Mathematical model of the World Ocean dynamics with algorithms of variational assimilation of temperature and salinity fields

An algorithm for solution of the problems of the World Ocean dynamics with assimilation of hydrophysical fields is described. A mathematical model of the general ocean circulation and a numerical algorithm for its solution are formulated. Model equations are written in a generalized σ-system of coordinates on a sphere with the North Pole displaced onto the continent. The model has a flexible hierarchical structure and consists of two parts: a forward prognostic model and its adjoint analogue. The forward and adjoint models supplemented with a cost functional minimization block may be joined into a variational observation data assimilation system. The numerical solution algorithm for the forward and adjoint models is constructed based on the method of multicomponent splitting. The method includes splitting with respect to physical processes and geometric coordinates. The algorithm is applied for simulation of the large-scale circulation of the World Ocean. Results of integration of the forward model for the period of 300 years under climatic atmospheric forcing are presented. Experiments in solving the forward problem with inclusion of a variational procedure for temperature and salinity field initialization are described.