FastOpt

A prototype Global Carbon Cycle Data Assimilation

System (CCDAS)

Marko Scholze1, Wolfgang Knorr2, Peter Rayner3,Thomas Kaminski4, Ralf Giering4

1 2 3 4

FastOpt

Overview

• Top-down vs. bottom-up

• Gradient method and optimisation

• Results: Optimal fluxes

• Uncertainties in parameters + results

• Uncertainties in fluxes + results

• Possible assimilation of flux data

• Conclusions and Outlook

FastOpt

Top-down / Bottom-upatm. CO2 data

inverseatmospheric

transportmodelling

net CO2fluxes at the

surface

processmodel

climate and other driving data

FastOpt

Carbon Cycle Data Assimilation

Biosphere Model: BETHY

Atmospheric Transport Model: TM2

Misfit to Observations

Parameters: 58

Fluxes: 800,000

Station Conc. 6,500

Misfit 1 Forward modelling:

Parameters –> Misfit

Adjoint or Tangent linear model:

Misfit / ∂ Parameters

parameter optimization

FastOpt

Figure taken from Tarantola '87

Space of m (model parameters)

First derivative (Gradient) of J(m) w.r.t. m (model parameters) :

–∂J(m)/∂m yields direction of steepest

descent

Gradient Method

Cost Function J(m)

FastOpt

Carbon Cycle Data Assimilation System (CCDAS)

CCDAS Step 2BETHY+TM2

only Photosynthesis, Energy&Carbon Balance

CO2

+ Uncert.

Optimized Params + Uncert.

Diagnostics + Uncert.

veg. indexsatellite +Uncert.

CCDAS Step 1full BETHY

PhenologyHydrology

AssimilatedPrescribedAssimilated

BackgroundCO2 fluxes*

* * ocean: Takahashi et al. (1999), LeQuere et al. (2000); emissions: Marland et al. (2001), Andres et al. (1996); land use: Houghton et al. (1990)

FastOpt

BETHY(Biosphere Energy-Transfer-Hydrology Scheme)

• GPP:

C3 photosynthesis – Farquhar et al. (1980)

C4 photosynthesis – Collatz et al. (1992)

stomata – Knorr (1997)

• Raut:

maintenance respiration = f(Nleaf, T) – Farquhar, Ryan (1991)

growth respiration ~ NPP – Ryan (1991)

• Rhet:

fast/slow pool resp. = wQ10 T/10 C fast/slow / fast/slow

slow –> infin.

average NPP = average Rhet (at each grid point)

<1: source>1: sink

t=1h

t=1h

t=1day

lat, lon = 2 deg

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Optimisation

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Optimised fluxes (1)

global fluxes

Major El Niño events

Major La Niña event

Post Pinatubo Period

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Optimised fluxes (2)normalized CO2 flux and ENSO

ENSO and terr. biosph. CO2:correlation seems strong

lag correlation(low-pass filtered)

correlation between Niño-3 SST anomaly and net CO2 flux shows maximum at 4 months lag, forboth El Niño and La Niña states

FastOpt

net CO2 flux to atm.gC / (m2 month)

during El Niño (>+1)

Optimised fluxes (3)

lagged correlationat 99% significance

-0.8 -0.4 0 0.4 0.8

flux sites?

FastOpt

Figure taken from Tarantola '87

J(x)

Second Derivative (Hessian) of J(m):

∂2J(m)/∂m2 yields curvature of J,provides estimateduncertainty in m

opt

Error Covariances in Parameters

Space of m (model parameters)

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Error Covariances in Parameters

first guess optimized prior unc. opt.unc. Vm(TrEv) Vm(EvCn) Vm(C3Gr) Vm(Crop)

µmol/m2s µmol/m2s % %Vm(TrEv) 60.0 43.2 20.0 10.5 0.28 0.02 -0.02 0.05Vm(EvCn) 29.0 32.6 20.0 16.2 0.02 0.65 -0.10 0.08Vm(C3Gr) 42.0 18.0 20.0 16.9 -0.02 -0.10 0.71 -0.31Vm(Crop) 117.0 45.4 20.0 17.8 0.05 0.08 -0.31 0.80

error covarianceexamples:

Cost function (misift):

J(

m ) 1

2[m

m 0]Cm0-1 [

m

m 0] 1

2[y (

m )

y 0]Cy-1 [

y (

m )

y 0 ]

model diagnostics

error covariance matrixof measurements

measurements

assumedmodel parameters

a priori covariance matrixof parameter + model errora priori

parameter values

Error covariance of parametersafter optimisation:

Cm 2J

mi, j2

1

= inverse Hessian

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Relative Error Reduction

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Error Covariances in Diagnostics

Error covariance of diagnostics, y,after optimisation (e.g. CO2 fluxes):

Cy(m opt)

yi(m opt)

m j

Cm

y i(m opt)

m j

T

error covarianceof parameters

adjoint ortangent linear

model

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Regional Net Carbon Balance and Uncertainties

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Comparison shows impact of a (pseudo) flux measurement in the broadleaf evergreen biome on Q10 estimated by an inversion of SDBM:

Upper panel: only concentration data

Lower panel: concentration data +pseudo flux measurement(mean: as predicted sigma: 10gC/m^2/year)

Details:Kaminski et al., GBC, 2001

a posteriori mean/uncertaintiesa priori mean/uncertainties

FastOpt

• CCDAS with 58 parameters can already fit 20 years

of CO2 concentration data

• Sizeable reduction of uncertainty for ~13 parameters

• terr. biosphere response to climate fluctuations

dominated by ENSO

• System can test model with uncertain parameters,

and deliver a posteriori uncertainties on parameters,

fluxes

Conclusions

FastOpt

• explore more parameter configurations• include fire as a process with uncertainties• need more constraints, e.g. eddy fluxes –>

reduce uncertainties• however: needs to solve scaling problem

(satellites?)• approach can be regionalized easily• extend approach to ocean carbon cycle• projection of uncertainties into future

Outlook