Equations of statistical interpolation

Author:    Pierre Gauthier

Email: pierre.gauthier@ec.gc.ca

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  • Equations of statistical interpolation
  • Optimal interpolation
  • Impact of local analysis
  • Variational formulation of statistical interpolation
  • Variational form: 3D-Var
  • Proof:
  • Hessian matrix and analysis error covariance
  • Steepest descent
  • Convergence of the minimisation and preconditioning
  • Preconditioning 3D-Var through a change a variables
  • Modelling background-error covariances
  • Homogeneous and isotropic correlations
  • Spectral representation of correlations
  • Diapositive PPT
  • Remarks
  • Elementary operators used in the analysis
  • Computation of the gradient
  • Example: assimilation of a single measure of wind intensity
  • Expression for the gradient of J0(x)
  • Dual form of the 3D-Var: the 3D-PSAS (Physical Space Assimilation System)
  • Impact of data selection
  • Diapositive PPT
  • Diapositive PPT
  • Summary

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