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Delft3D flexible Mesh suite
1D/2D/3D Modelling suite for integral water solutions
Technical Reference Manual
D-Water Quality Processes Library Description
DRAFT
DRAFT
DRAFT
Processes Library Descrip-
tion
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
DRAFT
Processes Library Description, Technical Reference Manual
Published and printed by:
Deltares
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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.
DRAFT
Contents
Contents
List of Figures vii
List of Tables ix
1 How to find your way in this manual 1
1.1 Introduction .................................. 1
1.2 Overview ................................... 1
1.3 Processes reference tables .......................... 3
1.4 What’s new? ................................. 4
1.5 Backward compatibility ............................ 6
1.6 Modelling water and sediment layers . . . . . . . . . . . . . . . . . . . . . 7
1.6.1 Usage notes ............................. 7
2 Oxygen and BOD 9
2.1 Reaeration, the air-water exchange of DO . . . . . . . . . . . . . . . . . . . 10
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
2.7 BOD, COD and SOD decomposition . . . . . . . . . . . . . . . . . . . . . 32
2.7.1 Chemical oxygen demand . . . . . . . . . . . . . . . . . . . . . . 32
2.7.2 Biochemical oxygen demand . . . . . . . . . . . . . . . . . . . . . 33
2.7.3 Measurements and relations . . . . . . . . . . . . . . . . . . . . . 33
2.7.4 Accuracy ............................... 34
2.8 Sediment oxygen demand . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.9 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 . . . . . . . . . . . . . . . . . 45
3 Nutrients 47
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 ........................... 78
4 Primary producers 81
4.1 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
5 Macrophytes 137
5.1 Framework of the macrophyte module . . . . . . . . . . . . . . . . . . . . . 138
5.1.1 Relation macrophyte module and other DELWAQ processes . . . . . 138
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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
5.2 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 . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.2.4 Temperature limitation . . . . . . . . . . . . . . . . . . . . . . . . 147
5.2.5 Decay of emerged and submerged biomass . . . . . . . . . . . . . 148
5.2.5.1 Hints for use . . . . . . . . . . . . . . . . . . . . . . . . 148
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
5.2.8.1 Hints for use . . . . . . . . . . . . . . . . . . . . . . . . 150
5.2.9 Uptake of nitrogen and phosphorus from water . . . . . . . . . . . . 151
5.2.10 Oxygen production and consumption . . . . . . . . . . . . . . . . . 151
5.2.11 Net growth of emerged and submerged vegetation and rhizomes . . . 152
5.3 Maximum biomass per macrophyte species . . . . . . . . . . . . . . . . . . 153
5.3.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.3.2 Hints for use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.4 Grazing and harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.4.1 Grazing ................................155
5.4.2 Hints for use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.4.3 Harvesting ..............................156
5.5 Light limitation for macrophytes . . . . . . . . . . . . . . . . . . . . . . . . 158
5.6 Vegetation coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.6.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.7 Vertical distribution of submerged macrophytes . . . . . . . . . . . . . . . . 161
5.7.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.7.1.1 Linear distribution (SwDisSMii=1) . . . . . . . . . . . . . . 161
5.7.1.2 Exponential distribution (SwDisSMii=2) . . . . . . . . . . . 163
5.7.2 Hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
6 Light regime 165
6.1 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
7 Primary consumers and higher trophic levels 187
7.1 Grazing by zooplankton and zoobenthos (CONSBL) . . . . . . . . . . . . . 188
7.2 Grazing by zooplankton and zoobenthos (DEBGRZ) . . . . . . . . . . . . . 199
8 Organic matter (detritus) 217
8.1 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
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
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Contents
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
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
9.15 Speciation of dissolved iron . . . . . . . . . . . . . . . . . . . . . . . . . . 310
9.16 Conversion salinity and chloride process . . . . . . . . . . . . . . . . . . . 315
10 Organic micropollutants 317
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
10.10 General contaminants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
11 Heavy metals 357
11.1 Partitioning of heavy metals . . . . . . . . . . . . . . . . . . . . . . . . . . 358
11.2 Reprofunctions for partition coefficients . . . . . . . . . . . . . . . . . . . . 371
12 Bacterial pollutants 375
12.1 Mortality of coliform bacteria . . . . . . . . . . . . . . . . . . . . . . . . . 376
13 Sediment and mass transport 379
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
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
13.14 Conversion of exchange variable to segment variable . . . . . . . . . . . . . 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 427
15.1 Computation of aggregate substances . . . . . . . . . . . . . . . . . . . . 428
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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
15.9 Inspecting the attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443
16 Deprecated processes descriptions 445
16.1 Growth and mortality of algae (MONALG) . . . . . . . . . . . . . . . . . . . 446
References 455
vi Deltares
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List of Figures
List of Figures
2.1 The reaeration rate RCRear (=klrear2020/H) as a function of water depth, flow
velocity and/or wind velocity for various options SWRear for the mass transfer
coefficient klrear ............................... 19
2.2 The distribution of gross primary production over a day . . . . . . . . . . . . 27
2.3 A typical oxygen demand curve . . . . . . . . . . . . . . . . . . . . . . . . 38
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 . . . . . . . . . . . . . . . . . . . . . . 39
2.5 Default and optional oxygen functions for decay of CBOD (O2FuncBOD) . . . 39
2.6 Optional function for the calculation of the first order rate constant for BOD and
NBOD .................................... 40
3.1 Figure 1 Default pragmatic oxygen limitation function for nitrification (O2FuncNit,
option 0). ................................... 53
3.2 Default pragmatic oxygen inhibition function for denitrification (O2Func, option
0). ...................................... 62
3.3 Variation of the equilibrium concentration AAP (eqAAP) as a function of PO4
and the maximum adsorption capacity (MaxPO4AAP). . . . . . . . . . . . . 70
3.4 Variation of the equilibrium concentration of AAP (eqAAP) as a function of PO4
and the partition coefficient of PO4 (KdPO4AAP). . . . . . . . . . . . . . . . 70
4.1 Example of the salinity dependent mortality function . . . . . . . . . . . . . 89
4.2 Primary production rate of algae species i as a function of temperature and
radiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.3 Limitation function for radiation (frad_i) for algae species i as a function of
radiation (Is,RAD) at different temperature ranging from 5 to 25 ◦C. . . . . . 115
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. . . . . . . . . . . . . . . . . . . . . . . . 134
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
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 sym-
bols used are explained in the text (T=Ht). . . . . . . . . . . . . . . . . . 135
5.1 Interactions between the nutrient cycles and the life cycle of macrophytes. . . 138
5.2 The different macrophytes growth forms that can be modeled with the Macro-
phyte Module. ................................139
5.3 The abbreviations for the parts of the vegetation that are used in the equations. 140
5.4 The light intensity under water – explanation of the variables in the light inten-
sity functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
5.5 Definition of the quantities used for determining the linear vertical distribution. . 162
5.6 Definition of the quantities used for determining the exponential vertical distri-
bution. ....................................163
5.7 Examples of the exponential vertical distribution for three values of the shape
parameter F.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
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 . . . . . . . . . . 184
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8.1 When an algae module is included. . . . . . . . . . . . . . . . . . . . . . . 220
8.2 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 floccu-
lation and density not included). . . . . . . . . . . . . . . . . . . . . . . . . 385
16.1 Example of the salinity dependent mortality function . . . . . . . . . . . . . 451
viii Deltares
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List of Tables
List of Tables
2.1 Definitions of the parameters in the above equations for REAROXY . . . . . . 17
2.2 Factor ’b’ (characteristic structure) for various structures. . . . . . . . . . . . 22
2.3 Definitions of the parameters in the above equations for REAROXY . . . . . . 22
2.3 Definitions of the parameters in the above equations for REAROXY . . . . . . 23
2.4 Definitions of the parameters in the equations for SATUROXY . . . . . . . . . 25
2.5 Definitions of the parameters in the above equations for VAROXY . . . . . . . 28
2.6 Definition of the parameters in the equations and the mode input for OXYMIN . 30
2.7 Definitions of the parameters in the above equations for POSOXY . . . . . . . 31
2.8 Typical values for oxygen demanding waste waters (values in [mgO2/l]) . . . . 32
2.9 SOBEK-WQ processes for coliform bacteria. . . . . . . . . . . . . . . . . . 44
2.10 Definitions of the parameters in the above equations for PROD_TEWOR. . . . 44
2.11 Definitions of the parameters in the above equations for DBOD_TEWOR. . . . 45
3.1 Definitions of the parameters in the above equations for NITRIF_NH4. Volume
units refer to bulk ( ) or to water ( ). ..................... 52
3.2 Definitions of the input parameters in the formulations for NH3FREE. . . . . . 56
3.3 Definitions of the parameters in the above equations for DENWAT_NO3. Vol-
ume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . 61
3.4 Definitions of the parameters in the above equations for DENSED_NO3. Vol-
ume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . 62
3.5 Definitions of the parameters in the above equations for ADSPO4AAP. Volume
units refer to bulk ( ) or to water ( ). ..................... 69
3.6 Definitions of the parameters in the above equations for VIVIANITE. Volume
units refer to bulk ( ) or to water ( ). ..................... 74
3.7 Definitions of the parameters in the above equations for APATITE. Volume
units refer to bulk ( ) or to water ( ). ..................... 77
3.8 Definitions of the parameters in the above equations for DISSI. Volume units
refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . . . . 80
4.1 Definitions of the input parameters in the formulations for BLOOM. . . . . . . 98
4.2 Definitions of the output parameters for BLOOM. . . . . . . . . . . . . . . . 101
4.3 Definitions of the input parameters in the above equations for SED(i), SEDPH-
BLO and SEDPHDYN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
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. . . . . . . . . . . . . . . . . . . . . . . 114
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
( ). .....................................117
4.6 Definitions of the output parameters in the above equations for PHY_DYN.
Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . 118
4.7 Definitions of the input parameters in the above equations for GROMRT_DS1,
TF_DIAT , DL_DIAT , RAD_DIAT S1, MRTDIAT_S1, MRTDIAT_S2and
NRALG_S1.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
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). ..............................130
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 VB-
STATUS(i). ..................................132
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5.1 Computation of the maximum biomass of three macrophyte species as a func-
tion of the Habitat Suitability Index. . . . . . . . . . . . . . . . . . . . . . . 154
6.1 Definitions of the input parameters in the formulations for CALCRAD. . . . . . 167
6.2 Definitions of the output parameters for CALCRAD. . . . . . . . . . . . . . . 168
6.3 Definitions of the input parameters in the formulations for CALCRADDAY. . . . 168
6.4 Table IV Definitions of the output parameters for CALCRADDAY. . . . . . . . 168
6.5 Definitions of the input parameters in the formulations for CALCRAD_UV. . . . 168
6.6 Definitions of the output parameters for CALCRAD_UV. . . . . . . . . . . . . 169
6.7 Definitions of the input parameters in the formulations for Extinc_VLG. . . . . 174
6.8 Definitions of the input parameters in the formulations for ExtinaBVLP (Extin-
aBVL) for BLOOM algae. . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
6.9 Definitions of the input parameters in the formulations for ExtPhDVL. . . . . . 175
6.10 Definitions of the output parameters for Extinc_VLG, ExtinaBVLP (ExtinaBVL),
ExtPhDVL. ..................................176
6.11 Definitions of the input parameters in the formulations for Extinc_UVG. . . . . 177
6.12 Definitions of the input parameters in the formulations for ExtinaBUVP (Ex-
tinaBUV) for BLOOM algae. . . . . . . . . . . . . . . . . . . . . . . . . . . 178
6.13 Definitions of the input parameters in the formulations for ExtPhDUV. . . . . . 178
6.14 Definitions of the output parameters for Extinc_UVG, ExtinaBUVP (ExtinaBUV),
ExtPhDUV. ..................................179
6.15 Definitions of the input parameters in the formulations for DAYRAD. . . . . . . 182
6.16 Definitions of the output parameters for DAYRAD. . . . . . . . . . . . . . . . 182
6.17 Definitions of the parameters in the above equations for SECCHI, exclusive of
input parameters for auxiliary process UITZICHT. . . . . . . . . . . . . . . . 186
7.1 Definitions of the input parameters in the formulations for CONSBL. . . . . . . 196
7.2 Definitions of the output parameters for CONSBL. . . . . . . . . . . . . . . . 198
7.3 Definitions of the input parameters in the formulations for DEBGRZ. . . . . . . 211
7.4 Definitions of the output parameters for DEBGRZ. . . . . . . . . . . . . . . . 216
8.1 Definitions of the input parameters in the above equations for DECFAST, DECMEDIUM
and DECSLOW. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . 224
8.1 Definitions of the input parameters in the above equations for DECFAST, DECMEDIUM
and DECSLOW. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . 225
8.1 Definitions of the input parameters in the above equations for DECFAST, DECMEDIUM
and DECSLOW. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . 226
8.2 Definitions of the input parameters in the above equations for DECREFR,
DECDOC and DECPOC5. Volume units refer to bulk ( ) or to water ( ). . . . 226
8.2 Definitions of the input parameters in the above equations for DECREFR,
DECDOC and DECPOC5. Volume units refer to bulk ( ) or to water ( ). . . . 227
8.3 Definitions of the parameters in the above equations for CONSELAC. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . 238
8.4 Definitions of the input parameters in the above equations for SED_(i), SEDN(i)
and SED_CAAP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
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 ( ). ............................247
9.4 Definitions of the parameters in the above equations for REARCO2. . . . . . 254
9.5 Definitions of the parameters in the above equations for SATURCO2. . . . . . 257
9.6 Processes in D-Water Quality with effects on pH . . . . . . . . . . . . . . . 258
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9.7 Definitions of the input parameters in the above equations for pH_simp. Vol-
ume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . 268
9.8 Definitions of the output parameters of pH_simp. Volume units refer to bulk
( ) or to water ( ). ..............................268
9.9 Definitions of the parameters in the above equations for VOLATCH4. . . . . . 273
9.10 The efinitions of the parameters in the above equations for SATURCH4. . . . . 275
9.11 Definitions of the parameters in the above equations for EBULCH4. . . . . . . 277
9.12 Definitions of the parameters in the above equations for OXIDCH4. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . 281
9.13 Definitions of the parameters in the above equations for OXIDSUD. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . 284
9.14 Definitions of the parameters in the above equations for PRECSUL. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . 287
9.15 Definitions of the input parameters in the above equations for SPECSUD. . . . 290
9.16 Definitions of the input parameters in the above equations for SPECSUDS1/2. 291
9.17 Definitions of the output parameters of SPECSUD and SPECSUDS1/2. . . . . 291
9.18 Definitions of the parameters in the above equations for PRIRON concerning
oxidizing iron. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . 298
9.19 Definitions of the parameters in the above equations for PRIRON concerning
reducing iron. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . 298
9.19 Definitions of the parameters in the above equations for PRIRON concerning
reducing iron. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . 299
9.19 Definitions of the parameters in the above equations for PRIRON concerning
reducing iron. Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . 300
9.20 Definitions of the parameters in the above equations for IRONRED. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . 302
9.20 Definitions of the parameters in the above equations for IRONRED. Volume
units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . 303
9.21 Definitions of the parameters in the above equations for SULPHOX. Volume
units refer to bulk ( ) or to water ( ) . . . . . . . . . . . . . . . . . . . . . 305
9.21 Definitions of the parameters in the above equations for SULPHOX. Volume
units refer to bulk ( ) or to water ( ) . . . . . . . . . . . . . . . . . . . . . 306
9.22 Definitions of the parameters in the above equations for IRONOX. Volume units
refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . . . . . . 309
9.23 Definitions of the input parameters in the above equations for SPECIRON. . . 313
9.23 Definitions of the input parameters in the above equations for SPECIRON. . . 314
9.24 Definitions of the output parameters of SPECIRON. . . . . . . . . . . . . . . 314
9.25 Definitions of the parameters in the above equations for SALINCHLOR. Vol-
ume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . . . 316
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 ( ). . . . . . . 323
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 ( ). . . . . . . . . . . . . . . . . . 324
10.3 Definitions of the output parameters for PARTWK_(i). (i) is a substance name.
Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . 324
10.3 Definitions of the output parameters for PARTWK_(i). (i) is a substance name.
Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . 325
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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. Vol-
ume 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
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 ( ). .................................366
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 ( ). . . . . . . 367
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. . . . . . . . . . . . . . . . . . . . 368
11.4 Definitions of the output parameters for PARTWK_(i). (i) is a substance name.
Volume units refer to bulk ( ) or to water ( ). . . . . . . . . . . . . . . . . . 369
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 ( ). ............................370
11.6 Definitions of input parameters in RFPART_(i), (i) is a substance name. . . . . 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. . . . . . . . . . . . . . . . . 382
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. . . . . . . . . . . . . . 388
13.3 Definitions of the input parameters in the formulations for SED_SOD. . . . . . 388
13.4 Definitions of the input parameters in the above equations for ADVTRA, DSP-
TRA and TRASE2_(i) (or TRSE2_(i) or TRSE2(i)). Volume units refer to bulk
( ), water ( ) or solids ( ). ..........................393
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13.5 Definitions of the input parameters in the above equations for S12TRA(i). . . . 401
13.6 Definitions of the input parameters in the above equations for RES_DM. . . . 402
13.7 Definitions of the input parameters in the above equations for BUR_DM. . . . 403
13.8 Definitions of the input parameters in the above equations for DIG_DM. . . . . 403
13.9 Definitions of the input and output parameters for VELOC . . . . . . . . . . . 406
13.10 Definitions of the input and output parameters for CHEZY . . . . . . . . . . . 408
13.11 Definitions of the input and output parameters for WAVE . . . . . . . . . . . 410
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. . . . . . . . . . . 411
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. . . . . . . . . . . 412
13.14 Definitions of the input and output parameters for CALTAU . . . . . . . . . . 415
13.15 Definitions of the input and output parameters for HDISPERVEL . . . . . . . 416
13.16 Definitions of the input and output parameters for HORZDISP . . . . . . . . . 417
13.17 Definitions of the input and output parameters for VERTDISP . . . . . . . . . 418
14.1 Definitions of the parameters in the above equations for TEMPERATUR. . . . 426
15.1 Definitions of the output parameters for COMPOS. (i) is POC1, POC2, POC3
or POC4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
15.2 Definitions of the input parameters in the above equations for S1_COMP and
S2_COMP. ..................................435
15.3 Definitions of the output parameters in the above equations for S1_COMP and
S2_COMP . ..................................436
15.4 Definitions of the input and output parameters . . . . . . . . . . . . . . . . . 443
16.1 Definitions of the input parameters in the formulations for MONALG. . . . . . 452
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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 con-
tains 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 Config-
uration Tool (PLCT) in order to connect state variables, input parameters, default values and
output parameters to mathematical formulations.
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:
Implementation List of substances or other state variables for which the process is
implemented, with references to other (auxiliary) processes used
Formulation Detailed description of mathematical formulations and all process
parameters and coefficients
Direction Definition of the schematisations (1DV, 1DH, 2DV, 2DH, 3D) for which
the process can be used
Directives for use Tips for use of the process and for the quantification of input param-
eters
References List of referenced literature
Parameter Tables Tabulated lists of all input parameters and coefficients, and of output
parameters (not included for some processes)
1.2 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,
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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.
Present D-Water Quality has two standard options for the modelling of sediment-water inter-
action, a simplified approach and an advanced approach. The user interface supports only
the simplified ’S1-S2’ approach, for which additional substances represent two sediment lay-
ers. 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.
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 ”sedi-
ment” (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 nota-
tion of parameters in formulations and provides tables with input and output parameters,
facilitating the specification of parameter values in the input of models. Process descrip-
tions 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 mi-
crophytobenthos. 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
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(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’.
1.3 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
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:
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 transport-
processes which calculate dispersions. When you model a substance find the associated pro-
cesses 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 asso-
ciated substances and transport processes. When you know the name of a velocity or dis-
persion (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.
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Table 8.1 and Table 9.1
These tables are indexed on respectively segment related and exchange related process-
input 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 2up 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 descrip-
tion of the process involved. You can also ’shop’ through this list to find items worthwhile
presenting.
Table 10.1 and Table 11.1
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.
Table 12.1 and Table 13.1
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 process-
output 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 stan-
dard 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 rele-
vant 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-
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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 repre-
senting 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 (micro-
phytobenthos), 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 aux-
iliary 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 inte-
grated 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, AP-
ATP (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 repre-
sent bacterial pollutant Enterococci.
Several new processes have been included to support the modelling of the new state vari-
ables. This includes VIVIANITE, APATITE (precipitation of phosphate), CONSELAC (con-
sumption of oxygen, nitrate, iron and sulfate, and the production of methane in the min-
eralization of organic matter), SPECSUD, OXIDSUD, SULPHOX, SPECSUDS1, SPEC-
SUDS2, 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 inor-
ganic carbon), and EnCocMRT (mortality of Enterococci).
Process LSEDTRA has been added for the transport processes in sediment for the mod-
eling of sediment-water interaction as based on the comprehensive layered sediment ap-
proach.
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
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(stems, branches, roots) is released at mortality.
1.5 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 <delwaq1.exe>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.
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, C-
POOCS3, 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.
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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
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: IM1is the first inorganic matter
fraction – the concentration of particulate matter in the water phase. Its counterpart in the
S1 layer is called IM1S1" and in the S2 layer it is called "IM1S2".
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.
1.6.1 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 IM1S1are 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, some-
times the pore water concentration is needed and therefore the porosity has been intro-
duced even for processes that mostly work for the water phase. The convention there
is:
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.
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2 Oxygen and BOD
Contents
2.1 Reaeration, the air-water exchange of DO . . . . . . . . . . . . . . . . . . 10
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
2.7 BOD, COD and SOD decomposition . . . . . . . . . . . . . . . . . . . . . 32
2.7.1 Chemical oxygen demand . . . . . . . . . . . . . . . . . . . . . . 32
2.7.2 Biochemical oxygen demand . . . . . . . . . . . . . . . . . . . . 33
2.7.3 Measurements and relations . . . . . . . . . . . . . . . . . . . . . 33
2.7.4 Accuracy ............................... 34
2.8 Sediment oxygen demand . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.9 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 . . . . . . . . . . . . . . . . 45
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2.1 Reaeration, the air-water exchange of DO
PROCESS: REAROXY
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.
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.
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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 con-
centrations of DO as follows:
Rrear =klrear ×(Coxs −max(Cox, 0.0))/H
klrear =klrear20 ×ktrear(T−20)
klrear20 =a×vb
Hc+d×W2
Coxs =f(T, Ccl or SAL)(delivered by SATUROXY)
fsat = 100 ×max(Cox, 0.0)
Coxs
with:
a, b, c, d coefficients with different values for each reaeration options
Ccl chloride concentration [gCl m−3]
Cox actual dissolved oxygen concentration [gO2m−3]
Coxs saturation dissolved oxygen concentration [gO2m−3]
fsat percentage of saturation [%]
Hdepth of the water column [m]
klrear reaeration transfer coefficient in water [m d−1]
klrear20 reaeration transfer coefficient at reference temperature 20 ◦C [m d−1]
ktrear temperature coefficient of the transfer coefficient [-]
Rrear reaeration rate [gO2m−3d−1]
SAL salinity [kg m−3]
Ttemperature [◦C]
vflow velocity [m s−1]
Wwind speed at 10 m height [m s−1]
Notice that the reaeration rate is always calculated on the basis of a positive dissolved oxy-
gen 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 temper-
ature 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
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The transfer coefficient is simplified to a constant, using the transfer coefficient as input pa-
rameter. 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
The relation is valid for rivers, and therefore independent of wind speed.
SWRear = 3
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 Dob-
bins (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.
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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.
SWRear = 8
The option is presently void and should not be used.
SWRear = 9
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 < 3ms−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 dhad to be scaled from cm h−1to m d−1. Consequently,
the coefficients are:
a= 0.0, b = 0.0, c = 0.0, d = 0.0744 ×fsc
fsc =Sc
Sc20 −0.5
Sc =d1−d2×T+d3×T2−d4×T3
with:
d1–4 coefficients
fsc scaling factor for the Schmidt number [-]
Sc Schmidt number at the ambient temperature [g m−3]
Sc20 Schmidt number at reference temperature 20 ◦C [d−1]
Ttemperature [◦C]
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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 d1d2d3d4
Sea water Salinity >5 kg m−31953.4 128.0 3.9918 0.050091
Fresh water Salinity ≤5 kg m−31800.6 120.1 3.7818 0.047608
SWRear = 12 (SOBEK-only)
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=0.0if
v < 3.93
5.32H0.356
(2.1)
(Owens et al.,1964):
a=5.32,b=0.67,c=0.85,d=0.0if
v < 3.93
5.32H0.356
(2.2)
klrear20 = max(klrearmin, klrear20)(2.3)
with:
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 pre-
vious relations, with respect to wind dependency, with respect to an additional forcing param-
eter, 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,
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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×Wb2+c1×Pc2×f sc
fsc =Sc
Sc20 −0.67
Sc =d1−d2×T+d3×T2−d4×T3
with:
a, b, c, d coefficients
klrear transfer coefficient in water [m d−1]
Pprecipitation, e.g. rainfall [mm h−1]
Sc Schmidt number at the ambient temperature [g m−3]
Sc20 Schmidt number at reference temperature 20 ◦C [d−1]
Ttemperature [◦C]
Wwindspeed 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 b1b2c1c2
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):
d1d2d3d4
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 coeffi-
cient 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,Wand Hfor options SWRear = 2, 3, 5, 6, 7 are
presented in Figure 2.1.
The coefficients a–c2are input parameters for option SWRear=13 only. The default values
are those for option 13.
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SWRear = 2
0
5
10
15
20
25
30
0 1 2 3 4 5 6 7
8
Veloc (m/s)
Depth=1m Depth=2m Depth=4m Depth=8m Depth=15m
SWRear = 3
0
5
10
15
20
25
30
01234567
8
Veloc (m/s)
R C R e a r ( 1 / d )
Depth=1m Depth=2m Depth=4m Depth=8m Depth=15m
The coefficients d1−4are input parameters for options SWRear = 10, 13. The default
values are the freshwater values, which are the same for both options.
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Oxygen and BOD
Table 2.1: Definitions of the parameters in the above equations for REAROXY
Name in
formulas1)
Name in
in/output
Definition Units
Cox OXY concentration of dissolved oxygen gO2m−3
Coxs SaturOXY saturation concentration dissolved oxygen
from SATUROXY
gO2m−3
aCoefAOXY coefficients for option 13 only -
b1CoefB1OXY -
b2CoefB2OXY -
c1CoefC1OXY -
c2CoefC2OXY -
d1CoefD1OXY coefficients for options 10 and 13 -
d2CoefD2OXY -
d3CoefD3OXY -
d4CoefD4OXY -
fcs – scaling factor for the Schmidt number -
fsat – percentage oxygen saturation %
H Depth depth of the water layer m
klrear20 KLRear water transfer coefficient for oxygen1) m d−1
kltemp TCRear temperature coefficient for reaeration -
P rain rainfall mm −1
Rrear – reaeration rate gO2m−3
d−1
SAL Salinity salinity kg m−3
Sc – Schmidt number for dissolved oxygen in wa-
ter
-
SWRear SWRear switch for selection of options for transfer
coefficient
-
T Temp temperature ◦C
v Velocity flow velocity m s−1
W VWind wind speed at 10 m height m s−1
1) See directives for use concerning the dimension of KLRear.
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SWRear = 5
0
5
10
15
20
25
30
01234567
8
Veloc (m/s)
R C R e a r ( 1 / d )
Depth=1m Depth=2m Depth=4m Depth=8m Depth=15m
SWRear = 6
0
5
10
15
20
25
30
01234567
8
Veloc (m/s)
R C R e a r ( 1 / d )
Depth=1m Depth=2m Depth=4m Depth=8m Depth=15m Depth=30m
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Oxygen and BOD
SWRear=7
Depth = 5m
0
1
2
3
4
5
6
7
0 2 4 6 8 10 12 14 16 18
20
Vwind
R C R e a r ( 1 / d )
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 (=klrear2020/H) as a function of water depth, flow
velocity and/or wind velocity for various options SWRear for the mass transfer
coefficient klrear
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2.2 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).
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 param-
eter SWdrear (= 0/1). The DO saturation concentration required for the process damrear is
calculated by an additional process SATUROXY.
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 formu-
lated as:
Rdrear =Cox −Coxt−1
∆t(2.4)
with:
Rdrear oxygen reaeration rate as a result of dam reaeration [gO2.m−3.d−1]
Cox oxygen concentration [gO2.m−3]
∆ttimestep [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
fdrear (Coxs(fdrear −1) + Coxup)(2.5)
with:
fdraer oxygen deficit ratio [−]
Coxs oxygen saturation concentration [gO2.m−3]
Coxup oxygen concentration upstream of weir [gO2.m−3]
Dam reaeration is always calculated on the basis of a positive dissolved oxygen concentra-
tion, whereas OXY may have negative values. Negative oxygen values equivalents represent
reduced substances.
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Notice that the reaeration rate is always calculated on the basis of a positive dissolved oxy-
gen 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 param-
eters 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.
SWdrear = 0
fdrear = 1.0+0.38 a b ∆h(1 −0.11 ∆h) (1 + 0.046 T)(2.6)
with:
awater quality factor [−]
bcharacteristic structure [−]
∆hdifference of water levels up- and downstream of the structure (hup −hdown)
[m]
hup water level upstream of structure [m]
hdown water level downstream of structure [m]
Twater temperature [◦C]
SWdrear = 1
Hybrid formulation for the oxygen deficit ratio of Gameson and Nakasone. If aand bare zero
the oxygen deficit ratio according to Nakasone is calculated.
fdrear = 1 + (fdrearn −1) a b (1 + 0.02(T−20)) (2.7)
fdrearn = exp 0.0675 ∆h1.28 3600 Q
L0.62
H0.439!(2.8)
with:
fdrearn oxygen deficit ratio according to Nakasone [−]
Qdischarge over structure [m3s−1]
Lwidth of crest structure [m]
Hwater 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 [gO2m−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.
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Processes Library Description, Technical Reference Manual
Table 2.2: Factor ’b’ (characteristic structure) for various structures.
weir type 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 0.80
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 -
b Coefbi dam reaeration coefficient of structure i -
Cbod CBOD5biological oxygen demand gO2.m−3
Cox
Coxs
Coxup
OXY
SaturOXY
OXY
concentration of dissolved oxygen
saturation conc. dissolved oxygen from saturoxy
oxygen concentration upstream of weir
gO2.m−3
gO2.m−3
gO2m−3
fdrear
fdrearn
-
-
oxygen deficit ratio
oxygen deficit ratio according to Nakasone
-
-
hup
hdown
W tLvLSti
W tLvRSti
Water level upstream of structure i(according to
definition in schematisation)
Water level downstream of structure i(according
to definition in schematisation)
m
m
H Depth depth of the top water layer m
L W idthsti width of crest of structure i m
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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 m3s−1
Rdrear - oxygen reaeration rate as a result of dam aeration gO2.m−3d−1
∆t Delt timestep d
T T emp temperature ◦C
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Processes Library Description, Technical Reference Manual
2.3 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.
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 temper-
ature 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).
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:
Coxs =a−b T + (c T )2−(d T )31−Ccl
m
For SWSatOxy = 2:
Coxs = exp a+b
Tf
+cln(Tf) + d Tf+SAL (m+n Tf+o T 2
f)32 000
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 [gO2m−3]
Twater temperature [◦C]
Tftemperature function [-]
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Oxygen and BOD
SAL salinity [kg m−3]
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
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:
SAL = 1.805 ×Cl / 1 000.
Additional references
WL | Delft Hydraulics (1980b)
Table 2.4: Definitions of the parameters in the equations for SATUROXY
Name in
formulas
Name in
input
Definition Units
Coxs SaturOXY saturation concentration of oxygen in water gO2m−3
Ccl Cl chloride concentration gCl m−3
SAL Salinity salinity kg m−3
SWSatOxy SWSatOxy switch for selection options for saturation
equation
-
TTemp water temperature ◦C
Tf–temperature function -
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Processes Library Description, Technical Reference Manual
2.4 Diurnal variation of DO
PROCESS: VAROXY
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 subsur-
face 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 con-
sumes 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 pro-
cess 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 pro-
cess 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.
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=F np +F rsp
H
with:
F np net primary production flux [gC m−2d−1]
F rsp respiration flux [gC m−2d−1]
Hdepth of the water column [m]
Rgpadaily average gross primary production rate [gC m−3d−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 t1and t2which
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:
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Oxygen and BOD
oxyg en
pro d.
(g /m 3 /d)
time (h)
0 24
12
12 -D Lx12 t1 t2 1 2+D Lx12
R gp
m ax
Figure 2.2: The distribution of gross primary production over a day
DL day length, fraction of a day [-]
Rgpmax maximal gross primary production rate during a day [gC m−3d−1]
t1time at which the maximal production is reached [h]
t2time at which the production starts to fade [h]
The net primary production as a function of the time in a day then follows from:
Rnp =
−F rsp
Hfor t≤(12 −12 DL)
Rgpmax
(t1−(12 −12 DL)) (t−(12 −12 DL)) −F rsp
Hfor (12 −12 DL)< t < t1
Rpgmax −F rsp
Hfor t1≤t≤t2
Rpgmax −Rgpmax
((12 + 12 DL)−t2)(t−t2)−F rsp
Hfor t2< t < (12 + DL 12)
−F rsp
Hfor t≥(12 + 12 DL)
with:
Rnp net primary production (or respiration) rate during a day [gC m−3d−1]
tactual 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.
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Processes Library Description, Technical Reference Manual
Table 2.5: Definitions of the parameters in the above equations for VAROXY
Name in
formulas
Name in
in/output
Definition Units
DL DayL day length, fraction of a day -
F np fPPtot net primary production flux gC m−2d−1
F rsp fResptot respiration flux gC m−2d−1
HDepth thickness of the computational cell m
SW OxyP rod SWOxyProd switch for the option to activate process
VAROXY
-
Rnp –net primary production (or respiration)
rate during a day
gC m−3d−1
Rgpa–average gross primary production rate
during a day
gC m−3d−1
Rgpmax –maximal gross primary production rate
during a day
gC m−3d−1
tItime DELWAQ time scu
t1T1MXPP time at which the maximal production is
reached
h
t2T2MXPP time at which the production starts to fade h
–AuxSys ratio between a day and system clock
units (86400)
s d−1
–Refhour time at the start of the simulation h
tTime time in a day h
t1T1MXPP time at which the maximal production is
reached
h
t2T2MXPP time at which the production starts to fade 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.
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Oxygen and BOD
2.5 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 pri-
mary 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.
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.
Implementation
Process OXYMIN can only be used in combination with the algae module DYNAMO, con-
sisting 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 concen-
tration 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 dis-
solved oxygen concentration in a day follows from half the DO-decrease during the night:
Coxmin1=Cox −0.5×2.67 ×Rrsp ×(1 −DL)
Rrsp =
2
X
i=1
(krspi×Calgi)
with:
Calg algae biomass [gC m−3]
Cox average dissolved oxygen concentration [gO2m−3]
Coxmin1minimal dissolved oxygen concentration in a day for estimation method 1 [gO2
m−3]
DL day length, fraction of a day [-]
krsp algae respiration rate constant [d−1]
Rrsp total algae respiration rate [gC m−3d−1]
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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
Calg1Green biomass of Green algae gC m−3
Calg2Diat biomass of Diatoms gC m−3
Cox OXY average dissolved oxygen concentration gO2m−3
Coxmin OXYMIN minimal dissolved oxygen concentration in a
day
gO2m−3
DL DayL day length, fraction of a day -
kgp1RcGroGreen gross primary prod. rate constant of Green al-
gae
d−1
kgp2RcGroDiat gross primary prod. rate constant of Diatoms d−1
krsp1RcRespGreen algae respiration rate constant of Green algae d−1
krsp2RcRespDiat algae respiration rate constant of Diatoms d−1
Rgp –total gross primary production rate gC m−3
d−1
Rrsp –total algae respiration rate gC m−3
d−1
iindex 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)
Rgp =
2
X
i=1
(kgpi×Calgi)
with:
Coxmin2minimal dissolved oxygen concentration in a day for estimation method 2 [gO2
m−3]
kgp gross primary production rate constant [d−1]
Rgp total net primary production rate [gC m−3d−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
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Oxygen and BOD
Table 2.7: Definitions of the parameters in the above equations for POSOXY
Name in
formulas
Name in
in/output
Definition Units
Cox OXY equivalent dissolved oxygen concentration gO2m−3
DO – positive dissolved oxygen concentration gO2m−3
2.6 Calculation of actual DO concentration
PROCESS: POSOXY
DELWAQ allows negative dissolved oxygen concentrations (DO). Decomposition of dead or-
ganic matter continues, when DO has become depleted using other substances such as ni-
trate 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 sub-
stances 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.
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 actual dissolved oxygen concentration [gO2m−3]
Cox equivalent dissolved oxygen concentration [gO2m−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.
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Processes Library Description, Technical Reference Manual
Table 2.8: Typical values for oxygen demanding waste waters (values in [mgO2/l])
Source CBOD5 CBODu NBODu COD
Municipal waste (untreated) 100-400 220
(120-580)
220
Combined sewer overflow (un-
treated)
170
(40-500)
220 -
Separate urban runoff (untreated) 19
(2-80)
- -
Background natural water (excl. al-
gae and detritus)
0 2-3
Background of natural water (incl.
algae and detritus)
2-3 10
Data from Thomann and Mueller (1987).
Explanation: CBOD5 = 5-day CBOD; CBODu = ultimate CBOD
2.7 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 pa-
rameters 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 mean-
ing. 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 car-
bonaceous 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 per-
manganate (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−1Cl. There is no fixed relation
between the results obtained with the Mn and Cr-method.
32 of 464 Deltares
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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 consump-
tion 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 meth-
ods: 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.
The heterotrophic carbonaceous oxidizing organisms are usually abundantly present in nat-
ural 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 be-
tween 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 CO2and H2O. Simplification to first order kinetics is used frequently. Fresh organic
matter is more susceptible to biochemical oxidation than older material. This preferential di-
gestion 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 O2are 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 sub-
sequently 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 het-
erotrophic 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) = 0.3Depth−0.434 [d−1] for depths <2.5m. (2.12)
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Processes Library Description, Technical Reference Manual
For deeper water bodies the authors assume 0.33 m d−1.
2.7.4 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 BOD-
test 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
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.
Because for each pool different types of measurements exist, DELWAQ accepts two differ-
ent 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 ac-
cepted. 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 sup-
plied 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
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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.
This process is implemented for CBOD5, CBODu, CBOD5_2, CBODu_2, COD_Cr, COD_Mn,
NBOD5 and NBODu.
Formulation
Substance aggregation:
BODu =CBODu +CBODu_2 + CBOD5×1−e−5×RcBOD−1+
+CBOD5_2×1−e−5×RcBOD_2−1
BOD5 = CBODu ×1−e−5×RcBOD+CBODu_2×1−e−5×RcBOD_2+
+CBOD5 + CBOD5_2
COD =COD_Cr
EffCOD_Cr +COD_Mn
EffCOD_Mn
NBOD =NBODu +NBOD5×1−e−5×RcBODN −1
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)×(OXY )−COXBOD
OOXBOD −COXBOD 10CurvBOD
+CF LBOD
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Processes Library Description, Technical Reference Manual
Functions for calculation of rate constant (’aging function’):
AgeIndx =COD
BOD5(2.13)
for AgeIndx ≤LAgeIndx:
AgeF un =UAgeF un (2.14)
for LAge < AgeIndx < LAgeIndx:
AgeF un = (UAgeF un−LAgeF un)×exp −AgeIndx −LAgeIndx
UAgeIndx 2!+LAgeF un
(2.15)
for AgeIndx ≥LAgeIndx:
AgeF un =LAgeF un (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
dNBOD5 = RcBODN ×(NBOD5) ×T cBODT emp−20 ×O2F uncBOD ×AgeF un
dNBODu =RcBODN ×(NBODu)×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_Mn =RcCOD ×(COD_Mn)×T cCODT emp−20
Oxygen demand:
SWOxyDem = 0: BOD determining (default)
dOxyBODCOD =dCBOD5+dCBOD5_2+dCBODu+dCBODu_2+dNBOD5+dNBODu
SWOxyDem = 1: COD determining (option)
dOxyBODCOD =dCOD_Cr +dCOD_Mn
SWOxyDem = 2: BOD ∧COD determining (option)
dOxyBODCOD =dBOD5 + dCBOD5_2 + dCBODu +dCBODu_2+
+dNBOD5 + dNBODu +dCOD_Cr +dCOD_Mn
where:
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CBOD5carbonaceous BOD (first pool) at 5 days [gO2m−3]
CBOD5_2carbonaceous BOD (second pool) at 5 days [gO2m−3]
CBODu carbonaceous BOD (first pool) ultimate [gO2m−3]
CBODu_2carbonaceous BOD (second pool) ultimate [gO2m−3]
AgeF un scaling function for decay rates [-]
AgeIndx ratio of CBOD5 and COD [-]
P HY T total phytoplankton concentration [gC m−3d−1]
AlgF rBOD fraction of algae that contribute to BOD [-]
BODu_P HY T calculated carbonaceous BOD at ultimate from PHYT [gO2m−3]
BOD5/uP hyt ratio BOD5 to BOD_ultimate for PHYT [-]
BOD5_P HY T calculated carbonaceous BOD at 5 days from PHYT [gO2m−3]
P OC total particulate organic carbon concentration [gC m−3d−1]
P OCF rBOD fraction of POC that contribute to BOD [-]
BODu_P OC calculated carbonaceous BOD at ultimate from POC [gO2m−3]
BOD5/infP O ratio BOD5 to BOD_ultimate for POC [-]
BOD5_P OC calculated carbonaceous BOD at 5 days from POC [gO2m−3]
BOD5calculated carbonaceous BOD at 5 days (incl. PHYT and POC) [gO2
m−3]
BODu calculated carbonaceous BOD at ultimate (incl. PHYT and POC)
[gO2m−3]
COD calculated chemical oxygen demand days [gO2m−3]
COD_Cr COD concentration by the Cr-method [gO2m−3]
COD_Mn COD concentration by the Mn-method [gO2m−3]
COXBOD critical oxygen concentration: [g m−3]
CF LBOD value of the oxygen function for oxygen levels below the critical oxy-
gen concentration [-]
CurvBOD factor that determines the curvature [-] between COXBOD and OOX-
BOD (-1 <CurvBOD <0)
dCBOD5decay flux of CBOD5 [gO2m−3d−1]
dCBOD5_2decay flux of CBOD5_2 [gO2m−3d−1]
dCOD_Cr decay flux of COD_Cr [gO2m−3d−1]
dCBODu decay flux of CBODu [gO2m−3d−1]
dCBODu_2decay flux of CBODu_2 [gO2m−3d−1]
dCOD_Mn decay flux of COD_Mn [gO2m−3d−1]
dNBOD5decay flux of NBOD5 [gO2m−3d−1]
dNBODu decay flux of NBODu [gO2m−3d−1]
dOxyBODCOD oxygen consumption flux of BOD and COD species [gO2m−3d−1]
EffCOD_Cr efficiency of the Cr_method [-]
EffCOD_Mn efficiency of the Mn_method [-]
LAgeF un lower value of age function [-]
LAgeIndx lower value of age index [-]
NBOD calculated nitrogenous BOD at ultimate [gO2m−3]
NBOD5nitrogenous BOD after 5 days [gO2m−3]
NBODu nitrogenous BOD ultimate [gO2m−3]
O2F unc oxygen function for decay of CBOD [-]
OXCCF oxygen to carbon ratio
OOXBOD optimum oxygen concentration: above this value the oxygen function
becomes 1.0 [gO2m−3]
OXY oxygen concentration [gO2m−3]
RcBOD reaction rate BOD (first pool) at 20 ◦C [d−1]
RcBOD_2reaction rate BOD_2 (second pool) at 20 ◦C [d−1]
RcBODN reaction rate BODN (second pool) at 20 ◦C [d−1]
RcCOD reaction rate COD (first pool) at 20 ◦C [d−1]
SW OxyDem switch that determines the oxygen consuming substance (0: BOD;
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Figure 2.3: A typical oxygen demand curve
1: COD; 2: COD+BOD) [-]
T cBOD temperature coefficient BOD [-]
T cBOD_2temperature coefficient BOD (second pool)[-]
T cCOD temperature coefficient COD [-]
T emp water temperature [◦C]
UAgeF un upper value of age function [-]
UAgeIndx upper value of age index [-]
Directives for use
To change the aging function from its default value (1.0) to the shape presented in Fig-
ure 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 con-
centration. 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)
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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
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 1 2 3 4 5
Oxygen concentration (mg/l)
O x y g e n f u n c t i o n B O D ( - )
CurvBOD = 0
CurvBOD = 0.5
CurvBOD = -0.3
OOXBOD
COXBOD
CFLBOD
Figure 2.5: Default and optional oxygen functions for decay of CBOD (O2FuncBOD)
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Figure 2.6: Optional function for the calculation of the first order rate constant for BOD
and NBOD
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2.8 Sediment oxygen demand
PROCESS: SEDOXYDEM
This process scales a user-defined sediment oxygen demand flux fSOD [gO2m−2d−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 sedi-
mentation. 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.
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.
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:
dSOD =fSOD
depth +RcSOD ×T cSODT emp−20 ×SOD
V olume ×O2func
O2func =
0if OXY < COXSOD
OXY −COXSOD
OOXSOD−COXSOD
1if OXY > OOXSOD
dOxSOD =dSOD
where
fSOD user-specified sediment oxygen demand [gO2m−2d−1]
SOD BOD/COD components, accumulated in sediment [gO2]
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RcSOD decay rate of SOD in sediment [d−1]
T cSOD temperature coefficient SOD decay [-]
depth depth of a DELWAQ segment [m]
V olume volume of a DELWAQ segment [m3]
dSOD decay of SOD (DELWAQ flux) [gO2m−3d−1]
dOxSOD oxygen consumption (DELWAQ flux) [gO2m−3d−1]
O2func oxygen function for decay of SOD [-]
OXY oxygen concentration in surface water [gO2m−3]
COXSOD critical oxygen concentration for SOD decay [gO2m−3]
OOXSOD optimal oxygen concentration for SOD decay [gO2m−3]
If SwCH4bub = 1:
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:
dOxMinSed = 2.67×(dMinDetCS1+dMinDetCS2+dMinOOCS1+dMinOOCS2)
where:
dOxMinSed oxygen consumption by mineralisation of DetC and OOC in sediment
[gO2m−3d−1]
dMinDetCS1mineralisation of DetC in sediment layer 1 [gC m−3d−1]
dMinDetCS2mineralisation of DetC in sediment layer 2 [gC m−3d−1]
dMinOOCCS1mineralisation of OOC in sediment layer 1 [gC m−3d−1]
dMinOOCCS2mineralisation of OOC in sediment layer 2 [gC m−3d−1]
The methane module computes the flux of methane, escaping from the water column to the
atmosphere. The flux is a function of dSOD +dOxMinSed.
F lCH4methane bubble flux [gO2m−2d−1]
Additional output parameter:
dCH4bubble flux expressed in DELWAQ units (=F lCH4/depth) [gO2m−3d−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 =fSOD∗+DifCH4bub +DifCH4dis
Depth −dOxMinSed
where:
fSOD∗calculated total oxygen consumption in sediment [gO2m−2d−1]
DifCH4bub oxygen consumption by CH4dissolving from bubbles [gO2m−2d−1]
DifCH4dis oxygen consumption by CH4diffusing from sediment towards water
column [gO2m−2d−1]
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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 posi-
tive contribution to the mass balance of oxygen. In that case, dOxSod acts as a correc-
tion 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 wa-
ter 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 con-
sumption 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)
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2.9 Production of substances: TEWOR, SOBEK only
2.9.1 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) (i) ∈ {ECOLI, FCOLI or TCOLI}.
2.9.2 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 mod-
elled explicitly.
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=ftewori(2.17)
with:
RteworiTEWOR production flux (g i.m−3)
fteworiTEWOR 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
RteworidTEWORi TEWOR production flux g.m−3
fteworifTEWORi TEWOR production flux g.m−3
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2.9.3 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.
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.
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
Rmini
1−exp(−5kmini)(2.19)
with:
C5icarbonaceous BOD (pool i) at 5 days [g O2m−3]
Cox dissolved oxygen [g O2m−3]
kminioxidation reaction rate BOD (pool i) [d−1]
Ksox half saturation constant for oxygen limitation on oxidation of BOD [g O2m−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
C5iCBOD5_i carbonaceous BOD (pool i) at 5 days g O2m−3
Cox OXY dissolved oxygen g O2m−3
CuiCBODu_i carbonaceous BOD (pool i) ultimate g O2m−3
kminiRCBOD_i oxidation reaction rate BOD (pool i) d−1
Ksox KMOX half saturation constant for oxygen limitation
on oxidation of BOD
g O2m−3
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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 . . . . . . . . . . . . . . . . . . . . . . . . . . 78
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3.1 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.
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.
Volume units refer to bulk ( ) or to water ( ).
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 nNit.
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:
NH+
4+ 2O2+H2O=⇒NO−
3+ 2H3O+
Nitrification ultimately removes ammonium (ammonia) and oxygen from the water phase and
produces nitrate. The process requires 4.57 gO2gN−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.
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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×Cox
Ksox ×φ+Cox
knit =knit20 ×ktnit(T−20)
knit = 0.0if T < Tcor Cox ≤0.0
k0nit = 0.0
k0nit =k0temp if T < Tcand Cox > 0.0
k0nit =k0ox if T≥Tcand Cox ≤0.0
k0nit = 0.0if Cox ≤Coxc ×φ
with:
Cam ammonium concentration [gN.m−3]
Cox dissolved oxygen concentration ≥0.0[g.m−3]
Coxc critical dissolved oxygen concentration [g.m−3]
knit Michaelis-Menten nitrification rate [gN.m−3d−1]
ktnit temperature coefficient for nitrification [-]
k0nit zeroth order nitrification rate [gN.m−3d−1]
k0ox zeroth order nitrif. rate at negative average DO concentrations [gN.m−3d−1]
k0temp zeroth order nitrification rate at low temperatures [gN.m−3d−1]
Ksox half saturation constant for dissolved oxygen limitation [g.m−3]
Ksam half saturation constant for ammonium limitation [gN.m−3]
Ttemperature [◦C]
T c critical temperature for nitrification [◦C]
φporosity [-]
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 temper-
ature drops below a critical value, only the zeroth order flux remains. The first order flux is
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corrected for water temperature and oxygen concentration. Below a critical oxygen concentra-
tion 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 in-
terpolation 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 +fox ×k1nit ×Cam
k1nit =k1nit20 ×ktnit(T−20)
0.0if T < Tc
with:
Cam ammonium concentration [gN m−3]
fox the oxygen limitation function [-]
k1nit first order nitrification rate [d−1]
ktnit temperature coefficient for nitrification [-]
k0nit zeroth order nitrification rate [gN m−3d−1]
Ttemperature [◦C]
Tccritical temperature for nitrification [◦C]
The oxygen limitation function reads:
fox =
foxmin if Cox ≤Coxc
(1 −foxmin)×Cox−Coxc
Coxo−Coxc 10a+foxmin if Coxc < Cox < Coxo
1.0if Cox ≥Coxo
with:
acurvature coefficient [-]
Cox dissolved oxygen concentration ≥0.0[g m−3]
Coxo optimal dissolved oxygen concentration [g m−3]
Coxc critical dissolved oxygen concentration [g m−3]
foxmin minimal value of the oxygen limitation function [-]
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 ammonium concentration [gN.m−3]
Cox dissolved oxygen concentration ≥0.0[g.m−3]
knit First order nitrification rate [gN.m−3.d−1]
Ksox half saturation constant for dissolved oxygen limitation [g.m−3]
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An important feature of Monod-kinetics is that the process rate saturates at high concen-
trations 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.
Directives for use
Formulation option SW V nN it = 0.0is 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 time-
step is too large!
The critical temperature for nitrification CT Nit is approximately 4 ◦C.
The rate RcNit20 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.
Concerning option SW V nNit1.0:
For a start, the zeroth order rates Rc0NitT and Rc0NitOx and the critical DO concen-
tration CoxNit 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 quanti-
fied 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 pro-
cess by assigning a value to KsAmNit that is high compared to the ambient ammonium
concentrations. By enlarging RcNit20 concurrently approximately the same rates can be
obtained as for first order kinetics.
Concerning option SW V nNit0.0:
The use of the curvature coefficient CurvNit of the oxygen limitation function is de-
scribed in WL | Delft Hydraulics (1994a). Linear interpolation between COXNit and
OOXNit occurs, when CurvNit is equal to 0.0, whereas the value -1 establishes
maximal curvature.
The optimal oxygen concentration OOXNit must be higher than the critical oxygen con-
centration COXNit (see Figure 3.1).
The limitation function can be made inactive by choosing a low value for the optimal oxy-
gen concentration OOXNit (e.g. a negative value).
By choosing a positive minimal value of the oxygen limitation function CF LNit the lim-
itation will have a user defined value at oxygen concentrations below the critical oxygen
concentration. This may result in nitrification when the average dissolved oxygen concen-
tration is negative.
Additional references
DiToro (2001), Smits and Van der Molen (1993), WL | Delft Hydraulics (1997c), Vanderborght
et al. (1977)
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Table 3.1: Definitions of the parameters in the above equations for NITRIF_NH4. Volume
units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in input Definition Units
a CurvNit curvature coefficient for the oxygen lim. func-
tion
-
Cam NH4ammonium concentration gN m−3
Cox OXY dissolved oxygen concentration g m−3
Coxc CoxNit critical DO concentration for nitrification g m−3
Coxo OoxNit optimal DO concentration for nitrification g m−3
foxmin CF LNit minimal value of the oxygen limitation function -
knit20 RcNit20 MM- nitrification reaction rate at 20 ◦C gN m−3d−1
k1nit20 RcNit first order nitrification rate at 20 ◦C d−1
ktnit T cNit temperature coefficient for nitrification -
k0ox Rc0NitOx zeroth order nitrification rate at negative DO gN m−3d−1
k0temp Rc0NitT zeroth order nitrification rate at low tempera-
tures
gN m−3d−1
k0nit Znit zeroth order nitrification rate gN m−3d−1
Ksam KsAmNit half saturation constant for ammonium limita-
tion
gN m−3
Ksox KsOxNit half saturation constant for DO limitation g m−3
Rnit – nitrification rate gN m−3d−1
-SW V nNit switch for selection of the process formula-
tions (pragmatic kinetics = 0.0, MM-kinetics =
1.0)
-
T T emp temperature ◦C
TcCT Nit critical temperature for nitrification ◦C
φ P OROS porosity m3m−3
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0246810
0
0.2
0.4
0.6
0.8
1
Nitrification as function of oxygen concentration
Dissolved oxygen (g/m3)
OOXNIT
COXNIT
Figure 3.1: Figure 1 Default pragmatic oxygen limitation function for nitrification
(O2FuncNit, option 0).
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3.2 Calculation of NH3
PROCESS: NH3FREE
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.
NH3is the product of the dissociation of the ammonium (NH+
4) ion:
NH+
4⇒NH3+H+
The reaction is characterised by the equilibrium constant K:
K0=aNH3aH+
aNH+
4
where:
aiactivity of species i[mol l−1]
Rearranging this equation and taking logarithms (pH =−10log(aH+)) results in:
log aNH3
aNH+
4!= log K0+pH
Because DELWAQ computes concentrations rather than activities, a corrected equilibrium
constant is introduced:
K=K0γNH+
4
γNH3
where:
γiactivity coefficient of species i[-]
K 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)
(NH+
4)=logK +pH
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 tempera-
ture, increasing temperature favours the dissociation of NH+
4(Millero,1995).
In DELWAQ, totalNH4is modelled as substance NH4, which is the sum of NH+
4and NH3.
The concentration of NH3is derived from the above equation and total NH4according to:
[NH3] =
[NH3]
[NH+
4]
1 + [NH3]
[NH+
4]
×(totalNH4)
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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 NH4concentration 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
The process calculates additional substance NH3 (g.m3), and is active in all types of compu-
tational elements.
Tabel 3.2 provides the definitions of the input parameters occurring in the formulations.
Formulation
The process is formulated as follows:
If NH3_Sw = 1 then
(totalNH4) = NH4×m3
l×1
M
log K=a+b×T
(NH3) = 10logK+pH
1 + 10logK+pH ×(totalNH4)
NH3=(NH3)×M×l
m3
frNH3 = (NH3)
(totalNH4)
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
(NH4) = NH4×m3
l×1
M×ρ
(NH3)=(NH4)/(1 + 10−pH
K)
NH3 = (NH3)×M×ρ×l
m3
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where:
NH3_Sw option parameter for calculation method [-]
NH3 concentration of ammonia [gN m−3]
(NH3) molar concentration of ammonia [mol l−1] or [mol kg−1H2O]
NH4 concentration of ammonium (DELWAQ substance) [gN m−3]
(NH4) molar concentration of ammonium [mol l−1] or [mol kg−1H2O]
a coefficient a of reprofunction 1 [-]
b coefficient b of reprofunction 1 [K−1]
frNH3 fraction NH3 of NH4 [-]
K dissociation constant [mol l−1] or [mol kg−1H2O]
M atomic weight of nitrogen (= 14) [g mol−1]
pH pH [-]
Sal salinity [g kg−1]
T water temperature [◦C]
ρdensity of water [kg l−1]
[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 KNH3rf1aand KNH3rf1a.
Table 3.2: Definitions of the input parameters in the formulations for NH3FREE.
Name in
formulas
Name in input Definition Units
NH4NH4ammonium concentration gN m−3
NH3_Sw NH3_Sw option for calculation method (1=reprofunction
1; 2=Millero)
-
a KNH3rf1acoefficient a of reprofunction 1 -
b KNH3rf1bcoefficient b of reprofunction 1 K−1
pH pH acidity -
Sal Salinity salinity psu
T T emp temperature ◦C
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3.3 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.
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.
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 ( ).
Implementation
Process DENWAT_NO3 has been implemented in a generic way, meaning that it can be ap-
plied 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 denitrifi-
cation 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:
4NO−
3+ 4H3O+=⇒2N2+ 5O2+ 6H2O
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Denitrification ultimately removes nitrate from the water phase and produces elemental nitro-
gen. The process delivers 2.86 gO2gN−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 con-
centration, 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.
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 dis-
solved 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 ×Cni
Ksni ×φ+Cni×fox
fox =1.0−Cox
Ksox×φ+Cox if Cox ≥0.0
1.0if Cox < 0.0
kden =kden20 ×ktden(T−20)
kden = 0.0if T < T c or Cox ≥Coxc ×φ
k0den = 0.0
k0den =k0temp if T < T c and Cox < Coxc ×φ
k0den =k0ox if T≥T c and Cox < Coxc ×φ
k0den = 0.0if Cox ≥Coxc ×φ
with:
Cni nitrate concentration [gN m−3]
Cox dissolved oxygen concentration ≥0.0[g m−3]
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Coxc critical dissolved oxygen concentration [g m−3]
fox oxygen inhibition function [-]
kden Michaelis-Menten denitrification rate [gN m−3d−1]
ktden temperature coefficient for denitrification [-]
k0den zeroth order denitrification rate [gN m−3d−1]
k0ox zeroth order denitrification rate at moderate DO concentrations [gN m−3d−1]
k0temp zeroth order denitrification rate at low temperatures [gN m−3d−1]
Ksni half saturation constant for nitrate limitation [gN m−3]
Ksox half saturation constant for dissolved oxygen inhibition [g m−3]
Ttemperature [◦C]
T c critical temperature for denitrification [◦C]
φporosity [-]
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 concentra-
tion, representing the DO-equivalent of reduced substances!)
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 +fox ×k1den ×Cni
k1den =0.0if T < Tc
k1den20 ×ktden(T−20)
with:
Cni nitrate concentration [gN m−3]
fox the oxygen inhibition function [-]
k1den first order denitrification rate [d−1]
ktden temperature coefficient for denitrification [-]
k0den zeroth order denitrification rate [gN m−3d−1]
Ttemperature [◦C]
Tccritical temperature for denitrification [◦C]
The oxygen inhibition function reads:
fox =
1.0if Cox ≤Coxo
Coxc −Cox
Coxc −Coxo + (ea−e) (Cox −Coxo)if Coxo < Cox < Coxc
0.0if Cox ≥Coxc
with:
acurvature coefficient [-]
Cox dissolved oxygen concentration ≥0.0[g m−3]
Coxo optimal dissolved oxygen concentration [g m−3]
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Coxc critical dissolved oxygen concentration [g m−3]
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 or-
der 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−2d−1]. The resulting denitrification
rate is divided by the depth of the water column Hin order to obtain the rate in [g.m−3d−1].
Directives for use
Formulation option SW V nDen = 0.0is 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 con-
centration CoxDen can be set to zero. In a next step the zeroth order rate for low tem-
peratures 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 rele-
vant for the current case.
