Radiation Attenuation

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Technical Description of the CSIRO SERM Ecological Model

1

CSIRO Simple Estuarine Response Model 1

Technical Description of the Ecological Model

Mark Baird 2

CSIRO Land and Water1 November 2001

Introduction

The CSIRO Simple Estuarine Response Model (SERM) has been developed to provide amodelling tool for the Australian continent's approximately 1000 estuaries. To capture thedynamics of ecological processes over a wide variety of Australian estuaries, the ecologicalmodel had been developed to be both simple, and to be composed of parameters whose valuesare not expected to vary significantly between estuaries. To work towards this goal, many of thekey biological processes have been described mechanistically. Mechanistic process descriptionsinclude attenuation of light through the water column and benthic biota, nutrient uptake and lightcapture by algae, and encounter rates of phytoplankton and zooplankton. Other descriptions,such as sediment chemistry, seagrass growth and the effect of higher trophic levels, where

processes are more complex, have been modelled empirically.

The ecological model described in this document is a modification of the CSIRO Port PhillipBay Environmental Study ecological model. In particular, the model is implemented using thesame box model approach and software as used in the PPB study, and contains a similarpartitioning of water column, epibenthic and sediment tracers. Further details can be found inMurray and Parslow (1997).

The most succinct description of SERM can be found on the website ( www.marine.csiro.au/serm) .This document fills in the details. It is composed of sections detailing the state variables (p 3),parameters (p 4), constants (p 7), ecological processes (p 8) that make up the model. Then

follows a description of the ecological model equations (p 13), physical model equations (p 17),ecological process descriptions (how the ecological model equations were derived, p 20) and alist of references (p 32). First, well define some terminology and abbreviations (p 2).

The original components of the model are submitted for publication:

Baird, M. E., S. J. Walker, B. B. Wallace, I. T. Webster and J. S. Parlsow (submitted). Towards a mechanistic modelof estuarine eutrophication. Estuarine, Coastal and Shelf Science. 1This work was partially funded by the generous support of the National Land and Water Resources Audit, aprogram of the National Heritage Trust, Australia.2 Corresponding address: School of Mathematics, UNSW, Sydney 2052 Australia ([email protected])


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2

Terminology and Abbreviations

System - for our purposes, the 'system' is the ecology of an estuary.

Model - a framework (in our case mathematical) used to aid our understanding of the system.

State Variables - state variables describe the state of the system. Indicators on the SERMinterface are a single or combination of state variables. The output of the model is the value of each of these state variables at each time point. The value of a state variable is changed either bya process, or a forcing. An example is nutrient concentration, which is changed by the process of nutrient uptake, or the forcing of a point source load.

Process - an underlying phenomena or collection of phenomenon. The major ecologicalprocesses are represented mathematically using the model equations. Processes change the valueof state variables. For example, nutrient uptake changes nutrient concentration.

Parameters - parameters are variables that are assumed to be constant within a particular system.There is some uncertainty as to the value parameters should take, and it is common to undertakea sensitivity analysis to investigate the effect of varying parameter values. An example of aparameter is the maximum growth rate of small phytoplankton.

Constants - constants are variables which, to a high degree of accuracy, do not vary betweensystems or in time. Examples include gravitation acceleration of the earth and the moleculardiffusivity of a chemical species.

Forcings and Boundary Conditions - forcings are inputs into the model (i.e. they change thevalue of the state variables) that are dependent on processes external to the model system. Theseinclude sunlight, river inputs, and boundary conditions.

Model Equations - model equations are mathematical representations of the processes linkingstate variables. They are made up of a combination of state variables, parameters and constants,and are formulated to represent, as well as is known (in some cases mechanistically, in othercases empirically) our best knowledge of what controls the rate of processes in the model. Inparticular, we are careful to ensure that the equations conserve mass. In other words, mass cannotbe created or destroyed, but rather moves between the different state variables or acrossboundaries.

Initial Conditions - each state variable must be given an initial condition, from which thesimulation begins. Ideally, if the model is run to a stable annual oscillation, the final resultshould be independent of initial conditions.

Mechanistic - a description of a process using an understanding of the underlying physicalprocesses.

Empirical - a description of a process determined using data from experiments or fieldobservations.


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3

State Variables

The model contains 29 state variables given below. The name of the variable in the code, and itsunits are also given. Note that some of the state variables represent fixed quantities of carbon,nitrogen and phosphorus. Such state variables are quantified in units of nitrogen, but contain afixed ratio of carbon to nitrogen to phosphorus (C:N:P) by atoms, given in brackets:

State Variable Symbol UnitsLarge phytoplankton (106:16:1) PL mg N m -3 Small phytoplankton (106:16:1) PS mg N m -3 Microphytobenthos (106:16:1) MPB mg N m -3 Seagrass (550:30:1) SG mg N m -2 Macroalgae (550:30:1) MA mg N m -2 Large zooplankton (106:16:1) ZL mg N m -3 Small zooplankton (106:16:1) ZS mg N m -3 Labile detritus at Redfield ratio (106:16:1) LDP mg N m -3 Labile detritus at Atkinson ratio (550:30:1) LDB mg N m -3 Refractory detrital carbon RDC mg C m -3 Refractory detrital nitrogen RDN mg N m -3 Refractory detrital phosphorus RDP mg P m -3 Dissolved organic carbon DOC mg C m -3 Dissolved organic nitrogen DON mg N m -3

Dissolved organic phosphorus DOP mg P m-3

Ammonia NH mg N m -3 Nitrate NO mg N m -3 Dissolved inorganic carbon DIC mg C m -3 Dissolved inorganic phosphate DIP mg P m -3 Particulate inorganic phosphate (unfloc.) PIP_unfloc mg P m -3 Particulate inorganic phosphate (floc.) PIP_floc mg P m -3 Total Suspended Solids (unflocculated) TSS_unfloc kg m -3 Total Suspended Solids (flocculated) TSS_floc kg m -3 Dissolved oxygen DO mg O 2 m-3

Light I W m -2 Temperature T CSalinity S PSU


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Parameters

There are 66 biological parameters. The symbol in the code, a description, and the values used inthe model are given below (parameter is dimensionless unless units are given).

Parameter Description Value (with units)E_ZL Growth efficiency, large zooplankton 0.38E_ZS Growth efficiency, small zooplankton 0.38SG_KN Half-saturation of SG N uptake in the sediment 5.0 mg N m -3 SG_KP Half-saturation of SG P uptake in the sediment 5.0 mg P m -3 ML_PL_T15 Linear mortality rate, large phytoplankton

(in sediment)0.14 d -1

ML_PS_T15 Linear mortality rate, small phytoplankton(in sediment)

0.14 d -1

ML_MA_T15 Linear mortality rate, macroalgae 0.00274 d -1 ML_SG_T15 Linear mortality rate, seagrass 0.00274 d -1 MQ_MPB_T15 Quadratic mortality rate, microphytobenthos 0.0003 d -1 (mg N m -3)-1 MQ_ZL_T15 Quadratic mortality rate, large zooplankton 0.02 d -1 (mg N m -3)-1 MQ_ZS_T15 Quadratic mortality rate, small zooplankton 0.02 d -1 (mg N m -3)-1 FDG_ZL Fraction of large zooplankton growth inefficiency

lost to detritus0.25

FDM_ZL Fraction of large zooplankton mortality lost todetritus

0.25

FDG_ZS Fraction of small zooplankton growth inefficiencylost to detritus 0.25

FDM_ZS Fraction of small zooplankton mortality lost todetritus

0.25

F_LD_RD Fraction of labile detritus converted to refractorydetritus

0.19

F_LD_DOM Fraction of labile detritus converted to dissolvedorganic matter

0.01

R_0_T15 Sediment net respiration rate at whichnitrification = 0

200 mg N m -2 d-1

R_D_T15 Sediment net respiration rate of denitrification

maximum

10 mg N m -2 d-1

Dmax Maximum efficiency of the removal of N bynitrification followed by denitrification

