heavy metals, this is caused by the fact that the dominant adsorbing metal species is the free
metal ion. The concentration of the free metal ion depends on the extent of pH dependent
2−
−
complexation of this ion by a number of ligands such as OH− , HCO−
3 , SO4 and Cl (at
oxidising conditions). The pH also directly influences adsorption via the competition of a free
metal ion with H3 O+ or a metal anion with OH− at the sorption sites of particulate matter.
Competition of heavy metals and macrochemical metals (Ca2+ , K+ , Na+ , etc.) regarding
sorption plays a role too, but the concentrations of these metals in surface water are rather
constant over time.

DR
AF

11.2

In order to allow the variation over time due to the pH and to take into account the dependency
of particulate matter composition, so-called repro-functions have been developed for the partition coefficient on the basis of multivariate (log)linear regression. These functions quantify
the partition coefficient as a function of the chemical composition of surface water and or the
CEC of suspended sediment in this surface water. Process RFPART_i calculates the partition
coefficient using such repro-functions.
The dependency of partitioning on the redox potential (the dissolved oxygen concentration)
and on the supersaturation of heavy metal minerals is not considered here. These aspects
are taken into account in the process of partitioning itself.
Implementation

Process RFPART_(i) delivers partition coefficients for three inorganic matter fractions IM 1 −
3, and has been implemented for the following heavy metals:
a. the sulfide forming metals Cd, Cu, Zn, Ni, Hg, Pb;
b. the hydroxide forming metal Cr: and
c. the anion forming “metal” As.

See Table 11.6 for the definition of input and output parameters.

Deltares

371 of 464

Processes Library Description, Technical Reference Manual

Formulation
Two forms of repro-functions have been implemented. A rather simplified function, that was
found to give satisfying results for cadmium in the North Sea (WL | Delft Hydraulics, 1993c)
is based on pH, salinity and CEC. A more complicated function was derived for several heavy
metals in the river Rhine (WL | Delft Hydraulics, 1993a). A selection can be made from these
2 options by means of switch SW Repro.

SWRepro = 1
The River Rhine repro-function is applied. This function reads:
2

Kp0 = 10a ×10(b×pH) ×10c×pH ×ALK d ×Cclg ×DOC l ×ALK m×pH ×ALK n×pH×log(ALK) ×ALK o×pH
(103 × CECi )
for i = 1, 2 and 3
0.2

T

Kpimi = Kp0 ×
with:

reference partition coefficient [m3 kgDW−1 ]
partition coefficient with respect to sediment fraction i [m3 kgDW−1 ]
−3
alkalinity [mole HCO−
3 m ]
chloride concentration [g m−3 ]
cation exchange capacity of sediment fraction i [eq gDW−1 ]
dissolved organic carbon concentration [gC m−3 ]
acidity [-]
metal specific coefficients
metal specific coefficients
metal specific coefficients

DR
AF

Kp0
Kpimi
ALK
Ccl
CECi
DOC
pH
a, b, c
d, g, l
m, n, o

Sediment (IM 1 − 3) basically includes inorganic matter and detritus (P OC ). However,
the model only applies the partition coefficient to concentrations of IM1-3, assuming that it
contains a certain percentage organic matter. Like other sediment components organic matter
contributes to the CEC . River Rhine suspended matter has an average CEC of 0.2 eq kg−1 .
The metal specific coefficients established for the River Rhine are (WL | Delft Hydraulics,
1993a):

Metal

cadmium
copper
lead
zinc
mercury
nickel
chromium
arsenic

a

b

c

d

l

g

m

n

o

-7.680
-10.351
-2.265
-25.811
-33.411
-22.654
-40.123
3.555

1.894
2.826
1.270
6.719
9.633
5.702
11.121
-0.164

-0.0604
-0.159
-0.0705
-0.394
-0.616
-0.329
-0.709
0.0098

-0.0583
0.994
0
1.337
0
0
0
-0.0159

-0.715
-0.101
-0.141
-0.201
-0.936
-0.171
-0.110
-0.196

0
-0.138
0
0
0
0
-0.244
0

0
-0.209
-0.112
0
0
0.289
0
0

0
-0.0255
-0.0141
-0.0590
0
-0.0388
0
0

0
0
0
-0.0270
0
-0.0492
0
0

From a theoretical point of view, the CEC -approach is incorrect for the anion forming metals
like arsenic and chromium. For pragmatic reasons no distinction has been made in the formulations between cation and anion forming metals. This seems acceptable because the CEC
is more or less proportional to the AEC (anion exchange capacity).

SWRepro = 2

372 of 464

Deltares

2

Heavy metals

The North Sea repro-function is applied. This function reads:

Kp0 = 10a × 10b×pH × (1.8 × 10+3 × Ccl + c)d
Kpimi = Kp0 × 103 × CECi for i = 1, 2 and 3
with:

Kp0
Kpimi
Ccl
CECi
pH
a, b, c, d

reference partition coefficient per unit CEC [m3 eq−1 ]
partition coefficient with respect to sediment fraction i [m3 kgDW−1 ]
chloride concentration [g m−3 ]
cation exchange capacity of sediment fraction i [eq gDW−1 ]
acidity [-]
metal specific coefficients

T

North Sea suspended sediment was estimated to have an average CEC of 0.2 eq kg−1 . The
values of the coefficients established for cadmium in the North Sea are (WL | Delft Hydraulics,
1993c): a = 4.27, b = 0.347, c = 5.0 and d = −1.9.

DR
AF

Directives for use
 Coefficients a–o are specific for a water system and/or for a metal. Obtained values for
one particular water system may not be suitable for other water systems. The user should
verify the validity of the coefficients used in the repro-functions. It is strongly advised to
check whether the calculated value of the partitioning coefficient is within the expected
range during the simulation (create output for Kpim1 ).
 Typical CEC values for some substances are: (i) kaolinite 0.3 eq kg−1 , (ii) illite 0.4 eq
kg−1 , (iii) montmorillonite 0.7 eq kg−1 and (iv) humic matter 2.0-3.0 eq kg−1 . The CEC of
suspended sediment can be estimated with:

CEC = CECpoc × f oc + CECsilt × f silt

The CEC of POC and the CEC of silt (fraction < 2µ = “silt”) are both about 0.01 eq kg−1 .
The percentage organic carbon in sediment f oc can be estimated from the percentage
organic matter by dividing with a factor 1.7 (humic material) to 2.5 (fresh detritus). Both
f oc and the percentage silt f silt are to be provided as percentage dry weight. Notice
that the input for the CEC must be specified in eq g−1 !
 In the above approach of the partition coefficient it is assumed that the detritus (P OC )
contribution is included in the adorption capacity. The effect of DOC is taken into account
as well. Algae are not included. Only Kppoc should therefore be made equal to 0.0.
However, it is possible to take the P OC contribution from the CEC and to define Kppoc
separately.
Additional references

WL | Delft Hydraulics (1991)

Deltares

373 of 464

Processes Library Description, Technical Reference Manual

Table 11.6: Definitions of input parameters in RFPART_(i), (i) is a substance name.

Name in input

Definition

ALK
Ccl
CECi

ALK
Cl
CECIM i

alkalinity∗
chloride concentration
cation exchange capacity of sediment
fractions i = 1, 2, 3
dissolved organic carbon concentration

mol m−3
g m−3
eq gDW−1

DR
AF

DOC

DOC

Units

T

Name in
formulas

gC m−3

Kpimi

Kd(i)IM i

partition coefficient for sediment fractions i = 1, 2, 3

m3 kgDW−1

a

CaRF Kp(i)

metal specific coefficients in the reprofunctions

various

b
c
d
g
l
m
n
o
pH

CbRF Kp(i)
CcRF Kp(i)
CdRF Kp(i)
CgRF Kp(i)
ClRF Kp(i)
CmRF Kp(i)
CnRF Kp(i)
CoRF Kp(i)
pH

SW Repro SW Repro

∗

(formula
defined)

acidity

-

switch for selection of partition coefficient
function (1 = Rhine repro, default; 2 =
North Sea repro)

-

mol m−3 = meq L−1

374 of 464

Deltares

12 Bacterial pollutants
Contents

DR
AF

T

12.1 Mortality of coliform bacteria . . . . . . . . . . . . . . . . . . . . . . . . . 376

Deltares

375 of 464

Processes Library Description, Technical Reference Manual

Mortality of coliform bacteria
PROCESS : ( I )MRT

Coliform bacteria originate from human and animal faeces and are often used as indicator for
the presence of disease vectors. The mortality of coliform bacteria is enhanced by temperature, salinity and solar radiation. The lethal effect of light is associated with short wavelengths,
ultraviolet radiation in particular. Approximately half of the lethal effect is due to light with
wavelength below 370 nm. Wavelengths over 500 nm are ineffective.

T

However, little or no mortality may occur at low temperatures. Distinction is made between
Escherigia Coli, feacal coli, total coliforms and Enterococci. Available formulations for the
mortality of coliforms are mainly empirical. The formulations as reported by Mancini (1978)
have been implemented. The formulations are equal for each coliform species, the coefficients
can be specified by the user.
Implementation

Process (i)MORT has been implemented for four “substances” (i), namely:

DR
AF

12.1

 ECOLI, FCOLI, TCOLI and ENCOC.

Processes CALCRADUV and CALCRADDAY can be used to deliver the intensity of UV light
at the top and the bottom of the water layers in the model as derived from visible light (solar
radiation). Process DAYLENGTH can be used to calculate daylength. Process Extinc_UVG
can be used to provide the total extinction coefficient of UV light.
Table 12.2 provides the definitions of the parameters occurring in the formulations.
Formulation

The mortality rate of coliform bacteria can be quantified with the following empirical function
of temperature, chlorinity and solar radiation (as derived from visible light):
For T > T ci :

Rmrti = kmrti × Cxi

(T −20)

kmrti = (kmbi + kmcli ) × ktmrti
kmcli = kcli × Ccl

+ kmrd
−ε×H

kmrd = krd × DL × f uv × I0 ×

1−e
ε×H

(12.1)
(12.2)
(12.3)



(12.4)

For T ≤ T ci :

Rmrti = 0.0

(12.5)

where:

Cx
DL
ε
f uv
376 of 464

concentration of coliform bacteria species i [MPN.m−3 ]
daylength, fraction of a day [-]
extinction of UV-radiation [m−1 ]
fraction of UV-radiation as derived from visible light [-]

Deltares

Bacterial pollutants

water depth [m]
daily solar radiation as visible light at the water surface [W.m−2 ]
chloride related mortality constant [m3 .g−1 .d−1 ]
basic mortality rate [d−1 ]
chloride dependent mortality rate [d−1 ]
radiation dependent mortality rate [d−1 ]
first order mortality rate [d−1 ]
radiation related mortality constant [m2 .W−1 .d−1 ]
temperature coefficient of the mortality rate [-]
mortality rate of coliform bacteria [MPN.m−3 .d−1 ]
temperature [◦ C]
critical temperature for mortality [◦ C]
chloride concentration [g.m−3 ]
index for coliform species, ECOLI, FCOLI, TCOLI and ENCOC

T

H
I0
kcl
kmb
kmcl
kmrd
kmrt
krd
ktmrt
Rmrt
T
Tc
Ccl
i

DR
AF

The daily average solar radiation is calculated by multiplying the total daily radiation with the
day length (hours of daylight per 24 hours). Notice that solar radiation has been defined as
the energy in visible light, the intensity of which is to be corrected for reflection at the water
surface.
Directives for use
 In clear water, for instance seawater, and at high radiation intensity, mortality rates up to
and over 50 d−1 have been observed (Mancini, 1978).
 The process uses RAD_uv as input parameter, but this is derived from RadSurf when
process CalcRadUV is active. This process must be active for models with more than one
water layer. If RadSurf is solar radiation (measured as visible light), RAD _uv is also
solar radiation (measured as visible light), but calculated with the extinction coefficient of
UV light. The mortality process converts visible light into UV light using F rU V V L.
 Average solar radiation (visible light) at the surface yields 160 W m−2 , but can be as high
as 250 W m−2 in sunny places. The fraction of UV-radiation of total light at the surface
of the earth is 6 percent, that is approximately 12 percent of solar radiation measured as
visible light, because visible light is approximately 50 percent of total light. The default
value of FrUVVL is therefore 0.12. (FrUVVL should be equal to 1.0 if Rad_UV is imposed
as UV light).
 The value of the radiation dependent mortality constant krd depends on the units in which
Rad_uv (RadSurf ) is specified. A value of 1.0 h langley−1 d−1 was found by Mancini
(1978), when the radiation was expressed in [langley h−1 ]. An indicative value of krd for
radiation in W m−2 is 0.0862 (m2 W−1 d−1 ).
 For other units of Rad_uv (RadSurf ) the conversion constants listed in Table 12.1 can
be helpful.
Table 12.1: Conversion constants

1 langley
1 einstein m−2 s−1
1 kLux
1 ergs m−2 s−1
1 lumen

1 cal cm−2
12.1 W m−2
3.75 W m−2
10−7 W m−2
0.005 W

4.18 J cm−2

370 < l < 540 nm
White light

 The UV-extinction coefficient ExtU V is high compared to the extinction coefficient of
visible light. A value of 3 m−1 is indicative.

Deltares

377 of 464

Processes Library Description, Technical Reference Manual

Table 12.2: Definitions of the parameters in the above equations for (i)MORT.

Name in input

Definition

Cxi

(i)

Ccl

Cl

concentration of coliform
species i1
chloride concentration

DL

DAY L

daylength, fraction of a day

-

ExtU V
F rU V V L

extinction of UV-radiation
fraction of UV-radiation as derived from
visible light

m−1
-

Depth

water depth (layer thickness)

m

RAD_uv

daily solar radiation as visible light at water surface

W.m−2

SpM rt(i)
RcM rt(i)

chloride dependent mortality constant
basic mortality rate
chloride dependent mortality rate
radiation dependent mortality rate
first order mortality rate
radiation dependent mortality constant
temperature coefficient of the mortality
rate

m3 .g−1 .d−1
d−1
d−1
d−1
d−1
m2 .W−1 .d−1
-

–

mortality rate of coliform bacteria

MPN.m−3 .d−1

T emp
CT M rt(i)

temperature
critical temperature for mortality

◦

H
I0
kcli
kmbi
kmcli
kmrdi
kmrti
krd
ktmrt
Rmrti
T
T ci
1

bacteria

DR
AF

ε
f uv

Units

T

Name in
formulas1

–
–
–

CF RAD
T cM rt(i)

MPN.m−3
gCl.m−3

◦

C
C

substances (i) are ECOLI, FCOLI,TCOLI and ENCOC

378 of 464

Deltares

13 Sediment and mass transport
Contents
13.1 Settling of sediment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
13.2 Calculation of settling fluxes of suspended matter . . . . . . . . . . . . . . 386
13.3 Transport in sediment for layered sediment

. . . . . . . . . . . . . . . . . 389

13.4 Transport in sediment and resuspension (S1/2) . . . . . . . . . . . . . . . 395
13.5 Calculation of horizontal flow velocity . . . . . . . . . . . . . . . . . . . . . 405
13.6 Calculation of the Chézy coefficient . . . . . . . . . . . . . . . . . . . . . 407
13.7 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
13.8 Calculation of wind fetch and wave initial depth . . . . . . . . . . . . . . . 411
13.9 Calculation of bottom shear stress . . . . . . . . . . . . . . . . . . . . . . 413

T

13.10 Computation of horizontal dispersion . . . . . . . . . . . . . . . . . . . . . 416
13.11 Computation of horizontal dispersion (one-dimension)

. . . . . . . . . . . 417

13.12 Allocation of dispersion from segment to exchange . . . . . . . . . . . . . 418
13.13 Conversion of segment variable to exchange variable . . . . . . . . . . . . 419

DR
AF

13.14 Conversion of exchange variable to segment variable . . . . . . . . . . . . 420

Deltares

379 of 464

Processes Library Description, Technical Reference Manual

Settling of sediment
PROCESS :

SED_( I ), S_( I ), CALVS_( I )

The inorganic sediment components settle on the bed sediment. After settling these substances become part of the sediment inorganic matter pools, depending on the way of modelling the bed sediment. The inorganic sediment components in the bed sediment are:
1 IMS1/2, IM2S1/2 and IM3S1/2 for the S1/2 approach
2 IM1-3, the same substances when sediment layers are simulated explicitly

T

After settling BOD and COD components become part of SOD (Sediment oxygen demand,
see also section 12.2), which is an "‘inoactive"’ substance.
Implementation

Process SED_(i) is implemented for the following substances (i):

 IM1, IM2 and IM3

DR
AF

13.1

This process is also used for the settling of algae biomass and organic detritus (POC1-4),
which is dealt with by the relevant sections of Chapters 4 and 7. Process CALVS_(i) delivers
the settling velocities as modified from the settling velocities supplied by the user (implemented for inorganic sediment IM1-3, and for algae biomass). The total suspended sediment
concentration for this is delivered by process COMPOS.
Process S_(i) is implemented for the following substances (i):

 CBOD5, CBOD5_2, CBOD5_3, CBODu, CBODu_2, NBOD5, NBODu, COD_Cr and COD_Mn
Table 13.1 provides the definitions of the input parameters occurring in the formulations.
Formulations

The settling rates of the inorganic matter components and the BOD and COD substances
are described as the sum of zero-order and first-order kinetics. The rates are zero, when
the shear stress exceeds a certain critical value, or when the water depth is smaller than
a certain critical depth. The settling probability is calculated according to the formulation of
Krone (1962). The settling velocity is calculated from a user-supplied settling velocity and the
flocculation effect, as determined from salinity, total suspended solid concentration and water
temperature (density effect). The rates are calculated according to:

Rseti = f taui ×

380 of 464

F seti
H

Deltares

Sediment and mass transport

if H < Hmin
F seti = 0.0
else


0 Cxi × H
F seti = min F seti ,
∆t
0
F seti = F set0i + si × Cxi




τ
f taui = max 0.0, 1 −
τ ci

DR
AF

where:

T

if τ = −1.0
f tau = 1.0
else

Cx
F set0
F set
f tau
H
Hmin
Rset
s
τ
τc
∆t
i

concentration of a substance [gDM/O_2 m−3 ]
zero-order settling flux of a substance [gDM/O_2 m−2 d−1 ]
settling flux of a substance [gDM/O_2 m−2 d−1 ]
shear stress limitation function [-]
depth of the water column [m]
minimal depth of the water column for resuspension [m]
settling rate of a substance [gDM/O_2 m−3 d−1 ]
settling velocity of a substance [m d−1 ]
shear stress [Pa]
critical shear stress for settling of a substance [Pa]
timestep in DELWAQ [d]
index for substance (i)

The settling velocity as dependent on flocculation is formulated as follows:

si = f temp × f sal × f con × s0i

f temp = kt(T −20)
ai − 1
π×S
ai + 1
)−(
) × cos(
)
f sal = (
2
2
Smax
Cs ni
f con = (
)
Csc

where:

a
Cs
Csc
f con
f sal
f temp
kt
ni
Deltares

coefficient for the enhancement of flocculation [-]
concentration of total suspended solids [gDM m−3 ]
critical concentration of total susp. solids above which flocc. occurs [gDM m−3 ]
function for the concentration dependency of flocculation, see Figure 13.1A [-]
function for the salinity function dependency of flocculation, range [0,EnhSedi),
see Figure 13.1B [-]
function for temperature dependency of settling [-]
temperature coefficient for settling (water density correction) [-]
constant for concentration effect on flocculation [-]

381 of 464

Processes Library Description, Technical Reference Manual

S
Smax
T
i

salinity [psu, g/kg]
salinity at which the salinity function is at its maximum [g/kg]
water temperature [◦ C]
index for substance (i)

Remarks:
 No more than the available amount of substance in the water column can settle in one
model time step.
 The parameter Hmin is purely a numerical parameter - it was introduced to avoid
having to use very small time steps in very shallow grid cells.

DR
AF

T

Directives for use
 In three-dimensional applications the settling flux in all segments above the bottom layer
is calculated as a transport flux instead of a process flux. Settling in the upper layers is
not related to the bottom shear stress. The settling velocity in each layer is equal to the
settling velocity in the bottom layer. The process flux for settling F set (ouput parameter
f Sed(i)) is zero for the upper layers. Also τ is set to zero in the output for all water layers
except the bottom layer.
 Note that if the bottom shear stress, τ , equals -1, the settling limitation function (settling
probability) equals one.
 Note that DELWAQ can reduce the settling flux of a component, if the available amount in
the water column is too small to fulfil the calculated flux within one time step. Reduce the
settling rate or the DELWAQ time step if this is not wanted.
 The calculation of settling velocity by process CALVS_i is triggered when you supply a
value for V 0Sed(i). By default, all three functions (temperature, flocculation and salinity)
are equal to unity.
 A reasonable value for kt (T CSed), the temperature influence on the sedimentation) is
1.01.
 The values of the critical suspended solid concentration Csc (CrSS ) and the coefficient
n(i) determine the increase of the settling velocity at concentrations above the critical
concentrations, see Figure 13.1, WL | Delft Hydraulics (1989), finds the following range for
n: 1 < n < 2.
 The effect of salinity on the flocculation and therefore on the settling velocity is presented
in Figure 13.2.
Table 13.1: Definitions of the input parameters in the above equations for SED_(i), S_(i)
and CALVS_(i). (i) is the name of a substance.

