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On analysis error covariances in variational data assimilation

Igor Yu. Gejadze 1 François-Xavier Le Dimet 2 Victor P. Shutyaev 3
1 University of Strathclyde
2 MOISE - Modelling, Observations, Identification for Environmental Sciences
Grenoble INP [2007-2019] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019], LJK [2007-2015] - Laboratoire Jean Kuntzmann [2007-2015], Inria Grenoble - Rhône-Alpes
3 INM-RAS - Institute of Numerical Mathematics [Moscou]
Abstract : The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function (analysis). The equation for the analysis error is derived through the errors of the input data (background and observation errors). This equation is used to show that in a nonlinear case the analysis error covariance operator can be approximated by the inverse Hessian of an auxiliary data assimilation problem which involves the tangent linear model constraints. The inverse Hessian is constructed by the quasi-Newton BFGS algorithm when solving the auxiliary data assimilation problem. A fully nonlinear ensemble procedure is developed to verify the accuracy of the proposed algorithm. Numerical examples are presented.
keyword : Data assimilation Optimal control Analysis error Hessian Covariance operator
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https://hal.inria.fr/inria-00391893
Contributor : Arthur Vidard <>
Submitted on : Friday, June 5, 2009 - 10:31:51 AM
Last modification on : Monday, September 7, 2020 - 12:00:04 PM

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Igor Yu. Gejadze, François-Xavier Le Dimet, Victor P. Shutyaev. On analysis error covariances in variational data assimilation. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2008, 30 (4), pp.1847-1874. ⟨10.1137/07068744X⟩. ⟨inria-00391893⟩

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