The critical oxygen concentration should not be given a value higher than 2 g m−3for
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 KsNiDen that is high compared to the ambient nitrate concentra-
tions. By enlarging RcDen20 concurrently approximately the same rates can be obtained
as for first order kinetics.
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.
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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. Vol-
ume units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in input Definition Units
a Curvat curvature coefficient for the oxygen inhib. func-
tion
-
Cni NO3nitrate concentration gN m−3
Cox OXY dissolved oxygen concentration g m−3
Coxc CoxDen optimal DO concentration for denitrification g m−3
Coxo OoxDen critical DO concentration for denitrification g m−3
kden20 RcDen20 MM- denitrification reaction rate at 20 ◦C gN m−3d−1
k1den20 RcDenW at first order denitrification reaction rate at 20 ◦C d−1
ktden T cDenW at temperature coefficient for denitrification -
k0ox Rc0DenOx zeroth order denitrification rate at moderate
DO
gN m−3d−1
k0temp Rc0DenT zeroth order denitrification rate at low temper-
atures
gN m−3d−1
k0den ZDenW at zeroth order denitrification rate gN m−3d−1
Ksni KsNiDen half saturation constant for nitrate limitation gN m−3
Ksox KsOxDen half saturation constant for DO inhibition g m−3
Rden – denitrification rate gN m−3d−1
-SW V nDen switch for selection of the process formulations
(pragmatic kinetics = 0.0, MM-kinetics = 1.0)
-
T T emp temperature ◦C
TcCT Den critical temperature for denitrification ◦C
φ P OROS porosity m3m−3
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Table 3.4: Definitions of the parameters in the above equations for DENSED_NO3. Vol-
ume units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in input Definition Units
Cni NO3nitrate concentration in the overlying water
layer
gN m−3
H Depth depth of the overlying water layer m
kden20 RcDenSed first-order denitrification reaction rate m d−1
ktden T cDenSed temperature coefficient for denitrification -
k0temp Rc0DenSed zeroth order denitrification rate gN m−2
Rden – denitrification rate gN m−3d−1
T T emp temperature ◦C
TcCT Den critical temperature for denitrification ◦C
0246810
0
0.2
0.4
0.6
0.8
1
Denitrification as function of oxygen concentration
Dissolved oxygen (g/m3)
OOXDEN
COXDEN
Figure 3.2: Default pragmatic oxygen inhibition function for denitrification (O2Func, option
0).
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3.4 Adsorption of phosphate
PROCESS: ADSPO4AAP
Dissolved phosphate, mainly present as ortho-phosphate (mainly present as H2PO−
4), ad-
sorbs onto suspended sediment, in particular to the iron(III)oxyhydroxides in sediment parti-
cles. Other adsorbing components are aluminium hydroxides and silicates, manganese ox-
ides 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.
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.
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. Nev-
ertheless, equilibrium is usually established within a few hours. Although process rates are
high, the adsorption process has been formulated kinetically for pragmatic reasons. One rea-
son 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 ( ).
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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 depen-
dent 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.
Table 3.5 provides the definitions of the parameters occurring in the formulations. The con-
centrations 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.
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 formula-
tions 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 par-
ticles range from ultimately simplified to rather complex pH- and DO dependent adsorption.
The adsorption capacity of (suspended) inorganic sediment can be calculated in two differ-
ent 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 (sus-
pended) inorganic sediment, whereas version (SW V nAdsP =1.0) calculates the adsorption
capacity from the individual inorganic matter concentrations IM1−3and pertinent iron frac-
tions. 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 quan-
tified as a constant fraction of the total inorganic phosphate concentration, which implies a
constant ratio between the dissolved and adsorbed phosphate concentrations:
Kdph =Cphde
Cphae
where:
Cphaeequilibrium adsorbed phosphate concentration [gP m−3]
Cphdeequilibrium dissolved phosphate concentration [gP m−3]
Kdph 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=Cpha +Cphd
1 + Kdph
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where:
Cpha the adsorbed phosphate concentration after the previous time-step [gP m−3]
Cphd the dissolved phosphate concentration after the previous time-step [gP m−3]
The sorption rate is calculated as:
Rsorp =Cphae−Cpha
∆t
where:
∆tcomputational time-step [d]
Simplified Langmuir adsorption (SWAdsP = 1)
The adsorption equilibrium can be considered as a chemical equilibrium described with the
following simplified reaction equation:
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:
Cadseequilibrium concentration of free adsorption sites in P equivalents [gP m−3]
Cphaeequilibrium adsorbed phosphate concentration [gP m−3]
Cphdeequilibrium dissolved phosphate concentration [gP m−3]
Kads adsorption equilibrium constant [m3gP−1]
φporosity [-]
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 con-
centration 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 =fcap ×
3
X
i=1
(ffei×Cimi)
fimi= (ffei×Cimi)/
3
X
i=1
(ffei×Cimi)
where:
Cadst total concentration of adsorption sites [gP m−3]
Cimiconcentration of inorganic matter fractions i=1, 2, 3 [gDW.m−3]
fimifraction of adsorbed phosphate bound to inorganic matter fractions i=1, 2, 3 [-]
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fcap phosphate adsorption capacity of inorganic matter [gP gFe−1]
ffeifraction reactive iron(III) in inorganic matter fractions i=1, 2, 3 [gFe gDW−1]
The fractions fimiare 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 (3.2)
Cadse=Cads =Cadst −Cpha (3.3)
where:
Cads the concentration of free ads. sites after the previous time-step [gP m−3]
Cpha the adsorbed phosphate concentration after the previous time-step [gP m−3]
Cphd the dissolved phosphate concentration after the previous time-step [gP m−3]
eindex for the chemical equilibrium value
The above equations result in the following equation for the equilibrium adsorbed phosphate
concentration:
Cphae= (Cpha +Cphd)/1 + φ
Kads ×Cads
if Cads < 0.0then 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 sorption reaction rate [d−1]
Rsorp adsorption or desorption rate [gP m−3d−1]
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×OHa
Cphde×Cadse
Kads =Kads20 ×ktads(T−20)
OH = 10−(14−pH)
where:
astochiometric reaction constant [-]
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Cadseequilibrium concentration of free adsorption sites [molFe l−1]
Cphaeequilibrium adsorbed phosphate concentration [molP l−1]
Cphdeequilibrium dissolved phosphate concentration [molP l−1]
Kads adsorption equilibrium constant [(mol l−1)a−1]
ktads temperature coefficient for adsorption [-]
OH molar hydroxyl concentration [mol l−1]
pH acidity [-]
eindex for the chemical equilibrium value
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:
Cadst =fcor ×
3
X
i=1
(ffei×Cimi)×1
56,000 ×φ
fcor = 1.0if Cox ≥Coxc ×φ
fcor =ffeox if Cox < Coxc ×φ
fimi= (ffei×Cimi)/
3
X
i=1
(ffei×Cimi)
where:
Cadst total molar concentration of adsorption sites [molFe l−1]
Cimiconcentration of inorganic matter fractions i=1,2,3 [gDW m−3]
Cox dissolved oxygen concentration [g m−3]
Coxc critical dissolved oxygen concentration [g m−3]
fcor correction factor for the oxidised iron(III) fraction [-]
fimifraction of adsorbed phosphate bound to inorganic matter fractions i=1, 2, 3 [-]
ffeifraction of reactive iron in inorganic matter fractions i=1,2,3 [gFe gDW−1]
ffeox fraction of oxidised iron(III) in the reactive iron fraction [-]
φporosity [-]
The fractions fimiare 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 the concentration of free ads. sites after the previous time-step [molFe l−1]
Cpha the adsorbed phosphate concentration after the previous time-step [gP m−3]
Cphd the dissolved phosphate concentration after the previous time-step [gP m−3]
eindex for chemical equilibrium value
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The above equations result in the following equation for the equilibrium adsorbed phosphate
concentration:
Cphae=(Cpha +Cphd)
31 000 ×φ×1 + OHa
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]
A positive value of the adsorption flux Rsorp represents adsorption of P O4, a negative value
represents desorption of P O4.
Directives for use
Version SW V nAdsP = 0.0uses RcAdsP gem as input name for the sorption rate in
the case of formulation option SW AdsP = 2.
Version SW V nAdsP = 0.0uses 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 O4may be approximately equal to respectively 3.8 (mole l−1)a−1and 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 S1and 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 IM1−3, the fine inorganic matter fraction
IM1in particular since AAP is predominantly adsorbed to IM1. When IM1−3are
not modelled explicitly but imposed, the settling velocity of AAP should be equal to the
settling velocity of the fine inorganic matter fraction IM1.
The phosphorus fractions F P IM 1,F P IM2and F P IM3(=fimi) in the inorganic
matter fractions are output parameters, that are used to correct the settling flux for differ-
ences in the settling velocities of IM1−3. 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)
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Table 3.5: Definitions of the parameters in the above equations for ADSPO4AAP. Volume
units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in input Definition Units
a a_OH −P O4stochiometric reaction constant for pH-
dependency
-
CimiIMi conc. of inorg. matter fractions i = 1,2,3 gDW m−3
Cox OXY dissolved oxygen concentration g m−3
Coxc Cc_oxP sor critical DO concentration for iron reduction g m−3
Cpha AAP adsorbed phosphate concentration gP m−3
Cphd P O4dissolved phosphate concentration gP m−3
fcap MaxP O4AAP phosphate adsorp. capacity of inorg. matter gP gFe−1
fimi– fraction ads. phosphate in inorg. matter fr. i =
1,2,3
-
ffeifr_F eIMi fraction react. iron in inorg. fr. i=1,2,3
(SW V nAdsP =1)
gFe gDW−1
„fr_F e fraction reactive iron in inorg. matter
(SW V nAdsP =0)
gFe gDW
ffeox fr_F eox fraction oxidised iron(III) in the reactive iron
fraction
-
Kdph KdP O4AAP distribution coefficient (SW AdsP = 0; see
directives!)
-
Kpads KdP O4AAP adsorption eq. constant (SW AdsP = 1) m3gP−1
Kads20 KadsP _20 molar adsorption equil. const. (SW AdsP =
2; see directives!)
(mol l−1)a−1
ksorp RCAdP O4AAP sorption reaction rate (SW V nAdsP = 1) d−1
„RcAdsP gem sorption reaction rate (SW V nAdsP = 0) d−1
ktads T CKadsP temperature coefficient for adsorption -
OH – hydroxyl concentration mol l−1
pH pH acidity -
Rsorp – sorption rate g m−3d−1
SW AdsP SW AdsP switch for selection of the formulation options -
-SW V nAdsP switch for selection of the original (= 0.0) or the
advanced (= 1.0) formulations
-
T T emp temperature ◦C
φ P OROS porosity m3m−3
∆t Delt computational time-step d
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0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
Equilibrium concentration of AAP as function of phosphate
TSS = 50 g/m3, partition coefficient = 0.1 m3/gDM
Phosphate concentration (gP/m3)
(gP/m3)
capacity = 0.001
capacity = 0.005
capacity = 0.01
Figure 3.3: Variation of the equilibrium concentration AAP (eqAAP) as a function of PO4
and the maximum adsorption capacity (MaxPO4AAP).
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
Equilibrium concentration of AAP as function of phosphate
TSS = 50 g/m3, capacity = 0.005 gP/m3
Phosphate concentration (gP/m3)
(gP/m3)
partition coefficient = 0.02
partition coefficient = 0.1
partition coefficient = 1.0
Figure 3.4: Variation of the equilibrium concentration of AAP (eqAAP) as a function of
PO4 and the partition coefficient of PO4 (KdPO4AAP).
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3.5 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 dis-
solution of vivianite, the precipitation of iron(III)oxyhydroxides and the adsorption of phosphate
to these minerals.
The precipitation of vivianite only occurs in a supersaturated solution at the absence of dis-
solved 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 de-
pendency 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.
Literature regarding sediment diagenesis as well as modelling exploits have provided indi-
cations 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 ( ).
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 dis-
solved oxygen concentration (Cox) can be either calculated by DELWAQ or imposed to DEL-
WAQ via the input.
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Formulation
The precipitation and dissolution equilibrium of vivianite can be described with the following
simplified reaction equation:
3Fe2+ + 2 PO3−
4⇔Fe3(PO4)2
The precipitation rate is formulated with first-order kinetics, with the difference between the ac-
tual dissolved phosphate concentration and the equilibrium dissolved concentration as driving
force (Smits and Van Beek (2013)):
Rprc =frp ×kprc ×(Cphd
φ−Cphde)×φ
0.0if Rprc < 0.0
kprc =kprc20 ×ktprc(T−20)
frp =1.0if Cox < Coxc ×φ
frp = 0.0if Cox ≥Coxc ×φ
with:
Cox dissolved oxygen concentration [g m−3]
Coxc critical dissolved oxygen concentration [g m−3]
Cphd dissolved phosphate concentration [gP m−3]
Cphde equilibrium dissolved phosphate concentration [gP m−3]
frp switch concerning the redox conditions for precipitation [-]
kprc precipitation reaction rate [d−1]
ktprc temperature coefficient for precipitation [-]
Rprc rate of precipitation [g m−3d−1]
Ttemperature [◦C]
φporosity [-]
The dissolution of vivianite is probably characterised by two steps: a) the oxidation of dis-
solved 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 dis-
solved Fe2+ concentration.) The dissolution rate can be formulated pragmatically as follows:
Rsol =frd ×ksol ×Cphpr ×Cox
φ
0.0if Rsol < 0.0
ksol =ksol20 ×ktsol(T−20)
frp =1.0if Cox < Coxc ×φ
frp = 0.0if Cox ≥Coxc ×φ
with:
Cphpr precipitated phosphate concentration [gP m−3]
frd switch concerning the redox conditions for dissolution [-]
ksol dissolution reaction rate [m3gO−1
2d−1]
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ktsol temperature coefficient for dissolution [-]
Rsol rate of dissolution [g m−3d−1]
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.
Directives for use
The formation of stable mineral “apatite” can also be included in the model. As an alterna-
tive, 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 dis-
solution may deviate substantially from experimentally determined values. The following
values are representative for fresh water sediments: EqV IV DisP = 0.05 gP m−3,
RcP recP 20 = 0.8d−1,RcDissP 20 = 0.005 m3gO−1
2d−1.
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 S1and AAP S2, the
precipitation process only affects P O4and V IV P in the water column. V IV P settles
and ends up in AAP S1and AAP S2.
Additional references
Santschi et al. (1990), Smits and Van der Molen (1993), Stumm and Morgan (1996), WL |
Delft Hydraulics (1997c)
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Table 3.6: Definitions of the parameters in the above equations for VIVIANITE. Volume
units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in input Definition Units
Cox OXY dissolved oxygen concentration g m−3
Coxc Cc_oxP sor critical DO concentration for iron reduction g m−3
Cphd P O4dissolved phosphate concentration gP m−3
Cphde EqV IV DisP equilibrium dissolved phosphate concentration gP m−3
Cphpr V IV P precipitated vivianite phosphate concentration gP m−3
frd – switch concerning redox conditions for dissolu-
tion
-
frp – switch concerning redox conditions for precipi-
tation
-
kprc20 RcP recP 20 vivianite precipitation reaction rate d−1
ktprc T cP recipP temperature coefficient for precipitation -
ksol20 RcDissP 20 vivianite dissolution reaction rate m3gO−1
2d−1
ktsol T cDissolP temperature coefficient for dissolution -
Rprc – vivianite precipitation rate g m−3d−1
Rsol – vivianite dissolution rate g m−3d−1
T T emp temperature ◦C
∆t Delt timestep d
φ P OROS porosity m3m−3
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3.6 Formation of apatite
PROCESS: APATITE
Phosphate may precipitate in various minerals that are stable under both oxidizing and reduc-
ing conditions. In literature regarding sediment diagenesis and sediment modelling, indica-
tions 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.
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 ( ).
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:
3Ca2+ + 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 ac-
tual dissolved phosphate concentration and the equilibrium dissolved concentration as driving
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force. In order to allow better control over the precipitation of apatite relative to the precipita-
tion of vivianite the precipitation rate is formulated as follows (Smits and Van Beek (2013)):
Rprc =frr ×kprc ×Cphd
φ−Cphde×φ
Rprc = 0.0if Rprc < 0.0
kprc =kprc20 ×ktprc(T−20)
with:
Cphd dissolved phosphate concentration [gP m−3]
Cphde equilibrium dissolved phosphate concentration [gP m−3]
frr ratio of the apatite and vivianite precipitation reaction rates [-]
kprc precipitation reaction rate [d−1]
ktprc temperature coefficient for precipitation [-]
Rprc rate of precipitation [g m−3d−1]
Ttemperature [◦C]
φporosity [-]
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:
Rsol =ksol ×Cphpr ×Cphde −Cphd
φ
Rsol = 0.0if Rsol < 0.0
ksol =ksol20 ×ktsol(T−20)
with:
Cphpr precipitated phosphate concentration [gP m−3]
ksol dissolution reaction rate [m3gP−1d−1]
ktsol temperature coefficient for dissolution [-]
Rsol rate of dissolution [g m−3d−1]
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 prod-
uct of the mineral formed. Solubility products determined in the laboratory tend to under-
estimate 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.
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When simulating the “inactive” substances in the sediment AAP S1and AAP S2, the
precipitation process only affects P O4and APATP in the water column. AP AT P settles
and ends up in AAP S1and 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 ( ).
Name in
formulas
Name in
input
Definition Units
Cphd P O4dissolved phosphate concentration gP m−3
Cphde EqAP AT DisP equilibrium dissolved phosphate con-
centration
gP m−3
Cphpr AP AT P precipitated “apatite” phosphate con-
centration
gP m−3
frr RatAP andV P ratio of the apatite and vivianite precipi-
tation rates
-
kprc20 RcP recP 20 vivianite precipitation reaction rate d1
ktprc T cP recipP temperature coefficient for precipitation -
ksol20 RcDisAP 20 apatite dissolution reaction rate m3gP−1d−1
ktsol T cDissolP temperature coefficient for dissolution -
Rprc – apatite precipitation rate g m−3d−1
Rsol – apatite dissolution rate g m−3d−1
T T emp temperature ◦C
∆t Delt timestep d
φ P OROS porosity m3.m−3
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3.7 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 sedi-
ment. 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.
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 ( ).
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 SiS1/2and 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 dissolved silicate concentration [gSi m−3]
Cside equilibrium dissolved silicate concentration [gSi m−3]
Csip opal silicate concentration [gSi m−3]
ksol dissolution reaction rate [m3gSi−1d−1]
φporosity [-]
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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:
ksol dissolution reaction rate [m3gSi−1d−1or d−1]
ktsol temperature coefficient for dissolution [-]
Ttemperature [◦C]
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 af-
fects Si and Opal in the water column. Opal settles and ends up in DET SiS1(and
DET SiS2), subjected to first-order decomposition.
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)
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Table 3.8: Definitions of the parameters in the above equations for DISSI. Volume units
refer to bulk ( ) or to water ( ).
Name in
formulas
Name in input Definition Units
Csid Si dissolved silicate concentration gSi m−3
Cside Ceq_DisSi equilibrium dissolved silicate concentration gSi m−3
Csip Opal opal silicate concentration gSi m−3
ksol20 RcDisSi20 second order dissolution reaction rate, or first
order dissolution rate
m3gSi−1d−1
d−1
ktsol T cDisSi temperature coefficient for dissolution -
Rsol - dissolution rate g m−3d−1
SW Dissi SW Dissi option (=0.0 for second order, =1.0 for first or-
der)
-
T T emp temperature ◦C
φ P OROS porosity m3m−3
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Contents
4.1 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
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4.1 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.
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
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:
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 ac-
count 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.
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4.2 Growth and mortality of algae (BLOOM)
PROCESS: BLOOM, BLOOM_P, ULVAFIX, ULVAFIX_P, PHY_BLO, PHY_BLO_P, DEPAVE,
VTRANS, DAYLENGTH
Algae are subject to gross primary production, respiration, excretion, mortality, grazing, re-
suspension 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 set-
tling are similar for other phytoplankton modules in DELWAQ, and are therefore dealt with in
separate process descriptions.
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 stoichiom-
etry, 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 phyto-
plankton groups and types that have been modelled before can be read from a database with
Delft3D.
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 ex-
pressed 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 be-
tween 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 inten-
sities. 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 optimi-
sation technique. The process rates are corrected for temperature dependency before being
used in the optimisation. Mortality is also corrected for salinity stress.
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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 trans-
port 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.
A macro algae species like Ulva 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 Ulva is simulated with the process UlvaFix.
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 [gO2m−3], and affects alkalinity (pH). Prefer-
ential 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 parame-
ters 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-
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defined input and output. BLOOM requires an additional input file <bloominp.frm>con-
taining 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:
<bloominp.d09>and <bloominp.spe>need to be available in the work directory.
Formulation
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:
1 the nutrient constraints;
2 the energy constraints;
3 the growth constraints; and
4 the mortality constraints.
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
i=1
(anutk,i ×Calgi)−Cnutck
with:
anutk,i stoichiometric constant of nutrient koriginating from dissolved inorganic nutri-
ent over organic carbon in algae biomass [gN/P/Si gC−1], an,aph or asi
Calgialgae biomass concentration [gC m−3]
Cnutkconcentration of dissolved inorganic nutrient k[gN/P/Si m−3]
Cnutckthreshold concentration of dissolved inorganic nutrient k[gN/P/Si m−3]
Ctnutkconcentration of total available nutrient k[gN/P/Si m−3]
iindex for algae species type [-]
kindex for nutrients, 1 = nitrogen, 2 = phosphorus, 3 = silicon, 4 = carbon [-]
nnumber of algae species types, equal to 15 [-]
Additional requirements are that Calgi≥0.0and 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.
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Extra constraints are added for the nutrients detritus nitrogen and detritus phosphorus. The
dissolved nutrient constraints are modified as follows:
Cdet2k=Cdet1k+
n
X
i=1
(adk,i ×Calgi)
Ctnutk=Cnutk+
n
X
i=1
((anutk,i −adk,i)×Calgi)−Cnutck
with:
adk,i stoichiometric constant of a nutrient originating from detritus over org. carbon in
algae biomass [gN/P gC−1], adn,adph or adsi
Cdet1kconcentration of a detritus nutrient at t1, the beginning of a time step [gN/P
mS−3]
Cdet2kconcentration of a detritus nutrient at t2, the end of a time step [gN/P m−3]
kindex for nutrients, 1 = nitrogen, 2 = phosphorus [-]
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 N2by nitrogen fixative algae:
Cen2 = Cen1 +
n
X
i=1
(aeni×Calgi)
Ctnut1=Cnut1+
n
X
i=1
((anut1,i −aeni)×Calgi)−Cnutc1
with:
aenistoichiometric constant of nitrogen orig. from el. nitrogen in algae biomass
[gN gC−1]
Cen1concentration of elementary nitrogen at t1, the beginning of a time step [gN m−3]
Cen2concentration 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 au-
totrophic algae when the stoichiometric constants aeniobtain 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.
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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 eamaxiexists, 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
i=1
(eai×Calgi)
eamini≤eat ≤eamaxi
eamini=eatmini−eb
eamaxi=eatmaxi−eb
eb =et −eat
with:
eaispecific extinction coefficient of an algae species type [m2gC−1]
eat total extinction coefficient of all algae [m−1]
eb extinction by other substances than algae [m−1]
et total extinction coefficient [m−1]
eaminiminimum extinction coefficient of algae i connected with background extinction
[m−1]
eatminiminimum total extinction coefficient connected with background extinction [m−1]
eamaximaximum extinction coefficient of algae i needed to avoid self shading [m−1]
eatmaxImaximum 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 eatmaxifor algae species type iis
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:
Efci=krspi+kmrti
kgpi
with:
Ef light efficiency factor [-]
Efcicritical light efficiency factor [-]
kgpispecific growth rate [d−1]
kmrtispecific mortality rate [d−1]
krspispecific maintenance respiration rate [d−1]
Once the critical efficiency factor is known, the pertinent critical light intensity (the total avail-
able amount of light) can be obtained from the efficiency versus photosynthic light intensity
table in input file <bloominp.frm>. The maximum extinction coefficient eatmaxiis calcu-
lated from this critical light intensity and the light intensity at the top of a water compartment
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(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 −fr)×fpa ×Itop ×(1 −exp (−eatmaxi×Ha))
eatmaxi×Ha
Iai=f(Efci)
with:
fpa fraction of photosinthetically active light in visible light, = 0.45 [-]
fr fraction of visible light reflected at the water surface [-]
Ha timestep average depth of a water compartment or water layer [m]
Iaicritical depth average intensity of photosynthetic light [W m−2]
Itop visible light intensity at the top of a water compartment/layer [W m−2]
zdepth [m]
The fraction of visible light reflected at the water surface fr is approximately 0.1 depending
on the time in a year. Both fr and fpa are allocated fixed values in BLOOM.
The maximal extinction coefficient is found via transformation of the integral.
The specific rates of growth, maintenance respiration and mortality are formulated as func-
tions of temperature:
kgpi=kpg0
i×ktpgT
ifor T F P MxAlg(i)=1.0
kgpi=kpg0
i×(T−ktpgi)for T F P MxAlg(i)=0.0
kgpi≥0.0
krspi=krsp0
i×ktrspT
i
kmrti=kmrt0
i×ktmrtT
ifor all algae except macro algae (Ulva)
kmrti=kmrt0
ifor Ulva when T < 25.0
kmrti=kmrt0
i×(T−25) for Ulva when T≥25.0
with:
kgp0growth rate at 0 ◦C [d−1], or per degree centigrade [◦C−1d−1]
ktgp temperature coefficient for growth [-], or temperature at which kgp0is equal to
zero
kmrt0specific mortality rate at 0 ◦C or at temperatures <25 ◦C [d−1], or per degree
centigrade at temperatures >25 ◦C [◦C−1d−1]
ktmrt temperature coefficient for mortality [-]
krsp0specific maintenance respiration rate at 0 ◦C [d−1]
ktrsp temperature coefficient for maintenance respiration [-]
Twater 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)
kmrt0
i=m2i−m1i
1 + exp (b1i×(Ccl −b2i)) +m1i
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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 m3gCl−1.
with:
b1icoefficient 1 of salinity stress function [g−1.m3]
b2icoefficient 2 of salinity stress function [g.m−3]
m1irate coefficient 1 of salinity stress function [d−1]
m2irate coefficient 2 of salinity stress function [d−1]
Ccl chloride concentration [g m−3]
m1and m2are the end members of the above function, meaning that the function obtains
the value m1at high Ccl, and the value m2for low Ccl. The mortality rate increases with
decreasing chloride concentration, when m2is 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 m1is 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 japplying to all types of this species is computed as:
Calgmaxi=Calg1i×exp ((kgpi×Efi−krspi)×∆tb)
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Calgmaxj=
m
X
i=l
Calgmaxi
Calgmaxj=Calgmaxjif Calgmaxj≥Calgcj
0if Calgmaxj< Calgcj
m
X
i=l
(Calg2i)≤Calgmaxj
∆tb =ft ×∆t
with:
Calgmax maximum concentration of an algae species or type at time t2, the end of a
timestep [gC m−3]
Calgc threshold biomass concentration of an algae species at time t1, the beginning
of a timestep [gC m−3]
Calg1biomass concentration of algae species jat time t1[gC m−3]
Calg2biomass concentration of algae species jat time t2[gC m−3]
ft ratio of the BLOOM timestep and the DELWAQ timestep ≥1.0[-]
Ef light efficiency factor [-]
kgp potential specific growth rate of the fastest growing type of an algae species
[d−1]
krsp specific maintenance respiration rate of the fastest growing type of an algae
species [d−1]
∆ttime step in DELWAQ [d]
∆tb time interval, the time step in BLOOM [d]
jindex for algae species [-]
iindex for algae species type [-]
lindex of the first algae type for species j[-]
mindex of the last algae type for species j,=l−1+ number of types species j−
1[-]
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.
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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
i=l
(Calgmini)
Calgminj=Calgminjif Calgminj≥Calgcj
0if Calgminj< Calgcj
m
X
i=l
(Calg2i)≥Calgminj
with:
Calgmin minimum concentration of an algae species type at time t2, the end of a time
step [gC m−3]
Calg1biomass concentration of an algae species type at time t1[gC m−3]
Calg2biomass concentration of an algae species type at time t2[gC m−3]
kmrt specific mortality rate of an algae species type [d−1]
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 numer-
ical 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:
Rgri=Calg2i−Calg1i
∆tb
Rgron,i =Rgri×(ani+adni+aeni)
Rgrop,i =Rgri×(aphi+adphi)
Rgrosi,i =Rgri×asii
Rgpi=Rgri+Rrspi+Rmrti
Rnpi=Rgpi−Rrspi
Rrspi=krspi×(Calg2i+Calg1i)
2
Rmrti=kmrti×(Calg2i+Calg1i)
2
with:
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Calg1ialgae biomass concentration at t1, the beginning of a time step [gC m−3]
Calg2ialgae biomass concentration at t2, the end of a time step [gC m−3]
krsp specific respiration rate [d−1]
kmrt specific mortality rate [d−1]
Rgp gross primary production rate [gC.m−3d−1]
Rgr growth rate for organic carbon [gC.m−3d−1]
Rgron growth rate for organic nitrogen [gN m−3.d−1]
Rgrop growth rate for organic phosphorus [gP m−3d−1]
Rgrosi growth rate for ”organic” silicate [gSi m−3d−1]
Rmrt mortality rate [gC m−3d−1]
Rnp net primary production rate [gC m−3d−1]
Rrsp respiration rate [gC m−3d−1]
∆tb time interval, the time step in BLOOM [d]
iindex for species group 1-4 [-]
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:
Rprdox,i = ani
ani+adni×Rnpi+Rauti×aoxi
Rcnsam,i =Rnpi×ani×fam
Rcnsni,i =Rnpi×ani×(1 −fam)
Rcnsph,i =Rnpi×aphi
Rcnssi,i =Rnpi×asii
Rcnss,i =Rnpi×asi
Rfixi=Rnpi×aeni
Rcnsoc1,i =Rnpi×adni
ani+adni
Rcnson1,i =Rnpi×adni
Rcnsop1,i =Rnpi×adphi
Rauti=fauti×Rmrti
Rautam,i =Rauti×ani
Rautph,i =Rauti×aphi
Rautsi,i =Rauti×asii
Rauts,i =Rauti×asi
Rprdoc1,i =Rmrti×(1 −fauti)×fdeti
Rprdon1,i =Rmrti×ani×(1 −fauti)×fdeti
Rprdop1,i =Rmrti×aphi×(1 −fauti)×fdeti
Rprdosi1,i =Rmrti×asii×(1 −fauti)×fdeti
Rprdos1,i =Rmrti×asi×(1 −fauti)×fdeti
Rprdoc2,i =Rmrti×(1 −fauti)×(1 −fdeti)
Rprdon2,i =Rmrti×ani×(1 −fauti)×(1 −fdeti)
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Rprdop2,i =Rmrti×aphi×(1 −fauti)×(1 −fdeti)
Rprdosi2,i =Rmrti×asii×(1 −fauti)×(1 −fdeti)
Rprdos2,i =Rmrti×asi×(1 −fauti)×(1 −fdeti)
with:
aen stoichiometric constant of nitrogen originating from elementary nitrogen in algae
biomass [gN gC−1]
an stoichiometric constant for ammonium/nitrate over carbon in algae biomass [gN
gC−1]
adn stoichiometric constant for detritus nitrogen over carbon in algae biomass [gN
gC−1]
aph stoichiometric constant for phosphate over carbon in algae biomass [gP gC−1]
adph stoichiometric constant for detritus phosphorus over carbon in algae biomass
[gP gC−1]
aox stoichiometric constant for oxygen over carbon in algae biomass [gO2gC−1]
asi stoichiometric constant for silicon over carbon in algae biomass [gSi gC−1]
as stoichiometric constant for sulfur over carbon in algae biomass [gS.gC−1]
fam fraction of ammonium in the consumed nitrogen nutrients [-]
fdet fraction of dead algae biomass allocated to fast decomposing detritus [-]
faut fraction of dead algae biomass autolysed [-]
Raut autolysis rate for dead algae biomass (organic carbon) [gC m−3d−1]
Rautam autolysis rate for ammonium [gN m−3d−1]
Rautph autolysis rate for phosphate [gP m−3d−1]
Rautsi autolysis rate for silicate [gSi m−3d−1]
Rautsautolysis rate for sulfide [gS m−3d−1]
Rcnsam consumption rate for ammonium [gN m−3d−1]
Rcnsni consumption rate for nitrate [gN m−3d−1]
Rcnsph consumption rate for phosphate [gP m−3d−1]
Rcnssi consumption rate for silicate [gSi m−3d−1]
Rcnssconsumption rate for sulfate [gS m−3d−1]
Rcnsoc1consumption rate for detritus carbon [gC m−3d−1]
Rcnson1consumption rate for detritus nitrogen [gN m−3d−1]
Rcnsoph1consumption rate for detritus phosphorus [gP m−3d−1]
Rfix nitrogen fixation (consumption) rate [gN m−3d−1]
Rprdox net production rate for dissolved oxygen [gO2m−3d−1]
Rprdoc1production rate for fast decomposing detritus carbon POC1 [gC m−3d−1]
Rprdon1production rate for fast decomposing detritus nitrogen PON1 [gN m−3d−1]
Rprdop1production rate for fast decomposing detritus phosphorus POP1 [gP m−3d−1]
Rprdosi1production rate for particulate soluble silicate OPAL [gSi m−3d−1]
Rprdos1production rate for fast decomposing detritus sulfur POS1 [gS m−3d−1]
Rprdoc2production rate for slowly decomposing detritus carbon POC2 [gC m−3d−1]
Rprdon2production rate for slowly decomposing detritus nitrogen PON2 [gN m−3d−1]
Rprdop2production rate for slowly decomposing detritus phosphorus POP2 [gP m−3
d−1]
Rprdosi2production rate for particulate soluble silicate OPAL [gSi m−3d−1]
Rprdos2production rate for slowly decomposing detritus sulfur POS2 [gS m−3d−1]
The stoichiometric constants for oxygen and sulfur over carbon aoxiand asiare 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.
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The fraction of ammonium in nitrogen nutrients consumed fam 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:
Calgt =
n
X
i=1
(Calgi)
Cadm =
n
X
i=1
(admi×Calgi)
Cchf = 1000 ×
n
X
i=1
(achfi×Calgi)
Can =
n
X
i=1
((ani+adni+aeni)×Calgi)
Caph =
n
X
i=1
((aphi+adphi)×Calgi)
Casi =
n
X
i=1
(asii×Calgi)
with:
achf stoch. constant for chlorophyll-a over carbon in algae biomass [gChf gC−1]
adm stoch. constant for dry matter over carbon in algae biomass [gDM gC−1]
Calgt total algae biomass concentration [gC m−3]
Can total concentration of nitrogen in algae biomass [gN m−3]
Caph total concentration of phosphorus in algae biomass [gP m−3]
Casi total concentration of silicon in algae biomass [gSi m−3]
Cadm total algae biomass concentration on a dry matter basis [gDM m−3]
Cchf 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
i=1 Rnpi
H
Rrspt =
n
X
i=1 Rrspi
H
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Rfixt =
n
X
i=1 Rfixi
H
with:
Rfixt total nitrogen fixation rate [gN m−2d−1]
Rrspt total algal maintenance respiration rate [gC m−2d−1]
Rnptt total algal primary production rate [gC m−2d−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”.
Process UlvaFix
Macro algae such as Ulva 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 pa-
rameter SDMixAlg(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, SDMixAlg(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 at-
tached 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:
fat =af −τ
τc
0.0≤fat ≤1.0
with:
af attachment affinity coefficient [-]
Calgibiomass concentration of the suspended algae species type [gC m−3]
Calg −jbiomass concentration of the attached algae species type [gC m−3]
fat target fraction of attached algae type [-]
τshear stress at the sediment water interface [Pa]
τc critical shear stress for resuspension [Pa]
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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:
if fat ≥Calgj
Calgi:
Rresj=((1.0−fat)×(Calgi+Calgj)) −Calgi
∆t
Rresi=−Rresj
if fat < Calgj
Calgi:
Rseti=Calgj−(fat ×(Calgi+Calgj))
∆t
Rresj=−Rseti
with:
Rresjresuspension rate of the attached algae species j [gC m−3d−1]
Rsetjsettling rate of the attached algae species j [gC m−3d−1]
Rresiresuspension rate of the suspended algae species i [gC m−3d−1]
Rsetisettling rate of the suspended algae species i [gC m−3d−1]
∆tb time interval, the timestep in BLOOM [d]
In case macro algae attached to sediment are included in the model BLOOM produces ad-
ditional 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 =(nt −1) ×Hant−1+Hnt
nt for nt ≤ft
with:
ft ratio of the BLOOM time step and the DELWAQ time step ≥1.0[-]
nt counter for number of DELWAQ time steps made in current BLOOM time step
[-]
Ha average water depth for the current BLOOM time step [m]
Hant running average water depth at DELWAQ time step nt in the current BLOOM
time step [m]
Hnt 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.
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Directives for use
The variable TimMultBl is a multiplication factor for the transport time step, that en-
ables 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 (aver-
age) 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 there-
fore 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 mortal-
ity flux, minus the autolysis and the flux to fast decomposing detritus. If slowly decompos-
ing 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 coeffi-
cients 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 stoi-
chiometric constant for nitrogen. Nitrogen fixation is not limited by the availability of the nu-
trient (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−1y−1
∼0.006 8 gN m−2d−1(Ross,1995). If PPMaxAlg(i)is set to be 0.1 1/d (after tem-
perature 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 mor-
tality 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 coeffi-
cients MND(i)m1and MND(i)m2. The salinity effect on mortality can be inactivated
by allocating the same value to MND(i)m1and MND(i)m2.
The current implementation of BLOOM allows for only one macro algae of macrophyte
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species, whereas in parameter naming Ulva was taken as a reference. With the default
value of 2.0 for FixGrad the target attached fraction fat 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 al-
gae 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 ex-
pressed in [J cm−2week−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 ad-
vanced approach the input parameter SwTICdummy (default value = 0.0) needs to be
allocated a value of 10.0 or higher. The limitation parameter KCO2of the simplified ap-
proach 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 KCO2for limitation is 1.0 gC.m3.
The sulfur content of algae will only be taken into account automatically, when SO4,
SUD,P OS1and P OS2are 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 Definition Units
CalgiBLOOMALG(i)biomass concentration of algae species type i gC m−3
Cam NH4ammonium concentration gN m−3
Ccl Cl chloride concentration gCl m−3
Cni NO3nitrate concentration gN m−3
Cph P O4phosphate concentration gP m−3
Csi Si dissolved inorganic silicate concentration gSi m−3
Cnutc1T hrAlgNH4threshold concentration for uptake of ammo-
nium
gN m−3
Cnutc2T hrAlgNO3threshold concentration for uptake of nitrate gN m−3
Cnutc3T hrAlgP O4threshold concentration for uptake of phos-
phorus
gP m−3
Cnutc4T hrAlgSi threshold concentration for uptake of silicate gSi m−3
–P ON1or
DetN
concentration of nitrogen in fast decomp. de-
tritus
gN m−3
continued on next page
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Table 4.1 – continued from previous page
Name in
formulas
Name in input Definition Units
–P OP 1or
DetP
concentration of phosphorus in fast decomp.
detritus
gP m−3
–SpecAlg(i)3 species identification number of types -
achfiChlaCAlg(i)algae type spec. stoch. const. chlorophyll
over carbon
gChf gC−1
admiDMCF Alg(i)algae type spec. stoch. const. dry matter over
carbon
gDM gC−1
aniNCRAlg(i)algae type spec. stoch. const. nutr. nitrogen /
carbon
gN gC−1
adniXNCRAlg(i)algae type spec. stoch. const. detr. nitrogen /
carbon
gN gC−1
aeniF NCRAlg(i)algae type spec. stoch. const. elem. nitrogen
/ carbon
gN gC−1
aphiP CRAlg(i)algae type spec. stoch. const. nutr. phos. /
carbon
gP gC−1
adphiXP CRAlg(i)algae type spec. stoch. const. detr. phos. /
carbon
gP gC−1
asiiSCRAlg(i)algae type spec. stoch. const. for silicon over
carbon
gSi gC−1
m1iMort0Alg(i)algae type spec. rate coefficient 1 of salinity
stress
d−1
m2iMort2Alg(i)algae type spec. rate coefficient 2 of salinity
stress
d−1
b1iMrtB1Alg(i)algae type spec. coefficient 1 of salinity stress
function
g−1.m3
b2iMrtB2Alg(i)algae type spec. coefficient 2 of salinity stress
function
g m−3
eaiExtV lAlg(i)algae species type specific extinction coeffi-
cient
m2gC−1
KCO2KCO2limitation constant for carbon gC m3
fautiF rAutAlg(i)fraction of dead algae biomass autolised -
fdetiF rDetAlg(i)fr. of dead algae biomass allocated to fast dec.
detritus
-
–SDMixAlg(i)distribution of an algae type over the water col-
umn
-
–F ixAlg(i)identifier for pairs of algae types attaching to
sediment (0 =not applying, >0= suspended,
<0= attached)
-
–SwBloomOut option for specific BLOOM output (0 = no, 1 =
yes)
-
–SW OxyP rod2option for calc. oxygen conc. (0 = daily av., 1
= daily var.)
-
continued on next page
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Table 4.1 – continued from previous page
Name in
formulas
Name in input Definition Units
–SW DepAve option depth aver. over BLOOM timestep (0 =
off, 1 = on)
-
H Depth depth of a water compartment or water layer m
Ha BloomDepth average depth during a BLOOM timestep m
V V olume volume of a water compartment or water layer m3
DL DayL daylength, fraction of a day -
et ExtV l4total extinction coefficient of visible light m−1
eat ExtV lP hyt4extinction coefficient of all agae species types m−1
Itop Rad light intensity at top of layer or compartment W m−2
kgp0
iP P MaxAlg(i)algae type spec. pot. gross primary prod. rate
at 0 ◦C
d−1
ktgpiT cP M xAlg(i)algae type spec. temperature coeff. for pri-
mary prod.
- or ◦C
–T F P MxAlg(i)option temperature dep. of prod. (0 = linear, 1
= exp.)
-
krsp0
iMRespAlg(i)algae type spec. maintenance respiration rate
at 0 ◦C
d−1
–MrtExAlg(i)algae type spec. extra rapid mortality rate d−1◦C−1
ktmrtiT cMrtAlg(i)algae type spec. temperature coefficient for
mortality
-
ktrspiT cRspAlg(i)algae type spec. temperature coef. for maint.
resp.
-
T T emp water temperature ◦C
af F ixGrad attachment affinity coefficient -
τ T au shear stress at the sediment water interface Pa
τc T auCrU lva critical shear stress for resuspension Pa
ft T imMultBl ratio of the BLOOM timestep and the DEL-
WAQ timestep
-
∆t Delt time interval, that is the DELWAQ timestep d
1(i) indicates algae species types 01-15. Biomass of algae species attached to the sediment
is expressed in [gC.m−2].
2For SW OXY P rod = 1.0process VAROXY is used to calculated the daily varying dis-
solved oxygen concentration (see description elsewhere in the manual).
3The species identification number needs to be an integer that is equal for all types that belong
to the same species.
4These parameters are calculated by processes ExtinaBVL and Extinc_VL.
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Table 4.2: Definitions of the output parameters for BLOOM.
Name in
formulas
Name in out-
put1
Definition Units
CalgtiP hyt total algae biomass concentration gC m−3
CdmiAlgDM total algae biomass conc. on a dry matter ba-
sis
gDM m−3
CchfiChlfa total chlorophyll-a concentration mgChf m−3
CaniAlgN total concentration of nitrogen in algae
biomass
gN m−3
CaphiAlgP total concentration of phosphorus in algae
biomass
gP m−3
CasiiAlgSi total concentration of silicon in algae biomass gSi m−3
–Limit Nit indicator for limitation by inorganic nitrogen -
or Lim_IN
–Lim_DetN indicator for limitation by detrital nitrogen -
–Lim_F ixN indicator for limitation by nitrogen fixation -
–Limit P ho indicator for limitation by inorganic phosphorus -
or Lim_IP
–Lim_DetP indicator for limitation by detrital phosphorus -
–Limit Sil indicator for limitation by silicon -
or Lim_Si
–Limit E indicator for limitation by energy (light) -
or Lim_light
–Lim_inhib indicator for limitation by photo inhibition -
–Limit Gro indicator for limitation by growth -
or
Lim_GALG
can be split into species specific Lim_G(i)
–Limit Mor indicator for limitation by mortality -
or
Lim_MALG
can be split into species specific Lim_M(i)
Rnpt fP P tot total net primary production gC m−2d−1
Rrspt fResptot total maintenance respiration gC m−2d−1
Rfixt f F ixNUpt total uptake of nitrogen by fixation gN m−2d−1
–RcP P Alg(i)algae type specific net primary production rate d−1
–RcMrtAlg(i)algae type specific net primary mortality rate d−1
–frF ixedAlg fraction of algae fixed to the sediment bed -
–BLALG(i)m2algae type specific biomass per m2gC m−2
1(i) indicates the algae species types that are used.
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4.3 Bottom fixation of BLOOM algae types
PROCESS: ULVAFIX
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 sus-
pended 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.
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:
frF ixedAlg =F ixGrad −T au
T auCrUlva with frF ixedAlg = [0,1]
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
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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).
With the default value of 2.0 for FixGrad the fraction fixed is 1.0 when Tau is less than Tau-
CrUlva and 0.0 when Tau is more than two times TauCrUlva. This can be modified by changing
the value of FixGrad.
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4.4 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 Xias 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).
When the S1/2 approach is followed phytoplankton biomass is allocated to the sediment de-
tritus pools as follows:
Algae C
DETCS1
settling
Water Sediment
OOCS1
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 SEDPH-
DYN 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 stochio-
metric 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 V0Sed(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.
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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=ftaui×F seti
H
ifH < Hmin F seti= 0.0
else
F seti= min F set0
i,Cxi×H
∆t
F set0
i=F set0i+si×Cxi
ifτ =−1.0ftau = 1.0
else
ftaui= max 0.0,1−τ
τci
where:
Cx concentration of the biomass of an algae species [gC m−3]
F set0zero-order settling flux of an algae species [gC m−2d−1]
F set settling flux of an algae species [gC m−2d−1]
ftau shearstress limitation function [-]
Hdepth of the water column [m]
Hmin minimal depth of the water column for resuspension [m]
Rset settling rate of an algae species [gC m−3d−1]
ssettling velocity of an algae species [m d−1]
τshearstress [Pa]
τc critical shearstress for settling of an algae species [Pa]
∆ttimestep in DELWAQ [d]
iindex 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 =fsj,i ×Rseti
where:
fsj,i stochiometric ratio of nutrient j in algae species i [gX gC−1]
Rsnj,i settling rate of nutrient j in algae species i [gX m−3d−1]
iindex for algae species (i)
jindex 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 MinDepth for set-
tling, which has a default value of 0.1 m. When desired MinDepth may be given a
different value.
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The settling fluxes fSedAlg (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), SEDPH-
BLO and SEDPHDYN.
Name in
formulas
Name in
input
Definition Units
Cx1
iBLOOM(i)1
or (i)1
concentration of biomass of algae species i,
for BLOOM or DYNAMO
gC m−3
F set0IZSed(i)zero-order settling flux of algae species i gC m−2d−1
fsj,i NCR(i)stoch. ratio N in algae species i for BLOOM gN gC−1
P CR(i)stoch. ratio P in algae species i for BLOOM gP gC−1
SCR(i)stoch. ratio Si in algae species i for BLOOM gSi gC−1
SuCr(i)stoch. ratio S in algae species i for BLOOM gS gC−1
or
NCrat(i)stoch. ratio N in algae species i for DYNAMO gN gC−1
P Crat(i)stoch. ratio P in algae species i for DYNAMO gP gC−1
SCrat(i)stoch. ratio Si in algae species i for DYNAMO gSi gC−1
SuCrat(i)stoch. ratio S in algae species i for DYNAMO gS gC−1
H Depth depth of the overlying water compartment m
Hmin MinDepth minimal water depth for settling and resus-
pension
m
siV Sed(i)input or calc. settling velocity algae species i m d−1
or
V0Sed(i)basic settling velocity of algae species i m d−1
τ T au shear stress Pa
τciT aucS(i)critical shear stress for settling of algae
species i
Pa
∆t Delt timestep in DELWAQ d
1) (i) is equal to one of the algae species names, BLOOM specific names connected to ALG01-
30, or Diat and Green.
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4.5 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. Mor-
tality 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
Processes GROMRT_(i), TF_(i), NL(i), DL_(i), RAD_(i), PPRLIM, NUTUPT_ALG and NU-
TREL_ALG have been implemented for the following substances:
Diat and Green
NH4, NO3, PO4 and Si
Table 4.4 provides the definitions of the input parameters occurring in the formulations.
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=fdli×fradi×fnuti×ftpi×kpp20
i
ftpi=ktp(T−20)
i
where:
Calg concentration of algae biomass [gC m−3]
fdl daylength limitation function [-]
fnut nutrient limitation function [-]
frad light limitation function [-]
ftp production temperature function [-]
kgp gross primary production rate constant [d−1]
knp net primary production rate constant [d−1]
kpp20 potential maximum production rate constant at 20 ◦C [d−1]
krsp total respiration rate constant [d−1]
ktp temperature constant for production [-]
Rnp net primary production rate [gC m−3d−1]
Twater temperature [◦C]
iindex for algae species
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The limitation function for nutrients is given by:
fnuti=Min(fni, fpi, fsii)
fni=Cnn
Cnn +Ksni
fpi=Cph
Cph +Kspi
fsii=Csi
Csi +Kssii
Cnn =Cam +Cni
fani
where:
Cam concentration of ammonium [gN m−3]
Cni concentration of nitrate [gN m−3]
Cnn concentration of preferred nutrient nitrogen [gN m−3]
Cph concentration of dissolved phosphate [gP m−3]
Csi concentration of dissolved silicate [gSi m−3]
fan preference of ammonium over nitrate [-]
fnut nutrient limitation function [-]
fn nitrogen limitation function [-]
fp phosphorus limitation function [-]
fsi silicon limitation function [-]
Ksn half saturation constant for nutrient nitrogen [gN m−3]
Ksp half saturation constant for phosphate [gP m−3]
Kssi half saturation constant for silicate [gSi m−3]
iindex for algae species
The limitation functions for daylength and light are given by:
fdli=min(DL, DLoi)
DLoi
if (Is/Ioi)≥1.0and (Ib/Ioi)≥1.0then fradi= 1.0
if (Is/Ioi)≥1.0and (Ib/Ioi)<1.0then
fradi=1 + ln(Is/Ioi)−(Is/Ioi)×e(−et×H)
et ×H
if (Is/Ioi)<1.0then
fradi=Is
Ioi×1−e(−et×H)
et ×H
Ioi=ftpi×Io20
i
Ibi=Isi×e(−et×H)
where:
DL daylength, fraction of a day [-]
DLo optimal daylength [d]
et total extinction coefficient [m−1]
fdl daylength limitation function [-]
frad light limitation function [-]
ftp production temperature function [-]
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Hwater depth [m]
Io optimal light intensity [W m−2]
Io20 optimal light intensity [W m−2]
Ib light intensity at the bottom [W m−2]
Is light intensity at water surface [W m−2]
iindex for algae species
Note that the value of Io_iis corrected for temperature. This results in a dependency of fradi
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:
Rnpmax,1= min(max(Cni +Cam, 0.0)
an1×∆t,max(Cph, 0.0)
ap1×∆t)
Rnpmax,2= min(max(Cni +Cam, 0.0)
an2×∆t,max(Cph, 0.0)
ap2×∆t,max(Csi, 0.0)
asi2×∆t)
Rnpmax = max(Rnpmax,1, Rnpmax,2)
Rnp = max(Rnp1, Rnp2)
if Rnp > Rnpmax then
Rnpc,2= min(Rnpmax
Rnp ×Rnp2, Rnpmax,2)
Rnpc,1=Rnpmax −Rnpc,2
∆Rnp2=Rnpc,2−Rnp2
∆Rnp1=Rnpc,1−Rnp1
else
Rnpc,1=Rnp1and Rnpc,2=Rnp2
∆Rnpc,1= 0.0and ∆Rnpc,2= 0.0
where:
an stoichiometric constant for N over C in algae biomass [gN gC−1]
ap stoichiometric constant for P over C in algae biomass [gP gC−1]
asi stoichiometric constant for Si over C in algae biomass [gSi gC−1]
Cam concentration of ammonium [gN m−3]
Cni concentration of nitrate [gN m−3]
Cph concentration of dissolved phosphate [gP m−3]
Csi concentration of dissolved silicate [gSi m−3]
Rnp total or partial net primary production rate [gC m−3d−1]
∆Rnp correction of the net primary production rate [gC m−3d−1]
∆tcomputational timestep [d]
cindex for corrected net primary production
max index for maximum net primary production
1index for green algae
2index for diatoms
The respiration rate is formulated as follows:
krspi=fgri×kgpi+ftmi×(1 −f gri)×kmr20
i
where:
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fgr growth respiration factor [-]
ftm mortality temperature function [-]
kmr20 maintenance respiration constant at 20 ◦C [d−1]
krsp total respiration rate constant [d−1]
iindex for algae species
The mortality rate is formulated as follows:
Rmrti=ftmi×kmrt20
i×Max((Calgi−Calgmini),0.0)
ftmi=ktm(T−20)
i
if S < Sminithen kmrt20
i=kmrt20
min,i
if S > Smaxithen kmrt20
i=kmrt20
max,i
else
kmrt20
i=kmrt20
min,i +(S−Smini)
(Smaxi−Smini)×(kmrt20
max,i −kmrt20
min,i)
where:
Calg concentration of algae biomass [gC m−3]
Calgmin minimum concentration of algae biomass [gC m−3]
ftm mortality temperature function [-]
kmrt20 mortality rate constant at 20 ◦C [d−1]
kmrt20
min minimum mortality rate constant at 20 ◦C [d−1]
kmrt20
max maximum mortality rate constant at 20 ◦C [d−1]
ktm temperature constant for mortality [-]
Rmrt mortality rate [gC m−3d−1]
Sambient salinity [psu] or [g kg−1]
Smin salinity limit for minimum mortality [psu] or [g kg−1]
Smax salinity limit for maximum mortality [psu] or [g kg−1]
Twater temperature [◦C]
iindex for algae species
Uptake and release of nutrients
Nutrients are taken up (consumed) proportional to net primary production as follows:
Ruami=fram ×
n=2
X
i
(ani×Rnpc,i)
Runii= (1 −fram)×
n=2
X
i
(ani×Rnpc,i)
Rupi=
n=2
X
i
(api×Rnpc,i)
Rusii=
n=2
X
i
(asii×Rnpc,i)
where:
an stoichiometric constant for N over C in algae biomass [gN gC−1]
ap stoichiometric constant for P over C in algae biomass [gP gC−1]
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asi stoichiometric constant for Si over C in algae biomass [gSi gC−1]
fram fraction of N consumed as ammonium [-]
Ruam ammonium uptake rate [gN m−3d−1]
Runi nitrate uptake rate [gN m−3d−1]
Rup phosphate uptake rate [gP m−3d−1]
Rusi silicate uptake rate [gSi m−3d−1]
Rnp net primary production rate [gC m−3d−1]
cindex for corrected net primary production
iindex for algae species
Algae prefer ammonium over nitrate. The fraction of N consumed as ammonium follows from:
if Cam < Camcthen
fram =Cam
Cam +Cni
else
Run =
n=2
X
i
(ani×Rnpc,i)
if (Cam −Camc)≥(Run ×∆t)then fram = 1.0
if (Cam −Camc)<(Run ×∆t)then
fram =(Cam −Camc)+(Camc/(Camc+Cni)) ×(Run ×∆t−Cam +Camc)
Run ×∆t
where:
an stoichiometric constant for N over C in algae biomass [gN gC−1]
Cam concentration of ammonium [gN m−3]
Camccritical concentration of ammonium [gN m−3]
Cni concentration of nitrate [gN m−3]
fram fraction of N consumed as ammonium [-]
Rnp net primary production rate [gC m−3d−1]
Run required nitrogen uptake in a timestep [gC m−3d−1]
∆tcomputational timestep [d]
cindex for corrected net primary production
iindex 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-
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ents are released proportional to mortality as follows:
Ran =frai×
n=2
X
i
(ani×Rmrti)
Rap =frai×
n=2
X
i
(api×Rmrti)
Rasi =frai×
n=2
X
i
(asii×Rmrti)
Rmc1=frpoc1
(1 −frai)×
n=2
X
i
(Rmrti)
Rmn1=frpoc1×
n=2
X
i
(ani×Rmrti)
Rmp1=frpoc1×
n=2
X
i
(api×Rmrti)
Rmsi1=frpoc1×
n=2
X
i
(asii×Rmrti)
Rmc2= (1 −frpoc1
(1 −frai))×
n=2
X
i
(Rmrti)
Rmn2= (1 −frpoc1−f rai)×
n=2
X
i
(ani×Rmrti)
Rmp2= (1 −frpoc1−f rai)×
n=2
X
i
(api×Rmrti)
Rmsi2= (1 −frpoc1−f rai)×
n=2
X
i
(asii×Rmrti)
where:
an stoichiometric constant for N over C in algae biomass [gN gC−1]
ap stoichiometric constant for P over C in algae biomass [gP gC−1]
asi stoichiometric constant for Si over C in algae biomass [gSi gC−1]
fra fraction released by autolysis [-]
frpoc1fraction released to detritus POC/N/P1 or OPAL [-]
Ran nitrogen NH4 release due to autolysis [gN m−3d−1]
Rap dissolved phosphate PO4 release due to autolysis [gP m−3d−1]
Rasi dissolved silicate Si release due to autolysis [gSi m−3d−1]
Rmc1detritus C release to POC1 due to mortality [gC m−3d−1]
Rmc2detritus C release to POC2 due to mortality [gC m−3d−1]
Rmn1detritus N release to PON1 due to mortality [gN m−3d−1]
Rmn2detritus N release to PON2 due to mortality [gN m−3d−1]
Rmp1detritus P release to POP1 due to mortality [gP m−3d−1]
Rmp2detritus P release to POP2 due to mortality [gP m−3d−1]
Rmsi1silicate release to OPAL due to mortality [gSi m−3d−1]
Rmsi2silicate release to OPAL due to mortality [gSi m−3d−1]
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Rmrt mortality rate [gC m−3d−1]
iindex for algae species
Directives for use
Because the limitation function for radiation (fradi) depends on temperature, the product
of kgpidepends 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 SalM2should be greater than the value of SalM1. If SalM1 = −1
then the procedure described above is not applied. In that case the mortality rate equals
Mort0(i).
Always make sure that the radiation input is coherent with the saturated radiation. Unde-
pleted solar radiation ranges from 100 to 500 W m−2at altitudes around 50◦North/South.
At other altitudes these values must be corrected. However, these values should be cor-
rected for e.g. clouds and the wavelength spectrum (0.45 is a frequently used value).
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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.
Name in
formulas
Name in
input
Definition Units
Calgi(i)concentration algae biomass (i) gC m−3
CalgminiMin(i)minimum conc. algae species (i) gC m−3
aniNCRat(i)stoich. constant N over C in algae (i) gN gC−1
apiP CRat(i)stoich. constant P over C in algae (i) gN gC−1
asiiSCRat(i)stoich. constant Si over C in algae (i) gN gC−1
Cam NH4concentration of ammonium gN m−3
CamcNH4Crit critical conc. of ammonium for uptake gN m−3
Cni NO3concentration of nitrate gN m−3
Cph P O4concentration of dissolved phosphate gP m−3
Csi Si concentration of dissolved silicate gSi m−3
DL DayL daylength, fraction of a day -
DLoiOptDL(i)optimal daylength for algae species (i) -
et ExtV L total extinction coefficient m−1
faniP rfNH4(i)pref. ammonium over nitrate for algae (i) -
fgriGResp(i)growth respiration factor for algae (i) -
fraiF rAut(i)fraction released by autolysis for algae (i) -
frpoc1F rDet(i)fraction released to detritus POC/N/P1 or
OPAL for algae (i)
-
H Depth water depth m
Is Rad light intensity at water surface W m−2
Io20
iRadSat(i)optimal light int. at 20 ◦C for algae (i) W m−2
kmr20
iMResp(i)maint. resp. const. at 20 ◦C of algae (i) d−1
kmrt20
min,i Mort0(i)min. mort. constant at 20 ◦C of algae (i) d−1
kmrt20
max,i MortS(i)max. mort. constant at 20 ◦C of algae (i) d−1
kpp20
iP P Max(i)max. prod. constant at 20 ◦C of algae (i) d−1
ktmiT CDec(i)temp. constant for mortality of algae (i) -
ktpiT CGro(i)temp. constant for production of algae (i) -
KsniKmDIN(i)half satur. const. nitrogen for algae (i) gN m−3
KspiKmP (i)half satur. const. phosphate for algae (i) gP m−3
KssiiKmSi(i)half satur. const. silicate for algae (i) gSi m−3
S Salinity salinity psu
SminiSalM1(i)salinity limit for Mort0 of algae (i) psu
SmaxiSalM2(i)salinity limit for MortS of algae (i) psu
T T emp water temperature ◦C
∆t Delt computational timestep d
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0 10 20 30 40 50 60
0
1
2
3
4
Primary production as function of light intensity
Intensity (PAR; W/m2)
(1/d)
temperature = 5C
temperature = 15C
temperature = 25C
Figure 4.2: Primary production rate of algae species i as a function of temperature and
radiation.
