# Convergence of Numerical Solutions of the Data Assimilation Problem for the Atmospheric General Circulation Model

Author Affiliations

^{1}Moscow Institute of Physics and Technology, Dolgoprudny 141700, RUSSIA

*Res. J. Recent Sci.,* **Volume 1, Issue (6),** Pages 16-21, June,2 **(2012)**

## Abstract

We consider a two-layer quasigeostrophic model of the general atmospheric circulation. It is assumed that there are field measurements of air velocity. These observations are used to find the unknown initial state of the model. The discrepancy between the observed values and the model results is measured by a cost function value. We prove the solvability of the optimization problem for positive values of the regularization parameter. The system of equations is approximated by an explicit spectral-difference scheme. A theorem is proved that the numerical solutions of the data assimilation problem converge to its exact solutions.

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