Modelling Aquatic Ecosystems - Course 701-0426-00, · PDF fileModelling Aquatic Ecosystems...

Modelling Aquatic EcosystemsCourse 701-0426-00, ETH Zürich

Spring 2017Nele Schuwirth & Peter [email protected], [email protected]

ETH Zürich, Department of Environmental Systems SciencesEawag, Swiss Federal Institute of Aquatic Science and Technology

Structure of the Course1. Introduction. Principles of modelling environmental systems.

Mass balance in a mixed reactor. Process table notation.Simple lake phyto- and zooplankton model. ecosim package.

2. Process stoichiometry (1).3. Process stoichiometry (2). stoichcalc package.4. Biological processes in lakes, the metabolic theory of ecology

(Chemical equilibria)Two box lake model for plankton and biogeochemical cycles.

5. Physical processes in lakesMass balance in a system of reactors and in continuous systems.

6. Transport and mixing in rivers.Model of O, N and P household and benthic populations in a river.

7. Additional processes and model extensions.8. Stochasticity and uncertainty. Individual based models.9. Examples and case studies. Preparation of exam and review.

Modelling Aquatic Ecosystems 2017 1

Lecture 4: Goals

• Review stoichiometry

• Biological processes in lakes

• (Chemical processes)

• Preview extended lake model

• Build your own model: selection of topics

Modelling Aquatic Ecosystems 2017 Lecture 4: Goals 2

New Challenge: Develop your own model

During the semester you have to develop and implement your ownmodel (alone or in groups of two), interpret simulation results andperform a simple sensitivity analysis.

We provide two topics to choose from.We will assign topics on 29.03.2017 (today).

You will deliver the R-files and results by the end of the semester(2.6.2017!) per email to [email protected].

In the oral exam we will ask you about your example (beside othertopics).

Modelling Aquatic Ecosystems 2017 Lecture 4: Goals 3

Process Stoichiometry

How to derive the stoichiometric coefficients νij?

• Chemical substance notation.

• Parameterized elemental mass fractions.

• General solution.

Modelling Aquatic Ecosystems 2017 Lecture 4: Review Stoichiometry 4

Review Stoichiometry

Questions to think about:

• Is it important to know the number of independent processespossible for a given set of substances of known composition?

• How can the number of required additional constraints bederived easily?Under which circumstances would this simple approach fail?

• Where to get the required additional constraints from?

Modelling Aquatic Ecosystems 2017 Lecture 4: Review Stoichiometry 5

Biological processes

It’s your turn:

• What happens in the process?Which substances/organisms are involved?• Explain qualitatative stoichiometry (process table).Additional constraints?• Explain the process rate.• Anything else special?

10 Minutes for preparation!

Modelling Aquatic Ecosystems 2017 Lecture 4: Biological Processes 6

Primary Production

What happens?

Primary production is the production of organic material frominorganic nutrients through photosynthesis.

This process provides the food for the subsequent trophic levels ofthe ecosystem foodweb.


Primary Production

Stoichiometry:

Process Substances / Organisms RateNH+

4 NO−3 HPO2−

4 HCO−3 O2 H+ H2O ALG

gN gN gP gC gO mol mol gDMPri. prod. NH+

4 − − − + ? ? 1 ρgro,ALG,NH4Pri. prod. NO−

3 − − − + ? ? 1 ρgro,ALG,NO3

Six unknown stoichiometric coefficients.Conservation of C, H, O, N, P and charge: 6 equations.No additional constraints needed.


