NCOF Development Workshop 2008

Assessments of Ecosystem Models using Assimilation Techniques

John Hemmings, Peter Challenor, Ian Robinson & Tom AndersonJohn Hemmings, Peter Challenor, Ian Robinson & Tom Anderson

What is the “Ecosystem Model” inEcosystem Model Assessment ?

• Free-running modelFree-running model• Assimilation system (sequential D.A.)Assimilation system (sequential D.A.)

Ocean Biogeochemical General Circulation ModelOcean Biogeochemical General Circulation Model

Ecosystem Sub-modelEcosystem Sub-model

• Fixed parameter modelFixed parameter model• Model structure and formulationModel structure and formulation

Outline

• The Calibration Process (Inverse D.A. Scheme)The Calibration Process (Inverse D.A. Scheme)• Allowing for UncertaintyAllowing for Uncertainty• Assessment of D.A. Scheme and Model Assessment of D.A. Scheme and Model • Combining Data from Different LocationsCombining Data from Different Locations

• Sequential Assimilation of Ocean ColourSequential Assimilation of Ocean Colour• Improving Forecasts and HindcastsImproving Forecasts and Hindcasts

The Calibration Process

ECO.MODEL

OPTIMIZER

COSTFUNC.

SimulatedObs.

MisfitCost

Calibration Obs.

BoundaryConditions

ForcingInitial

Conditions

FreeParameters

ScienceOutput

Sensitivity Analysis

ValidationObs.

Allowing for Uncertainty

The Misfit Formulation

Estimate 2SIM by:

1) Characterizing uncertainty in IC, physical forcing & boundary fluxes2) Propagating through model by ensemble runs

Misfit =

(xSIM - xOBS)2

2DEP

2DEP = 2

OBS + 2SIM

For a given parameter set, 2SIM is uncertainty due to

IC, physical forcing & boundary fluxes

Allowing for Uncertainty

External Input Data for 1-D Simulations

• Biogeochemical tracer profiles Biogeochemical tracer profiles BBi i (z, member)(z, member)

Initial conditions:

Forcing data:

• Sea-surface PAR Sea-surface PAR I (t, member)I (t, member)• Sea-surface salinity Sea-surface salinity S (t, member)S (t, member)• Mixed layer depth Mixed layer depth M (t, member)M (t, member)• Temperature Temperature T (z, t, member)T (z, t, member)• Vertical diffusion coefficient Vertical diffusion coefficient k (z, t, member)k (z, t, member)• Vertical velocity Vertical velocity w (z ,t, member)w (z ,t, member)

Boundary fluxes:

• Horizontal biogeochemical tracer fluxes Horizontal biogeochemical tracer fluxes HHi i (z, t, member)(z, t, member)

Allowing for Uncertainty

Marine Model Optimization Test-bed (MarMOT)

INPUT ITEMS (1 or more instances of each)

physical forcing

run options:ecosystem model, time-step, misfit spec. …

initial conditions

boundary conditions

observations

fixed parametersMODEL SPECIFIC

N SITES

N SITES

N SITES

N SITES

misfit costother validation stats.

model outputM CASES

free parameters (posterior)

MODEL SPECIFIC

free parameters (prior)

MODEL SPECIFIC

case table

Generic Function Analyzer

Model Evaluator

(1-D)Optimizermisfit

cost

Assessment CriteriaAssimilation Scheme & Calibration Data Set

• Fit to data from non-calibration yearsFit to data from non-calibration years- better than prior parameter set - better than prior parameter set

TWIN EXPERIMENTS REAL-WORLD EXPERIMENTS

• True solution known• Can test parameter recovery

• Ecosystem is real

• Idealized scenario may be unrepresentative

• Uncertainty in IC, forcing, horizontal fluxes and observations affects validation misfit

+

-

• No. of parameters constrained (with acceptable repeatability)No. of parameters constrained (with acceptable repeatability)

Assessment CriteriaEcosystem Model

Calibrated Model:

• Fit to data from non-calibration yearsFit to data from non-calibration years- better than cal. data climatology - better than cal. data climatology

Model Structure and Formulation:

• Fit to data from non-calibration yearsFit to data from non-calibration years- better than alternative model with same cal. data better than alternative model with same cal. data

Limitation: optimal calibration not possible for complex models

Ecosystem Model Assessment

An Example Model Comparison Experiment

OG99 NPZD:OG99 NPZD: Oschlies and Garçon (1999) Oschlies and Garçon (1999)HadOCC NPZD:HadOCC NPZD: Hadley Centre Ocean Carbon Cycle Model, Hadley Centre Ocean Carbon Cycle Model,Palmer and Totterdell (2001) - modifiedPalmer and Totterdell (2001) - modified