Name in
formulas

Name in
input

Definition

Units

Cx1i

(i)1

concentration of substance (i)

gDM m−3

a

EnhSed(i)

coefficient for the enhancement of flocculation of substance (i)

-

F set0i

ZSed(i)

zero-order settling flux of substance (i)

gDM m−2 d−1

H

Depth

depth of the water column, thickness
of water layer

m

continued on next page

382 of 464

Deltares

Sediment and mass transport

Table 13.1 – continued from previous page
Name in
formulas

Name in
input

Definition

Units

Hmin

M inDepth

minimal water depth for settling and resuspension

m

si

V Sed(i)

m d−1

s0i

V 0Sed(i)

settling velocity of substance (i) for
SED_(i)
settling velocity of substance (i) for
CALVS_(i)

Sal
Salmax

Salinity
SM ax

salinity
salinity at which the salinity function is
at its maximum

psu
psu

Cs

SS

gDM m−3

Csc

CrSS

ni

N (i)

concentration of total suspended
solids
critical concentration of total suspended solids for flocculation
constant for concentration effect on
flocculation

T emp
T cSed

temperature
temperature coefficient for settlingy

◦

T au
T aucS(i)

shear stress
critical shear stress for settling of substance (I )

Pa
Pa

Delt

timestep in DELWAQ

d

τ
τ ci
∆t
1

T

DR
AF

T
kt

m d−1

gDM m−3
-

C

-

) Substances are IM1, IM2 and IM3, or the BOD and COD substances. The latter only apply
for S_(i) input parameters.

Deltares

383 of 464

Processes Library Description, Technical Reference Manual

(m/d)
1

Sedimentation velocity as function of TSS
(n=1.5, V0Sed=0.1 m/d)
CrSS = 50
CrSS = 100
CrSS = 250

T

0.8
0.6
0.4

DR
AF

0.2

0

0

(m/d)
1

50

100
150
Total suspended sediment (gDM/m3)

200

250

200

250

Sedimentation velocity as function of TSS
(CrSS=100 gDM/m3, V0Sed=0.1 m/d)
n=0
n=1
n=2

0.8
0.6
0.4
0.2

0

0

50

100
150
Total suspended sediment (gDM/m3)

Figure 13.1: Sedimentation velocity (Vsed) as a function of total suspended solid concentration (SS) solely (no effect of salinity and density included) at A):a critical
suspended solid concentration and B) at one value of n (constant in the
sedimentation formulation)

384 of 464

Deltares

T

Sediment and mass transport

DR
AF

Effect of flocculation on the sedimentation velocity
(EnhSal=3, V0Sed=0.1 m/d)
(m/d)
1

SMax = 5 g/kg

0.8
0.6
0.4
0.2

0

0

2

4
6
Salinity (g/kg)

8

10

Figure 13.2: Sedimentation velocity (VSed) as a function of salinity solely (effect of flocculation and density not included).

Deltares

385 of 464

Processes Library Description, Technical Reference Manual

Calculation of settling fluxes of suspended matter
PROCESSES :

SUM_SEDIM, SEDPHBLO_P, SEDPHBLO, SEDPHDYN, SED_( I ),
SED_SOD, S_( I )

The settling fluxes of total dry matter, total inorganic matter (TIM), total organic matter (POC
with and without algae biomass) and total BOD (SOD) are derived from the settling fluxes of
the individual substances and phytoplankton (PHYT).
Implementation
Process SUM_SEDIM is implemented for the following substances:

T

 IM1, IM2, IM3, POC1, POC2, POC3, POC4, BLOOMALG1-30, Green and Diat

Processes SED_(i) deliver the settling fluxes of the individual inorganic matter and detritus
components. Process SEDPHBLO_P (or SEDPHBLO) delivers the algae biomass settling
flux f SedAlgDM for BLOOM. Process SEDPHDYN delivers the algae biomass settling flux
f SedAlgDM for DYNAMO.

DR
AF

13.2

The output parameters f SedT IM and f SedP OCnoa are used to calculate the settling
fluxes of organic micro-pollutants and heavy metals. Tabel 13.2 provides the definitions of the
input parameters.
Process SED_SOD is implemented for the following substance:

 SOD, CBOD5, CBOD5_2, CBOD5_3, CBODu, CBODu_2, NBOD5, NBODu, COD_Cr and
COD_Mn

Processes S_(i) deliver the settling fluxes of the individual BOD or COD components. The
process delivers an additional output parameter f SedSOD , the settling flux of total BOD
and or COD. Tabel 13.3 provides the definitions of the input parameters.
Formulation

The formulations for Sum_Sedim are:

f SedT IM =

f SedP OM noa =

3
X
i=1
4
X

f SedIMi

f SedP OCj × DM CF P OCj

j=1

f SedDM =
f SedP OCnoa =

3
X
i=1
4
X

f SedIMi × DM CF IMi + f SedP OM noa + f SedAlgDM
f SedP OCj

j=1

f SedP OC = f SedP OCnoa + f SedP hyt
where:

386 of 464

Deltares

Sediment and mass transport

fSedPHYT
fSedAlgDM
fSedPOC
fSedPOC_j
fSedPOCnoa
fSedPOMnoa
fSedTIM
fSedIM_i
fSedDM
DMCFIM_i
DMCFPOC_j

settling flux of total phytoplankton [gC m−2 d−1 ]
settling flux of total phytoplankton [gDM m−2 d−1 ]
settling flux of total particulate organic carbon [gC m−2 d−1 ]
settling flux of detritus fraction j [gC m−2 d−1 ]
settling flux of POC excluding algae [gC m−2 d−1 ]
settling flux of POC excluding algae [gDM m−2 d−1 ]
settling flux of total inorganic matter [gDM m−2 d−1 ]
settling flux of inorganic matter fraction i [gDM m−2 d−1 ]
settling flux of dry matter [gDM m−2 d−1 ]
dry matter conversion factor for inorganic matter fraction i (1-3) [gDM/gX]
dry matter conversion factor for detritus fraction j (1-4) [gDM/gX]

T

The formulations for SED _SOD are:
if SW OxyDem = 0;

f SedSOD = f SedBOD5 + f SedBOD5_2 + f SedBOD5_3 + f SedBODu+
+ f SedBODu_2 + f SedN BOD5 + f SedN BODu

DR
AF

if SW OxyDem = 1;

f SedSOD = f SedCODCr + f SedCODM n

if SW OxyDem = 2;

f SedSOD = f SedCODCr + f SedCODM n + f SedBOD5 + f SedBOD5_2 + f SedBOD5_
+ f SedBODu + f SedBODu_2 + f SedN BOD5 + f SedN BODu

where:

fSedSOD
fSed(i)
SwOxyDem

settling flux of sediment oxygen demand [gO m−2 d−1 ]
settling flux of the individual component (i) [gO m−2 d−1 ]
option parameter for substance definition (0=BOD, 1=COD, 2=BOD+COD)
[-]

Directives for use
 Because you are free to select any combination of sediment components, the defaults for
the calculation of fSedTIM, fSedPHYT and fSedPOC are zero.

Deltares

387 of 464

Processes Library Description, Technical Reference Manual

Table 13.2: Definitions of the input parameters in the formulations for SUM_SEDIM. (i) is
IM1, IM2 or IM3. (j) is POC1, POC2, POC3 or POC4.

Name in input

Definition

Units

DM CF IMi

DM CF (i)

dry matter conversion factor for inorganic matter (i)

gDW/gX

DM CF P OCj

DM CF (j)

dry matter conversion factor for detritus
fraction (j)

gC/gX

f SedIMi

f Sed(i)

settling flux of inorganic matter fraction
(i)

gDM m−2 d−1

f SedP OCj

f Sed(j)

settling flux of detritus fraction (j)

gC m−2 d−1

f SedAlgDM
f SedP HY T

f SedAlgDM
f SedP HY T

settling flux of total phytoplankton
settling flux of total phytoplankton

gDM m−2 d−1
gC m−2 d−1

DR
AF

T

Name in formulas

Table 13.3: Definitions of the input parameters in the formulations for SED_SOD.

Name in formulas

Name in input

Definition

SwOXY Dem

SwOXY Dem option parameter for substance defini-

Units
-

tion (0=BOD, 1=COD, 2=BOD+COD)

f SedBOD5
f SedBOD5_2
f SedBOD5_3
f SedBODu
f SedBODu

f SedN BOD5
f SedN BODu

f SedN BOD5 settling flux of N BOD5
f SedN BODu settling flux of N BODu_2

gO2 m−2 d−1
gO2 m−2 d−1

f SedCODCr
f SedCODM n

f SedCODCr settling flux of COD_Cr
f SedCODM n settling flux of COD_M n

gO2 m−2 d−1
gO2 m−2 d−1

388 of 464

settling flux of CBOD5
settling flux of CBOD5_2
settling flux of CBOD5_3
settling flux of CBODu
settling flux of CBODu_2

m−2 d−1
m−2 d−1
m−2 d−1
m−2 d−1
m−2 d−1

f SedBOD5
f SedBOD5_2
f SedBOD5_3
f SedBODu
f SedBODu_2

gO2
gO2
gO2
gO2
gO2

Deltares

Sediment and mass transport

Transport in sediment for layered sediment
PROCESSES :

ADVTRA, DSPTRA, TRASE2_( I ) (OR TRSE2_( I ), TRSE2( I ))

The substances simulated for the water column and the sediment are the same. A particulate
substance in the water column can settle to or resuspend from the same substance in the
sediment, and vice versa. A dissolved substance in the water column disperses to the same
substance in the pore water of the sediment, and vice versa.

T

Apart from settling (sedimentation) and resuspension (erosion), particulate substances present
in the sediment layers can be subject to burial, digging, seepage and dispersion. Burial results
from net settling and leads to the transport of substances from layer to layer in a downward
direction. Digging results from net resuspension and leads to the transport of substances
from layer to layer in an upward direction. The magnitude of a burial flux or a digging flux
between sediment layers depends also on whether layer thickness and porosity are fixed or
transient. Apart from the above advective processes, particulate substances or particulate
components of substances are also subject to dispersive transport between sediment layers
due to bioturbation.

DR
AF

13.3

Dissolved substances or dissolved components of substances in the sediment are subject to
advective transport resulting from downward or upward water flow, downwelling or upwelling,
both indicated as seepage. Dissolved components disperse between water column and top
sediment layer, and between sediment layers due to bio-irrigation, flow induced dispersion
and molecular diffusion. All dispersion processes can be formulated as diffusion.
The transport of substances across the lower sediment boundary in a model requires imposing the concentrations of substances below the “deep” sediment boundary.
The layered sediment formulations are generic, implying that all possible combinations of
settling fluxes, resuspension fluxes and fixed or transient layer thickness and porosity should
be covered. However, the formulations have been tested extensively for cases with (net)
settling only, in which sediment layer thickness and sediment porosity are constant over time.
Further testing needs to be done for resuspension, transient layer thickness and transient
porosity. A process for sediment consolidation that would be needed for transient porosity is
not available in the present processes library.
Volume units refer to bulk ( ), water ( ) or solids ( ).
b

w

s

Implementation

Processes ADVTRA, DSPTRA and TRASE2_(i) (or TRSE2_(i) or TRSE2(i)) with (i) equal to
a name of a substance have been implemented for the following substances:

 IM1, IM2, IM3
 BLOOMALG01 - BLOOMALG30 (BLOOM), Diat, Green (DYNAMO)
 POC1, PON1, POP1, POS1, POC2, PON2, POP2, POS2, POC3, PON3, POP3, POS3,







POC4, PON4, POP4, POS4, DOC, DON, DOP, DOS
NH4, NO3, PO4, AAP, APATP, VIVP, Si, Opal
OXY, SO4, SUD, SUP, CH4
FeIIIpa, FeIIIpc, FeIIId, FeS, FeS2, FeCO3, FeIId
OMP, 153, Atr, BaP, Diu, Flu, HCB, HCH, Mef
As, Cd, Cr, Hg, Ni, Pb, Va, Zn
Cl, Salinity

Deltares

389 of 464

Processes Library Description, Technical Reference Manual

 TIC, Alka
Processes ADVTRA and DSPTRA deliver the velocities for advection and dispersion for processes TRASE2_(i) (or TRSE2_(i) or TRSE2(i)). The latter processes deliver total transport velocities to be used by Delwaq for the calculation of fluxes by multiplication with concentrations. Process ADVTRA uses the settling flux of sediment dry matter from process
SUM_SEDIM. Processes TRASE2_(i) use the dissolved fractions of organic micropollutants
and heavy metals generated by processes PARTWK_(i). Porosity is delivered by auxiliary
process DMVOLUME. Shear stress can be provided by process CALTAU.
Table 13.4 provides the definitions of the input parameters occurring in the formulations.

Resuspension

T

Formulation

The resuspension flux of sediment dry matter is described as zero-order kinetics according to
Partheniades-Krone (SwErosion = 0.0):

DR
AF

F res0 = f tau × F res0

if H < Hmin F res0 = 0.0 else



Cdm
0
F res = min F res ,
A × ∆t
if τ = −1.0 f tau = 1.0 else


τ

f tau = max 0.0,
− 1.0
τc
where:

A
Cdm
F res0
F res
f tau
H
Hmin
τ
τc
∆t

surface area of overlying water compartment [m2 ]
amount of sediment dry matter in the top sediment layer [gDM ]
zero-order resuspension flux of sediment [gDM.m−2 .d−1 ]
resuspension flux of sediment [gDM.m−2 .d−1 ]
shear stress limitation function [−]
depth of the water column, thickness overlying water layer [m]
minimal depth of the water column for resuspension [m]
shear stress [P a]
critical shear stress for resuspension [P a]
timestep in DELWAQ [d]

Cdm and H are calculated by the model.
Advection
The burial of particulate substances results from (net) settling at the sediment-water interface, digging results from (net) resuspension at this interface. The advection of particulate
substances by burial or digging follows from:

F advp =

vp × f p × Cx
(1 − φ)

where:

390 of 464

Deltares

Sediment and mass transport

Cx
F advp
fp
vp
j

concentration of a substance [g.m−3 ]
particulate advection flux [g.m−2 .d−1 ]
particulate fraction of a substance [−]
volumetric burial or digging velocity [m.d−1 ]
porosity [−]
b

Fraction f p is equal to 1.0 for all particulate substances, except for organic micro-pollutants
and heavy metals. The model calculates f p for these substances as depending on adsorption.

ϕ=1−

T

For fixed porosities and fixed layer thickness burial and digging imply transport fluxes across
all the interfaces of the sediment layers. This includes the interface of the lower sediment
layer in the model and the deeper inactive sediment (boundary condition). The burial and
digging velocities vp are calculated in the model from the settling and resuspension fluxes in
such a way that constant porosity in and constant thickness (volume) of each sediment layer
is maintained. This uses the following definition of porosity:


i=n 
X
f pi × Cxi
ρi

DR
AF

i=1

where:

Cx
F advp
fp
ρ
i
n

concentration of a substance, a sediment component [g.m−3 ]
particulate advection flux [g.m−2 .d−1 ]
particulate fraction of a substance [−]
density of a solid matter component [g.m−2 .d−1 ]
index of a solid matter component [−]
number of solid matter components [−]
b

For transient layer thickness or for transient porosity the volumetric burial or digging velocity
vp is the sum of an imposed velocity and an additional velocity to maintain maximal layer
thickness or minimal layer thickness. In the case of fixed porosity the additional velocity also
serves to maintain porosity at its imposed value. The additional velocity is calculated within
the model.
Seepage can be upwelling or downwelling (infiltration). It affects only the dissolved substances. Seepage implies transport fluxes across the sediment-water interface, the interfaces
of the sediment layers, and the interface of the lower sediment layer and the deeper inactive
sediment. The seepage advection flux is:

F advd =

vd × f d × Cx
φ

where:

Cx
F advd
fd
vd
j

concentration of a substance [g.m−3 ]
dissolved advection flux [g.m−2 .d−1 ]
dissolved fraction of a substance [−]
volumetric seepage velocity [m.d−1 ]
porosity [−]
b

The fraction f d = 1 − f p is equal to 1.0 for all dissolved substances, except for organic
micro-pollutants and heavy metals.

Deltares

391 of 464

Processes Library Description, Technical Reference Manual

Dispersion
Bioturbation by benthic organisms causes the dispersion of particulate substances. The pertinent dispersion flux is approximated with:

F disp = max (1 − φ1 , 1 − φ2 ) ×Dp×

(f p1 × Cx1 / (1 − φ1 ) − f p2 × Cx2 / (1 − φ2 ))
(L1 + L2 )

where:

Cx
Dp
F disp
fp
L
φ

bulk concentration of a substance [g.m−3 ]
particulate dispersion coefficient [m2 .d−1 ]
particulate dispersion flux [g.m−2 .d−1 ]
particulate fraction of a substance [−]
dispersion length [m]
porosity [−]
1 and 2 refer to two adjacent sediment layers (grid cells)

indexes

T

b

DR
AF

Each dispersion length L is the half thickness of the sediment layer concerned. The bioturbation flux is zero at the sediment-water interface.
Benthic organisms also cause bio-irrigation, the dispersion of dissolved substances. Water
flow across the sediment causes micro-turbulence in the upper pore water, which is another
source of dispersion. The overall dispersion coefficient includes the effects of bio-irrigation,
flow and molecular diffusion. The dispersion of dissolved substances implies transport fluxes
across the sediment-water interface. These fluxes include the so-called return fluxes of nutrients to the water column and the sediment oxygen consumption flux. The dispersion flux of a
solute follows from:

F disd = min (φ1 , φ2 ) × Dd ×
where:

Cx
Dd
F disd
fd
L
φ

indexes

(f d1 × Cx1 /φ1 − f d2 × Cx2 /φ2 )
(L1 + L2 )

concentration of a substance [g.m−3 ]
diffusion or dispersion coefficient [m2 .d−1 ]
dissolved dispersion flux [g.m−2 .d−1 ]
dissolved fraction of a substance [−]
dispersion length [m]
porosity [−]
1 and 2 refer to two adjacent sediment layers (grid cells)
b

Each dispersion length L is the half thickness of the sediment layer concerned. For the
sediment-water interface L1 in the lower water layer is an input parameter. The bio-irrigation
flux is zero at the interface of the lower sediment layer and the deeper sediment (lower boundary).
Directives for use
1 Porosity φ is the input parameter Porinp which can be used for fixed porosity (constant)
as well as transient porosity (time series). The porosity is “fixed”, equal to the input value,
if Porinp is larger than 10−4 . If smaller, porosity is variable. Representative values of the
porosity are 0.4 for sandy sediment, 0.7 for silty sediment and 0.9 for peaty sediment
(partially consolidated top sediment in a water system!).
2 Poros is an output parameter that can be used to verify the imposed porosity. It is calculated by auxiliary process DMVolume that needs densities RhoIM and RhoOM as input
parameters.

