Modelling of Aquatic EcosystemsExercise 4: Biogeochemical-Ecological Lake Model

15.04.2015

P Phyto Zoo

Light and Temperature

=

Elemental composition

groALG groZOO

deathALG

v v

≠

Exercises 1-3

deathZOO

P Phyto

groALG groZOOO2

O2

Sedimentation

SPOM

N

POM

Epilimnion

Hypolimnion

Exercise 4

= =

Elemental composition

≠

Gaz exchange

MineralizationTurbulent

mixing

deathALGdeathZOO

≠

Zoo

Light and Temperature

Respiration

Exercise 4: Model summary

System: Lake

Reactor 1: Epilimnion

Reactor 2: Hypolimnion

Link: Metalimnion

State variables:

ALGZOOHPO4

NO3

NH4

O2

POMDPOMIsed.POMDsed.POMI

gro.ALG gro.ZOO

resp.ALG resp.ZOO

death.ALG death.ZOO

miner.POM nitri

gro.ALG gro.ZOO sed.POM

resp.ALG resp.ZOO miner.Sed.POM

death.ALG death.ZOO

miner.POM nitri

Degradable

Inert

Exercise 4: Stoichcalc integration in Ecosim

≠ ≠

Elemental composition

vstoichcalc

Growth

Death

Respiration

Mineralization

gro.ZOO <- new(Class = "process", name = "gro.ZOO", rate = expression(k.gro.ZOO*exp(beta.ZOO*(T-T0)) *(C.O2/(K.O2.ZOO+C.O2)) *C.ALG *C.ZOO), stoich = as.list(nu["gro.ZOO",]))

Process name

rate expression

stoichiometric coefficients

list(C.ZOO = expression(1), # gDM/gDM C.ALG = expression(-1/Y.ZOO))

Exercises 1-2: Manual definition

Exercise 3

Ecosim

Exercise 4

Exercise 4: Tasks

• Task 1: Model FormulationStudy and try to understand the model formulation given in section 9.4. Note that it may be useful to study the “intermediately complex" model described in section 9.3.

• Task 2: Model ImplementationStudy and try to understand the implementation of the model as provided in the model 94.r

• Task 3: Model ResultsPerform a simulation of the model and try to understand the time courses of the state variables and the overall mass fluxes of phosphorus and nitrogen compounds

• Questions

• Task 4: Sensitivity Analysis (OPTIONAL)Do simple sensitivity analyses by modifying some of the kinetic parameters and interpret the changes in the simulation results

Exercise 4: Environmental conditions

Winter mixing

Exercise 4: Model results

Exercise 4: Stoichiometric coefficients & Yields

process HPO4 NH4+ NO3

- O2 ALG ZOO POMD POMI SPOMD SPOMI

gro.ALGNO3- - - + 1

gro.ALGNH4+ - - + 1

resp.ALG + + - -1

death.ALG 0/+ 0/+ 0/+ -1/YZOO 1 (1-fI)YALG,death fIYALG,death

gro.ZOO + + - -1 (1-fI)fe/YZOO fIfe/YZOO

resp.ZOO + + - -1

death.ZOO 0/+ 0/+ 0/+ (1-fI)YZOO,death fIYZOO,death

nitri -1 + -

miner.ox.POM + + - -1

miner.ox.POM.sed + + - -1

miner.anox.POM.sed + + - -1

sed.POMD -1 1

sed.POMI -1 1

Why is it important that some stoichiometric coefficients are defined as “0/+”?

Due to biological reasons, for example:• If algae die they do not use any

phosphorus. • However, mathematically this can

happen in the model due to the mass conservation principle if the concentration of P in POM is higher than in algae!

• Therefore, we need a restriction of the maximum turnover of algae into POM.

Exercise 4: Stoichiometric coefficients & Yields

process HPO4 NH4+ NO3

- O2 ALG ZOO POMD POMI SPOMD SPOMI

gro.ALGNO3- - - + 1

gro.ALGNH4+ - - + 1

resp.ALG + + - -1

death.ALG 0/+ 0/+ 0/+ -1/YZOO 1 (1-fI)YALG,death fIYALG,death

gro.ZOO + + - -1 (1-fI)fe/YZOO fIfe/YZOO

resp.ZOO + + - -1

death.ZOO 0/+ 0/+ 0/+ (1-fI)YZOO,death fIYZOO,death

nitri -1 + -

miner.ox.POM + + - -1

miner.ox.POM.sed + + - -1

miner.anox.POM.sed + + - -1

sed.POMD -1 1

sed.POMI -1 1

How are the values YALG.death, YZOO.death calculated?

param$Y.ZOO.death <- min(1, param$alpha.N.ZOO / param$alpha.N.POM, param$alpha.P.ZOO / param$alpha.P.POM, param$alpha.C.ZOO / param$alpha.C.POM)

With this function we check whether N,P or C are limiting the turnover of dead algae or ZOO into POM.

If none of the POM concentrations is higher than the algae/ZOO concentration, Y is set to one. This means that all the algae/ZOO are turned into POM.

Exercise 4: metalimnion

System: Lake

Reactor 1: Epilimnion

Reactor 2: Hypolimnion

Link: Metalimnion

State variables:

ALGZOOHPO4

NO3

NH4

O2

POMDPOMIsed.POMDsed.POMI

gro.ALG gro.ZOO

resp.ALG resp.ZOO

death.ALG death.ZOO

miner.POM nitri

gro.ALG gro.ZOO sed.POM

resp.ALG resp.ZOO miner.Sed.POM

death.ALG death.ZOO

miner.POM nitri

Degradable

Inert

Exercise 4: process rates of mineralization

Exercise 4: mass balance N & P

Exercise 4: Sensitivity analysis

‘Shut down’ nitrification and mineralization

Exercise 4: Volumes and Areas

SPOM

POM

Sedimentation

mg/m3 s∙ -1

mg / m2

ρsed = vsed, POM / hhypo X CPOM

ρsed x V

ρsed x V x 1/A

mg s∙ -1

mg/m2 s∙ -1

mg / m3

hypolimnion <- new(Class = "reactor", name = "Hypo", volume.ini = expression(A*h.hypo), area = expression(A), conc.pervol.ini = list(...), # gDM/m3 conc.perarea.ini = list(...), # gDM/m2 cond = cond.hypo, processes = list(...))