Primary Production

Process rates:

ρgro,ALG,NH+4

= kgro,ALG,T0 · exp(βALG(T − T0)

)· I

KI + I

·min(

CHPO2−4

KHPO2−4 ,ALG + CHPO2−

4

,CNH+

4+ CNO−

3

KN,ALG + CNH+4

+ CNO−3

)

·pNH+

4CNH+

4

pNH+4

CNH+4

+ CNO−3

· CALG

ρgro,ALG,NO−3

= kgro,ALG,T0 · exp(βALG(T − T0)

)· I

KI + I

·min(

CHPO2−4

KHPO2−4 ,ALG + CHPO2−

4

,CNH+

4+ CNO−

3

KN,ALG + CNH+4

+ CNO−3

)

·CNO−

3

pNH+4

CNH+4

+ CNO−3

· CALG


Primary Production

Depth averaged version:

ρgro,ALG,NH4 = kgro,ALG·exp(βALG(T−T0)

)· 1λh log

(KI + I0

KI + I0 exp(−λh)

)

·min(

CHPO4

KHPO4 + CHPO4,

CNH4 + CNO3

KN + CNH4 + CNO3

)·

pNH+4

CNH+4

pNH+4

CNH+4

+ CNO−3

·CALG

ρgro,ALG,NO3 = kgro,ALG·exp(βALG(T−T0)

)· 1λh log

(KI + I0

KI + I0 exp(−λh)

)

·min(

CHPO4

KHPO4 + CHPO4,

CNH4 + CNO3

KN + CNH4 + CNO3

)·

CNO−3

pNH+4

CNH+4

+ CNO−3

·CALG


Respiration

Respiration is the inverse process of photosynthesis.

Respiration is an important process for the survival of organisms asit frees energy for live maintenance processes.

Respiration leads to cycling of nutrients between the organicallybound and inorganic phases.


Respiration


4 NO−3 HPO2−4 HCO−3 O2 H+ H2O ALG

gN gN gP gC gO mol mol gDMRespiration + + + − ? ? −1 ρresp,ALG


ρresp,ALG = kresp,ALG · exp(βALG(T − T0)

)· CO2

KO2 + CO2· CALG


Death

Death transfers living organisms into dead organic particles.

The accumulation of dead particles due to death, sloppy feedingand excretion leads to anoxic and anaerobic environments, due tooxygen consumption of mineralisation processes.

Natural organic particles have a wide spectrum of biodegradability.

In models of ecological systems, this is often represented by a(quickly) degradable and an inert fraction of organic matter.


Death


4 HPO2−4 HCO−

3 O2 H+ H2O ALG POMD POMIgN gP gC gO mol mol gDM gDM gDM

Death 0/+ 0/+ 0/+ 0/+ ? ? −1 (1− fI) fI ρdeath,ALG·YALG,death ·YALG,death

Eight unknown stoichiometric coefficients.Conservation of C, H, O, N, P and charge: 6 equations.Two additional constraints needed:

Ydeath = −(νdeath POMD + νdeath POMI)νdeath ALG

νdeath ALG ·Ydeath + νdeath POMD + νdeath POMI = 0

fI = −νdeath POMI

νdeath POMI + νdeath POMD

νdeath POMD fI − νdeath POMI(1− fI) = 0Modelling Aquatic Ecosystems 2017 Lecture 4: Biological Processes 14

Death

Process rate:ρdeath,ALG = kdeath,ALG · CALG


Consumption

Process formulation with fast and slowly (“inert”) degradablepartice production due to sloppy feeding and excretion and partialmineralization:


4 HPO2−4 HCO−

3 O2 H+ H2O ALG ZOO POMD POMIgN gP gC gO mol mol gDM gDM gDM gDM

GrowthZOO + + + − ? ?

−1YZOO

1(1− fI)fe

YZOO

fIfe

YZOOρgro,ZOO

Nine unknown stoichiometric coefficients.Conservation of C, H, O, N, P and charge: 6 equations.Three additional constraints needed.


Consumption

Three Constraints:

YZoo = −νgro,ZOO ZOO

νgro,ZOO ALG

νgro,ZOO ZOO + νgro,ZOO ALGYZOO = 0

fe = −(νgro,ZOO POMD + νgro,ZOO POMI)νgro,ZOO ALG

νgro,ZOO POMD + νgro,ZOO POMI + νgro,ZOO ALGfe = 0

fI = −νgro,ZOO POMI

νgro,ZOO POMI + νgro,ZOO POMD

νgro,ZOO POMDfI − νgro,ZOO POMI(1− fI) = 0


Consumption

Process rate:

ρgro,ZOO = kgro,ZOO·exp(βALG(T−T0)

)· CO2KO2 + CO2

·CALG·CZOO


Mineralization

Oxic mineralization transforms organic matter to dissolvednutrients and carbon dioxide under consumption of oxygen.