0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
Radiation limitation as function of light intensity
Intensity (PAR; W/m2)
temperature = 5C
temperature = 15C
temperature = 25C
Figure 4.3: Limitation function for radiation (frad_i) for algae species i as a function of
radiation (Is,RAD) at different temperature ranging from 5 to 25 ◦C.
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4.6 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 concen-
tration of algae biomass expressed in various units among which chlorophyll-a. The concen-
trations 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 ( ).
Implementation
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.
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=
n
X
i=1
Calgi
Calgt2=
n
X
i=1
(fdmi×Calgi)
Calgn =
n
X
i=1
(ani×Calgi)
Calgp =
n
X
i=1
(api×Calgi)
Calgsi =
n
X
i=1
(asii×Calgi)
Cchf =
n
X
i=1
(achfi×Calgi)
where:
achlf stochiometric ratio of chlorophyll-a in organic matter [mgChf gC−1]
an stochiometric ratio of nitrogen in organic matter [gN gC−1]
ap stochiometric ratio of phosphorus in organic matter [gP gC−1]
asi stochiometric ratio of silicate in organic matter [gSi gC−1]
Calg concentration of biomass of algae species i [gC m−3]
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Calgn concentration of organic nitrogen in algae biomass [gC m−3]
Calgp concentration of organic phosphorus in algae biomass [gC m−3]
Calgsi concentration of silicate in algae biomass [gC m−3]
Calgt1total concentration of algae biomass [gC m−3]
Calgt2total concentration of algae biomass [gDM m−3]
Cchl concentration of chlorophyll-a [mgChf m−3]
fdm dry matter conversion factor [gDM gC−1]
iindex for algae species [-]
nnumber of algae species, 6 for MONALG and GEMMPB, 2 for DYNAMO [-]
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
( ).
Name in
formulas
Name in in-
put1
Definition Units
aniNcrat(i)stochiometric ratio of nitrogen in algae
species (i)
gN gC−1
apiP Crat(i)stochiometric ratio of phosphorus in al-
gae species (i)
gP gC−1
asiiSCrat(i)stochiometric ratio of silicate in algae
species (i)
gSi gC−1
achf1GrT oChl stochiometric ratio of chlorophyll-a in
green algae
gChl gC−1
achf2DiT oChl stochiometric ratio of chlorophyll-a in di-
atoms
gChl gC−1
Calgi(i)concentration of biomass in algae
species (i)
gC m−3
fdmiDMCF (i)dry matter conversion factor for algae
species (i)
gDM gC−1
n NAlgDynamo number of algae species in DYNAMO, de-
fault=2, this should not be changed
-
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Table 4.6: Definitions of the output parameters in the above equations for PHY_DYN. Vol-
ume units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in in-
put1
Definition Units
Calgt1P hyt total algae biomass carbon concentration gC m−3
Calgt2AlgDM total algae biomass dry matter concentra-
tion
gDM m−3
Calgn AlgN concentration of organic nitrogen in algae
biomass
gN m−3
Calgp AlgP concentration of organic phosphorus in
algae biomass
gP m−3
Calgsi AlgSi concentration of silicate in algae biomass gSi m−3
Cchf Chlfa chlorophyll-a concentration mgChf m−3
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4.7 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
Processes GROMRT_DS1, TF_DIAT, DL_DIATS1, RAD_DIATS1, MRTDIAT_S1, MRTDIAT_S2
and NRALG_S1 have been implemented for the following substances:
DiatS1
NH4, NO3, PO4 and Si
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.
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:
Rnp =knp ×Malg
A×H
knp =kgp −krsp
kgp =fdl ×frad ×fnut ×ftp ×kpp20
ftp =ktp(T−20)
where:
Asurface area [m2]
fdl daylength limitation function [-]
fnut nutrient limitation function [-]
frad light limitation function [-]
ftp production temperature function [-]
Hwater depth [m]
kgp gross primary production rate constant [d−1]
knp net primary production rate constant [d−1]
kpp20 potential maximum production rate constant at 20 ◦C [d−1]
krsp total respiration rate constant [d−1]
ktp temperature constant for production [-]
Malg quantity of diatom biomass [gC]
Rnp net primary production rate [gC m−3d−1]
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Twater temperature [◦C]
The limitation function for nutrients is given by:
fnut =Min(fn, fp, fsi, 1.0)
fn =(RmnS1×(1 −frnb)+(Cnn/(Cnn +Ksn)) ×(Cnn/∆t)) ×A×H
an ×kpn ×Malg
fp =(RmpS1+ (Cph/(Cph +Ksp)) ×(Cph/∆t)) ×A×H
ap ×kpn ×Malg
fsi =(RmsiS1+ (Csi/(Csi +Kssi)) ×(Csi/∆t)) ×A×H
asi ×kpn ×Malg
Cnn =Cam +Cni
where:
Asurface area [m2]
an stoichiometric constant for N over C in diatom biomass [gN gC−1]
ap stoichiometric constant for P over C in diatom biomass [gP gC−1]
asi stoichiometric constant for Si over C in diatom biomass [gSi gC−1]
Cam concentration of ammonium [gN m−3]
Cni concentration of nitrate [gN m−3]
Cnn concentration of nutrient nitrogen [gN m−3]
Cph concentration of dissolved phosphate [gP m−3]
Csi concentration of dissolved silicate [gSi m−3]
fnut nutrient limitation function [-]
fn nitrogen limitation function [-]
fp phosphorus limitation function [-]
fsi silicon limitation function [-]
frnb fraction of mineralisation rate N allocated to bacteria in sediment [-]
Hwater depth [m]
Ksn half saturation constant for nutrient nitrogen [gN m−3]
Ksp half saturation constant for phosphate [gP m−3]
Kssi half saturation constant for silicate [gSi m−3]
Malg quantity of diatom biomass [gC]
RmnS1mineralisation rate for DETNS1 [gN m−3d−1]
RmpS1mineralisation rate for DETPS1 [gP m−3d−1]
RmsiS1mineralisation rate for DETSiS1 [gSi m−3d−1]
The limitation functions for daylength and light are given by:
fdl =min(DL, DLo)
DLo
frad =
1.0if (Is/Io)≥1.0
Ib
Io if (Ib/Io)<1.0
where:
DL daylength, fraction of a day [-]
DLo optimal daylength [-]
fdl daylength limitation function [-]
frad light limitation function [-]
Io optimal light intensity [W m−2]
Ib light intensity at the bottom [W m−2]
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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 =fgr ×kgp +ftm ×(1 −f gr)×kmr20
where:
fgr growth respiration factor [-]
ftm mortality temperature function [-]
kmr20 maintenance respiration constant at 20 ◦C [d−1]
krsp total respiration rate constant [d−1]
The mortality rate is formulated as follows:
Rmrt =ftm ×kmrt20 ×Malg
A×H
ftm =ktm(T−20)
where:
Asurface area [m2]
ftm mortality temperature function [-]
Hwater depth [m]
kmrt20 mortality rate constant at 20 ◦C [d−1]
ktm temperature constant for mortality [-]
Malg quantity of diatom biomass [gC]
Rmrt mortality rate [gC m−3d−1]
Twater 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. Up-
take 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 =fram ×Run
Runi = (1 −fram)×Run
RunS1=Min(an ×Rnp, (1 −frnb)×Rmn1)
Run =Max((an ×Rnp −RunS1),0.0)
RupS1=Min(ap ×Rnp, RmpS1)
Rup =Max((ap ×Rnp −RupS1),0.0)
RusiS1=Min(asi ×Rnp, RmsiS1)
Rusi =Max((asi ×Rnp −RusiS1),0.0)
where:
an stoichiometric constant for N over C in algae biomass [gN gC−1]
ap stoichiometric constant for P over C in algae biomass [gP gC−1]
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asi stoichiometric constant for Si over C in algae biomass [gSi gC−1]
fram fraction of N consumed as ammonium [-]
frnb fraction of mineralisation rate N allocated to bacteria in sediment [-]
Ruam ammonium uptake rate from the water column [gN m−3d−1]
Runi nitrate uptake rate from the water column [gN m−3d−1]
Run nitrogen uptake rate from the water column [gN m−3d−1]
RunS1nitrogen uptake rate from mineralisation DETNS1 [gN m−3d−1]
Rup phosphate uptake rate from the water column [gP m−3d−1]
RupS1phosphate uptake rate from mineralisation DETPS1 [gP m−3d−1]
Rusi silicate uptake rate from the water column [gSi m−3d−1]
RusiS1silicate uptake rate from mineralisation DETSiS1 [gSi m−3d−1]
RmnS1mineralisation rate for DETNS1 [gN m−3d−1]
RmpS1mineralisation rate for DETPS1 [gP m−3d−1]
RmsiS1mineralisation rate for DETSiS1 [gSi m−3d−1]
Rnp net primary production rate [gC m−3d−1]
Algae prefer ammonium over nitrate. The fraction of N consumed as ammonium follows from:
if Cam < Camcthen fram =Cam
Cnn
if (Run ×∆t)≤(Cam −Camc)then fram = 1.0
else
fram =(Cam −Camc)+(Camc/(Camc+Cni)) ×(Run ×∆t−Cam +Camc)
Run ×∆t
where:
an stoichiometric constant for N over C in diatom biomass [gN gC−1]
Cam concentration of ammonium [gN m−3]
Camccritical concentration of ammonium [gN m−3]
Cni concentration of nitrate [gN m−3]
Cnn concentration of nutrient nitrogen DIN [gN m−3]
fram fraction of N consumed as ammonium [-]
Rnp net primary production rate [gC m−3d−1]
Run nitrogen uptake rate from the water column [gC m−3d−1]
∆tcomputational 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
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(layer S1). Organic carbon and nutrients are released proportional to mortality as follows:
Ran =fra ×an ×Rmrt
Rap =fra ×ap ×Rmrt
Rasi =fra ×asiRmrt
Rmc1=frdet1
(1 −fra)×Rmrt
Rmn1=frdet1×an ×Rmrt
Rmp1=frdet1×ap ×Rmrt
Rmsi1=frdet1×asi ×Rmrt
Rmc2= (1 −frdet1
(1 −fra))×Rmrt
Rmn2= (1 −frdet1−f ra)×an ×Rmrt
Rmp2= (1 −frdet1−f ra)×ap ×Rmrt
Rmsi2= (1 −frdet1−f ra)×asi ×Rmrt
where:
an stoichiometric constant for N over C in algae biomass [gN gC−1]
ap stoichiometric constant for P over C in algae biomass [gP gC−1]
asi stoichiometric constant for Si over C in algae biomass [gSi gC−1]
fra fraction released by autolysis [-]
frdet1fraction released to detritus DetXS1 [-]
Ran nitrogen NH4 release due to autolysis [gN m−3d−1]
Rap dissolved phosphate PO4 release due to autolysis [gP m−3d−1]
Rasi dissolved silicate Si release due to autolysis [gSi m−3d−1]
Rmc1detritus C release to DetCS1 due to mortality [gC m−3d−1]
Rmc2detritus C release to OOCS1 due to mortality [gC m−3d−1]
Rmn1detritus N release to DetNS1 due to mortality [gN m−3d−1]
Rmn2detritus N release to OONS1 due to mortality [gN m−3d−1]
Rmp1detritus P release to DetPS1 due to mortality [gP m−3d−1]
Rmp2detritus P release to OOPS1 due to mortality [gP m−3d−1]
Rmsi1silicate release to DetSiS1 due to mortality [gSi m−3d−1]
Rmsi2silicate release to OOSiS1 due to mortality [gSi m−3d−1]
Rmrt mortality rate [gC m−3d−1]
Directives for use
The nutrient-carbon ratios for diatoms in the sediment are the same as for diatoms in the
water column.
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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_S2and
NRALG_S1.
Name in
formulas
Name in
input
Definition Units
Malg DiatS1quantity of benthic diatom biomass gC m−3
A Surf surface area m2
an NCRatDiat stoich. const. N over C in diatom biomass gN gC−1
ap P CRatDiat stoich. const. P over C in diatom biomass gN gC−1
asi SCRatDiat stoich. const. Si over C in diatom biomass gN gC−1
Cam NH4concentration of ammonium gN m−3
CamcNH4Crit critical conc. of ammonium for uptake gN m−3
Cni NO3concentration of nitrate gN m−3
Cph P O4concentration of dissolved phosphate gP m−3
Csi Si concentration of dissolved silicate gSi m−3
DL DayL daylength, fraction of a day -
DLo OptDLDiaS1optimal daylength for benthic diatoms -
fgr GRespDiaS1growth respiration factor -
fra F rAutDiatS fraction released by autolysis -
frdet1F rDetDiatS fraction released to detritus DetC/N/P/SiS1 -
frnb F rM inS1Bac frac. min. N allocated to sediment bacteria -
H Depth water depth m
Ib Rad light intensity at water surface W m−2
Io RadSatDiS1optimal light intensity for benthic diatoms W m−2
kmr20 MRespDiaS1maint. resp. const. at 20 ◦C of diatoms d−1
kmrt20 MrtSedDiat mortality constant at 20 ◦C of diatoms d−1
kpp20 P P MaxDiaS1max. prod. constant at 20 ◦C of diatoms d−1
ktm T CDecDiat temp. constant for mortality of diatoms -
ktp T CGroDiat temp. constant for production of diatoms -
Ksn KmDINDiaS1half satur. const. nitrogen for diatoms gN m−3
Ksp KmP DiatS1half satur. const. phosphate for diatoms gP m−3
Kssi KmSiDiatS1half satur. const. silicate for diatoms gSi m−3
RmnS1dMinDetNS1mineralisation rate for DETNS1 gN m−3d−1
RmpS1dMinDetP S1mineralisation rate for DETPS1 gP m−3d−1
RmsiS1dMinDetSiS mineralisation rate for DETSiS1 gSi m−3d−1
T T emp water temperature ◦C
∆t Delt computational timestep d
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4.8 Mortality and re-growth of terrestrial vegetation (VEGMOD)
PROCESSES: VBMORT(I), VB(I)_MRT3W, VB(I)_MRT3S, VBGROWTH(I), VB(I)UPT,
VB(I)_UPT3D, VB(I)AVAILN, VBSTATUS(I)
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 mod-
ule 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 inunda-
tion 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 param-
eters 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.
Each cohort of vegetation consists of the following above-ground and below-ground compart-
ments: 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 avail-
able 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 pre-
vented 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 sub-
stances:
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
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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 lay-
ers. 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.
Formulation
(Re-)Growth
The growth curve of a vegetation cohort is defined by 4 parameters; minimum biomass, maxi-
mum 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 sim-
ulation 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:
Mvega,i =(Mvegmin,i −Mvegmax,i)
1 + exp (sfi×(agi−aghb,i)/aghb,i)+Mvegmax,i
where:
ag age of vegetation [d]
aghb age of vegetation when half of attainable biomass is reached [d]
Mvegaattainable biomass in all compartments [gC.m−2]
Mvegmax maximum biomass in all compartments [gC.m−2]
Mvegmin minimum biomass in all compartments [gC.m−2]
sf shape factor of the growth function [-]
iindex 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:
Mvegi=fai×Mveg0,i/dmci
where:
dmc dry matter carbon ratio [gDM.gC−1]
fa percentage of area coverage [%]
Mveg actual biomass in all compartments [gC.m−2]
Mveg0initial 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 = (Mvega,i −Mvegi)/∆t
where:
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Rgrppotential growth rate of biomass in all compartments [gC.m−2.d−1]
∆tcomputational time step [d]
In a final step the growth is corrected for nutrient limitation. In case of nutrient limitation, the
above potential growth rates Rgrp,i are reduced to actual growth rates Rgr iin 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)).
When inundation occurs, the vegetation stops growing (SWVB(i)Gro = 0.0), and the veg-
etation 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 accord-
ingly. 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
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 up-
take 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 =fnln ×Rgri×
5
X
j=1
(fbij/vnlij)/H
Rupt,l =
9
X
i=1 nr
X
n=1
(Rupiln )!
where:
fb fraction of biomass in a compartment [-]
fn fraction of total available nutrient in a layer [-]
Hsediment layer thickness [-]
Rgr growth rate of biomass in all compartments [gC.m−2.d−1]
Rup uptake rate of nutrients in all compartments [gN/P/S.m−3.d−1]
Rupt total uptake rate of nutrients in all compartments [gN/P/S.m−3.d−1]
vn carbon nutrient ratio in vegetation biomass [gC.gN/P/S−1]
lindex for nutrient (1=nitrogen, 2=phosphorus, 3=sulfur)
iindex for vegetation cohorts (1–9)
jindex for biomass compartments (1=stem, 2=foliage, 3=branches, 4=roots, 5=fine
roots)
nindex 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.
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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 >tic,ithen agi=0.0 and SwVB iMrt =0.0
where:
ag age of biomass [d]
ti inundation period, the number of successive days of inundation [d]
ticcritical inundation period, the mortality lag time [d]
SwEmersion switch for inundation (0 = yes, 1 = no)
SwV BiMrt switch for mortality (0 = yes, 1 = no)
∆tcomputational time step [d]
iindex for vegetation cohorts (1–9)
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 ti0can 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×Mvegi
Rmrdklij =fhi×fdkij ×fbij ×Rmrti/(vnlij ×H)
where:
fb fraction of biomass in a compartment [-]
fd fraction of biomass released into a specific detritus fraction [-]
fh fraction of biomass in a layer [-]
Hwater layer or sediment layer thickness [-]
kmrt mortality rate constant [d−1]
Mveg actual biomass in all compartments [gC.m−2]
Rmrd release rate of detritus [gC/N/P/S.m−3.d−1]
Rmrt mortality rate of biomass [gC.m−2.d−1]
vn carbon nutrient ratio in vegetation biomass [gC.gC/N/P/S−1]
kindex for detritus fraction (1 = POX1, 2 = POX2, 3 = POX3, 5 = POX5)
lindex for carbon and nutrient (0 = carbon, 1 = nitrogen, 2 = phosphorus, 3 =
sulfur)
iindex for vegetation cohorts (1–9)
jindex 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.
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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 water-
sediment 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.
The distribution is determined from the total above-ground or the total below-ground biomass
per m2using 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:
Fsi=Cvegi(zmax ,i)
Mvegp,i/Hmax ,i
where:
F s shape constant for vertical distribution of biomass [-]
Cveg(zmax)above-ground or under-ground biomass at zmax [gC.m−3]
Mvegpabove-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 root-
ing depth [m]
iindex for vegetation cohorts (1–9)
The value of shape constant Fs varies from 0 to 2. When Fs =0the biomass Cveg is zero
at zmax, when Fs =1biomass Cveg is homogeneously distributed (constant over depth),
and when Fs =2biomass 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 Fon the distribution appear
from Figure 4.6.
A linear distribution function is formulated using two constants, aand b. Both are fixed when
Fis 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:
Cvegi(z) = ai×z+bi
ai=Mvegp,i
Hmax ,i×(2 −2×Fsi)
(Ht−zmax ,i)
bi=Mvegp,i
Hmax ,i×(Fsi×(zmax ,i+Ht)−2×zmax ,i)
(Ht−zmax ,i)
The biomass fraction fhiin a layer n between znand zn+1 follows from:
Zzn+1
zn
(Cvegi(z)/Mvegi)dz =A
2z2
n+1 −z2
n+B(zn+1 −zn)
fhi=Rzn+1
zn(Cvegi(z)/Mvegi)dz if zn> zmax ,i
Rzmax ,i
zn(Cvegi(z)/Mvegi)dz if zn≤zmax ,i
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with:
Zzn+1
zn
(Cvegi(z)/Mvegi)dz =A
2z2
n+1 −z2
n+B(zn+1 −zn)
where:
Cveg(z)above-ground or under-ground biomass at water or sediment depth z[gC.m−3]
fh fraction of biomass in a water or sediment layer [-]
Httotal water depth or total sediment depth [m]
Mveg biomass in all compartments [gC.m−2]
Mvegpabove-ground or under-ground biomass [gC.m−2]
zwater depth (positive) or sediment depth (negative) at bottom of a layer [m]
iindex for vegetation cohorts (1–9)
For Fs =1the integral reduces to:
fhi=Mvegp,i
Mvegi×(zn+1−zn)
Hmax ,i
if zn> zmax ,i
fhi=Mvegp,i
Mvegi×(zmax ,i−zn)
Hmax ,i
if zn< zmax ,iand 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−1for each veg-
etation type. For SwIniVB(i)=0.0 the model expects biomasses in tDM.ha−1for 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) over-
laps 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 VBFr-
MaxU (<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 NH4 concentration of ammonium gN.m−3
Cni NO3 concentration of nitrate gN.m−3
Cph PO4 concentration of dissolved phosphate gP.m−3
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Name in
formulas1
Name in
input1
Definition Units
Cap AAP concentration of adsorbed phosphate gP.m−3
Csu SO4 concentration of sulfate gS.m−3
Csud SUD concentration of dissolved sulfide gS.m−3
dmciDMcfVB(i) dry matter carbon ratio gDM.gC−1
faiIniCovVB(i) percentage of area coverage %
fbij F1VB(i) fraction of biomass in compartment 1 (stems) -
F2VB(i) fraction of biomass in comp. 2 (foliage) -
F3VB(i) fraction of biomass in comp. 3 (branches) -
F4VB(i) fraction of biomass in comp. 4 (roots) -
F5VB(i) fraction of biomass in comp. 5 (fine roots) -
fd1i2FfolPOC1 biomass fraction 2 (foliage) to detr. POX1 -
fd2i2FfolPOC2 biomass fraction 2 (foliage) to detr. POX2 -
fd1i5FfrootPOC1 biomass fraction 2 (fine roots) to detr. POX1 -
fd2i5FfrootPOC2 biomass fraction 2 (fine roots) to detr. POX2 -
Fs FfacVB(i) shape constant for vertical distr. of biomass -
H Depth water layer or sediment layer thickness m
Hmax VegHeVB(i) vegetation height (positive) m
Hmax RootDeVB(i) rooting depth (negative) m
HtTotalDepth total water depth or total sediment depth m
z LocalDepth depth to the bottom of a water layer m
z LocSedDept depth to the bottom of a sediment layer m
-Surf surface area of a grid cell m−2
-Volume volume of a grid cell m−3
kmrtiRcMrtVB(i) mortality rate constant d−1
Mveg VB(i) vegetation biomass in all five compartments gC.m−2
Mveg0IniVB(i) initial biomass in all five compartments tDM.ha−1
Mvegmax,i MaxVB(i) maximum biomass in all five compartments gC.m−2
Mvegmin,i MinVB(i) minimum biomass in all five compartments gC.m−2
sfiSfVB(i) shape factor of the growth function -
SWEmersion SWEmersion switch for inundation (0 = yes, 1 = no) -
SWDisVB(i) SWDisVB(i) option vert. distr. (1=const., 2=linear, 3=exp.) -
SwIniVB(i) SwIniVB(i) option init. biomass (0=biomass,1=coverage) -
IniVB(i)Dec IniVB(i)Dec option mort. at start of simul. (0=no, 1=yes) -
SwRegrVB(i) SwRegrVB(i) option for re-growth (0=no, 1=yes) -
VBFrMaxU VBFrMaxU max. fr. of nutrients taken up in a time step -
vn1ij CNF1VB(i) carbon nitrogen ratio in comp. 1 (stems) gC.gN−1
CNF2VB(i) carbon nitrogen ratio in comp. 2 (foliage) gC.gN−1
CNF3VB(i) carbon nitrogen ratio in comp. 3 (branches) gC.gN−1
CNF4VB(i) carbon nitrogen ratio in comp. 4 (roots) gC.gN−1
CNF5VB(i) carbon nitrogen ratio in comp. 5 (fine roots) gC.gN−1
vn2ij CPF1VB(i) carbon phosphorus ratio in comp. 1 (stems) gC.gP−1
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Name in
formulas1
Name in
input1
Definition Units
CPF2VB(i) carbon phosphorus ratio in comp. 2 (foliage) gC.gP−1
CPF3VB(i) carbon phos. ratio in comp. 3 (branches) gC.gP−1
CPF4VB(i) carbon phosphorus ratio in comp. 4 (roots) gC.gP−1
CPF5VB(i) carbon phos. ratio in comp. 5 (fine roots) gC.gP−1
vn3ij CSF1VB(i) carbon sulfur ratio in comp. 1 (stems) gC.gS−1
CSF2VB(i) carbon sulfur ratio in comp. 2 (foliage) gC.gS−1
CSF3VB(i) carbon sulfur ratio in comp. 3 (branches) gC.gS−1
CSF4VB(i) carbon sulfur ratio in comp. 4 (roots) gC.gS−1
CSF5VB(i) carbon sulfur ratio in comp. 5 (fine roots) gC.gS−1
tic,i CrnsfVB(i) critical inundation period, mortality lag time d
ti0,i Initnsfd inundation period prior to sim. start time d
∆tDelt computational time step d
1)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 VB-
STATUS(i).
Name in
formulas1
Name in
output1
Definition2Units
tiiAgeVB(i) age of vegetation biomass d
-fNVB(i)UP N vegetation uptake flux gN.m−2.d−1
fPVB(i)UP P vegetation uptake flux gP.m−2.d−1
fSVB(i)UP S vegetation uptake flux gS.m−2.d−1
fN1VB(i)UPy ammonium N vegetation uptake flux gN.m−2.d−1
fN2VB(i)UPy nitrate N vegetation uptake flux gN.m−2.d−1
fP1VB(i)UPy dissolved phosphate P vegetation uptake flux gP.m−2.d−1
fP2VB(i)UPy adsorbed phosphate P vegetation uptake flux gP.m−2.d−1
fS1VB(i)UPy sulfate S vegetation uptake flux gS.m−2.d−1
fS2VB(i)UPy dissolved sulfide S vegetation uptake flux gS.m−2.d−1
-fC1VB(i)P5 C flux from biomass comp. 1 to detritus POC5 gC.m−3.d−1
fN1VB(i)P5 N flux from biomass comp. 1 to detritus POC5 gN.m−3.d−1
fP1VB(i)P5 P flux from biomass comp. 1 to detritus POC5 gP.m−3.d−1
fS1VB(i)P5 S flux from biomass comp. 1 to detritus POC5 gS.m−3.d−1
fC2VB(i)P1 C flux from biomass comp. 2 to detritus POC1 gC.m−2.d−1
fN2VB(i)P1 N flux from biomass comp. 2 to detritus POC1 gN.m−2.d−1
fP2VB(i)P1 P flux from biomass comp. 2 to detritus POC1 gP.m−2.d−1
fS2VB(i)P1 S flux from biomass comp. 2 to detritus POC1 gS.m−2.d−1
fC2VB(i)P2 C flux from biomass comp. 2 to detritus POC2 gC.m−2.d−1
fN2VB(i)P2 N flux from biomass comp. 2 to detritus POC2 gN.m−2.d−1
fP2VB(i)P2 P flux from biomass comp. 2 to detritus POC2 gP.m−2.d−1
fS2VB(i)P2 S flux from biomass comp. 2 to detritus POC2 gS.m−2.d−1
fC2VB(i)P3 C flux from biomass comp. 2 to detritus POC3 gC.m−2.d−1
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Name in
formulas1
Name in
output1
Definition2Units
fN2VB(i)P3 N flux from biomass comp. 2 to detritus POC3 gN.m−2.d−1
fP2VB(i)P3 P flux from biomass comp. 2 to detritus POC3 gP.m−2.d−1
fS2VB(i)P3 S flux from biomass comp. 2 to detritus POC3 gS.m−2.d−1
fC3VB(i)P5 C flux from biomass comp. 3 to detritus POC5 gC.m−3.d−1
fN3VB(i)P5 N flux from biomass comp. 3 to detritus POC5 gN.m−3.d−1
fP3VB(i)P5 P flux from biomass comp. 3 to detritus POC5 gP.m−3.d−1
fS3VB(i)P5 S flux from biomass comp. 3 to detritus POC5 gS.m−3.d−1
fC4VB(i)P5 C flux from biomass comp. 4 to detritus POC5 gC.m−3.d−1
fN4VB(i)P5 N flux from biomass comp. 4 to detritus POC5 gN.m−3.d−1
fP4VB(i)P5 P flux from biomass comp. 4 to detritus POC5 gP.m−3.d−1
fS4VB(i)P5 S flux from biomass comp. 4 to detritus POC5 gS.m−3.d−1
fC5VB(i)P1 C flux from biomass comp. 5 to detritus POC1 gC.m−2.d−1
fN5VB(i)P1 N flux from biomass comp. 5 to detritus POC1 gN.m−2.d−1
fP5VB(i)P1 P flux from biomass comp. 5 to detritus POC1 gP.m−2.d−1
fS5VB(i)P1 S flux from biomass comp. 5 to detritus POC1 gS.m−2.d−1
fC5VB(i)P2 C flux from biomass comp. 5 to detritus POC2 gC.m−2.d−1
fN5VB(i)P2 N flux from biomass comp. 5 to detritus POC2 gN.m−2.d−1
fP5VB(i)P2 P flux from biomass comp. 5 to detritus POC2 gP.m−2.d−1
fS5VB(i)P2 S flux from biomass comp. 5 to detritus POC2 gS.m−2.d−1
fC5VB(i)P3 C flux from biomass comp. 5 to detritus POC3 gC.m−2.d−1
fN5VB(i)P3 N flux from biomass comp. 5 to detritus POC3 gN.m−2.d−1
fP5VB(i)P3 P flux from biomass comp. 5 to detritus POC3 gP.m−2.d−1
fS5VB(i)P3 S flux from biomass comp. 5 to detritus POC3 gS.m−2.d−1
RgrifVB(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 vegetation biomass density tC.ha−1
VB(i)Aha attainable vegetation biomass density tC.ha−1
-VB(i)Navail available nutrient N within rooting depth gN.m−2
VB(i)Pavail available nutrient P within rooting depth gP.m−2
VB(i)Savail available nutrient S within rooting depth gS.m−2
-SWVB(i)Dec switch continuation mortality (0 = no, 1 = yes) -
SWVB(i)Gro SWVB(i)Gro switch for growth (0 = no, 1 = yes) -
SWVB(i)Mrt 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.
2) Vegetation biomass compartments are 1=stems, 2=foliage, 3=branches, 4=roots and
5=fine roots.
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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).
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(a) (b)
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).
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5 Macrophytes
Contents
5.1 Framework of the macrophyte module . . . . . . . . . . . . . . . . . . . . 138
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
5.2 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 . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.2.4 Temperature limitation . . . . . . . . . . . . . . . . . . . . . . . . 147
5.2.5 Decay of emerged and submerged biomass . . . . . . . . . . . . 148
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
5.2.10 Oxygen production and consumption . . . . . . . . . . . . . . . . 151
5.2.11 Net growth of emerged and submerged vegetation and rhizomes . 152
5.3 Maximum biomass per macrophyte species . . . . . . . . . . . . . . . . . 153
5.3.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.3.2 Hints for use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.4 Grazing and harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.4.1 Grazing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.4.2 Hints for use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.4.3 Harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.5 Light limitation for macrophytes . . . . . . . . . . . . . . . . . . . . . . . . 158
5.6 Vegetation coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.6.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.7 Vertical distribution of submerged macrophytes . . . . . . . . . . . . . . . 161
5.7.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.7.2 Hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
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Figure 5.1: Interactions between the nutrient cycles and the life cycle of macrophytes.
5.1 Framework of the macrophyte module
5.1.1 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 macro-
phytes and their abiotic surroundings. It also indicates which relevant processes are already
included in D-Water Quality and which fluxes (and processes within macrophytes/ macro-
phyte 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).
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Macrophytes
5.1.2 Growth forms
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 Macro-
phyte Module.
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 D-
Water 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 be-
cause they have different interactions with water quality processes. The major changes con-
cern the nutrient uptake strategies, the dependence on light availability and the sedimenta-
tion/erosion processes (Calow and Petss,1992;?;Scheffer,1998). Emerged sections of
macrophytes can fully cover the water surface and thereby block light penetration and aera-
tion, 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.
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Figure 5.3: The abbreviations for the parts of the vegetation that are used in the equa-
tions.
5.1.3 Plant parts
In the formulas a single species ican consist of emerged parts and/or submerged parts and/or
root-rhizome parts. The emerged part is indicated by EMi, the submerged part by SMiand
the root-rhizome by RHi. Please note that EMi, SMiand RHirefer to the same species i.
This is illustrated in Figure 5.3. The submerged section SMican 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 litera-
ture) 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.
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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 har-
vested 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 (?).
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 miner-
alization 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 main-
tenance 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 con-
sequently 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.
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Submerged macroalgae
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.
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 sub-
merged 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.
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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]
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.
Emerging submerged non-rooted macrophytes
These plants have emerged parts, while their root system is in the water, but there are excep-
tions 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 condi-
tions 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 classi-
fications like the one from ?, adapted from ?put this category in the emergent unattached
growth form.
Water type and Habitat: stagnant water with organic sediment.
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5.2 Growth of submerged and emerged biomass of macrophytes
PROCESS: MACROPHYTI
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.
The growth rate is calculated via the following formula:
If EMi< MaxEMi
GrowthEMi=(EMi+RHi)×MaxGrowthEMi×LimLightEMi(5.1)
×LimT EMi×LimAgeEMi
Else
GrowthEMi= 0
If SMi< MaxSMi
GrowthSMi=(SMi+RHi)×MaxGrowthSMi×LimLightSMi
×LimT SMi×LimAgeSMi
Else
GrowthSMi= 0
where:
SMiBiomass of submerged (SM) species i [g C·m−2]
GrowthSMiGrowth of SM species i [g C·m−2·d−1]
MaxGrowthSMiPotential growth rate of SM species i [d−1]
LimLightSMiLight limitation factor SM species i [-]
LimTSMiTemperature limitation factor SM species i[-]
EMiBiomass of emerged species (EM) i[g C·m−2]
GrowthEMiGrowth of EM species i[g C·m−2·d−1]
MaxEMiMaximum biomass of EM species i[g C·m−2]
MaxGrowthEMiPotential growth rate of EM species i [d−1]
LimNutEMiNutrient limitation factor EM species i [-]
LimTEMiTemperature limitation factor EM species i [-]
The limitation factors are explained in the following subsections.
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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.
LimNH4EMi=NH4
NH4 + NH4hsEMi
(5.2)
LimNO3EMi=NO3
NO3 + NO3hsEMi
LimP O4EMi=P O4
P O4 + NO3hsEMi
LimNutEMi= min(LimP O4EMi,max(LimNH4EMi, LimNO3EMi))
where:
NH4 Ammonia concentration [g N·m−3]
NH4hsEMiHalf saturation concentration NH4 for growth of EM species i [g N·m−3]
LimNH4EMiAmmonium limitation factor for EM species i [-]
NO3 Nitrate concentration [g N·m−3]
NO3hsEMiHalf saturation concentration NO3 for growth of EM species i [g N·m−3]
LimNO3EMiNitrate limitation factor for EM species i [-]
PO4 Ortho-phosphorus concentration [g P·m−3]
PO4hsEMiHalf saturation concentration PO4 for growth EMi [g N·m−3]
LimPO4EMiPhosphorus limitation factor for EM species i [-]
LimNutEMiNutrient limitation factor for EM species i [-]
5.2.2 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(5.3)
CtranslocRHtoSMi=GrowthSMi
Else
CtranslocRHtoEMi=0
CtranslocRHtoSMi=0
If (GrowthEMi×NCratEMi+GrowthSMi×NCrateSMi)×dt < (NRHi−
NRHmini)
NtranslocRHtoEMi=GrowthEMi×NCratEMi(5.4)
NtranslocRHtoSMi=GrowthSMi×NCratSMi
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Else
NtranslocRHtoEMi=0
NtranslocRHtoSMi=0
If (GrowthEMi×P CratEMi+GrowthSMi×P CrateSMi)×dt < (P RHi−
P RHmini)
P translocRHtoEMi=GrowthEMi×P CratEMi(5.5)
P translocRHtoSMi=GrowthSMi×P CratSMi
Else
P translocRHtoEMi=0
P translocRHtoSMi=0
where:
RHiRhizome species i[g C·m−2]
RHminiCritical biomass of RH species i [g C·m−2]
dt Timestep of computation [d]
CtranslocRHtoEMiTranslocation of C from RH to EM species i [g C·m−2·d−1]
CtranslocRHtoSMiTranslocation of C from RH to SM species i [g C·m−2·d−1]
NRHiNitrogen content of rhizome [g N·m−2]
NRHminiCritical nitrogen content of RH species i [g N·m−2]
NtranslocRHtoEMiTranslocation of N from RH to EM species i [g N·m−2·d−1]
NtranslocRHtoSMiTranslocation of N from RH to SM species i [g N·m−2·d−1]
NCratEMiNitrogen-carbon ratio of EM species i [g N·g C−1]
NCratSMiNitrogen-carbon ratio of SM species i [g N·g C−1]
PRHiPhosphorus content of RH species i [g P·m−2]
PRHminiCritical phosphorus content of RH species i [g P·m−2]
PtranslocRHtoEMiTranslocation of P from RH to EM species i [g P·m−2·d−1]
PtranslocRHtoSMiTranslocation of P from RH to SM species i [g P·m−2·d−1]
PCratEMiPhosphorus-carbon ratio of EM species i [g P·g C−1]
PCratSMiPhosphorus-carbon ratio of SM species i [g P·g C−1]
5.2.3 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 < MinDLEMi
LimDLEMi= 0 (5.6)
If MinDLEMi< DL < OptDLEMi
LimDLEMi=DL −MinDLEMi
OptDLEMi−MinDLEMi
(5.7)
If DL > OptDLEMi
LimDLEMi= 1 (5.8)
The daylength limitation functions are the same for submerged macrophytes:
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If DL < MinDLSMi
LimDLSMi= 0 (5.9)
If MinDLSMi< DL < OptDLSMi
LimDLSMi=DL −MinDLSMi
OptDLSMi−MinDLSMi
(5.10)
If DL > OptDLSMi
LimDLSMi= 1 (5.11)
where:
DL Daylength [d]
LimDLEMiDaylength limitation factor for EM species i [-]
LimDLSMiDaylength limitation factor for SM species i [-]
OptDLEMiOptimum daylength for EM species i [d]
OptDLSMiOptimum daylength for SM species i [d]
MinDLEMiMinimum daylength for EM species i [d]
MinDLSMiMinimum daylength for SM species i [d]
5.2.4 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=KT20EMT−20
i
Else
LimT EMi= 0 (5.12)
If T > T critSMi
LimT SMi=KT20SMT−20
i
Else
LimT SMi= 0 (5.13)
where:
T Temperature [◦C]
TcritEMiCritical temperature for growth EM species i [◦C]
LimTEMiTemperature limitation factor for EM species i [-]
KT20EMiTemperature coefficient for EM species i [-]
TcritSMiCritical temperature for growth SM species i [◦C]
LimTEMiTemperature limitation factor for SM species i [-]
KT20SMiTemperature coefficient for SM species i [-]
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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 20EMT−20
i
DecaySMi=K1DecaySMi×SMi×(1 −LimDLSMi)×KDecayT 20SMT−20
i
(5.14)
where:
DecayEMiDecay of emerged part of species i (EMi) [g C ·m−2·d−1]
K1decayEMiFirst order autumn decay constant of EMi[d−1]
KDecayT 20EMiTemperature constant for decay of EMi[-]
DecaySMiDecay of submerged part of species i(SMi) [d−1]
K1decaySMiFirst order autumn decay constant of SMi[d−1]
KDecayT 20SMiTemperature constant for decay of SMi[-]
5.2.5.1 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.
5.2.6 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 pri-
mary 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 ra-
tios 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 sys-
tem (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:
CtranslocEMtoRHi=DecayEMi×F rEMtoRHi
NtranslocEMtoRHi=CtranslocEMtoRHi×min(NCRatRHi, NCRatEMi)
P translocEMtoRHi=CtranslocEMtoRHi×min(P CRatRHi, P CRatEMi)
(5.15)
For submerged vegetation:
CtranslocSMtoRHi=DecaySMi×F rSMtoRHi
NtranslocSMtoRHi=CtranslocSMtoRHi×min(NCRatRHi, NCRatSMi)
P translocSMtoRHi=CtranslocSMtoRHi×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).
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In the above formulae:
CtranslocEMtoRHiTranslocation of C from EM to RH species i [g C·m−2d−1]
FrEMtoRHiFraction of EM that becomes RH species i [-)
NtranslocEMtoRHiTranslocation of N from EMi to RHi [g N·m−2d−1]
NCratRHiNitrogen-carbon ratio of RH species i [g N·g C−1]
NCratEMiNitrogen-carbon ratio of EM species i [g N·g C−1]
PtranslocEMiTranslocation of P from EMi to rhizomes [g P·m−2d−1]
PCratRHiPhosphorus-carbon ratio of EM species i [g P·g C−1]
PCratEMiPhosphorus-carbon ratio of EM species i [g P·g C−1]
CtranslocSMtoRHiTranslocation of C from EM to RH species i [g C·m−2d−1]
FrSMtoRHiFraction of SM that becomes RH species i [-]
NtranslocSMtoRHiTranslocation of N from EMi to RHi [g N·m−2d−1]
NCratSMiNitrogen-carbon ratio of EM species i [g N·g C−1]
PtranslocSMiTranslocation of P from EMi to rhizomes [g P·m−2d−1]
PCratSMiPhosphorus-carbon ratio of EM species i [g P·g C−1]
5.2.7 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.
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−CtranslocEMtoRHi)×F rP OCxEMi+
(DecaySMi−CtranslocSMtoRHi)×F rP OCxSMi
(5.18)
The production of particulate organic nitrogen amnd phosphorus is calculated by:
P rodP ONxEMi=(DecayEMi×NCratEMi−NtranslocEMtoRHi)×F rP OCxEMi+
(DecaySMi×NCratEMi−NtranslocSMtoRHi)×F rP OCxSMi
P rodP OP xEMi=(DecayEMi×P CratEMi−P translocEMtoRHi)×F rP OCxEMi+
(DecaySMi×P CratEMi−P translocSMtoRHi)×F rP OCxSMi
(5.19)
where:
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POC1 Particulate organic carbon, fraction 1 [g C·m−3]
POC2 Particulate organic carbon, fraction 2 [g C·m−3]
POC3 Particulate organic carbon, fraction 3 [g C·m−3]
FrPOC1EMiFraction of decaying EMi that becomes POC1 [-]
FrPOC2EMii Fraction of decaying EMi that becomes POC2 [-]
FrPOC3EMii Fraction of decaying EMi that becomes POC3 [-]
FrPOC1SMii Fraction of decaying SMi that becomes POC1 [-]
FrPOC2SMii Fraction of decaying SMi that becomes POC2 [-]
FrPOC3SMii Fraction of decaying SMi that becomes POC3 [-]
ProdPOC1ii POC1 production from decaying vegetation i [g C·m−2·d−1]
ProdPOC2ii POC2 production from decaying vegetation i [g C·m−2·d−1]
ProdPOC3ii POC3 production from decaying vegetation i [g C·m−2·d−1]
PON1 Particulate organic nitrogen, fraction 1 [g N·m−3]
PON2 Particulate organic nitrogen, fraction 2 [g N·m−3]
PON3 Particulate organic nitrogen, fraction 3 [g N·m−3]
ProdPON1ii PON1 production from decaying vegetation i [g N·m−2·d−1]
ProdPON2ii PON2 production from decaying vegetation i [g N·m−2·d−1]
ProdPON3ii PON3 production from decaying vegetation i [g N·m−2·d−1]
POP1 Particulate organic phosphorus, fraction 1 [g P·m−3]
POP2 Particulate organic phosphorus, fraction 2 [g P·m−3]
POP3 Particulate organic phosphorus, fraction 3 [g P·m−3]
ProdPOP1ii POP1 production from decaying vegetation i [g P·m−2·d−1]
ProdPOP2ii POP2 production from decaying vegetation i [g P·m−2·d−1]
ProdPOP3ii POP3 production from decaying vegetation i [g P·m−2·d−1]
5.2.8 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.
Nuptakesediment =GrowthEMi×NCratEMi−NtranslocRHtoEMi+
GrowthSMi×NCratSMi−NtranslocRHtoSMi
P uptakesediment =GrowthEMi×P CratEMi−P translocRHtoEMi+
GrowthSMi×P CratSMi−P translocRHtoSMi
(5.20)
where:
Nuptakesediment Uptake of nitrogen from the sediment [g N·m−2]
Puptakesediment Uptake of phosphorus from the sediment [g P·m−2]
5.2.8.1 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.
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5.2.9 Uptake of nitrogen and phosphorus from water
TODO(??): TODOrevise this section - it is incomplete!
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 NH4< NH4critEMi
F rNH4EMi=NH4
NH4 + NO3
Else
F rNH4EMi= 1 (5.21)
NH4uptakeEMi=GRowthEMi×NCratEMi×F rN H4EMi
NO3uptakeEMi=GRowthEMi×NCratEMi×(1 −F rNH4EMi)
P O4uptakeEMi=GRowthEMi×P CratEMi(5.22)
where:
NH4critEMiCritical NH4 concentration for uptake by EMi [g N·m−2·d−1]
NH4uptakeEMiAmmonium uptake by emerged vegetation [g N·m−2·d−1]
NO3uptakeEMiNitrate uptake by emerged vegetation [g N·m−2·d−1]
PO4uptakeEMiOrtho-phosphorus uptake by emerged vegetation [g P·m−2·d−1]
FrNH4EMiFraction of NH4 in total nitrogen uptake [-]
5.2.10 Oxygen production and consumption
When macrophytes grow, they produce oxygen during the production of biomass. The stoi-
chiometric ratio between O2production [g O2] and CO2uptake 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 macro-
phyte model is limited to the oxygen that is involved in the decay of organic matter.
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5.2.11 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 vege-
tation:
EMi
dt =GrowthEMi−GrazeEMi−HarvestEMi−DecayEMi
SMi
dt =GrowthSMi−GrazeSMi−HarvestSMi−DecaySMi
RHi
dt =CtranslocEMtoRHi+CtranslocSMtoRHi−CtranslocRHtoEMi
CtranslocRHtoSMi−GrazeRHi
NRHi
dt =NtranslocEMtoRHi+NtranslocSMtoRHi−NtranslocRHtoEMi
NtranslocRHtoSMi−GrazeNRHi
P RHi
dt =P translocEMtoRHi+P translocSMtoRHi−P translocRHtoEMi
P translocRHtoSMi−GrazeP RHi(5.24)
In these formulae grazing and harvesting terms have been included (see Section 5.4).
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5.3 Maximum biomass per macrophyte species
PROCESS: MAXMACRO
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.
5.3.1 Implementation
The maximum biomass for each growth form and for each species is calculated as follows:
If PiHSIi>0:
MaxEMi=HSIi×P otEMi
PiHSIi
(5.25)
MaxSMi=HSIi×P otSMi
PiHSIi
Else
MaxEMi= 0
MaxSMi= 0
where:
EMiEmerged biomass of macrophyte species i [g C ·m−2]
HSIiHabitat Suitability Index for species i [-]
i Subscript for species [-]
MaxEMiMaximum biomass for EM species i [g C ·m−2]
PotEMiPotential biomass for EM species i [g C ·m−2]
SMiSubmerged biomass of macrophyte species i [g C ·m−2]
MaxSMiMaximum biomass for SM species i [g C ·m−2]
PotSMiPotential biomass for SM species i [g C ·m−2]
5.3.2 Hints for use
The competition between macrophyte species is not modelled as such. The species compo-
sition is fully determined by the user defined Habitat Suitability Indices. Table 5.1 shows some
examples.
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Table 5.1: Computation of the maximum biomass of three macrophyte species as a func-
tion of the Habitat Suitability Index.
example 1 parameter Name units species 1 species 2 species 3
HSI Habitat Suitability Index [-] 1 0 0
PotEM Potential biomass g/m21000 1000 1000
MaxEM Maximum biomass g/m21000 0 0
example 2 parameter Name units species 1 species 2 species 3
HSI Habitat Suitability Index [-] 1 1 1
PotEM Potential biomass g/m21000 1000 1000
MaxEM Maximum biomass g/m2333 333 333
example 3 parameter Name units species 1 species 2 species 3
HSI Habitat Suitability Index [-] 0.2 0.3 0.5
PotEM Potential biomass g/m21000 1000 1000
MaxEM Maximum biomass g/m2200 300 500
example 4 parameter Name units species 1 species 2 species 3
HSI Habitat Suitability Index [-] 0.2 0.3 0.5
PotEM Potential biomass g/m2500 1000 250
MaxEM Maximum biomass g/m2100 300 125
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5.4 Grazing and harvesting
PROCESS: GRZMACII AND HRVMACII
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.
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:
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 (<0.4m) ?.
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(5.26)
Else
GrazeEMi= 0
If SMi>(K0GrazeSMi+K1GrazeSMi×SMi)×dt:
GrazeSMi=K0GrazeSMi+K1GrazeSMi×SMi(5.27)
Else
GrazeSMi= 0
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If RHi>(K0GrazeRHi+K1GrazeRHi×RHi)×dt:
GrazeRHi=K0GrazeRHi+K1GrazeRHi×RHi(5.28)
GrazeNRHi=GrazeRHi×NHRi
RHi
GrazeP RHi=GrazeRHi×P HRi
RHi
Else
GrazeRHi= 0
GrazeNRHi= 0
GrazeP RHi= 0
where:
GrazeEMiGrazing of EM species i [g C·m−2·d−1]
K0GrazeEMiZero order grazing constant of EM species i [g C·m−2·d−1]
K1GrazeEMiFirst order grazing constant o fEM species i [d−1]
dt time step of the simulation [d]
GrazeSMiGrazing of SM species i [g C·m−2·d−1]
K0GrazeSMiZero order grazing constant of SM species i [g C·m−2·d−1]
K1GrazeSMiFirst order grazing constant of SM species i [d−1]
RHiRhizome species i [g C·m−2]
GrazeRHiGrazing of RH species i [g C·m−2·d−1]
K0GrazeRHiZero order grazing of RH species i [g C·m−2·d−1]
K1GrazeRHiFirst order grazing constant of RH species i [d−1]
GrazeNRHiGrazing of RH species i, nitrogen component [g N·m−2·d−1]
GrazePRHiGrazing of RH species I, phosphorus component [g P·m−2·d−1]
5.4.2 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=birds ×fooddemand
area (5.29)
where:
birds Number of birds in the colony [-]
fooddemand Amount of vegetation per bird per day [g C·d·−1]
area Lake area where the colony of birds is feeding [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 schemati-
sation.
5.4.3 Harvesting
Harvesting can be used as a management practise to reduce nuicance biomass (e.g. to im-
prove recreational values) or to remove nutrients from the system. Both emerged and sub-
merged vegetation can be removed from the water system. The harvesting can be modelled
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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:
HarvestSMi=K0HarvestSMi+K1HarvestSMi×SMi
ELSE
HarvestSMi= 0
where:
K0HarvestEMi Zero order harvesting of emerged vegetation [g C·m−2·d−1]
K1HarvestEMi First order harvesting constants of emerged vegetation [d−1]
dt Time step of computation [d]
HarvestEMi Harvesting of emerged vegetation [g C·m−2·d−1]
K0HarvestSMi Zero order harvesting of submerged vegetation [g C·m−2·d−1]
K1HarvestSMi First order harvesting constant of submerged vegetation [d−1]
HarvestSMi Harvesting of submerged vegetation [g C·m−2·d−1]
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5.5 Light limitation for macrophytes
PROCESS: RAD_SMII
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 (frad) is expressed as the ratio between the light intensity at the tip and the
satuaration light intensity:
frad = min(1,Itop
Isatii
)(5.30)
where:
frad light limitation factor [-]
Itop light intensity at the tip of the submerged part [-]
Isatii light intensity at which saturation occurs for submerged macrophyte ii [-]
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5.6 Vegetation coverage
PROCESS: COVERAGE
When a water body is covered by emerged macrophytes, the reaeration with oxygen and
the light intensity in the water are decreased. The parameter fcov 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.
5.6.1 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 au-
thors 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:
Itop1=Is ×(1 −f cov)(5.31)
where:
Itop1light intensity at the surface of the water layer (layer 1) [W·m−2]
Is light intensity at the water surface [W·m−2]
fcov fraction of the water surface covered by vegetation [-]
The light intensity of the subsequent layers is computed according by the process CalcRad,
see also Figure 5.4:
Itopn=Ibotn−1(5.32)
Ibotn=Itopn×e−ExvV ln×Hn(5.33)
where:
ExtVLnextinction of visible light in layer n [m−1]
Itop light intensity at the top of a water layer [W·m−2]
Ibot light intensity at the bottom of a water layer [W·m−2]
H thickness of the water layer, zn−1−zn[m]
n index for water layers [-]
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:
aamplification factor by scattering by sediment particles [-]
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Figure 5.4: The light intensity under water – explanation of the variables in the light inten-
sity functions.
The coverage fcov is calculated via:
fcov =X
i
EMi
MaxEMi
(5.35)
where:
CoverageEMiCoverage with emerged vegetation [-]
CoverageSMiCoverage with submerged vegetation [-]
fcov Total coverage on the basis of all emerged species [-]
EMiActual biomass emerged vegetation [g·m−2]
SMiActual biomass submerged vegetation [g·m−2]
MaxEMiMaximum biomass emerged vegetation [g·m−2]
MaxSMiMaximum biomass submerged vegetation [g·m−2]
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5.7 Vertical distribution of submerged macrophytes
PROCESS: MACDISII
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.
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.
5.7.1 Implementation
This process is implemented for different types of macrophytes, indicated by "ii" throughout
this document.
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 Ddepth of segment, layer thickness [m]
TotalDepth Ttotal depth water column [m]
LocalDepth Ldepth from water surface to bottom of segment [m]
SMii MTsubmerged macrophyte biomass in water column [gC/m2]
SwDisSMii type of macrophyte shape function (1: linear, 2: exponential)
HmaxSMii Hmax maximum height of macrohyte [m]
FfacSMii Fparameter F in shape function [-]
Figure 5.5 provides an overview of the geometrical quantities used in the calculation. Note
that the vertical co-ordinate zis 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 Fwith 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 Aand B, which
are formulated in terms of the total biomass MTand the shape parameter F:
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Figure 5.5: Definition of the quantities used for determining the linear vertical distribution.
m(z) = Az +B(5.36)
A=MT
Hmax
2−2F
T−zm
B=MT
Hmax
F(zm+T)−2zm
T−zm
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=Z1to 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 =RZ2
Z1m(z)dz
Else (top of plant inside layer): M12 =RZ2
Zmm(z)dz
By integrating the mass distribution function we can derive the biomass in the layer, e.g.:
ZZ2
Z1
m(z)dz =A
2(Z2
2−Z2
1) + B(Z2−Z1)(5.37)
The module calculates the following output items for submerged macrophyte species ii:
FrBmSMii Fraction of the macrophyte biomass in present layer [-]
BmLaySMii Macrophyte biomass density in present layer [gC/m3]
The fraction of the biomass in a layer from z=Z1to z=Z2is calculated as M12/MT.
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Figure 5.6: Definition of the quantities used for determining the exponential vertical distri-
bution.
5.7.1.2 Exponential distribution (SwDisSMii=2)
The exponential shape function is defined on an inverse vertical co-ordinate z’, which is de-
fined as (see also Figure 5.7):
z0=T−z(5.38)
The value of z0equals 0 at the bottom and it equals Hmax at the tip of the plant.
The mass distribution function is defined as follows:
m(z0) = A·eF z0/Hmax −1(5.39)
The shape function is defined by means of one parameter F. The constant Ais determined
by requiring that the integrated mass equals the total mass MT. A value of Fapproaching
0 defines a linear distribution. Increasing values of Fdefine a stronger and stronger con-
centration of the biomass near the plant tip (see ??). The value of A can be determined as:
A=MT
HmaxeF−1
F−1(5.40)
Consequently, the algorithm to calculate the biomass in a layer from z0=Z0
1to z0=Z0
2
proceeds as follows:
If Z0
1> Hmax (layer above top of plant): M12 = 0
If Z0
2< Hmax (layer entirely below top of plant): M12 =RZ0
2
Z0
1m(z0)dz0
Else (top of plant inside layer): M12 =RHmax
Z0
1m(z0)dz0
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(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.
By integrating the mass distribution function we can derive the biomass in the layer, e.g.:
ZZ0
2
Z0
1
m(z0)dz0=A·Hmax
eF Z0
2/Hmax −eF Z0
1/Hmax
F−(Z0
2−Z0
1)(5.41)
5.7.2 Hints
The module uses a work array ("IBotSeg") which is filled during the first call. This work ar-
ray 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 Fcan range from a small positive num-
ber 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:
FShare of biomass in top 10%
0.1 19
2 26
4 36
6 46
8 55
10 63
15 78
20 87
25 93
30 96
The maximum allowable value for Fis 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.
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6 Light regime
Contents
6.1 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
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6.1 Light intensity in the water column
PROCESS: CALCRAD, CALCRADDAY, CALCRAD_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.
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.
Implementation
Processes CALCRAD and CALCRADDAY deliver the intensity of total visible light (solar ra-
diation) 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. CAL-
CRADDAY 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.
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 total extinction coefficient [m−1]
Hthickness of the water layer [m]
Is light intensity at the water surface, just below the surface [W.m−2]
Itop light intensity at the top of a water layer [W.m−2]
Ibot light intensity at the bottom of a water layer [W.m−2]
iindex 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:
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aamplification factor due to scattering by sediment particles [-]
Hthickness of a sediment layer [m]
Itop light intensity at the top of a sediment layer [W.m−2]
Ibot light intensity at the bottom of a sediment layer [W.m−2]
iindex for sediment layer [-]
Itop at the sediment-water interface is equal to Ibot of the lower water layer.
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_UV is derived from RadSurf, when process CALCRAD_UV is active. Alterna-
tively it can be imposed as input parameter, but this is only applicable for a model with one
water layer. Process BACMORT converts Rad_UV 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
-
et ExtV l total extinction coefficient of vivible light m−1
Is Radsurf light intensity at water surface W.m−2
z1Depth thickness of a water or sediment layer m
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Table 6.2: Definitions of the output parameters for CALCRAD.
Name in
formulas
Name in
output
Definition Units
Itop Rad light intensity at the top of a water or sed-
iment layer
W.m−2
Ibot RadBot 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
formulas
Name in
output
Definition Units
a a_enh amplification factor due to scattering by
sed. particles
-
et ExtVl total extinction coefficient of visible light m−1
Is DayRadsurf light intensity at the water surface W.m−2
H 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 sed-
iment layer
W.m−2
Ibot DayRadBot light intensity at the bottom of a water or
sediment layer
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
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Table 6.6: Definitions of the output parameters for CALCRAD_UV.
Name in
formulas
Name in
output
Definition Units
Itop Rad_Uv1light intensity at the top of a water or sed-
iment layer
W.m−2
Ibot RadBot_Uv1light intensity at the bottom of a water or
sediment layer
W.m−2
1Total visible light or PAR as based on UV extinction!
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6.2 Extinction coefficient of the water column
PROCESS: EXTINC_VLG, EXTINABVLP (EXTINABVL), EXTPHDVL, EXTINC_UVG,
EXTINABUVP (EXTINABUV), EXTPHDUV
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.
Due to extinction the light intensity in the water column is reduced compared to the inten-
sity 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 sub-
stances 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 spe-
cific 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 sub-
stances DOC or accounted for in the background extinction coefficient, or in a salinity related
extinction coefficient.
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 sub-
stances. 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 avail-
able 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 pro-
cesses 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-
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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.
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.
