modeling ocean biogeochemistry
DESCRIPTION
Modeling Ocean Biogeochemistry. Galen A. McKinley University of Wisconsin - Madison ASP Summer School - Art of Climate Modeling June 7, 2006. What is Ocean Biogeochemistry?. Biology - micro-scale Chemistry - organic and inorganic Geology - interactions with solid Earth - PowerPoint PPT PresentationTRANSCRIPT
Modeling Ocean Modeling Ocean BiogeochemistryBiogeochemistryModeling Ocean Modeling Ocean BiogeochemistryBiogeochemistry
Galen A. McKinleyGalen A. McKinleyUniversity of Wisconsin - MadisonUniversity of Wisconsin - Madison
ASP Summer School - Art of Climate ASP Summer School - Art of Climate ModelingModeling
June 7, 2006June 7, 2006
Galen A. McKinleyGalen A. McKinleyUniversity of Wisconsin - MadisonUniversity of Wisconsin - Madison
ASP Summer School - Art of Climate ASP Summer School - Art of Climate ModelingModeling
June 7, 2006June 7, 2006
What is Ocean What is Ocean Biogeochemistry?Biogeochemistry?
What is Ocean What is Ocean Biogeochemistry?Biogeochemistry?
Biology - micro-scaleBiology - micro-scale Chemistry - organic and inorganicChemistry - organic and inorganic Geology - interactions with solid EarthGeology - interactions with solid Earth Physical interactions Physical interactions
Air-sea exchange; Particle settling rates; Air-sea exchange; Particle settling rates; Advection, diffusion, mixingAdvection, diffusion, mixing
Individual processes and systematics Individual processes and systematics are of key interestare of key interest
Biology - micro-scaleBiology - micro-scale Chemistry - organic and inorganicChemistry - organic and inorganic Geology - interactions with solid EarthGeology - interactions with solid Earth Physical interactions Physical interactions
Air-sea exchange; Particle settling rates; Air-sea exchange; Particle settling rates; Advection, diffusion, mixingAdvection, diffusion, mixing
Individual processes and systematics Individual processes and systematics are of key interestare of key interest
Why include Why include biogeochemistry in ocean biogeochemistry in ocean
models?models?
Why include Why include biogeochemistry in ocean biogeochemistry in ocean
models?models? Carbon CycleCarbon Cycle
Ocean carbon sink - past, present, Ocean carbon sink - past, present, futurefuture
Glacial / interglacial change Glacial / interglacial change
Trace gas emissions - Atm. chemistryTrace gas emissions - Atm. chemistry e.g. Dimethyl Sulfide (DMS): CCN, e.g. Dimethyl Sulfide (DMS): CCN,
emitted by phytoplankton, theorized emitted by phytoplankton, theorized climate feedbacksclimate feedbacks
Carbon CycleCarbon Cycle Ocean carbon sink - past, present, Ocean carbon sink - past, present,
futurefuture Glacial / interglacial change Glacial / interglacial change
Trace gas emissions - Atm. chemistryTrace gas emissions - Atm. chemistry e.g. Dimethyl Sulfide (DMS): CCN, e.g. Dimethyl Sulfide (DMS): CCN,
emitted by phytoplankton, theorized emitted by phytoplankton, theorized climate feedbacksclimate feedbacks
The ocean has absorbed 48% The ocean has absorbed 48% of anthropogenic COof anthropogenic CO22 emitted in emitted in
last 200 yrslast 200 yrs (Sabine et al., 2004)(Sabine et al., 2004)
Why include Why include biogeochemistry in ocean biogeochemistry in ocean
models?models?
Why include Why include biogeochemistry in ocean biogeochemistry in ocean
models?models? Carbon CycleCarbon Cycle
Ocean carbon sink - past, present, Ocean carbon sink - past, present, futurefuture
Glacial / interglacial change Glacial / interglacial change
Trace gas emissions - Atm. chemistryTrace gas emissions - Atm. chemistry e.g. Dimethyl Sulfide (DMS): CCN, e.g. Dimethyl Sulfide (DMS): CCN,
emitted by phytoplankton, theorized emitted by phytoplankton, theorized climate feedbacksclimate feedbacks
Carbon CycleCarbon Cycle Ocean carbon sink - past, present, Ocean carbon sink - past, present,
futurefuture Glacial / interglacial change Glacial / interglacial change
Trace gas emissions - Atm. chemistryTrace gas emissions - Atm. chemistry e.g. Dimethyl Sulfide (DMS): CCN, e.g. Dimethyl Sulfide (DMS): CCN,
emitted by phytoplankton, theorized emitted by phytoplankton, theorized climate feedbacksclimate feedbacks
Tem
pera
ture
pro
xyT
empe
ratu
re p
roxy
Why include Why include biogeochemistry in ocean biogeochemistry in ocean
models?models?