In the absence of dissolved oxygen (primarily in the sediment),mineralization can use nitrate, manganese oxide, iron hydroxide orsulfate for oxidizing organic matter.

Finally, methanogenesis can convert organic matter to nutrients,carbon dioxide and methane.

As mineralization is caused by bacteria and bacterial concentra-tions vary considerably from one (part of the) system to another,mineralization rate coefficients vary over many orders ofmagnitude.


Mineralization

Oxic Mineralization


4 HPO2−4 HCO−3 O2 H+ H2O POM

gN gP gC gO mol mol gDMOxic miner. + + + − ? ? −1 ρminer,ox,POM


Rate:

ρminer,ox,POM = kminer,ox,POM·exp(βBAC(T−T0)

)· CO2

KO2,miner + CO2·CPOM


Mineralization

Anoxic Mineralization


4 NO−3 N2 HPO2−

4 HCO−3 H+ H2O POM

gN gN gN gP gC mol mol gDMAnox. min. + − + + + ? ? −1 ρminer,anox,POM

Seven unknown stoichiometric coefficients. Conservation of C, H, O, N,P and charge: 6 equations. One additional constraint needed:

νminer,anox NO3 + νminer,anox N2 = 0

ρminer,anox,POM = kminer,anox,POM·exp(βBAC(T−T0)

)· KO2,miner

KO2,miner + CO2

· CNO3

KNO3,miner + CNO3· CPOM


Mineralization

Anaerobic Mineralization


4 HPO2−4 HCO−

3 Mn2+ H+ H2O MnO2 POMgN gP gC mol mol mol mol gDM

Mn oxide red. + + + + ? ? − −1 ρminer,MnO2,POM


4 HPO2−4 HCO−

3 Fe2+ H+ H2O FeOOH POMgN gP gC mol mol mol mol gDM

Fe hydrox. red. + + + + ? ? − −1 ρminer,FeOOH,POM


4 HPO2−4 HCO−

3 SO2−4 HS− H+ H2O POM

gN gP gC mol mol mol mol gDMSulfate reduction + + + − + ? ? −1 ρminer,SO4,POM


4 HPO2−4 HCO−

3 CH4 H+ H2O POMgN gP gC gC mol mol gDM

Methanogenesis + + + + ? ? −1 ρminer,CH4,POM


Nitrification

One step model:


4 NO−3 O2 H+ H2O

gN gN gO mol molNitrification −1 + − ? ? ρnitri

NH+4 + 2 O2 → NO−

3 + 2 H+ + H2O

Rate:

ρnitri = knitri · exp(βBAC(T − T0)

)· min

(CNH4

KNH4,nitri + CNH4,

CO2KO2,nitri + CO2

)


Nitrification

Two steps model:


4 NO−2 NO−

3 O2 H+ H2OgN gN gN gO mol mol

Ammonium oxidation −1 + − ? ? ρnitri,1Nitrite oxidation −1 + − ? ? ρnitri,2

NH+4 + 3

2 O2 → NO−2 + 2 H+ + H2O

NO−2 + 1

2 O2 → NO−3

Rate:

ρnitri = knitri · exp(βBAC(T − T0)

)· min

(CNH4

KNH4,nitri + CNH4,

CO2KO2,nitri + CO2

)ρnitri = knitri·exp

(βBAC(T−T0)

)·min

(CNO2

KNO2,nitri + CNO2,

CO2

KO2,nitri + CO2

)Modelling Aquatic Ecosystems 2017 Lecture 4: Biological Processes 24

Modelling Individual Taxa

There is no fundamental difference between modelling functionalgroups or individual taxa.

However, the number of taxa is much larger than the number offunctional groups. This leads to an extreme increase in the numberof model parameters.

This can be handled by applying the Metabolic Theory of Ecology.