392 of 464

Deltares

Sediment and mass transport

DR
AF

T

3 Input option parameter SwErosion can be used to choose the resuspension formulations.
The Partheniades-Krone formulations (SwErosion = 0.0) are given above. The De Boer
formulations (SwErosion = 1.0) have been documented elsewhere.
4 Input option parameter SwSediment can be used to choose fixed or variable layer thickness. SwSediment = 0.0 for fixed thickness, and SwSediment = 1.0 for variable thickness. These input parameters are also used to calculate initial volumes and quantities of
substances in all sediment grid cells.
5 With regard to layer thickness three parameters can be defined for each layer. FixTh
is used to quantify fixed layer thicknesses. MaxTh and MinTh specify the maximal and
minimal layer thickness in the case of transient layer thickness.
6 The seepage velocity is the input parameter Vseep, which has a negative value in the
case of downwelling.
7 Only in the case of transient layer thickness the volumetric burial and digging velocity
needs to be provided as input parameter VburDM. A positive value implies burial, a negative value digging
8 DifCoef affects mass transport of dissolved substances across all sediment interfaces,
except for the lower sediment boundary. Any value given for this interface will be ignored.
The first given value concerns the sediment-water interface. A representative summer
value for DifCoef near the sediment-water interface for a shallow freshwater system is
5.0 × 10−4 m2 d−1 . This value is the sum of bio-irrigation, flow induced dispersion and
molecular diffusion. The winter value can be 20 % of the summer value. Bio-irrigation
can be significantly faster in marine sediments. DifCoef decreases exponentially with
depth, and is practically equal to the molecular diffusion coefficient corrected for tortuosity (φ2 ) at depths below 0.1 m in freshwater systems, and below 0.4 m in marine
water systems. A representative value for the corrected molecular diffusion coefficient is
0.25 × 10−4 m2 d−1 .
9 TurCoef affects mass transport of particulate substances across all sediment interfaces,
except for the sediment-water interface. The first given value concerns the interface between the top sediment layer and the second layer. A representative summer value for
TurCoef near the sediment-water interface for a shallow freshwater system is 2.0 × 10−6
m2 d−1 . The winter value can be 10 % of the summer value. Bioturbation can be significantly faster in marine sediments. TurCoef decreases exponentially with depth, and is
practically equal to zero at depths below 0.1 m in freshwater systems, and below 0.4 m
in marine water systems.
10 The dispersion length at the water side of the sediment-water interface Diflen can usually
be provided as a constant value between 0.0005 and 0.001 m.
References

Smits and Van Beek (2013)

Table 13.4: Definitions of the input parameters in the above equations for ADVTRA, DSPTRA and TRASE2_(i) (or TRSE2_(i) or TRSE2(i)). Volume units refer to bulk
( ), water ( ) or solids ( ).
b

w

s

Name in formulas

Name in input

Definition

Units

A

Surf

surface area of overlying water compartment

m2

Dd
Dp

Dif Coef 1) dispersion coefficient for solutes
T urCoef 1) dispersion coefficient for particulates

Deltares

m2 .d−1
m2 .d−1

393 of 464

Processes Library Description, Technical Reference Manual

F res0

ZResDM

zero order resuspension flux

gDM.m−2 .d−1

Hmin

MinDepth

minimal water depth for resuspension

m

L1
−
−

Diflen

m
m
m

−

M inT h2)

dispersion length in the overlying water
fixed layer thickness
maximal layer thickness for variable
thickness
minimal layer thickness for variable
thickness

SwErosion
SwSediment

SwErosion
option (0= Part-Krone; 1= De Boer)
SwSediment option (0= fixed layers; 1= variable)

vp
vd

VburDM
Vseep

burial and digging velocity
seepage velocity

m.d−1
m.d−1

∆t

Delt

timestep

d−1

j
τ
τc
1)
2)

m
−
−

T

DR
AF

ρi

F ixT h2)
M axT h2)

RhoIM
RhoOM

density of inorganic matter
density of organic matter

g.m−3
g.m−3

P orinp2

input porosity

−

Tau
TauCrDM

shear stress
critical shear stress for resuspension

Pa
Pa

s

s

Needs to be specified for each interface in a sediment column.
Needs to be specified for each layer in a sediment column.

394 of 464

Deltares

Sediment and mass transport

Transport in sediment and resuspension (S1/2)
PROCESSES :

S12TRA( I ), RES_DM, BUR_DM, DIG_DM, S1_COMP, S2_COMP,
PARTS1_( I ), PARTS2_( I )

T

Sediment components as present in the model for sediment layers S1 and S2 are subject to
resuspension (erosion) and burial or digging. Components are released into the water column
due to resuspension (erosion). Burial leads to the transport of components from layer S1 to
layer S2, and to the removal of components from the layer S2 to deeper sediment (boundary).
Digging is the opposite of burial, and may transport components from deeper sediment to
layer 2 (boundary), and from layer S2 to layer S1. The “deep” sediment boundary for S2 is
defined by means of the concentrations of the components in the boundary layer. The fluxes
of these processes are proportional to the fluxes of total sediment (dry matter) for all sediment components. These components may include inorganic sediment, microphytobenthos
biomass, particulate detritus (C, N, P, Si), organic micropollutants and heavy metals.
The destination of the resuspension fluxes to the water column is as follows:

 the inorganic sediment components are allocated to similar substances in the water column;

DR
AF

13.4

 the biomass of microphytobenthos (DiatS1) is allocated to the particulate detritus pools
(POC/N/P1) and OPAL;

 the particulate detritus fractions DET(C,N,P,Si) and OO(C,N,P,Si) are allocated to the
particulate detritus pools (POC/N/P1) and OPAL, and to the particulate detritus pools
(POC/N/P2) and OPAL, respectively;
 inorganic adsorbed phosporus, organic micropollutants and heavy metals are allocated to
to similar substances in the water column .
Resuspension is shear stress dependent according to Partheniades-Krone (Partheniades,
1962; Krone, 1962) formulations. The resuspension rate is zero, when the shear stress exceeds a certain critical value, or when the water depth is smaller than a certain critical depth.
Volume units refer to bulk ( ), water ( ) or solids ( ).
b

w

s

Implementation

Processes S12TRA(i) with (i) equal to a name of a substance in the water column have been
implemented for the following substances:

 IM1, IM1S1, IM1S2, IM2, IM2S1, IM2S2, IM3, IM3S1 and IM3S2.

Process S12TRADiat has been implemented for the following substances:

 Diat, DiatS1, DiatS2 (DYNAMO), POC1, PON1, POP1 and Opal.
Processes S12TRA(i) with (i) equal to a name of a substance in the water column and
S12TRADetS have been implemented for the following substances:

 POC1, DetCS1, DetCS2, PON1, DetNS1, DetNS2, POP1, DetPS1, DetPS2, Opal, DetSiS1 and DetSiS2.
Processes S12TRA(i) with (i) equal to a name of a substance in the water column have been
implemented for the following substances:

Deltares

395 of 464

Processes Library Description, Technical Reference Manual

 POC2, OOCS1, OOCS2, PON2, OONS1, OONS2, POP2, OOPS1, OOPS2, Opal, OOSiS1
and OOSiS2.
Process S12TRAAAP has been implemented for the following substances:

 AAP, AAPS1 and AAPS2.
Processes S12TRA(i) with (i) equal to a name of a substance in the water column have been
implemented for the following substances:

 OMP, OMPS1, OMPS2, 153, 153S1, 153S2, Atr, AtrS1, AtrS2, BaP, BaPS1, BaPS2, Diu,

T

DiuS1, DiuS2, Flu, FluS1, FluS2, HCB, HCBS1, HCBS2, HCH, HCHS1, HCHS2, Mef,
MefS1 and MefS2.
Processes S12TRA(i) with (i) equal to a name of a substance in the water column have been
implemented for the following substances:

 As, AsS1, AsS2, Cd, CdS1, CdS2, Cr, CrS1, CrS2, Hg, HgS1, HgS2, Ni, NiS1, NiS2, Pb,

DR
AF

PbS1, PbS2, Va, VaS1, VaS2, Zn, ZnS1 and ZnS2.

Processes S12TRA(i) use the resuspension fluxes of sediment dry matter from process RES_DM,
the burial fluxes of sediment dry matter from process BUR_DM, and the digging fluxes of sediment dry matter from process DIG_DM. These processes derive the quantities of dry matter
in layers S1 and S2 from processes S1_COMP and S2_COMP, and the dry matter settling
flux from process SUM_SEDIM.
The processes for organic nutrients in detritus use input from processes S1_COMP and
S2_COMP with regard to stochiometric ratios for nutrients N, P and Si, the actual layer thicknesses and the densities of the sediment in the layers.
The processes for organic micropollutants and heavy metals use input from processes PARTS1_(i)
and PARTS1_(i) with regard to particulate concentrations.
Table 13.5 to 13.8 provide the definitions of the input parameters occurring in the formulations.
Formulation

Resuspension

The resuspension flux of sediment dry matter is described as the sum of zero-order and firstorder kinetics according to:

F resj 0 = f tauj × (F res0 + r × Cdmj /A)
F resj 0 = 1.0 else


Cdm
0
F resj = min F resj ,
A × ∆t

if H < Hmin

if DM S1 > 0.0 F resS2 = 0.0
if τ = −1.0 fτ = 1.0 else

f tauj = max(0.0, (

396 of 464

τ
− 1.0))
τ cj
Deltares

Sediment and mass transport

where:
surface area of overlying water compartment [m2 ]
amount of sediment dry matter [gDM ]
zero-order resuspension flux of sediment [gDM.m−2 .d−1 ]
resuspension flux of sediment [gDM.m−2 .d−1 ]
shear stress limitation function [−]
depth of the water column, thickness overlying water layer [m]
minimal depth of the water column for resuspension [m]
first-order resuspension rate [d−1 ]
shear stress [P a]
critical shear stress for resuspension [P a]
timestep in DELWAQ [d]
index for sediment layer S1 or S2.

T

A
Cdm
F res0
F res
f tau
H
Hmin
r
τ
τc
∆t
j

The resuspension of inorganic sediment components, organic carbon, nitrogen, phosphorus
and silicate components, adsorbed phosphate, micro-pollutants and heavy metals in the sediment follows from:

DR
AF

Rresi,j = f si,j × f ri,j × F resj /H
where:

fr
fs
Rres
i
j

fraction of a component in sediment dry matter [gX.gDM −1 ]
scaling factor [−] or [gX.gY −1 ]

resuspension rate of a component [gX.m−3 .d−1 ]
index for component i
index for sediment layer S1 or S2.
b

The ratio f s is a scaling factor that is equal to 1.0 for most substances. It is component
specific for the organic nutrients, in fact the stochiometric ratio of N, P or Si in organic detritus.
Burial

The burial fluxes can be calculated on the basis of sediment layers with fixed thicknesses or
on the basis of imposed burial rates.
For option SWSediment=0.0 layer thicknesses are kept constant. The burial fluxes of sediment dry matter follows from:

(
F inj +
F burj =
0.0

(Zj −Zf ixj )×ρj ×(1 −φj )
∆t

if Zj ≥ Zfix j

F in1 = Fset
F in2 = Fbur 1
where:
Fbur
Fin
Fset
Z
Zfix

ϕ

Deltares

burial flux of sediment [gDM.m−2 .d−1 ]
influx of sediment [gDM.m−2 .d−1 ]
settling flux of sediment [gDM.m−2 .d−1 ]
actual thickness of sediment layer [m]
fixed thickness of sediment layer [m]
porosity [−]

397 of 464

Processes Library Description, Technical Reference Manual

density of sediment dry matter (g.m−3 )

ρ
∆t
j

b

timestep in DELWAQ [d]
index for sediment layer S1 or S2.

For option SWSediment=1.0 layer the burial fluxes of sediment dry matter are described as
the sum of zero-order and first-order kinetics according to:

T

F burj = min ((F binj + F badj ), F bmax j )
F binj = F bur0j + rbj × Cdmj /A


(Zj − Zmax j ) × ρj × (1 − φj )
F badj = max 0 ,
∆t
Cdmj
F bmax j = F inj − F outj +
A × ∆t
Cdmj = A × Zj × ρj × (1 − φj )

DR
AF

F in1 = Fset
F in2 = Fbur 1

F out1 = Fres 1
F out2 = Fdig 1
where:

A
Cdm
F bad
F bin
F bmax
F bur0
F bur
F dig
F in
F out
F res
F set
rb
Z
Zf ix
Zmax
ϕ
ρ
∆t
j

surface area of overlying water compartment [m2 ]
amount of sediment dry matter [gDM ]
additional burial flux to obey maximal layer thickness [gDM.m−2 .d−1 ]
burial flux of sediment based on input parameters [gDM.m−2 .d−1 ]
maximal possible burial based on available sediment [gDM.m−2 .d−1 ]
zero-order burial flux of sediment [gDM.m−2 .d−1 ]
burial flux of sediment [gDM.m−2 .d−1 ]
digging flux of sediment [gDM.m−2 .d−1 ]
influx of sediment [gDM.m−2 .d−1 ]
outflux of sediment [gDM.m−2 .d−1 ]
resuspension flux of sediment [gDM.m−2 .d−1 ]
settling flux of sediment [gDM.m−2 .d−1 ]
first-order burial rate [d−1 ]
actual thickness of sediment layer [m]
fixed thickness of sediment layer [m]
maximal thickness of sediment layer [m]
porosity [−]
density of sediment dry matter [g.m−3 ]
b

timestep in DELWAQ [d]
index for sediment layer S1 or S2.

The burial of inorganic sediment components, organic carbon, nitrogen, phosphorus and silicate components, adsorbed phosphate, micro-pollutants and heavy metals in the sediment
follows from:

F buri,j = f si,j × f ri,j × F burj
Rburi,j = F buri,j /H
where:

398 of 464

Deltares

Sediment and mass transport

fr
fs
H
F bur
Rbur
i
j

fraction of a component in sediment dry matter [gX.gDM −1 ]
scaling factor [−] or [gX.gY −1 ]
depth of the water column, thickness overlying water layer [m]
burial flux of a component [gX.m−2 .d−1 ]
burial rate of a component [gX.m−3 .d−1 ]
index for component i
index for sediment layer S1 or S2.
b

The ratio f s is a scaling factor that is equal to 1.0 for most substances. It is component
specific for the organic nutrients, in fact the stochiometric ratio of N, P or Si in organic detritus.
Digging

T

As for burial the digging fluxes can be calculated on the basis of sediment layers with fixed
thicknesses or on the basis of imposed digging rates.
For option SWSediment=0.0 layer thicknesses are kept constant. The burial fluxes of sediment dry matter follows from:

DR
AF

if Zj < Zf ixj then

F digj = F outj +

(Zf ixj − Zj ) × ρj × (1 − φj )
∆t

if Zj = Zf ixj then

F digj = F outj

and

F out1 = Fres 1
F out2 = Fdig 1

where:

F dig
F out
F res
Z
Zf ix
ϕ
ρ
∆t
j

digging flux of sediment [gDM.m−2 .d−1 ]
outflux of sediment [gDM.m−2 .d−1 ]
resuspension flux of sediment [gDM.m−2 .d−1 ]
actual thickness of sediment layer [m]
fixed thickness of sediment layer [m]
porosity [−]
density of sediment dry matter [g.m−3 ]
b

timestep in DELWAQ [d]
index for sediment layer S1 or S2.

For option SWSediment=1.0 layer the digging fluxes of sediment dry matter are described
with zero-order kinetics according to:

F digj = min (F dig0j , F dmax j )
Cdm2
F dmax 1 =
A × ∆t
F dmax 2 = ∞
Cdm2 = A × Z2 × ρ2 × (1 − φ2 )
where:

Deltares

399 of 464

Processes Library Description, Technical Reference Manual

A
Cdm
F dig
Fdig0
Fdmax

Z
ϕ
ρ
∆t
j

surface area of overlying water compartment [m2 ]
amount of sediment dry matter [gDM ]
digging flux of sediment based on input parameters [gDM.m−2 .d−1 ]
zero-order digging flux of sediment [gDM.m−2 .d−1 ]
maximal possible digging based on available sediment [gDM.m−2 .d−1 ]
actual thickness of sediment layer [m]
porosity [−]
density of sediment dry matter (g.m−3 )
timestep in DELWAQ [d]
index for sediment layer S1 or S2.
b

T

The digging of inorganic sediment components, organic carbon, nitrogen, phosphorus and
silicate components, adsorbed phosphate, micro-pollutants and heavy metals in the sediment
is dependent on the quality of an underlying sediment layer. Using an option parameter it is
possible to allocate the quality of the layer itself or the quality of the underlying layer. Digging
follows from:
if SW Digj = 0.0 (quality of the layer itself)

DR
AF

F digi,j = f si,j × f ri,j × F digj

if SW Digj = 1.0 (quality of underlying layer)

F digi,j = f si,j+1 × f ri,j+1 × F digj
and

Rdigi,j = F digi,j /H
where:

fr
fs
H
F dig
Rdig
i
j

fraction of a component in sediment dry matter [gX.gDM −1 ]
scaling factor [−] or [gX.gY −1 ]
depth of the water column, thickness overlying water layer [m]
digging flux of a component [gX.m−2 .d−1 ]
digging rate of a component [gX.m−3 .d−1 ]
index for component i
index for sediment layer S1 or S2.
b

The ratio f s is a scaling factor that is equal to 1.0 for most substances. It is component
specific for the organic nutrients, in fact the stochiometric ratio of N, P or Si in organic detritus.
Directives for use
1 This transport process requires a lower boundary condition as to the composition of dry
matter and the nutrient stoichiometry of detrital organic matter. However, this lower boundary condition only comes into effect when digging is included in the model. If only S1
substances are simulated, it is required to include process S2_COMP that provides the
parameters for the boundary of S1, including FrDetCS2, FrOOCS2, N-CDETCS2, NCOOCS2, P-CDETCS2, P-COOCS2, S-CDETCS2, S-COOCS2 for organic matter. A
realistic boundary requires that all relevant input parameters of S2_COMP are allocated
an input value. If both S1 and S2 substances are simulated, the transport process uses its
additional input parameters that define an S3 boundary. For organic matter this concerns
FrDetCS3, FrOOCS3, FrDetNS3, FrOONS3, FrDetPS3, FrOOPS3, FrDetSiS3, FrOOSiS3,
the weight fractions of the various components in dry matter of boundary S3.

400 of 464

Deltares

Sediment and mass transport

DR
AF

T

2 T au can be simulated with process TAU. If not simulated or imposed Tau will have the
default value -1.0, which implies that resuspension is not affected by the shear stress.
3 Resuspension does not occur, when Depth is smaller than minimal depth MinDepth for
settling, which has a default value of 0.1 m. When desired MinDepth may be given a
different value.
4 The resuspension module checks from which layer resuspension should take place: only
if no mass is available in the uppermost layer (S1), resuspension can take place from
the second layer (S2). It is assumed that mass in layer S1 protects layer S2 against
resuspension in that timestep, even if the actual bottom shear stress exceeds the critical
shear stress for bottom layer S2 (T au > TauCrS2DM ).
5 Dry matter as such is not a DELWAQ substance. Dry matter is calculated from all the
substances which contributes to dry mass and are modelled.
6 Usually only the zeroth-order part of the resuspension formulation is used.
7 The scaling factor ScalCar is equal to 10−6 for organic micro-pollutants and heavy metals
for the conversion from mgX.kgDM−1 to gX.gDM. By default ScalCar is equal to 1.0 for all
other substances.
8 For both burial options, the user may want to define the fixed or maximum thickness of the
layers as a function of time. This means that some burial can occur even if the settling
rate and the user-defined burial rate are zero. This happens if the user-defined thickness
decreases.
9 The option parameter SWDigS1 = 0.0 (default) leads to the allocation of the quality of layer
S1 (f ri,1 , f si,1 ) to the digging flux for layer S1. This option should only be used if only
S1 is simulated. The option parameter SWDigS2 = 0.0 (default) leads to the allocation of
the quality of layer S2 (f ri,2 , f si,2 ) to the digging flux for layer S2.
10 The option parameter SWDigS1 = 1.0 leads to the allocation of the quality of underlying
boundary layer S2 (f ri,2 , f si,2 ) to the digging flux for layer S1, which is logical when S1
and S2 are simulated both. The option parameter SWDigS2 = 1.0 leads to the allocation
of the quality of underlying boundary layer S3 (f ri,3 , f si,3 ) to the digging flux for layer
S2. Boundary S3 is not simulated but imposed.
11 The fluxes fResS1(i), fResS2(i), fBurS1(i), fBurS2(i), fDigS1(i), fDigS2(i) are available as
additional output parameters [gX.m−2 .d−1 ].
References

Krone (1962), Partheniades (1962)

Table 13.5: Definitions of the input parameters in the above equations for S12TRA(i).

Name in
formulas

Name in input

Definition

Units

F burj
F digj
F resj

fBur(i)DM3
fDig(i)DM3
fRes(i)DM3

burial flux of sediment from layer j
digging flux of sediment to layer j
resuspension flux of sediment from layer j

gDM.m−2 .d−1
gDM.m−2 .d−1
gDM.m−2 .d−1

f ri,j

Fr(i)(j)

fraction of a component in sediment layer j
for inorganic sediment components, microphytobenthos, detritus components, and
AAP

gX.gDM −1

f ri,j

Q(i)DM(j)

content in sediment layer j for organic micropollutants and heavy metals

mgX.kgDM −1

continued on next page

Deltares

401 of 464

Processes Library Description, Technical Reference Manual

Table 13.5 – continued from previous page
Name in input

Definition

Units

f si,j

N-CDetC(j)
P-CDetC(j)
S-CDetC(j)
or
N-COOC(j)
P-COOC(j)
S-COOC(j)

ratio of DetN and DetC in sediment layer j
ratio of DetP and DetC in sediment layer j
ratio of DetSi and DetC in sediment layer j

gN.gC −1
gP.gC −1
gSi.gC −1

ratio of OON and OOC in sediment layer j
ratio of OOP and OOC in sediment layer j
ratio of OOSi and OOC in sediment layer j

gN.gC −1
gP.gC −1
gSi.gC −1

f si,j

ScalCar

scaling factor for all other components

-

H

Depth

depth of the overlying water compartment

m

SW Digj

SWDig(j)

option parameter,
=0.0 quality of layer itself,
=1.0 quality from underlying layer

-

DR
AF

T

Name in
formulas

1) (i) is equal to one of the components in sediment.
2) (j) is generally equal to S1 or S2, that represent the pertinent sediment layer. For f ri,j
and f si,j (j) also concerns underlying boundary layer S3.
3) These fluxes are calculated by processes SUM_SEDIM, RES_DM, BUR_DM and DIG_DM.

