In recent years, methods for studying and numerically solving problems of variational data assimilation, which are specific problems of optimal control, have been greatly developed in meteorology and oceanography, where observational data are assimilated in atmospheric and ocean models to obtain initial boundary conditions or other model parameters for subsequent modeling and forecasting. This paper considers the variational data assimilation algorithm for the sea dynamics model developed at the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences. This problem is formulated as an optimal control problem. An optimality system includes a direct equation, adjoint equations, satellite observations, and covariance matrices of observation and background errors. As an application, a mathematical model of the Black Sea dynamics with a block of variational assimilation of data on the sea surface temperature is considered. The data source in the proposed study is the Aqua satellite with the MODIS spectrometer and the SNPP satellite with the VIIRS spectrometer. A feature of these data is that they do not cover the entire study area, and the assimilation procedure uses a characteristic function that determines data availability at the time of assimilation. It is shown that introducing the data assimilation procedure into the model makes it possible to obtain sea surface temperature calculation results closer to the observed ones, improving the predictive properties of the numerical model.​