SWITCH User Manual D Water_Quality_Switch_Technical_Reference_Manual Water Quality Technical Reference
User Manual: Pdf D-Water_Quality_Switch_Technical_Reference_Manual
Open the PDF directly: View PDF 
.
Page Count: 42
| Download | |
| Open PDF In Browser | View PDF |
Water quality and aquatic ecology modelling suite
DR
AF
T
D-Water Quality
SWITCH
Technical Reference Manual
DR
AF
T
T
DR
AF
SWITCH
Prediction of the nutrient fluxes across the sedimentwater interface
Technical Reference Manual
D-Water Quality
Version: 4.00
SVN Revision: 52614
April 18, 2018
DR
AF
T
SWITCH, Technical Reference Manual
Published and printed by:
Deltares
Boussinesqweg 1
2629 HV Delft
P.O. 177
2600 MH Delft
The Netherlands
For sales contact:
telephone: +31 88 335 81 88
fax:
+31 88 335 81 11
e-mail:
software@deltares.nl
www:
https://www.deltares.nl/software
telephone:
fax:
e-mail:
www:
+31 88 335 82 73
+31 88 335 85 82
info@deltares.nl
https://www.deltares.nl
For support contact:
telephone: +31 88 335 81 00
fax:
+31 88 335 81 11
e-mail:
software.support@deltares.nl
www:
https://www.deltares.nl/software
Copyright © 2018 Deltares
All rights reserved. No part of this document may be reproduced in any form by print, photo
print, photo copy, microfilm or any other means, without written permission from the publisher:
Deltares.
Contents
Contents
List of Figures
v
List of Tables
vii
1 Introduction
1
2 Spatial schematisation and processes
3
3 Aerobic layer and the sediment oxygen demand
9
11
5 Detritus
13
6 Ammonium
7 Phosphate
DR
AF
8 Silicate
T
4 Denitrifying layer and nitrate
17
19
25
9 Temperature dependency and dispersion
27
References
29
Deltares
iii
DR
AF
T
SWITCH, Technical Reference Manual
iv
Deltares
List of Figures
List of Figures
Schematisation of the sediment layer in SWITCH . . . . . . . . . . . . . . .
Overview of the processes included in SWITCH . . . . . . . . . . . . . . . .
3
4
DR
AF
T
2.1
2.2
Deltares
v
DR
AF
T
SWITCH, Technical Reference Manual
vi
Deltares
List of Tables
List of Tables
Initialisation parameters for SWITCH . . . .
Initialisation parameters for SWITCH . . . .
Numerical input parameters for SWITCH . .
Physical input parameters for SWITCH . . .
Physical input parameters for SWITCH . . .
(Bio)chemical input parameters for SWITCH
(Bio)chemical input parameters for SWITCH
(Bio)chemical input parameters for SWITCH
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
4
5
5
5
6
6
7
8
DR
AF
T
2.1
2.1
2.2
2.3
2.3
2.4
2.4
2.4
Deltares
vii
DR
AF
T
SWITCH, Technical Reference Manual
viii
Deltares
1 Introduction
SWITCH was made as a sub-model of the surface water eutrophication model DBS for the
prediction of the nutrient fluxes across the sediment-water interface (WL | Delft Hydraulics,
1992). The acronym stands for Sediment Water Interaction by Transport and Chemistry.
SWITCH distinguishes four sediment layers and calculates the thicknesses of the aerobic and
denitrifying layers on the basis of a steady state approach. The concentrations of detritus,
ammonium, nitrate, phosphate and silicate in the sediment and the pore water are simulated
dynamically using mass balance equations.
DR
AF
T
SWITCH is applied as part of the eutrophication models, specific configurations of DELWAQ
among which DBS and GEM. The link between these models and sub-model SWITCH is
formed by the sediment-water exchange fluxes of dissolved oxygen, nutrients and organic
matter. SWITCH acts directly on substances in the water column, just like any other process
routine in DELWAQ. Specific facilities have been developed for the coupling of SWITCH to
DELWAQ. These include a fractional step numerical computation procedure and an sedimentwater aggregation procedure. The fractional step procedure takes care that SWITCH operates
according to an appropriate computational time step, equal to or smaller than the DELWAQ
time step, in order to maintain computational stability at steep concentration gradients and
large mass fluxes between water and sediment. The sediment-water aggregation procedure
allows the aggregation of several water segments with respect to SWITCH in order to establish
a reduction of the computational burden. This means that the exchange of substances with
the sediment underlying such a group of water segments is computed by SWITCH in one
stroke. Both procedures are described in the process documentation regarding SWITCH in
Chapter 8 of this manual.
Details with respect to background, objectives, starting-points and formulations of SWITCH
have been described in WL | Delft Hydraulics (1994b,c). The first version of SWITCH and
the first application for Lake Veluwe, the sediment of which is a mixture of silt and sand, have
also been described by Smits and Van der Molen (1993). Other applications of SWITCH
concerned the Lake Volkerak-Zoommeer (WL | Delft Hydraulics, 1995), with deep gullies and
silty sediment, the peat lakes Geerplas and Nannewijd (WL | Delft Hydraulics, 1997) and the
sandy coastal strip of the North Sea.
Volume units refer to bulk ( ) or to water ( ).
b
Deltares
w
1 of 32
DR
AF
T
SWITCH, Technical Reference Manual
2 of 32
Deltares
2 Spatial schematisation and processes
T
Figure 2.1 depicts the vertical schematisation of the ’active’ sediment layer in SWITCH. An
overview of the processes included in SWITCH is given in Figure 2.2. The ’active’ sediment
layer has a constant thickness (d), and is divided in 4 sub-layers. An upper layer (dh) and
a lower layer (dl=d4 ) have been defined in order to account for vertical characteristics such
as decomposition of organic matter, dispersion and porosity. These layers are also fixed.
A second partition follows from chemical differences. A thin top layer (do) is oxidising, the
remaining part (dh-do = d3 , > minimal value) of the upper layer is reducing. The oxidising
layer is divided in an oxygen containing layer d1 and a denitrifying layer d2 . Both d1 and d2
are variable, and are deduced from steady-state solutions of the mass balance equations for
dissolved oxygen and nitrate. In order to avoid numerical problems neither do nor d1 may
become infinitely thin, a minimal thickness (d1m ) has therefore been defined. However, the
denitrifying layer disappears entirely, when the nitrate concentration drops below a critical
value (Cnc ).
DR
AF
Additionally, a very thin meta-stable boundary layer has been defined, which contains the
detritus settled from the overlying water (and produced from microphytobenthos). From this
layer detritus is incorporated in the sediment as the consequence of bioturbation. Nutrients
produced from decomposition of detritus in the boundary layer are allocated to the oxygen
containing top layer. The same goes for the dissolved oxygen fluxes pertaining to these
processes. The boundary layer as such may affect the dispersion of dissolved substances
across the sediment-water interface, which can be taken into account in SWITCH.
Table 2.1 upto Table 2.4 present an overview of the input parameters for SWITCH. In addition
SWITCH needs mass fluxes from the water column connected with the settling of particulate substances and the dissolved concentrations in the water column for the calculation of
diffusive exchange and downwelling seepage.
