Methods of variational assimilation of observation data in problems of geophysical hydrodynamics

This paper presents the current state of research in the field of variational assimilation of observational data in problems of geophysical hydrodynamics, developed by G.I. Marchuk and his scientific school for many years. For the ocean dynamics model developed at the IWM RAS, we present a technology of four-dimensional variational assimilation of observational data (4D-Var) based on a combination of splitting and conjugate equation methods. The technology includes minimization of the cost functional describing the difference between the model solution and observational data with covariance matrices of observation errors and initial approximation. Application of the multicomponent splitting method makes it possible to solve the system of direct and coupled equations stepwise. Effective algorithms for solving variational problems of data assimilation on the basis of modern iterative processes with a special choice of iterative parameters are proposed. 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 are developed to investigate the sensitivity of the model solution to errors in observational data. The methodology is illustrated for a model of the Black Sea hydrothermodynamics with variational data assimilation to recover heat fluxes at the sea surface. The conclusion discusses the prospects for the development of this direction.