introduction to biogeochemical modelling (elements of...

ECEM’07 WorkshopBiogeochemical processes and fish dynamics in food web models forend-to-end conceptualisation of marine ecosystems.Theory and use of Ecopath with Ecosim.

Introduction to biogeochemical modelling(elements of system theory and language ..) (C. Solidoro )


A model is a representation of reality

(it captures essential features/particular aspects of reality)

tools for:

PREDICTION

UNDERSTANDING


two words about MODELS……Knowledge, in every field, is the result of a number of steps:

gathering of empirical information, also through collection direct observation

empirical understanding of phenomena (i.e. identification of relationships among vairables).

theoretical understanding of relationships amongvairables, (hypothesis of cause- effect mechanisms, identification of conceptual models, quantitativeunderstanding of phenomena (set up of a THEORY)

collection new data for corroboration /falsificationmodel

application of the model to new problems


different purposes, different representations ..

different models ..

statistic modelsdeterministic modelsstochastic models

toy modelsprocesses oriented models

numerical model


REALSIM

ACCURACY

Accurately describe specific situationsMay perform worse in other situationsTypically detailed

Account for known relationshipsMay be complex

GENERALITYApplicable in most situationsDon’t predict specific outcomes wellTypically “simple”Good for exploring relationships

(functionality)

(performance)

toy

proc orien

numeric

applied models

theoreticalmodels

functionalmodels

Modified from Levins (1968)


BGC models usually are:

deterministic

process oriented

(simple),

spatially resolved (coupled to transport models)

GENERALITY ACCURACY

REALSIM


DETERMINISTIC MODELS

Basic idea:1. a system (the piece of reality we are interested

in) can be efficiently described by a finite number of variables (state variables),

2. both the system and its evolution in time can be explained as a function of interactions (input, boundary conditions, controls) among the system and the remaining part of the universe


fitofito

Timescale

virus

zoofish

zoo

Space scale

small scales implie that in most case studies we have spatial heterogeinity and need of transport model


1m-1 years

50m – 10 km

Up to mesoscale

Dickey 2001


Coupling hydrodynamical and biological modules

[ ]>′′<−Θ∇∇+Θ∇⋅−=∂Θ∂ θukUt ii

igeneric passive tracer

[ ] ( )..,,, IITTqukUt ii

i ′+′+′+Θ+>′′<−Θ∇∇+Θ∇⋅−=∂Θ∂ θθ

generic active tracer

[ ] ( )..,,, ITqukUt ii

i Θ+>′′<−Θ∇∇+Θ∇⋅−=∂Θ∂ θ

proper time scale (x-y vs z; biology “slow”)

( )..,,,2 ITqz

wz

Kz

kUt

isi

iviHhi

i Θ+∂Θ∂

+⎥⎦

⎤⎢⎣

⎡∂Θ∂

∂∂

+Θ∇+Θ∇⋅−=∂Θ∂

standard formulationCrise et al. 2001


Biogeochemical ModelSet of Advection-Diffusion-Reaction equations:Conservation laws with source and sink terms

biophys tc

tc

tc

∂∂

+∂∂

=∂∂

)()()( cRcDcAtc

biophysphys ++=∂∂

Lineartransport term

Non linearreaction term

physic biology


0D application

(Rinaldi, Gatto, ….)

( )..,,, ITqt

i Θ=∂Θ∂

‘toys model’ ma anche applicazioni

( )..,,, ITqz

wz

Kzt

isi

iv

i Θ+∂Θ∂

+⎥⎦

⎤⎢⎣

⎡∂Θ∂

∂∂

=∂Θ∂orrizont. omogeno 1D

(many ! DCM jamart,77, varela 92,94)

‘process oriented model’

( )..,,,2 ITqkUt iHhi

i Θ+Θ∇+Θ∇⋅−=∂Θ∂

vert. omogeno 2D

(not very frequent)