Table 13.6: Definitions of the input parameters in the above equations for RES_DM.

Name in
formulas

Name in
input

Definition

Units

Cdmj

DM(j)

amount of sediment dry matter in sediment
layer j

gDM

ZResDM

zero-order resuspension flux of sediment

gDM.m−2 .d−1

Surf
Depth
MinDepth

surface area of overlying water comp.
depth of the overlying water compartment
minimal water depth for resusp. and settling

m2
m
m

VResDM

first-order resuspension rate of sediment

d−1

Tau

shear stress

Pa

τ cj

TaucR(j)DM

critical shear stress for resusp. from sediment layer j

Pa

∆t

Delt

timestep in DELWAQ

d

F res0
A
H
Hmin
r
τ

1)(j) is equal to S1 or S2, which represents the pertinent sediment layer

402 of 464

Deltares

Sediment and mass transport

Table 13.7: Definitions of the input parameters in the above equations for BUR_DM.

Name in
formulas

Name in input

Definition

Units

Fbur0 j

ZBurDM(j)

zero-order burial flux of sediment in layer j

gDM.m−2 .d−1

Fset

f SedDM 2) settling flux of sediment

gDM.m−2 .d−1

Fres j

fRes(j)DM

resuspension flux of sediment

gDM.m−2 .d−1

A

Surf

m2

Zj

ActTh(j)

Zf ixj

FixTh(j)

Zmaxj

MaxTh(j)

surface area of overlying water compartment
actual thickness of sediment layer j fixed
thickness of sediment layer j maximal thickness of sediment layer j
fixed thickness of sediment layer j maximal
thickness of sediment layer j
maximal thickness of sediment layer j

T

DR
AF

rbj

VBurDM(j)

m

first-order burial rate of sediment in layer j

SW Sediment
SWSediment option parameter,

m
m

d−1
-

=0.0 apply fixed layer thickness,
=1.0 apply burial kinetics

ϕj
ρj
∆t
1)
2)

Por(j)
Rho(j)

shear stress
critical shear stress for resusp. from sediment layer j

Pa
Pa

Delt

timestep in DELWAQ

d

(j) is equal to S1 or S2, which represents the pertinent sediment layer
fSedDM is calculated by process SUM_SEDIM

Table 13.8: Definitions of the input parameters in the above equations for DIG_DM.

Name in
formulas

Name in input

Definition

Units

F dig0j

ZDigDM(j)

zero-order digging flux of sediment in layer j

gDM.m−2 .d−1

F res1

fResS1DM2

resuspension flux of sediment in layer 1

gDM.m−2 .d−1

A
Zj
Zfix j

Surf
ActTh(j)
FixTh(j)

surface area of overlying water comp.
actual thickness of sediment layer j
fixed thickness of sediment layer j

m2
m
m

SWSedimentSWSediment option parameter,

-

=0.0 apply fixed layer thickness,
=1.0 apply burial kinetics

ϕj

Por(j)

shear stress

Pa
continued on next page

Deltares

403 of 464

Processes Library Description, Technical Reference Manual

Table 13.8 – continued from previous page
Name in
formulas

ρj

Name in input
Rho(j)

∆t

Delt

1)

Units

critical shear stress for resusp. from sediment layer j

Pa

timestep in DELWAQ

d

(j) is equal to S1 or S2, which represents the pertinent sediment layer
fResS1DM is calculated by process RES_DM.

DR
AF

T

2)

Definition

404 of 464

Deltares

Sediment and mass transport

Calculation of horizontal flow velocity
PROCESS :

VELOC

This process calculates the horizontal flow velocity in a segment. It is assumed that per
segment in at most two horizontal directions mass-flows of water are known. These directions
are assumed to be perpendicular to each other. In each direction the two flow velocities
are averaged. Next the horizontal flow velocity is calculated using Pythagoras’ theorem, the
minimum or the maximum from the two directions.

T

To account for model grids that are not aligned to the coordinate system, two parameters for
the grid orientation are available (see the table). Also the contributions in each directions may
be weighed differently – as the arithmetic mean of the velocities per exchange, weighed by
the flow rate or the area or using the maximum velocity value.
Formulation

DR
AF

13.5

V elocAvg1 =

F low1,1
Area1,1
F low2,1
Area2,1

+
2
+

F low1,2
Area1,2
F low2,2
Area2,2

V elocAvg2 =
2
q
V eloc = V elocAvg12 + V elocAvg22

where

F low1,1 horizontal "from"-flow direction 1 [m3 s−1 ]
F low1,2 horizontal "to"-flow direction 1 [m3 s−1 ]
F low2,1 horizontal "from"-flow direction 2 [m3 s−1 ]
F low2,2 horizontal "to"-flow direction 2 [m3 s−1 ]
Area1,1 horizontal "from"-area direction 1 [m2 ]
Area1,2 horizontal "to"-area direction 1 [m2 ]
Area2,1 horizontal "from"-area direction 2 [m2 ]
Area2,2 horizontal "to"-area direction 2 [m2 ]
V elocAvg1 average horizontal flow velocity direction 1 [m s−1 ]
V elocAvg2 average horizontal flow velocity direction 2 [m s−1 ]
V eloc
average horizontal flow velocity [m s−1 ]

Deltares

405 of 464

Processes Library Description, Technical Reference Manual

Directives for use
The process VELOC uses flows in the horizontal direction and therefore is only applicable if
one of both of the horizontal (1st and 2nd) directions are available (1DH, 2DH, 2DV, 3D).
Note: The computed flow velocity is not identical to the one that would have been computed
by Delft3D-FLOW. As a result, artificial peaks may occur near shallow areas. If you use this
velocity to estimate the shear stress for sediment transport, this causes large erosion fluxes.
It is better, if possible, to rely on the shear stresses as computed by the hydrodynamic model.
Table 13.9: Definitions of the input and output parameters for VELOC

Name in output

Definition

Units

–

Orient1

◦

–

Orient2

V elocmax

M axV eloc

Angle of the main positive flow direction
with the x-axis
Angle of the secondary positive flow direction (both optional)
Maximum velocity (useful to "clip" spurious
results)
Weighing method: 1 – linear average, 2 –
weighed by flow rate
3 – weighed by area, 4 – maximum contribution
Method for determining the velocity magnitude: 1 – Pythagoras,
2 – maximum, 3 – minimum
Velocity magnitude
Direction of the flow velocity
Velocity component in main direction
Velocity component in secondary direction

ms−1

–

V eloc
–

DR
AF

–

T

Name in
formulas

V elocAvg1
V elocAvg2

406 of 464

SW CalcV elo

SW AvgV elo

V elocity
F lowDir
V eloc1
V eloc2

◦

ms−1
[-]
[-]
[-]
[-]

◦

ms−1
ms−1

Deltares

Sediment and mass transport

Calculation of the Chézy coefficient
PROCESS :

CHEZY

Implementation
This process calculates the Chézy coefficient based on the Manning coefficient or Nikuradse
roughness length. For 3D calculations a corrected coefficient is calculated.
Formulation
Depth-averaged Velocities

1. White-Colebrook



H
= 18 log 12
ks

T

Two methods have been implemented to calculate the Chézy coefficient for depth averaged
velocities.

DR
AF

13.6

C2D

C2D
H
ks

10

(13.1)

Chézy coefficient for depth averaged conditions [m1/2 s−1 ]
water depth [m]
Nikuradse roughness length scale [m]

2. Manning (default)

√
6

C2D =

C2D
H
n

H
n

Chézy coefficient [m1/2 s−1 ]
total depth of water column (segment depth) [m]
Manning coefficient [m−1/3 s]

Three-dimensional Velocity

Under the requirement that the depth-averaged velocity of 3D computations equals the velocities obtained with the 2DH model the Chézy coefficient can de derived as follows:
Roughness height z0 of the bed:


κ C
− 1+ √2D
g

z0 = H e

(13.2)

with

z0
H
κ
g
C2D

Deltares

roughness height of the bed [m]
depth of the entire water column [m]
0.41 - Von Kármán coefficient [-]
9.811 - gravity constant [m s−2 ]
Chézy coefficient for 2D using the segment depth [m1/2 s−1 ]

407 of 464

Processes Library Description, Technical Reference Manual

Chézy coefficient for three-dimensional velocities

√

C3D



g
hb /2
ln 1 +
=
κ
z0
Chézy coefficient in case of 3D velocities [m1/2 s−1 ]
depth of the computational layer at the bed [m]
0.41 - Von Kármán coefficient [-]
9.811 - gravity constant [m s−2 ]
roughness height of the bed [m]

C3D
hb
κ
g
z0

T

Directives for use
 Chézy is sometimes available from hydrodynamical models (e.g. from Delft3D-FLOW
Delft3D-FLOW UM (2013)).
 For the three-dimensional case, the conversion from C2D to C3D is done within the CALTAU process, not the CHEZY process. This parameter is not output from the process.

DR
AF

Additional references
Delft3D-FLOW UM (2013)

Table 13.10: Definitions of the input and output parameters for CHEZY

Name in
formulas

Name in output

Definition

Units

ks
n
hb
H
SwChezy

Rough
M anncoef
Depth
T otalDepth
SwChezy

Nikuradse roughness length
Manning coefficient
Thickness of the segment (near the bed)
Depth of the entire water column
Choice for White-Colebrook or Manning

m
m−1/3 s
m
m
[-]

C2D

CHEZY

Two-dimensional Chézy coefficient

m1/2 s−1

408 of 464

Deltares

Sediment and mass transport

Waves
PROCESS :

WAVE

Formulations
The computation of the shear stress from wind generated waves uses three wave parameters:
the wave height H , the wave period T and the wave length L. They are calculated as follows
(Groen and Dorrestein, 1976; Holthuijsen, 1980):

g = 9.8
ρl = 1000

T

if InitDepth ≤ 0 : InitDepth = TotalDepth

g × F etch
vW ind2
g × InitDepth
dS =
vW ind2

FS =

DR
AF

13.7

HS = 0.24 × tanh(0.71 ×

d0.763
)
S



× tanh

0.015 × FS 0.45
tanh(0.71 × dS 0.763 )



HS × W ind2
H=
g

TS = 2π × tanh(0.855 × dS

0.365



) tanh

0.0345 × FS 0.37
tanh(0.855 × dS 0.365 )



TS × W ind
g


2
gT
2π × InitDepth
L=
tanh
2π
L0

T =

with

FS

standardized fetch [-]
TotalDepth total water depth [m]
InitDepth water depth were waves are generated [m]
dS
significant depth [-]
HS
significant wave height [-]
TS
significant wave period [-]

The wave length L can be calculated by a one-step iteration:

L0 =

Deltares

gT 2
2π

409 of 464

Processes Library Description, Technical Reference Manual

The wave length L, wave period T and water depth h satisfy the dispersion relation:

2π
T
2π
k=
L
ω 2 = gk tanh(k × T otalDepth)
ω=

with

ω
k

T

radial frequency [1/s]
wave number [1/m]

DR
AF

Directives for use
 By default the depth at the origin of the wave (InitDepth) equals the actual depth (TotalDepth), because the default value for InitDepth is −1. InitDepth and Fetch can be
determined from the wind direction by the processes WDepth and WFetch.
 This process can be active for non-layered and multi-layer models. The fact that the water
column is modelled in layers does not affect the result.
Table 13.11: Definitions of the input and output parameters for WAVE

Name in
formulas

Definition

Units

vW ind
V W ind
F etch
F etch
InitDepth InitDepth
T otalDepthT otalDepth

Wind velocity
Fetch length
Depth where the waves originate
Depth of the entire water column (if InitDepth = -1)

ms1
m
m
m

H
L
T

Significant wave height
Significant wave length
Significant wave period

m
m
s

410 of 464

Name in output

W aveHeight
W aveLength
W aveP eriod

Deltares

Sediment and mass transport

Calculation of wind fetch and wave initial depth
PROCESS :

WDEPTH, WFETCH

The wind fetch (F etch) and the wave initial depth (InitDepth) at which the waves have
been created can be provided by you as a (block) function of the wind direction.
Implementation

Formulations
Assume W inDir0 = 0◦
For W inDiri−1 < W indDir ≤ W inDiri

F etch = W F etch_i
InitDepth = W Depth_i

with

T

This process is implemented for the characteristics F etch and InitDepth, determining the
forming of waves.

DR
AF

13.8

W indDir actual wind direction [degr]
W inDiri wind direction of data pair i [degr]
W F etchi fetch of data pair i [m]
W Depthi wave initial depth of data pair i [m]

Directives for use
 A minimum of two data pairs and a maximum of eigth data pairs should be provided. The
first data pair applies to wind directions between 0◦ and W inDir1 , the second between
W inDir1 and W inDir2 , etc. The last data pair provided by you applies to all wind
direction ranging from the one but last provided W inDiri−1 to 360◦ .
 The wind direction is defined as the angle relative to north of the direction where the wind
is coming from, while the flow direction is defined as the angle of the direction where the
water is going to.
Table 13.12: Definitions of the input and output parameters for WDEPTH. (i) runs from 1
to 8. Only the input parameters for (i) is 1 and 2 are required.

Name in
formulas

Definition

Units

W indDir W indDir
W Depth( i)W Depth( i)
W inDir( i) W inDir( i)

Actual direction of the wind
Depth for wind from direction (i)
Direction (i) for wind

◦

InitDepth InitDepth

Depth to be used for wave parameters

m

Deltares

Name in output

m
◦

411 of 464

Processes Library Description, Technical Reference Manual

Table 13.13: Definitions of the input and output parameters for WFETCH. (i) runs from 1
to 8. Only the input parameters for (i) is 1 and 2 are required.

Name in
formulas

Name in output

Definition

Units

W indDir W indDir
W F etch( i) W F etch( i)
W inDir( i) W inDir( i)

Actual direction of the wind
Fetch length for wind from direction (i)
Direction (i) for wind

◦

F etch

Fetch length used for wave parameters

m

◦

DR
AF

T

F etch

m

412 of 464

Deltares

Sediment and mass transport

Calculation of bottom shear stress
PROCESS :

CALTAU

Implementation
The bottom shear stress is calculated as the sum of the shear stress caused by waves, flow
and ship movements. If the directions of the flow (FlowDir) and the wind (WindDir) are supplied
the wind and flow stresses are summed as vectors, otherwise as scalars. The stress by ship
movements is always added as a scalar as it is assumed to be independent of direction.

τ = τwind + τf low + τship

T

Formulations

Bed shear stress due to flow (used if the switch SW T auV eloc is set to 1, the default – see
below):

τf low =

ρl × g × V elocity 2
Chezy 2

DR
AF

13.9

The Chézy coefficients is either user input or can be calculated by the process CHEZY.
Bed shear stress due to wave friction, time averaged over half a wave period:

1
2
τwind = ρl fw Ubg,max
4
Ubg,max =

T sinh
2π
ω=
T
Ubg,max
Ag =
ω

πH

2π×T otalDepth
L



Ag [m] is the peak value of the horizontal displacement at the bottom.
s

τ × Chezy 2
CalV elT au =
ρl × g
The wave parameters H , T and L are input items, which can be calculated by process WAVE.
The wave height H is limited according to (Nelson, 1983):

H = min(0.55 × T otalDepth, H)
The wave friction factor fw can be calculated according to Tamminga (1987); Swart (1974) or
Soulsby (1997).

Deltares

413 of 464

Processes Library Description, Technical Reference Manual

SWTau = 1 (Tamminga, 1987):

s
fw = 0.16

Rough
Ubg,max × T /2π

SWTau = 2 (Swart, 1974):

r=

H
2 × Rough × sinh( 2π×T otalDepth
)
L

fw = 0.00251 exp(5.213r−0.19 )
else

DR
AF

fw = 0.32

T

if r > π/2 then

SWTau = 3 (Soulsby, 1997):

r=

H
)
2 × Rough × sinh( 2π×T otalDepth
L

fw = 0.237r−0.52
SW T au
SW T auV eloc
τ
τwind
τf low
τship

V eloc
Ubg,max
Rough

g
ρl
H
T
L
Fw
T auF low

switch to calculate the wave fraction factor [-]
switch to calculate the bottom shear stress due to flow from the flow
velocity or rely on T auF low instead [-]
bottom shear stress [N m−2 ]=[Pa]
part of bottom shear stress caused by wind [Pa]
part of bottom shear stress caused by flow velocity [Pa]
part of bottom shear stress defined by you, e.g. to describe the effect
of ships [Pa]
flow velocity [m s−1 ]
amplitude of the wave orbital velocity [m s−1 ]
Nikuradse bottom roughness length scale, calculated from the Chézy
coefficient via the inverse of Eq. (13.1) [m]
acceleration of gravity [m s−2 ]
density of water [kg m−3 ]
wave height [m]
wave period [s]
wave length [m]
wave (friction) factor [-]
bottom shear stress due to flow (used only if SW T auV eloc is set
to 2) [-]

Directives for use
 The bottom shear stress is sometimes available from hydrodynamic models. If so, you can
set the switch SW T auV eloc to 2. The component of the shear stress due to the flow
velocity is then taken from the input parameter TauFlow.

414 of 464

Deltares

Sediment and mass transport

 The process is meant to combine the contributions to the bottom shear stress from various
sources. If a hydrodynamic model provides a bottom shear stress that incorporates the
contribution from surface waves already, then you should take care not to add the wave
component via this process. (For instance you could put the shear stress as available from
the hydrodynamic model into the input parameter T au directly and not use this process
at all.)
Table 13.14: Definitions of the input and output parameters for CALTAU

Name in output

Definition

Units

Chezy
Depth
T otalDepth
V elocity
H
L
T
τf low
τship
SW T au

Chezy
Depth
T otalDepth
V elocity
W aveHeight
W aveLength
W aveP eriod
T auF low
T auShip
SW T au

Chezy coefficient
Thickness of the segment (near the bed)
Total water depth
Flow velocity
Significant wave height
Significant wave length
Significant wave period
Shear stress due to flow
Shear stress due to ships
Switch for determining the wave roughness
Switch for using flow velocity or given flow
shear stress

m−1/2 s−1
m
m
ms1
m
m
s
Pa
Pa
[-]

Total shear stress
Shear stress due to flow velocity
Shear stress due to wind
Velocity as derived from the total shear
stress
Total shear stress

Pa
Pa
Pa
ms−1

DR
AF

T

Name in
formulas

SW T auV elocSW T auV eloc
τ
τveloc
τwind
CalV elT au

T au
T auV eloc
T auW ind
CalV elT au

τ

T au

Deltares

[-]

[-]

415 of 464

Processes Library Description, Technical Reference Manual

Computation of horizontal dispersion
PROCESS :

HD ISPERV EL

Sometimes it is convenient to relate the horizontal dispersion to the flow velocity, for instance
in river systems or if the horizontal grid cells are too large to resolve important variations in
the flow field.
The process HDisperVel estimates a horizontal dispersion coefficient to the flow velocity via
the following basic formula:

T

DH = aV b H c + DH,background
Formulations

The actual formulation is more versatile than shown above:

 The horizontal dispersion coefficient is limited to a range (DH,min , DH,max ).
 The flow velocity is determined from the available flow rate and the area per exchange.

DR
AF

13.10

The formulation used is:


|f low/area|, if area > 10−10
velocity =
0
otherwise


Df acta × velocity Df actb × T otalDepthDf actc + Dback
horzdisp =
max(min(horzdisp, Dmax ), Dmin )
Table 13.15: Definitions of the input and output parameters for HDISPERVEL

Name in
formulas

Name in output

Definition

Units

f low

f low

Flow rate at exchange (automatically available)
Area at exchange (automatically available)
Factor a in dispersion calculation
Factor b in dispersion calculation
Factor c in dispersion calculation
Background dispersion coefficient
Minimum dispersion coefficient to be used
Maximum dispersion coefficient to be used
Mean total depth at the segments on either
side of the exchange

m3 s−1

Computed horizontal dispersion coefficient
at exchange

m2 s−1

area
Df acta
Df actb
Df actc
Dback
Dmin
Dmax
T otalDepth

area
Df acta
Df actb
Df actc
Dback
Dmin
Dmax
T otalDepth

horzdisp

horzdisp

416 of 464

m2
[-]
[-]
[-]
m2 s−1
m2 s−1
m2 s−1
m

Deltares

Sediment and mass transport

Computation of horizontal dispersion (one-dimension)
PROCESS :

H ORZ D ISPER

Sometimes it is convenient to relate the horizontal dispersion to the flow velocity, for instance
in network systems. Because the representative flow velocity may not be simply related to the
flow rate and the wet area per exchange, you have to specify the velocity explicitly. Furthermore the width and the bottom roughness of the channel are taken into account.
The process HorzDisper estimates a horizontal dispersion coefficient from the given flow
velocity, width and roughness via the following basic formula:

T

αV W 2
DH = p
H g/C 2
Formulations

The formulation using the names of the coefficients is:

DR
AF

13.11

V elocity × W idth2 × Chezy
DH = DispConst ×
√
T otalDepth × g

V elocity
W idth

T otalDepth
Chezy

DispConst
g

mean of the specified flow velocity at the segments on both sides of
the exchange [m/s]
mean of the specified width at the segments on both sides of the
exchange [m]
mean of the total depth at the segments on both sides of the exchange [m]
mean of the Chézy coefficients segments on both sides of the exchange [m1/2 /s]
horizontal dispersion coefficient (again specified at the segments
and averaged) [-]
gravitational acceleration (fixed at 9.81) [m/s2 ]

Table 13.16: Definitions of the input and output parameters for HORZDISP

Name in
formulas

Name in output

Definition

Units

V elocity
W idth
Chezy
T otalDepth
DispConst
–

V elocity
W idth
Chezy
T otalDepth
DispConst
HorzDispM x

Magnitude of the flow velocity
Width of the segments
Chezy coefficient
Total water depth
Coefficient for the horizontal dispersion
Maximum value for the dispersion coefficient

m−1
m
m−1/2 s−1
m2 s−1
ms1
m2 s−1

DH

HorzDisp

Calculated value for the dispersion coefficient

m2 s−1

Deltares

417 of 464

Processes Library Description, Technical Reference Manual

Allocation of dispersion from segment to exchange
PROCESS :

VERTDISP

This process converts values available within the computational segments to values on the
exchanges (contact surfaces) between two computational segments, in the third vertical direction only.
Implementation
The process is implemented for Vertical Dispersion.

