Convergence of solutions to the problem of data assimilation for a multilayer quasigeostrophic model of ocean dynamics

Modern geophysical satellites provide us with most detailed fields of oceanology observation data. This fact is causing particular interest in processing these data and has generated a large number of publications related to data assimilation in oceanic models. The aim of this paper is the study of the nature and conditions of the convergence of numerical solutions to the altimetry data assimilation problem for a multilayer quasigeostrophic ocean circulation model where the discretization parameters tend to zero. In the first section we present the statement of the problem and formulate the results concerning its solvability. Then we consider an implicit difference scheme for the system of equations of the model and the corresponding discrete data assimilation problem. In the second section we study the convergence of numerical solutions of the data assimilation problem to its exact solutions.