Why include Why include biogeochemistry in ocean biogeochemistry in ocean
models?models? Carbon CycleCarbon Cycle
Ocean carbon sink - past, present, Ocean carbon sink - past, present, futurefuture
Glacial / interglacial change Glacial / interglacial change
Trace gas emissions - Atm. chemistryTrace gas emissions - Atm. chemistry e.g. Dimethyl Sulfide (DMS): CCN, e.g. Dimethyl Sulfide (DMS): CCN,
emitted by phytoplankton, theorized emitted by phytoplankton, theorized climate feedbacksclimate feedbacks
Carbon CycleCarbon Cycle Ocean carbon sink - past, present, Ocean carbon sink - past, present,
futurefuture Glacial / interglacial change Glacial / interglacial change
Trace gas emissions - Atm. chemistryTrace gas emissions - Atm. chemistry e.g. Dimethyl Sulfide (DMS): CCN, e.g. Dimethyl Sulfide (DMS): CCN,
emitted by phytoplankton, theorized emitted by phytoplankton, theorized climate feedbacksclimate feedbacks
OutlineOutlineOutlineOutline
Carbon cycleCarbon cycle ObservationsObservations Key chemistryKey chemistry Large-scale processesLarge-scale processes
Modeling strategies and challengesModeling strategies and challenges
Selected resultsSelected results
Carbon cycleCarbon cycle ObservationsObservations Key chemistryKey chemistry Large-scale processesLarge-scale processes
Modeling strategies and challengesModeling strategies and challenges
Selected resultsSelected results
1980’s estimates from Sarmiento & Gruber (2002)
The Carbon CycleThe Carbon CycleThe Carbon CycleThe Carbon Cycle
Atlantic (A16) Atlantic (A16) Dissolved Inorganic Carbon Dissolved Inorganic Carbon
(DIC) (DIC) (umol/kg)(umol/kg)
Atlantic (A16) Atlantic (A16) Dissolved Inorganic Carbon Dissolved Inorganic Carbon
(DIC) (DIC) (umol/kg)(umol/kg)
Global sea-air COGlobal sea-air CO22 flux fluxGlobal sea-air COGlobal sea-air CO22 flux flux
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Takahashi et al. 2002Takahashi et al. 2002
Air-sea COAir-sea CO22 exchange exchangeAir-sea COAir-sea CO22 exchange exchange Air-sea exchange determined by air-Air-sea exchange determined by air-
water gradient of the partial pressure water gradient of the partial pressure of COof CO2 2 (pCO(pCO22): ):
pCOpCO22 = pCO = pCO22airair - pCO - pCO22
waterwater
And surface ocean turbulenceAnd surface ocean turbulence Parameterized with function of wind Parameterized with function of wind
speedspeed
pCOpCO22waterwater is determined by [H is determined by [H22COCO33
**],T,S],T,S
Air-sea exchange determined by air-Air-sea exchange determined by air-water gradient of the partial pressure water gradient of the partial pressure of COof CO2 2 (pCO(pCO22): ):
pCOpCO22 = pCO = pCO22airair - pCO - pCO22
waterwater
And surface ocean turbulenceAnd surface ocean turbulence Parameterized with function of wind Parameterized with function of wind
speedspeed
pCOpCO22waterwater is determined by [H is determined by [H22COCO33
**],T,S],T,S
Carbon Chemistry in Carbon Chemistry in SeawaterSeawater
Carbon Chemistry in Carbon Chemistry in SeawaterSeawater
Carbon reacts with waterCarbon reacts with water DIC = Dissolved Inorganic Carbon DIC = Dissolved Inorganic Carbon
= [CO= [CO22(aq)] + [H(aq)] + [H22COCO33] + [HCO] + [HCO33--] + [CO] + [CO33
==]]
= [H= [H22COCO33**] + [HCO] + [HCO33
--] + [CO] + [CO33==]]
At ocean pH, [HAt ocean pH, [H22COCO33**] only ~0.5% of ] only ~0.5% of
DIC. Thus, the balance of HCODIC. Thus, the balance of HCO33-- and and
COCO33== is key to setting pCO is key to setting pCO22
waterwater
Carbon reacts with waterCarbon reacts with water DIC = Dissolved Inorganic Carbon DIC = Dissolved Inorganic Carbon
= [CO= [CO22(aq)] + [H(aq)] + [H22COCO33] + [HCO] + [HCO33--] + [CO] + [CO33
==]]
= [H= [H22COCO33**] + [HCO] + [HCO33
--] + [CO] + [CO33==]]
At ocean pH, [HAt ocean pH, [H22COCO33**] only ~0.5% of ] only ~0.5% of
DIC. Thus, the balance of HCODIC. Thus, the balance of HCO33-- and and
COCO33== is key to setting pCO is key to setting pCO22
waterwater
What determines [HCOWhat determines [HCO33--] + ] +
[CO[CO33==]?]?