Modelling Aquatic Ecosystems 2017 Lecture 4: The Metabolic Theory of Ecology 25

The Metabolic Theory of Ecology

Statement: Biological process rates scale with the basal metabolicrate that itself scales universally with body mass and temperature:

rbasal = i0( M

M0

)bexp

(−Ea

kB

( 1T −

1T0

))

i0 normalization constantM individual body massb scaling exponentEa activation energykB Boltzmann constantT Temperature



Allometric Scaling of the Metabolic Rate



Biomass production rate


Chemical Equilibria

Chemical equilibria are important for

• the speciation of inorganic carbon, nitrogen and phosphoruscompounds,

• the precipitation and dissolution of calcite,

• the calculation of pH.

Modelling Aquatic Ecosystems 2017 Lecture 4: Chemical Processes 29

Chemical Equilibria

Process Chemical equation Equilibrium condition (Law of mass action)

Self-ionization of water H2O ↔ H+ + OH− COH− · CH+ = Kw

Carbonate equilibria CO2 + H2O↔ H2CO3CCO2

CH2CO3= KCO2,H2CO3

H2CO3 ↔ H+ + HCO−3

CH+ · CHCO−

3CH2CO3

= KHCO−

3 ,H2CO3

HCO−3 ↔ H+ + CO2−

3

CH+ · CCO2−

3C

HCO−3

= KCO2−

3 ,HCO−3

Composite carbonateequilibriumCH2CO∗

3= CH2CO3 + CCO2

H2CO∗3 ↔ H+ + HCO−

3

CH+ · CHCO−

3CH2CO∗

3

= KHCO−

3 ,H2CO∗3

Only valid for dilute aqueous solutions, otherwise use activity instead of concentration.


Chemical Equilibria

Process Chemical equation Equilibrium condition (Law of mass action)

