1. Modelling of Aquatic Ecosystems
Exercise 4: Biogeochemical-Ecological Lake Model 1

2. = ≠ Exercises 1-3 Light and Temperature P Phyto v Zoo v groALG groZOO
deathZOO
deathALG =
Elemental composition ≠

3. = ≠ ≠ Exercise 4 Virtual ecologist Light and Temperature Gaz exchange
Epilimnion P
Phyto
Zoo
groALG
groZOO O2 N O2
deathZOO
deathALG
Respiration
Hypolimnion
Mineralization
Sedimentation
Turbulent
mixing
POM =
Elemental composition
SPOM ≠ ≠

4. System: Lake Reactor 1: Epilimnion Reactor 2: Hypolimnion
Exercise 4: Model summary
System: Lake
State variables:
ALG
ZOO
HPO4
NO3
NH4 O2
POMD
POMI
sed.POMD
sed.POMI
Reactor 1: Epilimnion
gro.ALG
gro.ZOO
resp.ALG
resp.ZOO
death.ALG
death.ZOO
miner.POM
nitri
Link: Metalimnion
Reactor 2: Hypolimnion
Degradable
gro.ALG
gro.ZOO
sed.POM
resp.ALG
resp.ZOO
miner.Sed.POM
death.ALG
death.ZOO
miner.POM
nitri
Inert

5. ≠ Ecosim Exercise 4: Stoichcalc integration in Ecosim Growth
Elemental composition
Exercise 3
stoichcalc
Respiration v
Death
Mineralization
Ecosim
Process name
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",]))
rate expression
Exercise 4
stoichiometric coefficients
list(C.ZOO = expression(1), # gDM/gDM
C.ALG = expression(-1/Y.ZOO))
Exercises 1-2: Manual definition

6. Exercise 4: Tasks Task 1: Model Formulation
Study 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 Implementation
Study and try to understand the implementation of the model as provided in the model 94.r
Task 3: Model Results
Perform 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

7. Exercise 4: Environmental conditions
Winter mixing

8. Exercise 4: Model results

9. Exercise 4: Stoichiometric coefficients & Yields
process
HPO4
NH4+
NO3- O2
ALG
ZOO
POMD
POMI
SPOMD
SPOMI
gro.ALGNO3- - + 1
gro.ALGNH4+
resp.ALG -1
death.ALG
0/+
-1/YZOO
(1-fI)YALG,death
fIYALG,death
gro.ZOO
(1-fI)fe/YZOO
fIfe/YZOO
resp.ZOO
death.ZOO
(1-fI)YZOO,death
fIYZOO,death
nitri
miner.ox.POM
miner.ox.POM.sed
miner.anox.POM.sed
sed.POMD
sed.POMI
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.

10. Exercise 4: Stoichiometric coefficients & Yields
process
HPO4
NH4+
NO3- O2
ALG
ZOO
POMD
POMI
SPOMD
SPOMI
gro.ALGNO3- - + 1
gro.ALGNH4+
resp.ALG -1
death.ALG
0/+
-1/YZOO
(1-fI)YALG,death
fIYALG,death
gro.ZOO
(1-fI)fe/YZOO
fIfe/YZOO
resp.ZOO
death.ZOO
(1-fI)YZOO,death
fIYZOO,death
nitri
miner.ox.POM
miner.ox.POM.sed
miner.anox.POM.sed
sed.POMD
sed.POMI
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.

11. System: Lake Reactor 1: Epilimnion Reactor 2: Hypolimnion
Exercise 4: metalimnion
System: Lake
State variables:
ALG
ZOO
HPO4
NO3
NH4 O2
POMD
POMI
sed.POMD
sed.POMI
Reactor 1: Epilimnion
gro.ALG
gro.ZOO
resp.ALG
resp.ZOO
death.ALG
death.ZOO
miner.POM
nitri
Link: Metalimnion
Reactor 2: Hypolimnion
Degradable
gro.ALG
gro.ZOO
sed.POM
resp.ALG
resp.ZOO
miner.Sed.POM
death.ALG
death.ZOO
miner.POM
nitri
Inert

12. Exercise 4: process rates of mineralization

13. Exercise 4: mass balance N & P

14. Exercise 4: Sensitivity analysis
‘Shut down’ nitrification and mineralization

15. Exercise 4: Volumes and Areas
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(...))
ρsed = vsed, POM / hhypo X CPOM
mg/m3 ∙ s-1
mg∙s-1
ρsed x V
Sedimentation
mg / m3
mg/m2 ∙ s-1
ρsed x V x 1/A
POM
SPOM
mg / m2