Sensitivity of functionals in variational data assimilation for a sea thermodynamics model

Abstract

Abstract The sensitivity of functionals of the optimal solution to a variational data assimilation problem for the sea thermodynamics model is studied. The variational data assimilation problem is formulated as an optimal control problem to find the initial state and the boundary condition. The sensitivity of the response functions as functionals of the optimal solution with respect to the observation data is determined by the gradient of the response function and reduces to the solution of a non-standard problem being a coupled system of direct and adjoint equations with mutually dependent initial and boundary values. The algorithm to compute the gradient of the response function is presented, based on the Hessian of the original cost functional. The sensitivity analysis of the response function with respect to errors of observation data is carried out. Numerical examples are presented for the Black Sea thermodynamics model.