Phosphate equilibria H3PO4 ↔ H+ + H2PO−4

CH+ · CH2PO−

4CH3PO4

= KH2PO−

4 ,H3PO4

H2PO−4 ↔ H+ + HPO2−

4

CH+ · CHPO2−

4C

H2PO−4

= KHPO2−

4 ,H2PO−4

HPO2−4 ↔ H+ + PO3−

4

CH+ · CPO3−

4C

HPO2−4

= KPO3−

4 ,HPO2−4

Ammonium equilibrium NH+4 ↔ H+ + NH3

CH+ · CNH3C

NH+4

= KNH3,NH+

4

Calcite equilibrium Ca2+ + CO2−3 ↔ CaCO3 CCa2+ · C

CO2−3

= KCaCO3


Chemical Equilibria

Process H2O H+ OH− CO2 H2CO3 HCO−3 CO2−

3 Ratemol mol mol gC gC gC gC

H2O→ H+ + OH− −1 1 1 kw,fw

H2O← H+ + OH− 1 −1 −1 kw,bwCH+ COH−

CO2 + H2O→ H2CO3 −1/12 −1 1 kCO2,H2CO3 CCO2CO2 + H2O← H2CO3 1/12 1 −1 kH2CO3,CO2 CH2CO3H2CO3 → H+ + HCO−

3 1/12 −1 1 kH2CO3,HCO−

3CH2CO3

H2CO3 ← H+ + HCO−3 −1/12 1 −1 k

HCO−3 ,H2CO3

CH+ CHCO−

3HCO−

3 → H+ + CO2−3 1/12 −1 1 k

HCO−3 ,CO2−

3C

HCO−3

HCO−3 ← H+ + CO2−

3 −1/12 1 −1 kCO2−

3 ,HCO−3

CH+ CCO2−

3


Chemical Equilibria

Process H+ H3PO4 H2PO−4 HPO2−

4 PO3−4 NH+

4 NH3 Ratemol gP gP gP gP gN gN

H3PO4 → H+ + H2PO−4 1/31 −1 1 k

H3PO4,H2PO−4

CH3PO4

H3PO4 ← H+ + H2PO−4 −1/31 1 −1 k

H2PO−4 ,H3PO4

CH+ CH2PO−

4H2PO−

4 → H+ + HPO2−4 1/31 −1 1 k

H2PO−4 ,HPO2−

4C

H2PO−4

H2PO−4 ← H+ + HPO2−

4 −1/31 1 −1 kHPO2−

4 ,H2PO−4

CH+ CHPO2−

4HPO2−

4 → H+ + PO3−4 1/31 −1 1 k

HPO2−4 ,PO3−

4C

HPO2−4

HPO2−4 ← H+ + PO3−

4 −1/31 1 −1 kPO3−

4 ,HPO2−4

CH+ CPO3−

4

NH+4 → H+ + NH3 1/14 −1 1 k

NH+4 ,NH3

CNH+

4NH+

4 ← H+ + NH3 −1/14 1 −1 kNH3,NH+

4CH+ CNH3


Chemical Equilibria

In equilibrium, process rates for the forward and backwardtransformation reaction are the same.

Relation between equilibrium parameters K andkinetic parameters k:

Kw = kw,fwkw,bw

KCO2,H2CO3 = kH2CO3,CO2

kCO2,H2CO3

...


Chemical Equilibria

Precipitation and Dissolution:

Process CO2−3 Ca2+ CaCO3 Rate

gC mol mol

Ca2+ + CO2−3 → CaCO3 −12 −1 1 ρCaCO3,prec

Ca2+ + CO2−3 ← CaCO3 12 1 −1 ρCaCO3,diss


Chemical Equilibria

Saturation state: ratio between ion activity product and solubilityconstant

ΩCaCO3 =CCa2+CCO2−

3

KCaCO3

Ω > 1: oversaturationΩ < 1: undersaturation

Process rates for precipitation, if solution is oversaturated anddissolutionn if solution is undersaturated:

ρCaCO3,prec =

kCaCO3,prec(ΩCaCO3 − 1) if ΩCaCO3 > 10 if ΩCaCO3 ≤ 1

ρCaCO3,diss =

0 if ΩCaCO3 ≥ 1

kCaCO3,diss(1− ΩCaCO3) DCaCO3

KCaCO3 + DCaCO3

if ΩCaCO3 < 1


Sorption

Sorption of chemical substances to particles in the water columncan play an important role in aquatic systems.

Sorption of dissolved substances to sedimenting particles canincrease the elimination rate of substances from the water columnconsiderably.

Sorption is of particular interest for organic pollutants, heavymetals, and phosphate.


Sorption

Stoichiometry:

Process Substances Rate

dissolved adsorbedsubst. j subst. j

g gAdsorption of substance j −1 1 ρads,jDesorption of substance j 1 −1 ρdes,j


Sorption

Total concentration of a substance (open water phase):

C totj = Cj + CsSj

Cj : dissolved substance mass per unit volume of waterSj : adsorbed substance mass per unit mass of the sorbent

CS : concentration of particles (=sorbent) per unit volume of water

Total concentration of a substance (in the sediment):

C totj = θCj + (1− θ)ρsSj

θ: porosity (fraction of the volume filled by water)ρs: density of the solid material


Sorption

Simplest assumption: linear sorption kinetics

Process rates:ρads,j = kads,j · Cj

ρdes,j = kdes,j · Sj

Equilibrium:ρdes,j = ρads,j

Seq,j(Cj) = kads,jkdes,j

· Cj = KD,j · Cj


Sorption

Limited number of sorption sites:

Process rates:

ρads,j = kads,j · Cj · (Smax − Sj)

ρdes,j = kdes,j · Sj

Equilibrium:Seq,j(Cj) = Smax · Cj

KL + Cj

(Langmuir-Isotherm with KL = kdes,jkads,j

)


Sorption

Fast reversible sorption processes:

Process rate:ρsorb = kj · (Seq,j(Cj)− Sj)

Relaxation of the actually sorbed concentration to the equilibriumconcentration with a rate constant kj . Good approximation toequilibrium sorption, if kj is set to a sufficiently large value.


New Challenge: Develop your own model

During the semester you have to develop and implement your ownmodel (alone or in groups of two), interpret simulation results andperform a simple sensitivity analysis.