What determines [HCOWhat determines [HCO33--] + ] +
[CO[CO33==]?]?
Both the electronic charge and the Both the electronic charge and the carbon content of a parcelcarbon content of a parcel
Ocean charge balance = AlkalinityOcean charge balance = Alkalinity
Both the electronic charge and the Both the electronic charge and the carbon content of a parcelcarbon content of a parcel
Ocean charge balance = AlkalinityOcean charge balance = Alkalinity
AlkalinityAlkalinityAlkalinityAlkalinity Major Cations Major Cations = [Na= [Na++] + [K] + [K++] + 2[Mg] + 2[Mg++++] + 2 [Ca] + 2 [Ca++++] = ] =
+ 0.606 eq/kg+ 0.606 eq/kg Major Anions Major Anions = [Cl= [Cl--] + 2[SO4] + 2[SO4==] + [Br] + [Br--] = -0.604 eq/kg] = -0.604 eq/kg Global mean, difference is +0.002 eq/kgGlobal mean, difference is +0.002 eq/kg Carbon is one of the few elements that Carbon is one of the few elements that
can exist as ions of different charge, thus can exist as ions of different charge, thus it adjusts to balance the chargeit adjusts to balance the charge
Major Cations Major Cations = [Na= [Na++] + [K] + [K++] + 2[Mg] + 2[Mg++++] + 2 [Ca] + 2 [Ca++++] = ] =
+ 0.606 eq/kg+ 0.606 eq/kg Major Anions Major Anions = [Cl= [Cl--] + 2[SO4] + 2[SO4==] + [Br] + [Br--] = -0.604 eq/kg] = -0.604 eq/kg Global mean, difference is +0.002 eq/kgGlobal mean, difference is +0.002 eq/kg Carbon is one of the few elements that Carbon is one of the few elements that
can exist as ions of different charge, thus can exist as ions of different charge, thus it adjusts to balance the chargeit adjusts to balance the charge
AlkalinityAlkalinityAlkalinityAlkalinity
ALK = [NaALK = [Na++] + [K] + [K++] + 2[Mg] + 2[Mg++++] + 2 ] + 2 [Ca[Ca++++] - [Cl] - [Cl--] - 2[SO4] - 2[SO4==] - [Br] - [Br--] ]
≈ ≈ [HCO[HCO33--] + 2[CO] + 2[CO33
==]]
i.e. a change in alkalinity will alter i.e. a change in alkalinity will alter the distribution of the carbonate the distribution of the carbonate ionsions
ALK = [NaALK = [Na++] + [K] + [K++] + 2[Mg] + 2[Mg++++] + 2 ] + 2 [Ca[Ca++++] - [Cl] - [Cl--] - 2[SO4] - 2[SO4==] - [Br] - [Br--] ]
≈ ≈ [HCO[HCO33--] + 2[CO] + 2[CO33
==]]
i.e. a change in alkalinity will alter i.e. a change in alkalinity will alter the distribution of the carbonate the distribution of the carbonate ionsions
Simplified balance Simplified balance equationsequations
Simplified balance Simplified balance equationsequations
ALK ≈ [HCOALK ≈ [HCO33--] + 2[CO] + 2[CO33
==]]
DIC ≈ [HCODIC ≈ [HCO33--] + [CO] + [CO33
==]]
i.e. a parcel must both conserve i.e. a parcel must both conserve both its charge and its carbon both its charge and its carbon contentcontent
ALK ≈ [HCOALK ≈ [HCO33--] + 2[CO] + 2[CO33
==]]
DIC ≈ [HCODIC ≈ [HCO33--] + [CO] + [CO33
==]]
i.e. a parcel must both conserve i.e. a parcel must both conserve both its charge and its carbon both its charge and its carbon contentcontent
Rearranging and solvingRearranging and solvingRearranging and solvingRearranging and solving
[CO[CO33==] ≈ ALK - DIC ] ≈ ALK - DIC
[HCO[HCO33--] ≈ 2DIC - ALK] ≈ 2DIC - ALK
e.g. for constant DIC:e.g. for constant DIC:
if ALKif ALK, [CO, [CO33==]] and and
[HCO[HCO33--]]
[CO[CO33==] ≈ ALK - DIC ] ≈ ALK - DIC
[HCO[HCO33--] ≈ 2DIC - ALK] ≈ 2DIC - ALK
e.g. for constant DIC:e.g. for constant DIC:
