On the computation of the barotropic mode of a free-surface world ocean model

Abstract. The free-surface formulation of the equations of our world ocean model is briefly described. The barotropic mode equations are solved according to the split-explicit method, using different time steps for the external and internal modes. Because the numerical algorithm is implemented on the B-grid, a spurious, free-surface, two-grid interval mode may develop. This mode must be filtered out. The properties of two filters are theoretically investigated and their actual performance is tested in a series of numerical experiments. It is seen that one of these filters may severely perturb the local mass conservation, rendering it impossible to enforce the impermeability of the surface or the bottom of the ocean. The dynamics of the external mode is also examined, by studying the depth-integrated momentum equations. The depth-integral of the pressure force due to the slope of the ocean surface is approximately balanced by the depth-integral of the force ensuing from the horizontal variations of the density. The depth-integral of the Coriolis force is an order of magnitude smaller, except in the Southern Ocean. Two variational principles are resorted to for computing the fictitious ocean surface elevation corresponding to the approximate equilibrium between the dominant forces of the barotropic momentum equations.