T

Formulation

The process copies the value in the from segment of every exchange to the value at the
exchange area. In the current version no checks are implemented to verify whether the from
segment is indeed a real segment and not a boundary. This is not a problem if the process is
used in Delft3D.

DR
AF

13.12

Directives for use
 Be aware of the fact that this process only acts in the third direction, and that it does not
check for boundary segments.
Table 13.17: Definitions of the input and output parameters for VERTDISP

Name in
formulas

Name in output

Definition

Units

–
–

V ertDisper
ScaleV disp

Vertical dispersion at segment level
Scale factor that is applied (defaults to 1)

m2 s−1
[-]

V ertDisp

Computed
changes

m2 s−1

–

418 of 464

vertical

dispersion

at

ex-

Deltares

Sediment and mass transport

Conversion of segment variable to exchange variable
PROCESS :

S2X_RHO

This process calculates the value of segment related variables at an exchange area by linear
interpolation.
Implementation
This process is implemented for the variable RhoWater.

V arExc = V arF rom +
where

T

Formulation

V arT o − V arF rom
× XLenF rom
XLenT o + XLenF rom

DR
AF

13.13

VarExc

value of a segment-related variable at the exchange area
RhoExc : density of water [kg m−3 ]
XLenFrom DELWAQ "from"-length [m]
XLenTo
DELWAQ "to"-length [m]
VarFrom value of segment-related variable in "from"-segment
RhoWater density of water [kg m−3 ]
VarTo
value of segment-related variable in "to"-segment
RhoWater density of water [kg m−3 ]

Directives for use
 This process can be active if the third direction is defined.

Deltares

419 of 464

Processes Library Description, Technical Reference Manual

Conversion of exchange variable to segment variable
PROCESS :

RHOEXTOS, RHOGRTOS, VDISPTOS, VGRDTOS

This process converts values available on the exchanges (contact surfaces) between two computational segments to values within the computational segments in the third vertical direction
only!
Implementation

Formulation

T

The process is implemented for the Density, for the Density Gradient, for the Vertical Dispersion and for the Velocity Gradient.

The process copies the value at the exchange area between two segments to both the from
segment and the to segment of the exchange, if they do not represent a boundary. This is
done for the third (vertical) direction only.

DR
AF

13.14

Directives for use
 The results of the current version depend on the order of the exchanges in the pointer
table. Every segment gets two times a value: from the exchange where it is the from
segment and from the exchange where it is the to segment. The one that occurs last in
the pointer table determines the outcome. No averaging is performed.

420 of 464

Deltares

14 Temperature
Contents
14.1 Calculation of water temperature

. . . . . . . . . . . . . . . . . . . . . . 422

DR
AF

T

14.2 Calculation of temperature for flats run dry . . . . . . . . . . . . . . . . . . 424

Deltares

421 of 464

Processes Library Description, Technical Reference Manual

Calculation of water temperature
PROCESS :

TEMPERATUR

The water temperature can be modelled in two ways, one representing the absolute water
temperature and the other representing the excess water temperature (surplus above an ambient background temperature).

Implementation
This process is implemented for TEMPERATURE only.
Formulation

T

The water temperature process regulates the heat gain and loss of the water phase to the
atmosphere. The process takes into account evaporation, re-aeration and the influence of
wind on this process. The process is based on a relation for the heat exchange coefficient by
Sweers (1976)

DR
AF

14.1

If SwitchT emp = 0 the modelled temperature is the absolute temperature, in this case:

T = M odT emp
SurT emp = T − N atT emp

If SwitchT emp = 1 the modelled temperature is the surplus temperature, in this case:

SurT emp = M odT emp
T = SurT emp + N atT emp

The calculation of the heat exchange is in both cases:

dM odT emp = −RcHeat × F actRcHeat × Surtemp + ZHeatExch
4.48 + 0.049 × T + Fwind × (1.12 + 0.018 × T + 0.00158 × T 2 ) × 86400
RcHeat =
Cp × ρw × Depth
ρw = 1000.0 − 0.088 × T
Fwind = 0.75 × (3.5 + 2.05 × Vwind )
where

M odT emp
SwitchT emp
SurT emp
T
N atT emp
Depth
Vwind
Cp
RcHeat
F actRcHeat
ρw
ZHeatExch
dM odT emp

422 of 464

modelled temperature [◦ C]
switch modelled temperature is absolute (0) or surplus (1) [-]
surplus temperature [◦ C]
ambient water temperature [◦ C]
ambient natural background water temperature [◦ C]
depth of a DELWAQ segment [m]
wind velocity [m s−1 ]
specific heat of water [J kg−1 ◦ C−1 ]
rate constant for surplus temperature exchange [d−1 ]
factor on rate constant for surplus temperature exchange [-]
density of water at ambient water temperature [kg m−3 ]
zeroth order temperature exchange flux [◦ C d−1 ]
temperature exchange flux [◦ C d−1 ]

Deltares

Temperature

Directives for use
 The maximum value the temperature exchange flux can reach is limited to the amount of
surplus temperature present (−SurT emp/∆t).

DR
AF

T

If surplus temperature is modelled the ambient natural background temperature must be supplied as a constant value in time and place. Variable background temperature would lead to
an error in the energy balance of the system.

Deltares

423 of 464

Processes Library Description, Technical Reference Manual

Calculation of temperature for flats run dry
PROCESS :

TEMPERATUR

The temperature of mud- and sandflats in intertidal water systems can deviate strongly from
the water temperature during periods of emersion. The temperature increase on the flats
can be over 10 ◦ C. The rate of temperature increase can be as high as 3 ◦ C per hour. The
difference in temperature is to be accounted for in the rates of various biological processes,
the processes to which microphytobenthos is subjected in particular. The current simulation of
the temperature on flats is based on strongly simplified formulations, reflecting an pragmatic
estimation method that does not involve energy budget calculations.









water temperature;
air temperature;
solar radiation;
back radiation;
windspeed and relative air humidity;
quantity and temperature of precipitation; and
duration of the emersion period.

T

In principle, the temperature on a “run-dry” flat is a function of:

DR
AF

14.2

The following simplications are applied to the formulations in the model in order to incorporate
the various contributions to the temperature on the dry flat.
The temperature in the upper layer of a flat attains the air temperature within a short period.
Therefore, the air temperature is assigned to the top of a flat from the onset of a run-dry period.
Relative to the air temperature a further adjustment of the temperature is made according to
a gradual increase due to solar radiation and an instantaneous constant decrease due to
evaporation. Using the actual solar radiation intensity the temperature increase is scaled on
the basis of a maximal increase. The effect of reflection dependent on sediment properties
is implicit. The additional effects of back radiation and precipitation are generally small and
incidental. These effects are ignored. Water temperature is restored at the submersion of the
flat.
The actual solar radiation intensity is derived from the daily radiation and the daylength in an
auxiliary process DAYRAD. The water and air temperatures are input into the model.
Implementation

The “temperature at dry flats” process has been implemented as an additional, optional process in the generic process TEMPERATUR, that calculates the temperature of segments on
the basis of the selected option. Several options are available. The additional process can be
applied to the toplayer(s) of the sediment. The process can be made inactive using the option
parameter SW T empDF (default 0.0 = inactive; 1.0 = active).
The process modifies the input parameter T emp. Table 14.1 provides the definitions of the
parameters occurring in the formulations.
Formulation
In a first step the model checks whether emersion has taken place. The switch parameter SW emersion is set (0.0 = submersion, 1.0 = emersion) according to auxiliary process

424 of 464

Deltares

Temperature

EMERSION. In a second step the model identifies segments as water, top sediment layers
and deeper sediment layers. The top sediment layers belong to the upper sediment layer in
which the temperature adjusts to emersion. The thickness of this layer is Hst.
In the case of submersion of a certain segment the water temperature T emp is not modified. This temperature is assigned to both the water segment concerned and all underlying
sediment segments.
In the case of emersion of a certain segment the water temperature T emp is modified for
the top sediment layers above Hst. The water segments and the deeper sediment layers are
assigned water temperature T emp. The temperature of the top sediment layers is adjusted
as follows:

with:

(14.1)

∆T rad = ∆T req

T

and

DR
AF

T ts = T a + ∆T rad − ∆T ev
∆T rad = ∆t × RT rad + ∆T rad0
I
RT rad = RT rmax ×
Imax
I
∆T req = ∆T rmax ×
Imax
T = T ts

I
Imax
T
Ta
T ts
RT rad
RT rmax
∆t
∆T ev
∆T rad
∆T rad0
∆T req
∆T rmax

solar radiation intensity [W m−2 ]
maximal solar radiation intensity [W m−2 ]
temperature [◦ C]
air temperature [◦ C]
top sediment temperature in run-dry segments [◦ C]
rate of temperature increase due to solar radiation [◦ C d−1 ]
maximal rate of temperature increase due to solar radiation [◦ C d−1 ]
timestep [d]
temperature decrease due to evaporation [◦ C]
temperature increase due to solar radiation [◦ C]
temperature increase due to solar radiation in the previous timestep [◦ C]
equilibrium temperature increase due to solar radiation [◦ C]
maximal temperature increase due to solar radiation [◦ C]

Directives for use
 The formulations have been designed in such a way, that all contributions to the temperature can be manipulated by the user. The shortcomings of the strongly simplified
formulations can be compensated as much as possible by appropriate quantification of
the input parameters.
Additional references
Guarini et al. (2000)

Deltares

425 of 464

Processes Library Description, Technical Reference Manual

T

Table 14.1: Definitions of the parameters in the above equations for TEMPERATUR.

Name in
input/output

Definition

Hst

T hSedDT

thickness top sed. layer subjected
to temp. change

DR
AF

Name in
formulas

Units
m

DayRadSurf solar radiation intensity
RadM ax
maximal solar radiation intensity

W m−2
W m−2

RT radM ax

maximal rate of temp. increase due
to solar rad.

◦

SW emersion SW emersion switch that determines emersion or

-

I
Imax

RT rmax

submersion
switch that (de)activates modification of temperature (default 0 = inactive; 1 = active)

C d−1

SW T empDF

SW T empDF

T
Ta
T st

T emp
N atT emp
M odT emp

actual temperature
air temperature
top sediment temperature

◦

Delt
DelT ev

timestep
temperature decrease due to evaporation
maximal temperature increase due
to solar radiation

d
◦
C

∆t
∆T ev

∆T rmax

426 of 464

DelRadM ax

-

C
C
◦
C
◦

◦

C

Deltares

15 Various auxiliary processes
Contents
15.1 Computation of aggregate substances . . . . . . . . . . . . . . . . . . . . 428
15.2 Computation of the sediment composition (S1/2) . . . . . . . . . . . . . . 432
15.3 Allocation of diffusive and atmospheric loads . . . . . . . . . . . . . . . . 437
15.4 Calculation of the depth of water column or water layer . . . . . . . . . . . 438
15.5 Calculation of horizontal surface area . . . . . . . . . . . . . . . . . . . . 439
15.6 Calculation of gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
15.7 Calculation of residence time . . . . . . . . . . . . . . . . . . . . . . . . . 441
15.8 Calculation of age of water . . . . . . . . . . . . . . . . . . . . . . . . . . 442
. . . . . . . . . . . . . . . . . . . . . . . . . . . 443

DR
AF

T

15.9 Inspecting the attributes

Deltares

427 of 464

Processes Library Description, Technical Reference Manual

Computation of aggregate substances
PROCESS :

COMPOS

The simulated substances for detrital organic matter and algae biomass do not provide all
essential information to interprete and assess simulation output. The auxiliary process COMPOS provides the additional parameters needed. This concerns the nutrient composition of
particulate detritus and parameters that represent organic matter and total matter as measured.

T

The nutrient composition of particulate detritus is used in the model to simulate the settling
of organic nutrients (N, P, S) in particulate detritus, since these fluxes are computed relative
to the detritus carbon settling flux. Process COMPOS computes the stochiometric ratios of
nitrogen, phosphorus, sulfur and silicon in the individual detritus fractions for this purpose.
Process COMPOS also delivers the total particulate matter, carbon, nitrogen, phosphorus,
silicon and sulfur concentrations, the Kjeldahl-N concentration, and the concentrations of a
number of other aggregate substances. The total particulate concentrations are computed
with and without algae biomass.

DR
AF

15.1

Volume units refer to bulk ( ) or to water ( ).
b

w

Implementation

The process has been implemented for the following substances:

 simulated substances NO3, NH4, PO4, AAP, VIVP, APATP, Si, OPAL, SO4, SUD, SUP,
POC1, PON1, POP1, POS1, POC2, PON2, POP2, POS2, POC3, PON3, POP3, POS3,
POC4, PON4, POP4, POS4, DOC, DON, DOP, DOS, IM1, IM2 and IM3
 auxiliary substances Phyt, AlgN, AlgP, AlgSi, AlgS and AlgDM
The process does not directly influence state variables, since they do not generate mass
fluxes. It is generic, so that it applies to water as well sediment layers.
Table 15.1 provides the definitions of the output parameters as related to the formulations.
Formulation

The individual stochiometric nutrient ratios follow from:

Coci
Coni
Coci
api =
Copi
Coci
asi =
Cosi

ani =

where:

an
ap
as
Coc
428 of 464

stochiometric ratio of carbon and nitrogen in organic matter [gC gN−1 ]
stochiometric ratio of carbon and phosphorus in organic matter [gC gP−1 ]
stochiometric ratio of carbon and sulfur in organic matter [gC gS−1 ]
concentration of detritus carbon [gC m−3 ]
b

Deltares

Various auxiliary processes

concentration of detritus nitrogen [gN m−3 ]
concentration of detritus phosphorus [gP m−3 ]

Con
Cop
Cos
i

b

b

−3

concentration of detritus sulfur [gS m
]
index for the particulate detritus fraction [-]
b

The total particulate detritus pools follow from:

Cpon =
Cpop =

i=1
4
X
i=1
4
X
i=1
4
X
i=1
4
X

Coci
Coni
Copi
Cosi

DR
AF

Cpos =

4
X

T

Cpoc =

Cpom =

(f dmi × Coci )

i=1

where:

Cpoc
Cpon
Cpop
Cpos
Cpom
f dm
i

concentration of total particulate detritus carbon [gC m−3 ]
b

−3

concentration of total particulate detritus nitrogen [gN m

]

b

−3

concentration of total particulate detritus phosphorus [gP m

]

b

concentration of total particulate detritus sulfur [gS m−3 ]
b

concentration of total particulate detritus dry matter [gC m−3 ]
dry matter conversion factor [gDM gC−1 ]
index for the particulate detritus fraction [-]
b

The concentration of total inorganic sediment follows from:

Ctim =

3
X

(f idmj × Cimj )

j=1

where:

Cim
Ctim
f idm
j

concentration of inorganic sediment fraction [gDM m−3 ]
concentration of total inorganic dry matter [gDM m−3 ]
dry matter ratio of inorganic sediment fraction [gDM gDM−1 ]
index for the inorganic sediment fraction [-]
b

b

The other ”total” concentrations arise from summing the various simulated substances as
follows:

P OC = Cpoc + P hyt
T OC = P OC + DOC

Deltares

429 of 464

P ON
T ON
KjelN
DIN
T OT N

= Cpon + AlgN
= P ON + DON
= T ON + N H4
= N H4 + N O3
= T ON + DIN

P OP
T OP
P IP
T OT P

= Cpop + AlgP
= P OP + DOP
= AAP + V IV P + AP AT P
= T OP + P O4 + P IP

P OS = Cpos + AlgS
T OS = P OS + DOS
T OT S = T OS + SO4 + SU D + SU P

DR
AF

T OT Si = AlgSi + Opal + Si

T

Processes Library Description, Technical Reference Manual

T P M noa = Ctim + Cpom
T P M = SS = T P M noa + AlgDM

Directives for use
 The input parameters are the concentrations of the modelled substances and auxiliary
substances mentioned under section ”Implementation”, plus the dry matter carbon ratios
(fdm) of the particulate detritus fractions (DmCf P OC1, DmCf P OC2, DmCf P OC3,
DmCf P OC4, default = 2.5) and the dry matter ratio (fidm) of the inorganic sediment
fractions (DM CF IM 1, DM CF IM 2, DM CF IM 3, default = 1.0).
 Sulfur in algae biomass is not taken into account in the case of DYNAMO.
 T OT S is not defined for the modelling of substances FeS and FeS2.

430 of 464

Deltares

Various auxiliary processes

Table 15.1: Definitions of the output parameters for COMPOS. (i) is POC1, POC2, POC3
or POC4.

Name in
formulas

Name in
output

Definition

Units

ani

C − N (i)

gC gN−1

api

C − P (i)

asi

C − S(i)

stoch. ratio of carbon and nitrogen
detr. fraction i
stoch. ratio of carbon and phosphorus in detritus fraction i
stoch. ratio of carbon and sulfur in
detritus fraction i

T OC
P OC
P OM
Cpoc

T OC
P OC
P OM
P OCnoa

concentration total organic carbon

gC m−3

gC gP−1

T

gC gS−1

conc. total part. organic carbon

b

−3

gC m

b

−3

conc. total part. dry matter

gDM m

conc. total total part. org. carbon
without algae

gC m−3

b

b

P OM noa

conc. total part. dry matter without
algae

gDM m−3

T OT N
T ON
P ON
Cpon

T OT N
T ON
P ON
P ON noa

concentration total nitrogen

gN m−3

conc. total organic nitrogen

−3

DIN
KjelN

DR
AF

Cpom

gN m

b

gN m

conc. total part. org. nitrogen without algae

gN m−3

DIN
KjelN

conc. total diss. inorganic nitrogen

gN m−3

conc. total Kjeldahl nitrogen

gN m

T OT P
T OP
P OP
Cpop

T OT P
T OP
P OP
P OP noa

concentration total phosphorus

gP m−3

conc. total organic phosphorus

−3

gP m

conc. total part. org. phosphorus

gP m−3

conc. total part. org. phosphorus
without algae

gP m

P IP

P IP

conc. total part. inorg. phosphorus

gP m−3

T OT S
T OS
P OS
Cpos

T OT S
T OS
P OS
P OSnoa

conc. total sulfur

gS m−3

T OT Si
T MP
Ctim
T MP
T M P noa

Deltares

b

−3

conc. total part. organic nitrogen

conc. total organic sulfur

b

b

b

−3
b

b

b

b

−3
b

b

b

−3

gS m

b

−3

conc. total part. organic sulfur

gS m

conc. total part. org. sulfur without
algae

gS m−3

T OT Si

concentration total silicon

gSi m−3

SS
T IM
T MP
T M P noa

conc. total (susp.) sediment (solids)

gDM m−3

conc. total inorganic sediment
conc. total part. matter with algae
conc. total part. matter without algae

b

b

b

b

gDM m

−3

gDM m

−3

gDM m

−3

b

b

b

b

431 of 464

Processes Library Description, Technical Reference Manual

Computation of the sediment composition (S1/2)
PROCESS :

S1/2_COMP

The composition of the sediment is important information for evaluation of the results of water
quality simulations. The composition of sediment layers S1 is also used in the model to
simulate the burial of organic matter and nutrients (N, P, Si), since these fluxes are computed
relative to the sediment dry matter resuspension, burial and digging fluxes. For this purpose
the quantities of simulated substances, the fractions of major compo¬nents of dry matter and
the carbon-nutrient ratios for detritus are calculated.

T

Processes S1_COMP and S2_COMP calculate the total amount of dry matter in a sediment
layer and some major components, the thickness of the sediment layer, and the overall dry
matter density. The dry matter composition is expressed in fractions of total inorganic matter, total particulate organic carbon in detritus and total carbon in phyto-plankton biomass.
Additionally the processes deliver the amounts of all simulated substances on the basis of g
m−2 .