Figure 2.1: Schematisation of the sediment layer in SWITCH
Deltares
3 of 32
DR
AF
T
SWITCH, Technical Reference Manual
Figure 2.2: Overview of the processes included in SWITCH
As mentioned in the introduction SWITCH is applied as part of the eutrophication models,
specific configurations of DELWAQ among which DBS and GEM. In this setting the metastable boundary layer is modelled as the S1 sediment layer, which contains so-called “inactive
substances” such as detritus and benthic algae, together shaping up the benthic complex.
(However, benthic algae may be excluded from the simulation). All nutrient fluxes inferred by
the algae are accounted for, either directly in the boundary layer (S1) or in the upper sediment
layer 1 in SWITCH. Algae are incorporated from the boundary layer into the sediment in
exactly the same way as detritus, which is taken care of by the process called “burial”. The
way settling particulate matter is added to boundary layer S1 or directly to the upper sediment
layer 1 is described in the process description in Chapter 8 of this manual.
Table 2.1: Initialisation parameters for SWITCH
Parameter
Dissolved substances
Nitrate:
Layer 1
Ammonium:
Layer 1:
Layer 2–3:
Layer 4:
Silicate:
Layer 1–1:
Partitioned substances
Total inorganic phosphate content:
Layer 1–2:
Symbol in
appendix
Value
(indicative)
Units
Cn1
1.0
gN m−3
Ca1
Ca2
Ca4
1.5
3.0
4.0
gN m−3
gN m−3
gN m−3
Cs1
8.0
gSi m−3
Cp1
140.0
gP m−3
w
w
w
w
w
b
4 of 32
Deltares
Spatial schematisation and processes
Table 2.1: Initialisation parameters for SWITCH
Parameter
Value
(indicative)
105.0
Units
Layer 3:
Symbol in
appendix
Cp3
Layer 4:
Cp4
84.0
gP m−3
gP m−3
b
b
Fraction of phosphate in vivianite:
Layer 1–2:
Layer 3:
Layer 4:
Fraction of phosphate in stable mineral:
Layer 1–2:
Layer 3:
Layer 4:
0.1
0.3
0.5
-
fmp1
fmp3
fmp4
0.4
0.4
0.4
-
Particulate substances
Detritus content in the upper layer 1–3
Carbon
Cd1
700.0
gC m−3
Nitrogen
Cnd1
40.0
gN m−3
Phosphorus
Cpd1
3.5
gP m−3
DR
AF
T
fpp1
fpp3
fpp4
b
b
b
Detritus content in the lower layer 4
Carbon
Cd 4
160.0
gC m−3
Nitrogen
Cnd4
7.0
gN m−3
Phosphorus
Cpd4
0.7
gP m−3
b
b
b
Refractory detritus content in layer 1–4
Carbon
Crd1
0.0
gC m−3
Nitrogen
Crn1
0.0
gN m−3
Phosphorus
Crp1
0.0
gP m−3
b
b
b
Table 2.2: Numerical input parameters for SWITCH
Parameter
Symbol in
appendix
Value
Units
Minimal thickness (depth) of the aerobic layer 1
Crit. thickness layer 1 for obt. red. sorp. capacity
Crit. (=max) nitrate conc. for sulphate reduction
d1m
dom
0.0005
0.0009
m
m
Cnc
0.05
gN m−3
Table 2.3: Physical input parameters for SWITCH
Parameter
The sediment
Thickness (depth) of the aerobic top layer 11)
Thickness (depth) of the denitrifying layer 21)
Deltares
Symbol in
appendix
Value
Units
d1
d2
0.001
0.004
m
m
5 of 32
SWITCH, Technical Reference Manual
Table 2.3: Physical input parameters for SWITCH
Parameter
Symbol in
appendix
d3
Value
Units
0.015
m
d4 = dl
l
0.08
0.001
m
m
p1
0.75
m3 m−3
Porosity of the lower layer
p4
0.65
m3 m−3
Specific weight (density) of dry matter
Ws
2400.0
kg m−3
Thickness (depth) of the upper reducing layer
31)
Thickness (depth) of the lower reducing layer 4
Thickness (mixing length) of the water boundary layer
Porosity of the upper layer
w
b
w
vs
Ca5
Cdp5
0.0
4.0
m/day
gN m−3
0.05
gP m−3
DR
AF
Mass transport
Seepage (- downwelling or + upwelling)
Ammonium conc. at lower boundary in upw.
water
Phosphate conc. at lower boundary in upwelling water
Silicate conc. at lower boundary in upwelling
water
Sedimentation rate (gross sediment accretion
rate)
T
b
Resuspension rate
1)
w
Cs5
10.0
gSi m−3
Fs
0.0
m3
w
m−2
b
0.0
d−1
m3 m−2
fc
0.0
d−1
-
Dmo
Dma
Dmn
Dmp
Dms
5.5 · 10−5
9.0 „
9.3
4.2 „
4.7 „
m2
m2
m2
m2
m2
bt
3.0
2.0
365
0.2
d
-
Db
1.0 · 10−6
1.0 · 10−6
m2 d−1
m2 d−1
d
-
Fr
Fraction of surface area closed by the benthic
complex
Molecular diffusion coefficient oxygen
Molecular diffusion coefficient ammonium
Molecular diffusion coefficient nitrate
Molecular diffusion coefficient phosphate
Molecular diffusion coefficient silicate
Bio-irrigation multiplication factor;
mean
amplitude
period
phase
Bioturbation dispersion coefficient;
mean
amplitude
period
phase
w
365
0.2
b
d−1
d−1
d−1
d−1
d−1
d1 , d2 and d3 shape up the upper layer dh, which is constant in thickness just as dl (=d4 ).
Table 2.4: (Bio)chemical input parameters for SWITCH
Parameter
Symbol in
appendix
Value
Units
Detritus
6 of 32
Deltares
Spatial schematisation and processes
Table 2.4: (Bio)chemical input parameters for SWITCH
Incorp. rate from bound. layer into up. layer at
20 ◦ C1)
Temperature coefficient for incorporation*
Mineralisation rate in the boundary layer at 20
◦ 2)
C
Mineralisation rate in the upper layer at 20 ◦ C
Mineralisation rate in the lower layer at 20 ◦ C
Temperature coefficient for mineralisation
Add. frac. detritus turned into refractory org.
matter
Ammonium and Nitrate
Nitrification rate
Temperature coefficient for nitrification
Denitrification rate at 20 ◦ C
Temperature coefficient for denitrification
Stoich. constant for nitrogen in refractory org.
matter
Symbol in
appendix
rc20
Value
Units
0.04
d−1
kti
kc20
b
1.07
0.075
d−1
kc20
1
kc20
4
ktc
frf
0.055
0.0065
1.07
1.0
d−1
d−1
-
T
Parameter
50.0
1.07
50.0
1.07
0.04
d−1
d−1
gN gC−1
Phosphate
Adsorption capacity of oxidising layer 1-2
Caco
0.8
Adsorption capacity of upper reducing layer 3
Cacr
0.4 or -999
Half saturation constant for adsorption at 20 ◦ C
Temperature coefficient for half saturation constant
Precipitation rate at 20 ◦ C
Fraction precipitated phosphate into the stable
mineral
Saturation concentration for precipitation
Temperature coefficient for precipitation
Dissolution / oxidation rate of vivianite at 20 ◦ C
Ks20
kta
0.1
1.0
gP
kgDM−1
gP
kgDM−1
gP m−3
-
kp20
fm
0.8
0.0
d−1
-
Cdps
ktp
kdp20
0.05
1.0
0.01
Temperature coefficient for dissolution
Stoich. constant for phosphorus in refract. org.
