Abstract
We consider the data assimilation problem for a nonlinear evolution model to identify the initial condition. We derive an equation for the error of the optimal solution through the errors of the input data, which is based on the Hessian of a misfit functional, and study the solvability of the error equation. Fundamental control functions are used for error analysis. We obtain error sensitivity coefficients, using the singular vectors of the specific response operators in the error equation. We show the application of the data assimilation problem in hydrology and give numerical results.
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