Introduction to Ocean Biogeochemical Modeling
Transcript of Introduction to Ocean Biogeochemical Modeling
Introduction to Ocean Biogeochemical Modeling
Zouhair Lachkar �Center for Prototype Climate Modeling�New York University Abu Dhabi, UAE �
Goa Winter School, February 2015 �
Outline�
• Part 1: Marine biogeochemistry and climate�
• Part 2: Introduction to mathematical modeling�
• Part 3: Design of biogeochemical models�
• Part 4: Model validation�
• Part 5: Modeling application: eddies and biological production�
Outline�
• Part 1: Marine biogeochemistry and climate�
• Part 2: Introduction to mathematical modeling�
• Part 3: Design of biogeochemical models�
• Part 4: Model validation�
• Part 5: Modeling application: eddies and biological production�
The global ocean è a large carbon storage capacity
Part 1
Oceans have taken up ~ ½ fossil fuel emissions since preindustrial time
Setting the scene: Ocean & the carbon cycle
The sum of the 3 is: the dissolved inorganic carbon (DIC)
the role of chemistry: carbon speciation in seawater
Part 1 Setting the scene: Ocean sequestration of carbon
Sarmiento and Gruber, 2006
What maintains the vertical DIC gradient? the pumps of carbon
Vertical distribution of carbon in the the Ocean Part 1
Sarmiento and Gruber, 2006
The role of the solubility pump of C
Mechanisms of carbon downward transfer Part 1
Sarmiento and Gruber, 2006
The role of the biological pump of C
Mechanisms of the downward transfer of carbon Part 1
Mechanisms of the downward transfer of carbon
The prominent role of soft tissue pump…
Part 1
Sarmiento and Gruber, 2006
The global oceanic primary production
Oceans è 50% of the Earth’s global primary production
Part 1
ü Light & nutrients are the main limiting factors for biological production (vs. water & temperature) ü Primary producers are mostly micro organisms (phytoplankton,
phyton=plant, planktos = drifter) (vs. trees) ü Plankton is transported by currents
è Strong coupling between physics and biology in the ocean è Coupling: circulations affects biology and biology affects circulation
Biogeochemistry of Oceans vs. Land
Marine biogeochemistry’s main differences:
Part 1
Physics-Biogeochemistry coupling
Coastal upwelling off California
Part 1
Sarmiento and Gruber, 2006
Physics-Biogeochemistry coupling
High spatiotemporal variability (e.g., surface Chl)
Part 1
Oceanic net primary production (NPP)
What drives such large spatial variability?
Part 1
Sarmiento and Gruber, 2006
Drivers of oceanic primary production Part 1
Light: the main limitation of marine productivity
Drivers of oceanic primary production Part 1
Sarmiento and Gruber, 2006
The macro-nutrient limitation…
Drivers of oceanic primary production Part 1
Sarmiento and Gruber, 2006
Nitrate: the most limiting nutrient (in general)
Drivers of oceanic primary production Part 1
Sarmiento and Gruber, 2006
Phosphate: can be locally limiting (e.g., in the Atlantic)
Drivers of oceanic primary production Part 1
Sarmiento and Gruber, 2006
Good coupling but nitrate is generally depleted first…
Drivers of oceanic primary production Part 1
Sarmiento and Gruber, 2006
Silicate: important for silicifiers (e.g., diatoms)
Drivers of oceanic primary production Part 1
Sarmiento and Gruber, 2006
Micro-nutrient (e.g., Fe) è locally limiting (e.g., Southern Ocean)
Drivers of oceanic primary production Part 1
Sarmiento and Gruber, 2006
POC export è The strength of the biological C pump
Production is not the whole story… Part 1
Sarmiento and Gruber, 2006
POC export è The strength of the biological C pump
Production is not the whole story… Part 1
Sarmiento and Gruber, 2006
The plankton community composition role… Part 1
Sarmiento and Gruber, 2006
Until the early 90’s:""Steady state N cycle "New production = export production"NPP= new P (NO3) + regenerated P (NH4) "
During the 90’s""Major role of DOM "Role of bacteria in the surface è essential"
Since the mid 90’s""Atmosphehric deposition"N2 fixation "
The changing paradigms… Part 1
Sarmiento and Gruber, 2006
The changing paradigms…
The role of nitrogen cycle
Part 1
Outline�
• Part 1: Marine biogeochemistry and climate�
• Part 2: Introduction to mathematical modeling�
• Part 3: Biogeochemical models: a chronology and the state of the art �
• Part 4: Model validation�
• Part 5: Modeling application: eddies and biological production�
• Model: from latin modulus= small replica of a building • A model is a representation or simplified image of a real complex system • It is not a copy of that system. The same system can be represented by a
multitude of models. • Mathematical models are built around core principles such as mass or energy
balance, etc… • A good mathematical model è a comprehensible representation of the real
world that can be described mathematically • A model should explain the data in the simplest form possible (Ockham’s
razorè it is vain to do with more what can be done with less)
Part 2 What is a model?
