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F.-X. Le Dimet, V. Shutyaev, I. Gejadze
On optimal solution error in variational data assimilation: theoretical aspects
The problem of variational data assimilation for a nonlinear evolution model is considered to identify the initial condition. An equation for the error of the optimal solution through the statistical errors of input data is derived, based on the Hessian of the misfit functional and second-order adjoint techniques. The covariance operator of the optimal solution error is expressed through the covariance operators of input errors. Numerical algorithms are developed for constructing the covariance operator of the optimal solution error using the covariance operators of input errors.
Russian Journal of Numerical Analysis and Mathematical Modelling, Walter de Gruyter
Print ISSN: 0927-6467
Volume: 21, 03/2006
Pages: 139 - 152