0.7

X_CHLN nitrogen to Chlorophyll a ratio in phytoplankton byweight

7 mg N (mg Chl a) -1

k_w Background light attenuation coefficient 0.1 m -1 k_DON DON-specific light attenuation coefficient 0.0009 m -1 (mg N m -3)-1 k_DL Detrital N specific light attenuation coefficient 0.0038 m -1 (mg N m -3)-1 k_TSS TSS specific light attenuation coefficient 30.0 m -1 (kg m -3)-1 k_SWR_PAR fraction of incident solar radiation that is PAR 0.43


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Q10 Temperature coefficient for rate parameters 2.0PLumax Maximum growth rate of PL at Tref 1.25 d -1

PLrad Radius of the large phytoplankton cells 10 mPLabsorb Absorption coefficient of a PL cell 50000 m -1 PSumax Maximum growth rate of PS at Tref 1.25 d -1 PSrad Radius of the small phytoplankton cells 2.5 mPSabsorb Absorption coefficient of a PS cell 50000 m -1 MPBumax Maximum growth rate of MPB at Tref 0.35 d -1 MPBrad Radius of the microphytobenthos cells 10 mMPBabsorb Absorption coefficient of a MPB cell 50000 m -1 MAumax Maximum growth rate of MA at Tref 0.2 d -1 MAaA Nitrogen specific absorption cross-section of MA 1 x 10 -3 m2 mg N -1

SGumax Maximum growth rate of SG at Tref 0.1 d -1 SGaA Nitrogen specific absorption cross-section of SG 1 x 10 -5 m2 mg N -1 ZSumax Maximum growth rate of ZS at Tref 3 d -1 ZSrad Radius of the small zooplankton cells 12.5 mZSswim Swimming velocity for small zooplankton 100 m s -1 ZLumax Maximum growth rate of ZL at Tref 0.375 d -1 ZLrad Radius of the large zooplankton cells 50 mZLswim Swimming velocity for large zooplankton 200 m s -1 TKEeps Dissipation of turbulent kinetic energy in the water

column1 x 10 -6 m2 s-3

cf drag coefficient of the benthic surface 0.005Ub velocity at the top of the benthic boundary layer 0.1 m s -1 ks sand-grain roughness of the benthos 0.1 mF_RD_DOM fraction of refractory detritus that breaks down to

DOM0.05

r_floc rate at which TSS flocculates above 10 PSU 0.01 d -1 r_absP rate at which P reaches ab/desorbed equilibrium 1.0 d -1 P_buff_sed Phosphate buffering capacity of sediment 2650.0 kg kg -1 P_abs_coef Phosphate absorption coefficient 2.0 m 3 kgr_LDP_T15 Breakdown rate of labile detritus at 106:16:1 0.1 d -1 r_LDB_T15 Breakdown rate of labile detritus at 550:30:1 0.1 d -1 r_RD_T15 Breakdown rate of refractory detritus 0.0036 d -1 r_DOM_T15 Breakdown rate of dissolved organic matter 0.00176 d -1 Plank_resp Respiration as a fraction of max. growth rate 0.025Benth_resp Respiration as a fraction of max. growth rate 0.025


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Two further biological parameters had estuary-specific values:

K_CDOM Light attenuation of freshwater inflow estuary dependent [m -1]Tref Reference temperature for biological processes estuary dependent [ C]

In the SERM model, the estuary-specific biological parameters are set by choosing an estuarineparameter value.

In addition, there are 14 parameters within the physics model which relate to biologicalcomponents of the model:

w_PL sinking rate of PL 0.5 m d -1 w_PS sinking rate of PS 0.0 m d -1

w_MPB sinking rate of MPB 5.0 m d-1

w_TSS_unfloc sinking rate of TSS_unfloc 0.1 m d -1 w_TSS_floc sinking rate of TSS_floc 5.0 m d -1 w_PIP_unfloc sinking rate of PIP_unfloc 0.1 m d -1 w_PIP_floc sinking rate of PIP_floc 5.0 m d -1 w_RDC sinking rate of RDC 2.0 m d -1 w_RDN sinking rate of RDN 2.0 m d -1 w_RDP sinking rate of RDP 2.0 m d -1 w_LDP sinking rate of LDP 3.0 m d -1 w_LDB sinking rate of LDB 10.0 m d -1 nxsbs normalised excess bottom stress 0.005sedexch sediment exchange rate 10 -9 m s -1


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Constants

The model uses a number of constants. Most of them relate to stoichiometry ratios (the Redfieldratio for planktonic plants photons:C:N:P:O 2 = 1060:106:16:1:138; and the Atkinson ratio forbenthic plants photons:C:N:P:O 2 = 5500:550:30:1:716), although a few are physical constants.

Constant Description Value and unitsBOLT Boltzmann's constant 1.38066 x 10 -23 J K -1 PLANCK Planck's constant 6.62608 x 10 -34 J s -1 R Universal gas constant 8.31451 J K -1 mol -1 g gravitational acceleration 9.81 m s -2

AV Avogadro's number 6.02214 x 10 23 mol -1 DNO3_25_0 Mol. diffusivity of nitrate in S = 0, T = 25 C 19.0 x 10 -10 m2 s-1 DNH4_25_0 Mol. diffusivity of ammonia in S = 0, T = 25 C 19.8 x 10 -10 m2 s-1 DPO4_25_0 Mol. diffusivity of phosphate in S = 0, T = 25 C 7.34 x 10 -10 m2 s-1

red_A_I Redfield molecular ratio photons:P ratio 1060.0 mol(quanta) mol(P) -1 red_A_C Redfield molecular ratio C:P ratio 106.0 mol(C) mol(P) -1 red_A_N Redfield molecular ratio N:P ratio 16.0 mol(N) mol(P) -1 red_A_P Redfield molecular ratio P:P ratio 1.0 mol(P) mol(P) -1 red_A_O Redfield molecular ratio O 2:P ratio 138.0 mol(O 2) mol(P) -1 atk_A_I Atkinson molecular ratio photons:P ratio 5500.0 mol(quanta) mol(P) -1 atk_A_C Atkinson molecular ratio C:P ratio 550.0 mol(C) mol(P) -1

atk_A_N Atkinson molecular ratio N:P ratio 30.0 mol(N) mol(P)-1

atk_A_P Atkinson molecular ratio P:P ratio 1.0 mol(P) mol(P) -1 atk_A_O Atkinson molecular ratio O 2:P ratio 716.0 mol(O 2) mol(P) -1 MW_Carb Molecular weight of carbon 12.01 g C mol -1 MW_Nitr Molecular weight of nitrogen 14.01 g N mol -1 MW_Phos Molecular weight of phosphorus 30.97 g P mol -1 MW_Oxyg Molecular weight of oxygen 32.00 g O 2 mol -1 red_W_C Redfield weight ratio C:N 5.68 g C g N -1 red_W_N Redfield weight ratio N:N 1.00 g N g N -1 red_W_P Redfield weight ratio P:N 0.138 g P g N -1 red_W_O Redfield weight ratio O 2:N 19.7 g O 2 g N -1 atk_W_C Atkinson weight ratio C:N 15.7 g C g N -1 atk_W_N Atkinson weight ratio N:N 1.0 g N g N -1 atk_W_P Atkinson weight ratio P:N 0.074 g P g N -1 atk_W_O Atkinson weight ratio O 2:N 54.5 g O 2 g N -1 C_O_W Redfield /Atkinson weight ratio O 2:C 3.469 g O 2 g C -1


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Ecological Processes

The following list of processes are those appearing in the model equations. It should be notedthat some processes are a made up of a series of other process (i.e. PLgrowth is made up of PLuptakeNH, PLuptakeNO and PLuptakeDIP ). Such 'sub' processes are written in italics belowthe processes of which they are a component.

