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�






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


The role of the solubility pump of C

Mechanisms of carbon downward transfer Part 1


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


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


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


Drivers of oceanic primary production Part 1

Light: the main limitation of marine productivity



The macro-nutrient limitation…



Nitrate: the most limiting nutrient (in general)



Phosphate: can be locally limiting (e.g., in the Atlantic)



Good coupling but nitrate is generally depleted first…



Silicate: important for silicifiers (e.g., diatoms)



Micro-nutrient (e.g., Fe) è locally limiting (e.g., Southern Ocean)



POC export è The strength of the biological C pump

Production is not the whole story… Part 1


POC export è The strength of the biological C pump

Production is not the whole story… Part 1


The plankton community composition role… Part 1


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


The changing paradigms…

The role of nitrogen cycle

Part 1

Outline�



•  Part 3: Biogeochemical models: a chronology and the state of the art �



•  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



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



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�






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


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.


Fasham et al., 1993


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):


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


Detritus

f3: excretion

f2: grazing f1: production

f6: remineralization

f4: phytoplankton mortality

f5: zooplankton mortality


Nutrient

Part 3


Detritus

f3: excretion





∂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


Nutrient

Part 3


Detritus

f3: excretion





∂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


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


The model equations

Part 3

Gruber et al., 2006


The model equations

Part 3

Gruber et al., 2006


The model equations

Part 3

Gruber et al., 2006

Example 2: BEC model (Moore et al. 2004)


Part 3

Example 3: PISCES model (Aumont et al. 2003)


Part 3

flexible community structure and emergent properties

Example 4: “Darwin” ecosystem model (Follows et al. et al. 2007)


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



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



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



Part 3

Outline�






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 5 Application: eddies and productivity in upwelling systems

Application: eddies and productivity in upwelling systems Part 5

Gruber et al., 2011


Gruber et al., 2011


Gruber et al., 2011


Gruber et al., 2011


Gruber et al., 2011


Gruber et al., 2011


Gruber et al., 2011



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!

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Introduction to Ocean Biogeochemical Modeling