Numerical solution of a variational data assimilation problem for a 3D ocean thermohydrodynamics model with a nonlinear vertical heat exchange

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.