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Non-Linear Parameter Optimization of a Terrestrial Biosphere Model Using Atmospheric CO2 Observations

This study presents a non-linear parameter optimization approach for a terrestrial biosphere model using atmospheric CO2 observations within the Carbon Cycle Data Assimilation System (CCDAS). We outline the CCDAS set-up, including a two-stage assimilation process that integrates AVHRR data and atmospheric CO2 measurements. The methodology focuses on minimizing a cost function and calculating uncertainties through gradient and Hessian methods. The model, calibrated with extensive data, significantly reduces uncertainties in key parameters and enhances predictive capabilities for net carbon flux and growth rates over 20 years.

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Non-Linear Parameter Optimization of a Terrestrial Biosphere Model Using Atmospheric CO2 Observations

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  1. 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 2004 1 2 3 FastOpt

  2. Overview • CCDAS set-up • Calculation and propagation of uncertainties • Data fit • Global results • Summary

  3. Carbon Cycle Data Assimilation System (CCDAS) set-up • 2-stage-assimilation: • AVHRR data • (Knorr, 2000) • Atm. CO2 data • Background fluxes: • Fossil emissions (Marland et al., 2001 und Andres et al., 1996) • Ocean CO2(Takahashi et al., 1999 und Le Quéré et al., 2000) • Land-use (Houghton et al., 1990) Transport Model TM2(Heimann, 1995)

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

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

  6. 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)

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

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

  9. Data fit

  10. Global Growth Rate observed growth rate optimised modeled growth rate Atmospheric CO2 growth rate Calculated as:

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

  12. Parameters II Relative Error Reduction

  13. Carbon Balance Euroflux (1-26) and other eddy covariance sites* latitude N *from Valentini et al. (2000) and others net carbon flux 1980-2000 gC / (m2 year)

  14. Posterior uncertainty in net flux Uncertainty in net carbon flux 1980-2000 gC / (m2 year)

  15. 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.

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