A “real” system A model
• One motivation of building a model is to make predictions, BUT it is not the only motivation! Other motivations for modeling include:
• make sense out of collected data • develop theories and generalizable and
transferable insight • formulate new questions • plan new experiments • gain a mechanistic understanding of key
processes • get the synoptic perspective
Why model? Part 2
• Simple models è exploring mechanisms • Complex models è quantitative predictions • Different models have different strengths and
weaknesses • Best strategy è use different models (or
models with different levels of complexity)
Which model?
If a scenario or pattern is reproduced by various INDEPENDENT models è one can adopt the philosophy that truth is the intersection of lies (high robustness) (Levins 1966)
Part 2
model is validated against data, improved to better fit observations, then compared again against observations, etc… process stops when sufficient accuracy is reached.
Modeling is an iterative process Part 2
Anderson, 2005
Some modeling successes: the synoptic view Part 2
Some modeling successes: attribution of climate change to human activity
Part 2
IPCC 5th report,, 2013
Some modeling successes: linking theories to observations
Part 2
Start by defining: 1) the system boundaries 2) the state variables 3) internal and external relationships
Building a simple dynamical model: a how-to Part 2
Internal dynamics External forcing
Building a simple dynamical model: a how-to
4) write the mass balance equation
Part 2
We would like to model the concentration of phosphorus in an estuary. We note: Q : flow throw the estuary (inflow=outflow) V : volume of the estuary Cin: concentration of phosphorus in the inflow C : concentration of phosphorus in the estuary and outflow ks : sedimentation rate 1) Write the mass balance equation assuming
the sedimentation linearly increases with C. Find the steady state solution.
Q Q
C Cin
C V
k s
Example: modeling phosphorus in an estuary Part 2
We would like to model the concentration of phosphorus in an estuary. We note: Q : flow throw the estuary (inflow=outflow) V : volume of the estuary Cin: concentration of phosphorus in the inflow C : concentration of phosphorus in the estuary and outflow ks : sedimentation rate 1) Write the mass balance equation assuming
the sedimentation linearly increases with C. Find the steady state solution.
Q Q
C Cin
C V
k s
dMdt
=QCin −QC − ksM
dCdt
= kwCin − (ks + kw )C kw =QV
Example: modeling phosphorus in an estuary
with
Part 2
We would like to model the concentration of phosphorus in an estuary. We note: Q : flow throw the estuary (inflow=outflow) V : volume of the estuary Cin: concentration of phosphorus in the inflow C : concentration of phosphorus in the estuary and outflow ks : sedimentation rate 1) Write the mass balance equation assuming
the sedimentation linearly increases with C. Find the steady state solution.