matter
ktdp
ap
1.0
0.004
gP m−3
m−2.01
gP0.67
d−1
gP gC−1
ks20
Css
kts
0.09
10.0
1.0
d−1
gSi m−3
-
ac
3.1
an
4.57
gO2
gC−1
gO2
gN−1
DR
AF
kn20
ktn
kd20
ktd
aa
Silicate
Dissolution rate of opal silicate at 20 ◦ C
Saturation concentration for dissolution
Temperature coefficient for dissolution
Oxygen
Stoich. constant for consump. at mineralis. of
detritus
Stoich. constant for consump. at nitrification
Deltares
w
w
w
7 of 32
SWITCH, Technical Reference Manual
Table 2.4: (Bio)chemical input parameters for SWITCH
Parameter
Fraction oxygen in water at sediment-water interface
Fraction reduced substances retained from oxidation;
mean
amplitude
period
phase
Symbol in
appendix
fo
Value
Units
0.6
-
fro
0.0
0.0
365
0.2
d
-
1)
DR
AF
T
The incorp. rate is dealt with in the input for S1 detritus as a burial rate in 1/d, that can be
made approx. temperature dependent by providing a time dependent function.
2)
The decomposition rates and temperature coefficients for detritus in the boundary layer are
input for the S1 module of DELWAQ. Rates and coefficients have to be provided for org. C,
org. N and org. P.
8 of 32
Deltares
3 Aerobic layer and the sediment oxygen demand
The thickness of the aerobic layer is dependent on the oxygen consumption rate according to
the following steady-state equation:
p
2 · p1 · D · fo · CoO /Ro
d1 = d1m if d1 < d1m
d1 =
(3.1)
in which:
oxygen concentration in the overlying water [g m−3 ]
minimal thickness of the aerobic layer [m]
dispersion coefficient [m2 d−1 ]
ratio of the oxygen concentrations at the upper and lower sides of the water
boundary layer [-]
porosity [-]
oxygen consumption rate [g m3 bottom d−1 ]
T
CoO
d1m
D
fo
p
Ro
DR
AF
A subscript figure indicates a layer number or an interface number!
The introduction of ratio fo relates to the existence of a relatively stagnant boundary layer
in the overlying water, which contains a part of the oxygen gradient at the sediment-water
interface. The oxygen concentration at the interface is a certain fraction of the average oxygen
concentration in the water column.
Oxygen is consumed in the degradation of detritus in the boundary layer (complex-detritus
in the terminology of DBS) and of detritus in the aerobic layer, in the nitrification and in the
chemical oxidation. The oxygen consumption rate Ro is formulated as follows:
Ro = Fob /d1 + ac · kc1 · Cd1 + p1 · an · kn · Ca1 + Foc /d1
(3.2)
in which:
stoichiometric constant [gO2 gC−1 ]
stoichiometric constant [gO2 gN−1 ]
detritus concentration in the upper layer [gC m−3 B]
ammonium concentration in the aerobic layer [gN m−3 PW]
oxygen consumption in the boundary layer [gO2 m−2 d−1 ]
chemical oxygen demand [gO2 m−2 d−1 ]
degradation rate of detritus in the upper layer [d−1 ]
nitrification rate [d−1 ], equal to zero if Co0 = 0.0
ac
an
Cd1
Ca1
Fob
Foc
kc1
kn
The oxygen consumption in the boundary layer is connected with the degradation of detritus
on top of the sediments and is equal to:
Fob = ac · kcb · Cdb
(3.3)
in which:
Cdb
kcb
amount of complex-detritus in the boundary layer [gC m2 ]
degradation rate of complex-detritus in the boundary layer [d−1 ]
The chemical oxygen demand concerns the oxidation of reduced substances, such as iron(II),
manganese(II), sulphide and methane originating from the degradation of detritus in the anaerobic part of the ’active’ bottom. However, the reduced substances will not be oxidising completely. A part of the sulphide resulting from sulphate reduction precipitates with iron and may
Deltares
9 of 32
SWITCH, Technical Reference Manual
accumulate in the reduced part of the sediments. Methane may escape from the sediments
in gas bubbles. Consequently, the actual chemical oxygen demand is formulated as a fraction
of the potential chemical oxygen demand:
Foc = (1 − fro) · ac · (kc1 · Cd1 · (d2 + d3 ) + kc4 · Cd4 · d4 )
(3.4)
in which:
fro
kc4
fraction reduced substances permanently removed or fixed [-]
degradation rate of detritus in the lower layer [d−1 ]
The sediment oxygen demand is quantified with:
T
Note that the degradation of detritus in the denitrifying layer has been included entirely in
the chemical oxygen demand. This is not correct as such, since the elementary nitrogen
produced by denitrification is chemically inert. It is not oxidised, but escapes from the bottom.
A correction for the amount of nitrate consumed by denitrification can be made with fro. No
correction was made in the second version of SWITCH.
(3.5)
DR
AF
Fo = Fob + (ac · kc1 · Cd1 + p1 · an · kn · Ca1 ) · d1 + Foc
Maintaining a bottom oxygen demand under anaerobic conditions in the water column (kn =
0.0!) leads to a negative oxygen concentration in the water quality model representing the
surplus of reduced substances.
10 of 32
Deltares
4 Denitrifying layer and nitrate
Nitrate is formed from ammonium through nitrification in the aerobic top layer. It is subjected
to vertical transport and denitrification in the zone just below this layer (Vanderborght et al.,
1977a). The thickness of the denitrifying layer follows from the (approximate) steady-state
solution of the differential equation for nitrate in this layer:
d2 = 2(Cn1 − Cnc )/Cn1 ·
p
D/kd
(4.1)
d2 = 0.0 if Cn1 ≤ Cnc
in which:
first order denitrifcation rate [d−1 ]
nitrate concentration in the top layer [gN m−3 ]
critical nitrate concentration [gN m−3 ]
T
kd
Cn1
Cnc
The critical nitrate concentration is the maximal concentration at which sulphate reduction is
possible, about 0.1 gN m−3 .
DR
AF
The nitrate concentration in the aerobic and denitrifying layers follow from:
d Cn1
= (Fnb − Fn0 + Fn1 )/(p1 · d1 ) + kn · Ca1
dt
with:
(4.2)
Fn0 = 2p1 · D · (Cn1 − Cn0 )/(l + d1 )
Fn1 = −2p1 · kd · Cn2 ·
Cn2 =
p
D/kd
1
Cn1
2
in which:
Ca1
Fnb
Fn0
Fn1
l
Deltares
ammonium concentration in the top layer [gN m−3 ]
flux from the boundary layer [gN m−2 d−1 ]
dispersive return flux to the overlying water [gN m−2 d−1 ]
flux to the denitrifying layer [gN m−2 d−1 ]
thickness of the water boundary layer [m]
11 of 32
DR
AF
T
SWITCH, Technical Reference Manual
12 of 32
Deltares
5 Detritus
Organic carbon
All organic matter, which settles on the sediments is considered as detritus, regardless of its
origin. GEM distinguishes:
live phytoplankton, which enters the complex-detritus pool in the boundary layer due to
settling;
dead microphytobenthos, which enters the complex-detritus pool in the boundary layer
due to mortality;
fast decomposing detritus and slow decomposing detritus, that enter the complex-detritus
pool in the boundary layer as the net result of settling and resuspension; and
to settling.