Process Description UnitsPLgrowth the assimilation of dissolved inorganic compounds

into large phytoplankton biomassmg N m -3 s-1

PLuptakeDIC uptake rate of carbon by large phytoplankton mg C m -3 s-1 PLuptakeNH uptake rate of ammonia by large phytoplankton mg N m -3 s-1 PLuptakeNO uptake rate of nitrate by large phytoplankton mg N m -3 s-1

PLuptakeDIP uptake rate of phosphorus by large phytoplankton mg P m-3

s-1

PLreleaseO2 release of O 2 due to large phytoplankton growth mg O m

-3 s-1

PLmortality the loss rate of large phytoplankton to labile detritus atthe Redfield ratio (LDP)

mg N m -3 s-1

PSgrowth the assimilation of dissolved inorganic compoundsinto small phytoplankton biomass

mg N m -3 s-1

PSuptakeDIC uptake rate of carbon by small phytoplankton mg C m -3 s-1 PSuptakeNH uptake rate of ammonia by small phytoplankton mg N m -3 s-1

PSuptakeNO uptake rate of nitrate by small phytoplankton mg N m-3

s-1

PSuptakeDIP uptake rate of phosphorus by small phytoplankton mg P m -3 s-1 PSreleaseO2 release of O 2 due to small phytoplankton growth mg O m -3 s-1

PSmortality the loss rate of small phytoplankton to labile detritusat the Redfield ratio (LDP)

mg N m -3 s-1

MPBgrowth the assimilation of dissolved inorganic compoundsinto microphytobenthos biomass

mg N m -3 s-1

MPBuptakeDIC uptake rate of carbon by microphytobenthos mg C m -3 s-1

MPBuptakeNH uptake rate of ammonia by microphytobenthos mg N m-3

s-1

MPBuptakeNO uptake rate of nitrate by microphytobenthos mg N m -3 s-1 MPBuptakeDIP uptake rate of phosphorus by microphytobenthos mg P m -3 s-1 MPBreleaseO2 release of O 2 due to microphytobenthos growth mg O m -3 s-1

MPBmortality the loss rate of small phytoplankton to labile detritusat the Redfield ratio (LDP)

mg N m -3 s-1

ZSgrowth assimilation of small phytoplankton by smallzooplankton

mg N m -3 s-1


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ZSgrazePS small phytoplankton loss due to grazing by smallzooplankton

mg N m -3 s-1

ZSsloppyNH ammonia release by small zooplankton due toinefficient (or sloppy) grazing

mg N m -3 s-1

ZSsloppyDIP phosphorus release by small zooplankton due toinefficient (or sloppy) grazing

mg P m -3 s-1

ZSsloppyDIC carbon release by small zooplankton due to inefficient(or sloppy) grazing

mg C m -3 s-1

ZSsloppyO2 oxygen consumption by bacteria duringreminerialisation of small zooplankton sloppy grazing

mg O m -3 s-1

ZLgrowth assimilation of large phytoplankton andmicrophytobenthos by large zooplankton

mg N m -3 s-1

ZLgrazePL large phytoplankton loss due to grazing by largezooplankton

mg N m -3 s-1

ZLgrazeMB microphytobenthos loss due to grazing by largezooplankton

mg N m -3 s-1

ZLsloppyNH ammonia release by large zooplankton due toinefficient (or sloppy) grazing

mg N m -3 s-1

ZLsloppyDIP phosphorus release by large zooplankton due toinefficient (or sloppy) grazing

mg P m -3 s-1

ZLsloppyDIC carbon release by large zooplankton due to inefficient(or sloppy) grazing

mg C m -3 s-1

ZLsloppyO2 oxygen consumption by bacteria duringreminerialisation of large zooplankton sloppy grazing

mg O m -3 s-1

ZLmortality loss rate of large zooplankton mg N m -3 s-1 ZLmortLDP production of labile detritus at the Redfield ratio

(LDP) due to large zooplankton mortalitymg N m -3 s-1

ZLmortNH release of ammonia through large zooplanktonmortality

mg N m -3 s-1

ZLmortDIP release of phosphorus through large zooplanktonmortality

mg P m -3 s-1

ZLmortDIC release of carbon through large zooplankton mortality mg C m -3 s-1 ZLmortO2 oxygen consumption by bacteria during the

remineralisation of large zooplankton

mg O m -3 s-1

ZSmortality loss rate of small zooplankton mg N m -3 s-1 ZSmortLDP production of labile detritus at the Redfield ratio

(LDP) due to small zooplankton mortalitymg N m -3 s-1

ZSmortNH release of ammonia through small zooplanktonmortality

mg N m -3 s-1

ZSsloppyO2 oxygen release by the bacterial duringreminerialisation of small zooplankton sloppy grazing

mg O m -3 s-1

ZSmortO2 oxygen consumption by bacteria during theremineralisation of small zooplankton

mg O m -3 s-1


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LDPbreak the breakdown of labile detritus at the Redfield ratio

LDPtoNH remineralisation of labile detritus at the Redfield ratioto dissolved ammonia mg N m-3

s-1

LDPtoDIC remineralisation of labile detritus at the Redfield ratioto dissolved inorganic carbon

mg C m -3 s-1

LDPtoDIP remineralisation of labile detritus at the Redfield ratioto dissolved inorganic phosphorus

mg P m -3 s-1

LDPtoDOC dissolution of labile detritus at the Redfield ratio intodissolved organic carbon

mg C m -3 s-1

LDPtoDON dissolution of labile detritus at the Redfield ratio intodissolved organic nitrogen

mg N m -3 s-1

LDPtoDOP dissolution of labile detritus at the Redfield ratio into

dissolved organic phosphorus

mg P m -3 s-1

LDPtoRDC production of refractory detrital carbon from thebreakdown of labile detritus at the Redfield ratio

mg C m -3 s-1

LDPtoRDN production of refractory detrital nitrogen from thebreakdown of labile detritus at the Redfield ratio

mg N m -3 s-1

LDPtoRDP production of refractory detrital phosphorus from thebreakdown of labile detritus at the Redfield ratio

mg P m -3 s-1

LDPconO2 consumption of O 2 by bacterial remineralisation of LDP

mg O m -3 s-1

LDBbreak the breakdown of labile detritus at the Atkinson ratio mg N m -3 s-1

LDBtoNH remineralisation of labile detritus at the Atkinson ratioto dissolved ammonia mg N m-3

s-1

LDBtoDIC remineralisation of labile detritus at the Atkinson ratioto dissolved inorganic carbon

mg C m -3 s-1

LDBtoDIP remineralisation of labile detritus at the Atkinson ratioto dissolved inorganic phosphorus

mg P m -3 s-1

LDBtoDOC dissolution of labile detritus at the Atkinson ratio intodissolved organic carbon

mg C m -3 s-1

LDBtoDON dissolution of labile detritus at the Atkinson ratio intodissolved organic nitrogen

mg N m -3 s-1

LDBtoDOP dissolution of labile detritus at the Atkinson ratio into

dissolved organic phosphorus

mg P m -3 s-1

LDBtoRDC production of refractory detrital carbon from thebreakdown of labile detritus at the Atkinson ratio

mg C m -3 s-1

LDBtoRDN production of refractory detrital nitrogen from thebreakdown of labile detritus at the Atkinson ratio

mg N m -3 s-1

LDBtoRDP production of refractory detrital phosphorus from thebreakdown of labile detritus at the Atkinson ratio

mg P m -3 s-1

LDBconO2 consumption of O 2 by bacterial remineralisation of LDB

mg O m -3 s-1


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RDbreak breakdown of refractory detritus (not explicitly in themodel equations)

RDCtoDIC remineralisation of refractory detrital carbon intodissolved inorganic carbon

mg C m -3 s-1

RDNtoNH remineralisation of refractory detrital nitrogen intodissolved ammonia

mg N m -3 s-1

RDPtoDIP remineralisation of refractory detrital phosphorus intodissolved inorganic phosphorus

mg P m -3 s-1

RDCtoDOC dissolution of refractory detrital carbon into dissolvedinorganic carbon

mg C m -3 s-1

RDNtoDON dissolution of refractory detrital nitrogen intodissolved inorganic carbon

mg N m -3 s-1

RDPtoDOP dissolution of refractory detrital phosphorus intodissolved inorganic carbon

mg P m -3 s-1

RDCconO2 consumption of O 2 by bacterial remineralisation of RDC

mg O m -3 s-1

DOMbreak breakdown of dissolved organics (not explicitly in themodel equations)