Venice Lagoon

Adriatic Sea

Lido inlet

Malamocco inlet

Chioggia inlet

Can. d. Navi

Can. Giudecca

Is. S.ErasmoSIL

DES

LUS

OSE

TAG

NAV

MON

CUO

Venice

Can. S.Nicolò

Can. Treporti

ARIARadiazione

luminosaScambiotermico

Temperaturaacqua

Scambioattraverso lebocche

MAREADRIATICO

Det. N

Det. PDet. C

Zoo Fito Oxy

Inputdallagrondalagunare

BACINOSCOLANTE

diporto

RP

N-NOx-

N-NH4+

2N

P NSedimento

C

DeposizioniatmosfericheN, P

)()()( cRcDcAtc

biophysphys ++=∂∂

Solidoro et al 1995, 2004, 2005


Numerical Integration

physic submodel

COUPLING

forcing and parameters

biological submodel

new state

Operator splittingtechnique: forcings and

parameters are input foreach of the two

subsystems for the derivative computation in the proper time step. The

derivatives are coupledafterwards, allowing

different time steps forthe two processes and

therefore optimising the computational resources


( )..,,, ITq ΘThe BIOLOGICAL term

AmmoniaNitrate

Phosphate

Detritus

Netplankton106:16:1

Picoplankton106:16:1

Zooplankton48:12:1

VariableC:N:P ratio

PP

NN

DD

[N,P,D]

BGC meansN-P-C cycles ..


.. The microbial loop ..

phyto

zoo

nut

det

doc

bac

µzoo

don

azam, fenchel, thingstand, rassoulzadegan


Sinking vs recycling Fasham 1990


The mistivourous food web ( a continuum ..)

Legendere & Rassoulzadegan 1995


It is relatively straightforward toformulate more complex models toinclude explicitly differentfunctional groups of phytoplankton, zooplankton and bacteria, and toinclude regulation by multiple nutrients such anitrate, ammonium, silica, and iron.

Denman 2003


Proto-zooplankton Meso-zooplankton

Macro-zooplankton

DON(N

d)

DON(N

d) Phytoplankton

(P)

Phytoplankton(P) Nitrate

(No)

Nitrate(N

o)

Amonium(N

r)

Amonium(N

r)

Bacteria(B)

Bacteria(B) Zooplankton

(Z)

Zooplankton(Z) Detritus

(D)

Detritus(D)

Net-PhytoplanktonP2

Net-PhytoplanktonP2 Meso-Zooplankton

Z1

Meso-ZooplanktonZ1 Amonium

(Nr)

Amonium(N

r)

Nitrate(N

o)

Nitrate(N

o) Detritus

(D)

Detritus(D) DON

(Nd)

DON(N

d)

Pico-PhytoplanktonP1

Pico-PhytoplanktonP1 Protozoos

Z2

ProtozoosZ2 Bacteria

(B)

Bacteria(B)

Disolved inorganicnitrogen

Disolved inorganic

phosphorous

Phytoplankton

N P

Dyazotrophs

N P

Zooplankton

N P

Detritalnitrogen

Detritalphosphorous

Sinking Sinking

Dinitrogen

Fennel

FUNCTIONAL TYPES

DYNAMIC GREEN MODEL

GENERALITY ACCURACY

REALSIM

Pico-heterotrophs

Pico-autotrophs

Phyt

opla

nkto

nN

2-fix

ers

Phyt

opla

nkto

n ca

lcifi

ers

Phyt

opla

nkto

n D

MS-

prod

ucer

s

Mixed-phytoplanktonPhytoplankton silicifiers


Diatoms

Flagellates

Picophytoplankton

L PhotoadaptationLP(1)

Large Phyto.LP(4)

LP(2)

LP(3)

Oxygen

Carbon dioxide

O Dissolved GasesO(2)

O(3)

PhosphateNitrateAmmonium

Silicate

N Inorganic NutrientsN(1)

N(3)

N(5)

Red. EquivalentsN(6)

N(4)

ZMicrozooplankton

(s.s.)Heterotrophicnanoflagellates

MicrozooplanktonZi

(5)

Zi(6)

Carnivorous

Omnivorous

Z Mesozooplankton

Zi(3)

Zi(4)

B

Bacteria (aerobic

and anaerobic)

Bacterioplankton

Bi

Dissolved

Particulate (detritus)

R Organic Matter

Ri(1)

Ri(6)

Diatoms

Flagellates

Picophytoplankton

P PhytoplanktonPi

(1)

Large Phyto.Pi(4)

Pi(2)

Pi(3)

Vectors (Functional Group or Ordinary State Variables)

Organic matter flow (C,N,P,Si)

Inorganic nutrient flow (N,P,Si)

Gas exchange

Benthic-Pelagflow

Scalars (Ordinary State Variables)

Z

BFM

(ersem)


Street & phelps 27 Riley, 46 Steele, 60…..…..La Querelle 06

( … but problems still exist )


It is relatively straightforward to formulate more complex models …..

