Problem of initialization for the atmospheric general circulation model

We consider a two-layer quasigeostrophic model of the general atmospheric circulation, the main variables of which are barotropic and baroclinic components of a stream function. It is assumed that there are field measurements of air velocity. These observations are used for determining the unknown initial state of the model. The discrepancy between the observed values and the simulation results is measured by the cost function value. We prove the solvability to the optimization problem for positive values of a regularization parameter. The original model is approximated by a semi-explicit spectral-difference scheme with respect to which the discrete problem of initialization is posed. We obtain a theorem on the convergence of numerical solutions of the inverse problem to its exact solutions.