DOCtoDIC remineralisation of dissolved organic carbon intodissolved inorganic carbon

mg C m -3 s-1

DONtoNH remineralisation of dissolved organic nitrogen into

dissolved ammonia

mg N m -3 s-1

DOPtoDIP remineralisation of dissolved organic phosphorus intodissolved inorganic phosphorus

mg P m -3 s-1

DOCconO2 consumption of O 2 by bacterial remineralisation of DOC

mg O m -3 s-1

flocculate the flocculation of total suspended solids (TSS) fromthe unflocculated TSS (TSS_unfloc) to the flocculatedTSS (TSS_floc)

kg m -3 s-1

desorbedP the desorption (or, adsorption if negative) of

phosphorus from the particulate form (PIP) to thedissolved form (DIP)

mg P m -3 s-1

P_flocculate the transfer of PIP from PIP_unfloc to PIP_floc as aresult of the flocculation of TSS

mg P m -3 s-1

MAgrowth the assimilation of dissolved inorganic nitrogen,phosphorus and carbon into macroalgae biomass

mg N m -2 s-1

MAuptakeDIC uptake rate of carbon by macroalgae biomass mg C m -2 s-1 MAuptakeNH uptake rate of ammonia by macroalgae biomass mg N m -2 s-1


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MAuptakeNO uptake rate of nitrate by macroalgae biomass mg N m -2 s-1 MAuptakeDIP uptake rate of phosphorus by macroalgae biomass mg P m -2 s-1

MAreleaseO2 release of O 2 due to macroalgae growth mg O m-2

s-1

MAmortality the loss rate of macroalgae biomass to labile detritus atthe Atkinson ratio

mg N m -2 s-1

SGgrowth the assimilation of dissolved inorganic nitrogen,phosphorus and carbon into seagrass biomass

mg N m -2 s-1

SGuptakeDIC uptake rate of carbon by seagrass biomass mg C m -2 s-1 SGuptakeNH uptake rate of ammonia by seagrass biomass mg N m -2 s-1 SGuptakeNO uptake rate of nitrate by seagrass biomass mg N m -2 s-1 SGuptakeDIP uptake rate of phosphorus by seagrass biomass mg P m -2 s-1 SGreleaseO2 release of O 2 due to seagrass growth mg O m

-2 s-1

SGmortality the loss rate of seagrass biomass to labile detritus atthe Atkinson ratio

mg N m -2 s-1

nitrification the conversion by bacteria of ammonia to nitrite andthen nitrate

mg N m -3 s-1

denitrification the conversion by bacteria of nitrate to N 2 gas, whichis lost to the atmosphere

mg N m -3 s-1

In addition to the ecological processes, physical processes such as light absorption, particlesinking and fluid mixing are modelled. Light absorption is discussed below, while particlesinking and fluid mixing are part of the physical model and are described elsewhere (Murray andParslow, 1997).


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Model Equations

The model equations describe the change in the value of a state variable, as a sum of the effect of independent processes. The model equations have been group in water column, epibenthic andsediment categories. Epibenthic refers to processes occurring on the interface of the sedimentand water column, and depending on both the state of the sediment and the water column.

The equations have been written first in terms of the additional and subtraction of ecologicalprocesses. The quantification of these processes is given in the mathematical descriptions thatfollow in the next section. To apply these equations, a few points to watch for:

Epibenthic (EPI) processes have units per m 2. To convert to a change in a water column statevariable (which are specified per m 3 of water) divide by water column layer thickness. Toconvert to a change in sediment state variable (which are specified per unit porewatervolume) divide by sediment layer thickness and porosity.

Epibenthic processes have the ability to impact on either water column (WC) or sediment(SED) state variables.

Water column equations:

(dPL/dt) WC = PLgrowth - ZLgrazePL

(dPS/dt) WC = PSgrowth - ZSgrazePS

(dMB/dt) WC = MBgrowth - ZLgrazeMB

(dZL/dt) WC = ZLgrowth - ZLmortality

(dZS/dt) WC = ZSgrowth - ZSmortality

(dNH/dt) WC = - PLuptakeNH - PSuptakeNH - MBuptakeNH + ZLsloppyNH+ ZLmortNH + ZSsloppyNH + ZSmortNH + DONtoNH+ LDPtoNH + LDBtoNH + RDNtoNH

(dNO/dt) WC = - PLuptakeNO - PSuptakeNO - MBuptakeNO

(dLDP/dt) WC = ZLmortLDP + ZSmortLDP - LDPbreak

(dLDB/dt) WC = - LDBbreak

(dRDC/dt) WC = LDPtoRDC + LDBtoRDC - RDCtoDIC - RDCtoDOC

(dRDN/dt) WC = LDPtoRDN + LDBtoRDN - RDNtoNH - RDNtoDON

(dRDP/dt) WC = LDPtoRDP + LDBtoRDP - RDPtoDIP - RDPtoDOP


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(dDOC/dt) WC = LDPtoDOC + LDBtoDOC + RDCtoDOC - DOCtoDIC

(dDON/dt) WC = LDPtoDON + LDBtoDON + RDNtoDON - DONtoNH

(dDOP/dt) WC = LDPtoDOP + LDBtoDOP + RDPtoDOP - DOPtoDIP

(dDO/dt) WC = + PLreleaseO2 + PSreleaseO2 + MBreleaseO2- ZLmortO2 - ZLsloppyO2 - ZSmortO2 - ZSsloppyO2- LDPconO2 - LDBconO2- RDCconO2 + DOCconO2

(dDIC/dt) WC = -PLuptakeDIC - PSuptakeDIC - MBuptakeDIC + ZLmortDIC+ ZLgrazeDIC + ZSmortDIC + ZSgrazeDIC + DOCtoDIC+ LDPtoDIC + LDBtoDIC +RDCtoDIC

(dTSS_unfloc/dt) WC = - flocculate

(dTSS_floc/dt) WC = + flocculate

(dDIP/dt) WC = -PLuptakeDIP - PSuptakeDIP - MBuptakeDIP + ZLsloppyDIP+ ZLmortDIP + ZSsloppyDIP + ZSmortDIP + DOPtoDIP +LDPtoDIP + LDBtoDIP + RDPtoDIP + desorbedP

(dPIP_floc/dt) WC = -desorbedP_floc + P_flocculate

(dPIP_unfloc/dt) WC = -desorbedP_unfloc - P_flocculate

In the epibenthos:

(dMA/dt) EPI = MAgrowth - MAmortality

(dSG/dt) EPI = SGgrowth - SGmortality

(dNH/dt) WC = - MAuptakeNH

(dNH/dt) SED = - SGuptakeNH

(dNO/dt) WC = - MAuptakeNO

(dNO/dt) SED = - SGuptakeNO

(dLDB/dt) WC = + MAmortality

(dLDB/dt) SED = + SGmortality

(dO/dt) WC = + SGreleaseO2 + MAreleaseO2


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(dDIP/dt) WC = - MAuptakeDIP

(dDIP/dt) SED = - SGuptakeDIP

(dDIC/dt) WC = - MAuptakeDIC

(dDIC/dt) SED = - SGuptakeDIC

In the sediment:

(dPL/dt) SED = - PLmortality

(dPS/dt) SED = - PSmortality

(dMB/dt) SED = MBgrowth - MBmortality

(dNH/dt) SED = + LDPtoNH + LDBtoNH + DONtoNH + RDNtoNH- nitrification - MBuptakeNH

