Fast Opt

Non-Linear Parameter Optimisation of a Terrestrial

Biosphere Model Using Atmospheric CO2 Observation -

CCDAS

Marko Scholze1, Peter Rayner2, Wolfgang Knorr1, Thomas Kaminski3, Ralf Giering3 & Heinrich

Widmann1

European Geosciences Union, Nice, 27th April 2004FastOpt1 2 3

Overview

• CCDAS set-up• Calculation and propagation of

uncertainties• Data fit• Global results• Summary

Carbon Cycle Data Assimilation System (CCDAS) set-up

2-stage-assimilation:

1. AVHRR data(Knorr, 2000)

2. Atm. CO2 data

Background fluxes:1. Fossil emissions (Marland et al., 2001 und Andres et al., 1996)2. Ocean CO2 (Takahashi et al., 1999 und Le Quéré et al., 2000)3. Land-use (Houghton et al., 1990)Transport Model TM2 (Heimann, 1995)

Calibration Step

Flow of information in CCDAS. Oval boxes represent the various quantities. Rectangular boxes denote mappings between these fields.

Prognostic Step

Oval boxes represent the various quantities. Rectangular boxes denote mappings between these fields.

Methodology

Minimize cost function such as (Bayesian form):

DpMDpMpp pppJ DT

pT

)()()( 21

21 1

01

0 0

-- C C

where- is a model mapping parameters to observable quantities- is a set of observations- error covariance matrixC

DM

p

need of (adjoint of the model)Jp

Calculation of uncertainties

• Error covariance of parameters1

2

2

ji,

p pJ

C = inverse Hessian

T

pX p)p(X

p)p(X

CC

• Covariance (uncertainties) of prognostic quantities

Figure from Tarantola, 1987

Gradient Method

1st derivative (gradient) ofJ (p) to model parameters p:

yields direction of steepest descent.

pp

ppJ

)(

cost function J (p) p

Model parameter space (p)p

2nd derivative (Hessian)of J (p):

yields curvature of J.Approximates covariance ofparameters.

p

22 ppJ

)(

Data fit

Global Growth Rate

Calculated as:

observed growth rateoptimised modeled growth rate

Atmospheric CO2 growth rate

MLOSPOGLOB CCC 75.025.0

Parameters I• 3 PFT specific parameters (Jmax, Jmax/Vmax and )• 18 global parameters• 57 parameters in all plus 1 initial value (offset)

Param Initial Predicted Prior unc. (%) Unc. Reduction (%)

fautleafc-costQ10 (slow) (fast)

0.41.251.51.5

0.241.271.351.62

2.50.57075

3917278

(TrEv)(TrDec) (TmpDec) (EvCn) (DecCn) (C4Gr) (Crop)

1.01.01.01.01.01.01.0

1.440.352.480.920.731.563.36

25252525252525

7895629591901

Parameters II

Relative Error Reduction

Carbon Balance

latitude N*from Valentini et al. (2000) and others

Euroflux (1-26) and othereddy covariance sites*

net carbon flux 1980-2000gC / (m2 year)

Posterior uncertainty in net flux

Uncertainty in net carbon flux 1980-2000gC / (m2 year)

Summary• CCDAS with 58 parameters can fit 20 years of CO2

concentration data.• Significant reduction of uncertainty for ~15 parameters.• A tool to test model with uncertain parameters and to

deliver a posterior uncertainties on parameters and prognostics.

• Model is developed further within the system a low resolution version of the biosphere model is available (~20 times faster).

• Adjoint, tangent linear and Hessian code is derived by automatic differentiation (TAF) extremely easy update of derivative code for improved model versions.