T
refractory detritus, which enters the slow decomposing detritus pool in the lower layer due
DR
AF
SWITCH transfers the complex-detritus to the relatively fast decomposing sediment-detritus
pool. Resuspension (if occurring) leads to reincorporation of the detritus into the water column
as fast decomposing detritus. The model converts a fraction of the sediment-detritus into
refractory humic matter, which is stored in the sediment.
Summarising, detritus is subjected to settling, resuspension, incorporation from the boundary
layer into the sediment, degradation, humification and burial (Berner, 1974). The degradation
rate decreases while the organic matter is transported downwards in the sediment.
The concentrations of detritus in the boundary layer and the bottom layers are described with
the following differential equations:
d Cdb
dt
d Cd1
dt
d Cd4
dt
with:
= Fds − Fdb − kcb · Cdb
(5.1)
= (Fdb − Fb3 · Cd1 + Fd3 )/dh − kc1 · Cd1
(5.2)
= (Fxds + Fb3 · Cd1 − Fd3 )/d4 − (1 + frf) · kc4 · Cd4
(5.3)
Fds = sc · Cd0
Fdb = rc · Cdb
Fb3 = Fs − Fr ≥ 0.0
Fb4 = Fb3 · (1 − p1 )/(1 − p4 )
Fd3 = 2Db · (Cd4 /(1 − p4 ) − Cd1 /(1 − p1 ))/(dh + d4 )
Fxds = sc · Cxd0
in which:
Cd0
Cdb
Cd1
Cd4
Cxd0
Db
frf
Fb
Deltares
detritus concentration in the overlying water [gC m−3 ]
amount of detritus in the boundary layer [gC m−2 ]
detritus concentration in the upper layer [gC m−3 B]
detritus concentration in the lower layer [gC m−3 B]
refractory detritus concentration in the overlying water [g m−3 ]
bioturbation dispersion coefficient (m2 d−1 )
factor for the conversion of detritus into refractory organic matter [-]
burial flux based on displaced bottom volume (m3 B m−2 d−1 )
13 of 32
SWITCH, Technical Reference Manual
bioturbation flux [gC m−2 d−1 ]
flux of detritus incorporated in the upper layer [gC m−2 d−1 ]
flux of detritus settled from the overlying water [gC m−2 d−1 ]
resuspension flux based on displaced bottom volume [m3 B m−2 d−1 ]
sedimentation flux based on displaced bottom volume [m3 B m−2 d−1 ]
degradation rate of detritus in the boundary layer [d−1 ]
rate of incorporation in the upper layer [d−1 ]
sedimentation rate for detritus [m d−1 ]
flux of refractory detritus incorporated in the sediment [gC m−2 d−1 ]
Fd
Fdb
Fds
Fr
Fs
kcb
rc
sc
Fxds
The amount of detritus in the boundary layer (Cdb ) is not calculated in SWITCH itself but
in the S1 sediment module of DELWAQ (DBS or GEM). The decomposition rate and the
incorporation (burial) rate are input to this S1 module.
T
Notice that the conversion of detritus into refractory organic matter has been formulated as a
process that is proportional and additive to decomposition at the same time. frf can be seen
as an amplification factor. frf/(1 − frf) delivers the fraction of the degradable organic matter
that is converted into refractory organic matter.
DR
AF
SWITCH has input parameters with respect to settling and resuspension. The difference FsFr is in fact the net sediment accretion rate or the burial rate in case of a positive value, not to
be confused with the incorporation rate, which may also be called a burial rate. Notice that the
formulations in SWITCH regarding detritus are only valid for burial. Moreover, it is assumed
that all detritus has been degraded or converted before it arrives at the lower boundary of the
’active’ bottom layer, so that burial does not remove degradable detritus from the lower layer.
Only the ’average’ concentration of the refractory organic matter is calculated for the ’active’
bottom. The concentration is derived from:
d Crd1
dt
= (−Fb4 · Crd1 + frf · kc4 · Cd4 · d4 )/(dh + d4 )
(5.4)
Organic nitrogen
Similar equations have been formulated for organic nitrogen. The decomposable organic
nitrogen in detritus is converted into ammonium and into refractory organic nitrogen in the
following way:
d Cndb
dt
d Cnd1
dt
d Cnd4
dt
= Fnds − Fndb − kndb · Cndb
(5.5)
= (Fndb − Fb3 · Cnd1 + Fnd3 )/dh − (1 + fa1 ) · kc1 · Cnd1
(5.6)
= (Fxns + Fb3 · Cnd1 − Fnd3 )/d4 − (1 + fa4 + frf) · kc4 · Cnd4
(5.7)
with:
fa1 = (Cnd1 /Cd1 − aa)/aa
fa4 = (Cnd4 /Cd4 − aa)/aa
Fnds = sc · Cnd0
Fndb = rc · Cndb
Fnd3 = 2Db · (Cnd4 /(1 − p4 ) − Cnd1 /(1 − p1 ))/(dh + d4 )
Fxns = sc · Cxn0
in which:
14 of 32
Deltares
Detritus
stoichiometric constant for nitrogen in refractory detritus [gN gC−1 ]
detritus nitrogen concentration in the overlying water [gN m−3 ]
amount of detritus nitrogen in the boundary layer [gN m−2 ]
detritus nitrogen concentration in the upper layer [gN m−3 B]
detritus nitrogen concentration in the lower layer [gN m−3 B]
slow decomposing detritus nitrogen (OON) concentration in overlying water [gN
m−3 ]
correction factor for organic nitrogen degradation rate [-]
bioturbation flux [gN m−2 d−1 ]
flux of detritus nitrogen incorporated in the upper layer [gN m−2 d−1 ]
flux of detritus nitrogen settled from the overlying water [gN m−2 d−1 ]
flux of slow decomposing detritus nitrogen (OON) incorp. in sediment [gN m−2
d−1 ]
degradation rate of detritus nitrogen in the boundary layer [d−1 ]
aa
Cnd0
Cndb
Cnd1
Cnd4
Cxn0
fa
Fnd
Fndb
Fnds
Fxns
T
kndb
The amount of detritus nitrogen in the boundary layer (Cndb) is not calculated in SWITCH
itself but in the S1 sediment module of DELWAQ (DBS or GEM). The decomposition rate and
the incorporation (burial) rate are input to this S1 module.
DR
AF
The degradation rates of organic nitrogen are adjusted in such a way that the organic matter
is gradually stripped from nitrogen in excess of the nitrogen in refractory organic matter.