if ALKif ALK, [CO, [CO33==]] and and
[HCO[HCO33--]]
What happens to [HWhat happens to [H22COCO33**] and ] and
pCOpCO22 as [CO as [CO33==]] and and
[HCO[HCO33--]]??
What happens to [HWhat happens to [H22COCO33**] and ] and
pCOpCO22 as [CO as [CO33==]] and and
[HCO[HCO33--]]?? Full equationFull equation
DIC = [HDIC = [H22COCO33**] + [HCO] + [HCO33
--] + [CO] + [CO33==]]
As balance shifts away from [COAs balance shifts away from [CO33==], [H], [H22COCO33
**] and ] and pCOpCO22
waterwater are increased are increased
Full equationFull equation
DIC = [HDIC = [H22COCO33**] + [HCO] + [HCO33
--] + [CO] + [CO33==]]
As balance shifts away from [COAs balance shifts away from [CO33==], [H], [H22COCO33
**] and ] and pCOpCO22
waterwater are increased are increased
Carbon chemistry: Carbon chemistry: SummarySummary
Carbon chemistry: Carbon chemistry: SummarySummary
pCOpCO22 key for air-sea exchange key for air-sea exchange
pCOpCO22waterwater a function of [H a function of [H22COCO33
**], T, S], T, S
[H[H22COCO33**] is a small part of total DIC, ] is a small part of total DIC,
determined by balance with other determined by balance with other ionsions
[HCO[HCO33--], [CO], [CO33
==] set by alkalinity, or ] set by alkalinity, or charge balancecharge balance
pCOpCO22 key for air-sea exchange key for air-sea exchange
pCOpCO22waterwater a function of [H a function of [H22COCO33
**], T, S], T, S
[H[H22COCO33**] is a small part of total DIC, ] is a small part of total DIC,
determined by balance with other determined by balance with other ionsions
[HCO[HCO33--], [CO], [CO33
==] set by alkalinity, or ] set by alkalinity, or charge balancecharge balance
Solubility PumpSolubility PumpSolubility PumpSolubility Pump
Temperature influenceTemperature influenceTemperature influenceTemperature influenceMean sea-air COMean sea-air CO22 flux flux
pCO2 pCO2
UpwellingUpwellingUpwellingUpwelling
Atlantic DIC Atlantic DIC
Biological ProcessesBiological ProcessesBiological ProcessesBiological Processes
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
SeaWiFS - NASA
Organic Carbon PumpOrganic Carbon PumpOrganic Carbon PumpOrganic Carbon Pump
Carbonate pumpCarbonate pumpCarbonate pumpCarbonate pump
Removes DIC to Removes DIC to depth, but also depth, but also reduces ALKreduces ALK
ALKALK, [CO, [CO33==]] and and
[HCO[HCO33--]]
pCOpCO22waterwater increased increased
Removes DIC to Removes DIC to depth, but also depth, but also reduces ALKreduces ALK
ALKALK, [CO, [CO33==]] and and
[HCO[HCO33--]]
pCOpCO22waterwater increased increased
Ecosystem ComplexityEcosystem ComplexityEcosystem ComplexityEcosystem Complexity There are ~20,000 of identified species of There are ~20,000 of identified species of
phytoplankton in 4 major groupsphytoplankton in 4 major groups PicoplanktonPicoplankton Diatoms (silicate shells)Diatoms (silicate shells) Coccolithophorids (carbonate shells)Coccolithophorids (carbonate shells) DinoflagellitesDinoflagellites
Zooplankton - also great varietyZooplankton - also great variety Much variability in key aspectsMuch variability in key aspects
Carbon to Nutrient, Carbon to Chlorophyll ratiosCarbon to Nutrient, Carbon to Chlorophyll ratios Sinking velocities Sinking velocities Growth rates, mortality rates, etc.Growth rates, mortality rates, etc.
