Volume 31, Issue 2

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.

The problem of variational data assimilation for a model of ocean thermodynamics is formulated as an optimal control problem to find the boundary heat flux. The sensitivity of functionals of the optimal solution with respect to observations is studied. Computing the gradient of the functionals is reduced to the solution of a non-standard problem which is a coupled system involving direct and adjoint equations with mutually dependent boundary values. Solvability of the non-standard problem is studied based on the Hessian of the original cost function. An algorithm for computing the gradient of the response function related to the mean surface temperature is developed and justified. Numerical examples are presented for the Baltic Sea thermodynamics model.

A problem on pollution risk control related to local sources in region is formulated. Algorithm for solving the problem is proposed. The results of numerical experiment on the solution of the studied problem illustrating the effectiveness of the proposed algorithm are presented.

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition. The optimal solution (analysis) error arises due to the errors in the input data (background and observation errors). Under the Gaussian assumption the optimal solution error covariance can be constructed using the Hessian of the auxiliary data assimilation problem. The aim of this paper is to study the evolution of model errors via data assimilation. The optimal solution error covariances are derived in the case of imperfect model and for the weak constraint formulation, when the model euations determine the cost functional.

We consider a mathematical model of sea currents and tidal waves based on the marine dynamics primitive equations. The equations are written in the orthogonal coordinate system on sphere with arbitrary position of the poles. It makes it possible to increase horizontal resolution due to placement of a pole into vicinity of the considered sub-area. Two problems are solved: (1) joint computation of wind-generated, baroclinic and tidal currents in the Black and Azov Seas; (2) simulating mesoscale variability of coastal currents in the Black Sea. The second problem is solved with increased horizontal resolution in the coastal zone of Gelendzhik.