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On error covariances in variational data assimilation. (English) Zbl 1120.93056
Summary: The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function. The equation for the error of the optimal solution (analysis) is derived through the statistical errors of the input data (background and observation errors). The numerical algorithm is developed to construct the covariance operator of the analysis error using the covariance operators of the input errors. Numerical examples are presented.

93E20 Optimal stochastic control
93E25 Computational methods in stochastic control (MSC2010)
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