Methods for assimilation of observational data in problems of the physics of the atmosphere and the ocean

In this paper we review and analyze approaches to data assimilation in geophysical hydrodynamics problems, starting with the simplest successive schemes of assimilation and ending with modern variational methods. Special attention is paid to the the study of the problem of variational assimilation in the weak formulation and construction of covariance error matrices of the optimal solution. This is a new direction, to which the author made a contribution: an optimality system is formulated for the problem of variational data assimilation in a weak formulation and algorithms for deriving the covariance error matrices of the optimal solution are developed.

The study and numerical solution of the problem of heat and salinity transfer assuming ‘liquid’ boundaries

The problem of simulation of physical processes in water areas with ‘liquid’ boundaries is well known in geophysical hydrodynamics. In this paper we consider a problem of heat and salinity propagation as an example of approaches solving such problems and consisting in application of methods of variational assimilation of observation data. Using well known techniques of study and solution of inverse problems and optimal control problems, we propose an iterative solution algorithm, obtain conditions for existence of the solution, for unique and dense solvability of the problem, and for convergence of the iterative algorithm, The paper also presents results of numerical implementation of this algorithm in application to the water area of the Baltic sea.