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 param-
eters 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 _Uitz = 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 partial extinction coefficient of algae biomass [m−1]
eb background extinction coefficient [m−1]
edt partial extinction coefficient of dissolved organic matter [m−1]
ept partial extinction coefficient of particulate detritus [m−1]
emt partial extinction coefficient of macrophytes [m−1]
est partial extinction coefficient of suspended inorganic matter [m−1]
eot partial extinction coefficient of other substances as a function of salinity [m−1]
et partial extinction coefficient [m−1]
The background extinction coefficient and the partial extinction coefficient of macrophytes are
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input parameters. The other contributions are determined according to:
eat =
n
X
i=1
(eai×Calgi)
ept =
m
X
j=1
(epj×Cpocj)
edt =ed ×Cdoc
est =
3
X
k=1
(esk×Cimk)
eot =eo ×(1 −SAL/SALmax)
where:
Calgibiomass concentration of algae species group i [gC.m−3]
Cdetjconcentration of detritus component j [gC.m−3]
Cimkconcentration of suspended inorganic matter fraction k [gC.m−3]
ea specific extinction coefficient of an algae species type [m2.gC−1]
ed specific extinction coefficient of dissolved organic carbon [m2.gC−1]
eo spec. ext. coefficient of other substances based on relative salinity [m−1]
ep specific extinction coefficient of a particulate detritus component [m2.gC-1]
es spec. ext. coefficient of a suspended inorganic matter fraction [m2.gDM−1]
SAL actual salinity ([g.kg−1]≈[g.l−1])
SALmax maximal salinity ([g.kg−1]≈[g.l−1])
iindex for algae species [-]
jindex for detritus components [-]
kindex for suspended inorganic matter fractions [-]
nnumber for algae species, =30 for BLOOM, = 2 for DYNAMO [-]
mnumber of detritus components, =4 for POX [-]
Besides to the total extinction coefficient the processes deliver the partial extinction coeffi-
cients of algae biomass, particulate detritus, dissolved organic matter and suspended inor-
ganic matter.
For SW _Uitz = 1.0 the auxiliary process UITZICHT (Rijkswaterstaat, 1990) is applied for
the calculation of the extinction coefficients based on a background extinction and the con-
centrations 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.
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UITZICHT is applied when SW _Uitz = 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-
tensity is calculated as UV light, and specify the specific extinction coefficients for UV
light.
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Table 6.7: Definitions of the input parameters in the formulations for Extinc_VLG.
Name in
formulas
Name in
input
Definition Units
Cim1IM1conc. of inorg. susp. matter fraction 1 gDM.m−3
Cim2IM2conc. of inorg. susp. matter fraction 2 gDM.m−3
Cim3IM3conc. of inorg. susp. matter fraction 3 gDM.m−3
Cpoc1P OC1concentration of fast dec. part. detritus gC.m−3
Cpoc2P OC2conc. of medium dec. part. detritus gC.m−3
Cpoc3P OC3concentration of slow dec. part. detritus gC.m−3
Cpoc4P OC4concentration of refractory part. detritus gC.m−3
Cdoc DOC concentration of dissolved organic carbon gC.m−3
SAL Salinity actual salinity psu(g.kg−1)
eat ExtV lP hyt partial ext. coeff. of algae biomass m−1
eb ExtV lBak background extinction coefficient m−1
ep1ExtV lP OC1specific ext. coefficient of detritus POC1 m2.gC−1
ep2ExtV lP OC2specific ext. coefficient of detritus POC2 m2.gC−1
ep3ExtV lP OC3specific ext. coefficient of detritus POC3 m2.gC−1
ep4ExtV lP OC4specific ext. coefficient of detritus POC4 m2.gC−1
ed ExtV lDOC specific ext. coeff. of diss. detritus DOC m2.gC−1
emt ExtV lMacro partial ext. coefficient of macrophytes m−1
eo ExtV lSal0spec. ext. coeff. other subst. based on rel.
salinity
m−1
es1ExtV lIM1spec. ext. coefficient of inorg. matter IM1 m2.gDM−1
es2ExtV lIM2spec. ext. coefficient of inorg. matter IM2 m2.gDM−1
es3ExtV lIM3spec. ext. coefficient of inorg. matter IM3 m2.gDM−1
SALmax SalExt0maximal salinity psu(g.kg−1)
SW _Uitz Sw_Uitz1option parameter: if 0.0 no UITZICHT (de-
fault), if 1.0 UITZICHT is applied
-
–UitzDEP T 11diepte Z1m
–UitzDEP T 21diepte Z2m
–UitzCorCH1correctiefactor -
–UitzC_Det1coeff. C3 absorp. by glowing dried matter
and detritus
-
–UitzC_GL11coeff. C1 atten. by glowing dried matter
and detritus
-
–UitzC_GL21coeff. C2 atten. by glowing dried matter
and detritus
nm−1
–UitzHelHM1constant for the spectre -
–UitzT au1constant for calc. of the visibility depth -
–UitzAngle1angle of incidence of solar radiation ◦
–DMCF DetC1dry matter conversion factor for detritus gDM.gC−1
1Only concern alternative calculation method according to UITZICHT.
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Table 6.8: Definitions of the input parameters in the formulations for ExtinaBVLP (Extin-
aBVL) for BLOOM algae.
Name in
formulas
Name in
input1
Definition Units
CalgiBLOOMALG(i)biomass concentration of algae species
type i
gC.m−3
eaiExtV lAlg(i)algae species type specific extinction coef-
ficient
m2.gC−1
n NAlgBloom2number of algae species groups = 30 -
–SW _fixin_y2indicator for algae species attached to the
sediment = 1
-
–V olume3volume of water compartment or sediment
layer
m3
–F ixAlg(i)3identifier for pairs of algae types attaching
to sediment (0 = not applying, >0= sus-
pended, <0= attached)
-
1(i) indicates algae species types 1–30.
2Default values are fixed and must not be changed because they refer to additional input
F ixAlg(i).
3Parameters are added for conversion of biomass of algae attached to the sediment from
[gC.m−2] to [gC.m−3].
Table 6.9: Definitions of the input parameters in the formulations for ExtPhDVL.
Name in
formulas
Name in
input
Definition Units
Calg1Diat biomass concentration of diatoms gC.m−3
Calg2Green biomass concentration of green algae gC.m−3
ea1ExtV lDiat specific ext. coefficient for diatoms m2.gC−1
ea2EXtV lGreen specific ext. coefficient for green algae m2.gC−1
n NAlgDynamo1number of algae species groups = 2 -
–SW _fixin_y1indicator for algae species attached to the
sediment = 0
-
–V olume volume of water compartment or sediment
layer
m3
1The default values are fixed and must not be changed!
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Table 6.10: Definitions of the output parameters for Extinc_VLG, ExtinaBVLP (Extin-
aBVL), ExtPhDVL.
Name in
formulas
Name in
output1
Definition Units
eat ExtV lP hyt partial ext. coefficient of algae biomass m−1
edt ExtV lODS partial ext. coeff. of dissolved org. matter m−1
ept ExtV lOSS partial ext. coefficient of part. detritus m−1
est ExtV lISS partial ext. coeff. of susp. inorg. matter m−1
et ExtV l total extinction coefficient m−1
1Notice that the partial extinction coefficients ExtV lBak and ExtV lMacro are input pa-
rameters
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Table 6.11: Definitions of the input parameters in the formulations for Extinc_UVG.
Name in
formulas
Name in
input
Definition Units
Cim1IM1conc. of inorg. susp. matter fraction 1 gDM.m−3
Cim2IM2conc. of inorg. susp. matter fraction 2 gDM.m−3
Cim3IM3conc. of inorg. susp. matter fraction 3 gDM.m−3
Cpoc1P OC1concentration of fast dec. part. detritus gC.m−3
Cpoc2P OC2conc. of medium dec. part. detritus gC.m−3
Cpoc3P OC3concentration of slow dec. part. detritus gC.m−3
Cpoc4P OC4concentration of refractory part. detritus gC.m−3
Cdoc DOC concentration of dissolved organic carbon gC.m−3
SAL Salinity actual salinity psu(g.kg−1)
eat ExtUvP hyt partial ext. coeff. of algae biomass m−1
eb ExtUvBak background extinction coefficient m−1
ep1ExtUvP OC1specific ext. coefficient of detritus POC1 m2.gC−1
ep2ExtUvP OC2specific ext. coefficient of detritus POC2 m2.gC−1
ep3ExtUvP OC3specific ext. coefficient of detritus POC3 m2.gC−1
ep4ExtUvP OC4specific ext. coefficient of detritus POC4 m2.gC−1
ed ExtUvDOC specific ext. coeff. of diss. detritus DOC m2.gC−1
emt ExtUvMacro partial ext. coefficient of macrophytes m−1
eo ExtUvSal0spec. ext. coeff. other subst. based on rel.
salinity
m−1
es1ExtUvIM1spec. ext. coefficient of inorg. matter IM1 m2.gDM−1
es2ExtUvIM2spec. ext. coefficient of inorg. matter IM2 m2.gDM−1
es3ExtUvIM3spec. ext. coefficient of inorg. matter IM3 m2.gDM−1
SALmax SalExt0maximal salinity psu(g.kg−1)
SW _Uitz Sw_Uitz1option parameter: if 0.0 no UITZICHT (de-
fault), if 1.0 UITZICHT is applied
-
–UitzDEP T 11diepte Z1m
–UitzDEP T 21diepte Z2m
–UitzCorCH1correctiefactor -
–UitzC_Det1coeff. C3 absorp. by glowing dried matter
and detritus
-
–UitzC_GL11coeff. C1 atten. by glowing dried matter
and detritus
-
–UitzC_GL21coeff. C2 atten. by glowing dried matter
and detritus
nm−1
–UitzHelHM1constant for the spectre -
–UitzT au1constant for calc. of the visibility depth -
–UitzAngle1angle of incidence of solar radiation ◦
–DMCF DetC1dry matter conversion factor for detritus gDM.gC−1
1Only concern alternative calculation method according to UITZICHT.
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Table 6.12: Definitions of the input parameters in the formulations for ExtinaBUVP (Ex-
tinaBUV) for BLOOM algae.
Name in
formulas
Name in
input1
Definition Units
CalgiBLOOMALG(i)biomass concentration of algae species
type i
gC.m−3
eaiExtUvAlg(i)algae species type specific extinction coef-
ficient
m2.gC−1
n NAlgBloom2number of algae species groups = 30 -
–SW _fixin_y2indicator for algae species attached to the
sediment = 1
-
–V olume3volume of water compartment or sediment
layer
m3
–F ixAlg(i)3identifier for pairs of algae types attaching
to sediment (0 = not applying, >0= sus-
pended, <0= attached)
-
1(i) indicates algae species types 1–30.
2Default values are fixed and must not be changed because they refer to additional input
F ixAlg(i).
3Parameters are added for conversion of biomass of algae attached to the sediment from
[gC.m−2] to [gC.m−3].
Table 6.13: Definitions of the input parameters in the formulations for ExtPhDUV.
Name in
formulas
Name in
input
Definition Units
Calg1Diat biomass concentration of diatoms gC.m−3
Calg2Green biomass concentration of green algae gC.m−3
ea1ExtUvDiat specific ext. coefficient for diatoms m2.gC−1
ea2EXtUvGreen specific ext. coefficient for green algae m2.gC−1
n NAlgDynamo1number of algae species groups = 2 -
–SW _fixin_y1indicator for algae species attached to the
sediment = 0
-
–V olume volume of water compartment or sediment
layer
m3
1The default values are fixed and must not be changed!
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Table 6.14: Definitions of the output parameters for Extinc_UVG, ExtinaBUVP (Ex-
tinaBUV), ExtPhDUV.
Name in
formulas
Name in
output1
Definition Units
eat ExtUvP hyt partial ext. coefficient of algae biomass m−1
edt ExtUvODS partial ext. coeff. of dissolved org. matter m−1
ept ExtUvOSS partial ext. coefficient of part. detritus m−1
est ExtUvISS partial ext. coeff. of susp. inorg. matter m−1
et ExtUv total extinction coefficient m−1
1Notice that the partial extinction coefficients ExtUvBak and ExtUvMacro are input pa-
rameters
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6.3 Variable solar radiation during the day
PROCESS: DAYRAD
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.
Implementation
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.
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
tat day dand latitude φ:
Et=I0
π
¯
R2
R2(sin δsin φ+ cos δcos φcos ω)
where:
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
¯
R2
R2= 1 + 0.033 cos(ηd)
ω=|12 −h| × π
12
and:
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Etmaximum solar irradiance at time t [W.m−2]
I0sun constant = 1367 [W.m−2]
dday of the year (1-366; 1 = 1 January, 365 = 31 December) [d]
¯
R2
R2relative difference of distance earth-sun compared to average distance [-]
δangle between sun and earth surface at specific day [rad]
ωangle between sun and earth surface at hour h [rad]
hhour of the day [h]
φlatitude [rad]
The parameters above are calculated from the input parameters as follows:
d=IT IM E
86400 −Refday
h=IT IM E −int(Refday)×86400 −Reftime
3600
φ=Latitude
360 ×2π
where:
IT IM E DELWAQ time [scu]
Latitude latitude of area of interest [degrees]
RefDay day at start of the simulation [d]
Reftime 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
πׯ
R2
R2×(ω0sin δsin φ+ cos δcos φsin ω0)
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.
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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 Latitude thickness of a water or sediment layer degrees
Refday Refday time at the start of the simulation -
Table 6.16: Definitions of the output parameters for DAYRAD.
Name in
formulas
Name in
output
Definition Units
DayRad DayRadSurf actual light intensity at water surface as
varying over the day
W.m−2
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6.4 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
Formulation
E= 0.01721420632
Declin = 0.006918−
0.399921 ×cos(1 ×E×DayNr)−
0.006758 ×cos(2 ×E×DayNr)−
0.002697 ×cos(3 ×E×DayNr)+
0.070257 ×sin(1 ×E×DayNr)+
0.000907 ×sin(2 ×E×DayNr)+
0.001480 ×sin(3 ×E×DayNr)
T mp =−0.01454389765 −sin(Declin)×sin(LatRad)
cos(Declin)×cos(LatRad)
If T mp > 1.0
DayL = 0.0(6.1)
If T mp < −1.0
DayL = 1.0(6.2)
Else
DayL = 7.639437268 ×arccos(T mp)/24 (6.3)
ITIME DELWAQ time [scu]
Latitude latitude of area of interest [degr]
LatRad latitude of area of interest [rad]
DayNr number of the day for the calculation of the day length (1=1 January, 365 = 31
December) [-]
RefDay day at start of the simulation [d]
DayL daylength (fraction of a day - sunrise to sunset) [-]
Tmp temporarily variable for calculation [d]
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0 50 100 150 200 250 300 350
0
0.25
0.5
0.75
1
Day length as function of time of year
day number
(d)
latitude = 75
latitude = 65
latitude = 52.1
latitude = 10
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 Jan-
uary. 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 ref-
erence 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)
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6.5 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.
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.
Implementation
The auxiliary process SECCHI has been implemented for the following substances:
IM1, IM2, IM3, POC1, POC2, POC3, POC4.
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 _Uitz = 0.0 (UITZICHT not applied) the Poole-Atkins relation is applied:
SD =apa
et
where:
apa Poole-Atkins constant (1.7-1.9) [-]
et total extinction coefficient [m−1]
SD Secchi depth [m]
For SW _Uitz = 1.0 the auxiliary process UITZICHT is applied for the calculation of the Sec-
chi 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 IM1, IM2, IM3, P OC1, P OC2, P OC3and P OC4are only
used if auxiliary process UITZICHT is applied for the calculation of the total extinction
coefficient.
UITZICHT is applied when SW _Uitz = 1.0. In that case a number of additional input pa-
rameters are needed, among which ExtV LODS (partial extinction coefficient dissolved
organic matter) calculated by process ExtincVLG and Chlfa calculated by the active
phytoplankton module.
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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 -
et ExtV l total extinction coefficient m−1
SW _Uitz Sw_Uitz option parameter: if 0.0 no UITZICHT (de-
fault), if 1.0 UITZICHT is applied
-
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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) . . . . . . . . . . . . 199
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7.1 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, phospho-
rus 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.
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.
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 respi-
ration on the dissolved oxygen budget is ignored in the model.
The process formulations of CONSBL have been described in more detail by WL | Delft Hy-
draulics (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
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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)UnitSW 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 re-
leased 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.).
CONSBL has been implemented for the following substances:
for BLOOM,
ALGC, ALGN, ALGP, ALGSi, BLOOMALG01-BLOOMALG30, POC1, PON1, POP1, OPAL,
DETCS1, DETNS1, DETPS1, DETSiS1, NH4, NO3, PO4, Si, OXY, TIC and ALKA
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)UnitSW , with which the grazer biomass unit
can be selected for each grazer species group. When (i)UnitSW = 0.0the model as-
sumes that biomass concentrations provided in the input are expressed in [gC m−3]. When
(i)UnitSW = 1.0the 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
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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 t2is 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,
Cgrci=Cgr1i×(1 + kgri×∆t)
Cgr2i=Cgrciif Cgri2i> Cgrci
Cgr2i=Cgri2iif Cgri2i≤Cgrci
kgri=kgr20
i×ektgri×(T−20)
when Cgri2i< Cgr1i,
Cgrci=Cgr1i×(1 −kmrti×∆t)
Cgr2i=Cgrciif Cgri2i< Cgrci
Cgr2i=Cgri2iif Cgri2i≥Cgrci
kmrti=kmrt20
i×ektgri×(T−20)
with:
Cgr1igrazer biomass concentration at t1[ gC m−3]
Cgr2igrazer biomass concentration at t2[ gC m−3]
Cgrcigrazer biomass concentration constraint at t2[ gC m−3]
Cgri2iimposed grazer biomass concentration at t2[ gC m−3]
kgr maximal growth rate [d−1]
kgr20 maximal growth rate at 20 ◦C [d−1]
ktgr temperature coefficient of growth [-]
kmrt maximal natural mortality rate [d−1]
kmrt20 maximal natural mortality rate at 20 ◦C [d−1]
ktmrt temperature coefficient of mortality [-]
Twater temperature [◦C]
∆ttimestep [d]
iindex 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 Cfdci. 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
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grazers. Certain phytoplankton species and detritus fractions are more difficult to filtrate and
digest for the grazers than others.
Cfdi=fdpri×Cdet1+
m
X
j=1
(fapri×Calgj)
with:
Calgjbiomass concentration of algae species group j[ gC m−3]
Cfdifood concentration available to grazer species group i[ gC m−3]
Cdet1detritus organic carbon concentration [ gC m−3]
fdpripreference of a grazer species group ifor detritus [-]
fapri,j preference of a grazer species group ifor algae species group j[-]
mnumber of algae groups, different for (BLOOM) and (DYNAMO) [-]
iindex for grazer species groups (at most 5) [-]
jindex for algae species groups (depends on whether BLOOM is used or DY-
NAMO) [-]
The maximal filtration rate and the maximal uptake rate are defined as:
kfili=Cgr1i×ksfili×Cfdi
Ksfdi+Cfdi
ksfili=ksfil20
i×ektf ili×(T−20)
kupi=Cgr1i×kmupi
Cfdi
kmupi=kmup20
i×ektupi×(T−20)
with:
kfil filtration rate [d−1]
ksfil maximal specific filtration rate [m3gC−1d−1]
ksfil20 maximal specific filtration rate at 20 ◦C [m3gC−1d−1]
ktfil temperature coefficient for filtration [-]
kup uptake rate [d−1]
kmup maximal uptake rate [d−1]
kmup20maximal uptake rate at 20 ◦C [d−1]
ktup temperature coefficient for uptake [-]
Ksfd half saturation constant for uptake [gC m−3]
iindex 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:
Cfdci=kmupi
ksfili×Ksfdi+Cfdi
Cfdi
with:
Cfdcicritical concentration of food for grazer group i[gC m−3]
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The consumption process rate is equal to either the filtration or the uptake rate according to:
kcnsi=kfiliif Cfdi < Cf dci
kcnsi=kupiif Cfdi ≥Cfdci
with:
kcnsiconsumption process rate of grazer group i[d−1]
So far, all rates are referring to organic carbon as a nutrient to grazers. Since the nutrient sto-
chiometry 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:
Rdcns1k,i =fdpri×kcnsi×Cdetk
Racnsk,i,j =fapri,j ×kcnsi×anutk,j ×Calgj
with:
anutk,j stochiometric const. of nutr. kover org. carbon in algae j[gC/N/P/Si gC−1]
Cdetkdetritus concentration for nutrient k[gC/N/P/Si m−3]
fdpripreference of a grazer species group ifor detritus [-]
fapri,j preference of a grazer species group ifor algae species group j[-]
Racnsk,i,j cons. rate of grazer group ifor nutrient kin algae j[gC/N/P/Si m−3d−1]
Rdcns1k,i gross cons. rate of grazer group ifor nutrient kin detritus [gC/N/P/Si m−3d−1]
iindex for grazer species groups 1–5 [-]
jindex for algae species groups 1–15 (BLOOM) or 1–2 (DYNAMO) [-]
kindex 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 −fdeti)×Rdcns1k,i +
m
X
j=1
((1 −falgi,j)×Racnsk,i,j)
Rdcns2k,i = (1 −fdeti)×Rdcns1k,i+
m
X
j=1
((1 −falgi,j ×(1 −fsedi)) ×Racnsk,i,j )
Rsdpr1k,i =fdeti×fsedi×Rdcns1k,i +
m
X
j=1
(falgi,j ×fsedi×Racnsk,i,j)
with:
falgi,j egested fraction of algae j consumed by grazer i, = 1-yield [-]
fdetiegested fraction of detritus consumed by grazer i, = 1-yield [-]
fsedifraction of detritus egested by grazer iadded to the sediment detritus pool [-]
Ras1k,i total food assimilation rate for nutrient kfor grazer group i[gC/N/P/Si m−3d−1]
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Rdcns2k,i net cons. rate of grazer group ifor nutrient kin detritus [gC/N/P/Si m−3d−1]
Rsdpr1k,i total nutrient kin detr. prod. at the sediment for all grazers [gC/N/P/Si m−3d−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.
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 assimila-
tion rate the gross assimilation rate needs to be corrected for respiration.
The actual assimilation rates and the respiration rates follow from:
Ras21,i = min
k=1−4(Ras1k,i/bnutk,i)
Rrsp1k,i =bnutk,i ×frsp1i×Ras21,i
Rrsp2k,i =bnutk,i ×krsp2i×Cgr1i
Rrspk,i =Rrsp1k,i +Rrsp2k,i
Ras3k,i =Ras2k,i −Rrspk,i
frsp1i=frsp120
i×ektrsp1i×(T−20)
krsp2i=krsp220
i×ektrsp2i×(T−20)
with:
bnutk,i stochiometric const. of nutr. kover org. carbon in grazer i[gC/N/P/Si gC−1]
Cgr1igrazer biomass concentration at t1[gC m−3]
frsp1igrowth respiration fraction [-]
frsp120
igrowth respiration fraction at 20 ◦C [-]
ktrsp1temperature coefficient for growth respiration [-]
krsp2imaintenance respiration rate [d−1]
krsp220
imaintenance respiration rate at 20 ◦C [d−1]
ktrsp2temperature coefficient for maintenance respiration [-]
Rrspk,i total respiration rate for nutrient kand grazer i[gC/N/P/Si m−3d−1]
Rrsp1k,i growth respiration rate for nutrient kand grazer i[gC/N/P/Si m−3d−1]
Rrsp2k,i maintenance respiration rate for nutrient kand grazer i[gC/N/P/Si m−3d−1]
Ras2k,i actual nutrient kin food ass. rate for grazer group i[gC/N/P/Si m−3d−1],
Ras3k,i actual nutrient kin food ass. rate for grazer group i[gC/N/P/Si m−3d−1], di-
minished 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
t2is larger than supported by food assimilation, it must be diminished in order to meet the
food constraint. The corrected grazer biomass Cgr2cifollows from:
Rgr1i=(Cgr2i−Cgr1i×(1 −krsp2i×∆t))
∆t
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if Rgr1i> Ras31,i,
Cgr2ci=Cgr1i×(1 −krsp2i×∆t) + Ras31,i ×∆t
Rgri=Ras31,i
if Rgr1i≤Ras31,i,
Cgr2ci=Cgr2i
Rgri=Rgr1i
with:
Cgr1igrazer biomass concentration at t1[ gC m−3]
Cgr2igrazer biomass concentration at t2[ gC m−3]
Cgr2cicorrected grazer biomass concentration at t2 [ gC m−3]
Rgriactual growth rate for grazer group i[ gC m−3d−1]
Rgr1iimposed growth rate for grazer group i[ gC m−3d−1]
∆ttimestep [d]
Notice that Rgriis 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 −fsedi)×(Ras3k,i −Rask,i)
Rsdprk,i =Rsdpr2k,i +fsedi×(Ras3k,i −Rask,i)
with:
Rask,i nutrient kin food assimilation rate for grazer group i[gC/N/P/Si m−3d−1],
Rdcnsk,i net cons. rate of grazer group ifor nutrient kin detritus [gC/N/P/Si m−3d−1]
Rsdprk,i nutrient kin detr. prod. at the sediment for grazer i[gC/N/P/Si m−3d−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
i=1
(Racnsk,i,j)
Rtacnsk=
m
X
j=1
(Racnsk,j)
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Rtask=
n
X
i=1
(Rask,i)
Rtdcnsk=
n
X
i=1
(Rdcnsk,i)
Rtsdprk=
n
X
i=1
(Rsdprk,i)
Rtrspk=
n
X
i=1
(Rrspk,i)
with:
Racnsk,j total consumption rate for nutrient kin algae group j[gC/N/P/Si m−3d−1]
Rtacnsktotal consumption rate for nutrient kin algae [gC/N/P/Si m−3d−1]
Rtasktotal food assimilation rate for nutrient k[gC/N/P/Si m−3d−1]
Rtdcnsktotal consumption rate for nutrient kin detritus [gC/N/P/Si m−3d−1]
Rtrspktotal release rate for inorganic nutrient kby respiration [gC/N/P/Si m−3d−1]
Rtsdprktotal nutrient kin detr. prod. at the sediment for all grazers [gC/N/P/Si m−3d−1]
nnumber of grazer species groups (5; [-])
mnumber of algae species groups (2 for DYNAMO or 15 for BLOOM; [-])
iindex for grazer species groups [-]
jindex for algae species groups [-]
kindex for nutients, 1 = carbon, 2 = nitrogen, 3 = phosphorus, 4 = silicon [-]
9. Grazer biomass concentrations
CONSBL delivers some additional output parameters in the form of the biomass concen-
trations 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 t1at the beginning of the next timestep:
Cgr1i=Cgr2ci/fsi
with:
fsiscaling factor for the biomass of grazer group i[-]
The scaling factor fsimay 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)UnitSw, 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 = 0.0all detritus by
grazers will be allocated to the sediment overlying water compartment (layer). All pro-
duced detritus will be added to the sediment detritus pools when (i)F rDetBot = 1.0.
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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
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)GRZML 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 sub-
stances input that does no longer exist.
Additional references
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 Units
anut2,1NCratGreen green algae spec. stoch. constant nitro-
gen over carbon
gN gC−1
anut2,2NCratDiat diatoms spec. stoch. constant nitrogen
over carbon
gN gC−1
anut2,j NCRAlg(j)BLOOM algae group spec. stoch. const.
nitr. over carb.
gN gC−1
anut3,1P CratGreen green algae spec. stoch. constant phos.
over carbon
gP gC−1
anut3,2P CratDiat diatoms spec. stoch. constant phospho-
rus over carbon
gP gC−1
anut3,j P CRAlg(j)BLOOM algae group spec. stoch. const.
phos. over carb.
gP gC−1
anut4,1SCratGreen green algae spec. stoch. constant silicon
over carbon
gSi gC−1
anut4,2SCratDiat diatoms spec. stoch. constant silicon over
carbon
gSi gC−1
anut4,j SCRAlg(j)BLOOM algae group spec. stoch. const.
sil. over carb.
gSi gC−1
Cgri21Zooplank biomass concentration of zooplankton gC m−3or −2
Cgri22Mussel biomass concentration of mussel type
zoobenthos
gC m−3or −2
Cgri23Grazer3biomass concentration of grazer type 3 gC m−3or −2
Cgri24Grazer4biomass concentration of grazer type 4 gC m−3or −2
Cgri25Grazer5biomass concentration of grazer type 5 gC m−3or −2
Calg1Green biomass concentration of green algae
(DYNAMO)
gC m−3
continued on next page
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Table 7.1 – continued from previous page
Name in
formulas
Name in input Definition Units
Calg2Diat biomass concentration of diatoms (DY-
NAMO)
gC m−3
Calgj BLOOMALG(j)biomass concentration of a BLOOM al-
gae group
gC m−3
Cdet1P OC1detritus organic carbon concentration gC m−3
Cdet2P ON1detritus nitrogen concentration gN m−3
Cdet3P OP 1detritus phosphorus concentration gP m−3
Cdet4Opal opal silicate concentration gSi m−3
H Depth depth of a water compartment (layer) m
–(i)UnitSW group spec. option for biomass unit (1=g
m−2, 0=g m−3)
-
T T emp water temperature ◦C
V V olume volume of a water comp. (layer) or sedi-
ment layer
m3
∆t DELT time interval, that is the DELWAQ
timestep
d
bnut1,i (i)GRZST C stoch. constant for carbon over carbon in
grazer i
gC gC−1
bnut2,i (i)GRZST N stoch. constant for nitrogen over carbon
in grazer i
gN gC−1
bnut3,i (i)GRZST P stoch. constant for phosphorus over car-
bon in grazer i
gP gC−1
bnut4,i (i)GRZST Si stoch. constant for silicon over carbon in
grazer i
gSi gC−1
fapri,1(i)ALGP RGrn preference of grazer ifor green algae
(DYNAMO)
-
fapri,2(i)ALGP RDiatpreference of grazer ifor diatoms (DY-
NAMO)
-
fapri,j (i)ALGP R(j)preference of grazer ifor BLOOM algae
group j
-
fdpri(i)DET P R preference of grazer ifor detritus -
falgi,1(i)ALGF F Grnegested fraction of green algae con-
sumed by grazer i
-
falgi,2(i)ALGF F Diategested fraction of diatoms consumed by
grazer i
-
falgi,j (i)ALGF F (j)egested fraction of algae jconsumed by
grazer i
-
fdeti(i)DET F F egested fraction of detritus consumed by
grazer i
-
fsedi(i)F rDetBot fr. of produced detr. by grazer ito sedi-
ment detr. pool
-
continued on next page
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Table 7.1 – continued from previous page
Name in
formulas
Name in input Definition Units
fsi(i)GRZML scaling factor for the biomass of grazer i-
frsp120
i(i)GRZRE growth respiration fraction for grazer iat
20 ◦C
-
kgr20
i(i)GRZGM maximal growth rate of grazer iat 20 ◦C d−1
kmup20
i,k (i)GRZRM maximal uptake rate of grazer iat 20 ◦C d−1
kmrt20
i(i)GRZMM maximal mortality rate of grazer iat 20
◦C
d−1
krsp220
i(i)GRZSE maintenance respiration rate for grazer i
at 20 ◦C
d−1
Ksfdi(i)GRZMO half saturation constant for food uptake
by grazer i
gC m−3+
ksfil20
i(i)GRZF M maximal specific filtration rate of grazer i
at 20 ◦C
m3gC−1d−1
ktfil (i)TMPFM temperature coefficient of filtration for
grazer i
◦C−1
ktgr (i)T M P GM temperature coefficient of growth for
grazer i
◦C−1
ktmrt (i)T MP MM temperature coefficient of mortality for
grazer i
◦C−1
ktrsp1 (i)T MP RE temperature coeff. of growth respiration
for grazer i
◦C−1
ktrsp2 (i)T MP SE temperature coeff. of maintenance resp.
for grazer i
◦C−1
ktup (i)T MP RM temperature coefficient of uptake for
grazer i
◦C-1
1(i) indicates grazer species groups 1–5, respectively Z for zooplankton, M for mus-
sel 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 out-
put
Definition Units
Cgr11CZooplank biomass concentration of zooplankton gC m−3or −2
Cgr12CMussel biomass concentration of mussel type
zoobenthos
gC m−3or −2
Cgr13CGrazer3biomass concentration of grazer type 3 gC m−3or −2
Cgr14CGrazer4biomass concentration of grazer type 4 gC m−3or −2
Cgr15CGrazer5biomass concentration of grazer type 5 gC m−3or −2
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7.2 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.
The grazer module DEBGRZ simulates grazing using a fully dynamic approach, which con-
trasts 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.
Implementation
The module allows for maximally 5 different grazer populations or cohorts, which may be-
long to different species (groups), and which may be simulated separately or simultaneously.
Physiological parameter settings determine which species (group) is simulated. Option pa-
rameter 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 deter-
mines 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 indi-
vidual 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 total structural biomass ((i)_V),
2 total energy biomass ((i)_E),
3 total gonadal biomass ((i)_R), and
4 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-
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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,
ALGC, ALGN, ALGP, ALGSi, BLOOMALG01-BLOOMALG30, POC1, PON1, POP1, OPAL,
DETCS1, DETNS1, DETPS1, DETSiS1, NH4, NO3, PO4, Si, OXY, TIC and ALKA
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 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 Filtration, ingestion, and assimilation
1.2 Growth and maintenance
1.3 Maturity and reproduction
1.4 Respiration
1.5 Temperature dependency
2 From individuals to populations
2.1 Standard approach: isomorphs
2.2 Simplified approach: V1-morphs
2.3 Total grazer rates of change
2.4 Total algae, detritus and inorganic nutrient rates of change
2.5 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 indi-
vidual 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
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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=Cfdi
Ksfd0
i+Cfdi
in which
Ksfd0
i=Ksfdi1 + Ctim
Kstimi
with:
Cfdifood concentration available to grazer i[gC m−3]
Ctim concentration of inorganic matter [ g m−3]
fiscaled functional response of grazer i[-]
Ksfdihalf saturation constant for food uptake by grazer i[ gC m−3]
Ksfd0
ihalf saturation constant for food uptake by grazer iadjusted for the negative
influence of inorganic matter [ gC m−3]
Kstimihalf saturation constant for the negative effect of inorganic matter on food uptake
[gC m−3]
iindex for grazer species groups 1–5 [-]
The food concentration available to grazer iis the summed concentration of all edible parti-
cles. 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:
Cfdi=fdpri×Cdet1+
m
X
j=1
(fapri×Calgj)
with:
Cfdifood concentration available to grazer species group i[ gC m−3]
Calgjbiomass concentration of algae species group j[ gC m−3]
Cdet1detritus organic carbon concentration [ gC m−3]
fdpripreference of a grazer species group ifor detritus [-]
fapri,j preference of grazer type ifor algae type j[-]
mnumber of algae groups, different for (BLOOM) and (DYNAMO) [-]
iindex for grazer species groups (at most 5) [-]
jindex for algae species groups (depends on whether BLOOM is used or DY-
NAMO) [-]
According to the DEB theory, the energy ingestion rate is defined as:
P upte =kuptm20
i×fi×V
2
3
i×kTi
with:
fiscaled functional response of grazer type i[-]
kuptm20
imaximum surface-area-specific ingestion rate of grazer iat 20 ◦C [J cm−2d−1]
kTiArrhenius rate of change of chemical reaction processes due to temperature
(see section 1.5) [-]
P upteienergy ingestion rate [J ind−1d−1]
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Vistructural biovolume of an individual grazer of type i[cm3ind−1]
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 falg and detritus fdet. 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 car-
bon specific energy content of each food component.
P uptdi,j =P uptei×ceci
(1 −fdeti)
P uptai,j =P uptei×ceci
(1 −falgi,j)
with:
cecienergy to carbon conversion factor [ gC J−1]
fdetiegested fraction of detritus consumed by grazer i[-]
falgi,j egested fraction of algae jconsumed by grazer i[-]
P upteienergy ingestion rate of grazer i[J ind−1d−1]
P uptdiuptake rate of detritus for grazer i[gC ind−1d−1]
P uptai,j uptake rate of algal species jfor grazer i[gC ind−d−1]
Filtration rates are derived from the carbon uptake rates by increasing them by pseudofae-
ces 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−fie) is excreted as pseud-
ofaeces. 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 fildi,j =P uptdi,j/κI,i
P filai,j =P uptai,j/κI,i
P fildnk,i =P f ildi×Cdetk/Cdet1
P filank,i,j =P f ilak,i ×anutk,j
P filnk,i =P f ildnk,i +
m
X
j=1
(P filank,i,j )
with:
anutk,j stoichiometric constant of algal species jfor nutrient k[ gC/gN/gP/gSi gC−1]
Cdetkdetritus organic carbon concentration [gC m−3]
κI,i ingestion efficiency coefficient of grazer i[-]
P fildifiltration rate of detritus for grazer i[gC ind−1d−1]
P filai,j filtration rate of algal species jfor grazer i[gC ind−d−1]
P fildnk,i filtration rate of nutrient kfrom detritus for grazer i[gC ind−d−1]
P filank,i filtration rate of nutrient kfrom algal species jfor grazer i[gC ind−1d−1]
P filnk,i filtration rate of nutrient kfor grazer i[gC ind−1d−1]
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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 differ-
ences 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 −fdeti)×P f ildnk,i +
m
X
j=1
((1 −falgi,j)×κI,i ×P filank,i,j)!
P a1k=2−4,i =κI,i ×κA,i ×P fildnk,i +
m
X
j=1
(P filank,i,j )!
P a2k,i = min
k=1−4(P a1k,i/bnutk,i)
P defk,i =P uptnk,i −P a2k,i
with:
bnutk,i stoch. constant for nutrient kover carbon in grazer i[gC/gN/gP/gSi gC−1]
fdetiegested fraction of detritus consumed by grazer i[-]
falgi,j egested fraction of algae jconsumed by grazer i[-]
κI,i ingestion efficiency coefficient of grazer i[-]
κA,i assimilation efficiency coefficient of grazer i[-]
P a1k,i potential assimilation rate of nutrient k[gC/gN/gP/gSi ind−1d−1]
P a2k,i actual assimilation rate of nutrient k[J ind−1d−1]
P defk,i faeces production rate of nutrient k[gC/gN/gP/gSi ind−1d−1]
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=Ei/Vi
κi×Ei/Vi+kegi×κA,i ×kuptm20
i×kTi×kegi
kemi×V
2
3
i+kpmi×Vi×kTi
with:
κA,i assimilation efficiency coefficient of grazer i[-]
κfraction of mobilized energy to growth and maintenance of grazer i[-]
kegivolume-specific costs for growth of grazer i[J cm−3]
kemimaximum energy density of grazer i[ J cm−3]
kuptm20
imaximum surface area-specific ingestion rate of grazer iat 20 ◦C [J cm2d−1]
kpm20
ivolumetric costs of maintenance for grazer iat 20 ◦C [J cm−3d−1]
kTiArrhenius rate of change of chemical reaction processes due to temperature
(see section 1.5)[-]
P cienergy mobilization rate of grazer i[J ind−1d−1]
Vistructural biovolume of individual grazer of type i[cm3ind−1]
Eienergy reserves of individual grazer of type i[ J cm−3]
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A constant fraction κof 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,
P vi=κG,i ×P gi
if P gi≤0,
P vi= (1 + (1 −κG,i)) ×P gi
P mi=P mi+abs((1 −κG,i)×P gi)
in which:
κG,i =cvci
kegi×ceci
with:
ceciconversion coefficient from energy to carbon of grazer i[ gC J−1]
cvciconversion coefficient from volume to carbon of grazer i[gC cm−3]
κifraction of mobilized energy to growth and maintenance [-]
κG,i growth efficiency [-]
kegivolume specific costs for growth of grazer i[J cm−3]
kpmivolumetric costs of maintenance for grazer iat 20 ◦C [J cm−3d−1]
kTiArrhenius rate of change of chemical reaction processes due to temperature for
grazer i[-]
P gienergy flux to growth of grazer i[J ind−1d−1]
P mimaintenance rate of grazer i[J ind−1d−1]
P cienergy mobilization flux of grazer i[J ind−1d−1]
P vigrowth rate of structural biovolume of grazer i[cm3ind−1d−1]
Vistructural biovolume of individual grazer of type i[cm3ind−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 juve-
nile 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 develop-
ment 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 matu-
rity maintenance, gonadal tissue will be used instead. This will entail overhead costs that are
proportional to those for production of gonads.
P jji=1−κi
κi×kpmi×Vi×fjuvi×kTi
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P jai=1−κi
κi×kpmi×V pi×fadulti×kTi
P rji= (1 −κi)P ci×fjuvi−P jji
P rai= (1 −κi)P ci×fadulti−P jai
if P rai>0,
P ri=κR,i ×P rai
if P rai≤0,
P ri= (1 + (1 −κR,i)) ∗P rai
P jai=P jai+abs((1 −κR,i)∗P rai)
with:
fadult adult fraction of cohort/population of grazer type i[-]
fjuvijuvenile fraction of cohort/population of grazer type i[-]
κifraction of mobilized energy to growth and maintenance [-]
κR,i reproduction efficiency [-]
kpm20
ivolumetric costs of maintenance for grazer iat 20 ◦C[Jcm−3d−1]
P jjimaturity maintenance flux of juvenile grazers of type i[J ind−1d−1]
P jaimaturity maintenance flux of adult grazers of type i[J ind−1d−1]
P rjimaturity development flux of juvenile grazers of type i[J ind−1d−1]
P raienergy flux to reproduction of adult grazers of type i[J ind−1d−1]
P rigonadal production rate of adult grazers of type i[J ind−1d−1]
P cienergy mobilization flux of grazer type i[J ind−1d−1]
Vistructural biovolume of individual grazer of type i[cm3ind−1]
V pibiovolume at start of reproductive age for individual grazer of type i[cm3ind−1]
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 kspriuntil 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=ceci×Ri
cvci×fadult ×Vi+ceci×fadulti×Ei+ceci×Ri
with:
ceciconversion coefficient from energy to carbon of grazer i[gC J−1]
cvciconversion coefficient from volume to carbon of grazer i[gC cm−3]
fadult adult fraction of population [-]
κR,i fraction of reproduction flux to gonadal tissue [-]
ksprigonadal release rate at spawning for grazer i[d−1]
P raienergy flux to reproduction of adult grazers of type i[J ind−1d−1]
GSIigonadal somatic index of grazer type i[-]
Vistructural biovolume of individual grazer of type i[cm3ind−1]
Eienergy reserves of individual grazer of type i[J ind−1]
Rigonadal reserves of individual grazer of type i[J ind−1]
P spwispawning rate of grazer type i[J ind−1d−1]
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1.4 Respiration
Respiration is the sum of the maintenance rate, maturation flux, development flux, and over-
head 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 growth efficiency [-]
κR,i reproduction efficiency [-]
P rjidevelopment flux of grazer type i[J ind−1d−1]
P mimaintenance rate of grazer type i[J ind−1d−1]
P jaimaturation flux of grazer type i[J ind−1d−1]
P jjienergy flux to maturity maintenance of grazer type i[J ind−1d−1]
P resirespiration rate of grazer type i[J ind−1d−1]
1.5 Temperature dependency It is assumed that all physiological rates are affected by tem-
perature in the same way. This temperature effect is based on an Arrhenius type relation,
which describes the rates at ambient temperature Tas follows:
kT =e(T ai
T ref +273 −T ai
T+273 )×1 + eT ali
T ref +273 −T ali
T li+eT ahi
T hi
−T ahi
T ref +273
1 + eT ali
T+273 −T ali
T li+eT ahi
T hi
−T ahi
T+273
with:
kTiArrhenius rate of change of chemical reaction processes due to temperature [-]
Twater temperature [◦C]
T aref reference temperature (set to 20◦C) [◦C]
T aiArrhenius temperature for grazer i[K]
T ahiArrhenius temperature for rate of decrease at upper boundary for grazer i[K]
T aliArrhenius temperature for rate of decrease at lower boundary for grazer i[K]
T liLower temperature boundary for grazer i[K]
T hiUpper 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) initial-
ization 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 sys-
tem, 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
kmrt1Band kmrt2Bunequal 0:
kmrt1i=kmrt11,20
i×Lklmrt1i
i×kTi
kmrt2i=kmrt21
i×Lklmrt2i
i
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in which:
Li=V1/3
i/kshpi
with
kmrt1imortality rate [ d−1]
kmrt2iharvesting rate [ d−1]
kmrt11,20
ireference mortality rate of grazer ifor individuals of 1 cm at 20 [d−1]
kmrt21
ireference harvesting rate of grazer ifor individuals of 1cm [ d−1]
klmrt1ilength dependency coefficient of mortality rate [-]
klmrt2ilength dependency coefficient of harvesting rate [-]
kshpishape coefficient for grazer i[-]
kTiArrhenius rate of change of chemical reaction processes due to temperature [-]
Liindividual length of grazer i[cm]
Vistructural biovolume of individual grazer of type i[cm3ind−1]
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.
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 con-
stant 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 Lan input parameter in-
stead of an output parameter (L=Lref ). Note that reference length Lref erpresents
the average length (weighted by structural body volume) and thus characterizes the popu-
lation 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 Vbecomes
constant as well (V= (Lref /kshp)3). Note that individual energy reserves Eand
gonads Rwill 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 Vand 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. Underly-
ing 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
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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:
fjuvi=V p
V p +V ref if SwV 1=1
fjuvi= 0 if (SwV 1 = 0andVi> Vp)
fjuvi= 1 if (SwV 1 = 0andVi≤Vp)
fadulti= 1 −fjuvi
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 V1-
morphs 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:
Rgrvi=ceci×P vi×Cgrni
Rgrei=ceci×(P a2i−P ci)×Cgrni
Rgrri=ceci×P ri×Cgrni
Rgrni=0 if SwV 1 = 0
Rgrni=ceci×(P vi/Vi)×Cgrniif 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
Cgrninumber of individuals of grazer type i[#m−3] or [−2]
ceciconversion coefficient from energy to carbon of grazer i[gC J−1]
cvciconversion coefficient from volume to carbon of grazer i[gC cm−3]
kmrt1imortality rate of grazer type i[ d−1]
kmrt2iharvesting rate of grazer type i[ d−1]
P a2k,i actual assimilation rate of nutrient kfor grazer type i[J ind−1d−1]
P cienergy mobilization flux of grazer type i[J ind−1d−1]
P vigrowth rate of structural biovolume of grazer type i[cm3d−1]
P rigonadal production rate of adult grazers of type i[J ind−1d−1]
Rgrvitotal growth rate of structural volume of grazer i
Rgreitotal growth rate of energy reserves of grazer i
Rgrritotal growth rate of structural volume of grazer i
Rgrnitotal increase rate of number of individuals due to growth of grazer i
Rmrvitotal decrease rate of structural volume due to growth of grazer i[d−1]
Rmreitotal decrease rate of energy reserves due to mortality of grazer i[d−1]
Rmrritotal decrease rate of gonadal reserves due to mortality of grazer i[d−1]
Rmrnitotal decrease rate of number of individuals due to mortality of grazer i[d−1]
Vistructural biovolume of individual grazer of type i[cm3ind−1]
Eienergy reserves of individual grazer of type i[J ind−1]
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Rigonadal reserves of individual grazer of type i[J ind−1]
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
Cgrninumber of individuals of grazer type i[#m−3or −2]
P uptdnk,i uptake rate of nutrient kfrom detritus for grazer i[gC ind−d−1]
P uptank,i uptake rate of nutrient kfrom algal species jfor grazer i[gC ind−1d−1]
Racnsk,j total consumption rate for nutrient kin algae group j[gC/N/P/Si m−3d−1]
Rdcnsk,j total consumption rate for nutrient kin detritus [gC/N/P/Si m−3d−1]
iindex for grazer species groups [-]
jindex for algae species groups [-]
kindex for nutients, 1 = carbon, 2 = nitrogen, 3 = phosphorus, 4 = silicon [-]
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
fsus 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)×fsusi×bnutk,i
Rmrts1i,k = (Rmrvi+Rmrei+Rmrri)×fsedi×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 stoch. constant for nutrient kover carbon in grazer i[gC/gN/gP/gSi gC−1]
Cgrninumber of individuals of grazer type i[#m−3] or [−2]
ceciconversion coefficient from energy to carbon of grazer i[gC J−1]
P resirespiration rate of grazer type i[J ind−1d−1]
P spwispawning rate of grazer type i[J ind−1d−1]
P defk,i defaecation rate of nutrient k[gC/gN/gP/gSi ind−1d−1]
Rresi,k release rate of inorganic nutrient kby respiration [gC/N/P/Si m−3d−1]
Rspwi,k detritus production of nutrient kby spawning [J ind−1d−1]
Rdefk,i detritus production rate of nutrient kby defaecation [gC/gN/gP/gSi ind−1d−1]
iindex for grazer species groups [-]
jindex for algae species groups [-]
kindex for nutients, 1 = carbon, 2 = nitrogen, 3 = phosphorus, 4 = silicon [-]
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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:
CgrniTotal number of individuals of grazer i[#m−3] or [−2]
CgrciTotal carbon biomass of grazers [ gC ]
CgrdiTotal ash free dry weight of zooplankton [ gAFDW ]
CgrwiTotal wet weight of zooplankton [ gWW ]
ceciconversion coefficient from energy to carbon of grazer i[gC J−1]
cvciconversion coefficient from volume to carbon of grazer i[gC cm−3]
cdwciconversion coefficient from ash free dry weight to carbon for grazer i[gC gAFDW−1]
cwwciconversion coefficient from wet weight to carbon for grazer i[gC gWW−1]
Vistructural biovolume of individual grazer of type i[cm3ind−1]
Eienergy reserves of individual grazer of type i[J ind−1]
Rigonadal reserves of individual grazer of type i[J ind−1]
Individual length may be derived from the individual structural volume and the shape coeffi-
cient as follows:
Li=V1/3
i/kshpi
with
kshpishape coefficient of grazer type i[-]
Lilength of individual grazer of type i[cm]
Vistructural biovolume of individual grazer of type i[cm3ind−1]
The scaled energy density is a measure for the condition of the organisms, which can be ex-
pressed as the energy density relative to the maximum energy density. Similarly, the gonadal-
somatic 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×fadult ×Vi+ceci×fadulti×Ei+ceci×Ri
with:
fadult adult fraction of population of grazer i[-]
GSIiGonadal Somatic Index of grazer type i[J ind−1]
ceciconversion coefficient from energy to carbon of grazer i[gC J−1]
cvciconversion coefficient from volume to carbon of grazer i[gC cm−3]
kemimaximum energy density for grazer i[J cm−3]
Esiscaled energy density of grazer i[-]
Vistructural biovolume of individual grazer of type i[cm3ind−1]
Eienergy reserves of individual grazer of type i[J ind−1]
Rigonadal reserves of individual grazer of type i[J ind−1]
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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
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, 56:103-
106.
Kooijman, S.A.L.M. 2010. Dynamic Energy Budget theory for metabolic organization. Cam-
bridge 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 Dy-
namic 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 param-
eters 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 Definition Units
anut2,1NCratGreen green algae spec. stoch. constant nitro-
gen over carbon
gN gC−1
anut2,2NCratDiat diatoms spec. stoch. constant nitrogen
over carbon
gN gC−1
continued on next page
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Table 7.3 – continued from previous page
Name in
formulas
Name in input Definition Units
anut2,j NCRAlg(j)BLOOM algae group spec. stoch. const.
nitr. over carb.
gN gC−1
anut3,1P CratGreen green algae spec. stoch. constant phos.
over carbon
gP gC−1
anut3,2P CratDiat diatoms spec. stoch. constant phospho-
rus over carbon
gP gC−1
anut3,j P CRAlg(j)BLOOM algae group spec. stoch. const.
phos. over carb.
gP gC−1
anut4,1SCratGreen green algae spec. stoch. constant silicon
over carbon
gSi gC−1
anut4,2SCratDiat diatoms spec. stoch. constant silicon over
carbon
gSi gC−1
anut4,j SCRAlg(j)BLOOM algae group spec. stoch. const.
sil. over carb.
gSi gC−1
Cgrv1ZooplVstructural biomass concentration of zoo-
plankton
gC m−3or −2
Cgre1ZooplEenergy reserve biomass concentration of
zooplankton
gC m−3or −2
Cgrr1ZooplRgonadal biomass concentration of zoo-
plankton
gC m−3or −2
Cgrn1ZooplNnumber of individuals (density) of zoo-
plankton
# m−3or −2
Cgrv2MusselVstructural biomass concentration of mus-
sel
gC m−3or −2
Cgre2MusselEenergy reserve biomass concentration of
mussel
gC m−3or −2
Cgrr2MusselRgonadal biomass concentration of mus-
sel
gC m−3or −2
Cgrn2MusselNnumber of individuals (density) of mussel # m−3or −2
Cgrv3Grazer3Vstructural biomass concentration of
grazer type 3
gC m−3or −2
Cgre3Grazer3Eenergy reserve biomass concentration of
grazer type 3
gC m−3or −2
Cgrr3Grazer3Rgonadal biomass concentration of grazer
type 3
gC m−3or −2
Cgrn3Grazer3Nnumber of individuals (density) of grazer
type 3
# m−3or −2
Cgrv4Grazer4Vstructural biomass concentration of
grazer type 4
gC m−3or −2
Cgre4Grazer4Eenergy reserve biomass concentration of
grazer type 4
gC m−3or −2
Cgrr4Grazer4Rgonadal biomass concentration of grazer
type 4
gC m−3or −2
Cgrn4Grazer4Nnumber of individuals (density) of grazer
type 4
# m−3or −2
continued on next page
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Primary consumers and higher trophic levels
Table 7.3 – continued from previous page
Name in
formulas
Name in input Definition Units
Cgrv5Grazer5Vstructural biomass concentration of
grazer type 5
gC m−3or −2
Cgre5Grazer5Eenergy reserve biomass concentration of
grazer type 5
gC m−3or −2
Cgrr5Grazer5Rgonadal biomass concentration of grazer
type 5
gC m−3or −2
Cgrn5Grazer5Nnumber of individuals (density) of grazer
type 5
# m−3or −2
Calg1Green biomass concentration of green algae
(DYNAMO)
gC m−3
Calg2Diat biomass concentration of diatoms (DY-
NAMO)
gC m−3
Calgj BLOOMALG(j)biomass concentration of a BLOOM al-
gae group
gC m−3
Cdet1P OC1detritus organic carbon concentration gC m−3
Cdet2P ON1detritus nitrogen concentration gN m−3
Cdet3P OP 1detritus phosphorus concentration gP m−3
Cdet4Opal opal silicate concentration gSi m−3
Ctim Opal concentration of inorganic matter g m−3
H Depth depth of a water compartment (layer) m
–(i)UnitSW group spec. option for biomass unit (1=g
m−2, 0=g m−3)
-
–(i)_SwV 1group spec. option for upscaling (0=iso-
morphs(cohort), 1=V1morphs (popula-
tion))
-
T T emp water temperature ◦C
bnut1,i (i)_T C stoch. constant for carbon over carbon in
grazer i
gC gC−1
bnut2,i (i)_T N stoch. constant for nitrogen over carbon
in grazer i
gN gC−1
bnut3,i (i)_T P stoch. constant for phosphorus over car-
bon in grazer i
gP gC−1
bnut4,i (i)_T Si stoch. constant for silicon over carbon in
grazer i
gSi gC−1
fapri,1(i)_ALGP RGrnpreference of grazer ifor green algae
(DYNAMO)
-
fapri,2(i)_ALGP RDiatpreference of grazer ifor diatoms (DY-
NAMO)
-
fapri,j (i)_ALGP R(j)preference of grazer ifor BLOOM algae
group j
-
fdpri(i)_DET P R preference of grazer ifor detritus -
falgi,1(i)_ALGF F Grnegested fraction of green algae con-
sumed by grazer i
-
continued on next page
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Table 7.3 – continued from previous page
Name in
formulas
Name in input Definition Units
falgi,2(i)_ALGF F Diategested fraction of diatoms consumed by
grazer i
-
falgi,j (i)_ALGF F (j)egested fraction of algae jconsumed by
grazer i
-
fdeti(i)_DET F F egested fraction of detritus consumed by
grazer i
-
fsedi(i)_F rDetBot fr. of mortality flux of grazer ito sediment
detr. pool
-
fsusi(i)_F rDetBot fr. of mortality flux of grazer ito sediment
detr. pool
-
κI,i (i)_kappaI fr. of filtered food ingested by grazer i-
κA,i (i)_kappaA fr. of ingested food assimilated by grazer
i
-
κi(i)_kappa fr. of mobilized energy to growth and
maintenance of grazer i
-
κR,i (i)_kappaR fr. of reproduction flux to gonadal tissue
of grazer i
-
ceci(i)_cEC conversion coefficient from energy to car-
bon biomass of grazer i
gC J−1
cvci(i)_cV C conversion coefficient from volume to car-
bon biomass of grazer i
gC cm−3
cdwci(i)_cDW C conversion coefficient from carbon
biomass to ash free dry weight for grazer
i
gC gAFDW−1
cwwci(i)_cW W C conversion coefficient from carbon
biomass to wet weight for grazer i
gC gWW−1
GSIupri(i)_GSIupr energy threshold to start spawning for
grazer i
-
GSIlwri(i)_GSIlwr energy threshold to stop spawning for
grazer i
-
kegi(i)_EG volume-specific costs for growth of grazer
i
J cm−3
kemi(i)_EM maximum energy density of grazer iJ cm−3
kuptm20
i(i)_JXm maximum surface-area-specific ingestion
rate of grazer iat 20 ◦C
J cm2d−1
kmrt11,20
i(i)_rMor reference mortality rate of grazer ifor in-
dividuals of 1cm at 20 ◦C
d−1
kmrt21
i(i)_rHrv reference harvesting rate of grazer ifor
individuals of 1cm
d−1
klmrt1i(i)_cMor length dependency coefficient for mortal-
ity rate of grazer i
-
klmrt2i(i)_cHrv length dependency coefficient for har-
vesting rate of grazer i
-
kpm20
i(i)_P M volumetric costs of maintenance for
grazer iat 20 ◦C
J cm−3d−1
continued on next page
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Primary consumers and higher trophic levels
Table 7.3 – continued from previous page
Name in
formulas
Name in input Definition Units
kspri(i)_Rspw gonadal release rate at spawning for
grazer i
d−1
kshpi(i)_Shape shape coefficient for grazer i-
Ksfdi(i)_Xk half saturation constant for food uptake
by grazer i
gC m−3
Kstimi(i)_Y k half saturation constant for the negative
effect of inorganic matter on food uptake
by grazer i
gC m−3
Lrefi(i)_Lref reference length of individual grazer of
type i(only for V1morphs)
cm
T ai(i)_T a Arrhenius temperature for grazer iK
T ali(i)_T al Arrhenius temperature for rate of de-
crease at upper boundary for grazer i
K
T ahi(i)_T ah Arrhenius temperature for rate of de-
crease at lower boundary for grazer i
K
T li(i)_T l Lower temperature boundary of tolerance
range for grazer i
K
T hi(i)_T h Upper temperature boundary of tolerance
range for grazer i
K
T spmi(i)_MinST mp minimum spawning temperature for
grazer i
K
V pi(i)_V p biovolume at start of reproductive age for
grazer i
cm3ind−1
1(i) indicates grazer species groups 1–5, respectively Z for zooplankton, M for mus-
sel type zoobenthos, G3, G4 and G5 for user defined groups.
2(j) indicates BLOOM algae species groups 1–30.
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Table 7.4: Definitions of the output parameters for DEBGRZ.
Name in
formulas
Name in out-
put
Definition Units
Li(i)_LIndividual length of grazer icm
Esi(i)_Escaled Scaled energy density, which is a mea-
sure for the condition of the organism
-
GSIi(i)_GSI Gonadal Somatic Index of grazer type i-
Vi(i)_V ind Structural biovolume of individual grazer
of type i
cm3ind−1
Ei(i)_Eind Energy reserves of individual grazer of
type i
J ind−1
Ri(i)_Rind Gonadal reserves of individual grazer of
type i
J ind−1
Cgrci(i)_T otBiomassTotal carbon biomass concentration of
grazer type i
gC m−3or −2
Cgrdi(i)_T otAF DW Total ash free dry weight concentration of
grazer type i
gAFDW
m−3or −2
Cgrwi(i)_T otW W Wet weight concentration of grazer igWW m−3or −2
Cgrci(i)_Biomass Total carbon biomass of grazer igC
Cgrdi(i)_AF DW Total ash free dry weight of grazer igAFDW
Cgrwi(i)_W W Total wet weight of grazer igWW
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8 Organic matter (detritus)
Contents
8.1 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
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Processes Library Description, Technical Reference Manual
8.1 Decomposition of detritus
PROCESS: DECFAST, DECMEDIUM, DECSLOW, DECREFR, DECDOC AND
DECPOC5
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, ammo-
nium, phosphate and sulfide is called mineralization. During the decomposition process the
organic matter is gradually converted into material that is more resistant to microbial break-
down. 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 read-
ily 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 signifi-
cantly when exposed to oxygen, especially when solar radiation is available to speed up the
process by means of photo-oxidation.
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 result-
ing 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 accord-
ing 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 “de-
tritus” 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 re-
dox 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 ac-
count 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)
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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.
Carbon, nitrogen, phosphorus and sulfur in detritus are considered as separate state vari-
ables 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 mat-
ter 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 ac-
count, the decomposition rates of organic nitrogen, phosphorus and sulfur have been made a
function of the nutrient stochiometry of refractory detritus.
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 disconti-
nuity at a critically low temperature is not possible when using the processes described here.
Volume units refer to bulk ( ) or to water ( ).
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 formu-
lations.
