2026 , Volume 31, № 5, p.117-127

Purpose. This study addresses simulation for sea hydrothermodynamics by solving the problem of joint variational data assimilation of sea surface temperature and vertical temperature profiles. Data assimilation allows correcting the calculations for the numerical model using measurement of the environmental data.

Methods and Results. Mathematical model of the hydrothermodynamics of the Black and Azov Seas, developed at the Marchuk Institute of Numerical Mathematics of the RAS with a sigma- coordinate system is considered. A problem that combines variational data assimilation of sea surface temperature data and three-dimensional temperature fields with weekly averaging is formulated. A cost functional is introduced, incorporating satellite-derived sea surface temperature observations and vertical temperature profiles. The necessary condition for the minimum of this functional is recast as an optimality system, comprising the direct problem, the adjoint problem, and a control condition. The results of solving the stated problem are presented for the water areas of the Black and Azov Seas.

Conclusions. A comparison of numerical model results with and without assimilation was performed, demonstrating the efficiency of the assimilation procedures. It is shown that the combined variational assimilation of sea surface temperature data from the SNPP satellite and vertical profiles averaged over a week allows reproducing sea surface temperature with sufficient accuracy when comparing the simulation results with data from the Aqua and Terra satellites, which were not used in the assimilation process. Numerical experiments established that temperature profile assimilation can be performed once a week without loss of accuracy. Furthermore, the additional assimilation of profiles enables the generation of three-dimensional reanalysis fields for the studied region, which describe the thermohaline structure throughout the water column.