The problem of mathematical modelling of the large-scale circulation of the Baltic Sea is considered. Marine hydrodynamics equations are written in the spherical coordinate system with a displaced point of the North Pole. The geographical North Pole is shifted to the vicinity of St. Petersburg to increase the spatial resolution of the Gulf of Finland. The free surface, sigma-coordinate primitive equation model under the Boussinesq, continuity, and hydrostatic assumptions is solved numerically. The problem of estimation of the pollution of some ’protected’ marine sub-area by a passive tracer by means of the introducing an adjoint equation for the sensitivity function is formulated. The sensitivity function specifies the contribution of each basin point to the total pollution of the ’protected area’.