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Formulation
The biochemical decomposition of dead organic matter (detritus) is described here as the min-
eralization 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 min-
eralization and the conversion fluxes. The fractions are produced, converted and mineralized
according to the following schemes:
Algae C, waste C
POC2
POC3
DOC
CO
POC1
+
+
DOC
+
CO
2
CO
2
2
CO
2
CO
2
O
2
+O
2
POC4 +O
2
+O
2
CO
2
+O
2
+O
2
DOC
+CO
2
+O
2
Figure 8.1: When an algae module is included.
Vegtation C
POC2
POC3
DOC
CO
POC1
+
+
DOC
+
CO
2
CO
2
+O
2
+O
2
POC5 DOC
+
CO
2
CO
2
+O
2
+O
2
DOC
++O
2
CO
2
2
CO
2
CO
2
O
2
+O
2
POC4 +O
2
+O
2
CO
2
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
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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).
Mineralization
Mineralization has been formulated as a first-order kinetic process. The first-order mineraliza-
tion 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 =fel ×faccj,i ×kmini×Cxj,i
kmini=kmin20
i×ktmin(T−20)
where:
Cx organic carbon, nitrogen, phosphorus or sulfur concentration ([gC/N/P/S m−3];
xis oc,on,op or os)
facc acceleration factor for nutrient stripping [-]
fel limiting factor for electron acceptors [-]
kmin first-order mineralization rate [d−1]
kmin20 first-order mineralization rate at 20 ◦C [d−1]
ktmin temperature coefficient for mineralization [-]
Rmin mineral. rate for organic carbon, nitrogen, phosphorus or sulfur [gC/N/P/S m−3.d−1]
Ttemperature [◦C]
iindex for the organic matter fraction (1–5; see scheme above)
jindex for the nutrient (1–4, that is C, N, P and S)
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
kmin20
i=kmin20
i,max
if Coni/Coci < ani,min or Copi/Coci < api,min
kmin20
i=kmin20
i,min
else
kmin20
i=kmin20
i,min +fnuti×kmin20
i,max −kmin20
i,min
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Processes Library Description, Technical Reference Manual
fnuti= min ((Coni/Coci)−ani,min)
ani,max −ani,min
,((Copi/Coci)−api,min)
api,max −api,min
(if ani,max =ani,min or api,max =api,min then fnuti= 0.5!)
where:
an stochiometric constant of nitrogen in organic matter [gN gC−1]
ap stochiometric constant of phosphorus in organic matter [gP gC−1]
Coc organic carbon concentration [gC m−3]
Con organic nitrogen concentration [gN m−3]
Cop organic phosphorus concentration [gP m−3]
fnut limiting factor for nutrient availability [-]
iindex for the organic matter fraction (1–5; see scheme above)
max index for the maximal value, the upper limit
min index for the minimal value, the lower limit
The limiting factor for electron acceptors is simply a constant, the value of which depends on
the presence of dissolved oxygen and nitrate:
fel =
1.0if Cox > 0.0
bni if Cox < 0.0and Cni > 0.1
bsu if Cox < 0.0and Cni < 0.1
where:
bni attenuation constant in case nitrate is the prevailing electron acceptor [-]
bsu attenuation constant in case sulfate or carbon monoxide is the prevailing elec-
tron 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:
faccj,i = 1.0 + ((Cxj,i/Coci)−arj)
arj
with:
ar 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, phos-
phorus 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 re-
fractory 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
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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 dependen-
cies 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 phospho-
rus (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.
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: :
Rconj,i =bi×Rminj,i/faccj,i
where:
bconstant fraction of detritus C component iconverted into detritus C component
i+ 1 relative to and in addition to mineralization [-]
Rcon conversion rate for particulate organic carbon, nitrogen, phosphorus or sulfur to
slower particulate or dissolved fractions [gC/N/P/S m−3.d−1]
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 den-
itrification, 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 strip-
ping 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 OMDec=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 POX1−5and DOX can be
set to 0.15, 0.05, 0.005, 0.00001, 0,00001 and 0.001 d−1respectively, the maximal and
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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 con-
stants for refractory detritus a_dNpr,a_dPpr and a_dSpr can be set at 0.05 gN.gC−1,
0.005 gP.gC−1and 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 (C106N16P1S1) 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
audNf =aldNf or audP f =aldP 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 veg-
etation 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 de-
fined 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 ( ).
Name in
formulas1
Name in input Definition Units
ani,max au_dNf max. st. constant N in fast dec. detritus gN.gC−1
„au_dNm max. st. const. N in medium slow detr. gN.gC−1
„au_dNs max. st. constant N in slow dec. detritus gN.gC−1
ani,min al_dNf min. st. constant N in fast dec. detritus gN.gC−1
„al_dNm min. st. const. N in medium slow detr. gN.gC−1
„al_dNs min. st. constant N in slow dec. detritus gN.gC−1
api,max au_dP f max. st. constant P in fast dec. detritus gP.gC−1
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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 ( ).
Name in
formulas1
Name in input Definition Units
„au_dP m max. st. const. P in medium slow detr. gP.gC−1
„au_dP s max. st. constant P in slow dec. detritus gP.gC−1
api,min al_dP f min. st. const. P in fast dec. detritus gP.gC−1
„al_dP m min. st. const. P in medium slow detr. gP.gC−1
„al_dP s min. st. constant P in slow dec. detritus gP.gC−1
arja_dNpr stoch. constant N in refractory detritus gN.gC−1
„a_dP pr stoch. constant P in refractory detritus gP.gC−1
„a_dSpr stoch. constant S in refractory detritusitus gS.gC−1
bib_poc1poc2conv. fraction fast detr. into medium detr. -
„b_poc2poc3conv. fraction medium detr. into slow detr. -
„b_poc2doc conv. fr. medium detr. into diss. refr. detr. -
„b_poc3poc4conv. fr. slow detr. into part. refr. detr. -
„b_poc3doc conv. fr. slow detr. into diss. refr. detr. -
bni b_ni atten. const. for nitrate as el. acceptor -
bsu b_su atten. const. for sulfate as el. acceptor -
CociP OC1conc. organic carbon in fast detritus gC.m−3
„P OC2conc. organic carbon in medium detritus gC.m−3
„P OC3conc. organic carbon in slow detritus gC.m−3
ConiP ON1conc. organic nitrogen in fast detritus gN.m−3
„P ON2conc. organic nitrogen in medium detritus gN.m−3
„P ON3conc. organic nitrogen in slow detritus gN.m−3
CopiP OP 1conc. organic phosphorus in fast detritus gP.m−3
„P OP 2conc. organic phosphorus in medium de-
tritus
gP.m−3
„P OP 3conc. organic phosphorus in slow detritus gP.m−3
CosiP OP 1conc. organic sulfur in fast detritus gS.m−3
„P OP 2conc. organic sulfur in medium detritus gS.m−3
„P OP 3conc. organic sulfur in slow detritus gS.m−3
Cox OXY concentration of dissolved oxygen gO2m−3
Cni NO3concentration of nitrate gN m−3
faccj,i – accel. factors nutrient strip. for six detritus
components
-
fel – limiting factor for electron acceptors -
fnuti– limiting factors for nutrient availability -
kmin20
i,max ku_dF dcC20 max. min. rate fast detr-C at 20 ◦C d−1
„ku_dMdcC20 max. min. rate medium detr-C detr. at 20
◦C
d−1
„ku_dSdcC20 max. min. rate slow detr-C at 20 ◦C d−1
kmin20
i,min kl_dF dcC20 min. min. rate fast detr-C at 20 ◦C d−1
„kl_dMdcC20 min. min. rate medium detr-C at 20 ◦C d−1
„kl_dSdcC20 min. min. rate slow detr-C at 20 ◦C d−1
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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 ( ).
Name in
formulas1
Name in input Definition Units
ktmin kT _dec temperature coefficient for mineralization -
kmin20
i,max ku_dF dcN20 max. min. rate fast detr-N at 20 ◦C d−1
„ku_dMdcN20 max. min. rate medium detr-N at 20 ◦C d−1
„ku_dSdcN20 max. min. rate slow detr-N at 20 ◦C d−1
kmin20
i,min kl_dF dcN20 min. min. rate fast detr-N at 20 ◦C d−1
„kl_dMdcN20 min. min. rate medium detr-N at 20 ◦C d−1
„kl_dSdcN20 min. min. rate slow detr-N at 20 ◦C d−1
kmin20
i,max ku_dF dcP 20 max. min. rate fast detr-P at 20 ◦C d−1
„ku_dMdcP 20 max. min. rate medium detr-P at 20 ◦C d−1
„ku_dSdcP 20 max. min. rate slow detr-P at 20 ◦C d−1
kmin20
i,min kl_dF dcP 20 min. min. rate fast detr-P at 20 ◦C d−1
„kl_dMdcP 20 min. min. rate medium detr-P at 20 ◦C d−1
„kl_dSdcP 20 min. min. rate slow detr-P at 20 ◦C d−1
SW OM DecSW OM Dec option (0.0 = nutrient stripping; 1.0 = dif-
ferent rates)
-
T T emp temperature of water ◦C
T NatT emp temperature of air and sediment when
ran dry
◦C
1j = C, N, P or S; i = POC1, POC2 or POC3.
Table 8.2: Definitions of the input parameters in the above equations for DECREFR, DEC-
DOC and DECPOC5. Volume units refer to bulk ( ) or to water ( ).
Name in
formulas1
Name in input Definition Units
ani,max au_dNP OC5max. stoch. constant N in stem/root
POC5
gN.gC−1
ani,min al_dNP OC5min. stoch. constant N in stem/root POC5 gN.gC−1
api,max au_dP P OC5max. stoch. constant P in stem/root
POC5
gP.gC−1
api,min al_dP P OC5min. stoch. constant P in stem/root POC5 gP.gC−1
arja_dNpr stoch. constant N in refr. detritus gN.gC−1
„a_dP pr stoch. constant P in refr. detritus gP.gC−1
„a_dSpr stoch. constant S in refr. detritus gS.gC−1
bib_poc5poc4conv. fraction stem/root POC5 into part.
refr. detr.
-
„b_poc5doc conv. fraction stem/root POC5 into diss.
refr. detr.
-
bni b_ni attenuation constant for nitrate as elec-
tron acceptor
-
bsu b_su attenuation constant for sulfate as elec-
tron acceptor
-
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Table 8.2: Definitions of the input parameters in the above equations for DECREFR, DEC-
DOC and DECPOC5. Volume units refer to bulk ( ) or to water ( ).
Name in
formulas1
Name in input Definition Units
CociP OC4conc. organic C in part. refr. detritus gC.m−3
„P OC5conc. organic C in stems and roots gC.m−3
„DOC conc. organic C in diss. refr. detritus gC.m−3
ConiP ON4conc. organic N in part. refr. detritus gN.m−3
„P ON5conc. organic N in stems and roots gN.m−3
„DON conc. organic N in diss. refr. detritus gN.m−3
CopiP OP 4conc. organic P in part. refr. detritus gP.m−3
„P OP 5conc. organic P in stems and roots gP.m−3
„DOP conc. organic P in diss. refr. detritus gP.m−3
CosiP OP 4conc. organic S in part. refr. detritus gS.m−3
„P OP 5conc. organic S in stems and roots gS.m−3
„DOP conc. organic S in diss. refr. detritus gS.m−3
Cox OXY concentration of dissolved oxygen gO2.m−3
Cni NO3concentration of nitrate gN.m−3
fel - limiting factor for electron acceptors -
kmin20
ik_dprdcC20 min. rate part. refractory detr. at 20 ◦C d−1
„ku_P5dcC20 max. min. rate stem/root POC5 at 20 ◦C -
„kl_P5dcC20 min. min. rate stem/root POC5 at 20 ◦C d−1
„k_DOCdcC20 min. rate diss. refractory detr. at 20 ◦C d−1
ktmin kT _dec temperature coefficient for mineralisation -
T T emp temperature ◦C
T NatT emp temperature of air and sediment when
ran dry
◦C
1j = C, N, P or S; i = POC4, POC5 or DOC.
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8.2 Consumption of electron-acceptors
PROCESS: CONSELAC
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 poten-
tials 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), sul-
fate 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 fi-
nal products are more or less equal amounts of carbon dioxide and methane. The subsequent
redox processes are indicated as:
oxygen consumption;
denitrification;
manganese reduction;
iron reduction;
sulfate reduction; and
methanogenesis.
In principal the thermodynamically more favourable reduction process excludes the less fa-
vourable 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 col-
umn at aerobic conditions by highly specialised bacteria (aerobic denitrification). After deple-
tion 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, ni-
trate, iron(III), sulfate and organic matter, which replaces carbon monoxide as the actual elec-
tron acceptor. Methane as the product of organic matter decomposition by means of methano-
genesis 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
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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 am-
monium (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.
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.
Dead organic matter in natural water, also called detritus, is a complicated mixture of sub-
stances that vary greatly with respect to chemical structure. Therefore, the microbial decom-
position (oxidation) of detritus is described considering various fractions of organic matter,
each having its own decomposition rate. The decomposition of the organic fractions is de-
scribed 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 ( ).
Implementation
Process CONSELAC is generic in the sense that it is applied to both water layers and sedi-
ment 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.
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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 Michaelis-
Menten 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:
O2+CH2O=⇒CO2+H2O
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:
fox20 =Cox
Ksox ×φ+Cox
where:
Cox dissolved oxygen concentration [g.m−3]
fox20 unscaled relative contr. of oxygen consumption in mineralisation at 20 ◦C [-]
Ksox half saturation constant for dissolved oxygen limitation [gO2m−3]
φporosity [-]
The relative contribution is the following function of temperature:
fox =fox20 ×ktoxc(T−20)
where:
fox unscaled relative contribution of oxygen consumption in mineralisation [-]
ktoxc temperature coefficient for oxygen consumption [-]
Ttemperature [◦C]
Denitrification
Denitrification can be described as a number of consecutive chemical reactions in which oxy-
gen 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 accumu-
lation of the intermediate products including toxic nitrite and various toxic nitrogen oxides is
generally negligible. The overall reaction equation is:
4NO−
3+ 4H3O++ 5CH2O=⇒2N2+ 5CO2+ 11H2O
Denitrification ultimately removes nitrate from the water phase and produces elemental nitro-
gen that may escape into the atmosphere. The process delivers 2.86 gO2gN−1, instantly con-
sumed for the oxidation of organic matter. Consequently, the process consumes 0.933 gram N
230 of 464 Deltares
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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:
fni20 =Cni
Ksni ×φ+Cni×1−Cox
Ksoxi ×φ+Cox
where:
Cni nitrate concentration [gN m−3]
fni20 unscaled relative contribution of denitrification in mineralisation at 20 ◦C [-]
Ksni half saturation constant for nitrate limitation [gN m−3]
Ksoxi half saturation constant for dissolved oxygen inhibition [gO2.m−3]
The relative contribution of denitrification needs to be adjusted for (low) temperature:
fni =fct ×fni20 ×ktden(T−20)
fct = 1.0if T≥Tc
fct =fden if T < Tc
where:
fct reduction factor for temperatures below critical temperature [-]
fden reduction factor for denitrification below critical temperature [-]
fni unscaled relative contribution of denitrification in mineralisation [-]
ktden temperature coefficient for denitrification [-]
Ttemperature [◦C]
Tccritically low temperature for specific bacterial activity [◦C]
Imposing of a higher temperature coefficient than the coefficient for aerobic detritus compo-
sition leads to reduction of the relative contribution of denitrification. Below the critical tem-
perature, the contribution of denitrification may be reduced further to a low background level,
when fden 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:
fni = 0.0if Cox ≥Coxc1×φ
where:
Coxc1critical dissolved oxygen conc. for inhibition of denitrification [g m−3]
Iron reduction
Iron reduction is assumed to take place on the surface of iron minerals, the amorphous fraction
Fe(OH)3or FeOOH, which leads to the following reaction equation:
4F e(OH)3a+CH2O⇒4F eIId +CO2+ 3H2O+ 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
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the significant presence of dissolved oxygen. Therefore, the relative contribution of iron in the
mineralisation of organic matter is proportional to:
ffe20 =Cfea
Ksfe ×φ+Cfea×1−Cni
Ksnifei ×φ+Cni
where:
Cfea amorphous oxidizing iron concentration [gFe.m−3]
ffe20 unscaled relative contrib. of iron reduction in mineralisation at 20 ◦C [-]
Ksfe half saturation constant for iron limitation [gFe.m−3]
Ksnifei half saturation constant for nitrate inhibition of iron reduction [gN.m−3]
The relative contribution of iron reduction is adjusted for (low) temperatures in the same way
as in the case of denitrification:
ffe =fct ×ffe20 ×ktird(T−20)
fct = 1.0if T≥T c
fct =fird if T < T c
where:
fird reduction factor for iron reduction below critical temperature [-]
ffe unscaled relative contribution of iron reduction in mineralisation [-]
ktird 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:
ffe = 0.0if Cox ≥Coxc2×ϕ
where:
Coxc2= critical dissolved oxygen conc. for inhibition of iron reduction (g.m−3b)
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:
SO−2
4+ 2CH2O=⇒S−2+ 2CO2+ 2H2O
Sulfate reduction removes sulfate and ultimately produces sulfide, which may largely precip-
itate with iron(II). The process delivers 2 gO2gS−1, instantly consumed for the oxidation of
organic matter. Consequently, the process consumes 1.333 gram S per gram C. Sulfate re-
duction 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 pres-
ence of dissolved oxygen. Therefore, the relative contribution of sulfate in the mineralisation
of organic matter is proportional to:
fsu20 =Csu
Kssu ×φ+Csu×1−Cni
Ksnisui ×φ+Cni
with:
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Csu sulfate concentration [gS m−3]
fsu20 unscaled relative contrib. of sulfate reduction in mineralisation at 20 ◦C [-]
Kssu half saturation constant for sulfate limitation [gS m−3]
Ksnisui half saturation constant for nitrate inhibition of sulfate reduction [gN m−3]
The relative contribution of sulfate reduction is adjusted for (low) temperatures in the same
way as in the case of denitrification:
fsu =fct ×fsu20 ×ktsrd(T−20)
fct = 1.0if T≥Tc
fct =fsrd if T < Tc
where:
fsrd reduction factor for sulfate reduction below critical temperature [-]
fsu unscaled relative contribution of sulfate reduction in mineralisation [-]
ktsrd temperature coefficient for sulfate reduction [-]
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:
fsu = 0.0if Cox ≥Coxc3×φ
where:
Coxc3critical dissolved oxygen conc. for inhibition of sulfate reduction [g.m−3]
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:
2CH2O=⇒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:
fch420 =1−Csu
Kssui ×φ+Csu
where:
fch420 unscaled relative contribution of methanogenesis in mineralisation at 20 ◦C [-]
Kssui half saturation constant for sulfate inhibition [gS m−3]
The relative contribution of methanogenesis is adjusted for low temperatures in the same way
as in the case of denitrification:
fch4 = fct ×fch420 ×ktmet(T−20)
fct = 1.0if T≥Tc
fct =fmet if T < Tc
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where:
fch4unscaled relative contribution of methanogenesis in mineralisation [-]
fmet reduction factor for methanogenesis below critical temperature [-]
ktmet 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:
fch4 = 0.0if Cox ≥Coxc4×φor Cni ≥Cnic ×φ
where:
Coxc4critical dissolved oxygen conc. for inhibition of methanogenesis [g m−3]
Cnic critical nitrate conc. for inhibition of methanogenesis [gN m−3]
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 mat-
ter now follow from the requirement that the sum of these contributions equals one:
frox =fox
fox +fni +ffe+fsu +fch4
frni =fni
fox +fni +ffe+fsu +fch4
frfe =ffe
fox +fni +ffe+fsu +fch4
frsu =fsu
fox +fni +ffe+fsu +fch4
frch4 = 1 −frox −frni −ffe−frsu
where:
frox scaled contribution of dissolved oxygen consumption [-]
frni scaled contribution of denitrification [-]
frfe scaled contribution of iron reduction [-]
frsu scaled contribution of sulfate reduction [-]
frch4scaled 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:
Rmin1mineralisation flux for organic carbon in the fast decomposing detritus fraction
POC1 [gC m−3d−1]
Rmin2mineralisation flux for organic carbon in the slowly decomposing detritus fraction
POC2 [gC m−3d−1]
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Organic matter (detritus)
Rmin3mineralisation flux for organic carbon in the very slowly decomposing detritus
fraction POC3 [gC m−3d−1]
Rmin4mineralisation flux for organic carbon in the particulate refractory detritus frac-
tion POC4 [gC m−3d−1]
Rmin5mineralisation flux for organic carbon in dead stems and roots of vegetation
detritus fraction POC5 [gC m−3d−1]
Rmin6mineralisation flux for organic carbon in the dissolved refractory detritus fraction
DOC [gC m−3d−1]
Rtmin total mineralisation flux for organic carbon [gC m−3d−1]
Oxygen consumption
The mineralisation flux connected to oxygen consumption follows from:
Rcns = min frox ×Rtmin, 0.5×Cox
2.67 ×∆t
frox0=0.5×Cox
frox ×Rtmin ×2.67 ×∆t
where:
frox0corrected scaled relative contribution of oxygen consumption [-]
Rcns mineralisation flux connected to oxygen consumption [gC m−3d−1]
∆tthe 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 frox = 0.0as 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 minerali-
sation flux in the same straightforward way as in the case of oxygen consumption. As ex-
plained above negative nitrate concentrations might arise. A negative concentration leads to
frni = 0.0as 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:
Rden = min frni ×Rtmin, 0.9×Cni
0.933 ×∆t
frni0=0.9×Cni
frni ×Rtmin ×0.933 ×∆t
where:
Cni nitrate concentration [gN.m−3]
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frni0corrected scaled relative contribution of denitrification [-]
Rden mineralisation flux connected to denitrification [gC.m−3d−1]
∆tthe 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 miner-
alisation flux and the corrected contribution are calculated as follows:
Rird =min frfe ×Rtmin , 0.9×Cfea
18.67 ×∆t
frfe0=0.9×Cfea
frfe ×Rtmin ×18.67 ×∆t
where:
Cfea amorphous oxidizing iron concentration [gFem-3 ]
frfe0corrected scaled relative contribution of iron reduction [-]
Rird mineralisation flux connected to iron reduction [gC m-3 d-1]
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 frsu ×Rtmin, 0.9×Csu
1.33 ×∆t
frsu0=0.9×Csu
frsu ×Rtmin ×1.33 ×∆t
where:
Csu sulfate concentration [gS m−3]
frsu0corrected scaled relative contribution of sulfate reduction [-]
Rsrd mineralisation flux connected to sulfate reduction [gC m−3d−1]
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 methanogene-
sis follows from:
Rmet =am ×frch4×Rtmin
where:
am fraction of organic C actually turned into methane [-]
Rmet mineralisation flux connected to methanogenesis [gC m−3d−1]
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 reduc-
tion and sulfate reduction have changed due to limited stocks, the contribution of the other
processes need to be corrected too. This is achieved by
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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:
frch40= 1 −frox0−frni0−frfe0−frsu0
where:
frch40corrected scaled relative contribution of methanogenesis [-]
Directives for use
Indicative values for the limitation constants are: KsOxCon = 1.0gO2m−3,KsNiDen =
0.25 gN m−3,KsF eRed = 100 000.0gFe m3,KsSuRed = 2.0gS m−3.
Indicative values for the inhibition constants are: KsOxDenInh = 1.0gO2m−3,
KsNiIReInh = 0.2gN m−3,KsNiSReInh = 0.2gN m3,KsSuMetInh =
1.0gS 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 actu-
ally 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 ac-
count 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 gO2m−3, which is an appropriate value for physical
reasons.
The temperature coefficients are connected to the temperature coefficient of the decom-
position 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 re-
duction and methanogenesis for (low) temperature is based on retardation of consump-
tion of the respective electron acceptors compared to the aerobic decomposition of de-
tritus (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 en-
hancement 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.
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The critical concentrations for inhibition of denitrification, iron reduction, sulfate reduction
and methanogenesis should have low values. Recommended values are: CoxDenInh =
1.0in water column, and = 5.0 in sediment, CoxIRedInh = 0.05,CoxSRedInh =
0.05,CoxMetInh = 0.02,CniMetInb = 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 gO2gC−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-
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 rMetGen.
Coeffcient F rMetGeCH4is 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 CH2O. 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 Cap-
pellen (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 ( ).
Name in
formulas
Name in input Definition Units
Cox OXY dissolved oxygen concentration gO2m−3
Cni NO3nitrate concentration gN m−3
Cfea F eIIIpa particulate amorphous oxidizing iron con-
centration
gFe m−3
Csu SO4sulfate concentration gS m−3
Coxc1CoxDenInh critical diss. oxygen conc. inhibition of
denitrific.
gO2m−3
Coxc2CoxIRedInh critical diss. oxygen conc. inhibition of
iron red.
gO2m−3
Coxc3CoxSRedInh critical diss. oxygen conc. inhibition of
sulfate red.
gO2m−3
Coxc4CoxMetInh critical diss. oxygen conc. inhib. of
methanogenesis
gO2m−3
Cnic CniMetInb critical nitrate conc. inhibition of methano-
genesis
gN m−3
fox - unscaled rel. contr. of oxygen cons. in
mineralisation
-
fni - unscaled rel. contr. of denitrif. in mineral-
isation
-
continued on next page
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Organic matter (detritus)
Table 8.3 – continued from previous page
Name in
formulas
Name in input Definition Units
ffe - unscaled rel. contr. of iron red in mineral-
isation
-
fsu - unscaled rel. contr. of sulfate red. in min-
eralisation
-
fch4- unscaled rel. contr. of methanog. in min-
eralisation
-
frox - scaled rel. contr. of dissolved oxygen
consumption
-
frni - scaled rel. contribution of denitrification -
frfe - scaled rel. contribution of iron reduction -
frsu - scaled rel. contribution of sulfate reduc-
tion
-
frch4c- scaled rel. contribution of methanogene-
sis
-
fct - reduction factor for temp. below critical
temperature
-
fden RedF acDen reduction factor for denitr. below critical
temperature
-
fird RedF acIRed reduction factor for iron red. below critical
temperature
-
fsrd RedF acSRed reduction factor for sulfate red. below crit-
ical temperature
-
fmet RedF acMet reduction factor for methanog. below crit-
ical temperature
-
ktoxc T cOxCon temperature coefficient for oxygen con-
sumption
-
ktden T cDen temperature coefficient for denitrification -
ktird T cIred temperature coefficient for iron reduction -
ktsrd T cSRed temperature coefficient for sulfate reduc-
tion
-
ktmet T cM et temperature coefficient for methanogen-
esis
-
Ksox KsOxCon half saturation constant for oxygen limita-
tion
gO2m−3
Ksni KsNiDen half saturation constant for nitrate limita-
tion
gN m−3
Ksfe KsF iRed half saturation constant for iron limitation gFe m−3
Kssu KsSuRed half saturation constant for sulfate limita-
tion
gS m−3
Ksoxi KsOxDenInh half sat. const. for DO inhibition of deni-
trification
gO2m−3
Ksnifei KsNiIRdInh half sat. const. for nitrate inhib. of iron
reduction
gN m−3
Ksnisui KsNiSRdInh half sat. const. for nitrate inhib. of sulfate
reduction
gN m−3
continued on next page
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Table 8.3 – continued from previous page
Name in
formulas
Name in input Definition Units
Kssui KsSuMetInh half sat. const. for sulfate inhib. of
methanogenesis
gS m−3
Rcns - mineralisation flux connected to oxygen
consumption
gC m−3d−1
Rden - mineralisation flux connected to denitrifi-
cation
gC m−3d−1
Rird - mineralisation flux connected to iron red gC m−3d−1
Rsrd - mineralisation flux connected to sulfate
reduction
gC m−3d−1
Rmet - mineralisation flux connected to
methanogenesis
gC m−3d−1
Rmin1f_MinP OC1mineralisation flux for organic carbon in
the fast decomposing detritus fraction
POC1
gC m−3d−1
Rmin2f_MinP OC2mineralisation flux for organic carbon in
the slowly decomposing detritus fraction
POC2
gC m−3d−1
Rmin3f_MinP OC3mineralisation flux for organic carbon in
the very slowly decomposing detritus
fraction POC3
gC m−3d−1
Rmin4f_MinP OC4mineralisation flux for organic carbon in
the particulate refractory detritus fraction
POC4
gC m−3d−1
Rmin5f_MinP OC5mineralisation flux for organic carbon in
dead stems and roots, detritus fraction
POC5
gC m−3d−1
Rmin6f_MinDOC mineralisation flux for organic carbon in
the dissolved refractory detritus fraction
DOC
gC m−3d−1
am F rMetGeCH4fraction of organic C converted into
methane (CH4)
-
T T emp temperature ◦C
TcCT BactAc critically low temp. for specific bacterial
activity
◦C
∆t Delt computational time-step d
φ P OROS porosity m3m−3
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Organic matter (detritus)
8.3 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
For POX combined with the S1/2 approach the organic matter fractions are allocated to the
sediment detritus pools as follows:
Algae C
POC2
POC3
POC1 DETCS1 DETCS2
OOCS1 OOCS2
OOCS1 OOCS2
OOCS1 OOCS2
mortality settling burial
Water Sediment
POC4
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.
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Processes SEDN(i) deliver the settling rates of organic nutrients (i) relative to organic carbon
components (i). Process COMPOS provides the stochiometric ratios fs of the organic nutri-
ents (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 V0Sed(i).
Table 8.4 provides the definitions of the input parameters occurring in the formulations.
Formulation
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:
Rseti=ftaui×F seti
H
ifH < Hmin F seti= 0.0
else
F seti= min F set0
i,Cxi×H
∆t
F set0
i=F set0i+si×Cxi
ifτ =−1.0ftau = 1.0
else
ftaui= max 0.0,1−τ
τci
where:
Cx concentration of a substance [gC/P/Si m−3]
F set0zero-order settling flux of a substance [gC/P/Si m−2d−1]
F set settling flux of a substance [gC/P/Si m−2d−1]
ftau shear stress limitation function [-]
Hdepth of the water column [m]
Hmin minimal depth of the water column for resuspension [m]
Rset settling rate of a substance [gC/P/Si m−3d−1]
ssettling velocity of a substance [m d−1]
τshear stress [Pa]
τc critical shear stress for settling of a substance [Pa]
∆ttimestep in DELWAQ [d]
iindex for substance (i), POC1, POC2, POC3, POC4, AAP, VIVP, APATP, OPAL.
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The settling of organic nutrients is coupled to the settling of organic carbon as follows:
Rsnj,i =Rseti
fsj,i
where:
fsj,i stochiometric ratios carbon over nutrient j in detritus component i [gC gX−1]
Rsnj,i settling rate of nutrient j in organic detritus component i [gX m−3d−1]
iindex for organic carbon component (i); POC1, POC2, POC3, POC4
jindex for organic nutrient (j); PON1/2/3/4, POP1/2/3/4 and POS1/2/3/4
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 MinDepth for set-
tling, which has a default value of 0.1 m. When desired MinDepth may be given a
different value.
The primary settling fluxes fSed(i)delivered by processes SED_(i), and the additional
settling fluxes fSed(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
Cx1
i(i)1concentration of substance (i) gC/P/Si m−3
F set0iZSed(i)zero-order settling flux of sub-
stance (i)
gC/P/Si m−2d−1
fsj,i C−NP OC12stoch. ratio C and N in POC1 gC gN−1
C−NP OC2stoch. ratio C and N in POC2 gC gN−1
C−NP OC3stoch. ratio C and N in POC3 gC gN−1
C−NP OC4stoch. ratio C and N in POC4 gC gN−1
C−P P OC1stoch. ratio C and P in POC1 gC gN−1
C−P P OC2stoch. ratio C and P in POC2 gC gP−1
C−P P OC3stoch. ratio C and P in POC3 gC gP−1
C−P P OC4stoch. ratio C and P in POC4 gC gP−1
C−SP OC1stoch. ratio C and S in POC1 gC gS−1
C−SP OC2stoch. ratio C and S in POC2 gC gS−1
C−SP OC3stoch. ratio C and S in POC3 gC gS−1
C−SP OC4stoch. ratio C and S in POC4 gC gS−1
H Depth depth of the water column,
thickness of water layer
m
continued on next page
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Table 8.4 – continued from previous page
Name in
formulas
Name in
input
Definition Units
Hmin MinDepth minimal water depth for settling
and resuspension
m
siV SedP OC settling velocity of POC m d−1
V SedIM settling velocity of inorg. matter m d−1
V SedAAP settling velocity of AAP m d−1
V SedV IV P settling velocity of VIVP m d−1
V SedAP AT P settling velocity of APATP m d−1
V SedOP AL settling velocity of OPAL m d−1
τ T au shear stress Pa
τciT aucS(i)critical shear stress for settling
of substance (I)
Pa
∆t Delt timestep in DELWAQ d
1) 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.
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Organic matter (detritus)
8.4 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 phos-
phate 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.
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.
In addition to mineralization the desorption of phosphate can be taken into account. The ad-
sorbed phosphate in the water column AAP settles into AAP S1The 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 or-
ganic 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 ( ).
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-
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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 for-
mulated 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. Con-
sequently, the formulations are as follows:
Rmini,k =(k0mini,k
H+kmini,k ×Mxi,k
Vif T≥T c
k0mini,k
Hif T < T c
kmini,k =kmin20
i,k ×ktmin(T−20)
i
where:
Mx quantity of organic carbon, nitrogen, phosphorus or silicate ([gC/N/P/Si]; x is oc,
on, op, osi or aap)
k0min zero-order mineralization or desorption rate [gC/N/P/Si m−2d−1]
kmin first-order mineralization or desorption rate [d−1]
kmin20 first-order mineralization or desorption rate at 20 ◦C [d−1]
ktmin temperature coefficient for mineralization or desorption [-]
Rmin mineral. rate org. carbon, nitrogen, phosphorus or silicate, or desorption rate of
phosphate [gC/N/P/Si m−3d−1]
Ttemperature [◦C]
Tccritical temperature [◦C]
iindex for the detritus component
kindex for sediment layers S1 and S2
Directives for use
For a start, the first-order mineralization rates RcDetXS1and RcOOXS1can be set to
0.01 and 0.001 d−1, the zero-order mineralization rates ZMinDetXS1and ZminOOXS1
to 0.0 gX m−2d−1and the critical temperature CT Min 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 sed-
iment, 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
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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 detri-
tus components or AAP. (k) indicates sediment layer 1 or 2. Volume units refer
to bulk ( ) or to water ( ).
Name in
formulas1
Name in input Definition Units
Mxi(i)S(k)quantity of slow decomposing detritus carbon,
nitrogen, phosphorus, silicate, or refractory de-
tritus carbon, nitrogen, phosphorus, silicate, or
desorbing phosphate
gC/N/P/Si
H Depth depth of overlying water segment m
kmin20
iRc(i)S(k)first-order mineralisation or desorption rate d−1
ktminiT cBM(i)temperature coefficient for mineralization -
ktminiT cAAP S(k)temperature coefficient for desorption -
k0miniZMin(i)S(k)zero-order mineralization or desorption rate gX m−2
T T emp temperature ◦C
TcCT Min critical temperature for mineralization ◦C
TcCT MinAAP S critical temperature for desorption ◦C
V V olume volume of overlying water segment m3
1) i = one of the 7 detritus components or AAP.
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248 of 464 Deltares
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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
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
9.15 Speciation of dissolved iron . . . . . . . . . . . . . . . . . . . . . . . . . . 310
9.16 Conversion salinity and chloride process . . . . . . . . . . . . . . . . . . . 315
Deltares 249 of 464
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Processes Library Description, Technical Reference Manual
9.1 Air-water exchange of CO2
PROCESS: REARCO2
Carbon dioxide (CO2) in surface water tends to saturate with respect to the atmospheric car-
bon dioxide concentration. However, carbon dioxide production and consumption processes
in the water column counteract saturation, causing a CO2-excess or CO2-deficit. Furthermore,
the CO2concentration is dependent on the pH:
CO2+H2O⇔H2CO3+H2O⇔HCO−
3+H3O++H2O⇔CO2−
3+ 2H3O+
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 CO2concentrations, 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 (<3m
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 reaera-
tion 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 inter-
face and the water column average CO2concentration. 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 coef-
ficients, 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.
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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 con-
centrations of CO2as follows:
Rrear =klrear ×[Cco2s−max(Cco2,0.0)] /H
klrear =klrear20 ×ktrear(T−20)
klrear20 =a×vb
Hc+d×W2
Cco2s=f(T, Ccl or SAL)(delivered by SATURCO2)
fsat = 100 ×max(Cco2,0.0)
Cco2s
with:
a, b, c, d coefficients with different values for eleven reaeration options
Ccl chloride concentration [gCl m−3]
Cco2actual carbon dioxide concentration [gCO2m−3]
Cco2ssaturation carbon dioxide concentration [gCO2m−3]
fsat percentage of saturation [%]
Hdepth of the water column [m]
klrear reaeration transfer coefficient in water [d−1]
klrear20 reaeration transfer coefficient at reference temperature 20 ◦C [d−1]
ktrear temperature coefficient of the transfer coefficient [-]
Rrear reaeration rate [gCO2m−3d−1]
SAL salinity [kg m−3, ppt]
Ttemperature [◦C]
vstream velocity [m s−1]
Wwindspeed at 10 m height [m s−1]
Notice that the reaeration rate is always calculated on the basis of a positive carbon dioxide
concentration. Although not realistic, CO2may have negative values in the model due to the
consumption of CO2by 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−dand 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 klrear20 is to be provided as a value in
d−1in stead of in m d−1Consequently, 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, b = 0.969, c = 0.5, d = 0.0
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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 CO2using 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
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 dhad to be scaled from cm h−1to m d−1.
Consequently, the coefficients are:
a=F(T), b = 0.0, c = 0.0, d = 0.0744 ×fsc
F(T)=2.5×(0.5246 + 0.016256 ×T+ 0.00049946 ×T2)
fsc =Sc
Sc20 −0.5
Sc =d1−d2×T+d3×T2−d4×T3
with:
d1−4coefficients
fsc scaling factor for the Schmidt number [-]
Sc Schmidt number at the ambient temperature [m d−1]
Sc20 Schmidt number at reference temperature 20 ◦C [m d−1]
Ttemperature [◦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 d1d2d3d4
Sea water, Salinity >1kg m−32073.1 125.62 3.6276 0.043219
Fresh water, Salinity ≤1kg m−31911.1 118.11 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
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Inorganic substances and pH
basis of the Schmidt number. The relation for transfer coefficient is:
klrear =a×exp b1×Wb2+c1×Pc2×f sc (9.1)
fsc =Sc
Sc20 −0.67
(9.2)
Sc =d1−d2×T+d3×T2−d4×T3(9.3)
with:
a, b, c, d coefficients
klrear transfer coefficient in water [m.d−1]
Pprecipitation, e.g. rainfall [mm.h−1]
Sc Schmidt number at the ambient temperature [g.m−3]
Sc20 Schmidt number at reference temperature 20 ◦C [d−1]
Ttemperature [◦C]
Wwindspeed 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 b1b2c1c2
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):
d1d2d3d4
CoefD1CO2 CoefD2 CO2 CoefD3 CO2 CoefD4 CO2
1911.1 118.11 3.4527 0.04132
Directives for use
Options SW RearCO2=0,1,4provide 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 trans-
fer coefficient KLRearCO2has the unusual dimension d−1. Since high values of
KLRear may cause numerical instabilities, the maximum KLRearCO2value is limited
to 1.0 d−1.
When using option SW RearCO2=4the user should be aware that the input pa-
rameter KLRearCO2is used as a dimensionless scaling factor. The default value of
KLRearCO2is 1.0 in order to guarantee that scaling is not carried out when not explic-
itly wanted.
The coefficients a–c2are 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.
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Table 9.4: Definitions of the parameters in the above equations for REARCO2.
Name in for-
mulas1
Name in input Definition Units
Cco2DisCO2concentration of carbon dioxide gCO2m−3
Cco2s SaturCO2saturation conc. of carbon dioxide
from SATURCO2
gCO2m−3
a CoefACO2coefficients for option 13 only -
b1CoefB1CO2-
b2CoefB2CO2-
c1CoefC1CO2-
c2CoefC2CO2-
d1CoefD1CO2coefficients for option 11 and 13 -
d2CoefD2CO2-
d3CoefD3CO2-
d4CoefD4CO2-
fcs – scaling factor for the Schmidt num-
ber
-
fsat – percentage carbon dioxide satura-
tion
%
H Depth depth of the top water layer m
klrear20 KLRearCO2water transfer coefficient for carbon
dioxide1
m d−1
kltemp T CRearCO2temperature coefficient for reaera-
tion
-
P rain Rainfall mm h−1
Rrear – reaeration rate for carbon dioxide gCO2m−3
d−1
SAL Salinity salinity kg m−3
Sc – Schmidt number for carbon dioxide
in water
-
SW RearCO2SW RearCO2switch for selection of options for
transfer coefficient
-
T T emp temperature ◦C
v V elocity stream velocity m s−1
W V W ind windspeed at 10 m height m s−1
1KLRearCO2is a dimensionless scaling factor for option 4.
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Inorganic substances and pH
9.2 Saturation concentration of CO2
PROCESS: SATURCO2
The reaeration of carbon dioxide proceeds proportional to the difference of the saturation
CO2concentration and the actual dissolved CO2concentration. The saturation concentration
of CO2is primarily a function of the partial atmospheric CO2pressure, the water temperature
and the salinity. However, the partial atmospheric CO2pressure is assumed to be constant.
The calculation of the saturation concentration in DELWAQ is performed as a separate pro-
cess, 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 CO2saturation concentration in water required for the pro-
cess REARCO2. The process has been implemented with two options for the formula-
tions of the saturation concentration, which can be selected by means of input parameter
SW SatCO2(= 1 −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):
fac = 10−ftemp
ftemp =a−b
(T+ 273) −c×(T+ 273) + fcl ×(d−m×(T+ 273))
fcl =n+o×Ccl +p×Ccl2
For SW SatCO2 = 2 (Weiss,1974):
fac = exp a+b
T f +c×ln(T f) + SAL ×m+n×T f +o×T f2
T f =T+ 273
100
For both options:
Cco2s=P co2×fac ×44 ×1000
with:
a, b, c, d coefficients with different values for the two formulations
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Processes Library Description, Technical Reference Manual
m, n, o, p
Ccl chloride concentration [gCl m−3]
Cco2ssaturation carbon dioxide concentration in water [gCO2m−3]
fac factor for temperature and salinity dependency
fcl function for chloride concentration dependency
ftemp function for temperature dependency
P co2atmospheric carbon dioxide pressure [atm]
Ttemperature [◦C]
T f temperature function [◦C]
SAL salinity [kg m−3, ppt]
The coefficients in both formulations are fixed. The values are presented in the table below.
Option a b c d
SW SatOxy = 1 14.0184 2385.73 0.015264 0.28569
SW SatOxy = 2 -58.0931 90.5069 22.2940 -
Option m n o p
SW SatOxy = 1 0.6167×10−50.00147 0.3592×10−40.68×10−10
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 CO2is 3.162×10−4atm.
256 of 464 Deltares
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Inorganic substances and pH
Table 9.5: Definitions of the parameters in the above equations for SATURCO2.
Name in
formulas
Name in
input
Definition Units
Cco2s– saturation concentration of carbon diox-
ide in water
gCO2m−3
Ccl Cl chloride concentration gCl m−3
fac – factor for temperature and salinity depen-
dency
-
fcl – unction for chloride concentration depen-
dency
-
ftemp – function for temperature dependency -
P co2P AP CO2atmospheric carbon dioxide pressure atm
SAL Salinity salinity kg m−3
SW SatCO2SW SatCO2switch for selection options for saturation
equation
-
T T emp temperature ◦C
T f – temperature function -
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9.3 Calculation of the pH and the carbonate speciation
PROCESS:PH_SIMP
The pH, the carbonate speciation (CO2, pCO2, H2CO3, HCO−
3and CO2−
3) 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.
The dissolved [CO2] concentration is more than two orders of magnitude higher than the
concentration of carbonic acid [H2CO3]. 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:
TIC = [CO∗
2] + [HCO−
3] + [CO2−
3]
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.
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:
ALKA =[HCO−
3] + 2[CO2−
3] +[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 (K1) and the second
dissociation constant of carbonic acid (K2). The appropriate set is selected by the model
depending on salinity.
The pH is measured on the ‘total pH scale’ (pHT):
pHT=−10log([H+]+[HSO−
4]) >−10log([H+]) = pH
Not the free [H+] is measured but [H+]T (=[H+] + [HSO−
4]). In fresh water [HSO−
4] 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 descrip-
tion
equivalent chemical reaction stoichiometry
reaeration of CO2CO2(g) + H2O↔H2CO3
∗
(aq)TIC +0.273 a)
continued on next page
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Inorganic substances and pH
Table 9.6 – continued from previous page
process descrip-
tion
equivalent chemical reaction stoichiometry
primary production CO2+ H2O→CH2O+O2TIC -1.000
H2O -1.500
Corg +1.000
OXY +2.670
mineralisation of
organic C
CH2O+O2→CO2+ H2O TIC +1.000
H2O +1.500
Corg -1.000
OXY -2.670
denitrification NO−
3+ H+→1
2N2+11
4O2+1
2H2O NO3 -1.000 b)
ALKA +4.357
OXY +2.857
H2O +0.643
nitrification NH+
4+2O2↔NO−
3+2H++ H2O NH4 -1.000
OXY -4.571
NO3 +1.000
ALKA -8.714
H2O +1.286
Uptake of ammo-
nia c)
NH+
4→(NH3)org + H+NH4 -1.000
Norg +1.000
ALKA -4.357
Uptake of phos-
phate c)
H2PO−
4+ H+→(H3PO4)org PO4 -1.000
Porg +1.000
ALKA 1.968
Uptake of nitrate NO−
3+ H++ H2O→(NH3)org +2O2NO3 -1.000
ALKA +4.357
H2O -1.286
Norg +1.000
OXY -4.571
Atmospheric depo-
sition of nitrate
HNO3→H++ NO−
3NO3 +1.000
H+ +0.071
ALKA -4.357
Atmospheric
deposition of
ammonium
NH3+ H2O→NH+
4+ OH−NH4 +1.000
ALKA +4.357
Atmospheric depo-
sition of sulfate
H2SO4→2H++ SO2−
4SO4 +1.000
H+ +0.143
ALKA -8.714
continued on next page
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Table 9.6 – continued from previous page
process descrip-
tion
equivalent chemical reaction stoichiometry
aThe CO2flux in D-Water Quality has units gCO2m−3d−1and is converted to gC
m−3d−1.
bDenitrification in the sediment is thought to be a sink for nitrate. No alkalinity, oxygen
and water are added to the water column
cMineralisation reactions are the reverse of the uptake reactions
Implementation
Process pH_simp has been implemented for the following substances:
TIC, Alka and Salinity
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 param-
eter 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
DisCO2computed 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.
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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) + H2O⇔H2CO3
CO2(aq) + H2O⇔HCO−
3+ H+
HCO−
3⇔CO2−
3+ H+
B(OH)3+ H2O⇔B(OH)−
4+ H+
H2O⇔OH−+ H+
As the concentration of H2CO3is negligible compared to CO2(aq), and therefore the dissoci-
ation 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 com-
bined reaction based on CO2, which is the sum of H2CO3and CO2(aq). Consequently, the
chemical equilibria are described with:
K0=[CO2]
pCO2
K1=[H+][HCO−
3]
[CO2]
K2=[H+][CO2−
3]
[HCO−
3]
KB=[H+][B(OH)−
4]
[B(OH)3]
KW= [H+][OH−]
where:
K0solubility constant of carbon dioxide in water [mol kg−1atm−1]
K1first dissociation constant of carbonic acid [mol kg−1solution]
K2second dissociation constant of carbonic acid [mol kg−1solution]
KBdissociation constant of boric acid [mol kg−1solution]
KWdissociation constant of water [mol2kg−2solution]
The equilibrium constants are functions of the absolute temperature and the salinity. The
absolute temperature is defined as:
Tabs =T+ 273.15
where:
Tambient water temperature [◦C]
Tabs absolute temperature [K]
Because the model calculates bulk salinity, it is corrected for porosity as follows:
S=Salinity/ϕ
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where:
Ssalinity of the water phase [g kg−1water]
ϕporosity [-]
The following K1and K2formulations from Roy (1993) were determined in artificial water
and for total pH scale.
For Salinity (S) <5 g kg−1(psu):
ln K1= 290.9097 −14554.21/Tabs −45.0575 ×ln(Tabs)+
(−228.39774 + 9714.36839/Tabs + 34.485796 ×ln(Tabs)) ×S0.5+
(54.20871 −2310.48919/Tabs −8.19515 ×ln(Tabs)) ×S+
(−3.969101 + 170.22169/Tabs + 0.603627 ×ln(Tabs)) ×S1.5−
0.00258768 ×S2+ ln(1 −S×0.001005)
K1=eln K1
ln K2= 207.6548 −11843.79/Tabs −33.6485 ×ln(Tabs)+
(−167.69908 + 6551.35253/Tabs + 25.928788 ×ln(Tabs)) ×S0.5
(39.75854 −1566.13883/Tabs −6.171951 ×ln(Tabs)) ×S+
(−2.892532 + 116.270079/Tabs + 0.45788501 ×ln(Tabs)) ×S1.5−
0.00613142 ×S2+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)×S0.5+ 0.08468345 ×S
−0.00654208 ×S1.5+ ln(1 −0.001005 ×S)
K1=eln K1
ln K2=−9.226508 −3351.6106/Tabs −0.2005743 ×ln(Tabs)+
(−0.106901773 −23.9722/Tabs)×S0.5+ 0.1130822 ×S
−0.00846934 ×S1.5+ 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
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ln KB= (−8966.90 −2890.53 ×S0.5−77.942 ×S+ 1.728 ×S1.5−0.0996 ×S2)/Tabs
+ 148.0248 + 137.1942 ×S2+ 1.62142 ×S+
(−24.4344 −25.085 ×S0.5−0.2474 ×S)×ln(Tabs)+0.053105 ×S0.5×Tabs
KB=eln KB
ln KW= 148.96502 −13847.26/Tabs −23.6521 ×ln(Tabs)+
(118.67/Tabs −5.977 + 1.0495 ×ln(Tabs)) ×S0.5−0.01615 ×S
KW=eln KW
ln KCal =−171.9065 −0.077993 ×Tabs + 2839.319/Tabs + 71.595 ×ln(Tabs)+
(−0.77712 + 0.0028426 ×Tabs + 178.34/Tabs)×S0.5−
0.07711 ×S+ 0.0041249 ×S1.5
KCal =eln KCal
ln KArg =−171.9065 −0.077993 ×Tabs + 2903.293/Tabs + 71.595 ×ln(Tabs)+
(−0.068393 + 0.0017276 ×Tabs + 88.135/Tabs)×S0.5−
0.10018 ×S+ 0.0059415 ×S1.5
KArg =eln KArg
where:
Ssalinity in the water phase [g kg−1water or psu]
KCal solubility constant of calcite [mol2kg−2solution]
KArg solubility constant of aragonite [mol2kg−2solution]
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 equilib-
rium 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/(MW C ×ρw×m3tl ×ϕ))
AlkaM =mtmm ×(Alka/(MW HCO3×ρw×m3tl ×ϕ))
B=mtmm ×0.000416 ×(S/35)
[Ca2+] = mtmm ×0.01028 ×(S/35)
where:
mtmm conversion factor for mol to mmol (103) [mmol mol−1]
m3tl conversion factor for m3to litre (103) [l m−3]
MW C molar weight of carbon (12) [g mol−1]
MW HCO3molar weight of the bicarbonate ion (61) [g mol−1]
ρwdensity 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 [gHCO3m−3]
AlkaM molar alkalinity [mmolHCO3kg−1]
Bmolar total boric acid concentration [mmol kg−1]
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Ca2+ molar calcium ion concentration [mmol kg−1]
ϕporosity [-]
The equilibrium equations can now be substituted in the component sums resulting in:
T ICM ×(K1×[H+]+2×K1×K2)/([H+]2+K1×[H+] + K1×K2)+
B×KB/([H+] + KB) + KW/[H+]−[H+]−AlkaM = 0
From this quintic polynomial equation in [H+]the following outputs are generated:
pH =−10log[H+]
CO2 = mtmm ×m3tl ×MW CO2×ρw×T ICM ×
[H+]2/([H+]2+K1×[H+] + K1×K2)
pCO2w=F CO2/(exp(atpa ×(BV + 2 ×D)/(R×Tabs)))
F CO2 = atma ×CO2M/K0
BV = (−1636.75 + 12.0408 ×Tabs −0.0327957 ×T2
abs + 3.16528 ×10−5×T3
abs)/m3tcm3
D= (57.7−0.118 ×Tabs)/m3tcm3
HCO3 = MW C ×ρw×m3tl ×ϕ×
(T ICM ×K1×[H+])/(([H+]2+K1×[H+] + K1×K2)×mtmm)
CO3 = MW C ×ρw×m3tl ×ϕ×
(T ICM ×K1×K2)/(([H+]2+K1×[H+] + K1×K2)×mtmm)
BOH4 = M W B ×ρw×m3tl ×ϕ×B/(([H+] + KB)×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]
cm3tm3conversion factor for cm3to m3(106) [cm3m−3]
BV virial coefficient of carbon dioxide in air [m3mol−1]
Dvirial coefficient of pure carbon dioxide [m3mol−1]
H+proton activity [mol kg−1solution]
MW B molar weight of boron (10.8) [g mol−1]
MW CO2molar weight of carbon dioxide (44) [g mol−1]
Rideal gas constant [m3Pa K−1mol−1]
CO2dissolved carbon dioxide concentration [gCO2m−3]
CO2Mmolar dissolved carbon dioxide concentration [mmolCO2kg−1]
F CO2fugacity of carbon dioxide concentration [µatm−1]
pCO2wpartial pressure of carbon dioxide in water [µatm−1]
CO3dissolved carbonate CO2−
3concentration [gC m−3]
HCO3dissolved bicarbonate HCO3
−concentration [gC m−3]
BOH4dissolved borate B(OH)4
−concentration [gB m−3]
ΩCal saturation state of calcite [-]
ΩArg saturation state of aragonite [-]
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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−1or mol mol−1) of the carbon dioxide and the carbonate species
of total dissolved inorganic carbon (TIC) are calculated as follows:
fc2=HCO3
T IC
fc3=CO3
T IC
fc0= 1 −f c2−f c3
where:
fc0fraction CO2of TIC [−]
fc2fraction HCO3
−of TIC [−]
fc3fraction CO32−of TIC [−]
Version 1 (SwpH = 0.0)
The original version 1 uses only the formulations for K1and K2valid for salinity <5 psu. Boric
acid is not considered. The equilibrium equations substituted in the component sums result
in:
Alka ×[H+]2/K1+ (Alka −T IC)×[H+] + K2×(Alka −2×T IC) = 0
This quadratic equation in [H+]2delivers 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) + H2O⇔H2CO3
H2CO3+ H2O⇔HCO3
−+ H3O+
HCO3
−+ H2O⇔CO32−+ H3O+
It is common to combine the first and the second reaction, and to allocate an acidity constant
to the combined reaction based on H2CO3
∗, the sum of true H2CO3and CO2(aq). Conse-
quently, the chemical equilibria are described with:
Kc0=Ccd0
Ccd1
Kc1=Ccd2×H+
(Ccd0+Ccd1)
Kc2=Ccd3×H+
Ccd2
Ccdt =Ccd0+Ccd1+Ccd2+Ccd3
where:
Ccd0dissolved carbon dioxide [mol.l−1]
Ccd1dissolved H2CO3[mol.l−1]
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Ccd2dissolved HCO3
−[mol.l−1]
Ccd3dissolved CO32−[mol.l−1]
Ccdt total dissolved inorganic carbon [mol.l−1]
H+proton concentration [mol.l−1]
Kc0hydrolysis (equilibrium,) constant for CO2[-]
Kc1acidity (equilibrium, hydrolysis) constant for H2CO3
∗[mol.l−1]
Kc2acidity (equilibrium, hydrolysis) constant for HCO3
−[mol.l−1]
The proton concentration H+and the stability constants follow from:
H+= 10−pH
Kc0= 650.0
Kc1= 10lKc1
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
where:
pH acidity [-]
Ssalinity [psu]
Ttemperature [◦C]
T abs 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
Ccd1=Ccdt
(1 + Kc1/H++ (Kc1×Kc2)/(H+)2)×1
(1 + Kc0)
Ccd0=Kc0×Ccd1
Ccd2=Kc1×(Kc0+ 1) ×Ccd1
H+
Ccd3=Ccdt −Ccd0−Ccd1−Ccd2
if due to rounding off the resulting Ccd3≤0.0
Ccd3=Kc2×Ccd2
H+
where:
Ctic total dissolved inorganic carbon (gC.m−3)
ϕporosity
The constant 12 000 concerns the conversion from gC.m−3to mol.l−1. This constant is also
used to convert the above molar concentrations back into gC.m−3for the carbonate species.
A constant 44 000 is used to convert the molar concentration of dissolved carbon dioxide into
gCO2.m−3.
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The pertinent carbonate fractions (mol mol−1or g g−1) follow from:
fc0=Ccd0
Ccdt
fc1=Ccd1
Ccdt
fc2=Ccd2
Ccdt
fc3= 1 −f c0−f c1−f c2
if due to rounding off the resulting fc3≤0.0
fc3=Ccd3
Ccdt
where:
fc0fraction CO2of TIC [−]
fc1fraction H2CO3of TIC [−]
fc2fraction HCO3
−of TIC [−]
fc3fraction CO32−of TIC [−]
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 DisH2CO3and 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 pa-
rameters.
The CO2concentration 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 CO32−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)
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Table 9.7: Definitions of the input parameters in the above equations for pH_simp. Vol-
ume units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in
Input
Definition Units
SwpH SwpH option parameter for formulations -
(0.0 = old version; 1.0 = new version)
Alka Alka alkalinity gHCO3m−3
T IC T IC total dissolved inorganic carbon con-
centration
gC.m−3
pH pH imposed pH, acidity -
pH_max pH_max maximum pH -
pH_min pH_min minimum pH -
S Salinity salinity psu
T T EMP ambient water temperature ◦C
ϕ P OROS porosity -
Table 9.8: Definitions of the output parameters of pH_simp. Volume units refer to bulk
( ) or to water ( ).
Name in
formulas
Name in
Input
Definition Units
pH pH simulated pH, acidity -
CO2or
Ccd0
DisCO2concentration of dissolved CO2gCO2.m−3
HCO3or DisHCO3concentration of dissolved HCO3
−gC.m−3
Ccd1
CO3or
Ccd2
DisCO3concentration of dissolved CO32−gC.m−3
H2CO3or DisH2CO3concentration of dissolved H2CO3gC.m−3
Ccd3
fc0F rCO2dis fraction of dissolved carbon dioxide gC gC−1
fc1F rH2CO3dfraction of dissolved H2CO3gC gC−1
fc2F rHCO3dis fraction of dissolved HCO3
−gC gC−1
fc3F rCO3dis fraction of dissolved CO32−gC gC−1
BOH4BOH4dissolved borate B(OH)4
−concentra-
tion
gB m−3
pCO2wpCO2water partial pressure of carbon dioxide in
water
µatm−1
ΩCal SatCal saturation state of calcite -
ΩArg SatArg saturation state of aragonite -
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9.4 Volatilisation of methane
PROCESS: VOLATCH4
Methane (CH4) in surface water tends to escape to the atmosphere, because its partial at-
mospheric pressure is extremely low. Volatisation is enhanced by the difference of the CH4
saturation concentration and the actual CH4concentration, and by the difference of the veloc-
ities of the water and the overlying air. The saturation concentration is approximately zero.
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 (<3m 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.
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 coef-
ficients, 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.
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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 CH4as follows:
Rvol =klvol ×[Cch4s−max(Cch4,0.0)] /H
klvol =klvol20 ×ktvol(T−20)
klvol20 =a×vb
Hc+d×W2
Cch4s=f(T, P ch4) (delivered by SATURCH4)
fsat = 100 ×max(Cch4,0.0)
Cch4s
with:
a, b, c, d coefficients with different values for eleven reaeration options
Cch4actual dissolved methane concentration [gC m−3]
Cch4ssaturation methane concentration [gC m−3]
fsat percentage of saturation [%]
Hdepth of the water column [m]
klvol transfer coefficient in water [m d−1]
klvol20 transfer coefficient at reference temperature 20 ◦C [m d−1]
ktvol temperature coefficient of the transfer coefficient [-]
P ch4partial atmospheric methane pressure [gC m−3]
Rvol volatilisation rate [gC m−3d−1]
Ttemperature [◦C]
vstream velocity [m.s−1]
Wwindspeed at 10 m height [m.s−1]
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−dand 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 klvol20 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 pa-
rameter. Consequently, the coefficients are:
a=klvol20, b = 0.0, c = 0.0, d = 0.0
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SWVolCH4 = 4
The coefficients are according to O’ Connor and Dobbins (1956) for DO, but coefficient a
can be scaled for CH4using 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
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 dcan be scaled for CH4using the transfer coefficient as input parameter.
