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5. A posteriori error covariances in variational data assimilation

Author

Shutyaev, V.P., Le Dimet, F.X., Gejadze, I.Yu., Russian Foundation for Basic Research (Funder), MOISE Project (Funder), Scottish Funding Council via GRPE (Funder), Institute of Numerical Mathematics [Moscou] (INM-RAS), Russian Academy of Sciences [Moscow] (RAS), Modelling, Observations, Identification for Environmental Sciences (MOISE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), and University of Strathclyde [Glasgow]

Subjects
Numerical Analysis, Mathematical optimization, 010504 meteorology & atmospheric sciences, MathematicsofComputing_NUMERICALANALYSIS, 010103 numerical & computational mathematics, 01 natural sciences, Data assimilation, TA, Modeling and Simulation, A priori and a posteriori, Applied mathematics, Errors-in-variables models, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, QA, 0105 earth and related environmental sciences, Mathematics
Abstract

International audience; The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find some unknown parameters of the model. The equation for the error of the optimal solution is derived through the statistical errors of the input data (background, observation, and model errors). A numerical algorithm is developed to construct an a posteriori covariance operator of the analysis error using the Hessian of an auxiliary optimal control problem based on the tangent linear model constraints.

Published
2009

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