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E. Parmuzin, F.-X. Le Dimet, V. Shutyaev

On error analysis in variational data assimilation problem for a nonlinear convection–diffusion model

We consider the variational data assimilation problem to identify the initial condition for the 1D vertical heat exchange model governed by a non-stationary heat equation with nonlinear diffusion. We give the operator formulation of the problem and present solvability results. We derive an equation for the error of the optimal initial-value function through the errors of input data using the Hessian of the misfit functional. The fundamental control functions are used for error analysis. We obtain error sensitivity coefficients using singular vectors of the specific response operators in the error equation. Numerical examples are presented.

Russian Journal of Numerical Analysis and Mathematical Modelling, Walter de Gruyter

Print ISSN: 0927-6467
Volume: 21, 03/2006
Pages: 169 - 183

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