Consequently, the coefficients are:
a= 0.3, b = 0.0, c = 0.0, d =klvol20 ×0.028
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 < 3m s−1).
SWVolCH4 = 13
The relation according to Guérin (2006); Guérin et al. (2007) deviates strongly from the pre-
vious relations, with respect to wind dependency, with respect to an additional forcing param-
eter, 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×Wb2+c1×Pc2×f sc
fsc =Sc
Sc20 −0.67
Sc =d1−d2×T+d3×T2−d4×T3
with:
a, b, c, d coefficients
klrear transfer coefficient in water [m.d−1]
Pprecipitation, e.g. rainfall [mm.h−1]
Sc Schmidt number at the ambient temperature [g.m−3]
Sc20 Schmidt number at reference temperature 20 ◦C [d−1]
Ttemperature [◦C]
Wwindspeed 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:
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a b1b2c1c2
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):
d1d2d3d4
CoefD1 CH4 CoefD2 CH4 CoefD3 CH4 CoefD4 CH4
1897.8 114.28 3.2902 0.039061
Directives for use
Options SW V olCH4 = 0,1,4,9provide 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 olCH4has the unusual dimension d−1. Since high values of KLV olCH4
may cause numerical instabilities, the maximum KLV olCH4value 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 olCH4has the standard dimension m d−1.
When using options SW V olCH4=4or 9the user should be aware that the input
parameter KLV olCH4is used as a dimensionless scaling factor. The default value of
KLV olCH4is 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.
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Table 9.9: Definitions of the parameters in the above equations for VOLATCH4.
Name in
formulas1
Name in
input
Definition Units
Cch4CH4concentration of methane gC m−3
Cch4s SaturCH4saturation conc. of methane from SAT-
URCH4
gC m−3
a CoefACH4coefficients for option 13 only -
b1CoefB1CH4-
b2CoefB2CH4-
c1CoefC1CH4-
c2CoefC2CH4-
d1CoefD1CH4coefficients for option 13 only -
d2CoefD2CH4-
d3CoefD3CH4-
d4CoefD4CH4-
fcs – scaling factor for the Schmidt number -
fsat – percentage methane saturation %
H Depth depth of the top water layer m
klvol20 KLV olCH4water transfer coefficient for methane1d−1
ktvol T CV olCH4temperature coefficient for methane
volatilisation
-
P Rain rainfall mm h−1
Rvol – methane volatilisation rate gC m−3d−1
SW V olCH4SW V olCH4switch for selection of options for trans-
fer coefficient
-
T T emp temperature ◦C
v V elocity stream velocity m s−1
W V W ind windspeed at 10 m height m s−1
1See directives for use concerning the dimension of KLV olCH4
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9.5 Saturation concentration of methane
PROCESS: SATURCH4
The volatilization of methane proceeds proportional to the difference of the saturation CH4
concentration and the actual dissolved CH4concentration. The saturation concentration of
CH4is primarily a function of water temperature, allthough salinity affects the saturation con-
centration too.
The saturation concentration at the water surface is also proportional to the partial atmo-
spheric CH4pressure. 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 pro-
cess, the formulation of which has been described by DiToro (2001).
Implementation
Process SATURCH4 delivers the CH4saturation concentration in water required for the pro-
cess 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:
Cch4smethane saturation concentration at the water surface [gC m−3]
P ch4atmospheric methane pressure [atm]
Ttemperature [◦C]
Directives for use
A representative value for the atmospheric methane pressure AtmP rCH4is 10−5atm.
The name of the output parameter for the saturation concentration of methane is SaturCH4.
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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 wa-
ter
gC m−3
P ch4AtmP rCH4atmospheric methane pressure atm
T T emp temperature ◦C
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9.6 Ebullition of methane
PROCESS: EBULCH4
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 pro-
duction 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 CH4in sediment pore water or in deep water layers concerns
the equilibrium of water with a more or less pure methane gas phase. The saturation con-
centration 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).
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:
Rebu =f×Cch4/φ −Cch4s
∆tif Cch4/φ ≥Cch4s
Cch4s= 18.76 ×1 + H
10×(1.024)(20−T)
with:
Cch4dissolved methane concentration [gC m−3]
Cch4smethane saturation concentration [gC m−3]
fscaling factor [-]
Hwater depth [m]
Ttemperature [◦C]
∆Ttimestep in DELWAQ [day]
φporosity [-]
It is obvious that Rebu = 0.0at undersaturation.
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Directives for use
The scaling factor fScEbul 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
formulas
Name in input Definition Units
Cch4CH4dissolved methane concentration gC m−3
Cch4s– saturation concentration of methane in
water
gC m−3
f fScEbul scaling factor for methane ebullition -
H T otalDepth total depth of the water column m
Rebu – methane ebullition rate gC m−3d−1
T T emp temperature ◦C
∆t Delt computational time-step d
φ P OROS porosity -
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9.7 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.
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.
Volume units refer to bulk ( ) or to water ( ).
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=⇒CO2+ 2H2O
CH4+SO2−
4=⇒CO2+ 2H2S+ 2OH−
These processes require 5.33 gO2gC−1or 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
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Van Beek (2013)):
Roxi1=k0oxi1+koxi1×Cch4
Ksch4×φ+Cch4×Cox
Ksox ×φ+Cox
koxi1=koxi20
1×ktoxi(T−20)
1
koxi1= 0.0if T < T c
or Cox ≤0.0
or Cox ≤Coxc ×φ
k0oxi1= 0.0if Cox > Coxc ×φ
or Cox ≤0.0
Roxi2=k0oxi2+koxi2×Cch4
Ksch4×φ+Cch4×Csu
Kssu ×φ+Csu
koxi2=koxi20
2×ktoxi(T−20)
2
koxi2= 0.0if T < T c
or Csu ≤0.0
or Csu ≤Csuc ×φ
or Cox > Coxc ×φ
k0oxi2= 0.0if Csu > Csuc ×φ
or Csu ≤0.0
or Cox > Coxc ×φ
with:
Cch4dissolved methane concentration [gC m−3]
Cox dissolved oxygen concentration [gO2m−3]
Coxc critical dissolved oxygen concentration for oxidation with sulfate [gO2m−3]
Csu sulfate concentration [gS m−3]
Csuc critical sulfate concentration for oxidation with sulfate [gS m−3]
k0oxi1zero-order methane oxidation rate for diss. oxygen consumption [gC m−3d−1]
k0oxi2zero-order methane oxidation rate for sulfate consumption [gC m−3d−1]
koxi1Michaelis-Menten rate for oxidation with dissolved oxygen [gC m−3d−1]
ktoxi1temperature coefficient for oxidation with dissolved oxygen [-]
Ksch4half saturation constant for methane consumption [gC m−3]
Ksox half saturation constant for dissolved oxygen consumption [gO2m−3]
koxi2Michaelis-Menten rate for oxidation with sulfate [gC m−3d−1]
ktoxi2temperature coefficient for oxidation with sulfate [-]
Kssu half saturation constant for sulfate consumption [gS m−3]
Roxi1methane oxidation rate with DO [gC m−3d−1]
Roxi2methane oxidation rate with sulfate [gC m−3d−1]
Ttemperature [◦C]
T c critical temperature for methane oxidation [◦C]
φporosity [-]
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Directives for use
For a start, the zero-order rates Rc0MetOx and Rc0MetSu and the critical concentra-
tions CoxMet and CsuMet 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 propor-
tion 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 MetOx is approximately 3–4 ◦C.
An indicative value for the critical DO concentration CoxMet is 2 gO2m−3.
An indicative value for the temperature coefficients T cMetOx and T cM etSu is 1.07.
The oxidation with sulfate can simply be excluded from the simulation by setting rates
Rc0MetSu and RcMetSu20 equal to 0.0.
Additional references
DiToro (2001), WL | Delft Hydraulics (2002), Wijsman et al. (2001)
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Table 9.12: Definitions of the parameters in the above equations for OXIDCH4. Volume
units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in input Definition Units
Cch4CH4methane concentration gC m−3
Cox OXY dissolved oxygen concentration gO2m−3
Coxc CoxMet critical DO concentration for methane ox-
idation
gO2m−3
Csuc CsuMet critical sulfate concentration for methane
oxidation
gS m−3
Csu SO4sulfate concentration gS m−3
koxi20
1RcMetOx20 MM-rate for methane oxidation with DO
at 20 ◦C
gC m−3d−1
ktoxi1T cMetOx temp. coefficient for methane oxidation
with DO
-
koxi20
2RcMetSu20 MM-rate for methane oxid. with sulfate at
20 ◦C
gC m−3d−1
ktoxi2T cMetSu temp. coefficient for methane oxidation
with sulfate
-
Ksch4KsMet half saturation constant for methane con-
sumption
gC m−3
Ksox KsOxMet half saturation constant for DO con-
sumption
gO2m−3
Kssu KsSuMet half saturation constant for sulfate con-
sumption
gS m−3
k0oxi1Rc0MetOx zero-order methane oxid. rate for DO
consumption
gC m−3d−1
k0oxi2Rc0MetSu zero-order methane oxid. rate for sulfate
cons.
gC m−3d−1
Roxi1– rate of oxidation of methane with DO gC m−3d−1
Roxi2– rate of oxidation of methane with sulfate gC m−3d−1
T T emp temperature ◦C
T c CT MetOx critical temperature for methane oxida-
tion
◦C
φ P OROS porosity m3m−3
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9.8 Oxidation of sulfide
PROCESS: OXIDSUD
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 ( ).
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:
H2S+ 2O2+ 2OH−=⇒SO2−
4+ 2H2O
The process requires 2.0 gO2gS−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 pur-
poses. 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 oxida-
tion 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 homoge-
neously 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.
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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 = 0.0if Cox ≤0.0
k0oxi = 0.0if Cox > Coxc ×φ
with:
Cox dissolved oxygen concentration [gO2m−3]
Coxc critical dissolved oxygen concentration [gO2m−3]
Csud total dissolved sulfide concentration [gS m−3]
koxi pseudo second-order sulfide oxidation rate [gO−1
2m3d]
ktoxi temperature coefficient for sulfide oxidation [-]
k0oxi zero-order sulfide oxidation rate [gS m−3d−1]
Ttemperature [◦C]
φporosity [-]
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 SUD divided with timestep
∆t, when the flux as calculated with the above formulation is larger than SUD/∆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 concentra-
tions.
Additional references
DiToro (2001), Wang and Cappellen (1996), WL | Delft Hydraulics (2002), Wijsman et al.
(2001)
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Table 9.13: Definitions of the parameters in the above equations for OXIDSUD. Volume
units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in input Definition Units
Cox OXY dissolved oxygen concentration gO2m−3
Coxc CoxSUD critical dissolved oxygen concentration gO2m−3
Csud SUD total dissolved sulfide concentration gS m−3
∆t Delt timestep d
koxi20 RcSox20 pseudo second-order sulfide oxidation
rate at 20 ◦C
gO−1
2m3d−1
ktoxi T cSox temperature coefficient for sulfide oxida-
tion
-
k0oxi Rc0Sox zero-order sulfide oxidation rate gS m−3d−1
Roxi – sulfide oxidation rate gS m−3d−1
T T emp temperature ◦C
φ P OROS porosity m3m−3
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9.9 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.
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 tempera-
ture 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.
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 ( ).
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 con-
sidered, 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.
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Formulation
The precipitation and dissolution equilibrium of iron(II) sulfide can be described with the fol-
lowing simplified reaction equation:
F e2+ +S2−⇔F eS
The precipitation and dissolution rates are formulated with first-order kinetics, with the differ-
ence between the actual dissolved free sulfide concentration and the equilibrium dissolved
concentration as driving force (Smits and Van Beek (2013)):
Rprc = 32 000 ×kprc ×(Csd −Csde)×φif Csd ≥Cdse
Rdis = 32 000 ×kdis ×(Csde −Csd)×φif Csd < Cdse
kprc =kprc20 ×ktprc(T−20)
kdis =kdis20 ×ktdis(T−20)
with:
Csd dissolved free sulfide concentration [mol l−1]
Csde equilibrium dissolved free sulfide concentration [mol l−1]
kdis dissolution reaction rate [d−1]
kprc precipitation rate [d−1]
ktdis temperature coefficient for dissolution [-]
ktprc temperature coefficient for precipitation [-]
Rdis rate of dissolution [gS m−3d−1]
Rprc rate of precipitation [gS m−3d−1]
Ttemperature [◦C]
φporosity [-]
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 dis-
solution flux is made equal to half the concentration of precipitated sulfide SUP divided with
timestep ∆t, when the flux as calculated with the above formulation is larger than SUP/∆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 SUL-
FID 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.
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When simulating the substances in the sediment as “inactive” substances (the S1/2 ap-
proach) process SULFPR only affects SUD and SUP in the water column. Settled SUP
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 ( ).
Name in
formulas
Name in input Definition Units
Csd DisSW K dissolved free sulfide concentration mol l−l
Csde DisSEqF eS equilibrium dissolved free sulfide con-
centration for amorphous iron sulfide
mol l−1
Csup SUP precipitated sulfide concentration gS m−3
∆t Delt timestep d
kdis20 RcDisS20 dissolution reaction rate d−1
ktdis T cDisS temperature coefficient for dissolution -
kprc20 RcP rcS20 precipitation reaction rate d−1
ktprc T cP rcS temperature coefficient for precipitation -
Rdis – dissolution rate gS m−3d−1
Rprc – precipitation rate gS m−3d−1
T T emp temperature ◦C
φ P OROS porosity m3m−3
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9.10 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 dis-
solved 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.
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.
Volume units refer to bulk ( ) or to water ( ).
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’ sub-
stances, 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 formula-
tions. Table 9.17 provides the output parameters.
Formulation
The hydrolysis of hydrogen sulfide proceeds according to the following reaction equations:
H2S+H2O⇔HS−+H3O+
HS−+H2O⇔S2−+H3O+
The chemical equilibria are described with:
Ks1=Csd2×H+
Csd1
(9.4)
Ks2=Csd3×H+
Csd2
(9.5)
Csdt =Csd1+Csd2+Csd3(9.6)
with:
Csd1concentration of dissolved hydrogen sulfide [mol l−1]
Csd2concentration of hydrogen sulfide anion [mol l−1]
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Csd3concentration of free dissolved sulfide [mole l−1]
Csdt concentration of total dissolved sulfide [mol l−1]
H+proton concentration [mol l−1]
Ks1acidity (dissociation, equilibrium) constant for H2S [mol l−1]
Ks2acidity (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)
where:
kths temperature coefficient for HS−1equilibrium [-]
kth2stemperature coefficient for H2S equilibrium [-]
pH acidity [-]
Ttemperature [◦C]
The concentration of the relevant sulfide species in solution can now be calculated from:
Csdt =Csud
32 000 ×φ
Csd1=Csdt
(1 + Ks1/H++ (Ks1×Ks2)/(H+)2)
Csd2=Ks1×Csd1
H+
Csd3=Csdt −Csd1−Csd2
if due to round off the resulting Csd3≤0.0
Csd3=Ks2×Csd2
H+
where:
Csud concentration of total dissolved sulfide [gS m−3]
φporosity [-]
The constant 32 000.0 concerns the conversion from gS m−3to mol l−1.
The pertinent fractions follow from:
fs1=Csd1
Csdt
fs2=Csd2
Csdt
fs3= 1 −f s1−f s2
if due to rounding off the resulting fs3= 0.0
fs3=Csd3
Csdt
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Directives for use
The acidity constants for the hydrogen sulfides have to be provided in the input of the
model as logarithmic values (10log)!
The negative logarithms of the equilibrium constants at 20 ◦C are:
lKstH2S=−7.1and lKstHS =−14.0.
An indicative value for total sulfide concentration SUD is 32 mg/l or 10−3mol l−1.
The temperature dependencies are ignored by default temperature coefficients of the acid-
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.
Additional references
Stumm and Morgan (1996)
Table 9.15: Definitions of the input parameters in the above equations for SPECSUD.
Name in
formulas
Name in
input
Definition Units
Csdt - concentration of total dissolved sulfide mol l−1
Csud SUD concentration of total dissolved sulfide gS.m−3
lKs1lKstH2S log acidity constant for H2S (mol l−1) log(-)
lKs2lKstHS log acidity constant for HS−(mol l−1) log(-)
kth2s TcKstH2S temperature coefficient for KstH2S -
kths TcKstHS temperature coefficient for KstHS -
H+– proton concentration mol l−1
pH pH acidity -
T TEMP ambient temperature ◦C
ϕPOROS porosity m3w.m−3
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Table 9.16: Definitions of the input parameters in the above equations for SPECSUDS1/2.
Name in
formulas
Name in
input
Definition Units
Csdt – concentration of total dissolved sulfide mol l−1
Csud SUDS1/2 concentration of total dissolved sulfide gS.m−3
lKhs lKstHS log acidity constant for HS−(mol l−1) log(-)
lKh2s lKstH2S log acidity constant for H2S (mol l−1) log(-)
kth2s TcKstH2S temperature coefficient for KstH2S -
kths TcKstHS temperature coefficient for KstHS -
H+– proton concentration mol l−1
pH pH acidity -
T TEMP ambient temperature (currently not used) ◦C
ϕPORS1/2 porosity m3w.m−3
Table 9.17: Definitions of the output parameters of SPECSUD and SPECSUDS1/2.
Name in
formulas
Name in
input
Definition Units
Csd1DisH2SWK of dissolved hydrogen sulfide mol l−1
Csd2DisHSWK concentration of hydrogen sulfide anion mol l−1
Csd3DisSWK concentration of free dissolved sulfide mol l−1
fs1FrH2Sdis fraction of dissolved hydrogen sulfide -
fs2FrHSdis fraction of hydrogen sulfide anion -
fs3FrS2dis fraction of free dissolved sulfide -
Csd1DisH2SS1 concentration of dissolved hydrogen sulfide
in S1
mol l−1
Csd2DisHSS1 concentration of hydrogen sulfide anion in
S1
mol l−1
Csd3DisSS1 concentration of free dissolved sulfide in S1 mol l−1
Csd1DisH2SS2 concentration of dissolved hydrogen sulfide
in S2
mol l−1
Csd2DisHSS2 concentration of hydrogen sulfide anion in
S2
mol l−1
Csd3DisSS2 concentration of free dissolved sulfide in S2 mol l−1
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9.11 Precipitation, dissolution and conversion of iron
PROCESS: PRIRON
This process considers the precipitation dissolution and conversion of oxidizing and reducing
iron minerals.
Particulate oxidizing iron in the model consists of iron(III) oxyhydroxide chemically indicated
with Fe(OH)3or 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 crys-
talline pyrite and rather crystalline iron(II) carbonate (siderite) chemically indicated with FeS
FeS2and 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 FeS2is 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 H2S. Precipitation occurs at
reducing conditions when the solution is supersaturated either with regard to S2−or CO32−
that is when the at least one of the ion activity products overrides the pertinent solubility prod-
uct. 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).
Iron(II) sulfide and pyrite are thermodynamically unstable at oxidizing conditions. At the pres-
ence 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 depen-
dent. The pH dependency is due to the concentrations of the co-precipitating ions OH−S2−
and CO32−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 pH-
dependency with regard to carbonate can be taken into account via the calculation of the pH
dependent concentration of CO32−.
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
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The process has been implemented for the following substances:
FeIIIpa FeIIIpc FeIIId FeS FeS2 FeCO3 FeIId and SUD.
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 SPEC-
IRON 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 im-
posed for computation of the free carbonate fraction. Option parameter SWTICCO2 indicates
which substance is used.
Formulation
Precipitation and dissolution of iron(III)
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 dif-
ference of the ion activity and solubility products as driving force:
Rpfe3 = kpfe3×IAP1
Ksp1−1×ϕif IAP 1≥Ksp1
Rdfe3 = kdfe3×Cf ea ×1−IAP1
Ksp1if IAP 1< Ksp1
IAP1=Cfe3d×(OH−)3
Cfe3d=ffe31×Cf e3dt ×1
56 000 ×ϕ
OH−= 10−(14−pH)
Ksp1= 10lKsp1
Kfe1= 10lKfe1
kpfe3 = kpfe320 ×ktpfe3(T−20)
kdfe3 = kdfe320 ×ktdfe3(T−20)
where:
Cfea particulate amorphous oxidizing iron concentration [gFe.m−3]
Cfe3dt dissolved oxidizing iron concentration [gFe.m−3]
Cfe3dequilibrium dissolved free iron(III) concentration [mol.l−1]
ffe31fraction dissolved free iron(III) [-]
IAP 1ion activity product for Fe(OH)3[(mol.l−1)4]
Ksp1solubility product for Fe(OH)3[(mol.l−1)4]
kdfe3specific iron(III) dissolution rate [d−1]
kpfe3specific iron(III) precipitation rate [gFe.m−3.d−1]
ktdfe3temperature coefficient for iron(III) dissolution [-]
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ktpfe3temperature coefficient for iron(III) precipitation [-]
OH−hydroxyl concentration [mol.l−1]
pH acidity [-]
Rdfe3rate of amorphous iron(III) dissolution [gFe.m−3.d−1]
Rpfe3rate of amorphous iron(III) precipitation [gFe.m−3.d−1]
Ttemperature [◦C]
ϕporosity [-]
The constant of 56 000 concerns the conversion of gFe.m−3to mol.l−1.
The dissolution process must stop at the depletion of precipitated iron(III). Therefore the dis-
solution flux is made equal to half the concentration of amorphous precipitated iron(III) Cfea
divided with timestep ∆twhen the flux as calculated with the above formulation is larger than
Cfea/∆t.
Aging of iron(III)
The coversion of amorphous iron(III) oxyhydroxide (FeIIIpa) into crystalline iron(III) oxyhydrox-
ide (FeIIIpc) can be described with the following simplified reaction equation:
Fe(OH)3⇒FeOOH + H2O
The rate of aging is equal to:
Rafe3 = kafe3×Cf ea
kafe3 = kafe320 ×ktafe3(T−20)
where:
Cfea particulate amorphous oxidizing iron concentration [gFe.m−3]
kafe3specific iron(III) aging rate [d−1]
ktafe3temperature coefficient for iron(III) aging [-]
Rafe3rate of amorphous iron(III) aging [gFe.m−3.d−1]
Ttemperature [◦C]
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 sim-
plified reaction equations:
Fe2+ + S2−⇔FeS
Fe2+ + CO32−⇔FeCO3
The precipitation and dissolution rates are formulated with approximate kinetics with the dif-
ference of the ion activity and solubility products as driving force. The formulations for iron
294 of 464 Deltares
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Inorganic substances and pH
sulfide formation are:
Rpfes =kpfes ×IAP2
Ksp2−1×φif IAP 2≥Ksp2
Rdfes =kdfes ×Cf es ×1−IAP2
Ksp2if IAP 2< Ksp2
IAP2=Cfe2d×Csd3
Cfe2d=ffe21×Cf e2dt ×1
56 000 ×ϕ
Csd3=fs3×Csdt ×1
32 000 ×ϕ
Ksp2= 10lKsp2
kpfes =kpfes20 ×ktpfes(T−20)
kdfes =kdfes20 ×ktdfes(T−20)
where:
Cfes iron(II) sulfide concentration [gFe.m−3]
Cfe2dt dissolved reducing iron concentration [gFe.m−3]
Cfe2dequilibrium dissolved free iron(II) concentration [mol.l−1]
Csdt total dissolved sulfide concentration [gS.m−3]
Csd3dissolved free sulfide concentration [mol.l−l]
fs3fraction dissolved free sulfide [-]
IAP 2ion activity product for Fes [mol.l−12]
Ksp2solubility product for Fes [mol.l−12]
kdfes specific FeS dissolution rate [d−1]
kpfes specific Fes precipitation rate [gFe.m−3.d−1]
ktdfes temperature coefficient for FeS dissolution [-]
ktpfes temperature coefficient for FeS precipitation [-]
Rdfes rate of Fes dissolution [gFe.m−3.d−1]
Rpfes rate of Fes precipitation [gFe.m−3.d−1]
Ttemperature [◦C]
ϕporosity [-]
The constant of 56 000 concerns the conversion of gFe.m−3to mol.l−1.
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The formulations for iron carbonate formation are:
Rpfeco3 = kpfeco3×IAP3
Ksp3−1×φif IAP 3≥Ksp3
Rdfeco3 = kdfeco3×Cf eco3×1−IAP3
Ksp3if IAP 3< Ksp3
IAP3=Cfe2d×Cco3d
Cfe2d=ffe21×Cf e2td ×1
56 000 ×ϕ
Cco3d=fc3×Ctic ×1
12 000 ×ϕ
Ksp3= 10lKsp3
kpfeco3 = kpfeco320 ×ktpfeco3(T−20)
kdfeco3 = kdfeco320 ×ktdfeco3(T−20)
where:
Cfeco3iron(II) carbonate concentration [gFe.m−3]
Cfe2td dissolved reducing iron concentration [gFe.m−3]
Cfe2dequilibrium dissolved free iron(II) concentration [mol.l−1]
Ctic total dissolved inorganic carbon concentration [gC.m−3]
Cco3dtotal dissolved free carbonate concentration [mol.l−l]
fc3fraction dissolved free carbonate [-]
IAP 3ion activity product for FeCO3 [mol.l−12]
Ksp3solubility product for FeCO3 ([mol.l−12])
kdfeco3specific FeCO3 dissolution rate [d−1]
kpfeco3specific FeCO3 precipitation rate [gFe.m−3.d−1]
ktdfeco3temperature coefficient for FeCO3 dissolution [-]
ktpfeco3temperature coefficient for FeCO3 precipitation [-]
Rdfeco3rate of FeCO3 dissolution [gFe.m−3.d−1]
Rpfeco3rate of FeCO3 precipitation [gFe.m−3.d−1]
Ttemperature [◦C]
ϕporosity [-]
The constant of 12 000 concerns the conversion of gC.m−3to 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 ∆twhen the flux as calculated with the above formulation is
larger than Cfes/∆tor Cfeco3/∆t.
The total inorganic carbonate concentration is derived from TIC when SWTICCO2 = 0.0 (de-
fault) 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 equa-
tions:
FeS + S ⇒FeS2
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Inorganic substances and pH
or
FeS + H2S⇒FeS2+ H2
Nor elemental sulfide nor elemental hydrogen is included in the model consequently the elec-
trons transferred cannot be accounted for. Pragmatically the formation rate is formulated as
follows:
Rpyr =kpyr ×Cfes ×fs1×Csdt/ϕ
kpyr =kpyr20 ×ktpyr(T−20)
where:
Cfes iron(II) sulfide concentration [gFe.m−3]
Csdt total dissolved sulfide concentration [gS.m−3]
fs1fraction dissolved hydrogen sulfide [-]
kpyr specific pyrite formation rate (gS−1.m3.d−1)
ktpyr temperature coefficient for iron(III) aging [-]
Rpyr rate of pyrite formation [gFe.m−3.d−1]
Ttemperature [◦C]
ϕporosity [-]
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 SPEC-
CARB 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
(10log )!!!
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 se-
ries.
References
DiToro (2001),
Stumm and Morgan (1996),
Wang and Cappellen (1996),
WL | Delft Hydraulics (2002),
Wijsman et al. (2001)
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Table 9.18: Definitions of the parameters in the above equations for PRIRON concerning
oxidizing iron. Volume units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in
Input
Definition Units
Cfea FeIIIpa particulate amorphous oxidizing iron
concentration
gFe.m−3
Cfe3dt FeIIId dissolved oxidizing iron concentration gFe.m−3
Cfe3d – equilibrium dissolved free iron(III) con-
centration
mol.l−l
ffe31FrFe3dis fraction dissolved free iron(III)
IAP1– ion activity product for Fe(OH)3mol.l−14
lKsp1lKspFeOH3 log solubility product for Fe(OH)3
[mol.l−14]
log(-)
kafe320 RcAgFe320 specific iron(III) aging rate at 20 ◦C d−1
kdfe320 RcDisFe320 specific iron(III) dissolution rate at 20 ◦C d−1
kpfe320 RcPrcFe320 specific iron(III) precipitation rate at 20
◦C
gFe.m−3.d−1
ktafe3 TcAgFe3 temperature coefficient for iron(III) aging -
ktdfe3 TcDisFe3 temperature coefficient for iron(III) disso-
lution
-
ktpfe3 TcPrcFe3 temperature coefficient for iron(III) pre-
cipitation
-
OH−– hydroxyl concentration mol.l−1
pH pH acidity -
Rafe3 – rate of amorphous iron(III) aging gFe.m−3.d−1
Rdfe3 – rate of amorphous iron(III) dissolution gFe.m−3.d−1
Rpfe3 – rate of amorphous iron(III) precipitation gFe.m−3.d−1
T Temp temperature ◦C
∆tDelt timestep d
ϕPOROS porosity m3.m−3
Table 9.19: Definitions of the parameters in the above equations for PRIRON concerning
reducing iron. Volume units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in
Input
Definition Units
Cfes FeS iron(II) sulfide concentration gFe.m−3
Cfe2dt FeIId total dissolved reducing iron concentra-
tion
gFe.m−3
Cfe2d – equilibrium dissolved free iron(II) con-
centration
mol.l−l
ffe21FrFe2dis fraction dissolved free iron(II) −
298 of 464 Deltares
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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 ( ).
Name in
formulas
Name in
Input
Definition Units
Csdt SUD total dissolved sulfide concentration gS.m−3
Csd3– dissolved free sulfide concentration mol.l−l
fs1FrH2Sdis fraction dissolved hydrogen sulfide -
fs3FrS2dis fraction dissolved free sulfide -
Cfeco3 FeCO3 iron(II) carbonate concentration gFe.m−3
Ctic TIC or CO2 total dissolved inorganic carbon concen-
tration
gC.m−3
Cco3d – total dissolved sulfide concentration gCO2.m−3
fc3FrCO3dis fraction dissolved free carbonate mol.l−l
IAP2– ion activity product for FeS [mol.l−12]
lKsp2lKspFeS log solubility product for FeS [mol.l−12] log(-)
IAP3– ion activity product for FeCO3[mol.l−12]
Ksp3lKspFeCO3 log solubility product for FeCO3
[mol.l−12]
log(-)
kpyr20 RcPyrite20 specific pyrite formation rate at 20 ◦C gS−1.m3.d−1
kdfes20 RcDisFeS20 specific iron(II) sulfide dissolution rate at
20 ◦C
d−1
kpfes20 RcPrcFeS20 specific iron(II) sulfide precipitation rate
at 20 ◦C
gFe.m−3.d−1
kdfeco320 RcDisFeC20 specific iron(II) carbonate dissolution
rate at 20 ◦C
d−1
kpfeco320 RcPrcFeC20 specific iron(II) carbonate precipitation
rate at 20 ◦C
gFe.m−3.d−1
ktpyr TcPyrite temperature coefficient for pyrite forma-
tion
-
ktdfes TcDisFeS temperature coefficient for iron(II) sulfide
diss.
-
ktpfes TcPrcFeS temperature coefficient for iron(II) sulfide
prec.
-
ktdfeco3 TcDisFeCO3 temperature coefficient for iron(II) car-
bonate diss.
-
ktpfeco3 TcPrcFeCO3 temperature coefficient for iron(II) car-
bonate prec.
-
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
SWTICCO2 SWTICCO2 option parameter (0.0 = use TIC; 1.0 =
use CO2)
-
T Temp temperature ◦C
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Table 9.19: Definitions of the parameters in the above equations for PRIRON concerning
reducing iron. Volume units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in
Input
Definition Units
∆tDelt timestep d
ϕPOROS porosity m3.m−3
300 of 464 Deltares
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Inorganic substances and pH
9.12 Reduction of iron by sulfides
PROCESS: IRONRED
Particulate oxidizing iron in the model consists of iron(III) oxyhydroxide, chemically indicated
with Fe(OH)3or FeOOH. Particulate oxidizing iron can be reduced abiotically by dissolved sul-
fides 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 pro-
duce reducing iron Fe2+ and sulfate. See process CONSELAC for the biotic reduction of
iron.
For particulate oxidizing iron two fractions are distinguished in the model, an amorphous frac-
tion 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
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:
H2S + 8 Fe(OH)3⇒8 Fe2+ + SO42−+6H2O + 14 OH−
FeS + 8 Fe(OH)3⇒9 Fe2+ + SO42−+4H2O + 16 OH−
The reduction of iron oxyhydroxide requires 0.0714 gS.gFe−1in the cases of H2S and FeS,
and 0.125 gFe.gFe−1in the case of FeS.
The reduction reactions are formulated according to double first-order kinetics:
Rire1=kire1×Cfea ×fs1×Csdt
ϕ×ϕ
Rire2=kire2×Cfec ×fs1×Csdt
ϕ×ϕ
Rire3=kire3×Cfes ×Cfea
Rire4=kire4×Cfes ×Cfec
where:
Cfes particulate iron sulfide concentration [gFe.m−3]
Cfea particulate amorphous oxidizing iron concentration [gFe.m−3]
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Cfec particulate crystalline oxidizing iron concentration [gFe.m−3]
Csdt total dissolved sulfide [gS.m−3]
fs1fraction hydrogen sulfide [-]
kire1specific rate of amorphous iron reduction with H2S [1/(gS.m−3.d)]
kire2specific rate of crystalline iron reduction with H2S [1/(gS.m−3.d)]
kire3specific rate of amorphous iron reduction with FeS [1/(gFe.m−3.d)]
kire4specific rate of crystalline iron reduction with FeS [1/(gFe.m−3.d)]
Rire1rate of amorphous iron reduction with H2S [gFe.m−3.d−1]
Rire2rate of crystalline iron reduction with H2S [gFe.m−3.d−1]
Rire3rate of amorphous iron reduction with FeS [gFe.m−3.d]
Rire4rate of crystalline iron reduction with FeS [gFe.m−3.d]
ϕporosity [-]
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:
kirei=kire20
i×ktire(T−20)
where:
kirei20 specific rate of abiotic particulate iron reduction i at 20 ◦C [1/(gS.m−3.d)]
ktire temperature coefficient for abiotic particulate iron reduction [-]
Ttemperature [◦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 H2S should be higher than the specific rates of reduc-
tion 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 ( ).
Name in
formulas
Name in
Input
Definition Units
Cfes FeS particulate iron sulfide concentration gFe.m−3
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Table 9.20: Definitions of the parameters in the above equations for IRONRED. Volume
units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in
Input
Definition Units
Cfea FeIIIpa particulate amorphous oxidizing iron
concentration
gFe.m−3
Cfec FeIIIpc particulate crystalline oxidizing iron con-
centration
gFe.m−3
Csdt SUD total dissolved sulfide concentration gS.m−3
fs1FrH2Sdis fraction dissolved hydrogen sulfide (H2S) -
kire120 RcFeaH2S20 spec. rate of amorphous iron red. with
H2S at 20 ◦C
gS−1.m3.d−1
kire220 RcFecH2S20 spec. rate of crystalline iron red. with
H2S at 20 ◦C
gS−1.m3.d−1
kire320 RcFeaFeS20 spec. rate of amorphous iron red. with
FeS at 20 ◦C
gFe−1.m3.d−1
kire420 RcFecFeS20 spec. rate of crystalline iron red. with
FeS at 20 ◦C
gFe−1.m3.d−1
ktire TcFeRed temperature coeff. for abiotic iron reduc-
tion at 20 ◦C
-
Rire1- rate of amorphous iron reduction with
H2S
gFe.m−3.d−1
Rire2- rate of crystalline iron reduction with H2S gFe.m−3.d−1
Rire3- rate of amorphous iron reduction with
FeS
gFe.m−3.d−1
Rire4- rate of crystalline iron reduction with FeS gFe.m−3.d−1
T Temp temperature ◦C
∆tDelt timestep d
ϕPOROS porosity m3.m−3
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9.13 Oxidation of iron sulfides
PROCESS: SULPHOX
Particulate components FeS and FeS2are 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 FeCO3is assumed not to be oxidized directly. The iron in this
component is oxidized after dissolution.
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 pro-
cesses and has been implemented for the following substances:
place FeS, FeS2, FeIId, OXY and SO4
The iron from FeS and FeS2 is added to the dissolved reducing iron FeIId. The oxygen con-
sumed 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 formula-
tions.
Formulation
The following oxidation reactions are included in the model:
FeS + 2 O2⇒Fe2+ + SO42−
2 FeS2+7O2+ 4 OH−⇒2 Fe2+ + 4 SO42−+2H2O
The oxidation of iron sulfide requires 1.143 gO2.gFe−1or 2.0 gO2.gS−1. The oxidation of
pyrite requires 2.0 gO2.gFe−1or 1.75 gO2.gS−1.
The oxidation reactions are formulated according to double first-order kinetics:
Rsox1=ksox1×Cfes ×Cox
ϕ×ϕ
Rsox2=ksox2×Cfes2×Cox
ϕ×ϕ
where:
Cfes iron sulfide concentration [gFe.m−3]
Cfes2pyrite concentration [gFe.m−3]
Cox dissolved oxygen concentration [gO2.m−3]
ksox1specific rate of iron sulfide oxidation [1/(gO2.m−3.d)]
304 of 464 Deltares
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Inorganic substances and pH
ksox1specific rate of pyrite oxidation [1/(gO2.m−3.d)]
Rsox2rate of iron sulfide oxidation [gFe.m−3.d−1]
Rsox2rate of pyrite oxidation [gFe.m−3.d−1]
ϕporosity [-]
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:
ksoxi=ksox20
i×ktsox(T−20)
ksoxi= 0.0if Cox ≤0.0
where:
ksoxi20 specific rate of iron sulfide or pyrite oxidation at 20 ◦C [1/(gO2.m−3.d)]
ktsox temperature coefficient for iron sulfide oxidation [-]
Ttemperature [◦C]
The oxidation process must stop at the depletion of iron sulfide. Therefore, each of the oxida-
tion 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 ( )
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
ksox120 RcFeSox20 specific rate of iron sulfide oxidation at
20 ◦C
gO2
−1.m3.d−1
ksox220 RcFeS2ox20 specific rate of pyrite oxidation at 20 ◦C gO2
−1.m3.d−1
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Table 9.21: Definitions of the parameters in the above equations for SULPHOX. Volume
units refer to bulk ( ) or to water ( )
Name in
formulas
Name in
Input
Definition Units
ktsox TcFeSox 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
T Temp temperature ◦C
∆tDelt timestep d
ϕPOROS porosity m3.m−3
306 of 464 Deltares
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Inorganic substances and pH
9.14 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)2are 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).
Particulate components FeS and FeS2are 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 FeCO3is as-
sumed not to be oxidized directly. The iron in this component is only oxidized after dissolution.
Implementation
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:
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+4H+⇒4 Fe3+ +2H2O
4 Fe(OH)++ O2+4H+⇒4 Fe3+ +2H2O + OH−
4 Fe(OH)2+ O2+4H+⇒4 Fe3+ +2H2O+2OH−
10 Fe2+ + 2 NO3
−+ 12 H+⇒10 Fe3+ + N2+6H2O
10 Fe(OH)++ 2 NO3
−+ 12 H+⇒10 Fe3+ + N2+6H2O + 10 OH−
10 Fe(OH)2+ 2 NO3
−+ 12 H+⇒10 Fe3+ + N2+6H2O + 20 OH−
The processes require 0.143 gO2.gFe−1or 0.05 gN.gFe−1.
Deltares 307 of 464
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The oxidation reactions are formulated according to double first-order kinetics:
Rioo = (kioo1×ffe1+kioo2×ffe2+kioo3×ffe3)×CfeIId
ϕ×Cox
ϕ×ϕ
Rion = (kion1×ffe1+kion2×ffe2+kion3×ffe3)×CfeIId
ϕ×Cni
ϕ×ϕ
where:
CfeIId total dissolved reducing iron concentration [gFe.m−3]
Cox dissolved oxygen concentration [gO2.m−3]
Cni nitrate concentration [gN.m−3]
ffeifraction Fe2+ (i=1), Fe(OH)+(i=2) or Fe(OH)2(i=3) in FeIId [-]
kiooispecific rate of iron i oxidation with dissolved oxygen [1/(gO2.m−3.d)]
kionispecific rate of iron i oxidation with nitrate [1/(gN.m−3.d)]
Rioo total rate of iron oxidation with oxygen [gFe.m−3.d−1]
Rion total rate of iron oxidation with nitrate [gFe.m−3.d−1]
ϕporosity [-]
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:
kiooi=kioo20
i×ktiox(T−20)
kiooi= 0.0if Cox ≤0.0
kioni=kion20
i×ktiox(T−20)
kioni= 0.0if Cox ≤0.0
where:
kiooi20 specific rate of iron i oxidation with oxygen at 20 ◦C [1/(gO2.m−3.d)]
kioni20 specific rate of iron i oxidation with nitrate at 20 ◦C [1/(gO2.m−3.d)]
ktiox temperature coefficient for iron oxidation [-]
Ttemperature [◦C]
The oxidation process must stop at the depletion of dissolved iron. Therefore, the total oxi-
dation 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
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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 ( ).
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
ffe1FrFe2dis fraction of Fe2+ in FeIId -
ffe2FrFe2OHd fraction of FeOH+in FeIId -
ffe3FrFe2OH2d fraction of Fe(OH)2in FeIId -
kioo120 RcI1oxox20 specific rate of Fe2+ oxidation with oxy-
gen at 20 ◦C
gO2
−1.m3.d−1
kioo220 RcI2oxox20 specific rate of FeOH+oxid. with oxygen
at 20 ◦C
gO2
−1.m3.d−1
kioo320 RcI3oxox20 specific rate of Fe(OH)2oxid. with oxy-
gen at 20 ◦C
gO2
−1.m3.d−1
kion120 RcI1oxni20 specific rate of Fe2+ oxidation with ni-
trate at 20 ◦C
gN−1.m3.d−1
kion220 RcI2oxni20 specific rate of FeOH+oxidation with ni-
trate at 20 ◦C
gN−1.m3.d−1
kion320 RcI3oxni20 specific rate of Fe(OH)2oxid. with nitrate
at 20 ◦C
gN−1.m3.d−1
ktiox TcIox temperature coefficient for iron oxidation
Rioo - rate of iron oxidation with dissolved oxy-
gen
gFe.m−3.d−1
Rion - rate of iron oxidation with nitrate gFe.m−3.d−1
T Temp temperature ◦C
∆tDelt timestep d
ϕPOROS porosity m3.m−3
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Processes Library Description, Technical Reference Manual
9.15 Speciation of dissolved iron
PROCESS: SPECIRON
Iron ions in solution associate with numerous anions, but under oxidizing conditions the dom-
inant 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.
The computed iron speciation is used in processes PRIRON and IRONOX to calculate pre-
cipitation/dissolution rates of iron minerals and oxidation rates of dissolved iron(II).
Implementation
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.
The processes have been implemented for the following substances:
FeIIId and FeIId.
The process calculates equilibrium speciation, not the associated mass fluxes. Table I pro-
vides 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 equa-
tions:
Fe3+ +2H2O⇔FeOH2+ + H3O+
Fe3+ +4H2O⇔Fe(OH)2++2H3O+
The chemical equilibria are described with:
Kfe31=Cfe3d2×H+
Cfe3d1
Kfe32=Cfe3d3×(H+)2
Cfe3d1
Cfe3dt = (Cfe3d1+Cfe3d2+Cfe3d3)×56 000 ×ϕ
where
Cfe3d1concentration of free dissolved Fe3+ [mol.l−1]
Cfe3d2concentration of dissolved FeOH2+ [mol.l−1]
Cfe3d3concentration of dissolved Fe(OH)2+[mol.l−1]
Cfe3dt concentration of total dissolved oxidizing iron [gFe.m−3]
310 of 464 Deltares
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Inorganic substances and pH
H+proton concentration [mol.l−1]
Kfe31stability (equilibrium, hydrolysis) constant for FeOH2+ [mol.l−1]
Kfe32stability (equilibrium, hydrolysis) constant for Fe(OH)2+[mol.l−1]
ϕporosity
The constant 56 000 concerns the conversion from gFe.m−3to mol.l−1.
The proton concentration H+and the temperature dependent stability constants follow from:
H+= 10−pH
Kfe31= 10lKfe31×ktfe3(T−20)
1
Kfe32= 10lKfe32×ktfe3(T−20)
2
where
ktfe31temperature coefficient for FeOH2+ equilibrium [-]
ktfe32temperature coefficient for Fe(OH)2+equilibrium [-]
pH acidity [-]
Ttemperature [◦C]
The concentration of the relevant iron(III) species in solution can now be calculated from:
Cfe3d1=Cfe3dt
(1 + Kfe31/H++Kfe32/(H+)2)×1
56 000 ×φ
Cfe3d2=Kfe31×Cfe3d1
H+
Cfe3d3=Cfe3dt
56 000 ×ϕ−Cfe3d1−Cfe3d2
if due to rounding off the resulting Cfe3d3<0.0
Cfe3d3=Kfe32×Cfe3d1
(H+)2
The pertinent fractions follow from:
ffe31=Cfe3d1
Cfe3dt ×56 000 ×ϕ
ffe32=Cfe3d2
Cfe3dt ×56 000 ×ϕ
ffe33= 1 −ffe31−ffe32
if due to rounding off the resulting ffe3<0.0
ffe33=Cfe3d3
Cfe3dt ×56 000 ×ϕ
Iron(II)
The hydrolysis of dissolved reducing iron proceeds according to the following reaction equa-
tions:
Fe2+ +2H2O⇔FeOH++ H3O+
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Fe2+ +4H2O⇔Fe(OH)2+2H3O+
The chemical equilibria are described with:
Kfe21=Cfe2d2×H+
Cfe2d1
Kfe22=Cfe2d3×(H+)2
Cfe2d1
Cfe2dt = (Cfe2d1+Cfe2d2+Cfe2d3)×56 000 ×ϕ
where
Cfe2d1concentration of free dissolved Fe2+ [mol.l−1]
Cfe2d2concentration of dissolved FeOH+[mol.l−1]
Cfe2d3concentration of dissolved Fe(OH)2[mol.l−1]
Cfe2dt concentration of total dissolved reducing iron [gFe.m−3]
H+proton concentration [mol.l−1]
Kfe21stability (equilibrium, hydrolysis) constant for FeOH+[mol.l−1]
Kfe22stability (equilibrium, hydrolysis) constant for Fe(OH)2+[mol.l−1]
ϕporosity
The constant 56 000 concerns the conversion from gFe.m−3to mol.l−1.
The proton concentration H+and the temperature dependent stability constants follow from:
H+= 10−pH
Kfe21= 10lKfe21×ktfe2(T−20)
1
Kfe22= 10lKfe22×ktfe2(T−20)
2
where
ktfe21temperature coefficient for FeOH+equilibrium [-]
ktfe22temperature coefficient for Fe(OH)2equilibrium [-]
pH acidity [-]
Ttemperature [◦C]
The concentration of the relevant iron(II) species in solution can now be calculated from:
Cfe2d1=Cfe2dt
(1 + Kfe21/H++Kfe22/(H+)2)×1
56 000 ×φ
Cfe2d2=Kfe21×Cfe2d1
H+
Cfe3d2=Cfe2dt
56 000 ×ϕ−Cfe2d1−Cfe2d2
if due to rounding off the resulting Cfe2d3= 0.0
Cfe2d3=Kfe22×Cfe2d1
(H+)2
312 of 464 Deltares
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Inorganic substances and pH
The pertinent fractions follow from:
ffe21=Cfe2d1
Cfe2dt ×56 000 ×ϕ
ffe22=Cfe2d2
Cfe2dt ×56 000 ×ϕ
ffe23= 1 −ffe21−ffe22
if due to rounding off the resulting ffe2= 0.0
ffe23=Cfe2d3
Cfe2dt ×56 000 ×ϕ
Directives for use
The stability constants have to be provided in the input of the model as logarithmic values
(10log )!
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 sta-
bility 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 10−4mg/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 10−3mole.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)
gFe.m−3
Cfe2dt FeIId concentration of total dissolved reducing
iron(II)
gFe.m−3
lKfe31lKstFe3OH log stability constant for Fe3OH2+
(l.mol−1)
log(-)
lKfe32lKstFe3OH2 log stability constant for Fe3OH2+
(l.mol−1)
log(-)
ktfe31TcKFe3OH temperature coefficient for KstFe3OH -
ktfe32TcKFe3OH2 temperature coefficient for KstFe3OH2 -
lKfe21lKstFe2OH log stability constant for Fe2OH+
(l.mol−1)
log(-)
lKfe22lKstFe2OH2 log stability constant for Fe2OH2
(l.mol−1)
log(-)
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Table 9.23: Definitions of the input parameters in the above equations for SPECIRON.
Name in
formulas
Name in
Input
Definition Units
ktfe21TcKFe2OH temperature coefficient for KstFe2OH -
ktfe22TcKFe2OH2 temperature coefficient for KstFe2OH2 -
H+– proton concentration mol.l−1
pH pH acidity -
T Temp temperature ◦C
ϕPOROS porosity m3.m−3
Table 9.24: Definitions of the output parameters of SPECIRON.
Name in
formulas
Name in
output
Definition Units
Cfe3d1DisFe3 concentration of free dissolved
iron(III)
mol.l−1
Cfe3d2DisFe3OH concentration of dissolved
FeOH2+
mol.l−1
Cfe3d3DisFe3OH2 concentration of dissolved
Fe(OH)2+
mol.l−1
ffe31FrFe3dis fraction of free dissolved iron(III) -
ffe32FrFe3OHd fraction of dissolved FeOH2+ -
ffe33FrFe3OH2d fraction of dissolved Fe(OH)2+-
Cfe2d1DisFe2 concentration of free dissolved
iron(II)
mol.l−1
Cfe2d2DisFe2OH concentration of dissolved
FeOH+
mol.l−1
Cfe2d3DisFe2OH2 concentration of dissolved
Fe(OH)2
mol.l−1
ffe21FrFe2dis fraction of free dissolved iron(II) -
ffe22FrFe2OHd fraction of dissolved FeOH+-
ffe23FrFe2OH2d fraction of dissolved Fe(OH)2-
314 of 464 Deltares
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Inorganic substances and pH
9.16 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 or-
ganic 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 concentra-
tion can be calculated from salinity and vice versa as described below.
The empirical relation between salinity and the chloride concentration (chlorosity) used is:
S= 0.03 + 1.805 ×Cl
ρw
The chloride concentration is expressed as gCl.m−3when density is expressed as kg.m−3.
Volume units refer to bulk ( ) or to water ( ).
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):
ρw= 1000 + 0.7×Cl
1000 ×rscl −0.0061 ×(T−4.0)2
S=S0+rscl ×Cl
ρw
The conversion of salinity into chloride follows from (SWSalCl = 1.0):
ρw= 1000 + 700 ×S
(1000 −S)×rscl −0.0061 ×(T−4.0)2
Cl =(S−S0)×ρw
rscl
where:
Deltares 315 of 464
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Cl chloride concentration (g.m−3)
rscl ratio of salinity and chloride in water (g.g−1)
Ssalinity (g.kg−1; psu; ppt; ‰)
S0minimal salinity at zero Cl (g.kg−1; psu; ppt; ‰)
Ttemperature (◦C)
ρwdensity of water with dissolved salts (kg.m−3)
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).
References
Greenberg et al. (1980)
Table 9.25: Definitions of the parameters in the above equations for SALINCHLOR. Vol-
ume units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in
input
Definition Units
Cl Cl chloride concentration g.m−3
SSalinity salinity g.kg−1
S0–salinity at zero Cl g.kg−1
rscl GtCl ratio of salinity and chloride in water g.g−1
SW SalCl SWSalCl option parameter for simulated substance –
TTemp temperature ◦C
ρw–density of water with dissolved salt kg.m−3
316 of 464 Deltares
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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
10.10 General contaminants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
Deltares 317 of 464
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10.1 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 phyto-
plankton (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.
Slow diffusion in solid matter has been acknowledged to take place after fast equilibrium ad-
sorption 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.
Volume units refer to bulk ( ) or to water ( ).
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:
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.
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The above substance names concern the situation, where equilibrium partitioning is simu-
lated. 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.
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.
Tables 10.1 and 10.2 provide the definitions of the input parameters occurring in the formula-
tions. 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:
fdf =φ
φ+Kppoc0×(Cpoc +Xdoc ×Cdoc) + Kpalg0×Calg
fdoc = (1 −f df )×Kppoc0×Xdoc ×Cdoc
Kppoc0×(Cpoc +Xdoc ×Cdoc) + Kpalg0×Calg
fpoc = (1 −f df )×Kppoc0×Cpoc
Kppoc0×(Cpoc +Xdoc ×Cdoc) + Kpalg0×Calg
falg = (1 −fdf −fdoc −fpoc)
where:
Calg/poc/doc concentration of algae biomass, dead particulate organic matter mat-
ter, and dissolved organic matter [gC m−3]
falg/poc/doc fraction of a micropollutant adsorbed to algae, dissolved organic mat-
ter, dead particulate organic matter [-]
fdf freely dissolved fraction of a micropollutant [-]
Kpalg/poc0partition coefficient for algae and dead particulate organic matter
[m3gC−1]
Xdoc adsorption efficiency of DOC relative to POC [-]
φporosity ([m3m−3]; equal to 1.0 for the water column)
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
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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 [ 10log(l.kgC−1)], corrected for temperature:
logKppoc =logKppoc20 +a×(1
(T+ 273.15) −1
293.15)
logKpalg =logKpalg20 +a×(1
(T+ 273.15) −1
293.15)
Kppoc0= 10logKppoc ×10−6
Kpalg0= 10logKpalg ×10−6
where:
atemperature coefficient [K]
Kpalg/poc20 partition coefficient for algae and dead particulate organic matter at
a temperature of 20 ◦C [L kgC−1]
Ttemperature [◦C]
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 previ-
ous 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:
fp0=fpoc0+falg0=Cmpp0
Cmpt0
fpe =fpoc +falg
if fp < fpe then
ksorp =ln(2)
tads
else
ksorp =ln(2)
tdes
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and
fp =fpe −(fpe −fp0)×exp(−ksorp ×∆t)
fdf =fdfe ×(1 −fp)
(1 −fpe)
fdoc =fdoce ×(1 −fp)
(1 −fpe)
fpoc =fpoce ×fp
fpe
falg =falge ×fp
fpe
where:
Cmpt/mpp0total and particulate concentration of micropollutant after the previ-
ous time-step [g m−3]
falg/poc0fractions of micropollutant adsorbed to algae and dead particulate
organic matter after the previous time step [-]
fp0/p/pe total particulate micropollutant fraction after the previous time-step,
at the end of the present timestep, and in equilibrium [-]
ksorp sorption rate [d−1]
For both options the sorption rate is calculated as:
Rsorp =fp ×Cmpt0−Cmpp0
∆t
where:
Rsorp sorption rate [g m−3d−1]
∆ttimestep 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:
Cmpdf =fdf ×Cmpt0
φ
Cmpdoc =fdoc ×Cmpt0
φ
Cmpd =Cmpdf +Cmpdoc
Cmpp = (fpoc +falg)×Cmpt0
Cmppoc =fpoc ×Cmpt0
Cpoc
Cmpalg =falg ×Cmpt0
Calg
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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 concentra-
tion adsorbed to DOC;
the apparent overall partition coefficient; and
the micropollutant contents of total suspended solids, detritus and phytoplankton.
The micro-pollutant content of total suspended solids and the apparent partition coefficient
follow from:
Cmppt =Cmpp ×106
Css
Kpt =Cmppt ×10−3
Cmpd +Cmpdoc
where:
Css the total suspended solids concentration [g m−3].
Cmppt the micropollutant content of total suspended solids [mg kg−1].
Kpt the apparent overall parttion coefficient [m3kg−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 ( 10log) 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 DOCS1/2for 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) = alog(Kow)+b(a= 0.8−1.0and b= 0.0−0.3; these coefficients
are different for the various types of micropollutants).
The input parameters SW SedY es/N o and OMP 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.
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Additional references
WL | Delft Hydraulics (1992b), DiToro and Horzempa (1982), Karickhoff et al. (1979), ?,Con-
nolly 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 ( ).
Name in
formulas
Name in input Definition Units
-OMP Group identifier of group 4 substances (organic
micropollutants)
-
Calg P HY T 1phytoplankton concentration gC m−3
Cdoc DOC dissolved organic matter concentration gC m−3
CimiIMi conc. inorg. particulate fractions i=1,2,3 gDW m−3
Cpoc P OCnoa2particulate organic matter concentration
without algae
gC m−3
Cmpt (i)total micropollutant concentration g m−3
Cmpd (i)−dis total dissolved micropollutant conc. g m−3
Cmpp (i)−par totsl particulate micropollutant conc. g m−3
Css SS total suspended matter concentration gDW m−3
logKpalg lKphy(i)10 logarithm of part. coeff. for phyto-
plankton
10log (L
kgC−1)
logKppoc lKpoc(i)10 logarithm of part. coeff. for POC 10log (L
kgC−1)
a T cKp(i)temperature coefficient of partition coef-
ficient
K
−W SedNo3option for process in water column (de-
fault = 0.0)
-
tads HLT Ads(i)half-life-time adsorption process d
tdes HLT Des(i)half-life-time desorption process d
T T emp temperature K
V V olume volume K
Xdoc XDOC(i)adsorption efficiency of DOC relative to
POC
-
φ P OROS porosity m3m−3
∆t Delt timestep d−1
1) Delivered by processes PHY_BLO (BLOOM) or PHY_DYN (DYNAMO).
2) Delivered by process COMPOS.
3) Default value must not be changed.
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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 ( ).
Name in
formulas
Name in input Definition Units
A Surf surface area m2
Calg P HY T S(k)1phytoplankton quantity gC
Cdoc DOCS(k)dissolved organic matter concentration gC m−3
CimiIMiS(k)quantity inorg. particulate fractions
i=1,2,3
gDW
Cpoc P OCS(k)1part. organic matter without algae gC
Cmpt (i)S(k)quantity of total micropollutant g
Cmpd (i)S(k)−dis quantity of total diss. org. micro-poll. g
Cmpp (i)S(k)−par quantity of total part. org. micro-poll. g
Css DMS(k)1total quantity of total sediment gDW
logKpalg lKphy(i)S(k)10 logarithm of part. coeff. for phyt. log(L kgC−1)
logKppoc lKpoc(i)S(k)10 logarithm of part. coeff. for POC log(L kgC−1)
a T cKp(i)S(k)temperature coefficient of partition co-
efficient
K
-SW SedY es2identifier for processes PARTS1/2 -
tads HLT Ads(i)S(k)half-life-time adsorption process d
tdes HLT Des(i)S(k)half-life-time desorption process d
Xdoc XDOC(i)adsorption efficiency of DOC relative
to POC
-
T T emp temperature K
V V olume volume m−3
Z ActT hS(k)thickness of sediment layer m
φ P ORS(k)porosity m3m−3
∆t Delt timestep d−1
1) Delivered by processes S1_COMP and S1_COMP.
2) 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 ( ).
Name in
formulas
Name in input Definition Units
Cmpt (i)tot total micropollutant concentration g m−3
Cmpd Dis(i)freely dissolved micropollutant conc. g m−3
Cmpdoc Doc(i)DOC adsorbed micropollutant conc. g m−3
fdf F r(i)Dis freely diss. micropoll. fraction (not bound
to DOC!)
-
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Table 10.3: Definitions of the output parameters for PARTWK_(i). (i) is a substance name.
Volume units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in input Definition Units
fdoc F r(i)DOC fraction micropollutant adsorbed to DOC -
fpoc F r(i)P OC fraction micropollutant adsorbed to POC -
falg F r(i)P HY T fraction micropollutant adsorbed to phy-
toplankton
-
Kpt Kd(i)SS apparent overall partition coefficient for
susp. solids
m3kgDW−1
-Q(i)P OC micropoll. content of particulate detritus g gC−1
-Q(i)P HY T micropoll. content of phyt. biomass g gC−1
Cmppt Q(i)SS micropollutant content of total sus-
pended solids
mg kgDW−1
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 ( ).
Name in
formulas
Name in
input1
Definition Units
Name in
formulas
Name in input Definition Units
Cmpt (i)S(k)tot total mass of the micropollutant g
Cmpd Dis(i)S(k)freely dissolved micropollutant conc. g m−3
Cmpdoc Doc(i)S(k)DOC adsorbed micropollutant conc. g m−3
fdf F r(i)DisS(k)freely diss. micropoll. fraction (not bound
to DOC!)
-
fdoc F r(i)DOCS(k)fraction micropollutant adsorbed to DOC -
fpoc F r(i)P OCS(k)fraction micropollutant adsorbed to POC -
falg F r(i)P HY T S(k)fraction micropollutant adsorbed to phy-
toplankton
-
Kpt Kd(i)DMS(k)apparent overall partition coefficient for
susp. solids
m3kgDW−1
-Q(i)P OCS(k)micropollutant content of part. detritus g gC−1
-Q(i)P HY T S(k)micropollutant content of phyt. biomass g gC−1
Cmppt Q(i)DMS(k)micropollutant content of total sus-
pended solids
mg kgDW−1
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10.2 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.