Why many BGC models like to be simple (rough?)


However, the number of parameters thatmust be specified from observationsincreases approximately as the square of the number of compartments and quicklysurpasses our ability to constrainthem properly from observations. Moreover, ecosystem models often becomeunstable for small changes in parametervalues, and increasing complexity may notlead to increased stability.

Denman 2003


the number of parameters will usually begreater than nember of fluxes

FASHAM 28 parPFT 100-200 ??

Probablity of Instability, abrupt changes, chaosincrease …. EVEN for FORCED model

May 73, Smale 76, Kuztnesov 93


…calibration is not the answer

Not all paraemters can be identified by calibration(fitting vs experiemtnal observation)

problems are:over and/or underdetermination (# eqs vx # unknown)no exact solutionexistence of multiple optimal solutions

(there are more than one combianation of parameterswhich give the same fit. This is WITHIN equations and cannot be solved)

hnnVm +

=NfSolidoro 2003Matear 2001Vallino 2000


How complex a model should be still is anopen question.

Costanza & Sklar (1985)

The main recommendation is that the use of a single ultimate’ecosystem model is ill-advised, while the omparative and confirmatory use of multiple ‘minimum-realistic’ models isstrongly recommended. (Fulton 2003 ?)


In addition we want to be 3D …

… Deades long integration of transport + 50 variables for grid point over 100 meter gridcovering thousands of square kilometers, …

GENERALITY ACCURACY

REALSIM

?


Attempts at simplify (paraemterization) exist ..

Steele 98

implicit treatment of the microbialloop. the proportion oftotal grazing thatflows directly tomesozooplankton, can vary accordingto nitrateavailability or total phytoplankton

.. but also Armstrong, Denman …


kintetics (choice functinal forms)

structure identification (box and arrows)

First parameter choice

Sensitivit analysis

calibration

corroboration (validation)

applications

After structure identification one has tochoose kinetics and paraemters


Standard complexitypelagicmodel

Cossarini e Solidoro 2006


[ ]PhyPhyPhyPhy sgrazingmortrespgrowth

dtPhyd ink−−−−=

[ ]ZooZooZoo excretmortgrazingKeff

dtZood

−−⋅= equations in the water quality submodel(mass balances)

[ ] [ ] { } nitrificdecaydecayexcretresprNNHgrowthr

dtNHd

SedNDetNZooPhynctot

Phync −+++⋅+⋅⋅−=++44

[ ] [ ] denitrifnitrificNNOgrowthr

dtNOd

tot

phync −+⋅⋅−=−−33

[ ] { } SedPDetPZooPhypcPhypc decaydecayexcretresprgrowthrdt

POd+++⋅+⋅−=

−34

[ ] ( ) DetCDetNPhytoZooZoo sinkdecaymortmortgrazingKeffdt

DetCd−−++⋅−= 1

[ ] ( ){ } DetNDetCZooPhyZoonc sinkdecaymortmortgrazingKeffrdt

DetNd−−++⋅−⋅= 1

[ ] ( ){ } DetPDetPZooPhyZoopc inksdecaymortmortgrazingKeffrdt

DetPd−−++⋅−⋅= 1

[ ]SedChyPDetC decaysinksink

dtSedCd

−+=

[ ]SedNhyPncDetN decaysinkrsink

dtSedNd

−⋅+=

[ ]SedPhyPpcDetP decaysinkrsink

dtSedPd

−⋅+=

[ ] [ ] [ ]( )OxyDOKrearnitrificardecaydecayrespgrowthrdtOxyd

satnoSedCDetCPhytoPhyoc −⋅+⋅−−−−⋅=


{ } [ ]PhyFFFFGPgrowth PNTIPhy ⋅⋅⋅⋅⋅= max

⎟⎟⎠

⎞⎜⎜⎝

⎛−

= opt

k

II

opt

kI e

IIF

1

( )( )

