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Inversion strategy

Inversion strategy. 4D-var method adjoint model of TM3 CH4-only version has been developed optimize surface fluxes and initial CH4 field expected: in the beginning adjustments to CH4 field, later to surface fluxes time frame: 1 week to 1 month. 4D var (1). background error covariance.

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Inversion strategy

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  1. Inversion strategy • 4D-var method • adjoint model of TM3 CH4-only version has been developed • optimize surface fluxes and initial CH4 field • expected: in the beginning adjustments to CH4 field, later to surface fluxes • time frame: 1 week to 1 month

  2. 4D var (1)

  3. background error covariance control vector observation operator state vector x = [c,...] observation error covariance observation 4D var (2) • cost function • model

  4. adjoint model 4D var (3) • gradient of the cost function

  5. Preconditioning • S diagonal matrix with standard deviations • LLTsymmetric matrix with correlations

  6. First experiments • First week of January 2000 • Sat.obs. taken from perturbed model run • Optimize emissions only • Background error covariance • Standard deviation: 50% of emission • Horizontal correlation function: Gaussian with length scale of 1000 km • Observation error covariance • Diagonal; standard deviation: 0.5% of column

  7. A priori emissions

  8. Perturbed run 50% enhanced emissions

  9. Effect on CH4 field after one week

  10. Pseudo satellite observations

  11. Optimized CH4 emissions

  12. Resulting CH4 field

  13. Setting obs to 2%

  14. Adding 0.5% noise to sat.data

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