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
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 quanti-
ties 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
i=1
(focsedi×Cimi
1−focsedi×f ctr )
where:
Cim the concentration or quantity of inorganic matter [gDM m−3or gDM]
Cpoc the concentration or quantity of particulate organic carbon [gC m−3or gOC]
fctr weight conversion factor [gDM gOC−1]
focsed content organic carbon in total of sediment fraction [gOC gDM−1]
iindex for sediment component
The conversion factor fctr enters the equation because the content of organic matter focsed
is provided as organic carbon per dry matter total sediment for each fraction. From the con-
verted organic content, the inorganic fraction and the total weight of the sediment in dry weight
is calculated. Then, using the content of organic matter focsed 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.
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Name in
formulas
Name in input Definition Units
CimiIM (i)S(k)concentration of inorganic particulate
fractions i = 1,2,3
DW m−3
fctr DMCFOOC weight conversion factor for water col-
umn
gDW gC−1
DMCFOOCS weight conversion factor for sediment
layers
gDW gC−1
focsediFCSEDIM (i)S(k)content organic carbon in total of sedi-
ment fractions
gOC gDM−1
1) (i) is 1, 2 or 3 for IM1, IM2 or IM3. (k) is 1 or 2 for sediment layer S1 or S2.
Table 10.6: Definitions of the ouput parameters in the above equations for MAKOOC,
MAKOOCS1 and MAKOOCS2.
Name in
formulas
Name in inputDefinition Units
Cpoc P OCnoa conc. of total particulate organic carbon
in water (with or without algae biomass!)
gC m−3
Cpoc P OCS(k)quantity of total part. organic car-
bon in sediment (with or without algae
biomass!)
gC
1) (i) is 1, 2 or 3 for IM1, IM2 or IM3. (k) is 1 or 2 for sediment layer S1 or S2.
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10.3 Dissolution of organic micropollutants
PROCESS: DISOMP_(I)
Organic micropollutants may be discharged into a water system contained in an organic sol-
vent. 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.
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 dis-
solves 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 pro-
cess it is assumed that conditions for the eventual dissolution of all micropollutant are fulfilled.
Equilibrium sorption with respect to the solvent is ignored.
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 mi-
cropollutant repartitions among various organic phases also defined in the model.
Volume units refer to bulk ( ) or to water ( ).
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 for-
mulations 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 con-
centration 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 dis-
solved 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.
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Formulation
Assuming the eventual dissolution of all micropollutant in a solvent the dissolution is formu-
lated as a first order kinetic process:
Rdis =−kdis ×Cios
kdis =kdis20 ×ktdis(T−20)
where:
Cios concentration of micropollutant in organic solvent in water [g.m−3]
kdis20 dissolution rate constant at 20 ◦C [d−1]
ktdis temperature constant for dissolution [-]
Rdis dissolution rate [g.m−3.d−1]
The micropollutant dissolved from the organic solvent is allocated to the total micropollutant
(i) or to the dissolved micropollutant (i)-dis.
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 0.3−1.5d−1. An indicative
value for the dissolution rate of PCB153 is 0.7d−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 ( ).
Name in
formulas
Name in input Definition Units
Cios (i)-ios micropollutant in organic solvent
concentration
g.m−3
kdis20 RcDis(i) dissolution rate constant at 20 ◦Cd−1
ktdis T cDis(i)temperature constant of dissolution −
Rdis −dissolution rate g.m−3.d−1
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10.4 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.
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 condi-
tions, 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.
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 calcu-
late the overall degradation fluxes for sediment layers S1 and S2. In order to account for dif-
ferent 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−2d−1] in stead of [g m−3d−1].
Two options are available with respect to the formulation of the rate of degradation. An option
can be selected with parameter SW V nDegMP . 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.
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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 SWOXY-
PARWK 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
Two different sets of formulations are available. These sets differ with respect to the dis-
tinction of oxidising and reducing conditions and the pollutant fractions that are subjected to
degradation.
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 +k1deg20 ×ktdeg(T−20) ×frdeg ×Cmpt
where:
Cmpt total micropollutant concentration [g.m−3]
frdeg fraction subjected to degradation [-]
k0deg zeroth order degradation rate [g.m−3.d−1]
k1deg first order degradation rate [d−1]
ktdeg temperature coefficient of degradation [-]
Rdeg degradation rate [g.m−3.d−1]
Ttemperature [◦C]
Tccritical temperature for degradation [◦C]
The first order degradation rate at 20 ◦Ck1deg20 [d−1] depends on the redox conditions
according to:
k1deg20 =kdego20 if SW OXY = 1
kdegr20 if SW OXY = 0
where:
k1dego first order degradation rate at oxidising conditions [d−1]
k1degr first order degradation rate at reducing conditions [d−1]
The switch is determined as function of the dissolved oxygen concentration in process SWOXY-
PARWK.
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−3d−1] and [g m−3]. (After all
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fluxes have been quantified, they are multiplied with the water volume in order to obtain fluxes
in terms of [g d−1]!)
Factor frdeg is different for various options imposed with SW Deg with respect to the con-
centration fraction that is subjected to degradation.
Option 0
frdeg = 1.0(default)
Option 1
frdeg =fdf
Option 2
frdeg =fdf +fdoc
where:
fdf freely dissolved fraction of the micropollutant [-]
fdoc 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 +k1deg20 ×ktdeg(T−20) ×fdf ×Cmpt
where:
Cmpt total micropollutant concentration [g.m−3]
fdf freely dissolved fraction of the micropollutant [-]
k0deg zeroth order degradation rate [g.m−3.d−1]
k1deg first order degradation rate [d−1]
ktdeg temperature coefficient of degradation [-]
Rdeg degradation rate [g.m−3.d−1]
Ttemperature [◦C]
Tccritical 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]!)
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Directives for use
Formulation option SW V nDegM P = 0.0is 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.
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 (i)total micropollutant concentration g m−3
frdeg - fraction subjected to degradation -
fdf F r(i)Dis freely dissolved micropollutant fraction -
fdoc F r(i)Doc DOC-bound dissolved micropollutant fraction -
SW Deg SW Deg(i)switch for selection of one of the options -
SW OXY SW W aterCh switch for oxidising and reducing conditions,
computed with SWOXYPARWK
-
-SW V nDegM P switch for selection of formulations (no redox
dependency = 0.0, with redox dependency =
1.0)
-
k0deg ZLoss(i)zeroth-order degradation rate g m−3d−1
kdego20 RcDegO(i)first-order degr. rate at oxid. cond. and at 20
◦C
d−1
kdegr20 RcDegR(i)first-order degr. rate at red. cond. and at 20
◦C
d−1
k1deg20 Rc(i)first-order degradation rate at 20 ◦C d−1
ktdeg T c(i)temperature constant of degradation -
Rdeg - overall degradation rate g m−3d−1
T T emp ambient temperature ◦C
TcCT Loss critical temperature for degradation ◦C
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Table 10.9: Definitions of the parameters in the above equations for LOS_S1/2_(i). (i) is
a substance name.
Name in
formulas
Name in input Definition Units
H Depth depth of overlying water segment m
Cmtt (i)S1/2total micropollutant concentration g
frdeg - factor for conc. fraction subjected to
degradation
-
fdf F r(i)DisS1/2freely dissolved micropollutant fraction -
fdoc F r(i)DocS1/2DOC-bound dissolved micropollutant
fraction
-
SW Deg SW Deg(i)S1/2switch that allows selection of one of the
options
-
SW OXY SW P oreChS1/2switch for oxidising and reducing condi-
tions computed with SWOXYPARWK
-
-SW V nDegM P switch for selection of formulations (no
redox dependency = 0.0, with redox de-
pendency = 1.0)
-
k0deg ZLoss(i)S1/2zeroth-order degradation rate g m−2d−1
kdego20 RcDgO(I)S1/2first-order degr. rate at oxid. cond. and
at 20 ◦C
d−1
kdegr20 RcDgR(i)S1/2first-order degr. rate at red. cond. and
at 20 ◦C
d−1
k1deg20 Rc(i)S1/2first-order degradation rate at 20 ◦C d−1
ktdeg T c(i)Sed temperature constant of degradation -
Rdeg - overall degradation rate g.d−1
T T emp ambient temperature ◦C
TcCT Loss critical temperature for degradation ◦C
V V olume volume m3
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Organic micropollutants
10.5 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.
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 simu-
lated 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 oreChS1and SW P oreChS2for 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.
Volume units refer to bulk ( ) or to water ( ).
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 if Cox/φ > Coxc
SW OXY = 0 if Cox/φ ≤Coxc
with:
Cox actual dissolved oxygen concentration [g m−3]
Coxc critical dissolved oxygen concentration [g m−3]
φporosity (Section 1.6.1) [-]
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.
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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 lay-
ers. 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 pres-
ence 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 ( ).
Name in
formulas
Name in
input/output
Definition Units
Cox OXY dissolved oxygen concentration g m−3
Coxc CoxPart critical dissolved oxygen concentration g m−3
φPOROS porosity (Section 1.6.1) -
SWOXY SWWaterKch switch for oxidising or reducing cond. wa-
ter column
-
SWOXY SWPoreChS1 switch for oxidising or reducing cond.
sediment S1
-
SWOXY SWPoreChS2 switch for oxidising or reducing cond.
sediment S2
-
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Organic micropollutants
10.6 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.
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.
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 kland kgare inputs to VOLAT. These parameters are calculated with
‘process’ TRCOEF_(i) . The (freely) dissolved fraction of a micropollutant fdf concentration
is also input to VOLAT_(i) . This parameter is calculated with partitioning process PARTWK_(i)
.
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Formulation
The volatilization rate for a specific water segment is equal to:
Rvol =kvol ×(Cd −Cde)
H
with:
Cd freely dissolved micropollutant concentration [g m−3]
Cde freely dissolved micropollutant concentration in equilibrium [g m−3]
Hwater depth [m]
kvol overall transfer coefficient for volatilization [m d−1]
Rvol volatilization rate [g m−3d−1]
The dissolved concentrations follow from:
Cd =fdf ×Ct
Cde =Cg
He
with:
Ct total micropollutant concentration [g m−3]
Cg micropollutant concentration in the atmosphere [g m−3]
fdf freely dissolved micropollutant fraction [-]
He 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 = 1/1
kl
+1
(He ×kg)
with:
kltransfer coefficient for the liquid film [m d−1]
kgtransfer coefficient for the gas film [m d−1]
The dimensionless Henry’s constant He at ambient temperature is derived from Henry’s con-
stant 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 for-
mula is used to calculate the dimensionless Henry’s constant He at ambient temperature:
He =Ng
Nl ×e(a1+a2/(T+273.15))
Ng =P
Rg ×(Tref + 273.15)
a2= (Tref + 273.15) ×(ln (Hemr)−a1)
Hemr =Hepr ×Nl
P
with:
a1temperature coefficient for volatization entropy [-]
a2temperature coefficient for volatilization enthalpy [K−1]
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Hemr ref. Henry’s constant on the basis of mole fraction
[(molefr gas) (molefr water)−1]
Hepr ref. Henry’s constant on the basis of vapour pressure [Pa m3mol−1]
Ng number of moles in a m3gas [m−3]
Nl number of moles in a m3water (55510 m−3)
Patmospheric pressure (1.01×105Pa)
Rg the gas constant (8.314 Pa m3mol−1K−1)
Tambient temperature [◦C]
Tref reference temperature [◦C]
Coefficient a2represents the specific enthalpy of volatilization for the micropollutant, divided
by the gas constant (∆H◦/Rg). The coefficient a1is 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−1K−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:
Hep=P m
Cd =He ×R×(Tref + 273.15)
Hep=Hem×R×(Tref + 273.15) ×Ng
Nl =Hem×P
Nl
Hem=e−∆Ho
Rg×(T+273.15) +∆So
Rg
with:
He dimensionless Henry’s constant on the basis of concentration
[(mol m−3) (mol m−3)−1]
HemHenry’s constant on the basis of mole fraction [(molefr gas).(molefr water)−1]
HepHenry’s constant on the basis of vapour pressure [Pa.m3mol−1]
P m partial vapour pressure of a micropollutant [Pa]
Runiversal gas constant [Pa.m3mol−1K−1]
∆H◦enthalpy of volatilization for a micropollutant [kJ mol−1]
∆S◦entropy of volatilization for a micropollutant [kJ mol−1K−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 pro-
cesses. This parameter may range from less than 10−2to up to 103Pa m3mol−1:
In the range of 10−2to 1.0 Pa m3mol−1the 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 102Pa m3mol−1the liquid-phase and the gas-phase resistance
are both important. Volatilization for pollutants in this range is less rapid than for pollu-
tants 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 m3mol−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.
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Note that the temperature at which a Henry’s constant is measured in the literature Tref
should be used as model input.
Additional references
Mackay et al. (1980), Ten Hulscher et al. (1992)
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Table 10.11: Definitions of the parameters in the above equations. (i) is a substance
name.
Name in
formulas
Name in input Definition Units
a1T F He(i)temperature coefficient for volatization
entropy
-
a2- temperature coefficient for volatilization
enthalpy
K−1
Cd - dissolved micropollutant concentration g.m−3
Cde - freely dissolved micropollutant concen-
tration in equilibrium with the atmo-
sphere
g.m−3
Cg Atm(i)micropollutant concentration in the atmo-
sphere
g.m−3
Ct (i)total micropollutant concentration in the
water
g.m−3
fdf - freely dissolved micropollutant fraction -
H Depth depth of the upper water segment m
He - dimensionless Henry’s constant of mi-
cropollutant (i) at ambient temperature
[(mol.m−3).(mol.m−3)−1]
-
Hemr - Henry’s constant of micropoll. (i)
on the basis of mole fractions at ref.
Temp.[(mfr.Gas).(mfr.water)−1]
-
Hepr HeT ref (i)Henry’s constant of micropollutant (i) on
the basis of vapour pressure at reference
temperature
Pa.m3.mol−1
kl- transfer coefficient for a micropollutant
for the liquid film
m.d−1
kg- transfer coefficient for a micropollutant
for the gas film
m.d−1
Ng- number of moles in a m3gas m−3
Nl- number of moles in a m3water m−3
P- atmospheric pressure Pa
R- universal gas constant Pa.m3.mol−1.K−1
Rvol - volatilization rate g.m−3.d−1
T T emp ambient water temperature ◦C
Tref T ref (i)reference temperature ◦C
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0.001
0.01
0.1
1
10
100
1 2 3 4 5 6 7 8
Volatilisation rate as a function of wind
(SwTrcoef=0)
wind (m/s)
(m/d)
0.001
0.01
0.1
1
10
100
1 2 3 4 5 6 7 8
Volatilisation rate as a function of wind
(SwTrcoef=1)
wind (m/s)
(m/d)
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).
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Organic micropollutants
10.7 Transport coefficients
PROCESS: TRCOEF_i
The transfer coefficients kland kgare used to quantify the exchange of organic micropollu-
tants 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, klfor the liquid film and kgfor the gas film bordering the interface
between water and atmosphere. These coefficients are in fact mass transfer velocities.
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 imple-
mented, 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
m3mol−1and 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.
Implementation
The micropollutant specific transfer coefficients kgand klare 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:
kg= 273.15 ×(W+v)×r18
Mw
for W < 1.9m s−1:
kl= 5.64 ×v0.969
H0.673 ×r32
Mw
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for 1.9 m s−1≤W < 5m s−1:
kl= 5.64 ×v0.969
H0.673 ×r32
Mw ×e(0.526×(W−1.9))
for W≥5m s−1:
kl= 5.64 ×v0.969
H0.673 ×r32
Mw ×e(0.526×(5.0−1.9)) ×1+(W−5.0)0.7
with:
Mw molecular weight of the micropollutant [g mol−1]
vwater flow velocity [m s−1]
Wwindspeed at 10 meters above water level [m s−1]
The water flow velocity vhas to be larger than a critical small value (0.001 m s−1). When
smaller than the critical value, vis set equal to this value.
Option 1
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 < 0.3m s−1:
kl= 86 400 ×10−6+ 0.0144 ×u2.2
√Scl
for u≥0.3m s−1:
kl= 86 400 ×10−6+ 0.00341 ×u
√Scl
with:
ScgSchmidt number for the micropollutant in the atmosphere [-]
SclSchmidt number for the micropollutant in the water [-]
ufriction velocity [m.s−1]
The friction velocity at the water surface uis 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)
Scg= 86 400 ×ηg
ρg×Dg
Scl= 86 400 ×ηl
ρl×Dl
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ρg=1.293
1+0.00367 ×T
ρl= 1 000 −0.088 ×T
ηg= 10−5×(1.32 + 0.009 ×T)
ηl= 0.001
with:
Dgmolecular diffusion coeff. of micropollutant in air [m2d−1]
Dlmolecular diffusion coeff. of micropollutant in water [m2d−1]
Tambient temperature [◦C]
ρgdensity of air [kg m−3]
ρldensity of water [kg m−3]
ηgdynamic viscosity of air [Pa s−1]
ηldynamic viscosity of water [Pa s−1]
Directives for use
Wind speed and water flow velocity are provided in [m s−1], whereas the transfer coeffi-
cients 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)
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Table 10.12: Definitions of the parameters in the above equations for TRCOEF_(i). (i) is
a substance name.
Name in
formulas
Name in input Definition Units
DgGDif(i)molecular diffusion coeff. of micropol. (i)
in air
m2d−1
DlLDif(i)molecular diffusion coeff. of micropol. (i)
in water
m2d−1
H Depth depth of the upper water segment m
klKl(i)transfer coefficient for micropollutant (i)
for the liquid film
m d−1
kgKg(i)transfer coefficient for micropollutant (i)
for the gas film
m d−1
Mw Mol(i)molecular weight of micropollutant (i) g mol−1
option SW T rCoef switch that allows selection of one of the
options
-
Scg- Schmidt number for a micropollutant in
the atmosphere
-
Scl- Schmidt number for a micropollutant in
the water
-
u- friction velocity at the water surface m s−1
v V elocity water flow velocity m s−1
W V W ind wind speed at 10 meter above water
level
m s−1
T T emp ambient water temperature ◦C
ηg- dynamic viscosity of air [Pa s−1] kg m−1.s−1
ηl- dynamic viscosity of water [Pa s−1] kg m−1.s−1
ρg- density of air kg m−3
ρl- density of water kg m−3
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10.8 Settling of micropollutants
PROCESS: SED_(i)
Organic micro-pollutants adsorb to detritus and algae. Heavy metals also adsorb to sus-
pended 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.
When the S1/S2 approach is followed, the micropollutants are allocated to the sediment mi-
cropollutant pools as follows:
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,
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 sub-
stances (IM1, IM2, IM3, POC, PHYT) for this.
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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 (IM1/2/3),
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 gener-
ated 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:
Rsetj=ftauj×F setj
H
ifH < Hmin
F setj= 0.0
else
F setj= min F set0
j,Cxj×H
∆t
F set0
j=F set0j+sj×Cxj
ifτ =−1.0
ftau = 1.0
else
ftauj= max 0.0,1−τ
τcj
where:
Cx concentration of a carrier substance ([gDM m−3] or [gC m−3])
F set0zero-order settling flux of a carrier substance ([gDM m−2d−1] or [gC m−2d−1])
F set settling flux of a carrier substance ([gDMm−2d−1] or [gC m−2d−1])
ftau shear stress limitation function [-]
Hdepth of the water column [m]
Hmin minimum depth of the water column for settling and resuspension [m]
Rset settling rate of a carrier substance ([gDM m−3d−1] or [gC m−3d−1])
ssettling velocity of a carrier substance [m d−1]
τshear stress [Pa]
τc critical shear stress for the settling of a carrier substance [Pa]
∆ttimestep in DELWAQ (d)
jindex 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 =fsi,j ×Rsetj
where:
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fsi,j conc. of micro-pollutant i in carrier substance j ([gX gDM−1] or [gX gC−1])
Rsetjsettling rate carrier substance j ([gDW m−3d−1] or [C m−3d−1])
Rsmpi,j settling rate of micro-pollutant i in carrier substance j [gX m−3d−1]
iindex for micro-pollutant (i)
jindex for carrier substance (j), IM1, IM2, IM3, POC or PHYT
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 MinDepth for set-
tling, which has a default value of 0.1 [m]. When desired MinDepth may be given a
different value.
The settling fluxes fSed(i)and fSed(j)are available as additional output parameters.
Table 10.13: Definitions of the input parameters in the above equations for SED_(i).
Name in
formulas
Name in
input
Definition Units
Cx1
j(j1)concentration of carrier substance (j) gC/DM m−3
F set0jZSed(j)zero-order sett. flux of carrier subst. (j) gC/DM.m−2d−1
F setjfSedIM12settling flux of carrier substance IM1 gDM m−2d−1
fSedIM22settling flux of carrier substance IM2 gDM m−2d−1
fSedIM32settling flux of carrier substance IM3 gDM m−2d−1
fSedP HY T 2settling flux of carrier substance PHYT gC m−2d−1
fSedP OCnoa2settling flux of carrier substance POC
without algae biomass
gC m−2d−1
fsi,j Q(i)IM13metal conc. in inorg. part. fraction IM1 g gDW−1
Q(i)IM2metal conc. in inorg. part. fraction IM2 g gDW−1
Q(i)IM3metal conc. in inorg. part. fraction IM3 g gDW−1
Q(i)P HY T micro-pollutant conc. in algae PHYT g gC−1
Q(i)P OC micro-pollutant conc. in POC g gC−1
–F r(i)IM13fraction metal ads. to inorg. IM1 -
–F r(i)IM2fraction metal ads. to inorg. IM2 -
–F r(i)IM3fraction metal ads. to inorg. IM3 -
–F r(i)P HY T fraction micro-pollutant ads. to phyto-
plankton
-
–F r(i)P OC fraction micro-pollutant ads. to POC -
H Depth depth of the overlying water compartment m
Hmin MinDepth minimum water depth for settling and re-
suspension
m
sjV Sed(j)settling velocity of carrier substance (j) m d−1
τ T au shear stress Pa
τcjT aucS(j)crit. shear stress for settling of carrier
substance (j)
Pa
∆t Delt timestep in DELWAQ d
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Table 10.13: Definitions of the input parameters in the above equations for SED_(i).
Name in
formulas
Name in
input
Definition Units
1) 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.
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10.9 Sediment-water exchange of dissolved micropollutants
PROCESSES: SWEOMP_(I)
Dissolved organic micropollutants may be exchanged between sediment and overlying wa-
ter 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. Dis-
persive 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.
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.
Volume units refer to bulk ( ) or to water ( ).
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 con-
centration 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 dis-
solved 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)
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Formulation
The advective transport flux at the sediment-water interface due to seepage is formulated as
follows:
Rseep =vseep ×Cmpd
Cmpd =Cmpds1=Cmpdfs1+Cmpdocs1if vseep ≥0.0
Cmpdw=Cmpdfw+Cmpdocwif vseep < 0.0
where:
Cmpd total dissolved micropollutant concentration [g.m−3]
Cmpdoc DOC-bound dissolved micropollutant concentration [g.m−3]
Cmpdf freely dissolved micropollutant concentration [g.m−3]
Rseep seepage transport flux [g.m−2.d−1]
vseep volumetric seepage velocity [m.d−1]
s1index for the top sediment S1
windex for water
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 =Cmpds2=Cmpdfs2+Cmpdocs2if vseep ≥= 0.0
Cmpds1=Cmpdfs1+Cmpdocs1if vseep < 0.0
where:
s1index for the top sediment S1
s2index 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 ×(Cmpds1−Cmpdw)
Lsw
where:
Ddispersion coefficient (m2.d−1)
Lmixing length (m)
Rdisp dispersive transport flux (g.m−2.d−1)
ϕporosity of the sediment (-)
sw index for the sediment-water interface
s1index for the top sediment S1
windex for water
A positive flux results in the transport of micropollutant from the sediment to the overlying wa-
ter, a negative flux in the transport of micropollutant from the overlying water to the sediment.
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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 index for the interface of sediment S1 and S2
s1index for the deep sediment S1
s2index 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.
For the sediment-water interface only the dominant transport process is active in any time
step as follows from:
Rseep = 0.0, if |vseep|< ϕ.s1.Dsw/Lsw
Rdisp = 0.0, if |vseep| ≥ ϕ.s1.Dsw/Lsw
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 micropollu-
tant (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
1V 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.
2DisCoefSW and DisCoefSS always have positive values. The minimal value of the dis-
persion coefficients is the molecular diffusion coefficient adjusted for tortuosity. This ad-
justment 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 ( ).
Name in
formulas
Name in
input
Definition Units
Cmpdfw Dis(i) freely dissolved micropollutant concentra-
tion water
g.m−3
Cmpdfs1Dis(i)S1 freely dissolved micropollutant conc. in sed-
iment S1
g.m−3
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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 ( ).
Name in
formulas
Name in
input
Definition Units
Cmpdfs2Dis(i)S2 freely dissolved micropollutant conc. in sed-
iment S2
g.m−3
CmpdocwDoc(i) DOC-bound micropollutant concentration in
water
g.m−3
Cmpdocs1Doc(i)S1 DOC-bound micropollutant conc. in sedi-
ment S1
g.m−3
Cmpdocs2Doc(i)S2 DOC-bound micropollutant conc. in sedi-
ment S2
g.m−3
Cmpd (i)-dis total dissolved micropollutant concentration
in water
g.m−3
Dsw DisCoefSW dispersion coefficient at the sediment-water
interface
m2.d−1
Dss DisCoefSS dispersion coefficient at the sediment S1/2
interface
m2.d−1
Lsw MixLsw mixing length across the sediment-water in-
terface
m
Lss MixLss mixing length across the sediment S1/2 in-
terface
m
vseep VSeep volumetric seepage velocity m.d−1
Rdisp - dispersive transport rate g.m−2.d−1
Rseep - seepage transport rate g.m−2.d−1
ϕs1PORS1 porosity of the top sediment S1 -
ϕs2PORS2 porosity of the deep sediment S2 -
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10.10 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.
Substance cascade3, may be subject to decay and may be transformed into cascade4
and cascade5.
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.
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
dt =−diCi
The transformation process of cascade(i) into cascade(j) (index j larger than index i) is also
assumed to be of first-order:
dCi
dt =−tijCi
dCj
dt = +tijCi
where:
Ciconcentration of contaminant cascade(i) [g.m−3]
Cjconcentration of contaminant cascade(j) [g.m−3]
didecay rate of contaminant cascade(i) [d−1]
tij 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 re-
strictions. Substance cascade2 may therefore simultaneously be transformed into cascade3,
cascade4 as well as cascade5, similarly for all others.
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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
formulas
Name in input Definition Units
C1cascade1 Generic contaminant cascade1 g.m−3
C2cascade2 Generic contaminant cascade2 g.m−3
C3cascade3 Generic contaminant cascade3 g.m−3
C4cascade4 Generic contaminant cascade4 g.m−3
C5cascade5 Generic contaminant cascade5 g.m−3
d1decayc1 Decay rate constant for cascade1 d−1
d2decayc2 Decay rate constant for cascade2 d−1
d3decayc3 Decay rate constant for cascade3 d−1
d4decayc4 Decay rate constant for cascade4 d−1
d5decayc5 Decay rate constant for cascade1 d−1
t12 trans1to2 Transformation rate constant for
cascade1 to cascade2
d−1
t13 trans1to3 Transformation rate constant for
cascade1 to cascade3
d−1
t14 trans1to4 Transformation rate constant for
cascade1 to cascade4
d−1
t15 trans1to5 Transformation rate constant for
cascade1 to cascade5
d−1
t23 trans2to3 Transformation rate constant for
cascade2 to cascade3
d−1
t24 trans2to4 Transformation rate constant for
cascade2 to cascade4
d−1
t25 trans2to5 Transformation rate constant for
cascade2 to cascade5
d−1
t34 trans3to4 Transformation rate constant for
cascade3 to cascade4
d−1
t35 trans3to5 Transformation rate constant for
cascade3 to cascade5
d−1
t45 trans4to5 Transformation rate constant for
cascade4 to cascade5
d−1
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11 Heavy metals
Contents
11.1 Partitioning of heavy metals . . . . . . . . . . . . . . . . . . . . . . . . . 358
11.2 Reprofunctions for partition coefficients . . . . . . . . . . . . . . . . . . . 371
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11.1 Partitioning of heavy metals
PROCESS: PARTWK_i AND PARTS1/2_i
Partitioning is the process in which a substance is distributed among various dissolved, ad-
sorbed 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).
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 oxyhy-
droxides, aluminium hydroxides, manganese oxide and clays such as illite. Moreover, the ad-
sorption 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 reduc-
tion of iron and manganese at low redox potential, implying the loss of adsorption capac-
ity 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. How-
ever, the effects of pH and complexation on sorption can be taken into account, when using
so-called repro-functions for the partition coefficient.
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 co-
precipitation with iron(II) sulfides is likely to occur.
Slow diffusion in solid matter has been acknowledged to take place after fast equilibrium ad-
sorption 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 dis-
solved 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 ( ).
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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−3as 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 concentra-
tions g m−3as 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 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
The above substance names concern the situation, where equilibrium partitioning is simu-
lated. 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 DOC-
adsorbed 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 val-
ues for properties are substance specific. The private parameters HMGroup1/2/3identify
the group to which a heavy metal belongs.
The concentrations of inorganic matter (Cim1–3), detritus (Cpoc), dissolved organic mat-
ter (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 COM-
POS, 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 con-
centrations can be generated by processes SPECSUD, SPECSUDS1 and SPECSUDS2. Pro-
cess 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.
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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:
fdf =φ
φ+P3
i=1(Kpim0
i×Cimi) + Kppoc0×(Cpoc +Xdoc ×Cdoc) + Kpalg0×Calg
for i = 1, 2 and 3:
fimi=(1 −fdf)×Kpim0
i×Cimi
P3
i=1(Kpim0
i×Cimi) + Kppoc0×(Cpoc +Xdoc ×Cdoc) + Kpalg0×Calg
fdoc =(1 −fdf)×Kppoc0×Xdoc ×Cdoc
P3
i=1(Kpim0
i×Cimi) + Kppoc0×(Cpoc +Xdoc ×Cdoc) + Kpalg0×Calg
fpoc =(1 −fdf)×Kppoc0×Cpoc
P3
i=1(Kpim0
i×Cimi) + Kppoc0×(Cpoc +Xdoc ×Cdoc) + Kpalg0×Calg
falg = (1 −fdf −fim1−fim2−fim3−fdoc −fpoc)
where:
Calg/poc/doc concentration of algae biomass, dead particulate organic matter mat-
ter, and dissolved organic matter [gC m−3]
Cimiconcentration of inorganic matter fractions i = 1, 2 and 3 [gDW m−3]
falg/poc/doc fraction of micropollutant adsorbed to algae, dead particulate organic
matter dissolved organic matter, [-]
fimifraction of micropollutant adsorbed to inorganic matter fractions i =
1, 2 and 3 [-]
fdf freely dissolved fraction of a micropollutant [-]
Kpalg/poc0partition coefficient for algae and dead particulate organic matter
[m3gC−1]
Kpim0
ipartition coefficient for inorganic matter fractions i = 1, 2 and 3 [m3
gDW−1]
Xdoc adsorption efficiency of DOC relative to POC [-]
φporosity ([m3m−3]; equal to 1.0 for the water column)
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).
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Heavy metals
The partition coefficients in the above equations expressed in [m3gC−1] or in [m3gDW−1]
are derived from the input parameters expressed in [m3kgC−1] or [m3kgDW−1]:
Kpim0
i=Kpimi
1000 for i= 1,2and 3
Kppoc0=Kppoc
1000
Kppoc0=Kppoc
1000
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 metal fractions are corrected for slow sorption propor-
tional 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:
fp0=fim0
1+fim0
2+fim0
3+fpoc0+falg0=Chmp0
Chmt0
fpe =fim1+fim2+fim3+fpoc +falg
and
ksorp =(ln(2)
tads if fp < fpe
ln(2)
tdes if fp ≥fpe
with
fp =fpe −(fpe −fp0)×exp(−ksorp ×∆t)
fdf =fdfe ×(1 −fp)
(1 −fpe)
fdoc =fdoce ×(1 −fp)
(1 −fpe)
fimi=fimei×fp
fpe for i= 1,2and 3
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fpoc =fpoce ×fp
fpe
falg =falge ×fp
fpe
where:
Chmt/hmp0total and particulate conc. of metal after the previous time-step [g
m−3]
fimi0fractions of metal adsorbed to inorganic matter fractions I = 1, 2 or 3
after the previous time step [-]
falg/poc0fractions of metal adsorbed to algae and dead particulate organic
matter after the previous time step [-]
fp0/p/pe total particulate metal fraction after the previous time-step, at the end
of the present timestep, and in equilibrium [-]
ksorp sorption reaction rate [d−1]
For both options the sorption rate is calculated as:
Rsorp =fp ×Chmt0−Chmp0
∆t
where:
Rsorp sorption rate [g m−3d−1]
∆ttimestep of DELWAQ [d−1]
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 =fdf ×Chmt0
φ
Chmdoc =fdoc ×Chmt0
φ
Chmd =Chmdf +Chmdoc
Chmp = (fim1+fim2+fim3+fpoc +falg)×Chmt0
Chmimi=fimi×Chmt0
Cpoc for i= 1,2or 3
Chmpoc =fpoc ×Chmt0
Cpoc
Chmalg =falg ×Chmt0
Calg
For PARTS1_(i) and PARTS2_(i) the calculation of the dissolved concentrations also requires
division with the volume of the layer (V=Z·A).
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Oxidising conditions (SWOXY = 1), with precipitation
The above equations need a modification for group 2 metals such as chromium. These met-
als 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 formula-
tions 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 Crdf0. The molar freely dissolved concentration
follows from:
Crdf0=Chmdf
Crdf0
m=Crdf0
Mw ×10+3
with:
Crdf0
mmolar freely dissolved chromium concentration [mol l−1]
Mw molecular weight of chromium [g mol−1]
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)
Crfr0
m=Crdf0
m
1 + 10logKCr1×OH + 10logKCr2×OH2+ 10logKCr3×OH3
where:
Crfr0
mmolar free chromium ion concentration [mol l−1]
logKCr1/2/3the three equilibrium constants for hydroxyl complexation of chromium
[10log((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:
IAP =Crfr0
m×OH3
SOL = 10logKCrS
where:
logKCrS solubility equilibrium constant for chromium hydroxide [ 10log(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 precip-
itation is derived from the equilibrium free chromium ion concentration:
Crfrm=10logKCrS
OH3
Crdfm=Crfrm×1 + 10logKCr1×OH + 10logKCr2×OH2+ 10logKCr3×OH3
Crdf =Crdfm×Mw ×10+3
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fcor =Crdf
Crdf0
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 fpr
must be equal to:
fpr = 1 −f cor
The corrected sorbed fractions and concentrations for chromium are:
fdf =fdf0×(1 −fpr)
fdoc =fdoc0×(1 −fpr)
fimi=fim0
i×(1 −fpr)for i= 1,2or 3
fpoc =fpoc0×(1 −fpr)
falg =falg0×(1 −fpr)
Chmdf =Crdf ×(1 −fpr)
Chmdoc =Chmdoc0×(1 −fpr)
Chmd =Chmd0×(1 −fpr)
Chmp = (fim1+fim2+fim3+fpoc +falg +fpr)×Chmt0
Chmimi=Chmim0
i×(1 −fpr)for i= 1,2or 3
Chmpoc =Chmpoc0×(1 −fpr)
Chmalg =Chmalg0×(1 −fpr)
The group 2 metals such as chromium have been excluded from slow sorption as a conse-
quence 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 formula-
tions 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 (MeS0and
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×Mw ×10+3
where:
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Chmdfmmolar total dissolved metal concentration [mol l−1]
Csd molar dissolved sulfide S2−concentration [mol l−1]
Chsd molar dissolved hydrogen sulfide HS−concentration [mol l−1]
logKhm1/2the two equilibrium constants for sulfide complexation of a metal
[10log(l mol−1)]
logKhmS solubility equilibrium constant for metal sulfide [ 10log((l mol−1)2)]
Mw 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.
The fractions of the dissolved and precipitated species add up to one. Consequently the
various concentrations and fractions are:
fdf =Chmdfm×φ
Chmt0
fpr = 1 −f df
fdoc =fim1=fim2=fim3=fpoc =falg = 0.0
Chmdoc =Chmim1=Chmim2=Chmim3=Chmpoc =Chmalg = 0.0
Chmd =Chmdf
Chmp =fpr ×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 ad-
sorbed 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:
Chmpt =Chmp ×10+6
Css
Kpt =Chmpt ×10−3
Chmd +Chmdoc
where:
Css the total suspended solids concentration [g m−3].
Chmpt the metal content of total suspended solids [mg kg−1].
Kpt the apparent overall partition coefficient [m3kg−1].
The contents of the individual particulate fractions are calculated in a similar way.
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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−3kgC−1] or [m−3kgDW−1].
The concentrations of DOCS1/2for 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 coeffi-
cients, since the sorption capacity of sediments may vary substantially among water sys-
tems. In case three inorganic sediment fractions are considered one could take the par-
tition 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.
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 ( ).
Name in
formulas
Name in input Definition Units
Calg P HY T 1phytoplankton concentration gC m−3
Cdoc DOC dissolved organic matter conc. gC m−3
CimiIMi conc. inorg. part. fractions i = 1,2,3 gDW m−3
Cpoc P OCnoa2particulate organic matter concentration
without algae
gC m−3
Chmt (i)total metal concentration g m−3
Chmd (i)−dis total dissolved metal concentration g m−3
Chmp (i)−par total particulate metal concentration g m−3
Css SS2total suspended matter concentration gDW m−3
Kpalg Kd(i)P HY T partition coefficient for phytoplankton
(see directives!)
m−3kgC−1
KpimiKd(i)IMi part. coeff. for inorg. fractions i = 1,2,3 m−3kgDW−1
continued on next page
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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−3kgC−1
SW OXY SW W aterKCh3switch for oxidising or reducing condi-
tions
-
tads HLT Ads(i)half-life-time adsorption process d
tdes HLT Des(i)half-life-time desorption process d
Xdoc XDOC(i)ads. efficiency of DOC relative to POC -
V V olume volume m−3
ϕ P OROS porosity m3m−3
∆t Delt timestep d
1Delivered by processes PHY_BLO (BLOOM) or PHY_DYN (DYNAMO).
2Delivered by process COMPOS.
3Can be computed by process SWOXYPARWK.
4Default 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 ( ).
Name in
formulas
Name in input Definition Units
A Surf surface area m2
Calg P HY T S(k)1phytoplankton quantity gC
Cdoc DOCS(k)dissolved organic matter concentration gC m−3
CimiIMiS(k)quantity of inorganic particulate frac-
tions i = 1,2,3
gDW
Cpoc P OCS(k)1particulate organic matter quantity gC
Chmt (i)S(k)quantity total heavy metal g
Chmd (i)S(k)−dis quantity total dissolved heavy metal g
Chmp (i)S(k)−par quantity total particulate heavy metal g
Css DMS(k)1quantity of total sediment gDW
Kpalg Kd(i)P HY T S(k)partition coeff. for phytoplankton (see
directives!)
m−3kgC−1
Kpimi Kd(i)IMiS(k)part. coeff. for inorg. fractions i = 1,2,3 m−3kgDW−1
Kppoc Kd(i)P OCS(k)part. coeff. for POC (see directives!) m−3kgC−1
SW OXY SW P oreChS(k)2switch for oxidising or reducing condi-
tions
-
continued on next page
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Table 11.2 – continued from previous page
Name in
formulas
Name in input Definition Units
tads HLT Ads(i)S(k)half-life-time adsorption process d
tdes HLT Des(i)S(k)half-life-time desorption process d
Xdoc XDOC(i)ads. efficiency of DOC relative to POC -
V- volume m−3
Z ActT hS(k)thickness of sediment layer m
ϕ P ORS(k)porosity m3m−3
∆t Delt timestep d
1Delivered by processes S1_COMP and S1_COMP.
2Can be computed by process SWOXYPARWK.
3Default value must not be changed.
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 K1)
or DisHSS(k)
molar diss. hydrogen sulfide HS−con-
centration
mol l−1
Csd DisSW K or
DisSS(k)
molar dissolved sulfide S2−concen-
tration
mol l−1
logKCr1logK(i)OH1metal hydroxyl compl. constant
(1xOH; group 2)
10log(l mol−1)
logKCr2logK(i)OH2metal hydroxyl compl. constant
(2xOH; group 2)
10log((l mol−1)2)
logKCr3logK(i)OH3metal hydroxyl compl. constant
(3xOH; group 2)
10log((l mol−1)3)
logKCrS logK(i)Sol metal hydroxide solubility constant
(group 2)
10log((l mol−1)4)
logKhm1logK(i)Saq metal sulfide S2−complexation con-
stant (group 1)
10log(l mol−1)
logKhm2logK(i)HSaq metal hydr. sulfide HS−compl. con-
stant (group 1)
10log(l mol−1)
logKhmS logK(i)Ss metal sulfide solubility const. (group 1) 10log((l mol−1)2)
MwiMolW t(i)molecular weight of a metal g mol−1
pH pH or pHS(k)acidity -
1) The sulfide concentrations can be generated by processes SPECSUD, SPESUDS1 and
SPECSUDS2.
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Table 11.4: Definitions of the output parameters for PARTWK_(i). (i) is a substance name.
Volume units refer to bulk ( ) or to water ( ).
Name in
formulas
Name in output Definition Units
Chmt (i)tot total metal concentration g m−3
Chmd Dis(i)freely dissolved metal concentration g m−3
Chmdoc Doc(i)DOC adsorbed metal concentration g m−3
fdf F r(i)Dis freely dissolved metal fraction (not
bound to DOC!)
-
fdoc F r(i)DOC fraction metal adsorbed to DOC -
fim1F r(i)IM1fraction metal ads. to inorg. fraction IM1 -
fim2F r(i)IM2fraction metal ads. to inorg. fraction IM2 -
fim3F r(i)IM3fraction metal ads. to inorg. fraction IM3 -
fpoc F r(i)P OC fraction metal adsorbed to POC -
falg F r(i)P HY T fraction metal ads. to phytoplankton -
fpr F r(i)Sulf fraction metal precipitated -
Kpt Kd(i)SS apparent overall partition coefficient for
susp. solids
m3kgDW−1
-Q(i)IM1metal content of inorg. matter fr. IM1 g gDW−1
-Q(i)IM2metal content of inorg. matter fr. IM2 g gDW−1
-Q(i)IM3metal content of inorg. matter fr. IM3 g gDW−1
-Q(i)P OC metal content of particulate detritus g gC−1
-Q(i)P HY T metal content of phytoplankton biomass g gC−1
Chmpt Q(i)SS metal content of total suspended solids mg kgDW−1
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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 ( ).
Name in
formulas
Name in output Definition Units
Chmt (i)S(k)tot total metal concentration g m−3
Chmd Dis(i)S(k)freely dissolved metal concentration g m−3
Chmdoc Doc(i)S(k)DOC adsorbed metal concentration g m−3
fdf F r(i)DisS(k)freely dissolved metal fraction (not
bound to DOC!)
-
fdoc F r(i)DOCS(k)fraction metal adsorbed to DOC -
fim1F r(i)IM1S(k)fraction metal ads. to inorg. fraction IM1 -
fim2F r(i)IM2S(k)fraction metal ads. to inorg. fraction IM2 -
fim3F r(i)IM3S(k)fraction metal ads. to inorg. fraction IM3 -
fpoc F r(i)P OCS(k)fraction metal adsorbed to POC -
falg F r(i)P HY T S(k)fraction metal ads. to phytoplankton -
fpr F r(i)SulfS(k)fraction metal precipitated -
Kpt Kd(i)DMS(k)apparent overall partition coefficient for
susp. solids
m3kgDW−1
-Q(i)IM1S(k)1 metal content of inorg. matter fr. IM1 g gDW−1
-Q(i)IM1S(k)metal content of inorg. matter fr. IM2 g gDW−1
-Q(i)IM1S(k)metal content of inorg. matter fr. IM3 g gDW−1
-Q(i)P OCS(k)metal content of part. detritus g gC−1
-Q(i)P HY T S(k)metal content of phytopl. biomass g gC−1
Chmpt Q(i)DMS(k)metal content of total suspended solids mg kgDW−1
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11.2 Reprofunctions for partition coefficients
PROCESS: RFPART_(i)
The partition coefficient for (heavy) metals is a function of the composition of particulate mat-
ter, and therefore varies substantially among surface water systems. Strongly adsorbing com-
ponents 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!)
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
complexation of this ion by a number of ligands such as OH−, HCO−
3, SO2−
4and Cl−(at
oxidising conditions). The pH also directly influences adsorption via the competition of a free
metal ion with H3O+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.
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 par-
tition 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 IM1−
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.
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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:
Kp0= 10a×10(b×pH)×10c×pH2×ALKd×Cclg×DOCl×ALKm×pH ×ALKn×pH×log(ALK)×ALKo×pH2
Kpimi=Kp0×(103×CECi)
0.2for i = 1, 2 and 3
with:
Kp0reference partition coefficient [m3kgDW−1]
Kpimipartition coefficient with respect to sediment fraction i [m3kgDW−1]
ALK alkalinity [mole HCO−
3m−3]
Ccl chloride concentration [g m−3]
CECication exchange capacity of sediment fraction i [eq gDW−1]
DOC dissolved organic carbon concentration [gC m−3]
pH acidity [-]
a, b, c metal specific coefficients
d, g, l metal specific coefficients
m, n, o metal specific coefficients
Sediment (IM1−3) 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 a b c d l g m n o
cadmium -7.680 1.894 -0.0604 -0.0583 -0.715 0 0 0 0
copper -10.351 2.826 -0.159 0.994 -0.101 -0.138 -0.209 -0.0255 0
lead -2.265 1.270 -0.0705 0 -0.141 0 -0.112 -0.0141 0
zinc -25.811 6.719 -0.394 1.337 -0.201 0 0 -0.0590 -0.0270
mercury -33.411 9.633 -0.616 0 -0.936 0 0 0 0
nickel -22.654 5.702 -0.329 0 -0.171 0 0.289 -0.0388 -0.0492
chromium -40.123 11.121 -0.709 0 -0.110 -0.244 0 0 0
arsenic 3.555 -0.164 0.0098 -0.0159 -0.196 0 0 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 formu-
lations 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
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The North Sea repro-function is applied. This function reads:
Kp0= 10a×10b×pH ×(1.8×10+3 ×Ccl +c)d
Kpimi=Kp0×103×CECifor i = 1, 2 and 3
with:
Kp0reference partition coefficient per unit CEC [m3eq−1]
Kpimipartition coefficient with respect to sediment fraction i [m3kgDW−1]
Ccl chloride concentration [g m−3]
CECication exchange capacity of sediment fraction i [eq gDW−1]
pH acidity [-]
a, b, c, d metal specific coefficients
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= 5.0and d=−1.9.
Directives for use
Coefficients a–oare 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−1and (iv) humic matter 2.0-3.0 eq kg−1. The CEC of
suspended sediment can be estimated with:
CEC =CECpoc ×foc +CECsilt ×fsilt
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 foc can be estimated from the percentage
organic matter by dividing with a factor 1.7 (humic material) to 2.5 (fresh detritus). Both
foc and the percentage silt fsilt 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)
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Table 11.6: Definitions of input parameters in RFPART_(i), (i) is a substance name.
Name in
formulas
Name in input Definition Units
ALK ALK alkalinity∗mol m−3
Ccl Cl chloride concentration g m−3
CECiCECIMi cation exchange capacity of sediment
fractions i= 1,2,3
eq gDW−1
DOC DOC dissolved organic carbon concentration gC m−3
KpimiKd(i)IMi partition coefficient for sediment frac-
tions i= 1,2,3
m3kgDW−1
a CaRF Kp(i)metal specific coefficients in the repro-
functions
various
b CbRF Kp(i)(formula
c CcRF Kp(i)defined)
d CdRF Kp(i)
g CgRF Kp(i)
l ClRF Kp(i)
m CmRF Kp(i)
n CnRF Kp(i)
o CoRF Kp(i)
pH pH acidity -
SW Repro SW Repro switch for selection of partition coefficient
function (1 = Rhine repro, default; 2 =
North Sea repro)
-
∗mol m−3= meq L−1
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12 Bacterial pollutants
Contents
12.1 Mortality of coliform bacteria . . . . . . . . . . . . . . . . . . . . . . . . . 376
Deltares 375 of 464
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12.1 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 tempera-
ture, 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.
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:
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(12.1)
kmrti= (kmbi+kmcli)×ktmrt(T−20)
i+kmrd (12.2)
kmcli=kcli×Ccl (12.3)
kmrd =krd ×DL ×fuv ×I0×1−e−ε×H
ε×H(12.4)
For T≤T ci:
Rmrti= 0.0(12.5)
where:
Cx concentration of coliform bacteria species i[MPN.m−3]
DL daylength, fraction of a day [-]
εextinction of UV-radiation [m−1]
fuv fraction of UV-radiation as derived from visible light [-]
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Bacterial pollutants
Hwater depth [m]
I0daily solar radiation as visible light at the water surface [W.m−2]
kcl chloride related mortality constant [m3.g−1.d−1]
kmb basic mortality rate [d−1]
kmcl chloride dependent mortality rate [d−1]
kmrd radiation dependent mortality rate [d−1]
kmrt first order mortality rate [d−1]
krd radiation related mortality constant [m2.W−1.d−1]
ktmrt temperature coefficient of the mortality rate [-]
Rmrt mortality rate of coliform bacteria [MPN.m−3.d−1]
Ttemperature [◦C]
T c critical temperature for mortality [◦C]
Ccl chloride concentration [g.m−3]
iindex for coliform species, ECOLI, FCOLI, TCOLI and ENCOC
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−1have 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−2in 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−1d−1was found by Mancini
(1978), when the radiation was expressed in [langley h−1]. An indicative value of krd for
radiation in W m−2is 0.0862 (m2W−1d−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 cal cm−24.18 J cm−2
1 einstein m−2s−112.1 W m−2370 < l < 540 nm
1 kLux 3.75 W m−2
1 ergs m−2s−110−7W m−2
1 lumen 0.005 W White light
The UV-extinction coefficient ExtUV is high compared to the extinction coefficient of
visible light. A value of 3 m−1is indicative.
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Table 12.2: Definitions of the parameters in the above equations for (i)MORT.
Name in
formu-
las1
Name in input Definition Units
Cxi(i) concentration of coliform bacteria
species i1
MPN.m−3
Ccl Cl chloride concentration gCl.m−3
DL DAY L daylength, fraction of a day -
ε ExtUV extinction of UV-radiation m−1
fuv F rUV V L fraction of UV-radiation as derived from
visible light
-
H Depth water depth (layer thickness) m
I0RAD_uv daily solar radiation as visible light at wa-
ter surface
W.m−2
kcliSpMrt(i)chloride dependent mortality constant m3.g−1.d−1
kmbiRcMrt(i)basic mortality rate d−1
kmcli– chloride dependent mortality rate d−1
kmrdi– radiation dependent mortality rate d−1
kmrti– first order mortality rate d−1
krd CF RAD radiation dependent mortality constant m2.W−1.d−1
ktmrt T cMrt(i)temperature coefficient of the mortality
rate
-
Rmrti– mortality rate of coliform bacteria MPN.m−3.d−1
T T emp temperature ◦C
T ciCT Mrt(i)critical temperature for mortality ◦C
1substances (i) are ECOLI, FCOLI,TCOLI and ENCOC
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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
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
13.14 Conversion of exchange variable to segment variable . . . . . . . . . . . . 420
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Processes Library Description, Technical Reference Manual
13.1 Settling of sediment
PROCESS: SED_(I), S_(I), CALVS_(I)
The inorganic sediment components settle on the bed sediment. After settling these sub-
stances become part of the sediment inorganic matter pools, depending on the way of mod-
elling 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
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
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 (imple-
mented 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=ftaui×F seti
H
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ifH < Hmin
F seti= 0.0
else
F seti= min F set0
i,Cxi×H
∆t
F set0
i=F set0i+si×Cxi
ifτ =−1.0
ftau = 1.0
else
ftaui= max 0.0,1−τ
τci
where:
Cx concentration of a substance [gDM/O_2 m−3]
F set0zero-order settling flux of a substance [gDM/O_2 m−2d−1]
F set settling flux of a substance [gDM/O_2 m−2d−1]
ftau shear stress limitation function [-]
Hdepth of the water column [m]
Hmin minimal depth of the water column for resuspension [m]
Rset settling rate of a substance [gDM/O_2 m−3d−1]
ssettling velocity of a substance [m d−1]
τshear stress [Pa]
τc critical shear stress for settling of a substance [Pa]
∆ttimestep in DELWAQ [d]
iindex for substance (i)
The settling velocity as dependent on flocculation is formulated as follows:
si=ftemp ×fsal ×fcon ×s0i
ftemp =kt(T−20)
fsal = (ai+ 1
2)−(ai−1
2)×cos(π×S
Smax)
fcon = ( Cs
Csc)ni
where:
acoefficient for the enhancement of flocculation [-]
Cs concentration of total suspended solids [gDM m−3]
Csc critical concentration of total susp. solids above which flocc. occurs [gDM m−3]
fcon function for the concentration dependency of flocculation, see Figure 13.1A [-]
fsal function for the salinity function dependency of flocculation, range [0,EnhSedi),
see Figure 13.1B [-]
ftemp function for temperature dependency of settling [-]
kt temperature coefficient for settling (water density correction) [-]
niconstant for concentration effect on flocculation [-]
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Ssalinity [psu, g/kg]
Smax salinity at which the salinity function is at its maximum [g/kg]
Twater temperature [◦C]
iindex 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.
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
fSed(i)) is zero for the upper layers. Also τis 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 V0Sed(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
Cx1
i(i)1concentration of substance (i) gDM m−3
a EnhSed(i)coefficient for the enhancement of floc-
culation of substance (i)
-
F set0iZSed(i)zero-order settling flux of substance (i) gDM m−2d−1
H Depth depth of the water column, thickness
of water layer
m
continued on next page
382 of 464 Deltares
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Sediment and mass transport
Table 13.1 – continued from previous page
Name in
formulas
Name in
input
Definition Units
Hmin MinDepth minimal water depth for settling and re-
suspension
m
siV Sed(i)settling velocity of substance (i) for
SED_(i)
m d−1
s0iV0Sed(i)settling velocity of substance (i) for
CALVS_(i)
m d−1
Sal Salinity salinity psu
Salmax SMax salinity at which the salinity function is
at its maximum
psu
Cs SS concentration of total suspended
solids
gDM m−3
Csc CrSS critical concentration of total sus-
pended solids for flocculation
gDM m−3
niN(i)constant for concentration effect on
flocculation
-
T T emp temperature ◦C
kt T cSed temperature coefficient for settlingy -
τ T au shear stress Pa
τciT aucS(i)critical shear stress for settling of sub-
stance (I)
Pa
∆t Delt timestep in DELWAQ d
1) Substances are IM1, IM2 and IM3, or the BOD and COD substances. The latter only apply
for S_(i) input parameters.
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Processes Library Description, Technical Reference Manual
0 50 100 150 200 250
0
0.2
0.4
0.6
0.8
1
Sedimentation velocity as function of TSS
(n=1.5, V0Sed=0.1 m/d)
CrSS = 50
CrSS = 100
CrSS = 250
Total suspended sediment (gDM/m3)
(m/d)
0 50 100 150 200 250
0
0.2
0.4
0.6
0.8
1
Sedimentation velocity as function of TSS
(CrSS=100 gDM/m3, V0Sed=0.1 m/d)
n = 0
n = 1
n = 2
Total suspended sediment (gDM/m3)
(m/d)
Figure 13.1: Sedimentation velocity (Vsed) as a function of total suspended solid concen-
tration (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
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Sediment and mass transport
0246810
0
0.2
0.4
0.6
0.8
1
Effect of flocculation on the sedimentation velocity
(EnhSal=3, V0Sed=0.1 m/d)
SMax = 5 g/kg
Salinity (g/kg)
(m/d)
Figure 13.2: Sedimentation velocity (VSed) as a function of salinity solely (effect of floc-
culation and density not included).
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Processes Library Description, Technical Reference Manual
13.2 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:
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 fSedAlgDM for BLOOM. Process SEDPHDYN delivers the algae biomass settling flux
fSedAlgDM for DYNAMO.
The output parameters fSedT 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 fSedSOD, 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:
fSedT IM =
3
X
i=1
fSedIMi
fSedP OM noa =
4
X
j=1
fSedP OCj×DM CF P OCj
fSedDM =
3
X
i=1
fSedIMi×DMCF IMi+f SedP OMnoa +fSedAlgDM
fSedP OCnoa =
4
X
j=1
fSedP OCj
fSedP OC =f SedP OCnoa +f SedP hyt
where:
386 of 464 Deltares
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Sediment and mass transport
fSedPHYT settling flux of total phytoplankton [gC m−2d−1]
fSedAlgDM settling flux of total phytoplankton [gDM m−2d−1]
fSedPOC settling flux of total particulate organic carbon [gC m−2d−1]
fSedPOC_j settling flux of detritus fraction j [gC m−2d−1]
fSedPOCnoa settling flux of POC excluding algae [gC m−2d−1]
fSedPOMnoa settling flux of POC excluding algae [gDM m−2d−1]
fSedTIM settling flux of total inorganic matter [gDM m−2d−1]
fSedIM_i settling flux of inorganic matter fraction i [gDM m−2d−1]
fSedDM settling flux of dry matter [gDM m−2d−1]
DMCFIM_i dry matter conversion factor for inorganic matter fraction i (1-3) [gDM/gX]
DMCFPOC_j dry matter conversion factor for detritus fraction j (1-4) [gDM/gX]
The formulations for SED_SOD are:
if SW OxyDem = 0;
fSedSOD =fSedBOD5 + fSedBOD5_2 + fSedBOD5_3 + fSedBODu+
+fSedBODu_2 + fSedNBOD5 + fSedNBODu
if SW OxyDem = 1;
fSedSOD =fSedCODCr +fSedCODMn
if SW OxyDem = 2;
fSedSOD =fSedCODCr +fSedCODMn +fSedBOD5 + fSedBOD5_2 + fSedBOD5_3+
+fSedBODu +fSedBODu_2 + fSedNBOD5 + fSedNBODu
where:
fSedSOD settling flux of sediment oxygen demand [gO m−2d−1]
fSed(i) settling flux of the individual component (i) [gO m−2d−1]
SwOxyDem 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.
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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 formu-
las
Name in input Definition Units
DMCF IMiDMCF (i)dry matter conversion factor for inor-
ganic matter (i)
gDW/gX
DMCF P OCjDMCF (j)dry matter conversion factor for detritus
fraction (j)
gC/gX
fSedIMifSed(i)settling flux of inorganic matter fraction
(i)
gDM m−2d−1
fSedP OCjfSed(j)settling flux of detritus fraction (j) gC m−2d−1
fSedAlgDM fSedAlgDM settling flux of total phytoplankton gDM m−2d−1
fSedP HY T fSedP HY T settling flux of total phytoplankton gC m−2d−1
Table 13.3: Definitions of the input parameters in the formulations for SED_SOD.
Name in formu-
las
Name in input Definition Units
SwOXY Dem SwOXY Dem option parameter for substance defini-
tion (0=BOD, 1=COD, 2=BOD+COD)
-
fSedBOD5fSedBOD5settling flux of CBOD5gO2m−2d−1
fSedBOD5_2fSedBOD5_2settling flux of CBOD5_2gO2m−2d−1
fSedBOD5_3fSedBOD5_3settling flux of CBOD5_3gO2m−2d−1
fSedBODu f SedBODu settling flux of CBODu gO2m−2d−1
fSedBODu_2fSedBODu settling flux of CBODu_2gO2m−2d−1
fSedNBOD5fSedNBOD5settling flux of NBOD5gO2m−2d−1
fSedNBODu fSedNBODu settling flux of NBODu_2gO2m−2d−1
fSedCODCr fSedCODCr settling flux of COD_Cr gO2m−2d−1
fSedCODMn f SedCODMn settling flux of COD_Mn gO2m−2d−1
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13.3 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.
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.
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 impos-
ing 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 ( ).
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
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Processes Library Description, Technical Reference Manual
TIC, Alka
Processes ADVTRA and DSPTRA deliver the velocities for advection and dispersion for pro-
cesses TRASE2_(i) (or TRSE2_(i) or TRSE2(i)). The latter processes deliver total trans-
port velocities to be used by Delwaq for the calculation of fluxes by multiplication with con-
centrations. 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.