)()(

max

maxmax

opt

opt

TTmTT

opt

mT e

TTTTF −⋅

−⋅

⋅⎥⎥⎦

⎤

⎢⎢⎣

⎡

−−

= αα [ ]totNtot NKN +=NF

[ ] [ ][ ]−− += 34

34 POKPOF PP

[ ] [ ]−+ += 34tot NHN NO

[ ] ⎟⎟⎠

⎞⎜⎜⎝

⎛∫ ⋅+⋅−

⋅=k

Phy dzPhyKselfkKest

sunk eII 0

( )maxm ,TminT T=

[ ] [ ][ ]OxyKOxyF oxyoxy +=

[ ];10det DetXFQKdecdecay oxyDetX ⋅⋅⋅=

[ ]( ) 103 119.0 QKdeniNOdenitrif ⋅−⋅= −


Mostly empirical, with a posteriori ‘phyisological’ derivation


GPmax 0.18 [h-1] max growth rate for phyto (optimal values of T , I and nutrients)KmPho 0.006 [h-1]death rate for phytoplanktonKrPhy 0.003 [h-1]respiration rate for phytoplanktonKN 0.05 [mg N/L] halfsaturation constant for nitrogen assimilationKP 0.01 [mg P/L] halfsaturation constant for phosphorus assimilationTopt 27 [° C] optimal temperature for phytoplankton growthTmaxx 41 [°C] inhibition temperature for phytoplankton growth ? 0.15 [°C-1] Lassiter e Kearnes exponential coefficient rnc 0.15 mg N/mg C N/C ratio in phytoplankton (Redfield ratio)rpc 0.023 mg P/mg ] N/C ratio in phytoplankton (Redfield ratio)Light parametersIopt 50000 [lux]optimal light for phytoplankton growthKselfPhy 4. [mg C-Phy/L] self-shading coefficient for phytoplanktonKest 1.0 [m-1] shading coefficient Parameters of zooplankton dynamicKgr 0.04 [h-1] max grazing rate Kgphyto 1. [mg C-Fito/L] halfsaturation constant for grazing formulationKmZoo 0.006 [h-1]death rate for zooplankton KeffZoo 0.5 [dimensionless] grazing efficiency KeZoo 0.002 [h-1]excretion rate for zooplankton Parameters of nitrogen dynamicKnit 0.0043 [h-1] nitrification rate at 20°CKdenii 1.6 [mg NO3-/l/h] denitrification rateParameters of sediment and detritus dynamicsKdecDet 0.0048 [h-1] decay rate of organic detritus at 20° C

…….

28 parametri


1. choose subset parameters Sensitivity analysis ,Tuning importanceRanking of parameters

what’s the purpose ?What about data ?What about error in data?

2. Define cost function

IF you can .(data assimilation,Adjoint, simplex brute force..)

3. Get parameter values by fitting

There is not sucha thing as a model, but only a model for a purpose

Tuning is possible for subsets of parameters


..validation …

..capability to fit new data

Need to define a skill function


authors Dim Area Temporal Scale

Spatial Scale

Physical submodel

Biological submodel Coupling Objective

Prod I

Prod. II

Nutr Det/ Doc

Bact DO T L Nutr Turb

Morel & Andre 91 0D West Med

Year Basin - 1 - - - - - - L - - Pr. Prod. From CZCS

Antoine et al. 95 0D East Med

Year Basin - 1 - - - - - - L - - Pr. Prod. From CZCS

Bethoux 91 box Med Sea Asymptotic Basin box - - N,P - - - - - - - Nutrient Balances Sarmiento et al 88 Box Med Sea Asymptotic Basin Box - - PO4 - - DO - - - - Nutrient Balances &

Anoxia Klein & Coste 84 1D NW Med Days 50m Mellor

Yamada 2 - - Nut - - - - - Nut - Influence Wind

Nut. as passive tracer Varela et al 92 1D NW Med Days 200 m Mellor

Yamada 2 2 1 Nrid

Nox - - - T L Nut - Influence Focings on

DCM Zakardijan &

Prieur 94 1D West Med months 200m - 1 1 Nrid

Nox - - DO - L Nut Turr Influence Turbulence

Allen et al. 98 1D Adriatic year 200 m Mellor Yamada 2

E R S E M T L Nut - Ecosystem Study

Tusseau et al 97 1D Ligurian Sea Year 200 m Termal

2 (physiological)

- Nrid Nox Si

DetSi Dom1 (mono) Dom2 (poly)

Bac - T L Nut - Calibrated. Used as Bound Condition for

3D Simulations. Levi et al. 98 1D Ligurian Sea Year 100m Box 1 2 Nrid

Nox

Doms Doml Dets Detl

Bac T L Nut - Fluxes Eval.

