Recovery of boundary functions on external and internal open boundaries in an open sea hydrodynamic problem

The inverse problem of recovering boundary functions on external and internal open boundaries for an open sea hydrodynamic model based on the linearized shallow water equations is considered. The external open boundary is meant as the boundary separating the considered water area from the world ocean. The internal open boundary is introduced to use the domain decomposition method. The inverse problem is studied theoretically, including the proof of its unique and dense solvability. An iterative algorithm for its solution is formulated, which combines variational data assimilation with the domain decomposition method. The theoretical study is illustrated by numerical results obtained for a test problem.