There are ~20,000 of identified species of There are ~20,000 of identified species of phytoplankton in 4 major groupsphytoplankton in 4 major groups PicoplanktonPicoplankton Diatoms (silicate shells)Diatoms (silicate shells) Coccolithophorids (carbonate shells)Coccolithophorids (carbonate shells) DinoflagellitesDinoflagellites
Zooplankton - also great varietyZooplankton - also great variety Much variability in key aspectsMuch variability in key aspects
Carbon to Nutrient, Carbon to Chlorophyll ratiosCarbon to Nutrient, Carbon to Chlorophyll ratios Sinking velocities Sinking velocities Growth rates, mortality rates, etc.Growth rates, mortality rates, etc.
Best Modeling Strategy?Best Modeling Strategy?Best Modeling Strategy?Best Modeling Strategy?
Simple vs. Complex ?Simple vs. Complex ?
Simple EquationsSimple EquationsSimple EquationsSimple Equations
€
dN
dt= −α
N
N + No
I
I + Io+ remin
vs. Complex vs. Complex EquationsEquations
vs. Complex vs. Complex EquationsEquations
Simple Simple EcosystemEcosystem
Simple Simple EcosystemEcosystem
PROSPROS Reduced Reduced
computational computational costcost
More direct More direct understanding of understanding of resultsresults
PROSPROS Reduced Reduced
computational computational costcost
More direct More direct understanding of understanding of resultsresults
CONSCONS No species shiftsNo species shifts
Will it work for Will it work for past or future past or future climate? climate?
More difficult to More difficult to compare to compare to observationsobservations
CONSCONS No species shiftsNo species shifts
Will it work for Will it work for past or future past or future climate? climate?
More difficult to More difficult to compare to compare to observationsobservations
Modeling global COModeling global CO22 flux flux (mol/m(mol/m22/yr)/yr)
Modeling global COModeling global CO22 flux flux (mol/m(mol/m22/yr)/yr)
McKinley et al. 2004
MITgcm Data
Complex Complex EcosystemEcosystemComplex Complex
EcosystemEcosystem
PROSPROS More realisticMore realistic Allows species Allows species
shifts with climateshifts with climate More direct More direct
comparison to datacomparison to data Enhanced process Enhanced process
understandingunderstanding
PROSPROS More realisticMore realistic Allows species Allows species
shifts with climateshifts with climate More direct More direct
comparison to datacomparison to data Enhanced process Enhanced process
understandingunderstanding
CONSCONS Computational Computational
costs increase by costs increase by 10x’s10x’s
Many unconstrained Many unconstrained parametersparameters
More difficult to More difficult to interpretinterpret
CONSCONS Computational Computational
costs increase by costs increase by 10x’s10x’s
Many unconstrained Many unconstrained parametersparameters
More difficult to More difficult to interpretinterpret
Surface Surface ChlorophyllChlorophyll
Surface Surface ChlorophyllChlorophyll
Lima & Doney, 2004Lima & Doney, 2004
Biogeochemical model Biogeochemical model intercomparison: North intercomparison: North
Pacific Pacific
Biogeochemical model Biogeochemical model intercomparison: North intercomparison: North
Pacific Pacific
Seven independent Seven independent modelsmodels
Seven independent Seven independent modelsmodels
ROMSROMS MITMIT UMDUMD NCOMNCOM ECCO-ECCO-CCSM*CCSM*
MPIMPI PISCES-TPISCES-T
ResolutioResolutionn
0.5 x 0.5 x
0.50.51.0 x1.0 x
0.3-1.00.3-1.01.0 x 1.0 x
0.3-0.70.3-0.72.0 x2.0 x
0.50.53.0 x3.0 x
0.6-1.60.6-1.6VariesVaries
