Numerical algorithm for the adjoint sensitivity study of the Adem Ocean Thermodynamic Model

Abstract

The adjoint method is applied to derive simple integral formulas for the sensitivity study of the Adem Ocean Thermodynamic Model to small variations both in the heat forcing and in the initial and boundary conditions In each formula, the adjoint model solution is a useful source of information about the contribution of such variations to average sea surface temperature anomaly in a certain region. Thanks to special conditions set at inflow and outflow liquid boundaries- the main and adjoint thermodynamic models are well-posed in the sense of Hadamard (1923) not only for closed, but also for open oceanic basins. Balanced and absolutely stable implicit finite-difference schemes of the 2nd order approximation both in space and m time are constructed for the main and adjoint ocean thermodynamic models. The schemes are based on the splitting method and easily solved by the factorization. Both unsplit and split difference operators ofthese schemes satisfy the discreto Lagrange identity at every time step. In the nondissipative and unforced case when there is no flux across the liquid boundaries, the schemes have two conservation laws each.