Formulation
Resuspension
The resuspension flux of sediment dry matter is described as zero-order kinetics according to
Partheniades-Krone (SwErosion = 0.0):
F res0=ftau ×F res0
if H < Hmin F res0= 0.0else
F res = min F res0,Cdm
A×∆t
if τ=−1.0ftau = 1.0else
ftau = max 0.0,τ
τc −1.0
where:
Asurface area of overlying water compartment [m2]
Cdm amount of sediment dry matter in the top sediment layer [gDM]
F res0zero-order resuspension flux of sediment [gDM.m−2.d−1]
F res resuspension flux of sediment [gDM.m−2.d−1]
ftau shear stress limitation function [−]
Hdepth of the water column, thickness overlying water layer [m]
Hmin minimal depth of the water column for resuspension [m]
τshear stress [P a]
τc critical shear stress for resuspension [P a]
∆ttimestep in DELWAQ [d]
Cdm and Hare calculated by the model.
Advection
The burial of particulate substances results from (net) settling at the sediment-water inter-
face, digging results from (net) resuspension at this interface. The advection of particulate
substances by burial or digging follows from:
F advp=vp ×fp ×Cx
(1 −φ)
where:
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Cx concentration of a substance [g.m−3]
F advpparticulate advection flux [g.m−2.d−1]
fp particulate fraction of a substance [−]
vp volumetric burial or digging velocity [m.d−1]
jporosity [−]
Fraction fp is equal to 1.0 for all particulate substances, except for organic micro-pollutants
and heavy metals. The model calculates fp for these substances as depending on adsorp-
tion.
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:
ϕ= 1 −
i=n
X
i=1 fpi×Cxi
ρi
where:
Cx concentration of a substance, a sediment component [g.m−3]
F advpparticulate advection flux [g.m−2.d−1]
fpparticulate fraction of a substance [−]
ρdensity of a solid matter component [g.m−2.d−1]
iindex of a solid matter component [−]
nnumber of solid matter components [−]
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 sub-
stances. 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 ×fd ×Cx
φ
where:
Cx concentration of a substance [g.m−3]
F advddissolved advection flux [g.m−2.d−1]
fd dissolved fraction of a substance [−]
vd volumetric seepage velocity [m.d−1]
jporosity [−]
The fraction fd = 1 −fp is equal to 1.0for all dissolved substances, except for organic
micro-pollutants and heavy metals.
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Dispersion
Bioturbation by benthic organisms causes the dispersion of particulate substances. The per-
tinent dispersion flux is approximated with:
F disp= max (1 −φ1,1−φ2)×Dp×(fp1×Cx1/(1 −φ1)−fp2×Cx2/(1 −φ2))
(L1+L2)
where:
Cx bulk concentration of a substance [g.m−3]
Dp particulate dispersion coefficient [m2.d−1]
F dispparticulate dispersion flux [g.m−2.d−1]
fpparticulate fraction of a substance [−]
Ldispersion length [m]
φporosity [−]
indexes 1 and 2 refer to two adjacent sediment layers (grid cells)
Each dispersion length Lis the half thickness of the sediment layer concerned. The bioturba-
tion 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 nutri-
ents to the water column and the sediment oxygen consumption flux. The dispersion flux of a
solute follows from:
F disd= min (φ1, φ2)×Dd ×(fd1×Cx1/φ1−f d2×Cx2/φ2)
(L1+L2)
where:
Cx concentration of a substance [g.m−3]
Dd diffusion or dispersion coefficient [m2.d−1]
F disddissolved dispersion flux [g.m−2.d−1]
fd dissolved fraction of a substance [−]
Ldispersion length [m]
φporosity [−]
indexes 1 and 2 refer to two adjacent sediment layers (grid cells)
Each dispersion length Lis the half thickness of the sediment layer concerned. For the
sediment-water interface L1in 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 bound-
ary).
Directives for use
1 Porosity φis 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 0.4for sandy sediment, 0.7for silty sediment and 0.9for peaty sediment
(partially consolidated top sediment in a water system!).
2Poros is an output parameter that can be used to verify the imposed porosity. It is calcu-
lated by auxiliary process DMVolume that needs densities RhoIM and RhoOM as input
parameters.
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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 thick-
ness. SwSediment = 0.0for fixed thickness, and SwSediment = 1.0for variable thick-
ness. 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 nega-
tive value digging
8DifCoef 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 m2d−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 tortu-
osity (φ2) at depths below 0.1min freshwater systems, and below 0.4min marine
water systems. A representative value for the corrected molecular diffusion coefficient is
0.25 ×10−4 m2d−1.
9TurCoef affects mass transport of particulate substances across all sediment interfaces,
except for the sediment-water interface. The first given value concerns the interface be-
tween 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
m2d−1. The winter value can be 10 % of the summer value. Bioturbation can be signif-
icantly faster in marine sediments. TurCoef decreases exponentially with depth, and is
practically equal to zero at depths below 0.1min freshwater systems, and below 0.4m
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, DSP-
TRA and TRASE2_(i) (or TRSE2_(i) or TRSE2(i)). Volume units refer to bulk
( ), water ( ) or solids ( ).
Name in for-
mulas
Name in in-
put
Definition Units
ASurf surface area of overlying water com-
partment
m2
Dd DifCoef1) dispersion coefficient for solutes m2.d−1
Dp T urCoef 1) dispersion coefficient for particulates m2.d−1
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F res0ZResDM zero order resuspension flux gDM.m−2.d−1
Hmin MinDepth minimal water depth for resuspension m
L1Diflen dispersion length in the overlying water m
−F ixT h2) fixed layer thickness m
−MaxT h2) maximal layer thickness for variable
thickness
m
−MinT h2) minimal layer thickness for variable
thickness
m
SwErosion SwErosion option (0= Part-Krone; 1= De Boer) −
SwSediment SwSediment option (0= fixed layers; 1= variable) −
vp VburDM burial and digging velocity m.d−1
vd Vseep seepage velocity m.d−1
∆tDelt timestep d−1
ρiRhoIM density of inorganic matter g.m−3
RhoOM density of organic matter g.m−3
j P orinp2input porosity −
τTau shear stress P a
τc TauCrDM critical shear stress for resuspension P a
1) Needs to be specified for each interface in a sediment column.
2) Needs to be specified for each layer in a sediment column.
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13.4 Transport in sediment and resuspension (S1/2)
PROCESSES: S12TRA(I), RES_DM, BUR_DM, DIG_DM, S1_COMP, S2_COMP,
PARTS1_(I), PARTS2_(I)
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 sedi-
ment 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 col-
umn;
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 ex-
ceeds a certain critical value, or when the water depth is smaller than a certain critical depth.
Volume units refer to bulk ( ), water ( ) or solids ( ).
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, Det-
SiS1 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:
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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,
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,
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 sed-
iment 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 thick-
nesses 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 first-
order kinetics according to:
F resj
0=ftauj×(F res0 + r×Cdmj/A)
if H < Hmin F resj
0= 1.0else
F resj=min F resj
0,Cdm
A×∆t
if DMS1>0.0F resS2 = 0.0
if τ=−1.0fτ= 1.0else
ftauj= max(0.0,(τ
τcj−1.0))
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where:
Asurface area of overlying water compartment [m2]
Cdm amount of sediment dry matter [gDM]
F res0zero-order resuspension flux of sediment [gDM.m−2.d−1]
F res resuspension flux of sediment [gDM.m−2.d−1]
ftau shear stress limitation function [−]
Hdepth of the water column, thickness overlying water layer [m]
Hmin minimal depth of the water column for resuspension [m]
rfirst-order resuspension rate [d−1]
τshear stress [P a]
τc critical shear stress for resuspension [P a]
∆ttimestep in DELWAQ [d]
jindex for sediment layer S1 or S2.
The resuspension of inorganic sediment components, organic carbon, nitrogen, phosphorus
and silicate components, adsorbed phosphate, micro-pollutants and heavy metals in the sed-
iment follows from:
Rresi,j =fsi,j ×fri,j ×F resj/H
where:
fr fraction of a component in sediment dry matter [gX.gDM−1]
fs scaling factor [−] or [gX.gY −1]
Rres resuspension rate of a component [gX.m−3.d−1]
iindex for component i
jindex for sediment layer S1 or S2.
The ratio fs 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 sedi-
ment dry matter follows from:
F burj=(F inj+(Zj−Zf ixj)×ρj×(1−φj)
∆tif Zj≥Zfix j
0.0
F in1=Fset
F in2=Fbur1
where:
Fbur burial flux of sediment [gDM.m−2.d−1]
Fin influx of sediment [gDM.m−2.d−1]
Fset settling flux of sediment [gDM.m−2.d−1]
Zactual thickness of sediment layer [m]
Zfix fixed thickness of sediment layer [m]
ϕporosity [−]
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ρdensity of sediment dry matter (g.m−3)
∆ttimestep in DELWAQ [d]
jindex 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:
F burj= min ((F binj+F badj), F bmax j)
F binj=F bur0j+rbj×Cdmj/A
F badj= max 0,(Zj−Zmax j)×ρj×(1−φj)
∆t
F bmax j=F inj−F outj+Cdmj
A×∆t
Cdmj=A×Zj×ρj×(1−φj)
F in1=Fset
F in2=Fbur1
F out1=Fres1
F out2=Fdig1
where:
Asurface area of overlying water compartment [m2]
Cdm amount of sediment dry matter [gDM]
F bad additional burial flux to obey maximal layer thickness [gDM.m−2.d−1]
F bin burial flux of sediment based on input parameters [gDM.m−2.d−1]
F bmax maximal possible burial based on available sediment [gDM.m−2.d−1]
F bur0zero-order burial flux of sediment [gDM.m−2.d−1]
F bur burial flux of sediment [gDM.m−2.d−1]
F dig digging flux of sediment [gDM.m−2.d−1]
F in influx of sediment [gDM.m−2.d−1]
F out outflux of sediment [gDM.m−2.d−1]
F res resuspension flux of sediment [gDM.m−2.d−1]
F set settling flux of sediment [gDM.m−2.d−1]
rb first-order burial rate [d−1]
Zactual thickness of sediment layer [m]
Zfix fixed thickness of sediment layer [m]
Zmax maximal thickness of sediment layer [m]
ϕporosity [−]
ρdensity of sediment dry matter [g.m−3]
∆ttimestep in DELWAQ [d]
jindex for sediment layer S1 or S2.
The burial of inorganic sediment components, organic carbon, nitrogen, phosphorus and sil-
icate components, adsorbed phosphate, micro-pollutants and heavy metals in the sediment
follows from:
F buri,j =fsi,j ×fri,j ×F burj
Rburi,j =F buri,j /H
where:
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fr fraction of a component in sediment dry matter [gX.gDM−1]
fs scaling factor [−] or [gX.gY −1]
Hdepth of the water column, thickness overlying water layer [m]
F bur burial flux of a component [gX.m−2.d−1]
Rbur burial rate of a component [gX.m−3.d−1]
iindex for component i
jindex for sediment layer S1 or S2.
The ratio fs 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
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 sedi-
ment dry matter follows from:
if Zj< Zfixjthen
F digj=F outj+(Zfixj−Zj)×ρj×(1−φj)
∆t
if Zj=Zfixjthen
F digj=F outj
and
F out1=Fres1
F out2=Fdig1
where:
F dig digging flux of sediment [gDM.m−2.d−1]
F out outflux of sediment [gDM.m−2.d−1]
F res resuspension flux of sediment [gDM.m−2.d−1]
Zactual thickness of sediment layer [m]
Zfix fixed thickness of sediment layer [m]
ϕporosity [−]
ρdensity of sediment dry matter [g.m−3]
∆ttimestep in DELWAQ [d]
jindex 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)
F dmax 1=Cdm2
A×∆t
F dmax 2=∞
Cdm2=A×Z2×ρ2×(1−φ2)
where:
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Asurface area of overlying water compartment [m2]
Cdm amount of sediment dry matter [gDM]
F dig digging flux of sediment based on input parameters [gDM.m−2.d−1]
Fdig0 zero-order digging flux of sediment [gDM.m−2.d−1]
Fdmax maximal possible digging based on available sediment [gDM.m−2.d−1]
Zactual thickness of sediment layer [m]
ϕporosity [−]
ρdensity of sediment dry matter (g.m−3)
∆ttimestep in DELWAQ [d]
jindex for sediment layer S1 or S2.
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)
F digi,j =fsi,j ×fri,j ×F digj
if SW Digj= 1.0 (quality of underlying layer)
F digi,j =fsi,j+1×fri,j+1×F digj
and
Rdigi,j =F digi,j /H
where:
fr fraction of a component in sediment dry matter [gX.gDM−1]
fs scaling factor [−] or [gX.gY −1]
Hdepth of the water column, thickness overlying water layer [m]
F dig digging flux of a component [gX.m−2.d−1]
Rdig digging rate of a component [gX.m−3.d−1]
iindex for component i
jindex for sediment layer S1 or S2.
The ratio fs 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 bound-
ary 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, N-
COOCS2, 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.
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2T 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 10−6for organic micro-pollutants and heavy metals
for the conversion from mgX.kgDM−1to 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 (fri,1,fsi,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 (fri,2,fsi,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 (fri,2,fsi,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 (fri,3,fsi,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 in-
put
Definition Units
F burjfBur(i)DM3 burial flux of sediment from layer j gDM.m−2.d−1
F digjfDig(i)DM3 digging flux of sediment to layer j gDM.m−2.d−1
F resjfRes(i)DM3 resuspension flux of sediment from layer j gDM.m−2.d−1
fri,j Fr(i)(j) fraction of a component in sediment layer j
for inorganic sediment components, micro-
phytobenthos, detritus components, and
AAP
gX.gDM−1
fri,j Q(i)DM(j) content in sediment layer j for organic micro-
pollutants and heavy metals
mgX.kgDM−1
continued on next page
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Table 13.5 – continued from previous page
Name in
formulas
Name in in-
put
Definition Units
fsi,j N-CDetC(j) ratio of DetN and DetC in sediment layer j gN.gC−1
P-CDetC(j) ratio of DetP and DetC in sediment layer j gP.gC−1
S-CDetC(j) ratio of DetSi and DetC in sediment layer j gSi.gC−1
or
N-COOC(j) ratio of OON and OOC in sediment layer j gN.gC−1
P-COOC(j) ratio of OOP and OOC in sediment layer j gP.gC−1
S-COOC(j) ratio of OOSi and OOC in sediment layer j gSi.gC−1
fsi,j ScalCar scaling factor for all other components -
H Depth depth of the overlying water compartment m
SW DigjSWDig(j) option parameter,
=0.0 quality of layer itself,
=1.0 quality from underlying layer
-
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 fri,j
and fsi,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
CdmjDM(j) amount of sediment dry matter in sediment
layer j
gDM
F res0ZResDM zero-order resuspension flux of sediment gDM.m−2.d−1
ASurf surface area of overlying water comp. m2
HDepth depth of the overlying water compartment m
Hmin MinDepth minimal water depth for resusp. and settling m
rVResDM first-order resuspension rate of sediment d−1
τTau shear stress P a
τcjTaucR(j)DM critical shear stress for resusp. from sedi-
ment layer j
P a
∆tDelt timestep in DELWAQ d
1)(j) is equal to S1 or S2, which represents the pertinent sediment layer
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Table 13.7: Definitions of the input parameters in the above equations for BUR_DM.
Name in
formulas
Name in in-
put
Definition Units
Fbur0 jZBurDM(j) zero-order burial flux of sediment in layer j gDM.m−2.d−1
Fset fSedDM2) settling flux of sediment gDM.m−2.d−1
FresjfRes(j)DM resuspension flux of sediment gDM.m−2.d−1
ASurf surface area of overlying water compart-
ment
m2
ZjActTh(j) actual thickness of sediment layer j fixed
thickness of sediment layer j maximal thick-
ness of sediment layer j
m
ZfixjFixTh(j) fixed thickness of sediment layer j maximal
thickness of sediment layer j
m
ZmaxjMaxTh(j) maximal thickness of sediment layer j m
rbjVBurDM(j) first-order burial rate of sediment in layer j d−1
SW SedimentSWSediment option parameter,
=0.0 apply fixed layer thickness,
=1.0 apply burial kinetics
-
ϕjPor(j) shear stress P a
ρjRho(j) critical shear stress for resusp. from sedi-
ment layer j
P a
∆t Delt timestep in DELWAQ d
1) (j) is equal to S1 or S2, which represents the pertinent sediment layer
2) 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 in-
put
Definition Units
F dig0jZDigDM(j) zero-order digging flux of sediment in layer j gDM.m−2.d−1
F res1fResS1DM2 resuspension flux of sediment in layer 1 gDM.m−2.d−1
ASurf surface area of overlying water comp. m2
ZjActTh(j) actual thickness of sediment layer j m
Zfix jFixTh(j) fixed thickness of sediment layer j m
SWSedimentSWSediment option parameter,
=0.0 apply fixed layer thickness,
=1.0 apply burial kinetics
-
ϕjPor(j) shear stress P a
continued on next page
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Table 13.8 – continued from previous page
Name in
formulas
Name in in-
put
Definition Units
ρjRho(j) critical shear stress for resusp. from sedi-
ment layer j
P a
∆tDelt timestep in DELWAQ d
1) (j) is equal to S1 or S2, which represents the pertinent sediment layer
2) fResS1DM is calculated by process RES_DM.
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13.5 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.
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
V elocAvg1=
F low1,1
Area1,1+F low1,2
Area1,2
2
V elocAvg2=
F low2,1
Area2,1+F low2,2
Area2,2
2
V eloc =qV elocAvg2
1+V elocAvg2
2
where
F low1,1horizontal "from"-flow direction 1 [m3s−1]
F low1,2horizontal "to"-flow direction 1 [m3s−1]
F low2,1horizontal "from"-flow direction 2 [m3s−1]
F low2,2horizontal "to"-flow direction 2 [m3s−1]
Area1,1horizontal "from"-area direction 1 [m2]
Area1,2horizontal "to"-area direction 1 [m2]
Area2,1horizontal "from"-area direction 2 [m2]
Area2,2horizontal "to"-area direction 2 [m2]
V elocAvg1average horizontal flow velocity direction 1 [m s−1]
V elocAvg2average horizontal flow velocity direction 2 [m s−1]
V eloc average horizontal flow velocity [m s−1]
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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
formulas
Name in output Definition Units
–Orient1Angle of the main positive flow direction
with the x-axis
◦
–Orient2Angle of the secondary positive flow direc-
tion (both optional)
◦
V elocmax MaxV eloc Maximum velocity (useful to "clip" spurious
results)
ms−1
–SW CalcV elo Weighing method: 1 – linear average, 2 –
weighed by flow rate
[-]
3 – weighed by area, 4 – maximum contri-
bution
[-]
–SW AvgV elo Method for determining the velocity magni-
tude: 1 – Pythagoras,
[-]
2 – maximum, 3 – minimum [-]
V eloc V elocity Velocity magnitude ms−1
–F lowDir Direction of the flow velocity ◦
V elocAvg1V eloc1Velocity component in main direction ms−1
V elocAvg2V eloc2Velocity component in secondary direction ms−1
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13.6 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
Two methods have been implemented to calculate the Chézy coefficient for depth averaged
velocities.
1. White-Colebrook
C2D= 18 10log 12H
ks(13.1)
C2DChézy coefficient for depth averaged conditions [m1/2s−1]
Hwater depth [m]
ksNikuradse roughness length scale [m]
2. Manning (default)
C2D=
6
√H
n
C2DChézy coefficient [m1/2s−1]
Htotal depth of water column (segment depth) [m]
nManning coefficient [m−1/3s]
Three-dimensional Velocity
Under the requirement that the depth-averaged velocity of 3D computations equals the veloc-
ities obtained with the 2DH model the Chézy coefficient can de derived as follows:
Roughness height z0of the bed:
z0=H e−1+ κ C2D
√g(13.2)
with
z0roughness height of the bed [m]
Hdepth of the entire water column [m]
κ0.41 - Von Kármán coefficient [-]
g9.811 - gravity constant [m s−2]
C2DChézy coefficient for 2D using the segment depth [m1/2s−1]
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Chézy coefficient for three-dimensional velocities
C3D=√g
κln 1 + hb/2
z0
C3DChézy coefficient in case of 3D velocities [m1/2s−1]
hbdepth of the computational layer at the bed [m]
κ0.41 - Von Kármán coefficient [-]
g9.811 - gravity constant [m s−2]
z0roughness height of the bed [m]
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 C2Dto C3Dis done within the CAL-
TAU process, not the CHEZY process. This parameter is not output from the process.
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
ksRough Nikuradse roughness length m
n Manncoef Manning coefficient m−1/3s
hbDepth Thickness of the segment (near the bed) m
H T otalDepth Depth of the entire water column m
SwChezy SwChezy Choice for White-Colebrook or Manning [-]
C2DCHEZY Two-dimensional Chézy coefficient m1/2s−1
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13.7 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 Tand the wave length L. They are calculated as follows
(Groen and Dorrestein,1976;Holthuijsen,1980):
g= 9.8
ρl= 1000
if InitDepth ≤0 : InitDepth = TotalDepth
FS=g×F etch
vW ind2
dS=g×InitDepth
vW ind2
HS= 0.24 ×tanh(0.71 ×d0.763
S)×tanh 0.015 ×FS0.45
tanh(0.71 ×dS0.763)
H=HS×W ind2
g
TS= 2π×tanh(0.855 ×dS0.365) tanh 0.0345 ×FS0.37
tanh(0.855 ×dS0.365)
T=TS×W ind
g
L=gT 2
2πtanh 2π×InitDepth
L0
with
FSstandardized fetch [-]
TotalDepth total water depth [m]
InitDepth water depth were waves are generated [m]
dSsignificant depth [-]
HSsignificant wave height [-]
TSsignificant wave period [-]
The wave length Lcan be calculated by a one-step iteration:
L0=gT 2
2π
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The wave length L, wave period T and water depth h satisfy the dispersion relation:
ω=2π
T
k=2π
L
ω2=gk tanh(k×T otalDepth)
with
ωradial frequency [1/s]
kwave number [1/m]
Directives for use
By default the depth at the origin of the wave (InitDepth) equals the actual depth (To-
talDepth), 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
Name in output Definition Units
vW ind V W ind Wind velocity ms1
F etch F etch Fetch length m
InitDepth InitDepth Depth where the waves originate m
T otalDepthT otalDepth Depth of the entire water column (if Init-
Depth = -1)
m
H W aveHeight Significant wave height m
L W aveLength Significant wave length m
T W aveP eriod Significant wave period s
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13.8 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
This process is implemented for the characteristics F etch and InitDepth, determining the
forming of waves.
Formulations
Assume W inDir0= 0◦
For W inDiri−1< W indDir ≤W inDiri
F etch =W F etch_i
InitDepth =W Depth_i
with
W indDir actual wind direction [degr]
W inDiriwind direction of data pair i[degr]
W F etchifetch of data pair i[m]
W Depthiwave 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 inDir1and W inDir2, etc. The last data pair provided by you applies to all wind
direction ranging from the one but last provided W inDiri−1to 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
Name in output Definition Units
W indDir W indDir Actual direction of the wind ◦
W Depth(i)W Depth(i)Depth for wind from direction (i) m
W inDir(i)W inDir(i)Direction (i) for wind ◦
InitDepth InitDepth Depth to be used for wave parameters m
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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 Actual direction of the wind ◦
W F etch(i)W F etch(i)Fetch length for wind from direction (i) m
W inDir(i)W inDir(i)Direction (i) for wind ◦
F etch F etch Fetch length used for wave parameters m
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13.9 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
Formulations
Bed shear stress due to flow (used if the switch SW T auV eloc is set to 1, the default – see
below):
τflow =ρl×g×V elocity2
Chezy2
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:
τwind =1
4ρlfwU2
bg,max
Ubg,max =πH
Tsinh 2π×T otalDepth
L
ω=2π
T
Ag=Ubg,max
ω
Ag[m] is the peak value of the horizontal displacement at the bottom.
CalV elT au =sτ×Chezy2
ρl×g
The wave parameters H,Tand Lare input items, which can be calculated by process WAVE.
The wave height His limited according to (Nelson,1983):
H= min(0.55 ×T otalDepth, H)
The wave friction factor fwcan be calculated according to Tamminga (1987); Swart (1974) or
Soulsby (1997).
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SWTau = 1 (Tamminga,1987):
fw= 0.16sRough
Ubg,max ×T/2π
SWTau = 2 (Swart,1974):
r=H
2×Rough ×sinh(2π×T otalDepth
L)
if r > π/2then
fw= 0.00251 exp(5.213r−0.19)
else
fw= 0.32
SWTau = 3 (Soulsby,1997):
r=H
2×Rough ×sinh(2π×T otalDepth
L)
fw= 0.237r−0.52
SW T au switch to calculate the wave fraction factor [-]
SW T auV eloc switch to calculate the bottom shear stress due to flow from the flow
velocity or rely on T auF low instead [-]
τbottom shear stress [N m−2]=[Pa]
τwind part of bottom shear stress caused by wind [Pa]
τflow part of bottom shear stress caused by flow velocity [Pa]
τship part of bottom shear stress defined by you, e.g. to describe the effect
of ships [Pa]
V eloc flow velocity [m s−1]
Ubg,max amplitude of the wave orbital velocity [m s−1]
Rough Nikuradse bottom roughness length scale, calculated from the Chézy
coefficient via the inverse of Eq. (13.1) [m]
gacceleration of gravity [m s−2]
ρldensity of water [kg m−3]
Hwave height [m]
Twave period [s]
Lwave length [m]
F w wave (friction) factor [-]
T auF low 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.
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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
formulas
Name in output Definition Units
Chezy Chezy Chezy coefficient m−1/2s−1
Depth Depth Thickness of the segment (near the bed) m
T otalDepth T otalDepth Total water depth m
V elocity V elocity Flow velocity ms1
H W aveHeight Significant wave height m
L W aveLength Significant wave length m
T W aveP eriod Significant wave period s
τflow T auF low Shear stress due to flow Pa
τship T auShip Shear stress due to ships Pa
SW T au SW T au Switch for determining the wave rough-
ness
[-]
SW T auV elocSW T auV eloc Switch for using flow velocity or given flow
shear stress
[-]
τ T au Total shear stress Pa
τveloc T auV eloc Shear stress due to flow velocity Pa
τwind T auW ind Shear stress due to wind Pa
CalV elT au CalV elT au Velocity as derived from the total shear
stress
ms−1
τ T au Total shear stress [-]
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13.10 Computation of horizontal dispersion
PROCESS: HDISPERVEL
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:
DH=aV bHc+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.
The formulation used is:
velocity =|flow/area|,if area > 10−10
0otherwise
horzdisp =Dfacta×velocityDf actb×T otalDepthDfactc+Dback
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
flow flow Flow rate at exchange (automatically avail-
able)
m3s−1
area area Area at exchange (automatically available) m2
DfactaDfactaFactor a in dispersion calculation [-]
DfactbDfactbFactor b in dispersion calculation [-]
DfactcDfactcFactor c in dispersion calculation [-]
Dback Dback Background dispersion coefficient m2s−1
Dmin Dmin Minimum dispersion coefficient to be used m2s−1
Dmax Dmax Maximum dispersion coefficient to be used m2s−1
T otalDepth T otalDepth Mean total depth at the segments on either
side of the exchange
m
horzdisp horzdisp Computed horizontal dispersion coefficient
at exchange
m2s−1
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13.11 Computation of horizontal dispersion (one-dimension)
PROCESS: HORZDISPER
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. Further-
more 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:
DH=αV W 2
Hpg/C2
Formulations
The formulation using the names of the coefficients is:
DH=DispConst ×V elocity ×W idth2×Chezy
T otalDepth ×√g
V elocity mean of the specified flow velocity at the segments on both sides of
the exchange [m/s]
W idth mean of the specified width at the segments on both sides of the
exchange [m]
T otalDepth mean of the total depth at the segments on both sides of the ex-
change [m]
Chezy mean of the Chézy coefficients segments on both sides of the ex-
change [m1/2/s]
DispConst horizontal dispersion coefficient (again specified at the segments
and averaged) [-]
ggravitational 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 V elocity Magnitude of the flow velocity m−1
W idth W idth Width of the segments m
Chezy Chezy Chezy coefficient m−1/2s−1
T otalDepth T otalDepth Total water depth m2s−1
DispConst DispConst Coefficient for the horizontal dispersion ms1
–HorzDispMx Maximum value for the dispersion coeffi-
cient
m2s−1
DHHorzDisp Calculated value for the dispersion coeffi-
cient
m2s−1
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13.12 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 di-
rection only.
Implementation
The process is implemented for Vertical Dispersion.
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.
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 Vertical dispersion at segment level m2s−1
–ScaleV disp Scale factor that is applied (defaults to 1) [-]
–V ertDisp Computed vertical dispersion at ex-
changes
m2s−1
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13.13 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.
Formulation
V arExc =V arF rom +V arT o −V arF rom
XLenT o +XLenF rom ×XLenF rom
where
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.
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13.14 Conversion of exchange variable to segment variable
PROCESS: RHOEXTOS, RHOGRTOS, VDISPTOS, VGRDTOS
This process converts values available on the exchanges (contact surfaces) between two com-
putational segments to values within the computational segments in the third vertical direction
only!
Implementation
The process is implemented for the Density, for the Density Gradient, for the Vertical Disper-
sion and for the Velocity Gradient.
Formulation
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.
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.
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14 Temperature
Contents
14.1 Calculation of water temperature . . . . . . . . . . . . . . . . . . . . . . 422
14.2 Calculation of temperature for flats run dry . . . . . . . . . . . . . . . . . . 424
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14.1 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 am-
bient background temperature).
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)
Implementation
This process is implemented for TEMPERATURE only.
Formulation
If SwitchT emp = 0 the modelled temperature is the absolute temperature, in this case:
T=ModT emp
SurT emp =T−NatT emp
If SwitchT emp = 1 the modelled temperature is the surplus temperature, in this case:
SurT emp =ModT emp
T=SurT emp +N atT emp
The calculation of the heat exchange is in both cases:
dModT emp =−RcHeat ×F actRcHeat ×Surtemp +ZHeatExch
RcHeat =4.48 + 0.049 ×T+Fwind ×(1.12 + 0.018 ×T+ 0.00158 ×T2)×86400
Cp×ρw×Depth
ρw= 1000.0−0.088 ×T
Fwind = 0.75 ×(3.5+2.05 ×Vwind)
where
ModT emp modelled temperature [◦C]
SwitchT emp switch modelled temperature is absolute (0) or surplus (1) [-]
SurT emp surplus temperature [◦C]
Tambient water temperature [◦C]
NatT emp ambient natural background water temperature [◦C]
Depth depth of a DELWAQ segment [m]
Vwind wind velocity [m s−1]
Cpspecific heat of water [J kg−1◦C−1]
RcHeat rate constant for surplus temperature exchange [d−1]
F actRcHeat factor on rate constant for surplus temperature exchange [-]
ρwdensity of water at ambient water temperature [kg m−3]
ZHeatExch zeroth order temperature exchange flux [◦C d−1]
dModT emp temperature exchange flux [◦C d−1]
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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).
If surplus temperature is modelled the ambient natural background temperature must be sup-
plied as a constant value in time and place. Variable background temperature would lead to
an error in the energy balance of the system.
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Processes Library Description, Technical Reference Manual
14.2 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.
In principle, the temperature on a “run-dry” flat is a function of:
water temperature;
air temperature;
solar radiation;
back radiation;
windspeed and relative air humidity;
quantity and temperature of precipitation; and
duration of the emersion period.
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 pro-
cess 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 parame-
ter SW emersion is set (0.0 = submersion, 1.0 = emersion) according to auxiliary process
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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 modi-
fied. 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:
T ts =T a + ∆T rad −∆T ev (14.1)
∆T rad = ∆t×RT rad + ∆T rad0and ∆T rad = ∆T req
RT rad =RT rmax ×I
Imax
∆T req = ∆T rmax ×I
Imax
T=T ts
with:
Isolar radiation intensity [W m−2]
Imax maximal solar radiation intensity [W m−2]
Ttemperature [◦C]
T a air temperature [◦C]
T ts top sediment temperature in run-dry segments [◦C]
RT rad rate of temperature increase due to solar radiation [◦C d−1]
RT rmax maximal rate of temperature increase due to solar radiation [◦C d−1]
∆ttimestep [d]
∆T ev temperature decrease due to evaporation [◦C]
∆T rad temperature increase due to solar radiation [◦C]
∆T rad0temperature increase due to solar radiation in the previous timestep [◦C]
∆T req equilibrium temperature increase due to solar radiation [◦C]
∆T rmax 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 tem-
perature 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)
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Table 14.1: Definitions of the parameters in the above equations for TEMPERATUR.
Name in
formulas
Name in
input/output
Definition Units
Hst T hSedDT thickness top sed. layer subjected
to temp. change
m
I DayRadSurf solar radiation intensity W m−2
Imax RadMax maximal solar radiation intensity W m−2
RT rmax RT radM ax maximal rate of temp. increase due
to solar rad.
◦C d−1
SW emersion SW emersion switch that determines emersion or
submersion
-
SW T empDF SW T empDF switch that (de)activates modifica-
tion of temperature (default 0 = in-
active; 1 = active)
-
T T emp actual temperature ◦C
T a NatT emp air temperature ◦C
T st ModT emp top sediment temperature ◦C
∆t Delt timestep d
∆T ev DelT ev temperature decrease due to evap-
oration
◦C
∆T rmax DelRadMax maximal temperature increase due
to solar radiation
◦C
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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
15.9 Inspecting the attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . 443
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Processes Library Description, Technical Reference Manual
15.1 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 COM-
POS provides the additional parameters needed. This concerns the nutrient composition of
particulate detritus and parameters that represent organic matter and total matter as mea-
sured.
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.
Volume units refer to bulk ( ) or to water ( ).
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:
ani=Coci
Coni
api=Coci
Copi
asi=Coci
Cosi
where:
an stochiometric ratio of carbon and nitrogen in organic matter [gC gN−1]
ap stochiometric ratio of carbon and phosphorus in organic matter [gC gP−1]
as stochiometric ratio of carbon and sulfur in organic matter [gC gS−1]
Coc concentration of detritus carbon [gC m−3]
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Various auxiliary processes
Con concentration of detritus nitrogen [gN m−3]
Cop concentration of detritus phosphorus [gP m−3]
Cos concentration of detritus sulfur [gS m−3]
iindex for the particulate detritus fraction [-]
The total particulate detritus pools follow from:
Cpoc =
4
X
i=1
Coci
Cpon =
4
X
i=1
Coni
Cpop =
4
X
i=1
Copi
Cpos =
4
X
i=1
Cosi
Cpom =
4
X
i=1
(fdmi×Coci)
where:
Cpoc concentration of total particulate detritus carbon [gC m−3]
Cpon concentration of total particulate detritus nitrogen [gN m−3]
Cpop concentration of total particulate detritus phosphorus [gP m−3]
Cpos concentration of total particulate detritus sulfur [gS m−3]
Cpom concentration of total particulate detritus dry matter [gC m−3]
fdm dry matter conversion factor [gDM gC−1]
iindex for the particulate detritus fraction [-]
The concentration of total inorganic sediment follows from:
Ctim =
3
X
j=1
(fidmj×Cimj)
where:
Cim concentration of inorganic sediment fraction [gDM m−3]
Ctim concentration of total inorganic dry matter [gDM m−3]
fidm dry matter ratio of inorganic sediment fraction [gDM gDM−1]
jindex for the inorganic sediment fraction [-]
The other ”total” concentrations arise from summing the various simulated substances as
follows:
P OC =Cpoc +P hyt
T OC =P OC +DOC
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Processes Library Description, Technical Reference Manual
P ON =Cpon +AlgN
T ON =P ON +DON
KjelN =T ON +NH4
DIN =NH4 + NO3
T OT N =T ON +DIN
P OP =Cpop +AlgP
T OP =P OP +DOP
P IP =AAP +V IV P +AP AT P
T OT P =T OP +P O4 + P IP
P OS =Cpos +AlgS
T OS =P OS +DOS
T OT S =T OS +SO4 + SUD +SUP
T OT Si =AlgSi +Opal +Si
T P Mnoa =Ctim +Cpom
TPM =SS =T P Mnoa +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,
DmCfP OC4, default = 2.5) and the dry matter ratio (fidm) of the inorganic sediment
fractions (DM CF IM1,DMCF IM2,DMCF 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
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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
aniC−N(i)stoch. ratio of carbon and nitrogen
detr. fraction i
gC gN−1
apiC−P(i)stoch. ratio of carbon and phospho-
rus in detritus fraction i
gC gP−1
asiC−S(i)stoch. ratio of carbon and sulfur in
detritus fraction i
gC gS−1
T OC T OC concentration total organic carbon gC m−3
P OC P OC conc. total part. organic carbon gC m−3
P OM P OM conc. total part. dry matter gDM m−3
Cpoc P OCnoa conc. total total part. org. carbon
without algae
gC m−3
Cpom P OMnoa conc. total part. dry matter without
algae
gDM m−3
T OT N T OT N concentration total nitrogen gN m−3
T ON T ON conc. total organic nitrogen gN m−3
P ON P ON conc. total part. organic nitrogen gN m−3
Cpon P ONnoa conc. total part. org. nitrogen with-
out algae
gN m−3
DIN DIN conc. total diss. inorganic nitrogen gN m−3
KjelN KjelN conc. total Kjeldahl nitrogen gN m−3
T OT P T OT P concentration total phosphorus gP m−3
T OP T OP conc. total organic phosphorus gP m−3
P OP P OP conc. total part. org. phosphorus gP m−3
Cpop P OP noa conc. total part. org. phosphorus
without algae
gP m−3
P IP P IP conc. total part. inorg. phosphorus gP m−3
T OT S T OT S conc. total sulfur gS m−3
T OS T OS conc. total organic sulfur gS m−3
P OS P OS conc. total part. organic sulfur gS m−3
Cpos P OSnoa conc. total part. org. sulfur without
algae
gS m−3
T OT Si T OT Si concentration total silicon gSi m−3
T MP SS conc. total (susp.) sediment (solids) gDM m−3
Ctim T IM conc. total inorganic sediment gDM m−3
T MP T M P conc. total part. matter with algae gDM m−3
T MP noa T MP noa conc. total part. matter without algae gDM m−3
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15.2 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.
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 mat-
ter, 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.
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 occur-
ring 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:
Mdmk=
n
X
l=1
(fdmi,k ×Mxi,k)
frxi,k =Mxi,k
Mdmk
frphak=Mphak
Mdmk
where:
Mdm total amount of dry matter in a layer [gDM]
Mpha amount of adsorbed phophate in a layer [gP]
Mx amount of substance x in a layer [gX]
fdm dry matter conversion factor [gDM gDM−1, gDM gC−1]
frpha weight fraction of adsorbed phosphate in dry matter [gP gDM−1]
432 of 464 Deltares
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Various auxiliary processes
frx weight fractions of major components in dry matter [gX gDM−1]
iindex for major components in the sediment [-]
kindex for sediment layer S1 or S2 [-]
nnumber 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 =Moci,k
Moni,k
api,k =Moci,k
Mopi,k
asii,k =Moci,k
Mosii,k
where:
an stochiometric ratio of carbon over nitrogen in detritus fraction k[gC gN−1]
ap stochiometric ratio of carbon over phosphorus in detritus fraction k[gC gP−1]
asi stochiometric ratio of carbon over silicon in detritus fraction k[gC gSi−1]
Moc amount of carbon in particulate detritus fraction k[gC]
Mon amount of nitrogen in particulate detritus fraction k[gN m−3]
Mop amount of phosphorus in particulate detritus fraction k[gP m−3]
Mosi amount of silicon in particulate detritus fraction k[gSi m−3]
iindex for particulate detritus fractions [-]
kindex for sediment layer S1 or S2 [-]
The total amounts of major components in the sediment layer S1 or S2 are:
Mimtk=
3
X
j=1
(Mimj,k)
Moctk=
2
X
i=1
(Moci,k)
Malgtk=
n
X
l=1
(Malgl,k)
Mpomk=
n
X
l=1
(fdml×Malgl) +
2
X
i=1
(fdmi×Moci,k)
where:
fdm dry matter conversion factor [gDM gC−1]
Malg amount of biomass of algae species [gC]
Malgt total amount of algae biomass [gC]
Mim amount of a sediment inorganic matter fraction [gDW]
Mimt total amount of sediment inorganic matter [gDW]
Moct total amount of carbon in particulate detritus [gC]
Mpom total amount of organic matter in the sediment [gDM gDM−1]
iindex for particulate detritus fractions [-]
jindex for sediment inorganic matter fractions [-]
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Processes Library Description, Technical Reference Manual
kindex for sediment layer S1 or S2 [-]
lindex for algae / microphytobenthos species [-]
nnumber of algae / microphytobenthos species, n=1 currently [-]
The comprehensive composition of the sediment layers S1 and S2 is calculated with:
Cxi,k =Mxi,k
A
where:
Asurface area of the water overlying water compartment [m2]
Cx surface concentration of substance x in a layer [gX m−2]
Mx amount of substance x in a layer [gX]
iindex for all sediment components including the nutrients in detritus [-]
kindex for sediment layer S1 or S2 [-]
The relevant physical properties of the sediment layers S1 and S2 follow from:
V dmk=
n
X
i=1
(fdmi,k ×Cxi,k/ρi)
ρdmk=Cdmk
V dmk
Zk=V dmk
(1 −φk)×A
where:
Asurface area of the water overlying water compartment [m2]
Cdm surface concentration of dry matter [gDM m−2]
fdm dry matter conversion factor [gDM gDM−1, gDM gC−1]
V dm sediment dry matter volume [m3]
Zthickness of the sediment layer [m]
φporosity of the sediment [-]
ρsolid matter density of a major sediment component k[gDM m−3DM]
ρdm density of sediment dry matter [gDM m−3DM]
iindex for major components in the sediment [-]
kindex for sediment layer S1 or S2 [-]
nnumber 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 (frxi,k; see the table with output parameters) may not equal 1.
434 of 464 Deltares
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Various auxiliary processes
Table 15.2: Definitions of the input parameters in the above equations for S1_COMP and
S2_COMP.
Name in
formulas
Name in input Definition Units
A Surf surface area of the overlying water
compartment
m2
fdmj,k DMCF IM1dry matter conv. factor sed. inorg. mat-
ter fraction 1
gDM gDM−1
or DMCF IM2dry matter conv. factor sed. inorg. mat-
ter fraction 2
gDM gDM−1
DMCF IM3dry matter conv. factor sed. inorg. mat-
ter fraction 3
gDM gDM−1
fdmi,k DMCF DetCS dry matter conv. factor detr. fraction 1 gDM gC−1
DMCF OOCS dry matter conv. factor detr. fraction 2 gDM gC−1
fdml,k DMCF DiatS dry matter conv. factor algae species 1 gDM gC−1
Malgl,k DiatS(k)amount of biomass of algae species 1 gC
Mimj,k IM1S(k)amount of sed. inorg. matter fraction 1 gDW
IM2S(k)amount of sed. inorg. matter fraction 2 gDW
IM3S(k)amount of sed. inorg. matter fraction 3 gDW
Moci,k DetCS(k)amount of detr. C in part. fraction 1 gC
OOCS(k)amount of detr. C in part. fraction 2 gC
Moni,k DetNS(k)amount of detr. N in part. fraction 1 gN
OONS(k)amount of detr. N in part. fraction 2 gN
Mopi,k DetP S(k)amount of detr. P in part. fraction 1 gP
OOP S(k)amount of detr. P in part. fraction 2 gP
Mosii,k DetSiS1(k)amount of detr. Si in part. fraction 1 gSi
OOSiS1(k)amount of detr. Si in part. fraction 2 gSi
Mpha AAP S(k)amount of adsorbed phosphate gP
φ P ORS(k)sediment porosity -
ρiRHOIM1density of sed. inorg. matter fr. 1 gDM m−3
RHOIM2density of sed. inorg. matter fr. 2 gDM m−3
RHOIM3density of sed. inorg. matter fr. 3 gDM m−3
RHODetC density of detritus fraction 1 gDM m−3
RHOOOC density of detritus fraction 2 gDM m−3
RHODiat density of biomass of algae species 1 gDM m−3
1(k) is sediment layer 1 or 2.
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Table 15.3: Definitions of the output parameters in the above equations for S1_COMP
and S2_COMP .
Name in
formulas
Name in output Definition Units
ani,k1C−
NDetCS(k)
stoch. ratio C over N in detr. fraction 1 gC gN−1
or C−NOOC(k)stoch. ratio C over N in detr. fraction 2 gC gN−1
api,k C−
P DetCS(k)
stoch. ratio C over P in detr. fraction 1 gC gP−1
or C−P OOCS(k)stoch. ratio C over P in detr. fraction 2 gC gP−1
asii,k C−SDetCS(k)stoch. ratio C over Si in detr. fraction 1 gC gSi−1
C−SOOCS(k)stoch. ratio C over Si in detr. fraction 2 gC gSi−1
Calgl,k DiatS(k)M2surface conc. of algae species 1 gC m−2
Cimj,k IM1S(k)M2surf. conc. of sed. inorg. matter fr. 1 gDW m−2
IM2S(k)M2surf. conc. of sed. inorg. matter fr. 2 gDW m−2
IM3S(k)M2surf. conc. of sed. inorg. matter fr. 3 gDW m−2
Coci,k DetCS(k)M2surf. conc. of detr. C in part. fr. 1 gC m−2
or OOCS(k)M2surf. conc. of detr. C in part. fr. 2 gC m−2
Coni,k DetNS(k)M2surf. conc. of detr. N in part. fr. 1 gN m−2
or OONS(k)M2surf. conc. of detr. N in part. fr. 1 gN m−2
Copi,k DetP S(k)M2surf. conc. of detr. P in part. fr. 1 gP m−2
or OOP S(k)M2surf. conc. of detr. P in part. fr. 1 gP m−2
Cosii,k DetSiS1(k)M2surf. conc. of detr. Si in part. fr. 1 gSi m−2
OOSiS1(k)M2surf. conc. of detr. Si in part. fr. 1 gSi m−2
Cxi, k AAP S(k)M2surface conc. of adsorbed phosphate gP m−2
Zk ActT hS(k)thikness of sediment layer m
frxi,k F rIM1S(k)fraction inorg. matter 1 in sediment gDM gDM−1
F rIM2S(k)fraction inorg. matter 2 in sediment gDM gDM−1
F rIM3S(k)fraction inorg. matter 3 in sediment gDM gDM−1
F rDetCS(k)fraction detritus 1 in sediment gC gDM−1
F rOOCS(k)fraction detritus 2 in sediment gC gDM−1
F rCF DiatS(k)fraction algae species 1 in sediment gC gDM−1
MdmkDMS(k)total amount of dry matter gDM
MimtkT IMS(k)total amount of sed. inorganic matter gDM
MoctkP OCS(k)total amount of part. organic carbon gC
MalgtkP HY T S(k)total amount of algae biomass gC
MpomkP OMS(k)total amount of organic matter gDM
ρdmkRHOS(k)density of sediment dry matter gDM m−3
1(k) is sediment layer 1 or 2.
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Various auxiliary processes
15.3 Allocation of diffusive and atmospheric loads
PROCESS: DFWAST_I, ATMDEP_I
Both processes calculate diffusive fluxes. The processes convert user input in [g m−2d−1] to
DELWAQ required units of [g m−3d−1].
Implementation
These processes are implemented for IM1, IM2, IM3, NO3, NH4, PO4, all heavy metals and
all organic micro-pollutants.
Formulation
Diffusive waste load:
dDfwasti=fDfwasti
depth (15.1)
Atmospheric deposition:
dAtmDepi=fAtmDepi
depth (15.2)
where
dDfwastidiffusive waste load [g m−3d−1]
dAtmDepiatmospheric waste load [g m−3d−1]
fDfwastidiffusive waste load [g m−2d−1]
fAtmDepiatmospheric waste load [g m−2d−1]
depth 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.
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15.4 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 multi-
layer water column.
Implementation
Not relevant in this context.
Formulation
Depth =V olume
Surf
T otalDepth =
n
X
i=1
Depthi
LocalDepthm=
m
X
j=1
Depthj
where
Depth depth of a DELWAQ segment [m]
V olume volume of a DELWAQ segment [m3]
Surf horizontal surface area of a DELWAQ segment [m2]
T otaldepth depth of entire water column [m]
Localdepthmdepth from the surface to bottom of DELWAQ segment m [m]
mindex of the layer
ntotal number of layers
Directives for use
Either Depth or Surf must be supplied by you (or a water quantity model)!
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15.5 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.
Formulation
Surf =Volume
Depth
where
Depth depth of a DELWAQ segment [m]
Volume volume of a DELWAQ segment [m3]
Surf 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)!
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15.6 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.
Formulation
V arGrd =V arT o −V arF rom
XLenT o +XLenF rom
VarGrd gradient in space of segment-related variable
(a) VelocGrd gradient in horizontal flow velocity [m s−1m−1]
(b) RhoGrd gradient in density of water [kg m−3m−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]
Directives for use
This process can be active if the third direction is defined.
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15.7 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 [m3s−1] — as derived from SOBEK,
Delft3D or another hydrodynamic model. Dispersion is not taken into account.
Formulation
ResT im =V olume
Pexchanges |F low|/2(15.3)
where
ResT im residence time [s]
V olume DELWAQ water volume of a segment [m3]
F low DELWAQ water flow over an exchange [m3s−1]
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’.
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15.8 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.
Implementation
In a single water quality simulation a maximum of five sources can be distinguished:
i= 1,2,3,4and 5
Formulation
ageT ri=
ln dT ri
cT ri
RcDecT ri
dDecT ri=RcDecT ri×dT ri
where
ageT riage of tracer i[d]
cT riconcentration of conservative tracer i[g m−3]
dT riconcentration of decayable tracer i[g m−3]
RcDecT rifirst order decay rate constant for decayable tracer i[d−1]
dDecT riflux for decayable tracer i[g m−3d−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.
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15.9 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
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:
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.
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 param-
eter 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 [-]
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16 Deprecated processes descriptions
Contents
16.1 Growth and mortality of algae (MONALG) . . . . . . . . . . . . . . . . . . 446
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16.1 Growth and mortality of algae (MONALG)
PROCESS: MND1DIAT-M, MND2FLAG-M, MND3DIAT-F, MND4FLAG-F, MND(I)TEMP,
MND(I)LLIM, MND(I)NLIM
Algae are subject to gross primary production, respiration, excretion, mortality, grazing, re-
suspension 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 set-
tling. These processes are equally valid for other algae modules, and are therefore dealt with
in separate process descriptions.
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.
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 ac-
cording 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 (Klep-
per,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 con-
centrations [gC m−3]. Primary production involves the uptake of inorganic nutrients [gN/P/Si
m−3] and the production of dissolved oxygen [gO2m−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.
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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.
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!
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=fnuti×flti×kgpi×Calgi
kgpi=kpg10
i×ftmpi
ftmpi=ktpg(T−10)
i
with:
Calg algal biomass concentration [gC m−3]
flt light limitation factor [-]
fnut Monod nutrient limitation factor [-]
ftmp temperature limitation factor for production [-]
kgp potential gross primary production rate [d−1]
kgp10 potential gross primary production rate at 10 ◦C [d−1]
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ktgp temperature coefficient for primary production [-]
Rgp gross primary production rate [gC m−3d−1]
Twater temperature [◦C]
iindex 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.
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:
fnuti=fami+ (1 −fami)×fnii
fami=Cam ×Cph ×Csi
(Ksami×Cph ×Csi +Cam ×Ksphi×Csi +Cam ×Cph ×Kssii+Cam ×Cph ×Csi)
fnii=Cni ×Cph ×Csi
(Ksnii×Cph ×Csi +Cni ×Ksphi×Csi +Cni ×Cph ×Kssii+Cni ×Cph ×Csi)
with:
fam ammonium specific nutrient limitation factor [-]
fni nitrate specific nutrient limitation factor [-]
Cam ammonium concentration [gN m−3]
Cni nitrate concentration [gN m−3]
Cph phosphate concentration [gP m−3]
Csi dissolved inorganic silicate concentration [gSi m−3]
Ksam half saturation constant for ammonium [gN m−3]
Ksni half saturation constant for nitrate [gN m−3]
Ksph half saturation constant for phosphate [gP m−3]
Kssi 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):
flti=Pn
k=1 Pm
j=1 (Rrgpi,j,k ×∆z×∆t)
(86400 ×H)
Rrgpi,j,k =Iri,j,k ×(ci+ 2)
Ir2
i,j,k +ci×Iri,j,k + 1
Iri,j,k =Ij,k
Ioi
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ci=Ioi
(kgpi/di)−2
Ioi=Io10
i×ktpg(T−10)
i
Ij,k =Itopk×e(−et×zj)
with:
cshape coefficient of the production factor [-]
dinitial slope of the light-production curve [gC d−1.W m−2)−1]
et total extinction coefficient of visible light [m−1]
flt light limitation factor [-]
Hdepth of a water compartment or water layer [m]
Ilight intensity at depth zjand time tk[W m−2]
Io optimal light intensity [W m−2]
Ir light intensity at depth zjand time tk, relative to optimal intensity [-]
Itop light intensity at depth zo(top of layer or compartment) and time t [W m−2]
kgp potential gross primary production rate [d−1]
ktgp temperature coefficient for primary production [-]
Rrgp gross production at depth zjand time tk, relative to maximal production [-]
zdepth [m]
∆ttime interval for light limitation integration, that is the DELWAQ timestep [s]
∆zdepth interval for light limitation integration ([m]; = H/m)
iindex for species group 1–4 [-]
jindex for depth interval 1–m [-]
kindex for time interval 1–n [-]
nnumber of time intervals in a day ([-]; = 86 400/∆t)
mnumber of depth intervals in a water compartment or water layer [-]
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. Main-
tenance respiration is temperature dependent. Growth respiration depends on the primary
production rate. The total respiration rate is given by:
Rrspi=krspi×Calgi+frspi×Rgpi
krspi=krsp10
i×ktrsp(T−10)
i
with:
frsp fraction of gross production respired [-]
krsp maintenance respiration rate [d−1]
krsp10 maintenance respiration rate at 10 ◦C [d−1]
ktrsp temperature coefficient for maintenance respiration [-]
Rrsp total respiration rate [gC m−3d−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=fexci×(1 −fnuti)×Rgpi
with:
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fexc fraction of gross production excreted at the absence of nutrient limitation [-]
Rexc excretion rate [gC m−3d−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 mod-
elling of grazers. Salinity driven mortality is described with a sigmoidal function of chlorinity
(NIOO/CEMO,1993), leading to the following formulations:
Rmrti=kmrti×Calgi
kmrti=kmrt10
i×ktmrt(T−10)
i
kmrt10
i=m1i−m2i
1 + e(b1i×(Ccl−b2i)) +m2ifor fresh water algae, MND(i)T ype = 2.0
kmrt10
i=m2i−m1i
1 + e(b1i×(Ccl−b2i)) +m1ifor marine algae, MND(i)T ype = 1.0
with:
b1coefficient 1 of salinity stress function [g−1m3]
b2coefficient 2 of salinity stress function [g m−3]
m1rate coefficient 1 of salinity stress function [d−1]
m2rate coefficient 2 of salinity stress function [d−1]
Ccl chloride concentration [g m−3]
kmrt total mortality process rate [d−1]
kmrt10 total mortality process rate at 10 ◦C [d−1]
ktmrt temperature coefficient for mortality [-]
Rmrt total mortality rate [gC m−3d−1]
m1and m2are the end members of the above function, meaning that the function obtains
the value m1at high Ccl, and the value m2for low Ccl. The mortality rate increases with
decreasing chloride concentration, when m2is 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 m1is 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
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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 stochiometric constant for nitrogen over carbon in algae biomass [gN.gC−1]
aph stochiometric constant for phosphorus over carbon in algae biomass [gP.gC−1]
aox stochiometric constant for oxygen over carbon in algae biomass [gO2.gC−1]
asi stochiometric constant for silicon over carbon in algae biomass [gSi.gC−1]
Rcnsam net consumption rate for ammonium [gN m−3d−1]
Rcnsni net consumption rate for nitrate [gN m−3d−1]
Rcnsph net consumption rate for phosphate [gP m−3d−1]
Rcnssi net consumption rate for silicate [gSi m−3d−1]
Rprdox net production rate for dissolved oxygen [gO2m−3d−1]
Rprdoc net production rate for detritus organic carbon [gC m−3d−1]
Rprdon net production rate for detritus organic nitrogen [gN m−3d−1]
Rprdop net production rate for detritus organic phosphorus [gP m−3d−1]
Rprdosi net production rate for opal silicate [gSi m−3d−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).
fam and fnut 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-
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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
(fnuti×(1 −flti×fnuti))gi
with:
achf stoch. constant for carbon over chlorophyll in algae biomass [gC gChf−1]
achfmin minimal stoch. const. for carbon over chlorophyll in algae biomass [gC gChf−1]
Cchf chlorophyll concentration connected with an algae group [gChf m−3]
gscaling coefficient for growth limitation factor [-]
The total concentration of chlorophyll is calculated by a separate process PHY_GEM, which
is described elsewhere in this manual.
Directives for use
The process rates of gross primary production and maintenance respiration have a tem-
perature 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 coeffi-
cients MND(i)m1and MND(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 NH4ammonium concentration gN m−3
Ccl Cl chloride concentration gCl m−3
Cni NO3nitrate concentration gN m−3
Cph P O4phosphate concentration gP m−3
Csi Si dissolved inorganic silicate concentra-
tion
gSi m−3
Calg1MND1Diat−
m
biomass concentration of marine di-
atoms
gC m−3
continued on next page
1(i) indicates species groups 1-4.
2This parameter is only used for initialisation during the first timestep.
3This parameter is calculated by processes ExtPhGVL and Extinc_VL.
4This parameter is not part of the input.
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Table 16.1 – continued from previous page
Name in
formulas
Name in input Definition Units
Calg2MND2F lag−
m
biomass concentration of marine flagel-
lates
gC m−3
Calg3MND3Diat−
f
biomass concentration of fresh water di-
atoms
gC m−3
Calg4MND4F lag−
f
biomass concentration of fresh water
flagellates
gC m−3
-MND(i)T ype type of algae group (1 = brackish/marine,
2 = fresh)
-
achfiMND(i)AChl2
0group specific stoch. const. carbon over
chlorophyll
gC.gChf−1
achfmin,i MND(i)amchl group spec. min. stoch. const. carbon
over chlorophyll
gC.gChf−1
aniMND(i)NCratgroup specific stoch. const. for nitrogen
over carbon
gN.gC−1
aoxi-4group specific stoch. const. for oxygen
over carbon
gO2.gC−1
aphiMND(i)P Crat group spec. stoch. const. for phosphorus
over carbon
gP.gC−1
asiiMND(i)SiCratgroup specific stoch. const. for silicon
over carbon
gSi.gC−1
m1iMND(i)m1group spec. rate coefficient 1 of salinity
stress function
d−1
m2iMND(i)m2group spec. rate coefficient 2 of salinity
stress function
d−1
b1iMND(i)b1group specific coefficient 1 of salinity
stress function
g−1m3
b2iMND(i)b2group specific coefficient 2 of salinity
stress function
g m−3
diMND(i)schl group specinitial slope of the light-
production curve
gC d−1.(W
m−2)−1
et ExtV l3total extinction coefficient of visible light m−1
giMND(i)bgroup spec. scaling coef. for growth limi-
tation factor
-
KsamiMND(i)Kam group specific half saturation constant
for ammonium
gN m−3
KsniiMND(i)Kni group specific half saturation constant
for nitrate
gN m−3
KsphiMND(i)Kph group specific half saturation constant
for phosphate
gP m−3
KssiiMND(i)Ksi group specific half saturation constant
for silicate
gSi m−3
continued on next page
1(i) indicates species groups 1-4.
2This parameter is only used for initialisation during the first timestep.
3This parameter is calculated by processes ExtPhGVL and Extinc_VL.
4This parameter is not part of the input.
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Table 16.1 – continued from previous page
Name in
formulas
Name in input Definition Units
fexciMND(i)bexgroup spec. frac. gross prod. excr ˙
at abs.
of nutr. lim.
-
frspiMND(i)rprgroup specific fraction of gross produc-
tion respired
-
H Depth depth of a water compartment or water
layer
m
IoiMND(i)Iopt group specific optimal light intensity W m−2
Itop Rad light intensity at top of layer or compart-
ment
W m−2
kgp10
iMND(I)P m10 group spec. potential gross primary
prod. rate at 10 ◦C
d−1
krsp10
iMND(i)rmt10 group spec. maintenance respiration
rate at 10 ◦C
d−1
ktgpiMND(i)ktgp group spec. temperature coefficient for
primary prod.
-
ktmrtiMND(i)mt group spec. temperature coefficient for
mortality
-
ktrspiMND(i)rt group spec. temperature coef. for main-
tenance resp.
-
kmrts,i MND(i)MorSedgroup spec. mortality process rate in
sediment
d−1
T T emp water temperature ◦C
-IT IM E time s
∆t IDT time interval, that is the DELWAQ
timestep
s
m Nr_dz number of depth intervals in a water
comp. or layer
-
1(i) indicates species groups 1-4.
2This parameter is only used for initialisation during the first timestep.
3This parameter is calculated by processes ExtPhGVL and Extinc_VL.
4This parameter is not part of the input.
454 of 464 Deltares
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