Q Q
C Cin
C V
k s
dMdt
=QCin −QC − ksM
dCdt
= kwCin − (ks + kw )C kw =QV
C∞ =kwCin
(ks + kw )
Example: modeling phosphorus in an estuary
with
dCdt
= 0
Part 2
• 1798: 1st population model (Thomas Malthus, 1798): Population growth proportional to population size (dP/dt= a P), exponential increase left unchecked would lead to dire consequences! • 1845: Logistic model (Pierre-Francois Verhulst, 1845): Carrying capacity concept K (dP/dt=(1-P/K)a P) • 1925-1926: 1st coupled Prey-Predator model (Lotka, Volterra): describe cycles of populations: dP/dt=(a-cZ)P, dZ/dt=(bP –d)Z • 1946, 1949: 1st coupled biological-chemical-physical model of plankton dynamics (Riley): phytoplankton growth rate µ depends on environmental conditions and grazing rate • 1958: 1st NPZ model described by 3 independent differential equations in 2 layers (Steele): lack of computational resources è integration by hand! • 1970s-1980s: first 1D NPZ simulations, sensitivity to model structure (size classes, age,
stage,…), new bgc processes (bacteria, detritus, microbial loop,…), first 2D NPZ simulations
A chronology of ecosystem models: early works Part 2
• Fasham et al, 1990, NPZD models coupled to 3D GCMS
• 1st coupled physical-biogeochemical models late 1980s, beginning of 90s:
• Diagnostic: flux restoring (Najjar et al 1992, OCMIP, 1990s)
• Prognostic: models with little biology (Meir-Reimer 1990-1993)
• NPZD with multiple size classes, multiple nutrients, Fe, …(PISCES, BEC,…)
• Plankton Functional Type models (groupings of phytoplankton species, which have a ecological functionality in common, e.g., nitrogen fixers, calcifiers, DMS producers and silicifiers)(e.g., PlankTOM)
• Darwinian model (Follows et al 2007)
A chronology of ecosystem models: the last two decades Part 2
Outline�
• Part 1: Marine biogeochemistry and climate�
• Part 2: Introduction to mathematical modeling�
• Part 3: Design of biogeochemical models�
• Part 4: Model validation�
• Part 5: Modeling application: eddies and biological production�
1) Define (biotic and abiotic) compartments Reduce complexity to manageable proportions: A golden rule: when aggregating/combining groups of organisms make sure turnover times are comparable! Turnover times are closely coupled to growth rates; growth rates closely related to organism size è theoretical basis to size-related compartments
Part 3 How to build a simple ecosystem model?
Fasham et al., 1993
1) Define (biotic and abiotic) compartments Reduce complexity to manageable proportions: A golden rule: when aggregating/combining groups of organisms make sure turnover times are comparable! Turnover times are closely coupled to growth rates; growth rates closely related to organism size è theoretical basis to size-related compartments
2) Choose the model currency: N, P, C, Chl, biomass, energy,…(generally N). For a multi-currency use elemental ratios to convert from one currency to another.
Part 3 How to build a simple ecosystem model?
Fasham et al., 1993
1) Define (biotic and abiotic) compartments Reduce complexity to manageable proportions: A golden rule: when aggregating/combining groups of organisms make sure turnover times are comparable! Turnover times are closely coupled to growth rates; growth rates closely related to organism size è theoretical basis to size-related compartments
2) Choose the model currency: N, P, C, Chl, biomass, energy,…(generally N). For a multi-currency use elemental ratios to convert from one currency to another. 3) Define and model the transfer (fluxes) between compartments (there is no equivalent to Navier Stockes equation for biology however a common representation exists):
Part 3 How to build a simple ecosystem model?
Fasham et al., 1993
Nutrient Phytoplankton Zooplankton
Detritus
How to build a simple ecosystem model? Part 3
Phytoplankton Zooplankton
Detritus
How to build a simple ecosystem model?
Nutrient
Part 3
Phytoplankton Zooplankton
Detritus
f3: excretion
f2: grazing f1: production
f6: remineralization
f4: phytoplankton mortality
f5: zooplankton mortality
How to build a simple ecosystem model?
Nutrient
Part 3
Phytoplankton Zooplankton
Detritus
f3: excretion
f2: grazing f1: production
f6: remineralization
f4: phytoplankton mortality
f5: zooplankton mortality
∂N∂t
= f3 + f6 − f1
∂P∂t
= f1 − f2 − f4
∂Z∂t
= f2 − f3 − f5
∂D∂t
= f4 + f5 − f6
∂(P + Z + N +D)∂t
= 0
How to build a simple ecosystem model?