DR
AF

15.2

Implementation

In principle processes S1_COMP and S2_COMP can be combined with all phytoplankton
and microphytobenthos modules. The processes have been implemented for the following
substances:

 IM1S1, IM2S1, IM3S1, DETCS1, DETNS1, DETPS1, DETSiS1, OOCS1, OONS1, OOPS1,
OOSiS1, AAPS1, DiatS1; and

 IM1S2, IM2S2, IM3S2, DETCS2, DETNS2, DETPS2, DETSiS2, OOCS2, OONS2, OOPS2,
OOSiS2, AAPS2, DiatS2.

The processes do not directly influence state variables, since they do not generate mass
fluxes. Tables 15.2 and 15.3 provide the definitions of the input and output parameters occurring in the formulations.
Formulation

The total amount of dry matter and the fractions of its major components in the sediment layer
S1 or S2 follow from:

M dmk =

n
X

(f dmi,k × M xi,k )

l=1

M xi,k
M dmk
M phak
f rphak =
M dmk

f rxi,k =

where:

M dm
M pha
Mx
f dm
f rpha
432 of 464

total amount of dry matter in a layer [gDM]
amount of adsorbed phophate in a layer [gP]
amount of substance x in a layer [gX]
dry matter conversion factor [gDM gDM−1 , gDM gC−1 ]
weight fraction of adsorbed phosphate in dry matter [gP gDM−1 ]

Deltares

Various auxiliary processes

f rx
i
k
n

weight fractions of major components in dry matter [gX gDM−1 ]
index for major components in the sediment [-]
index for sediment layer S1 or S2 [-]
number of major components that contribute to dry matter [-], n = 6, including
IM1S1/2, IM2S1/2, IM3S1/2, DETCS1/2, OOCS1/2 and DiatS1/2

The individual stochiometric nutrient ratios are computed according to:

ani,k =

M oci,k
M oni,k

api,k =

M oci,k
M opi,k
M oci,k
M osii,k

T

asii,k =
where:

stochiometric ratio of carbon over nitrogen in detritus fraction k [gC gN−1 ]
stochiometric ratio of carbon over phosphorus in detritus fraction k [gC gP−1 ]
stochiometric ratio of carbon over silicon in detritus fraction k [gC gSi−1 ]
amount of carbon in particulate detritus fraction k [gC]
amount of nitrogen in particulate detritus fraction k [gN m−3 ]
amount of phosphorus in particulate detritus fraction k [gP m−3 ]

DR
AF

an
ap
asi
M oc
M on
M op
M osi
i
k

b

b

amount of silicon in particulate detritus fraction k [gSi m−3 ]
index for particulate detritus fractions [-]
index for sediment layer S1 or S2 [-]
b

The total amounts of major components in the sediment layer S1 or S2 are:
3
X

M imtk =

(M imj,k )

j=1

M octk =

2
X

(M oci,k )

i=1

M algtk =

n
X

(M algl,k )

l=1

M pomk =

n
X
l=1

(f dml × M algl ) +

2
X

(f dmi × M oci,k )

i=1

where:

f dm
M alg
M algt
M im
M imt
M oct
M pom
i
j
Deltares

dry matter conversion factor [gDM gC−1 ]
amount of biomass of algae species [gC]
total amount of algae biomass [gC]
amount of a sediment inorganic matter fraction [gDW]
total amount of sediment inorganic matter [gDW]
total amount of carbon in particulate detritus [gC]
total amount of organic matter in the sediment [gDM gDM−1 ]
index for particulate detritus fractions [-]
index for sediment inorganic matter fractions [-]

433 of 464

Processes Library Description, Technical Reference Manual

k
l
n

index for sediment layer S1 or S2 [-]
index for algae / microphytobenthos species [-]
number of algae / microphytobenthos species, n=1 currently [-]

The comprehensive composition of the sediment layers S1 and S2 is calculated with:

Cxi,k =

M xi,k
A

where:

T

surface area of the water overlying water compartment [m2 ]
surface concentration of substance x in a layer [gX m−2 ]
amount of substance x in a layer [gX]
index for all sediment components including the nutrients in detritus [-]
index for sediment layer S1 or S2 [-]

A
Cx
Mx
i
k

The relevant physical properties of the sediment layers S1 and S2 follow from:

(f dmi,k × Cxi,k /ρi )

DR
AF

V dmk =

n
X
i=1

Cdmk
V dmk
V dmk
Zk =
(1 − φk ) × A
ρdmk =

where:

A
Cdm
f dm
V dm
Z
φ
ρ
ρdm
i
k
n

surface area of the water overlying water compartment [m2 ]
surface concentration of dry matter [gDM m− 2]
dry matter conversion factor [gDM gDM−1 , gDM gC−1 ]
sediment dry matter volume [m3 ]
thickness of the sediment layer [m]
porosity of the sediment [-]
solid matter density of a major sediment component k [gDM m−3 DM]
density of sediment dry matter [gDM m−3 DM ]
index for major components in the sediment [-]
index for sediment layer S1 or S2 [-]
number of major components that contribute to dry matter (-), n = 6 [-]

Directives for use
 Organic nutrients and adsorbed inorganic phosphorus do not contribute to the dry matter
and the volume of the sediment! Notice that because of this the sum of all fractions in the
sediment (f rxi,k ; see the table with output parameters) may not equal 1.

434 of 464

Deltares

Various auxiliary processes

Table 15.2: Definitions of the input parameters in the above equations for S1_COMP and
S2_COMP.

Name in input

Definition

Units

A

Surf

surface area of the overlying water
compartment

m2

f dmj,k

DM CF IM 1

factor sed. inorg. mat-

gDM gDM−1

or

DM CF IM 2

factor sed. inorg. mat-

gDM gDM−1

factor sed. inorg. mat-

gDM gDM−1

f dml,k

DM CF DetCS
DM CF OOCS
DM CF DiatS

dry matter conv.
ter fraction 1
dry matter conv.
ter fraction 2
dry matter conv.
ter fraction 3
dry matter conv.
dry matter conv.
dry matter conv.

factor detr. fraction 1
factor detr. fraction 2
factor algae species 1

gDM gC−1
gDM gC−1
gDM gC−1

M algl,k

DiatS(k)

amount of biomass of algae species 1

DM CF IM 3

DR
AF

f dmi,k

T

Name in
formulas

gC

M imj,k

IM 1S(k)
IM 2S(k)
IM 3S(k)

amount of sed. inorg. matter fraction 1
amount of sed. inorg. matter fraction 2
amount of sed. inorg. matter fraction 3

gDW
gDW
gDW

M oci,k

DetCS(k)
OOCS(k)
DetN S(k)
OON S(k)
DetP S(k)
OOP S(k)
DetSiS1(k)
OOSiS1(k)

amount of detr.
amount of detr.
amount of detr.
amount of detr.
amount of detr.
amount of detr.
amount of detr.
amount of detr.

gC
gC
gN
gN
gP
gP
gSi
gSi

M pha

AAP S(k)

amount of adsorbed phosphate

gP

φ

P ORS(k)

sediment porosity

-

RHOIM 1
RHOIM 2
RHOIM 3
RHODetC
RHOOOC
RHODiat

density of sed. inorg. matter fr. 1
density of sed. inorg. matter fr. 2
density of sed. inorg. matter fr. 3
density of detritus fraction 1
density of detritus fraction 2
density of biomass of algae species 1

gDM m−3
gDM m−3
gDM m−3
gDM m−3
gDM m−3
gDM m−3

M oni,k
M opi,k

M osii,k

ρi

1

C in part. fraction 1
C in part. fraction 2
N in part. fraction 1
N in part. fraction 2
P in part. fraction 1
P in part. fraction 2
Si in part. fraction 1
Si in part. fraction 2

(k) is sediment layer 1 or 2.

Deltares

435 of 464

Processes Library Description, Technical Reference Manual

Table 15.3: Definitions of the output parameters in the above equations for S1_COMP
and S2_COMP .

Name in output

Definition

Units

ani,k 1

C
−
N DetCS(k)
C − N OOC(k)
C
−
P DetCS(k)
C−P OOCS(k)
C−SDetCS(k)
C −SOOCS(k)

stoch. ratio C over N in detr. fraction 1

gC gN−1

stoch. ratio C over N in detr. fraction 2
stoch. ratio C over P in detr. fraction 1

gC gN−1
gC gP−1

stoch. ratio C over P in detr. fraction 2
stoch. ratio C over Si in detr. fraction 1
stoch. ratio C over Si in detr. fraction 2

gC gP−1
gC gSi−1
gC gSi−1

Calgl,k

DiatS(k)M 2

surface conc. of algae species 1

gC m−2

Cimj,k

IM 1S(k)M 2
IM 2S(k)M 2
IM 3S(k)M 2

surf. conc. of sed. inorg. matter fr. 1
surf. conc. of sed. inorg. matter fr. 2
surf. conc. of sed. inorg. matter fr. 3

gDW m−2
gDW m−2
gDW m−2

DetCS(k)M 2
OOCS(k)M 2
DetN S(k)M 2
OON S(k)M 2
DetP S(k)M 2
OOP S(k)M 2
DetSiS1(k)M 2
OOSiS1(k)M 2

surf.
surf.
surf.
surf.
surf.
surf.
surf.
surf.

gC m−2
gC m−2
gN m−2
gN m−2
gP m−2
gP m−2
gSi m−2
gSi m−2

AAP S(k)M 2

surface conc. of adsorbed phosphate

gP m−2

ActT hS(k)

thikness of sediment layer

m

F rIM 1S(k)
F rIM 2S(k)
F rIM 3S(k)
F rDetCS(k)
F rOOCS(k)
F rCF DiatS(k)

fraction inorg. matter 1 in sediment
fraction inorg. matter 2 in sediment
fraction inorg. matter 3 in sediment
fraction detritus 1 in sediment
fraction detritus 2 in sediment
fraction algae species 1 in sediment

gDM gDM−1
gDM gDM−1
gDM gDM−1
gC gDM−1
gC gDM−1
gC gDM−1

M dmk
M imtk
M octk
M algtk
M pomk

DM S(k)
T IM S(k)
P OCS(k)
P HY T S(k)
P OM S(k)

total amount of dry matter
total amount of sed. inorganic matter
total amount of part. organic carbon
total amount of algae biomass
total amount of organic matter

gDM
gDM
gC
gC
gDM

ρdmk

RHOS(k)

density of sediment dry matter

gDM m−3

or

api,k
or

Coci,k
or

Coni,k
or

Copi,k
or

DR
AF

asii,k

Cosii,k
Cxi, k
Zk
f rxi,k

1

T

Name in
formulas

conc.
conc.
conc.
conc.
conc.
conc.
conc.
conc.

of detr.
of detr.
of detr.
of detr.
of detr.
of detr.
of detr.
of detr.

C in part. fr. 1
C in part. fr. 2
N in part. fr. 1
N in part. fr. 1
P in part. fr. 1
P in part. fr. 1
Si in part. fr. 1
Si in part. fr. 1

(k) is sediment layer 1 or 2.

436 of 464

Deltares

Various auxiliary processes

Allocation of diffusive and atmospheric loads
PROCESS :

DFWAST_I, ATMDEP_I

Both processes calculate diffusive fluxes. The processes convert user input in [g m−2 d−1 ] to
DELWAQ required units of [g m−3 d−1 ].
Implementation

Formulation
Diffusive waste load:
dDfwasti =

fDfwasti

depth

T

These processes are implemented for IM1, IM2, IM3, NO3, NH4, PO4, all heavy metals and
all organic micro-pollutants.

DR
AF

15.3

(15.1)

Atmospheric deposition:
dAtmDepi =

fAtmDepi

depth

(15.2)

where

dDfwasti
dAtmDepi
fDfwasti
fAtmDepi
depth

diffusive waste load [g m−3 d−1 ]
atmospheric waste load [g m−3 d−1 ]
diffusive waste load [g m−2 d−1 ]
atmospheric waste load [g m−2 d−1 ]
depth of a DELWAQ segment [m]

Directives for use
 Waste loads are normally not considered processes and are provided separately by you.
This method is inconvenient when large amounts of segments are involved as is the case
with diffusive wastes. In this case it is advised to use one of the two processes described
in this section.

Deltares

437 of 464

Processes Library Description, Technical Reference Manual

Calculation of the depth of water column or water layer
PROCESS :

DEPTH

Depth of a segment (computational element of DELWAQ) is calculated from the horizontal
surface area (user-defined) and the volume. TOTDEPTH calculates the total depth of a multilayer water column.
Implementation

Formulation

V olume
Surf
n
X
T otalDepth =
Depthi
Depth =

T

Not relevant in this context.

DR
AF

15.4

LocalDepthm =

i=1
m
X

Depthj

j=1

where

Depth
V olume
Surf
T otaldepth
Localdepthm
m
n

depth of a DELWAQ segment [m]
volume of a DELWAQ segment [m3 ]
horizontal surface area of a DELWAQ segment [m2 ]
depth of entire water column [m]
depth from the surface to bottom of DELWAQ segment m [m]
index of the layer
total number of layers

Directives for use
 Either Depth or Surf must be supplied by you (or a water quantity model)!

438 of 464

Deltares

Various auxiliary processes

Calculation of horizontal surface area
PROCESS :

DYNSURF

The horizontal surface area (SURF) of a segment (computational element of DELWAQ) is
calculated from the depth (user defined) and the volume (DELWAQ).
Implementation
Not relevant in this context.

Surf =
where

Volume
Depth

T

Formulation

DR
AF

15.5

Depth
Volume
Surf

depth of a DELWAQ segment [m]
volume of a DELWAQ segment [m3 ]
horizontal surface area of a DELWAQ segment [m2 ]

Directives for use
 Either Depth or Surf must be supplied by you (or a water quantity model)!

Deltares

439 of 464

Processes Library Description, Technical Reference Manual

Calculation of gradients
PROCESS :

GRD_RHO, GRD_VE

This process calculates the gradient in space of segment-related variables at an exchange
area.
Implementation
This process is implemented for the variables Veloc and RhoWater.

V arGrd =
VarGrd

V arT o − V arF rom
XLenT o + XLenF rom

T

Formulation

gradient in space of segment-related variable
(a) VelocGrd gradient in horizontal flow velocity [m s−1 m−1 ]
(b) RhoGrd gradient in density of water [kg m−3 m−1 ]
XLenFrom DELWAQ "from"-length [m]
XLenTo
DELWAQ "to"-length [m]
VarFrom value of segment related variable in "from"-segment
(a) Veloc horizontal flow velocity [m s−1 ]
(b) RhoWater density of water [kg m−3 ]
VarTo
value of segment related variable in "to"-segment
(a) Veloc horizontal flow velocity [m s−1 ]
(b) RhoWater density of water [kg m−3 ]

DR
AF

15.6

Directives for use
 This process can be active if the third direction is defined.

440 of 464

Deltares

Various auxiliary processes

Calculation of residence time
PROCESS :

RESTIM

This process calculates the residence time of water in a computational cell. The process only
takes into account the advective transport — i.e. flows in [m3 s−1 ] — as derived from SOBEK,
Delft3D or another hydrodynamic model. Dispersion is not taken into account.
Formulation

where

(15.3)

T

V olume
exchanges |F low| /2

ResT im = P

ResT im residence time [s]
V olume DELWAQ water volume of a segment [m3 ]
F low
DELWAQ water flow over an exchange [m3 s−1 ]

DR
AF

15.7

Directives for use

The process RESTIM can be used in all schematisations.

 No user input is required.
 You can access the RESTIM process in the PLCT through the state variable ‘Continuity’.

Deltares

441 of 464

Processes Library Description, Technical Reference Manual

Calculation of age of water
PROCESS :

AGE

The ‘age’ of water from a specific source in a computational cell is defined as the difference in
time between the actual time and the time at which the water entered the model area through
the source and is thus equal to the travel time from the source to the computational cell.
Common sources are boundaries and discharges (for example rivers).
Evaluation of the travel time (‘age’) of water from several sources may be valuable in the early
stages of a water quality study as an indicator for the importance of water quality processes.

T

Implementation

In a single water quality simulation a maximum of five sources can be distinguished:

i = 1, 2, 3, 4 and 5

DR
AF

15.8

Formulation

ln

ageT ri =



dT ri
cT ri



RcDecT ri
dDecT ri = RcDecT ri × dT ri
where

ageT ri age of tracer i [d]
cT ri
concentration of conservative tracer i [g m−3 ]
dT ri
concentration of decayable tracer i [g m−3 ]
RcDecT ri first order decay rate constant for decayable tracer i [d−1 ]
dDecT ri flux for decayable tracer i [g m−3 d−1 ]
Directives for use
 Two substances have to be defined for every source that has to be distinguished. The
first of these substances is conservative (cT ri ), the other is decayable (dT ri ). For a
correct calculation of the age, both substances must have the same concentration at all
the source: it is advised to specify a concentration of 1.0 at the source that has to be
distinguished and a concentration of 0.0 at all the other sources.

442 of 464

Deltares

Various auxiliary processes

Inspecting the attributes
PROCESS :

ATTRIBOUT

Within D-Water Quality each segment has two or more attributes:

 Attribute 1 is used to determine if the segment should participate in the calculation. It

A value of 1 means the segment is in middle of the water column, that is, not adjacent
to the surface or the bottom.
A value of 2 means the segment is at the surface and should therefore be involved in
processes like reaeration.
A value of 3 means the segment is at the bottom and should therefore be involved in
processes like sedimentation oxygen demand or settling of suspended matter.
A value of 0 means the segment is adjacent to the surface and the bottom and should
therefore be involved in all processes. This type of segment is typical for 1D and 2D
applications.

DR
AF

T







is in fact a dynamic attribute: if the segment becomes dry during the calculation, its first
attribute is set to 0, indicating it is not active at that moment. Other segments may be set
inactive permanently.
 Attribute 2 indicates the position of the segment in the water column:



15.9

 It is also possible to define your own attributes, even attributes that change in time. Their
meaning is determined by the process routines that actually use them.

 To output all attributes, in an "aggregated" form, specify an attribute "0". For instance for
an active segment at the surface (and only the standard attributes defined) the result will
be: 21, where the digit 2 is the value of the second attribute and the digit 1 is the value of
the first.
To make inspection of an attribute possible, you can use this process: it fills the output parameter Attribute with the value of the selected attribute for each segment. When you set AttribIdx
to zero, you will retrieve all attributes in one number where the last digit is the first attribute,
the before last digit is the second attribute, etcetera.
Table 15.4: Definitions of the input and output parameters

Name in
input/output

Definition

Units

AttribIdx

Index of the attribute to output

[-]

Attribute

Output parameter

[-]

Deltares

443 of 464

DR
AF

T

Processes Library Description, Technical Reference Manual

444 of 464

Deltares

16 Deprecated processes descriptions
Contents

DR
AF

T

16.1 Growth and mortality of algae (MONALG) . . . . . . . . . . . . . . . . . . 446

Deltares

445 of 464

Processes Library Description, Technical Reference Manual

Growth and mortality of algae (MONALG)
PROCESS :

MND1D IAT- M , MND2F LAG - M , MND3D IAT- F, MND4F LAG - F, MND( I )T EMP,
MND( I )LL IM , MND( I )NL IM

Algae are subject to gross primary production, respiration, excretion, mortality, grazing, resuspension and settling. Net growth is the result. Net primary production is defined as the
difference of gross primary production and respiration. The algae module MONALG includes
specific formulations for these processes with the exception of grazing, resuspension and settling. These processes are equally valid for other algae modules, and are therefore dealt with
in separate process descriptions.

T

MONALG considers four different algae species groups: marine diatoms, marine flagellates,
fresh water diatoms and fresh water flagellates. Diatoms differ from flagellates among other
things by their dependency on dissolved silicon for growth. Separate processes have been
implemented for each of these groups (i), which allows the application of group average or
species specific process coefficients. Other fresh water species discharged by rivers into
estuaries should be allocated to the detritus pool.

DR
AF

16.1

The distinction between fresh water and marine species groups refers to conditions typical for
estuaries, that may contain both fresh water and marine algae species. Fresh water algae die
when entering the saline water body of an estuary, whereas marine species die when entering
the upstream fresh water body.
MONALG contains a combination of formulations for phytoplankton derived from various
ecosystem models (Klepper et al., 1994; Scholten and Van der Tol, 1994; NIOO/CEMO, 1993;
WL | Delft Hydraulics, 1988; Rijkswaterstaat/DGW, 1993). The module uses a mechanistic
approach to describe algae dynamics. The primary production in MONALG is formulated according to Monod kinetics. A general feature of this type of kinetics is that the production
rate is multiplicatively limited by environmental factors like nutrient availability, light availability,
and temperature. The chlorophyll content dependency of the production rate is ignored (Klepper, 1989). The remaining processes are based on first-order kinetics with respect to algae
biomass.
The total extinction coefficient and the available light averaged over the water column are
calculated with separate processes described elsewhere. These processes are similar for
other algae modules.
The algae processes affect a number of other model substances apart from the biomass concentrations [gC m−3 ]. Primary production involves the uptake of inorganic nutrients [gN/P/Si
m−3 ] and the production of dissolved oxygen [gO2 m−3 ]. Preferential uptake of ammonium
over nitrate is included in the model (McCarthy et al., 1977). Respiration consumes dissolved
oxygen. Excretion and mortality produce detritus [gC/N/P m−3 ] and opal silicate [gSi m−3 ].
The process fluxes concerning these substances are derived from the algae process fluxes
by means of multiplication with stochiometric constants. These ratios reflect the chemical
composition of the algae biomass, which is assumed to be invariable over time.
All fluxes are daily averaged in connection with the way light limitation is integrated over a day.
Consequently, nutrient uptake is assumed to be a continuous process over a day, whereas in
reality it is a discontinuous process.