(dNO/dt) SED = nitrification - denitrification - MBuptakeNO

(dLDP/dt) SED = PLmortality + PSmortality + MBmortality - LDPbreak

(dLDB/dt) SED = -LDBbreak

(dRDC/dt) SED = LDPtoRDC + LDBtoRDC - RDCtoDIC - RDCtoDOC

(dRDN/dt) SED = LDPtoRDN + LDBtoRDN - RDNtoNH - RDNtoDON

(dRDP/dt) SED = LDPtoRDP + LDBtoRDP - RDPtoDIP - RDPtoDOP

(dDOC/dt) SED = LDPtoDOC + LDBtoDOC + RDCtoDOC - DOCtoDIC

(dDON/dt) SED = LDPtoDON + LDBtoDON + RDNtoDON - DONtoNH

(dDOP/dt) SED = LDPtoDOP + LDBtoDOP + RDPtoDOP - DOPtoDIP

(dDO/dt) SED = + MBreleaseO2 - LDPconsO2 - LDBconsO2- RDCconsO2 - DOCconsO2

(dDIP/dt) SED = - MBuptakeDIP + DOPtoDIP + LDPtoDIP+ LDBtoDIP+ RDPtoDIP + desorbedP

(dPIP_floc/dt) SED = -desorbedP_floc


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(dPIP_unfloc/dt) SED = -desorbedP_unfloc

(dDIC/dt) SED = - MBuptakeDIC + DOCtoDIC + LDPtoDIC+ LDBtoDIC + RDCtoDIC


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Physical Processes Description

The ecological code used by SERM contains the physical processes of light attenuation and thetemperature dependence of ecological processes, which are discussed below. The physical codecontains particulate sinking, which, as it directly impacts the ecological state variables, is alsodiscussed below. The transport of ecological tracers by the physical code is dealt with in thedescription of the physical code.

Light attenuation.

In the model, light is attenuated through the water column, the benthic macroalgae, the seagrass,and the microphytobenthos sequentially. Photosynthetically available radiation (PAR) at thebottom of a layer of water, I bot [mol photon m -2 s-1], is given by:

Ibot = I topexp(-K d dz)

where I top is the PAR at the top of the layer [mol photon m -2 s-1], dz is the thickness of the layer[m], and K d is the total attenuation coefficient of the water [m -1]. K d is given by the sum of theeach attenuating component in the water:

Kd = k W + n PS aA PS + n PL aA PL + n MPB aA MPB + k DON DON + k DL(LD + RDN) + k TSS TSS+ K CDOM (35 - S) / 35

where k w is the background attenuation coefficient of water [m -1], n PS, aA PS, n PL, aA PL and n MPB and aA MPB are the concentration [cell m -3] and absorption cross-section [m 2 cell -1] of cells of small phytoplankton, large phytoplankton and microphytobenthos respectively, k DON and k DL arethe nitrogen-specific attenuation coefficients of the dissolved organic matter and labile detritus[mg N -1 m2], k TSS is the mass specific attenuation coefficient of total suspended solids [kg -1 m2].LD, RDN and DON are the concentrations of biomass of labile detritus, refractory detritus anddissolved organic matter [mg N m -3], and TSS is the concentration of total suspended solids [kgm -3]. K CDOM is the attenuation coefficient of the non-living constituents of fresh water flowinginto the estuary [m -1] and S is salinity [PSU]. The average irradiance in the layer, I av [mol photonm -2 s-1], is given by:

Iav = (I top - Ibot) / (K d dz)

In the model, light reaching the benthos is first attenuated by macroalgae. The light below themacroalgae is given by:

I below MA = I bot exp(-MA aA MA)

where MA is the biomass of macroalgae [mg N m -2] and aA MA is the biomass-specific absorptioncross-section [mg N -1 m2]. The light below the seagrass is given by:

Ibelow SG = I below MA exp(-SG aA SG)


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where SG is the biomass of seagrass [mg N m -2] and aA SG is the biomass-specific absorptioncross-section [mg N -1 m2]. The PPBES ecological model considered the reduced growth rate of seagrass due to epiphytes. In this paper, we have considered epiphytes to be part of the benthicmacroalgae. Epiphytes and macroalgae both receive light before seagrass and, sharing the samesurface, have a similar effective benthic boundary layer thickness. As epiphytes and macroalgaehave similar maximum supply rates of nutrient and light, and shade the seagrass in a similarmanner, the assumption they make up one class of autotroph seemed reasonable 3.

Finally, the remaining light passes through the microphytobenthos at the surface of the sediment:

Ibelow MPB = Ibelow SG exp(-n MPB aA MPB dz)

where n MPB is the concentration of microphytobenthos cells [cell m -3] with an absorption cross-section of aA MPB [m2 cell -1] in a sediment layer dz thick [m]. By including only attenuation dueto microphytobenthos we are assuming that the microphytobenthos lie in the surface layer of thesediment. The average light flux available to the microphytobenthos cells is given by:

Iav = (I below SG - Ibelow:MPB ) / (n MPB aAMPB dz)

The above description of the light field in an estuarine environment is significantly different tothat employed in the PPBES ecological model, and other aquatic ecological models (Fasham,1990, Madden et. al., 1996). Autotroph absorption cross-sections have been used to parameteriseboth the dependence of autotroph growth rate on light availability and the attenuation of light asit passes through the water column and benthos. In all, ten parameters with well defined physicalinterpretations were used to model the effect of light on ecological processes. The PPBESecological model contained the physically well-defined k w, k DON , k DL (and in principle k TSS andk CDOM ), but also contained five empirically-determined half-saturation constants relating growthrate to incident light, and two parameters to describe the relationship between light attenuationand chlorophyll concentration (twelve parameters in all). The additional two parameters wererequired by the PPBES model because phytoplankton growth and the attenuation rate of lightwere considered independent processes. In contrast, the above presented mechanistic modeltakes advantage of the common physical process of light capture by cells that determines bothlight attenuation through the water column and phytoplankton photosynthesis.

Sinking

Phytoplankton cells (large and small), microphytobenthos, and detritus (refractory and labile)often have a different density than water. Their resultant change in concentration of particle X,[X], from a water column layer as a result of sinking is given by:

d [X] /dt = - w_X [X] / layer thickness

where w_X is the sinking rate [m d -1].

3 A problem with this assumption is that epiphytes have a Redfield C:N:P ratio, and probably a maximum growthrate closer to suspended algae than macroalgae. Nonetheless, for the benefit of simplicity, the assumption thatepiphytes and macroalgae are modelled as one autotrophic class was used.


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Temperature dependence

A number of ecological processes are temperature dependent. To capture this, the relevantbiological parameters have been multiplied by:

Tcorr = Q 10(T-Tref)/10

where Q 10 is the temperature coefficient for rate parameters [dimensionless], and Tref is thereference temperature [ C]. Biological parameters with a temperature dependence are:mL_PL_T15, mL_MA_T15, mL_SG_T15, mQ_MB_T15, mQ_ZL_T15, mQ_ZS_T15,mS_MA_T15, mS_SG_T15, r_LDP_T15, r_LDB_T15, r_RD_T15, r_DOM_T15, PLumax,PSumax, MBumax, ZSumax, ZLumax, ZSswim, Zlswim.

Temperature, T, (and salinity, S) have a secondary effect on some ecological processes(particularly grazing) by changing the viscosity of water. The changing the viscosity of waterand the molecular diffusivity of chemical species with temperature and salinity is modelledfollowing Wolf-Gladrow et al. (1997):

viscosity (T, S = 0) = 0.00123161 - 1.228e-5 T + 4.009e-8 T 2

viscosity (T, S = 35) = viscosity (T, S = 0) /(0.9508-0.0007379*T)

viscosity(T, S) = viscosity (T, S = 35) *(S/35) + viscosity (T, S = 0) *(35-S)/35

For molecular diffusivity:

D (T, S) = D25S0 * viscosity(T, S) * (T+273.15)/(viscosity (T, S = 0) *298.15)


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Ecological Process Description

Primary Production (plant growth)

Primary productivity (the organic synthesis from inorganic substances) is determined for eachautotroph (large and small phytoplankton, microphytobenthos, macroalgae and seagrass) from afunctional form specifying the interaction of the maximum supply rates of nutrients and light,and the maximum growth rate. Note that this is fundamentally different to the typical Monod orMichaelis-Menton type growth functions, which use half-saturation constants. This scheme(called the CR model in Baird and Emsley, 1999) is preferred because maximum rates can bemechanistically determined. The CR model requires the determination of the maximum growthrate, m [s -1], and the maximum supply rates of nutrients, k N [mol N s -1], and light, k I [mol(quanta) m -2 s-1], and the stoichiometry of each autotroph [units vary - see below]. Thedetermination of maximum supply rates depends on morphology and location of the autotroph.The following considers phytoplankton (suspended algal cells), benthic microalgae (algal cells inthe surface sediment layer), macroalgae attached to the bottom, and seagrass.