Nutrient
Part 3
Phytoplankton Zooplankton
Detritus
f3: excretion
f2: grazing f1: production
f6: remineralization
f4: phytoplankton mortality
f5: zooplankton mortality
∂N∂t
= f3 + f6 − f1
∂P∂t
= f1 − f2 − f4
∂Z∂t
= f2 − f3 − f5
∂D∂t
= f4 + f5 − f6
∂(P + Z + N +D)∂t
= 0 f1 = µmaxγNγ IP
How to build a simple ecosystem model?
Nutrient
Part 3
μmax (T) = α (1.066)T
f1 = µmaxγNγ IP
Model the production flux: the maximum growth rate μmax Part 3
N+KNµ=µN
max
f1 = µmaxγNγ IP
Model the production flux: the nutrient limitation Part 3
γN =N1
KN1+N1
N2
KN2+N2
×... γN = minN1
KN1+N1
, N2
KN2+N2
,...!
"##
$
%&&
N+KNµ=µN
max
f1 = µmaxγNγ IP
Model the production flux: the nutrient limitation Part 3
f1 = µmaxγNγ IP
Model the production flux: the light limitation Part 3
f1 = µmaxγNγ IP
Model the production flux: the light limitation
P-I curve
α
Vp
γI
Part 3
è Average phytoplankton Chl/C ratio (θ) ~ 0.02 mg Chl / mg C (variations between 0.005 to 0.05)
è θ varies with species (e.g., θdiatom ~0.025, θdinoflagelate ~ 0.01)
è θ varies with light and nutrient resources
θ ↗ when light ↘
θ ↗ when nutrients ↗
è Different models of θ exist:
Diagnostic : θ = f(I, N, T) (Cloern et al, 1995 ; …)
Prognostic : dθ/dt = f(I,N,T) (Geider et al., 1998 ; ...)
Model the production flux: the Chl-to-C ratio Part 3
PKPgGP +
= 22
2
PKPgG
P +=
1) Grazing is not very well known è different forms for the grazing funcNon (Michaelis-‐Menton, Sigmoid, etc…)
2) When mulNple preys exist è prey preferences p are defined p is either constant or p(P)
3) Z mortality is usually quadraNc (stabilizes the system + be[er fit with observaNons)
Model the grazing flux: some general considerations Part 3
Example 1: N2PZD2 model (Gruber et al. 2006)
The schematic diagram
Part 3
Gruber et al., 2006
Example 1: N2PZD2 model (Gruber et al. 2006)
The model equations
Part 3
Gruber et al., 2006
Example 1: N2PZD2 model (Gruber et al. 2006)
The model equations
Part 3
Gruber et al., 2006
Example 1: N2PZD2 model (Gruber et al. 2006)
The model equations
Part 3
Gruber et al., 2006
Example 2: BEC model (Moore et al. 2004)
The schematic diagram
Part 3
Example 3: PISCES model (Aumont et al. 2003)
The schematic diagram
Part 3
flexible community structure and emergent properties
Example 4: “Darwin” ecosystem model (Follows et al. et al. 2007)
The schematic diagram
Part 3
Effects of increasing biogeochemical complexity
From Friedrichs et al. 2006, 2007
Part 3
When biological parameters are optimized è Changes in physics produces far greater changes than change in ecosystem complexity
Effects of increasing biogeochemical complexity
From Friedrichs et al. 2006, 2007
Part 3
• When too many parameters are optimized è the more complex models have little predictive skill
• With an improved optimization scheme, more complex models do as good as
less complex models è additional complexity may not be advantageous
Effects of increasing biogeochemical complexity
From Friedrichs et al. 2006, 2007
Part 3
However, higher complexity models with a small number of optimized parameters are more portable (better fit when applied simultaneously to regions with different ecological regimes)
No opNmizaNon Individual opNmizaNon
Simultaneous opNmizaNon Cross-‐validaNon
Effects of increasing biogeochemical complexity
From Friedrichs et al. 2006, 2007
Part 3
Outline�
• Part 1: Marine biogeochemistry and climate�
• Part 2: Introduction to mathematical modeling�
• Part 3: Design of biogeochemical models�
• Part 4: Model validation�
• Part 5: Modeling application: eddies and biological production�
A “bad” model è
A good model è
Part 4 How to avoid the trap of false models tested by inadequate data*?
