The problem on propagation of long waves in a domain of arbitrary form with the sufficiently smooth boundary on a sphere is considered. The boundary consists of solid parts
passing along the coastline and liquid parts passing through the water area. We assume, free
surface level observation data on liquid boundary is known. In general case the boundary
condition on liquid part of boundary contains unknown boundary function, which must be
found together with component of velocity vector and free surface level. We put an assimilation
observation data problem by Prof. V.I. Agoshkov methodology. To solve our ill-posed inverse
problem an approach, based on optimal control methods and adjoint equations theory, is used.
Numerical solution of direct and adjoint problems is based on finite elements method. Parallel
software using MPI is discussed.