The ’sediment-average’ concentration of the refractory organic nitrogen follows from:
d Crn1
dt
= (−Fb4 · Crn1 + frf · kc4 · Cnd4 · d4 )/(dh + d4 )
(5.8)
Organic phosphorus
The following equations describe the organic phosphorus in accordance with the above:
d Cpdb
dt
d Cpd1
dt
d Cpd4
dt
with:
= Fpds − Fpdb − kpdb · Cpdb
(5.9)
= (Fpdb − Fb3 · Cpd1 + Fnd3 )/dh − (1 + fp1 ) · kc1 · Cpd1
(5.10)
= (Fxps + Fb3 · Cpd1 − Fnd3 )/d4 − (1 + fp4 + frf) · kc4 · Cpd4
(5.11)
fp1 = (Cpd1 /Cd1 − ap)/ap
fp4 = (Cpd4 /Cd4 − ap)/ap
Fpds = sc · Cpd0
Fpdb = rc · Cpdb
Fpd3 = 2Db · (Cpd4 /(1 − p4 ) − Cpd1 /(1 − p1 ))/(dh + d4 )
Fxps = sc · Cxp0
in which:
ap
Cpd0
Cpdb
Cpd1
Cpd4
Deltares
stoichiometric constant for phosphorus in refractory detritus [gP gC−1 ]
detritus phosphorus concentration in the overlying water [gP m−3 ]
amount of detritus phosphorus in the boundary layer [gP m−2 ]
detritus phosphorus concentration in the upper layer [gP m−3 B]
detritus phosphorus concentration in the lower layer [gP m−3 B]
15 of 32
SWITCH, Technical Reference Manual
Cxp0
slow decomposing detritus phosphorus (OOP) concentration overlying water
[gP m−3 ]
correction factor for organic phosphorus degradation rate [-]
bioturbation flux [gP m−2 d−1 ]
flux of detritus phosphorus incorporated in the upper layer [gP m−2 d−1 ]
flux of detritus phosphorus settled from the overlying water [gP m−2 d−1 ]
flux of slow decomp. detritus phosphorus (OOP) incorp. in sediment [gP m−2
d−1 ]
degradation rate of detritus phosphorus in the boundary layer [d−1 ]
fp
Fpd
Fpdb
Fpds
Fxps
kpdb
The amount of detritus phosphorus in the boundary layer (Cndb ) is not calculated in SWITCH
itself but in the S1 sediment module of DELWAQ (DBS or GEM). The decomposition rate and
the incorporation (burial) rate are input to this S1 module.
d Crp1
= (−Fb4 · Crp1 + frf · kc4 · Cpd4 · d4 )/(dh + d4 )
DR
AF
dt
T
The ’sediment-average’ concentration of the refractory organic phosphorus follows from:
16 of 32
Deltares
6 Ammonium
Ammonium is released the degradation of detritus and is nitrified by bacteria under aerobic
conditions (Berner, 1974; Vanderborght et al., 1977b). Ammonium adsorbs to a certain extent
to clays in the sediments. The adsorption equilibrium is pH dependent. It is estimated that
about 25 to 50 % of the ammonium present in silty sediments may be adsorbed (partition
coefficient ≈ 1). This is a relatively small quantity compared to the high turn-over rates of
ammonium in sediments. Thus, the adsorption offers only a small buffering capacity, which
implies that no large mass fluxes are involved in the adsorption of ammonium. A change of
ammonification is quickly followed by a proportional change of the ammonium concentration
in the pore water. It is therefore justified to ignore the adsorption of ammonium in SWITCH.
d Ca1
dt
d Ca2
d Ca4
dt
with:
= (Fab − Fa0 + Fa1 + Fas0 − Fas1 )/(p1 · d1 ) + (1 + fa1 ) · kc1 · Cnd1 /p1 − kn · Ca1
(6.1)
= (−Fa1 + Fa3 + Fas1 − Fas3 )/(p1 · (d2 + d3 )) + (1 + fa1 ) · kc1 · Cnd1 /p1
DR
AF
dt
T
The ammonium concentrations in the aerobic top layer, the remaining part of the upper layer
(d2 +d3 ) and the lower reducing layer (dl) are described with:
= (−Fa3 + Fas3 − Fas4 )/(p4 · d4 ) + (1 + fa4 ) · kc4 · Cnd4 /p4
(6.2)
(6.3)
Fab = kndb · Cdb
Fa0 = 2p1 · D · (Ca1 − Ca0 )/(l + d1 )
Fa1 = 2p1 · D · (Ca2 − Ca1 )/do
Fa3 = (p1 + p4 ) · D · (Ca4 − Ca2 )/(d − d1 )
Fas0 = −vs · Ca0
if vs < 0.0
Fas1 = −vs · Ca1
Fas3 = −vs · Ca2
Fas4 = −vs · Ca4
Fas0 = −vs · Ca1
if vs > 0.0
Fas1 = −vs · Ca2
Fas3 = −vs · Ca4
Fas4 = −vs · Ca5
in which:
Ca5
Fab
Fa0
Fa1−3
Fas0
Fas1−3
Deltares
ammonium concentration in the lower boundary layer [gN m−3 ]
flux from degradation detritus in boundary layer [gN m−2 d−1 ]
dispersive return flux to the overlying water [gN m−2 d−1 ]
dispersive flux between two adjacent layers [gN m−2 d−1 ]
seepage flux at the sediment-water interface [gN m−2 d−1 ]
seepage flux between two adjacent layers [gN m−2 d−1 ]
17 of 32
SWITCH, Technical Reference Manual
Fas4
kndb
vs
seepage flux at the lower boundary [gN m−2 d−1 ]
degradation rate of detritus nitrogen in the boundary layer [d−1 ]
seepage velocity [m d−1 ]
It is assumed that no dispersive transport occurs across the interface of the ’active’ and ’inactive’ parts of the bottom. The assumption implies that the concentration of a dissolved
substance is the same at both sides of the lower boundary of the bottom in the model. It
is a reasonable assumption when seasonal variations in the concentration of a dissolved
substance is small at the lower boundary. Moreover, a long-term shift in the ammonium concentration in the ’inactive’ bottom does hardly affect the sediment-water exchange fluxes.
DR
AF
T
SWITCH stops nitrification (kn = 0.0) when the dissolved oxygen concentration in the water
column is equal to or less than 0.0.
18 of 32
Deltares
7 Phosphate
Bacterial activity liberates phosphate from organic matter just like ammonium. In contrast
with ammonium, phosphate adsorbs strongly to several components of the sediments, the
hydroxides of iron(III) and aluminum in particular. Iron(III) hydroxide is present in a relatively
high concentration in the oxidising layer, where it is stable. The concentration declines at
the interface of the oxidising and reducing layers and goes down further in the reducing layer
under the influence of reduction processes. Consequently, the adsorption is much stronger in
the oxidising layer than in the reducing layer (Van Raaphorst et al. (1988); Brinkman and Van
Raaphorst (1986); Lijklema (1980); Berner (1974)).
T
Phosphate also precipitates in minerals, the identity of which has not been determined unequivocally (WL | Delft Hydraulics, 1994a). Vivianite (iron(II)phosphate) is being mentioned
as the main mineral, but vivianite is not stable under oxidising conditions. Apatite (calcium
phosphate) may be present as a stable mineral in marine water sediments. Coprecipitation
with several carbonates and sulphides is also possible.
DR
AF
SWITCH assumes equilibrium for the adsorption process, whereas precipitation and dissolution are formulated as slow processes. The assumption of equilibrium has the advantage, that
only inorganic phosphate and precipitated phosphate need to be calculated explicitly on the
basis of mass balances. The dissolved and adsorbed phosphate concentrations follow from
the equilibrium condition for adsorption. The following four fractions are distinguished:
Cpp = fpp · Cp
(7.1)
Cmp = fmp · Cp
Cdp = fdp · Cp/p
Cap = fap · Cp
fap + fdp + fpp + fmp = 1
in which:
Cp
Cap
Cdp
Cmp
Cpp
fap
fdp
fmp
fpp
total inorganic phosphate concentration [gP m−3 B]
adsorbed phosphate concentration [gP m−3 B]
dissolved phosphate concentration [gP m−3 PW]
concentration of phosphate in a stable mineral [gP m−3 B]
concentration of phosphate in vivianite [gP m−3 B]
adsorbed fraction [-]
dissolved fraction [-]
stable mineral fraction [-]
vivianite fraction [-]
These fractions are relevant for the mass balance equation for total inorganic phosphate,
because the processes affect only one or two of the fractions.