We provide two topics to choose from.We will assign topics on 29.03.2017 (now).

You will deliver the R-files and results by the end of the semester(2.6.2017!) per email to [email protected].

In the oral exam we will ask you about your example (beside othertopics).

Modelling Aquatic Ecosystems 2017 Lecture 4: Develop your own model 43

Two Box O and P Lake Model

Model extensions for model 9.3:

• dissolved oxygen, suspended particulate organic matter(POM) and sedimented organic particulate organic matter(SPOM) as additional state variables

• division of the water body into epilimnion and hypolimnion

• gas exchange at the surface, turbulent exchange,sedimentation of organic particles

• respiration of algae and zooplankton and mineralization ofPOM and SPOM

Modelling Aquatic Ecosystems 2017 Lecture 4: Preview Extended Lake Models 44


Process Substances / Organisms RateHPO2−

4 O2 ALG ZOO POM SPOMgP gO gDM gDM gDM gDM

Growth of algae − + 1 ρgro,ALG

Respiration of algae + − −1 ρresp,ALG

Death of algae 0/+ 0/+ −1 YALG,death ρdeath,ALG

Growth of zooplankton 0/+ −−1

YZOO1

feYZOO

ρgro,ZOO

Respiration of zoopl. + − −1 ρresp,ZOO

Death of zooplankton 0/+ 0/+ −1 YZOO,death ρdeath,ZOO

Mineral. of org. part. + − −1 ρminer,POM

Min. of org. part. in sed. + − −1 ρminer,SPOM

Sed. of org. particles −1 1 ρsed,POM



0 50 100 150 200 250 300 350

0.00

0.02

0.04

0.06

0.08

0.10

C.HPO4.Epi, C.HPO4.Hypo

t

C.H

PO

4.E

pi, C

.HP

O4.

Hyp

o

C.HPO4.EpiC.HPO4.Hypo

0 50 100 150 200 250 300 350

05

1015

2025

C.O2.Epi, C.O2.Hypo

t

C.O

2.E

pi, C

.O2.

Hyp

o

C.O2.EpiC.O2.Hypo

0 50 100 150 200 250 300 350

01

23

45

67

C.ALG.Epi, C.ALG.Hypo

t

C.A

LG.E

pi, C

.ALG

.Hyp

o

C.ALG.EpiC.ALG.Hypo

0 50 100 150 200 250 300 350

0.0

0.2

0.4

0.6

0.8

C.ZOO.Epi, C.ZOO.Hypo

t

C.Z

OO

.Epi

, C.Z

OO

.Hyp

o

C.ZOO.EpiC.ZOO.Hypo

0 50 100 150 200 250 300 350

0.0

0.5

1.0

1.5

2.0

C.POM.Epi, C.POM.Hypo

t

C.P

OM

.Epi

, C.P

OM

.Hyp

o

C.POM.EpiC.POM.Hypo

0 50 100 150 200 250 300 350

05

1015

2025

D.POM.Hypo

t

D.P

OM

.Hyp

o

D.POM.Hypo


Biogeochemical-Ecological Lake Model

Model extensions for model 9.4:

• We differentiate degradable (POMD, SPOMD) and inert(POMI and SPOMI) fractions

• We add ammonium (NH+4 ) and nitrate (NO−

3 ) as statevariables, and consider nitrification.

• We add anoxic mineralization in the sediment as additionalprocesses leading to oxygen depletion and denitrification.



Process Substances / Organisms RateHPO2−

4 NH+4 NO−

3 O2 ALG ZOO POMD POMI SPOMD SPOMIgP gN gN gO gDM gDM gDM gDM gDM gDM

Gro. ALG NO3 − − + 1 ρgro,ALG,NO3

Gro. ALG NH4 − − + 1 ρgro,ALG,NH4

Resp. ALG + + − −1 ρresp,ALG

Death ALG 0/+ 0/+ 0/+ −1 (1 − fI)·YALG,death

fI· YALG,death ρdeath,ALG

Gro. ZOO + + −−1

YZOO1

(1− fI)fe

YZOO

fIfe

YZOOρgro,ZOO

Resp. ZOO + + − −1 ρresp,ZOO

Death ZOO 0/+ 0/+ 0/+ −1 (1 − fI)·YZOO,death

fI· YZOO,death ρdeath,ZOO

Nitri. −1 + − ρnitri

Oxic mineral. + + − −1 ρminer,ox,POM

Ox. min. sed. + + − −1 ρminer,ox,SPOM

Anox. min. sed. + + − −1 ρminer,anox,SPOM

Sed. POMD −1 1 ρsed,POMD

Sed. POMI −1 1 ρsed,POMI



Rates (1):

