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 transcript:

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

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

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

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

4D VAR

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

Dept of Mathematics University of Surrey Incremental 4D Var

Source Estimation

Testing VAR Relative error (TLM) Gradient test

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

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