The mineral phosphate fractions can be determined after solution of the mass balance equations for these components. The precipitation process is formulated with first order kinetics.
The driving force is the difference between the actual concentration and the saturation concentration of ortho-phosphate dissolved in the pore water. In principle, the latter may be
determined from the solubility product of the phosphate mineral, when its identity has been
established. No distinction was made between the precipitation rates and the saturation concentrations of vivianite and the stable mineral, as the in-situ properties of these minerals are
unknown. The precipitation rate is a function of the driving force, the nature of which depends
Deltares
19 of 32
SWITCH, Technical Reference Manual
on the rate limiting mechanism. The function is linear when diffusion to the surface of the mineral is the rate limiting process. In case that the surface reaction is rate limiting, the function
may be non-linear. However, the assumption of simple first order reaction kinetics ignoring
the role of coprecipitants seems reasonable in this stage, considering that the precipitation
rate has not yet been determined accurately and that the dissolved iron concentration is not
simulated.
The development of the concentrations of the stable mineral phosphate is described with:
d Cmp1
dt
= p1 · fm · kp · (fdp1 · Cp1 /p1 − Cdps )+
(−Fr · fmp1 · Cp1 − Fb2 · fmp1 · Cp1 )/do+
2Db · (fmp3 · Cp3 − fmp1 · Cp1 )/(1 − p1 )/(do + d3 )/do
dt
DR
AF
(Fb2 · fmp1 · Cp1 − Fb3 · fmp3 · Cp3 )/d3 −
2Db · (fmp3 · Cp3 − fmp1 · Cp1 )/(1 − p1 )/(do + d3 )/d3 +
2Db · (fmp4 · Cp4 /(1 − p4 ) − fmp3 · Cp3 /(1 − p1 ))/(d3 + d4 )/d3
d Cmp4
dt
Cdps
fm
Fr
kp
(7.3)
= p4 · fm · kp · (fdp4 · Cp4 /p4 − Cdps )+
(Fb3 · fmp3 · Cp3 − Fb4 · fmp4 · Cp4 )/d4 −
2Db · (fmp4 · Cp4 /(1 − p4 ) − fmp3 · Cp3 /(1 − p1 ))/(d3 + d4 )/d4
in which:
(7.2)
= p1 · fm · kp · (fdp3 · Cp3 /p1 − Cdps )+
T
d Cmp3
(7.4)
saturation concentration for dissolved ortho-phosphate [gP m−3 PW]
fraction of precipitated phosphorus stored in the stable mineral [-]
resuspension flux based on bottom volume [m3 m−2 d−1 ]
precipitation rate [d−1 ]
Vivianite forms in the reducing parts of the sediments. It dissolves gradually when transported
into the oxidising layer by means of bioturbation of the sediments. This hypothesis can be
justified as follows:
Vivianite (iron(II) phosphate) is unstable under oxidising conditions (Lijklema, 1980).
The concentration of dissolved Fe(II), and in some parts also the concentration of dissolved ortho-phosphate, is much higher in the reducing layer than in the oxidising layer.
The solubility product is probably only exceeded in the reducing layer.
The formulation of the dissolution process is not straight forward. The dissolution is probably
characterised by two steps: a) the oxidation of dissolved Fe2+ , b) the dissolution of vivianite
at a very low dissolved Fe2+ -concentration. The driving force may therefore be the difference
between the Fe2+ -concentration near the vivianite crystals and the average dissolved Fe2+ concentration. The latter may approximately be equal to zero, due to oxidation.
The dissolution rate may then be formulated as follows:
Rdis = kdis · Cpp · Cfe
(7.5)
in which:
Cfe
kdis
20 of 32
dissolved Fe2+ -concentration near the surface of vivianite crystals [gFe m−3 ]
(second order) dissolution rate constant [m3 gFe−1 d−1 ]
Deltares
Phosphate
dissolution rate [gP m−3 d−1 ]
Rdis
The dissolved Fe2+ -concentration near the surface of the crystals is calculated from the solubility product (equilibrium constant) and the dissolved phosphate concentration with:
Cfe = (Ls /Cdp2 )0.33
(7.6)
in which:
Ls
solubility product of vivianite
T
Equations (7.5)–(7.6) have been combined to make the dissolution rate dependent on the
dissolved phosphate concentration (power -0.67). The solubility product becomes an implicit
part of the dissolution rate constant. The resulting formulation meets the demand that the
dissolution process slows down when the dissolved phosphate concentration increases.
The mass balances for phosphate in vivianite in three layers are:
d Cpp1
dt
= −kdp · fpp1 · Cp1 · (fdp1 · Cp1 /p1 )−0.67 +
DR
AF
(−Fr · fpp1 · Cp1 − Fb2 · fpp1 · Cp1 )/do+
2Db · (fpp3 · Cp3 − fpp1 · Cp1 )/(1 − p1 )/(do + d3 )/do
d Cpp3
dt
(7.7)
= p1 · kp · (fdp3 · Cp3 /p1 − Cdps )+
(Fb2 · fpp1 · Cp1 − Fb3 · fpp3 · Cp3 )/d3 −
2Db · (fpp3 · Cp3 − fpp1 · Cp1 )/(1 − p1 )/(do + d3 )/d3 +
2Db · (fpp4 · Cp4 /(1 − p4 ) − fpp3 · Cp3 /(1 − p1 ))/(d3 + d4 )/d3
d Cpp4
dt
(7.8)
= p4 · kp · (fdp4 · Cp4 /p4 − Cdps )+
(Fb3 · fpp3 · Cp3 − Fb4 · fpp4 · Cp4 )/d4 −
2Db · (fpp4 · Cp4 /(1 − p4 ) − fpp3 · Cp3 /(1 − p1 ))/(d3 + d4 )/d4
(7.9)
in which:
dissolution rate (m−2.01 gP0.67 d−1 )
kdp
The dissolved fraction can be derived from the following Langmuir adsorption isoterm:
Cap = Cam · Cdp/(Ks + Cdp)
(7.10)
Cam = Cac · (1 − p) · Ws
in which:
Cac
Cam
Ks
Ws
adsorption capacity [gP kg−1 DM]
maximal concentration of adsorbed phosphate [gP m−3 B]
half saturation concentration [gP m−3 PW]
specific weight of the sediments [kg m−3 ]
The adsorption capacity depends on the oxidising iron (III) and aluminum contents of the sediments. This sediment property is different for the oxidising layer and the reducing layer. The
oxidising iron content and (therefore) the adsorption capacity decrease in a downward direction. Iron(III) is reduced to iron(II) in connection with the degradation of organic matter. The
oxidising iron gradient is smoothed by bioturbation of the sediment, which results in upward
transport of iron(II) formed in the reducing layer and in downward transport of iron(III) formed
Deltares
21 of 32
SWITCH, Technical Reference Manual
in the oxidising layer. Moreover, the adsorption capacities change in time due to changes
of the temperature dependent rates of degradation of organic matter and bioturbation. Both
processes affect the position of the interface between the layers and the amounts of oxidising
iron present in the layers. This is taken into account in SWITCH, whereas the dependency on
pH and salinity of the adsorption parameters is not considered explicitly.