Solidoro et al. 98 1D Tirrenian Sea year 100 m diffusive 2 1 Nrid Nox PO4

DetN DetP DetC

- DO T L Nut - Sensitivity Analisys

Napolitano et al. 97 1D Ionian, Rhodus Gyre

year 200 m Mellor Yamada 2.5

1 1 Nrid Nox

Det - - T L Nut - Ecosystem Study

Pinazo et al 96 3D Gulf of Lions 20 days 250 Km Full 2.5

1 - Nrid Nox Q

DetN DetC - DO T L Nut - Influence Forcing & Nut. Cycle

Civitarese et al. 96 3D Ionian Sea Year 200 Km MOM 1 - N D - - T L Nut - Nutrient Balance Tusseau et al. 98 3D Gulf of Lions Year 200 Km General

Circulat. 2

(physiological)

- Nrid Nox Si

DetSi Dom1 (mono) Dom2 (poly)

Bac - T L Nut - Fluxes Eval.

Bergamasco et al. 98

3D North Adriatic months 100 Km POM (nesting off

line)

1 - N - - DO T L Nut - Fluxes, Nesting , Influence Biology

Zavatarelli et al. 98 3D Adriatic year 800 Km POM (MY 2.5)

ERSEM T L Nut - Ecosystem Study

Crise et al 98; Crispi et al. 99

3D Mediterranean years basin MOM 1 - N DetN - - T L Nut - Ecosystem Study

Crispi et al. 98 3D Mediterranean years basin MOM 2 1 Nrid Nox PO4

DetN DetP DetC

- DO T L Nut - Ecosystem Study

BGC have shownto be reliableenough tobe increasinglyused in application …

Arhonditsis & Brett 2003


APP MED SEA

Crise et al 2001


Understanding system functioning

Crise et al 2001


APP VENEZIA

2041.63612 145

35109

6

DIN9.5

Phyto Zoo

Losses1099 Recycling

102 5.024833

36122

43

69

DIN Phyto Zoo

Losses

69 3.4 0.2769427 17

234 7

SouthernSubbasinVol. 0.15 kmSurf. 90 km

3

2

DINPhyto Zoo

Losses

Recycling

1

491

1265

982

1324

601

682

1431

1034

21

1017

471

828

317

63580

1

388

1029

47

CentralSubbasinVol. 0.21 kmSurf. 110 km

3

2

NorthernSubbasinVol. 0.32 kmSurf. 186 km

3

2

Adr

iatic

Sea

Dr a

inag

e B

asin

0.4

Recycling

Solidoro et al 2004


-0.7384.73

0.842

0.340.34

2.52

0.2194.07

0.944

1.260.05

2.05

4.97

0.058

2.02

9.595

1.685

-3.96

-1.097

-0.044

-0.119

Fitoplancton0.024 mg N/l

NO3-

0.46 mg N/l

NH4+

0.06 mg N/l

Zooplancton0.0023 mgN/l

Detrito N0.013mgN/l

Sedimento N0.041mg N/m2

0.3611

+ AQUACULTURE+ control Nutrient load+ DA

Solidoro et al 2001, Pastres et al. 2001, Cossarini et al. 2004


base for end-to-end conceptualization marine ecosystem

virus

whale

fitozoo

fish

Space scale

Timescale


…another chapter of the story …


Evolution of Mediterranean Ecosystem Models

Green = Box,Conceptual,reviews 6

Yellow = 1D BGC N 12

Grey = 1D BGC multinutrient 4

Magenta = 1D BGC ERSEM 7

Turquoise = 3D BGC 19 (6 ERSEM)

White = Data assimilation 9


virus

whale

fitozoo

fish

space scale

timescale

biological resolution

TL

E2E vs EcApp ??

introduction to biogeochemical modelling (elements of...

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