Maximum uptake rates of suspended algal cells. Suspended algal cells (phytoplankton) obtainnutrients from the water column, and light as a function of the average light in the layer in whichthey are suspended. Biomass is quantified per m 3.

The maximum supply rates of nutrients (limited by molecular diffusion to a perfectly absorbingcell) is given by:

DN k N =

where is the diffusion shape factor [m]; D is the molecular diffusivity of the nutrient [m2

s-1

],and N is the concentration of the nutrient in the water column [mol m -3]. for a sphere is 4 r,where r is the radius [m]. The diffusion shape factor for more complicated shapes (spheroids,cubes etc.) can be found in Baird and Emsley (1999) or Baird (1999).

The maximum supply rate of light is given by:cellav I aA I k =

where cellaA is the absorption cross section of a cell [m 2]; and I av is the average PAR radiation[mol (photons) m -2 s-1] in the layer. The absorption cross section of a sphere is given by:

( )( )( )

+=

2

22

2

21121

r C

er C r aA

r C

cell

where C [m -1] is the absorption coefficient. For a black cell, 2 Cr approaches , andcellaA approaches r2 and for a non-absorbing cell, 2 Cr approaches 0, and cellaA approaches 0.

The absorption cross section more complicated shapes can be found in Baird and Emsley (1999)and Baird (1999).

Maximum uptake rates of benthic macroalgae. Benthic macroalgae reside on the top of thesediment, take nutrients out of the water column, and are exposed to light that reaches the bottomof the water column. Biomass is quantified per m 2.


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The maximum supply rate of nutrients is strongly influenced by shear stress at thewater/sediment interface. The effect of this on nutrient uptake has been quantified by analogywith an experimental investigation of heat transfer, surface roughness and pressure drop in pipes.The application of this analogy to heat transfer to benthic communities has been demonstrated(Baird and Atkinson, 1997, Thomas et al., 2000).

First a friction velocity, U* [m s -1] (a characteristic velocity used to represent the velocity withinthe momentum boundary layer) is determined:

2 / * f b cU U = where U b is the velocity of the fluid away from the boundary [m s -1], c f is the friction coefficient,a dimensionless measure of the shear stress exerted on a fluid by the surface, arising from bothskin friction and form drag.

Then a Reynold's roughness number, Re k , a non-dimensional measure of the surface roughness isdetermined:

s

k

k U *Re =

where k s is an equivalent (in creating friction) sand-grain roughness dimension [m], and is thekinematic viscosity [m 2 s-1]. The Stanton number, St m [-], the ratio of the uptake of a substance tothe advection of that substance past the surface, can be calculated from:

( )( )129.02 += k f f m St ccSt where 48.8Re19.5 44.02.01 = ScSt k k

and Sc is the Schmidt number, (Sc = /D), the ratio of molecular diffusivity of momentum to themolecular diffusivity of mass. From the Stanton number, the maximum uptake rate, k N, [mol Nm -2] is given by:

N U St k bm N = where N is the nutrient concentration in the water column [mol N m -3]. As discussed later, St mUb = D / , where is the benthic diffusive boundary layer thickness, and is a function of , D,temperature and k s, and is of the order of 0.1 mm for a typical benthic macrophyte.

The maximum light capture by the macroalgae is given by: MA I aA MA I k = exp(1

where I is the incident radiation at the top of the macroalgae [mol(photons) m -2 s-1]; MA is thebiomass of macroalgae [mg N m -2]; and MAaA is the nitrogen-specific absorption cross-section of macroalgae [m 2 mg N -1].

Maximum uptake rates of seagrass . Seagrass obtain their nutrients from the sediment, and theirlight after it has passed through the water column and benthic macroalgae.

For seagrass, a maximum supply rate of nutrients through the root system is difficult to quantify.Instead, a maximum supply rate can be "back-calculated" from a half-saturation and a maximumgrowth rate, using


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k N = SG m N /K m

where SG is the biomass of seagrass [mol N m -2]; m is the maximum growth rate [s -1], N is thesediment pore-water nutrient concentration [mol N m -3], and K m [mol N m -3] is anexperimentally determined half-saturation constant of growth when fitted to the Monod growthequation. The implication of the last equation is that the rate of nutrient uptake increases withbiomass (like phytoplankton cells), but unlike macroalgae (which has a constant uptake per m 2).The increase in uptake with biomass is probably realistic, as a higher biomass of seagrass wouldhave a larger root system (in the same way that a higher biomass of phytoplankton cells wouldhave a larger surface area).

Maximum light uptake by seagrass is given by:( )SG I aASG I k *exp(1 =

where I is the light that has passed through the macroalgae; SG is the biomass of seagrass [mol Nm -2]; and SGaA is the nitrogen-specific absorption cross-section of seagrass [m 2 mg N -1].

Maximum uptake rates of benthic microalgae. Benthic microalgae exist in the top layer of thesediment. The maximum nutrient uptake (from the sediment porewater) is the same as forsuspended algal cells (although the diffusion coefficient may be reduced). The maximum lightcapture is given by:

MB MB MB I naAn I k / exp(1 = where I is the light that has passed through the water column, macroalgae and seagrass [mol(photons) m -2 s-1], n MB is the concentration of cells [cell m -3]; MBaA is the absorption cross-

section of the benthic microalgae [m2

].Growth rates of autotrophs

We now have the maximum uptake rates of light and nutrients for a number of autotrophsclasses. How do we combine these rates and the maximum growth rate to obtain a prediction of the growth rate at a particular nutrient concentration and irradiance? We are not able to continueour strict mechanistic derivations to intracellular processes, which are both less well understoodand far more complex than the extracellular processes described above. To combine the rates wewill make two assumptions (which are more fully explored in Baird et. al. , 2001) to guide ourfinal form. In essence, though, we are now pursuing an empirical approach.

The uptake rate of nutrients and light (or at least fixed carbon, which is the storage medium forenergy) is a function of the resource already stored. For a light and nitrate limited system:

Uptake of N = k N(1-R N)Uptake of I = k I(1-R I)

where R is a measure, between 0 and 1, or the reserves of a nutrient available for growth. Nowassume that growth rate [s -1] is determined by a linear product of R for both light and nitrate:

= m . R N . R I


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The balance between growth and uptake becomes:

k I(1-R I) = m .R I .R I mI k N(1-R I) = m .RN . R I mN

where m N and m I are stoichiometry coefficients, or the number of moles of N, I per unit of biomass (either cell or m -2). I will call this the benthic solution. Because of the convention of representing C:N:P ratio relative to P, it is easiest to define a m P = 9140*(4 /3)r 3 /106(Baird,1999), and use the Redfield ratio of 848:106:16:1 of photons:C:N:P to obtain m I, m C, andmN.

For cells that divide (and therefore have to share luxury resource between cells), the solutionbecomes:

k I(1-R I) = m .RN .R I (m I + R IRImax)k N(1-R N) = m .RN .R I (mN + R NRNmax )

To obtain a growth rate (from = m . R N . R I ) requires knowledge of R N and R I. Ideally in anecological model, R N and R I will be state variables, and their values are tracked through time (asin Baird and Emsley, 1999).

However, with a number of algal and seagrass species, this may be too time consuming. Instead,if it is assumed that the autotroph has reached an equilibrium growth state, R N and R I can bedetermined at every time point if m, m I, mN, k N and k I are known. The equilibrium state is

obtained by solving the two non-linear simultaneous equations by applying Newton's method forsolving systems of non-linear equations, truncating the Taylor series approximation to one term,and using Gaussian elimination to solve the intermediate linear simultaneous equations, untilsuccessive approximations were within 10 -9 (Baird and Emsley, 1999).