0.3x0.3 0.3x0.3 in in tropicstropics
2.0 x 2.0 x
0.5-1.50.5-1.5
EcosysteEcosystem m complexitcomplexityy
HighHigh LowLow HighHigh HighHigh HighHigh HighHigh HighHigh
YearsYears 1990-1990-20042004
1980-1980-19981998
1979-1979-20032003
1951-1951-19991999
1958-1958-20042004
1948-1948-20032003
1948-1948-20042004
AuthorsAuthors Chai, Shi,Chai, Shi,
JiiangJiiangMcKinley, McKinley, Follows, Follows, MarshallMarshall
Christian, Christian, MurtuguddMurtuguddee
Chai, Chai, Shi,Shi,
JiiangJiiang
Doney, Doney, Moore, Moore, LindsayLindsay
WetzelWetzel LeQuereLeQuere* Preindustrial* Preindustrial
Subtropical cycle: Station Subtropical cycle: Station ALOHAALOHA
Subtropical cycle: Station Subtropical cycle: Station ALOHAALOHA
Data, Takahashi et al. 2005, submittedData, Takahashi et al. 2005, submitted
Station ALOHA pCOStation ALOHA pCO2 2
variabilityvariabilityStation ALOHA pCOStation ALOHA pCO2 2
variabilityvariability
High-latitude seasonal High-latitude seasonal cycle: Kuril region cycle: Kuril region
High-latitude seasonal High-latitude seasonal cycle: Kuril region cycle: Kuril region
Modeling ChallengesModeling ChallengesModeling ChallengesModeling Challenges Lack of data constraintsLack of data constraints
Ecosystem parametersEcosystem parameters Variability at large-scaleVariability at large-scale High latitudesHigh latitudes
Alkalinity / Freshwater fluxesAlkalinity / Freshwater fluxes Remineralization controls Remineralization controls Gas exchange Gas exchange
Lack of data constraintsLack of data constraints Ecosystem parametersEcosystem parameters Variability at large-scaleVariability at large-scale High latitudesHigh latitudes
Alkalinity / Freshwater fluxesAlkalinity / Freshwater fluxes Remineralization controls Remineralization controls Gas exchange Gas exchange
SummarySummarySummarySummary
Biogeochemistry of the carbon cycle Biogeochemistry of the carbon cycle is infinitely complexis infinitely complex
How much complexity must be How much complexity must be modeled?modeled? Ongoing debateOngoing debate Depends on timescales and questions Depends on timescales and questions
of interestof interest
Biogeochemistry of the carbon cycle Biogeochemistry of the carbon cycle is infinitely complexis infinitely complex
How much complexity must be How much complexity must be modeled?modeled? Ongoing debateOngoing debate Depends on timescales and questions Depends on timescales and questions
of interestof interest
Suggested readingSuggested readingSuggested readingSuggested reading Text: Sarmiento and Gruber (2006) Text: Sarmiento and Gruber (2006)
Ocean Biogeochemical DynamicsOcean Biogeochemical Dynamics Complex ecosystem modelsComplex ecosystem models
Fasham et al. 1993Fasham et al. 1993 Moore et al. 2002a,b; Lima and Doney 2004Moore et al. 2002a,b; Lima and Doney 2004 Dutkiewicz et al. 2005Dutkiewicz et al. 2005
SimpleSimple ecosystem modelsecosystem models Najjar et al. 1992Najjar et al. 1992 McKinley et al. 2004McKinley et al. 2004 Dunne et al. 2005Dunne et al. 2005
Text: Sarmiento and Gruber (2006) Text: Sarmiento and Gruber (2006) Ocean Biogeochemical DynamicsOcean Biogeochemical Dynamics
Complex ecosystem modelsComplex ecosystem models Fasham et al. 1993Fasham et al. 1993 Moore et al. 2002a,b; Lima and Doney 2004Moore et al. 2002a,b; Lima and Doney 2004 Dutkiewicz et al. 2005Dutkiewicz et al. 2005
SimpleSimple ecosystem modelsecosystem models Najjar et al. 1992Najjar et al. 1992 McKinley et al. 2004McKinley et al. 2004 Dunne et al. 2005Dunne et al. 2005