446 of 464

Deltares

Deprecated processes descriptions

Implementation
The algae module MONALG has been implemented as four processes for each of the four
algae groups:

 the main process, where all process rates are calculated: MND(i), with different process
names for the different species groups (i) to be modelled: MND1Diat-m, MND2Flag-m,
MND3Diat-f, MND4-Flag-f;
 extra process: MND(i)Temp, calculating the limitation function for temperature;
 extra process: MND(i)LLim, calculating the limitation function for light; and
 extra process: MND(i)NLim, calculating the limitation function for nutrients.

T

The processes have been implemented in a generic way, which means that they are applicable
both to water and sediment compartments. Live algae that settle eventually end up in the
top sediment layer. Mortality and resuspension are the only active processes for sediment
compartments, meaning that algae in sediment do not grow but are slowly converted into
detritus. The current implementation of MONALG does not allow using any of the sediment
options S1/2 and GEMSED!

DR
AF

MONALG calculates process rates for the following substances:

 MND1Diat-m, MND2Flag-m, MND3Diat-f, MND4Flag-f, POC1, PON1, POP1, Opal, NH4,
NO3, PO4, Si and OXY.

Table 16.1 provide the definitions of the parameters occurring in the user-defined input and
output.
Formulation

Formulations are subsequently presented for primary production, respiration, excretion and
mortality. The rates and additional output are presented in the final sections.
The rate formulation for primary production is composed of limiting factors for temperature,
nutrients and light. The rates of the other processes are dependent on the temperature,
and in the case of mortality also on the chloride concentration. The processes lead to the
consumption and production of nutrients and dissolved oxygen, or to the production of detritus
components.
Primary production
Gross primary production is formulated as a temperature dependent first order process limited
by light and nutrient availability:

Rgpi = f nuti × f lti × kgpi × Calgi
kgpi = kpgi10 × f tmpi
(T −10)

f tmpi = ktpgi
with:

Calg
f lt
f nut
f tmp
kgp
kgp10
Deltares

algal biomass concentration [gC m−3 ]
light limitation factor [-]
Monod nutrient limitation factor [-]
temperature limitation factor for production [-]
potential gross primary production rate [d−1 ]
potential gross primary production rate at 10 ◦ C [d−1 ]

447 of 464

Processes Library Description, Technical Reference Manual

ktgp
Rgp
T
i

temperature coefficient for primary production [-]
gross primary production rate [gC m−3 d−1 ]
water temperature [◦ C]
index for species group 1-4 [-]

The nutrient limitation factor has been described in various ways. In most models Liebig’s law
of the minimum is applied to calculate the overall nutrient limitation. Here the additive model
described by O’ Neill et al. (1989) was selected. This additive model assumes that more than
one nutrient can be limiting at the same time, and that the limitations add up according to
multiplication of the Michaelis-Menten functions for individual nutrients.

f nuti = f ami + (1 − f ami ) × f nii

T

The model must deal with several complications. Firstly, the limitation factors for diatoms
and flagellates are slightly different, because only diatoms need silicate. Secondly, algae can
use two inorganic sources of nitrogen, although they prefer ammonium. Consequently, the
limitation factor must consider both the availability of and affinity for ammonium and nitrate.
The following nutrient limitation factor takes all this into account:

Cam × Cph × Csi
(Ksami × Cph × Csi + Cam × Ksphi × Csi + Cam × Cph × Kssii + Cam × Cph × Csi)
Cni × Cph × Csi
f nii =
(Ksnii × Cph × Csi + Cni × Ksphi × Csi + Cni × Cph × Kssii + Cni × Cph × Csi)
with:

DR
AF

f ami =

f am
f ni
Cam
Cni
Cph
Csi
Ksam
Ksni
Ksph
Kssi

ammonium specific nutrient limitation factor [-]
nitrate specific nutrient limitation factor [-]
ammonium concentration [gN m−3 ]
nitrate concentration [gN m−3 ]
phosphate concentration [gP m−3 ]
dissolved inorganic silicate concentration [gSi m−3 ]
half saturation constant for ammonium [gN m−3 ]
half saturation constant for nitrate [gN m−3 ]
half saturation constant for phosphate [gP m−3 ]
half saturation constant for silicate [gSi m−3 ]

Phytoplankton production is limited, if the light availability in the water column is less than
the temperature dependent optimal radiation for a phytoplankton species. Below this optimal
radiation light limitation is a saturating function of light availability. There is inhibition if light
availability exceeds the optimum.
Light limitation depends on a functional relationship between in situ light intensity and primary
production. This function must be integrated over time and depth to obtain the daily and depth
averaged light limitation factor. The integration by discretisation is done according to Eilers
and Peeters (1988):

P

n
k=1

f lti =

(86400 × H)

Rrgpi,j,k =
Iri,j,k =

448 of 464


(Rrgp
×
∆z
×
∆t)
i,j,k
j=1

Pm

Iri,j,k × (ci + 2)

+ ci × Iri,j,k + 1

2
Iri,j,k

Ij,k
Ioi
Deltares

Deprecated processes descriptions

ci =

Ioi
−2
(kgpi /di )
(T −10)

Ioi = Io10
i × ktpgi

Ij,k = Itopk × e(−et×zj )
with:

T

shape coefficient of the production factor [-]
initial slope of the light-production curve [gC d−1 .W m−2 )−1 ]
total extinction coefficient of visible light [m−1 ]
light limitation factor [-]
depth of a water compartment or water layer [m]
light intensity at depth zj and time tk [W m−2 ]
optimal light intensity [W m−2 ]
light intensity at depth zj and time tk , relative to optimal intensity [-]
light intensity at depth zo (top of layer or compartment) and time t [W m−2 ]
potential gross primary production rate [d−1 ]
temperature coefficient for primary production [-]
gross production at depth zj and time tk , relative to maximal production [-]
depth [m]
time interval for light limitation integration, that is the DELWAQ timestep [s]
depth interval for light limitation integration ([m]; = H/m)
index for species group 1–4 [-]
index for depth interval 1–m [-]
index for time interval 1–n [-]
number of time intervals in a day ([-]; = 86 400/∆t)
number of depth intervals in a water compartment or water layer [-]

DR
AF

c
d
et
f lt
H
I
Io
Ir
Itop
kgp
ktgp
Rrgp
z
∆t
∆z
i
j
k
n
m

The Rrgpi,j,k factor has a sinusoidal shape within the daylength period (light hours), and is
equal to zero outside this period.
Respiration
Algal respiration is simulated as of maintenance respiration and growth respiration. Maintenance respiration is temperature dependent. Growth respiration depends on the primary
production rate. The total respiration rate is given by:

Rrspi = krspi × Calgi + f rspi × Rgpi
(T −10)

krspi = krsp10
i × ktrspi

with:

f rsp
krsp
krsp10
ktrsp
Rrsp

fraction of gross production respired [-]
maintenance respiration rate [d−1 ]
maintenance respiration rate at 10 ◦ C [d−1 ]
temperature coefficient for maintenance respiration [-]
total respiration rate [gC m−3 d−1 ]

Excretion
Excretion is a function of nutrient stress (Klepper, 1989). Excretion decreases with increasing
nutrient limitation. It is modelled as a fraction of the gross primary production as follows:

Rexci = f exci × (1 − f nuti ) × Rgpi
with:

Deltares

449 of 464

Processes Library Description, Technical Reference Manual

f exc
Rexc

fraction of gross production excreted at the absence of nutrient limitation [-]
excretion rate [gC m−3 d−1 ]

Mortality
Algal mortality is caused by temperature dependent natural mortality, salinity stress mortality,
and grazing by consumers. The latter process is described elsewhere in relation to the modelling of grazers. Salinity driven mortality is described with a sigmoidal function of chlorinity
(NIOO/CEMO, 1993), leading to the following formulations:

Rmrti = kmrti × Calgi
(T −10)

kmrti = kmrt10
i × ktmrti

m1i − m2i
+m2i
for fresh water algae, M N D(i)T ype = 2.0
1 + e(b1i ×(Ccl−b2i ))
m2i − m1i
+ m1i
for marine algae, M N D(i)T ype = 1.0
kmrt10
i =
1 + e(b1i ×(Ccl−b2i ))

with:

coefficient 1 of salinity stress function [g−1 m3 ]
coefficient 2 of salinity stress function [g m−3 ]
rate coefficient 1 of salinity stress function [d−1 ]
rate coefficient 2 of salinity stress function [d−1 ]
chloride concentration [g m−3 ]
total mortality process rate [d−1 ]
total mortality process rate at 10 ◦ C [d−1 ]
temperature coefficient for mortality [-]
total mortality rate [gC m−3 d−1 ]

DR
AF

b1
b2
m1
m2
Ccl
kmrt
kmrt10
ktmrt
Rmrt

T

kmrt10
i =

m1 and m2 are the end members of the above function, meaning that the function obtains
the value m1 at high Ccl, and the value m2 for low Ccl. The mortality rate increases with
decreasing chloride concentration, when m2 is larger than m1. This situation which applies
to marine algae is depicted in the example of figure 16.1. The mortality rate increases with
increasing chloride concentration, when m1 is larger than m2. This situation applies to fresh
water algae.
In case DELWAQ-G is applied the mortality is the only process that is active with respect
to algae biomass. The first-order mortality rate in the sediment has a specific temperature
independent mortality process rate kmrts, i [d−1 ].
Resulting process rates affecting model substances
The consumption and production rates for nutrients and dissolved oxygen are derived from
the production rate as follows:

Rprdox,i = (Rgpi − Rrspi ) × aoxi
Rcnsam,i = (Rgpi − Rrspi ) × ani × f ami /f nuti
Rcnsni,i = (Rgpi − Rrspi ) × ani × (1 − f ami /f nuti )
Rcnsph,i = (Rgpi − Rrspi ) × aphi
Rcnssi,i = (Rgpi − Rrspi ) × asii
Rprdoc,i = (Rmrti + Rexci )
Rprdon,i = (Rmrti + Rexci ) × ani
450 of 464

Deltares

T

Deprecated processes descriptions

DR
AF

Figure 16.1: Example of the salinity dependent mortality function. m1 = 0.08 d−1 ; m2 =
0.16 d−1 ; b2 = 11000 (equivalent with 20 ppt salinity) [gCl m−3 ]; b1 = 0.001
and 0.002 m3 .gCl−1 .

Rprdop,i = (Rmrti + Rexci ) × aphi

Rprdosi,i = (Rmrti + Rexci ) × asii

with:

an
aph
aox
asi
Rcnsam
Rcnsni
Rcnsph
Rcnssi
Rprdox
Rprdoc
Rprdon
Rprdop
Rprdosi

stochiometric constant for nitrogen over carbon in algae biomass [gN.gC−1 ]
stochiometric constant for phosphorus over carbon in algae biomass [gP.gC−1 ]
stochiometric constant for oxygen over carbon in algae biomass [gO2 .gC−1 ]
stochiometric constant for silicon over carbon in algae biomass [gSi.gC−1 ]
net consumption rate for ammonium [gN m−3 d−1 ]
net consumption rate for nitrate [gN m−3 d−1 ]
net consumption rate for phosphate [gP m−3 d−1 ]
net consumption rate for silicate [gSi m−3 d−1 ]
net production rate for dissolved oxygen [gO2 m−3 d−1 ]
net production rate for detritus organic carbon [gC m−3 d−1 ]
net production rate for detritus organic nitrogen [gN m−3 d−1 ]
net production rate for detritus organic phosphorus [gP m−3 d−1 ]
net production rate for opal silicate [gSi m−3 d−1 ]

The immediate release of inorganic nutrients due to mortality (autolysis) of algae is simulated
in GEM as the fast decay of the labile detritus fraction (POC1, PON1, POP1).

f am and f nut are used to calculate the preference for ammonium uptake. The ratio of
the ammonium specific limitation factor and the overall nutrient limitation factor defines the
fraction of nitrogen obtained from ammonium.
Chlorophyll to carbon ratio
MONALG delivers some additional output parameters, such as the chlorophyll content of the
algae, expressed as the carbon to chlorophyll ratio, and the chlorophyll concentration. The
carbon to chlorophyll ratio depends on the availability of light and nutrients. The ratio is mod-

Deltares

451 of 464

Processes Library Description, Technical Reference Manual

elled with an empirical function of the light and nutrient limitation factors (Klepper, 1989). The
chlorophyll concentration for each algae group is calculated according to:

Cchfi =

Calgi
achfi

achfi =

achfmin,i
(f nuti × (1 − f lti × f nuti ))gi

with:
stoch. constant for carbon over chlorophyll in algae biomass [gC gChf−1 ]
minimal stoch. const. for carbon over chlorophyll in algae biomass [gC gChf−1 ]
chlorophyll concentration connected with an algae group [gChf m−3 ]
scaling coefficient for growth limitation factor [-]

T

achf
achf min
Cchf
g

The total concentration of chlorophyll is calculated by a separate process PHY_GEM, which
is described elsewhere in this manual.

DR
AF

Directives for use
 The process rates of gross primary production and maintenance respiration have a temperature basis of 10 ◦ C. That means that input values have to be corrected when provided
for a more common temperature basis of 20 ◦ C.
 The growth limitation for a specific nutrient can be made inactive by allocating value zero
to the half saturation constant for this nutrient.
 The salinity effect on mortality can be inactivated by allocating the same value to coefficients M N D(i)m1 and M N D(i)m2.
 Always make sure that the light input (observed solar radiation) is consistent with the
light related parameters of MONALG. This concerns the use of either visible light or the
photosynthetic fraction of visible light (approximately 45 %). The input incident light time
series should have been corrected for cloudiness and reflection (approximately 10 %).
Additional references

WL | Delft Hydraulics (1997c)

Table 16.1: Definitions of the input parameters in the formulations for MONALG.

Name in
formulas

Name in input

Definition

Units

Cam
Ccl
Cni
Cph
Csi

N H4
Cl
N O3
P O4
Si

ammonium concentration
chloride concentration
nitrate concentration
phosphate concentration
dissolved inorganic silicate concentration
biomass concentration of marine diatoms

gN m−3
gCl m−3
gN m−3
gP m−3
gSi m−3

Calg1

M N D1Diat−
m

gC m−3

continued on next page
1

(i) indicates species groups 1-4.
This parameter is only used for initialisation during the first timestep.
3
This parameter is calculated by processes ExtPhGVL and Extinc_VL.
4
This parameter is not part of the input.
2

452 of 464

Deltares

Deprecated processes descriptions

Table 16.1 – continued from previous page
Name in
formulas

Name in input

Definition

Units

Calg2

biomass concentration of marine flagellates
biomass concentration of fresh water diatoms
biomass concentration of fresh water
flagellates
type of algae group (1 = brackish/marine,
2 = fresh)

gC m−3

-

M N D2F lag−
m
M N D3Diat−
f
M N D4F lag−
f
M N D(i)T ype

achfi

M N D(i)AChl02 group specific stoch. const. carbon over

Calg4

achfmin,i
ani

DR
AF

aoxi

aphi
asii

m1i
m2i
b1i
b2i
di
et
gi

chlorophyll
M N D(i)amchl group spec. min. stoch. const. carbon
over chlorophyll
M N D(i)N Crat group specific stoch. const. for nitrogen
over carbon
4
group specific stoch. const. for oxygen
over carbon
M N D(i)P Crat group spec. stoch. const. for phosphorus
over carbon
M N D(i)SiCratgroup specific stoch. const. for silicon
over carbon
M N D(i)m1
group spec. rate coefficient 1 of salinity
stress function
M N D(i)m2
group spec. rate coefficient 2 of salinity
stress function
M N D(i)b1
group specific coefficient 1 of salinity
stress function
M N D(i)b2
group specific coefficient 2 of salinity
stress function
M N D(i)schl group specinitial slope of the lightproduction curve
3
ExtV l
total extinction coefficient of visible light
M N D(i)b
group spec. scaling coef. for growth limitation factor

Ksami

gC m−3
gC m−3
gC.gChf−1

T

Calg3

M N D(i)Kam group specific half saturation constant

Ksnii

M N D(i)Kni

Ksphi

M N D(i)Kph

Kssii

M N D(i)Ksi

for ammonium
group specific half saturation constant
for nitrate
group specific half saturation constant
for phosphate
group specific half saturation constant
for silicate

gC.gChf−1
gN.gC−1
gO2 .gC−1
gP.gC−1
gSi.gC−1
d−1
d−1
g−1 m3
g m−3
gC
d−1 .(W
−2 −1
m )
m−1
gN m−3
gN m−3
gP m−3
gSi m−3

continued on next page
1

(i) indicates species groups 1-4.
This parameter is only used for initialisation during the first timestep.
3
This parameter is calculated by processes ExtPhGVL and Extinc_VL.
4
This parameter is not part of the input.
2

Deltares

453 of 464

Processes Library Description, Technical Reference Manual

Table 16.1 – continued from previous page
Name in
formulas

Name in input

Definition

Units

f exci

M N D(i)be x

-

f rspi

M N D(i)rp r

group spec. frac. gross prod. excrȧt abs.
of nutr. lim.
group specific fraction of gross production respired

H

Depth

depth of a water compartment or water
layer

m

Ioi
Itop

M N D(i)Iopt
Rad

group specific optimal light intensity
light intensity at top of layer or compartment

W m−2
W m−2

kgp10
i

M N D(I)P m10 group spec. potential gross primary

ktgpi

ktmrti
ktrspi

kmrts,i
T
-

∆t
m
1

prod. rate at 10 C
M N D(i)rm t10 group spec. maintenance respiration
rate at 10 ◦ C
M N D(i)ktgp group spec. temperature coefficient for
primary prod.
M N D(i)mt
group spec. temperature coefficient for
mortality
M N D(i)rt
group spec. temperature coef. for maintenance resp.
M N D(i)M orSed
group spec. mortality process rate in
sediment

DR
AF

krsp10
i

T

◦

-

d−1
d−1
d−1

T emp

water temperature

◦

IT IM E
IDT

time
time interval, that is the DELWAQ
timestep
number of depth intervals in a water
comp. or layer

s
s

N r_dz

C

-

(i) indicates species groups 1-4.
This parameter is only used for initialisation during the first timestep.
3
This parameter is calculated by processes ExtPhGVL and Extinc_VL.
4
This parameter is not part of the input.
2

454 of 464

Deltares

References
APHA, 1989. “Standard methods for the examination of water and wastewater.” American
Public Health Association. 17th edition.
Banks, R. and F. Herrera, 1977. “Effect of wind and rain on surface reaeration.” ASCE 103
(EE3): 489.
Berner, R., 1974. The Sea: Marine Chemistry, vol. 5, chap. Kinetic models for the early
diagenesis of nitrogen, sulphur, phosphorus and silicon in anoxic marine sediments, pages
427–450. John Wiley & Sons, New York, pp.
BLOOM UM, 1985. A mathematical model to compute phytoplankton blooms. WL | Delft
Hydraulics, Delft, The Netherlands, 2 ed. (F.J. Los).

T

Boudreau, B., 1996. “A method-of-lines code for carbon and nutrient diagenesis in aquatic
sediments.” Computers and Geosciences 22 (5): 479–496.

DR
AF

Burns, L., 1982. “Identification and evaluation of fundamental transport and transformation
process models.” In K. Dickson, A. Maki and J. Cairns, eds., Modeling the fate of chemicals
in the aquatic environment, pages 101–126. Ann Arbor Science Publishers.
Butts T. A, M., Asce and R. Evans, 1983. “Small stream channel dam aeration characteristics.”
Journal of Environmental Engineering Vol. 109(3): 555–573.
Calow, P. and G. Petss, 1992. The rivers handbook, vol. Volume I. Blackwell, Oxford.
Churchill, M., H. Elmore and R. Buckingham, 1962. “The prediction of reaeration rates.” ASCE
88 (SA4): 1.
Connolly, J. P., H. A. Zahakos, J. Benaman, C. K. Ziegler, J. R. Rhea and K. Russell, 2000. “A
model of PCB Fate in the Upper Hudson River.” Environ. Sci. Technol. 34: 4076–4087.
D-WAQ PLT, 2013. D-Water Quality Processes Library Tables, Technical Reference Manual.
Deltares, 4.00 ed.
DBS, 1991. Mathematical Simulation of Algae Blooms by the Model bloom ii. WL | Delft
Hydraulics, Delft, The Netherlands, 2 ed. Vol. 1 Documentation Report, Vol. 2 Figures T68
(F.J. Los).
DBS, 1994. Delwaq-bloom ii-switch, Simulation model for the eutrophication of surface water.
WL | Delft Hydraulics, Delft, The Netherlands, 4.10 (concept 0.05) ed. System Document,
(in Dutch; M.P. van der Vat).
Delft3D-FLOW UM, 2013. Delft3D-FLOW User Manual. Deltares, 3.14 ed.
Deltares, 2017. Sediment Water Interaction. Deltares, 3.0 ed.