Again, this is a time consuming procedure. However, the solution for a range of supply rates canbe placed in a look-up table, which reduces the computation time.

Autotrophic Respiration

Respiration is the release of energy from organic compounds. More complex models of

autotrophic growth include respiration explicitly. In the SERM model, respiration is accountedfor in two ways. The photon requirement for growth relative to P, red_A_I or atk_A_I is elevatedfrom the theoretical minimum of 8 to 10. Secondly, the first Presp or Bresp (which were set at0.025 for SERM) fraction of light that is required for the maximum growth rate are not countedtowards growth. The increase from 8 to 10 is to account for the respiration during growth, whilePresp and Bresp ensure a growth is only greater than respiration at a non-zero light level.

Secondary Production (animal growth)

The only secondary production explicitly modelled is zooplankton growth. Zooplankton cells areonly found in the water column and consume only phytoplankton. The model contains of two


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classes of zooplankton, small (ZS) and large (ZL), which graze on the small and large (both MBand PL) phytoplankton respectively. Zooplankton growth is calculated from the encounter ratesof phytoplankton and zooplankton cells (Jackson, 1996). If the encounter rate exceeds maximumgrowth rate of the zooplankton cell, the grazing rate is set to the encounter rate. To go throughthe calculation for small zooplankton.

Encounter rates are based on number of cells per unit volume, so a conversion between biomass[mg N m -3] and cell numbers [cell m -3] is required for both predator (ZS) and prey species (PS):

ZScells = ZS/(ZSm*16*14010)PScells = PS/(PSm*16*14010)

The encounter rate between one predator and a population of prey cells [cell (PS) m -3] is givenby:

encounter_rate_ZS = PScells*ZSphi_PS [cell (PS) s -1]

where ZSphi_PS [m 3 s-1] is the encounter rate coefficient between species ZS and PS. Theencounter rate coefficient is based on the encounter rate of spheres by summing three processesthat bring predators and prey into contact: diffusion, relative motion (swimming and sinking) andfluid shear:

phi = phidiff + phirelmotion + phishear

The diffusive encounter rate is calculated using:

phidiff = (2.0*BOLT*Twater/(3.0*density*dyn_viscosity))*(1/PSrad+1/ZSrad)*(PSrad+ZSrad)

where PSrad is the radius of small phtyoplankton [m], ZSrad is the radius of small zooplankton[m], viscosity is the dynamic viscosity of the water [kg s -1 m-1], epsilon is the dissipation of turbulent kinetic energy [m 2 s-3], density is the density of water [kg m -3] and BOLT isBoltzmann's constant [J K -1] and Twater is the temperature of the water [ C]. The relative motionencounter rate is given by:

phirelmotion = (PSrad+ZSrad) 2*Ueff

where Ueff is the effective relative motion between PS and ZS [m s -1]. Relative motion (otherthan resulting from diffusion and shear) consists of two primary sources: the relative sinkingvelocities of the two cells, and the swimming velocities of the two cells. In the NLWRAapplication, we have included only the swimming velocities, which are combined to an effectiverelative velocity by:

fast

fast sloweff U

U U U

3

3 22 +=

where Uslow is the slower of PSswim and ZSswim, and Ufast is the faster of PSswim andZSswim. PSswim [m s -1] has been determined from a general size-based relationship:


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PSswim = 0.004 PSrad 0.26

while ZSswim is specified as a parameter. The encounter rate coefficient due fluid shear is givenby:

phishear = 1.3*(epsilon/kin_viscosity) 0.5*(PSrad+ZSrad) 3

where PSswim is the swimming velocity of the prey [m s -1], ZSswim is the swimming velocityof the predator [m s -1] and kin_viscosity is the kinematic viscosity [m 2 s-1].

The maximum ingestion rate, however, is limited by how fast the predator can grow. Themaximum growth rate is in units of s -1, and must be converted to cells of prey ingested tomaintain the maximum growth rate [cell (PS) cell (ZS) -1 s-1]

max_ingestion_rate_ZS = ZSumax*(ZSm/PSm)/E_ZS

where E_ZS is the efficiency of small zooplankton growth. The clearance rate of PS cells by ZScells becomes the minimum of the encounter rate and the maximum ingestion rate per ZS cellsmultiplied by the number of ZS cells:

ZS_CLEAR = min(max_ingestion_rate_ZS, encounter_rate_ZS)*ZScells

We know need to convert back to units of biomass for grazing loss of PS, ZSgrazePS, and thesubsequent gain in biomass of ZS (account for an efficiency loss)

ZSgrazePS = ZS_CLEAR / (PSm*16*14010))

ZSgrowth = E_ZS * ZSgrazePS

The same procedure is undertaken for large zooplankton, ZL, except that large zooplankton feedon two types of algal cells, large phytoplankton and suspended microphytobenthos. In this case,it was chosen to have no feeding preference between the two prey types, so that their loss rateswas always in proportion to their encounter rates (even if the large zooplankton were ingestionrate limited).

Mortality (unmodelled trophic level effects)

A mortality rate is specified for a number of the plants and animals to represent loss processeswhich are not already considered. Given that we consider physical loss terms (sinking andadvection) in the physical model, and grazing loss on phytoplankton by zooplankton, mortalityessentially becomes the effect of unparameterised trophic levels (such as viruses, fish larvae,whales etc.) and trophic interactions (bacterial decay). The mortality terms in the model are:

In the water column:

The only mortality terms in the water column are loss rates of zooplankton:


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ZLmortality = mQ_ZL * ZL * ZLZSmortality = mQ_ZS * ZS * ZS

A quadratic form was chosen to represent the effect of higher trophic levels. As zooplanktonincrease in numbers, their predators are expected to increase as well, and the combined effectmay be best captured using a quadratic form.

In the epibenthos

Both seagrass and macroalgae are given mortality rates, primarily to capture the effect of grazing.

MAmortality = mL_MA * MASGmortality = mL_SG * SG

In both cases, a linear loss rate was assumed.

In the sediment

Loss rates are given for phytoplankton cells (linear to represent bacterial decay of unviablecells), and microphytobenthos (quadratic to represent a higher trophic level):

MAmortality = mL_MA * MASGmortality = mL_SG * SG

Total Suspended Solids flocculation

We consider two classes of suspended solids: flocculated (TSS_floc) [kg m -3] and unflocculated(TSS_unfloc) [kg m -3], with sinking rates of w_floc [m s -1] and w_unfloc [m s -1] respectively.The rate at which TSS flocculates [kg m -3 d-1] (i.e. moves from TSS_unfloc to TSS_floc) is adiscontinuous function of the salinity, S, and a parameter giving the maximum flocculation rate,r_floc [s -1]:

S > 10.0 flocculate = TSS_unfloc*r_floc6.0 < S < 10.0 flocculate = TSS_unfloc*r_floc * (S-6.0)/4.0

S < 6.0 flocculate = 0

Additional factors influencing flocculation rate, but in the ecological model, include adependence of TSS concentration, particle size distribution and shear rates.

Phosphate absorption / desorption reactions

In the water column, the reversible absorption / desorption reactions for PIP_floc and PIP_unflocare described by:


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-d(PIP_floc)/dt = d(DIP)/dt = [PIP_floc - P_abs_coef*TSS*DIP]*r_abs_P

-d(PIP_unfloc)/dt = d(DIP)/dt = [PIP_unfloc - P_abs_coef*TSS*DIP]*r_abs_P

P_abs_coef is the phosphate absorption coefficient [L g -1 or m 3 kg -1], r_abs_P [s -1] is the rate atwhich absorption / desorption equilibrium is reach, and:

TSS = TSS_floc + TSS_unfloc

PIP = PIP_floc + PIP_unfloc

In the water column, PIP moves from PIP_unfloc to PIP_floc at the same flocculation rate asTSS_unfloc moves to TSS_floc.

