Volume 22, Issue 2

We study an inverse problem of the mathematical tide theory: a tidal potential problem for a semi-discrete model. The closure equation is constructed using observation data on the sea-level function on a part of the boundary and in the interior of the domain. Problems of existence and uniqueness of the solution are considered. An iteration algorithm for solving the problem is formulated.

A new ocean hydrothermodynamics model is developed. The problem of variational assimilation of sea level function data is formulated and investigated. The results of numerical experiments are given.

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function. The equation for the error of the optimal solution (analysis) is derived through the statistical errors of the input data (background and observation errors). The numerical algorithm is developed to construct the covariance operator of the analysis error using the covariance operators of the input errors. Numerical examples are presented.

We consider a variational data assimilation problem with the aim to reconstruct the initial condition for a 3D ocean hydrodynamics problem with the inclusion of a quasilocal model of vertical heat exchange in the ocean, which is described by a nonstationary heat conduction equation with a nonlinear diffusion coefficient. We develop and justify algorithms for the numerical solution of the problem. We give the results of test calculations using the Indian Ocean as example.

We present a numerical procedure of variational assimilation of observation data in the ocean. The procedure is intended for the σ-coordinate model of oceanic general circulation (OGC) developed at the Institute of Numerical Mathematics (INM) of the RAS. Model equations are written in a special symmetrized form. The numerical algorithm for solving a direct problem is based on the splitting method with respect to physical processes and space coordinates. Due to the splitting method the model is effectively realized by implicit schemes and uses a rather large time step in simulation. We obtained a differential system of adjoint equations for the OGC INM model. We write adjoint equations for each subsystem of the split model, which are then combined to form a full adjoint model. The procedure reduces to the construction of a number of relatively simple split subsystems for the adjoint model, which are also solved by implicit time schemes. The special symmetrized form of writing the primitive equations allows us to use the basic procedures from the direct model. The variational assimilation procedure is applied to solving the problem of the initialization of the Indian Ocean.