Post on 28-Dec-2015
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(...))