Band 21, Heft 2

We study an inverse problem of the mathematical tidal theory, i.e., the tide potential problem, and construct a closure equation based on observation of the sea level function (free surface elevation).We consider the existence and uniqueness of a solution and formulate an iteration algorithm for solving the problem studied.

In this paper, we study the observation data assimilation problem for the sea level elevation to seek the optimal value of the function appearing in the boundary condition. We prove the optimization problem solvability and derive the necessary optimality condition.

The problem of variational data assimilation for a nonlinear evolution model is considered to identify the initial condition. An equation for the error of the optimal solution through the statistical errors of input data is derived, based on the Hessian of the misfit functional and second-order adjoint techniques. The covariance operator of the optimal solution error is expressed through the covariance operators of input errors. Numerical algorithms are developed for constructing the covariance operator of the optimal solution error using the covariance operators of input errors.

A numerical model of the Indian Ocean circulation is developed at the Institute of Numerical Mathematics, Russian Academy of Sciences, and the results of simulation of monsoon current variability are presented. The model resolution is 1/8° in longitude, 1/12° in latitude with 21 unevenly vertical levels. The model was run for 15 years using monthly mean atmospheric data from NCEP reanalysis. The annual cycle of surface and subsurface currents, temperature and salinity fields are analysed for the final 15th year. The model reproduces the Summer Monsoon and Winter Monsoon Currents, their annual cycles, space structures and magnitudes. The modelled Somali Current has a good resemblance to observations with model velocities exceeding 2 ms −1 and the transport about 70 Sv during the Summer Monsoon. The model results show that a turn of the Somali Current from the summer to winter direction is accompanied by the generation of anticyclonic eddies that drift westward by the β -effect and dissipate in the Somalia shore and the Gulf of Aden. The monsoon variability of equatorial surface currents and equatorial undercurrents is analysed. It is shown that these currents are mainly generated by zonal wind stress, which is dominated at the equator by a semi-annual harmonic. Therefore, the equatorial surface currents and the compensating equatorial subsurface undercurrents also change directions with a semi-annual periodicity. It is found that gradient currents caused by river run-off make an important contribution to the circulation in the Bay of Bengal. The main features of quasistationary vigorous eddies like Great Whirl, Socotra High, Lakshadweep High, and Lakshadweep Low are well reproduced.

We consider the variational data assimilation problem to identify the initial condition for the 1D vertical heat exchange model governed by a non-stationary heat equation with nonlinear diffusion. We give the operator formulation of the problem and present solvability results. We derive an equation for the error of the optimal initial-value function through the errors of input data using the Hessian of the misfit functional. The fundamental control functions are used for error analysis. We obtain error sensitivity coefficients using singular vectors of the specific response operators in the error equation. Numerical examples are presented.