Dickson, A. G., 1990. “Thermodynamics of the dissociation of boric acid in synthetic seawater
from 273.15 to 318.15 K.” Deep Sea Res. 37: 755–766.
Dickson, A. G. and C. Goyet, eds., 1994. DOE, Handbook of methods for the analysis of the
various parameters of the carbon dioxide system in the sea water; version 2, ORNL/CDIAC74.
DiToro, D., 1986. Sediment Oxygen Demand: Processes Modelling and Measurement, chap.
A diagenic oxygen equivalents model of sediment oxygen demand. Institute of Nat. Res.
Univ. of Georgia.
DiToro, D., 2001. Sediment Flux Modeling. Inc. Publication, New York.

Deltares

455 of 464

Processes Library Description, Technical Reference Manual

DiToro, D. and L. Horzempa, 1982. Environ. Sci. Technol 16: 594–602.
Eilers, P. and J. Peeters, 1988. “A model for the relationship between light intensity and the
rate of photosynthesis in phytoplankton.” Ecological Modelling 42: 185–198.
Fair, G., J. Geijer and D. Okun, 1968. “Waste and Waste water engineering, Volume 2.” John
Wiley & Sons Inc, New York.
Gameson, A., 1957. “Weirs and Aeration of rivers.” Journal of the Institution of Water Engineers Vol. 6 (11): 477–490.
Greenberg, A., J. Connors and D. Jenkins, 1980. “Standard methods for the examination of
water and waste water.” APHA-AWWA-WPCF, U.S.A.

T

Groen, P. and R. Dorrestein, 1976. Sea waves. Oceanographic and Maritime Meteorology 11,
Royal Dutch Meteorological Institute. 124 p. (in Dutch).
Guarini, J.-M., G. Blanchard, P. Gros, D. Gouleau and C. Bacher, 2000. “Dynamic model of
the short-term variability of microphytobenthic biomass on temperate intertidal mudflats.”
M.Sc. Mar. Ecol. Pro. Ser. 195: 291–303.

DR
AF

Guérin, F., 2006. Emission de gaz a effet de serre (CO2, CH4) par une retenue de barrage hydroélectrique en zone tropicale (Petit-Saut, Guyane française): expérimentation et
modélisation. Ph.D. thesis, Université Paul Sabatier (Toulouse III). 246 pp.
Guérin, F., G. Abril, D. Serça, C. Delon, S. Richard, R. Delmas and L. Varfalry, 2007. “Gas
transfer velocities of CO2 and CH4 in a tropical reservoir and its river downstream.” Journal
of Marine Systems 66: 161–172.
Harris, G., 1986. “Phytoplankton ecology.” Chapman and Hall, London.

Holthuijsen, L. H., 1980. Waves in oceanic and coastal waters. Campbridge University Press.
IMPAQT UM, 1996. IMPAQT 4.00, User manual. WL | Delft Hydraulics, Delft, The Netherlands,
4.00 ed. (H.L.A. Sonneveldt and J.G.C. Smits).
Karickhoff, S., D. Brown and T. Scott, 1979. “Sorption of hydrophobic pollutants on natural
sediments. 13: 241-248.” Water Research 13: 241–248.
Klepper, O., 1989. “Not yet known.”

Klepper, O., M. van der Tol, H. Scholten and P. Herman, 1994. “SMOES: a simulation model
for the Oosterschelde ecosystem. Part I: Description and uncertainty analysis.” Hydrobiologia 282/283: 437–45.
Krone, R., 1962. Flume studies of transport of sediment in estuarial shoaling processes
(Final report). Tech. rep., University of California, Hydraulics Engineering and Sanitary
Engineering Laboratory, Berkeley, USA.
Langbein, W. and W. Durum, 1967. “The aeration capacity of streams.” US Geol. Survey 542:
–.
Liss, P. and P. Slater, 1974. “Flux of gasses across the air-sea interface.” Nature 247: 181–
184.
Los, F. J., 2009. Eco-hydrodynamic modelling of primary production in coastal waters and
lakes using BLOOM. Ph.D. thesis, Wageningen University. ISBN 978-90-8585-329-9.
Luff, R. and A. Moll, 2004. “Seasonal dynamics of the North Sea sediments using a threedimensional coupled sediment-water model system.” Continetal Shelf Research 24: 1099–
1127.

456 of 464

Deltares

References

Lyman, W., W. Reehl and D. Rosenblatt, 1990. Handbook of chemical property estimation
methods. American Chemical Society, Washington D.C.,.
Mackay, D., W. Shiu and R. Sutherland, 1980. Dynamics, Exposure and hazard assessment
of toxic chemicals, chap. Estimating volatilization and water column diffusion rates of hydrophilic constants. ISBN 0-250-50301-3. Ann Arbor Science Publishers.
Mancini, J. L., 1978. “Numerical estimates of coliform mortality rates under various conditions.”
Journal Water Pollution Control Federation -: 2477–2484.
McCarthy, J., W. Taylor and J. Taft, 1977. “Nitrogenous nutrition of the plankton in the Chesapeake Bay. 1. Nutrient availability and phytoplankton preferences.” Limnology & Oceanography 22: 996–1011.

T

Metcalf and Eddy, 1991. Wastewater Engineering: treatment, disposal and reuse. McGrawHill.
Millero, F., 1982. “The thermodynamics of seawater at one atmosphere.” Ocean Sci, Eng. 7:
403–460.

DR
AF

Millero, F., 1995. “Thermodynamics of the carbon dioxide system in the oceans.” Geoch. Et
Cosmoch. Acta 59 (4): 661–677.
Molen, D. Van der, F. Los, L. van Ballegooijen and M. van der Vat, 1994a. “Mathematical modelling as a tool for management in eutrophication control of shallow lakes.” Hydrobiologia
276: 479–492.
Molen, D. van der, F. Los, L. van Ballegooijen and M. van der Vat, 1994b. “Mathematical modelling as a tool for management in eutrophication control of shallow lakes.” Hydrobiologica
275/276: 479–492.
Mucci, A., 1983. “The solubility of calcite and aragonite in seawater at various salinities,
temperatures and one atmosphere total pressure.” Amer. J. Sci. 283: 780–799.
Nakasone, H., 1975. “Derivation of aeration equation and its verification study on the aeration
at falls and spillways.” Transactions J.S.I.D.R.E. pages 42–48.
Nelson, R., 1983. “Wave heights in depth-limited conditions.” In 6th Australian Conference on
Coastal and Ocean Engineering, Gold Coast, Australia.
NIOO/CEMO, 1993. MOSES: Model of the Scheldt estuary. Tech. rep., NIOO/CEMO, Yerseke,
The Netherlands.
O’ Connor, D., 1983. “Wind effects on gass-liquid transfer coefficients.” Journal of Environmental Engineering 109: 3 pp.
O’ Connor, D. and W. Dobbins, 1956. “The mechanism of reaeration in natural streams. ASCE.
82 (no. SA6): 469.” J.San.Eng. ASCE 82 (no. SA6): 469.
O’ Connor, D. and J. St. John, 1982. Modeling the fate of chemicals in the aquatic environment, chap. Assessment of modeling the fate of chemicals in the aquatic environment. Ann
Arbor Science Publishers.
O’ Neill, R., D. DeAngelis, J. Pastor, B. Jackson and W. Post, 1989. “Multiple nutrient limitations in ecological models.” Ecological Modelling 46: 147–163.
Owens, M., R. Edwards and J. Gibbs, 1964. “Some reaeration studies in streams.” Int. J. Air
and Water Pollution 8: 641.

Deltares

457 of 464

Processes Library Description, Technical Reference Manual

Partheniades, E., 1962. A study of erosion and deposition of cohesive soils in salt water.
Ph.D. thesis, University of California, Berkeley, USA. 182 p.
Rai, D., L. Eary and J. Zachara, 1989. “Environmental chemistry of chromium.” The Science
of the Total Environment 86: 15–23.
Rijkswaterstaat/DGW, 1993. The impact of marine eutrophication on phytoplankton and benthic suspension feeders: results of a mesocosm pilot study. Tech. Rep. DGW-93.039, Rijkswaterstaat, The Hague, The Netherlands. NIOO/CEMO-654.
Rijkswaterstaat/RIKZ, 1990. UITZICHT, a model for the calculation of visibility and exctinction.
Tech. Rep. 90.058, Rijkswaterstaat. (in Dutch; DBW-RIZA, H. Buitenveld).

T

Rijkswaterstaat/RIKZ, 1991. Eutrofiëring, primaire productie en zuurstofhuishouding in de Noordzee. Tech. Rep. GWAO-91.083, Rijkswaterstaat. (in Dutch; DGW-RIKZ, J.C.H. Peeters,
H.A. Haas,L. Peperzak).
Ross, S., 1995. “Overview of the Hydrochemistry and Solute Processes in British Wetlands.”
In H. J.M.R. and A. Heathwaite, eds., Hydrology and Hydrochemistry of British Wetlands.
John Wiley & Sons Ltd.

DR
AF

Roy, N. R. e. a., 1993. “The dissociation constants of carbonic acid in seawater at salinities 5
to 45 and temperatures 0 to 45 ◦ C.” Marine Chemistry 44: 249–267.
Santschi, P., P. Höhener, G. Benoit and M. B. ten Brink, 1990. “Chemical processes at the
sediment water-interface.” Mar. Chem. 30: 269–315.
Scheffer, M., 1998. Ecology of Shallow Lakes. Chapman and Hall.

Schink, D. and N. Guinasso, 1978. “Effects of bioturbation on sediment seawater interaction.”
Mar. Geology 23: 133–154.
Schnoor, J., C. Sato, D. McKechnie and D. Sahoo, 1987. Processes, coefficients, and models
for simulating toxic organics and heavy metals in surface waters. Section 4: reactions of
heavy metals. Tech. Rep. EPA/600/3-87/015, University of Iowa. P.85-139.
Scholten, H. and M. van der Tol, 1994. “SMOES: a simulation model for the Oosterschelde
ecosystem. Part II: Calibration and validation.” Hydrobiologia 282/283: 453–474.
Schroepfer, G., M. Robins and R. Susag, 1964. “The research program on the Mississippi
river in the vicinity of Minneapolis and St. Paul.” In Advances in Water Pollution Research,
vol. 1. Pergamon, London.
Smits, J. and J. van Beek, 2013. “ECO: A Generic Eutrophication Model Including Comprehensive Sediment-Water Interaction.” PLoS ONE 8(7): e68104 page 24 pp. DOI:
10.1371/journal.pone.0068104.
Smits, J. and D. Van der Molen, 1993. “Application of SWITCH, a model for sediment-water
exchange of nutrients, to Lake Veluwe in the Netherlands.” Hydrobiologia 253: 281–300.
Soetaert, K., P. Herman and J. Middelburg, 1996. “A model of early diagenetic processes
from the shelf to abyssal depth.” Geochimica et Cosmochimica Acta 60 6: 1019–1040.
Soulsby, R., 1997. Dynamics of marine sands, a manual for practical applications. Thomas
Telford, London.
Stowa, 2002. Verbetering waterkwaliteitsonderzoek. Voorstel aanpassingen TEWOR. Tech.
rep., Witteveen+Bos, Deventer.

458 of 464

Deltares

References

Stumm, W. and J. Morgan, 1981. Aquatic chemistry. An introduction emphasizing chemical
equilibria in natural water. John Wiley & Sons, Inc.
Stumm, W. and J. Morgan, 1987. “Aquatic Chemistry.” John Wiley and Sons, New York.
Stumm, W. and J. Morgan, 1996. Aquatic chemistry, Chemical Equilibria and Rates in Natural
Water. John Wiley & Sons, Inc., New York, third ed.
Swart, 1974. Offshore sediment transport and equilibrium beach profiles. Ph.D. thesis, Delft
University of Technology, Delft, The Netherlands. Delft Hydraulics Publ. 131.
Sweers, H. E., 1976. “A nomogram to estimate the heat exchange coefficient at the air-water
interface as a function of windspeed and temperature; a critical survey of some literature.”
Journal of Hydrology 30: –.

T

Tamminga, G., 1987. Influence of a constant south-westerly wind on the erosion in Lake
IJssel. Tech. rep., Hydraulics and Discharge-Hydrology Department, Wageningen.

DR
AF

Ten Hulscher, T., L. Vandervelde and W. Bruggeman, 1992. “Temperature dependence of
henry law constants for selected chlorobenzenes, polychlorinated biphenyls and aromatic
hydrocarbons.” Environ. Toxicol. Chem 11: 1595–1603.
Thomann, R. V. and J. A. Mueller, 1987. Principles of Surface Water Quality Modelling and
Control. Harper & Row publishers, New York.
Truesdale, G., A. Downing and G. Lowden, 1955. “The solubility of oxygen in pure water and
seawater.” J. Appl. Chem 5: 53.
Vanderborght, J., R. Wollast and G. Billen, 1977. “Kinetic models of diagenesis in disturbed
sediments: Part II. Nitrogen diagenesis.” Limnol. Oceanogr 22: 794–803.
Velds, C., 1992. Zonnestraling in Nederland. Tech. rep., K.N.M.I. (Royal Dutch Meteorological
Institute).
Wang, Y. and P. V. Cappellen, 1996. “A multicomponent reactive transport model of early
diagenesis: Application to redox cycling in coastal marine sediments.” Geochimica et Cosmochimica Acta 60 60 16: 2993–3014.
Wanninkhof, R., 1992. “Relationship between wind and gas exchange over the ocean.” Journal of Geophysical Research 97 (C5): 7373–7382.
Weiss, R., 1970. “The solubility of nitrogen, oxygen and argon in water and seawater.” Deep
Sea Reasearch 17: 721–735.
Weiss, R., 1974. “Carbon dioxide in water and seawater.” Marine chemistry 2(3): 203–216.
Westrich, J. and R. Berner, 1984. “The role of sedimentary organic matter in bacterial sulfate
reduction: The G model tested.” Limnol. Oceanogr 29 2: 236–249.
Wijsman, J., P. Herman, J. Middelburg and K. Soetaert, 2001. “A model for early diagenetic
processes in sediments of the continental shelf of the Black Sea.” Est. Coast. Shelf Sci 54:
403–421.
WL | Delft Hydraulics, 1978. Natural reaeration of surface water by the wind. Tech. Rep.
R1318-II, WL | Delft Hydraulics, Delft, The Netherlands. Report on literature study (in
Dutch; J.A. van Pagee).
WL | Delft Hydraulics, 1980a. Microbial decomposition of organic matter and nutrient regeneration in natural waters and sediments. Tech. Rep. R1310-5, WL | Delft Hydraulics, Delft,
The Netherlands. Report on literature study (J.G.C. Smits).

Deltares

459 of 464

Processes Library Description, Technical Reference Manual

WL | Delft Hydraulics, 1980b. Natural reaeration of surface water. Literature study R1149,
WL | Delft Hydraulics, Delft, The Netherlands. (in Dutch; G.A.L. Delvigne).
WL | Delft Hydraulics, 1988. GREWAQ: an ecological model for Lake Grevelingen. Documentation report T0215.03, WL | Delft Hydraulics, Delft, The Netherlands.
WL | Delft Hydraulics, 1989. Flow-induced erosion of cohesive beds, a literature survey,
rapport Z161-31, February, 1989. DELFT HYDRAULICS, 1989. Literature survey Z161-31,
WL | Delft Hydraulics, Delft, The Netherlands. Winterwerp, J.C.
WL | Delft Hydraulics, 1990. A grazing module for the eutrophication model JSBACH. Research report T462, WL | Delft Hydraulics, Delft, The Netherlands. (in Dutch; W.M. Mooij).

T

WL | Delft Hydraulics, 1991. Modelmatig onderzoek naar de oorzaak van verontreiniging
van bodemsediment in de Noordzee en Waddenzee. Research report T537, WL | Delft
Hydraulics, Delft, The Netherlands. (in Dutch).
WL | Delft Hydraulics, 1991a. Mathematical simulations of Algae Blooms by the Model
BLOOM II, Version 2. Vol. 1-Documentation Report; Vol.2 - Figures. Documentation report T68, WL | Delft Hydraulics, Delft, The Netherlands. (F.J. Los).

DR
AF

WL | Delft Hydraulics, 1992a. Description DBS (DELWAQ-BLOOM-SWITCH). Model documentation T542.70, WL | Delft Hydraulics, Delft, The Netherlands. (in Dutch; F.J. Los et
al.).
WL | Delft Hydraulics, 1992b. Immobilisation of pollutants in dredging sludge and solid
waste materials. Part 4: Degredation and sorption of organic micropollutants. Tech. Rep.
T737/T989, WL | Delft Hydraulics, Delft, The Netherlands. (in Dutch; J. J. G. Zwolsman).
WL | Delft Hydraulics, 1992c. Process formulations DBS. Model documentation T542, WL |
Delft Hydraulics, Delft, The Netherlands. (in Dutch; F.J. Los et al.).
WL | Delft Hydraulics, 1993a. Adsorptie van zware metalen aan zwevend stof. Research
report T584, WL | Delft Hydraulics, Delft, The Netherlands. (M. Kroot, in Dutch).
WL | Delft Hydraulics, 1993b. Extension of the "Stofstromen instrument" (Policy Analysis of
Water Management for the Netherlands). Tech. Rep. T1020, WL | Delft Hydraulics, Delft,
The Netherlands. (P.M.A. Boderie and J.J.G. Zwolsman; in Dutch).
WL | Delft Hydraulics, 1993c. Omgaan met risico’s voor marine ecosystemen (RISMARE).
Research report T537.40, WL | Delft Hydraulics, Delft, The Netherlands. (in Dutch).
WL | Delft Hydraulics, 1994a. Operationalisation of the water quality model for the Scheldt
Estuary. Research report T1089, WL | Delft Hydraulics, Delft, The Netherlands. (in Dutch).
WL | Delft Hydraulics, 1994b. Phosphate minerals in sediment: Literature study and analysis
of field data. Research report T584, WL | Delft Hydraulics, Delft, The Netherlands. (N.M.
de Rooij and J.J.G. Zwolsman; in Dutch).
WL | Delft Hydraulics, 1997c. GEM, a Generic Ecological Model for estuaries. Model documentation T2087, WL | Delft Hydraulics, Delft, The Netherlands. (J.G.C. Smits et al.).
WL | Delft Hydraulics, 1998. Ecological model for the Lagoon of Venice. Technical description
of the model instrument T2161, WL | Delft Hydraulics, Delft, The Netherlands. Modelling
results T2162 (M.T. Villars, F.J. Los).
WL | Delft Hydraulics, 2002. Sediment-water exchange of substances, Diagenesis modelling
phase 2. Research report Q2935.30, WL | Delft Hydraulics, Delft, The Netherlands, Delft.
(J.G.C. Smits).

460 of 464

Deltares

References

DR
AF

T

Zeebe, R. and D. Wolf-Gladrow, 2001. “CO2 in seawater: equilibrium, kinetics, and isotopes.”
Elsevier Oceanography Series 65. Elsevier, Amsterdam, London, New York.

Deltares

461 of 464

DR
AF

T

Processes Library Description, Technical Reference Manual

462 of 464

Deltares

DR
AF
T

T
DR
AF

Photo by: Mathilde Matthijsse, www.zeelandonderwater.nl

PO Box 177
2600 MH Delft
Boussinesqweg 1
2629 VH Delft
The Netehrlands

+31 (0)88 335 81 88
sales@deltaressystems.nl
www.deltaressystems.nl

DR
AF
T
Source Exif Data: 
File Type                       : PDF
File Type Extension             : pdf
MIME Type                       : application/pdf
PDF Version                     : 1.5
Linearized                      : No
Page Count                      : 481
Page Mode                       : UseOutlines
Author                          : Deltares
Title                           : Processes Library User Manual
Subject                         : 
Creator                         : LaTeX hyperref
Producer                        : ps2pdf
Keywords                        : Deltares, Technical, Reference, Manual, Processes, Library
Create Date                     : 2018:04:18 05:37:48+02:00
Modify Date                     : 2018:04:18 05:37:48+02:00
Trapped                         : False
PTEX Fullbanner                 : This is MiKTeX-pdfTeX 2.9.6588 (1.40.18)
EXIF Metadata provided by EXIF.tools

Navigation menu