Variational assimilation of observation data in the mathematical model of the Black Sea taking into account the tide-generating forces

A mathematical model of the dynamics of the Black and the Azov Seas is considered taking into account tide-generating forces. The problem of variational assimilation of sea surface temperature (SST) data is formulated and studied. Based on variational assimilation of satellite altimetry data, we propose an algorithm for solving the inverse problem of reconstruction of potential forces afflecting the formation of the mean level and present a method of approximate solution of this problem. We also present numerical experiments concerning the study of the influence of tide-generating forces on the dynamics of the Black Sea and restoration of the heat flux function in the problem of variational data assimilation of SST observations.