Thanks to Ben Ward & Andrew Yool for providing OCCAM output at BATS

Combining Data from Different Locations

Identifying Calibration Provinces

NERC Data Assimilation Thematic Programme

Zero-D NPZ model fit to daily Zero-D NPZ model fit to daily chlorophyll + winter nitrate at chlorophyll + winter nitrate at calibration stationscalibration stations

Split-domain calibration method Split-domain calibration method (Hemmings, Srokosz, Challenor & (Hemmings, Srokosz, Challenor & Fasham, 2004):Fasham, 2004):

identifies optimal geographic identifies optimal geographic ranges for single parameter sets ranges for single parameter sets by selecting promising stations to by selecting promising stations to aggregateaggregate

Final provinces chosen by Final provinces chosen by misfit cost at validation stationsmisfit cost at validation stations

Sequential Assimilation of Ocean ColourCASIX Chlorophyll Assimilation Scheme in FOAM-HadOCC

3D analysis

2D analysis of log(Chl)

2D analysis of P

ΔN

ΔP

ΔZ

ΔD

Δalk

ΔDIC

Model forecast

N:Chl

Observations

• Aim: improve air-sea COAim: improve air-sea CO22 flux by improving surface DIC and alkalinity, hence pCO flux by improving surface DIC and alkalinity, hence pCO22

• 2-D analysis of log2-D analysis of log1010(Chl) uses FOAM analysis correction scheme (as for SST)(Chl) uses FOAM analysis correction scheme (as for SST)• Surface phytoplankton increments derived using model nitrogen:chl (dynamic)Surface phytoplankton increments derived using model nitrogen:chl (dynamic)• Other variables adjusted by a new material balancing scheme (Hemmings, Barciela & Other variables adjusted by a new material balancing scheme (Hemmings, Barciela & Bell, 2008) Bell, 2008)

Rosa Barciela, Matt Martin, Mike Bell, Adrian Hines (Met Office)John Hemmings (NOCS)

DAILY ANALYSIS CYCLE

Sequential Assimilation of Ocean ColourMaterial Balancing Scheme for Nitrogen and Carbon

• Surface phytoplankton increment Surface phytoplankton increment given as inputgiven as input

• Relative increments to other nitrogen Relative increments to other nitrogen pools depend on the likely pools depend on the likely contributions to phytoplankton error contributions to phytoplankton error from growth and loss from growth and loss

• Nitrogen conserved at each grid Nitrogen conserved at each grid point (if possible)point (if possible)

• DIC increment conserves carbonDIC increment conserves carbon

• Sub-surface scheme prevents Sub-surface scheme prevents formation of unrealistic sub-surface formation of unrealistic sub-surface minima in DINminima in DIN

Sequential Assimilation of Ocean ColourEvaluation of Material Balancing in 1-D Twin Experiments

Free runFree run

Assimilating Chl & PAssimilating Chl & P

Assimilating Chl onlyAssimilating Chl only

60ºN

40ºN

50ºN

30ºN

Sequential Assimilation of Ocean Colour3-D Evaluation of Chlorophyll Assimilation Scheme

Biogeochemical errors due to excessive vertical transport of nutrients not corrected by Biogeochemical errors due to excessive vertical transport of nutrients not corrected by chlorophyll assimilation (intentionally)chlorophyll assimilation (intentionally)

TWIN EXPERIMENTSTWIN EXPERIMENTS REAL-WORLD EXPERIMENTSREAL-WORLD EXPERIMENTS

Surface ChlorophyllSurface Chlorophyll

Un-assimilated VariablesUn-assimilated Variables

Need biogeochemical Need biogeochemical balancing scheme when balancing scheme when assimilating T&S profilesassimilating T&S profiles

Impact of Physical D.A.(link to MARQUEST)

DIN

Chlorophyll

physics DA on

DA off

physics DA onDA off

??

Improving Forecasts and Hindcasts: the Role of Parameter OptimizationA Non-identical Twin Experiment

Truth:Truth: HadOCC HadOCCEcosystem Model:Ecosystem Model: Simplified HadOCC with 4 free parameters Simplified HadOCC with 4 free parametersCalibration data:Calibration data: Chlorophyll (daily), DIN & pCO Chlorophyll (daily), DIN & pCO22 (monthly) (monthly)

Improving Forecasts and Hindcasts: the Role of Parameter OptimizationSequential Chlorophyll Assimilation Results

TRUTH

ORIGINAL

ORIGINAL + CHL D.A.

OPTIMIZED

OPTIMIZED + CHL D.A.

Surface Chlorophyll

Surface Phytoplankton

Surface DIN

Surface pCO2

Improving Forecasts and HindcastsApplication of Different Assimilation Methods

Sequential Data Assimilation

• Improve hindcast stateImprove hindcast state• Improve initial conditions for short-term forecastsImprove initial conditions for short-term forecasts

Parameter Optimization (Inverse D.A. Methods)

• Improve long-term forecastImprove long-term forecast• Improve performance of sequential schemesImprove performance of sequential schemes