Tentative simulations with the complex chemical model HADES showed that the iron(III) contents of the oxidising layer and the reducing layer are related to the thickness of the oxidising layer (WL | Delft Hydraulics, 1991). The adsorption capacity increases with increasing
thickness of the oxidising layer. However, it has not been possible yet to formulate this relation deterministically. Empirical relations, determined by means of model calibration for Lake
Veluwe, have been introduced in SWITCH in stead. The relations used in SWITCH are:
Cam3 = fac1 · fac3 · Cac · (1 − p1 ) · Ws
Cam4 = 0.5fac4 · Cac · (1 − p4 ) · Ws
fac1 = ((d1 + d2 )/0.005)0.25
DR
AF
fac3 = ((d1 + d2 )/dh)0.25
T
Cam1 = fac1 · Cac · (1 − p1 ) · Ws
fac4 = dh/(dh + d4)
in which:
Cam1
Cam3
Cam4
Cac
fac
maximal concentration of adsorbed phosphate in the oxidising layer [gP m−3 B]
maximal concentration of adsorbed phosphate in the upper reducing layer [gP
m−3 B]
maximal concentration of adsorbed phosphate in the lower reducing layer [gP
m−3 B]
time average adsorption capacity of the oxidising layer [gP kg−1 DM]
empirical factor linking up the ads. capacity with layer thickness [-]
The adsorption capacity of the oxidising layer becomes bigger than the ’average’ capacity
(Cac) when the thickness of the oxidising layer becomes bigger than 0.005 m, which is about
half the maximal thickness of the oxidising layer. The adsorption capacities of the reducing
layers depend also on the values of dh and d4 (input parameters for SWITCH). The thicker the
reducing layers are, the smaller their depth average adsorption capacities are. This is logical
considering the fact that the capacity decreases with depth.
The adsorption capacity of the oxidising layer is set equal to the capacity of the upper reducing
layer, when the depth of the oxidising layer (do=d1 +d2 ) becomes smaller than critical thickness
dom. It is assumed in fact that the excess adsorption capacity in the upper layer disappears
completely, when the oxidising layer collapses. Consequently, the concentration gradient of
dissolved phosphate increases steeply, which generates so-called “explosive” phosphate return fluxes.
An earlier approach, which defined the adsorption capacities of the lower reducing layer 4
as a constant fraction (=0.2) of the adsorption capacity of the upper reducing layer 3, is also
available in SWITCH as an alternative option.
SWITCH requires input for the adsorption capacity of the oxidising top layer (layers 1–2) and
the adsorption capacity of the upper reducing layer 3. The model uses the constant ratio
option when the adsorption capacity of the upper reducing layer is given a positive value. In
case this parameter obtains a negative value (for instance -999), the layer depth dependent
option is applied.
22 of 32
Deltares
Phosphate
A quadratic equation in fdp is obtained when equation (7.10) is substituted in equations (7.1).
The positive root is:
fdp = {(1 − fmp − fpp) · Cp − p · Ks − Cam+
√
((1 − fmp − fpp) · Cp − p · Ks − Cam)2 + 4(1 − fmp − fpp) · Cp · p · Ks /(2Cp)
(7.11)
Having defined al four phosphate fractions, the mass balances for total inorganic phosphate in
the oxidising layer, the upper reducing layer and the lower reducing layer have been formulated
as follows:
d Cp1
dt
= (Fpb + Fps − Fp0 + Fp2 + Fps0 − Fps2 −
Fr · Cp1 + Fpd2 − Fb2 · Cp1 )/do + (1 + fp1 ) · kc1 · Cpd1
dt
T
d Cp3
(7.12)
= (−Fp2 + Fp3 + Fps2 − Fps3 − Fpd2 + Fpd3 +
Fb2 · Cp1 − Fb3 · Cp3 )/d3 + (1 + fp1 ) · kc1 · Cpd1
= (−Fp3 + Fps3 − Fps4 − Fpd3 +
DR
AF
d Cp4
(7.13)
dt
Fb3 · Cp3 − Fb4 · Cp4 )/d4 + (1 + fp4 ) · kc4 · Cpd4
with:
(7.14)
Fpb = kpdb · Cpdb
Fp0 = 2p1 · D · (fdp1 · Cp1 /p1 − fdp0 · Cp0 )/(l + do)
Fp2 = 2D · (fdp3 · Cp3 − fdp1 · Cp1 )/(do + d3 )
Fp3 = (p1 + p4 ) · D · (fdp4 · Cp4 /p4 − fdp3 · Cp3 /p1 )/(d3 + d4 )
Fpd2 = 2Db · ((fpp3 + fmp3 + fap3 ) · Cp3 − (fmp1 + fap1 ) · Cp1 )/(1 − p1 )/(do + d3 )
Fpd3 = 2Db · ((fpp4 + fmp4 + fap4 ) · Cp4 /(1 − p4 ) − (fpp3 + fmp3 + fap3 ) · Cp3 /(1 − p1 ))/(d3 + d4
Fps0 = −vs · fdp0 · Cp0 /p1
if vs < 0 · 0
Fps2 = −vs · fdp1 · Cp1 /p1
Fps3 = −vs · fdp3 · Cp3 /p1
Fps4 = −vs · fdp4 · Cp4 /p4
Fps0 = −vs · fdp1 · Cp1 /p1
if vs > 0 · 0
Fps2 = −vs · fdp3 · Cp3 /p1
Fps3 = −vs · fdp4 · Cp4 /p4
Fps4 = −vs · Cdp5
in which:
Cdp5
Fb
Fr
Fpb
Deltares
dissolved phosphate concentration in the lower boundary layer [gP.m−3 ]
burial flux based on sediment volume [m3 m−2 d−1 ]
resuspension flux based on sediment volume [m3 m−2 d−1 ]
flux from degradation detritus in boundary layer [gP m−2 d−1 ]
23 of 32
SWITCH, Technical Reference Manual
Fps
Fp0
Fp2−3
Fpd2−3
Fps0
Fps2−3
Fps4
sedimentation flux of adsorbed phosphate [gP m−2 d−1 ]
dispersive return flux to the overlying water [gP m−2 d−1 ]
dispersive flux between two adjacent layers [gP m−2 d−1 ]
bioturbation flux between two adjacent layers [gP m−2 d−1 ]
seepage flux at the sediment-water interface [gP m−2 d−1 ]
seepage flux between two adjacent layers [gP m−2 d−1 ]
seepage flux at the lower boundary [gP m−2 d−1 ]
DR
AF
T
Notice, that the resuspension of phosphate is taken into account explicitly, because of the
importance for the phosphate budget in the overlying water. Phosphate adsorbed to resuspended sediments may desorb in the water column.
24 of 32
Deltares
8 Silicate
Reactive silicate enters the sediment primarily in the form of opal silicate, the remains of
diatom skeletons. Opal silicate dissolves gradually, because pore water is undersaturated with
respect to silicate. The process is retarded by coating of the particles with minerals of iron
and aluminum. Dissolved silicate may adsorb onto aluminum silicates and may precipitate
in stable minerals (Berner, 1974; Vanderborght et al., 1977a; Schink and Guinasso, 1978).
Because all these processes are very slow and poorly understood, it was decided to include
in SWITCH only the dissolution process.
