Non-Linear Parameter Optimisation of a Terrestrial Biosphere Model Using Atmospheric CO 2 Observation - CCDAS Marko Scholze 1, Peter Rayner 2, Wolfgang Knorr 1, Thomas Kaminski 3, Ralf Giering 3 & Heinrich Widmann 1 European Geosciences Union, Nice, 27 th April 2004 FastOpt 12 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. CO 2 data Background fluxes: 1.Fossil emissions (Marland et al., 2001 und Andres et al., 1996) 2.Ocean CO 2 (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): where - is a model mapping parameters to observable quantities - is a set of observations - error covariance matrix  need of (adjoint of the model)

Calculation of uncertainties Error covariance of parameters = inverse Hessian Covariance (uncertainties) of prognostic quantities

Figure from Tarantola, 1987 Gradient Method 1 st derivative (gradient) of J (p) to model parameters p: yields direction of steepest descent. cost function J (p) Model parameter space (p) 2 nd derivative (Hessian) of J (p): yields curvature of J. Approximates covariance of parameters.

Data fit

Global Growth Rate Calculated as: observed growth rate optimised modeled growth rate Atmospheric CO 2 growth rate

Parameters I 3 PFT specific parameters (J max, J max /V max and  ) 18 global parameters 57 parameters in all plus 1 initial value (offset) ParamInitialPredictedPrior unc. (%)Unc. Reduction (%) fautleaf c-cost Q 10 (slow)  (fast)  (TrEv)  (TrDec)  (TmpDec)  (EvCn)  (DecCn)  (C4Gr)  (Crop)

Parameters II Relative Error Reduction

Carbon Balance latitude N *from Valentini et al. (2000) and others Euroflux (1-26) and other eddy covariance sites* net carbon flux gC / (m 2 year)

Posterior uncertainty in net flux Uncertainty in net carbon flux gC / (m 2 year)

Summary CCDAS with 58 parameters can fit 20 years of CO 2 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.