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Dept of Mathematics University of Surrey VAR and modelling the carbon cycle Sylvain Delahaies Ian Roulstone Dept of Mathematics University of Surrey NCEO.

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Presentation on theme: "Dept of Mathematics University of Surrey VAR and modelling the carbon cycle Sylvain Delahaies Ian Roulstone Dept of Mathematics University of Surrey NCEO."— Presentation transcript:

1 Dept of Mathematics University of Surrey VAR and modelling the carbon cycle Sylvain Delahaies Ian Roulstone Dept of Mathematics University of Surrey NCEO Theme 7: Data Assimilation

2 GPPC root C foliage C litter RaRa AfAf ArAr AwAw LfLf LrLr LwLw RhRh D Photosynthesis & plant respiration Phenology & allocation Senescence & disturbance Microbial & soil processes Climate drivers GPPC root C wood C foliage C litter C SOM/CWD RaRa AfAf ArAr AwAw LfLf LrLr LwLw RhRh D Photosynthesis & plant respiration Phenology & allocation Senescence & disturbance Microbial & soil processes Climate drivers DALEC evergreen

3 Initial carbon pools: C f, C r, C w, C l, C s Parameters: p 1,...., p 11 Atmospheric Co2 concentration

4 4DVAR 4DVar data assimilation finds the trajectory that best combines a back- ground estimation of the control variable, the model and observations.

5 4D VAR

6 Minimizing the cost function : 4DVAR Conjugate gradient method Preconditioning using the Hessian matrix Minimization subject to box constraints

7 Dept of Mathematics University of Surrey Incremental 4D Var

8 Source Estimation

9 Testing VAR Relative error (TLM) Gradient test

10 4DVAR : linearized model and perfect observations variableRelative error Cf 0.59E-12 Cr0.49E-05 Cl0.24E-01 Cw0.39E-05 Cs0.33E-03 p10.18E-02 p20.68E-10 p30.45E-10 p40.77E-05 p50.12E-11 p60.25E-01 p70.24E-06 p90.39E-05 p100.32E-03 p110.98E-09

11 4DVAR : linearized, obs with small Gaussian error variableRelative error Cf 0.21E-03 Cr0.89E+01 Cl0.26E+05 Cw0.39E+01 Cs0.33E+03 p10.18E+05 p20.68E-03 p30.45E-03 p40.77E+01 p50.12E-03 p60.25E+05 p70.24E+00 p90.39E+01 p100.32E+03 p110.98E-03

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