ρgro,ALG,NH4 = kgro,ALG·exp(βALG(T−T0)

)· 1λh log

(KI + I0

KI + I0 exp(−λh)

)

·min(

CHPO4

KHPO4 + CHPO4,

CNH4 + CNO3

KN + CNH4 + CNO3

)· pNH4CNH4

pNH4CNH4 + CNO3·CALG

ρgro,ALG,NO3 = kgro,ALG·exp(βALG(T−T0)

)· 1λh log

(KI + I0

KI + I0 exp(−λh)

)

·min(

CHPO4

KHPO4 + CHPO4,

CNH4 + CNO3

KN + CNH4 + CNO3

)· CNO3

pNH4CNH4 + CNO3·CALG



Rates (2):

ρresp,ALG = kresp,ALG · exp(βALG(T − T0)

)· CO2

KO2 + CO2· CALG

ρdeath,ALG = kdeath,ALG · CALG

ρgro,ZOO = kgro,ZOO · exp(βALG(T − T0)

)· CO2

KO2 + CO2· CALG · CZOO

ρresp,ZOO = kresp,ZOO · exp(βZOO(T − T0)

)· CO2

KO2 + CO2· CZOO

ρdeath,ZOO = kdeath,ZOO · CZOO



Rates (3):

ρnitri = knitri·exp(βBAC(T−T0)

)·min

(CNH4

KNH4,nitri + CNH4,

CO2

KO2,nitri + CO2

)



Rates (4):

ρminer,ox,POM = kminer,ox,POM·exp(βBAC(T−T0)

)· CO2

KO2,miner + CO2·CPOMD

ρminer,ox,SPOM = kminer,ox,SPOM · exp(βBAC(T − T0)

)· CO2

KO2,miner + CO2· CSPOMD

KPOM,miner,sed + CSPOMD

ρminer,anox,SPOM = kminer,anox,SPOM · exp(βBAC(T − T0)

)· CNO3

KNO3,miner + CNO3·(

CSPOMD

KPOM,miner,sed + CSPOMD

)2



Rates (5):

ρsed,POMD = vsed,POM

hhypo· CPOMD

ρsed,POMI = vsed,POM

hhypo· CPOMI



Fluxes:

J epiint,O2 = vex,O2 A (CO2,sat − CO2)

Jepi meta = AmetaKz,metahmeta

(Cepi −Chypo)

J epi metaPOMD = Ameta vsed,POM C epi

POMD

J epi metaPOMI = Ameta vsed,POM C epi

POMI



0 100 300 500 700

0.00

0.04

0.08

0.12

C.NH4.Epi, C.NH4.Hypo

t

C.N

H4.

Epi

, C.N

H4.

Hyp

o

C.NH4.EpiC.NH4.Hypo

0 100 300 500 700

0.0

0.2

0.4

0.6

0.8

C.NO3.Epi, C.NO3.Hypo

t

C.N

O3.

Epi

, C.N

O3.

Hyp

o

C.NO3.EpiC.NO3.Hypo

0 100 300 500 700

0.00

0.02

0.04

0.06

0.08

0.10


t

C.H

PO

4.E

pi, C

.HP

O4.

Hyp

o


0 100 300 500 700

05

1015

2025

C.O2.Epi, C.O2.Hypo

t

C.O

2.E

pi, C

.O2.

