Abstract <p>This article presents the current state of research in the field of variational assimilation of observational data in geophysical hydrodynamics problems, developed by G.I. Marchuk and his scientific school over many years. A technology of 4D variational assimilation of observational data (4D‑Var), based on a combination of splitting and adjoint equation methods, is presented for the ocean dynamics model developed at the Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS). The technology includes minimization of the cost functional describing the difference between the model solution and observational data with covariance matrices of observational errors and the initial approximation. Application of the multicomponent splitting method allows for a step-by-step solution of the system of forward and adjoint equations. Efficient algorithms for solving variational data assimilation problems are proposed based on modern iterative processes with a special choice of iterative parameters. Developing G.I. Marchuk’s idea of searching for energy-active zones in the ocean that determine its heat exchange with the atmosphere, new algorithms for analyzing the sensitivity of the model solution to observational data errors are developed. The methodology is illustrated by the Black Sea hydrothermodynamics model with variational data assimilation for reconstructing heat fluxes on the sea surface. The prospects for developing this direction are discussed in the conclusion.</p>