In the sediment, we assume a constant quantity of TSS. Given the same P_abs_coef, a porosityof = 0.547 and a density of sediment of = 2650 kg m -3, a constant sediment bufferingcapacity, P_buff_sed, is given by:

P_buff_sed = (1- ) K D = (1-0.547)*2*2650 = 2,400 kg kg -1

The absorption / desorption reaction becomes independent of TSS, and is given by:

-d(PIP_floc)/dt = d(DIP)/dt = [PIP_floc/P_buff_sed- DIP]*r_abs_P-d(PIP_unfloc)/dt = d(DIP)/dt = [PIP_unfloc/P_buff_sed- DIP]*r_abs_P

Detritus (organic suspended particles) and dissolved organic matter processes

Detrital and organic matter processes are represented the same in both the water column andsediment, although nitrification / denitrification occurs only in the sediment (see below). Non-living organic matter is represented in three major components: labile detritus (fast breakingdown organic particles), refractory detritus (slow breaking down organic particles) and dissolvedorganic matter (dissolved organic molecules). Labile detritus is composed of two classes basedon the stoichiometry of the elements making up the labile detritus: one at the Redfield ratio(C:N:P 106:16:1) (LDP), and one at the Atkinson ratio (C:N:P 550:30:1) (LDB). LDP is typicalof aquatically-derived plant detritus, while LDB is typical of terrestrial plants, and seagrasses.Refractory detritus and dissolved organic matter are composed of three pools each: a carbon(RDC and DOC), a nitrogen (RDN and DON) and phosphorus (RDP and DOP) [see figure].

Rates of decay

The rates of detrital and dissolved organic matter decay are specified by breakdown rates of r_LDP, r_LDB, r_RD and r_DOM. For refractory detritus and dissolved organic matter, whichare sub-divided into carbon, nitrogen and phosphorus pools, the breakdown rates of all pools areequal.

Destination of decay material


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As well as quantifying the rates of decay, we need to specify the destination of the decayedmaterial. To do this, we represent the fraction of the decaying matter reaching equal breakdownpool. The fractions for labile detritus are specified as the fraction of labile detritus (both LDP andLDB) breaking down to refractory detritus, F_LD_RD, and dissolved organic matter,F_LD_DOM. The remaining fraction, (1- F_LD_RD - F_LD_DOM), is broken down todissolved inorganic pools (DIC, NH and DIP). For refractory detritus (carbon, phosphorus andnitrogen pools), the fraction breaking down to dissolved organic matter is given by F_RD_DOM,while the remaining is broken down to dissolved inorganic pools (DIC, NH and DIP).

The above listed detrital and organic matter breakdown processes can be written follows:

The breakdown of LDP is given by:

LDPbreak = r_LDP * LDP

where the component going to each dissolved organic matter pool is given by:

LDPtoDOC = r_LDP * LDP * F_LD_DOM * red_W_CLDPtoDON = r_LDP * LDP * F_LD_DOM

LDPtoDOP = r_LDP * LDP * F_LD_DOM * red_W_P

and the component going to each refractory detritus pool by:

LDPtoRDC = r_LDP * LDP * F_LD_RD * red_W_CLDPtoRDN = r_LDP * LDP * F_LD_RD

LDPtoRDP = r_LDP * LDP * F_LD_RD * red_W_P

leaving the remainder to go into dissolved inorganic nutrients pools:

LDPtoNH = r_LDP * LDP * (1.0 - F_LD_RD - F_LD_DOM)LDPtoDIC = r_LDP * LDP * (1.0 - F_LD_RD - F_LD_DOM)

* red_W_CLDPtoDIP = r_LDP * LDP * (1.0 - F_LD_RD - F_LD_DOM)

* red_W_P

with the fraction going into dissolved inorganic nutrients consumes oxygen at a rate:

LDPconO2 = red_W_O * r_LDP * LDP * (1.0 - F_LD_RD - F_LD_DOM)

A similar set of terms for the breakdown of LDB are given by:

LDBbreak = r_LDB * LDB

where the component going to each dissolved organic matter pool is given by:


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LDBtoDOC = r_LDB * LDB * F_LD_DOM * red_W_CLDBtoDON = r_LDB * LDB * F_LD_DOM

LDBtoDOP = r_LDB * LDB * F_LD_DOM * red_W_P

and the component going to each refractory detritus pool by:

LDBtoRDC = r_LDB * LDB * F_LD_RD * red_W_CLDBtoRDN = r_LDB * LDB * F_LD_RD

LDBtoRDP = r_LDB * LDB * F_LD_RD * red_W_P

leaving the remainder to go into dissolved inorganic nutrients pools:

LDBtoNH = r_LDB * LDB * (1.0 - F_LD_RD - F_LD_DOM)LDBtoDIC = r_LDB * LDB * (1.0 - F_LD_RD - F_LD_DOM)

* red_W_CLDBtoDIP = r_LDB * LDB * (1.0 - F_LD_RD - F_LD_DOM)

* red_W_P

with the fraction going into dissolved inorganic nutrients consumes oxygen at a rate:

LDBconO2 = red_W_O * r_LDB * LDB * (1.0 - F_LD_RD - F_LD_DOM)

The breakdown of each pool of refractory detritus is given by:

RDxbreak = RDx * r_RD

where RDx represents each of the pools (carbon, nitrogen and phosphorus) of refractory detritus.The resulting breakdown of refractory to dissolved organic matter is given by:

RDCtoDOC = RDC * r_RD * F_RD_DOMRDNtoDON = RDN * r_RD* F_RD_DOMRDPtoDOP = RDP * r_RD* F_RD_DOM

with the remainder going to dissolved inorganic nutrient pools:

RDCtoDIC = RDC * r_RD * (1 - F_RD_DOM)RDNtoNH = RDN * r_RD * (1 - F_RD_DOM)RDPtoDIP = RDP * r_RD * (1 - F_RD_DOM)

with the consumption of O 2 assumed to be a function of the carbon fraction of RD:

RDCconO2 = RDC * r_RD * (1 - F_RD_DOM) * C_O_W

The breakdown of each pool of dissolved organic matter is given by:

DOxbreak = r_DOM * DOx


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where DOx represents each of the pools (carbon, nitrogen and phosphorus) of dissolved organicmatter. The resulting breakdown of dissolved organic matter to dissolved inorganic nutrients isgiven by:

DOCtoDIC = DOC * r_DOMDONtoNH = DON * r_DOMDOPtoDIP = DOP * r_DOM

with the consumption of O 2 assumed to be a function of the carbon fraction of DOM:

DOCconO2 = DOC * r_DOM * C_O_W

Sediment Nitrification and Denitrification

In the sediment, ammonia is subject to conversion to nitrite and then nitrate by bacteria(nitrification). A different group of bacteria are capable of converting nitrate to nitrite and thennitrogen gas (denitrification). These interacting processes have not been modelled individually,but instead their combined effect has been empirically approximated (see PPBES for moredetails).

The empirical approximation is based on evidence that increased respiration decreases the loss of nitrogen to N 2 gas. The loss of efficiency is thought to be primarily in the nitrification step(rather than the final denitrification step). The net respiration rate is given by:

respiration = LDPtoNH + LDBtoNH + DONtoNH + RDNtoNH - MBgrowth

where respiration is an areal flux (so must be corrected for sediment thickness). The amount of nitrification is given by:

nitrification = respiration * Nitrific_eff

where a change in nitrification efficiency, Nitrific_eff, is assumed to account for the reduction inthe overall conversion of NH to N 2. The empirical approximation for is Nitrific_eff :

Nitrific_eff = Nitrific_eff_max * emax(1.0 - respiration / R_0)

Denitrification rate is then given by:

Denitrification = Nitrification * Denitrific_eff

where Dentrific_eff represents the decrease in denitrification rate at very low respiration rates(below R_D):

Denitrific_eff = emin(respiration / R_D, 1.0)


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The percent of the ammonia that is respired which is released to the atmosphere as N 2 gas istherefore given by:

PercentDenitri = 100 * Denitrific_eff * Nitrific_eff


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