(*): J. Steele
Stow et al., 2009
How to avoid the trap of false models tested by inadequate data*?
(*): J. Steele
A “bad” model è
A “good” model è
Part 4
Stow et al., 2009
Surface Chl-‐a
Model validation: the “looks pretty good” test Part 4
Lachkar et al., 2011
JMS Special Issue on Skill Assessment for Coupled Biological/Physical Models of Marine Systems, Volume 76, Issues 1-‐2, 2009
Model validation: more advanced techniques Part 4
Model validation: Taylor diagram Part 4
IPCC 5th report, 2013
• Root mean squared error
• Reliability index
• Average bias
• Modeling efficiency
Model validation: other metrics… Part 4
Stow et al., 2009
Model validation: analysis of residuals & misfit structure Part 4
Doney et al., 2009
Pattern analysis: using EOFs or SOMs to explore to what extent the model reproduces major spatial and temporal variability modes (e.g., Stow et al., 2009)
Model validation: alternative approaches Part 4
When comparing models and observations, be aware of: • observation uncertainty
• observation footprint (potential mismatch with model grid)
• local heterogeneity (e.g., meso and submesoscale variability)
Model validation: representativeness of observations Part 4
Outline�
• Part 1: Marine biogeochemistry and climate�
• Part 2: Introduction to mathematical modeling�
• Part 3: Design of biogeochemical models�
• Part 4: Model validation�
• Part 5: Modeling application: eddies and biological production�
Part 5 Application: eddies and productivity in upwelling systems
Application: eddies and productivity in upwelling systems Part 5
Gruber et al., 2011
Application: eddies and productivity in upwelling systems Part 5
Gruber et al., 2011
Application: eddies and productivity in upwelling systems Part 5
Gruber et al., 2011
Application: eddies and productivity in upwelling systems Part 5
Gruber et al., 2011
Application: eddies and productivity in upwelling systems Part 5
Gruber et al., 2011
Application: eddies and productivity in upwelling systems Part 5
Gruber et al., 2011
Application: eddies and productivity in upwelling systems Part 5
Gruber et al., 2011
Application: eddies and productivity in upwelling systems Part 5
Application: eddies and productivity in upwelling systems Part 5
Gruber et al., 2011
• Models è mechanistic understanding of phenomena • The conceptual model should encapsulate the essential entities and
processes of the system of interest, rather than everything and anything that is known.
• Ockham’s razorè problem when models are used for “what if” scenarios (beyond or at the boundary of existing observations)
• Nonlinearity, a characteristic feature of biological systems, magnifies small perturbations
• Parameter fitting è potential issue when fitting too many unconstrained parameters è data fit at the expense of predictive capability
• Different questions è different models
Summary Final remarks
References
-‐ Eddy-‐induced reducNon of biological producNon in eastern boundary upwelling systems, N. Gruber, Z. Lachkar, H. Frenzel, P. Marchesiello, M. Munnich, J.C. McWilliams, T. Nagai, and G.K. Pla[ner, Nature Geoscience, 2011 -‐ Eddy-‐resolving simulaNon of plankton ecosystem dynamics in the California Current System, N. Gruber, H. Frenzel, S. Doney, P. Marchesiello, J.C. McWilliams, J.R. Moisan, J. Oram, G.K. Pla[ner, K. Stolenzbach, DSRI, 2006. -‐ Ocean biogeochemical dynamics, J. Sarmiento, N. Gruber, 2006.
-‐ A chronology of plankton dynamics in silico: how computer models have been used to study marine ecosystems, W. Gentleman, Hydrobiologia, 2002. -‐ A nitrogen-‐based model of plankton dynamics in the oceanic mixed layer, M. Fasham, H. W. Ducklow and S. M. McKlevie, JMR, 1990. -‐ Ecosystem model complexity versus physical forcing: quanNficaNon of their relaNve impact with assimilated Arabian Sea data, DSRII, 2006. -‐ Assessment of skill and portability in regional marine biogeochemical models: Role of mulNple planktonic groups, M. Friedrichs, et al., JGR, 2007. -‐ Skill assessment for coupled biological/physical models of marine systems, C. Stow et al., JMS, 2009.
References
Contact: [email protected]
End Happy modeling!