T
Furthermore it is assumed that opal silicate is present in abundance in estuarine sediment.
This seems a reasonable assumption considering the high productivity of diatoms and the
slowness of the dissolution process. The rate is than only dependent on the difference between the saturation concentration and the actual dissolved concentration of silicate.
Sub-layers are not distinguished with respect to silicate. The mass balance of dissolved silicate in the pore water of the sediment is:
d Cs1
with:
= (Fsb − Fs0 + Fss0 − Fss4 )/(pa · d) − ks · (Cs1 − Css )
(8.1)
DR
AF
dt
pa = (p1 · dh + p4 · dl)/d
Fs0 = 2pa · D · (Cs1 − Cs0 )/(l + dh)
Fss0 = −vs · Cs0
if vs < 0 · 0
Fss4 = −vs · Cs1
Fss0 = −vs · Cs1
if vs > 0 · 0
Fss4 = −vs · Cs5
in which:
Cs1
Cs5
Css
Fsb
Fs0
Fss0
Fss4
ks
pa
Deltares
dissolved silicate concentration [gSi m−3 ]
dissolved silicate concentration in the lower boundary layer [gSi m−3 ]
saturation dissolved silicate concentration [gSi m−3 ]
dissolution flux of opal silicate in the boundary layer [gSi m−2 d−1 ]
dispersive return flux to the overlying water [gSi m−2 d−1 ]
seepage flux at the sediment-water interface [gSi m−2 d−1 ]
seepage flux at the lower boundary [gSi m−2 d−1 ]
dissolution rate [d−1 ]
average porosity [-]
25 of 32
DR
AF
T
SWITCH, Technical Reference Manual
26 of 32
Deltares
9 Temperature dependency and dispersion
All process rates are temperature dependent according to:
k = k20 kt(T −20)
(9.1)
in which:
first order process rate [d−1 ]
first order process rate at 20 ◦ C [d−1 ]
temperature coefficient [-]
k
k20
kt
Temperature coefficients may vary between 1.04 and 1.12.
D = Dm + (bt − 1)Dm
(9.2)
dispersion coefficient [m2 d−1 ]
molecular diffusion coefficient [m2 d−1 ]
amplification factor for bio-irrigation [-]
DR
AF
in which:
T
Dispersion in the pore water is the result of molecular diffusion and bio-irrigation. The dispersion coefficient is defined as:
D
Dm
bt
The amplification factor can be provided to the model as a sinus function with a period of one
year and a maximum in the summer. The dispersion coefficient for bioturbation (Db) can be
assigned a similar function.
The dispersion coefficient at the water-sediment interface is multiplied with (1-fc), which reduces the dispersion flux according to the fraction of the surface area closed by mats of
benthic algae.
Deltares
27 of 32
DR
AF
T
SWITCH, Technical Reference Manual
28 of 32
Deltares
References
Berner, R., 1974. The Sea: Marine Chemistry, vol. 5, chap. Kinetic models for the early
diagenesis of nitrogen, sulphur, phosphorus and silicon in anoxic marine sediments, pages
427–450. John Wiley & Sons, New York, pp.
Brinkman, A. and W. van Raaphorst, 1986. De fosfaathuishouding van het Veluwemeer.
Master’s thesis, Twente University, The Netherlands. (in Dutch).
Lijklema, L., 1980. “Interaction of ortho-phosphate with iron(III) and aluminum hydroxides.”
Envir. Sci. Technol 14: 537–541.
Schink, D. and N. Guinasso, 1978. “Effects of bioturbation on sediment seawater interaction.”
Mar. Geology 23: 133–154.
T
Smits, J. and D. Van der Molen, 1993. “Application of SWITCH, a model for sediment-water
exchange of nutrients, to Lake Veluwe in the Netherlands.” Hydrobiologia 253: 281–300.
DR
AF
Van Raaphorst, W., P. Ruardij and A. Brinkman, 1988. The Ecosystem of the Western Wadden Sea: Field Research and Mathematical modelling, chap. The assessment of benthic
phosphorus regeneration in an estuarine ecosystem model, pages 23–36. Netherlands
Institute for Sea Research, Texel.
Vanderborght, J., R. Wollast and G. Billen, 1977a. “Kinetic models of diagenesis in disturbed
sediments: Part I. Mass transfer properties and silica diagenesis.” Limnol. Oceanogr 22:
787–793.
Vanderborght, J., R. Wollast and G. Billen, 1977b. “Kinetic models of diagenesis in disturbed
sediments: Part II. Nitrogen diagenesis.” Limnol. Oceanogr 22: 794–803.
WL | Delft Hydraulics, 1991. HADES; Ontwikkeling en verkennende berekeningen. Research
report T584, WL | Delft Hydraulics, Delft, The Netherlands. (in Dutch; N.M. de Rooij).
WL | Delft Hydraulics, 1992. Process formulations DBS. Model documentation T542, WL |
Delft Hydraulics, Delft, The Netherlands. (in Dutch; F.J. Los et al.).
WL | Delft Hydraulics, 1994a. Phosphate minerals in sediment: Literature study and analysis
of field data. Research report T584, WL | Delft Hydraulics, Delft, The Netherlands. (N.M.
de Rooij and J.J.G. Zwolsman; in Dutch).
WL | Delft Hydraulics, 1994b. Switch, a model for sediment-water exchange of nutrients;
Part 1: Formulation; Part 2: Calibration/Application for Lake Veluwe. Research report
T542/T584, WL | Delft Hydraulics, Delft, The Netherlands. (J.G.C. Smits).
WL | Delft Hydraulics, 1994c. SWITCH, a model for sediment-water exchange of nutrients.
Part 3: Reformulation and recalibration for Lake Veluwe. Research report T584, WL | Delft
Hydraulics, Delft, The Netherlands. (J.G.C. Smits).
WL | Delft Hydraulics, 1995. Application DBS Lake Volkerak-Zoommeer, Phase 1. Tech. Rep.
T1440/T880, WL | Delft Hydraulics, Delft, The Netherlands. (in Dutch; B.F. Michielsen).
WL | Delft Hydraulics, 1997. Testing of DB-SWITCH regarding the applicability on peat lakes
Geerplas and Nannewijd. Research report T1697, WL | Delft Hydraulics, Delft, The Netherlands. (in Dutch; J.G.C. Smits).
Deltares
29 of 32
DR
AF
T
SWITCH, Technical Reference Manual
30 of 32
Deltares
DR
AF
T
T
DR
AF
Photo by: Mathilde Matthijsse, www.zeelandonderwater.nl
PO Box 177
2600 MH Delft
Rotterdamseweg 185
2629 HD Delft
The Netherlands
+31 (0)88 335 81 88
sales@deltaressystems.nl
www.deltaressystems.nl
Source Exif Data:
File Type : PDF File Type Extension : pdf MIME Type : application/pdf PDF Version : 1.5 Linearized : No Page Count : 42 Page Mode : UseOutlines Author : Deltares Title : SWITCH User Manual Subject : Creator : LaTeX hyperref Producer : ps2pdf Keywords : Deltares, User, Manual, SWITCH, Water, Quality, Aquatic, Ecology Create Date : 2018:04:18 06:15:41+02:00 Modify Date : 2018:04:18 06:15:41+02:00 Trapped : False PTEX Fullbanner : This is MiKTeX-pdfTeX 2.9.6588 (1.40.18)EXIF Metadata provided by EXIF.tools