Hyp

o

C.O2.EpiC.O2.Hypo

0 100 300 500 700

01

23

45

67


t

C.A

LG.E

pi, C

.ALG

.Hyp

o

C.ALG.EpiC.ALG.Hypo

0 100 300 500 700

0.0

0.2

0.4

0.6

0.8


t

C.Z

OO

.Epi

, C.Z

OO

.Hyp

o

C.ZOO.EpiC.ZOO.Hypo

0 100 300 500 700

0.0

0.5

1.0

1.5

C.POMD.Epi, C.POMD.Hypo

t

C.P

OM

D.E

pi, C

.PO

MD

.Hyp

o C.POMD.EpiC.POMD.Hypo

0 100 300 500 700

0.0

0.1

0.2

0.3

0.4

C.POMI.Epi, C.POMI.Hypo

t

C.P

OM

I.Epi

, C.P

OM

I.Hyp

o

C.POMI.EpiC.POMI.Hypo

0 100 300 500 700

010

2030

40

D.POMD.Hypo, D.POMI.Hypo

t

D.P

OM

D.H

ypo,

D.P

OM

I.Hyp

o D.POMD.HypoD.POMI.HypoModelling Aquatic Ecosystems 2017 Lecture 4: Preview Extended Lake Models 55


0 100 300 500 700

0.00

0.04

0.08

0.12

C.NH4.Epi, C.NH4.Hypo

t

C.N

H4.

Epi

, C.N

H4.

Hyp

o

C.NH4.EpiC.NH4.Hypo

0 100 300 500 700

0.0

0.2

0.4

0.6

0.8

C.NO3.Epi, C.NO3.Hypo

t

C.N

O3.

Epi

, C.N

O3.

Hyp

o

C.NO3.EpiC.NO3.Hypo

0 100 300 500 700

0.00

0.02

0.04

0.06

0.08

0.10


t

C.H

PO

4.E

pi, C

.HP

O4.

Hyp

o


0 100 300 500 700

05

1015

2025

C.O2.Epi, C.O2.Hypo

t

C.O

2.E

pi, C

.O2.

Hyp

o

C.O2.EpiC.O2.Hypo

0 100 300 500 700

01

23

45

67


t

C.A

LG.E

pi, C

.ALG

.Hyp

o

C.ALG.EpiC.ALG.Hypo

0 100 300 500 700

0.0

0.2

0.4

0.6

0.8


t

C.Z

OO

.Epi

, C.Z

OO

.Hyp

o

C.ZOO.EpiC.ZOO.Hypo

0 100 300 500 700

0.0

0.5

1.0

1.5

C.POMD.Epi, C.POMD.Hypo

t

C.P

OM

D.E

pi, C

.PO

MD

.Hyp

o C.POMD.EpiC.POMD.Hypo

0 100 300 500 700

0.0

0.1

0.2

0.3

0.4

C.POMI.Epi, C.POMI.Hypo

t

C.P

OM

I.Epi

, C.P

OM

I.Hyp

o

C.POMI.EpiC.POMI.Hypo

0 100 300 500 700

010

2030

40

D.POMD.Hypo, D.POMI.Hypo

t

D.P

OM

D.H

ypo,

D.P

OM

I.Hyp

o D.POMD.HypoD.POMI.Hypo


Exercises

1. Introduction to R and the ecosim package.Demonstration of the implementation of a simple lakephytoplankton model.

2. Phytoplankton-zooplankton model for a mixed lake.

3. Practice of stoichiometric calculations.Introduction to the stoichcalc package.

4. Two box lake model for plankton and biogeochemical cycles.

5. River benthos and water column model with sessile algae andbacteria and O, P and N cycles

6. Consideration of environmental stochasticity and uncertainty.

Modelling Aquatic Ecosystems 2017 Lecture 4: Outlook 57

Outlook Lecture 5

• Physical processes in Lakes

• Mass balance in multibox systems

• Mass balance in continuous systems

• Transport and mixing in lakes

• Sedimentation, gas exchange

Modelling Aquatic Ecosystems 2017 Lecture 4: Outlook 58

Modelling Aquatic Ecosystems - Course 701-0426-00, · PDF fileModelling Aquatic Ecosystems...

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