Parameterization of ocean self-attraction and loading in numerical models of the ocean circulation

The effect of ocean self-attraction and loading (SAL) is considered in a global, barotropic ocean model forced by atmospheric wind stress, atmospheric pressure, and tidal forcing. Periods shorter than 7 days are considered. The model is integrated with a proper calculation of these effects in terms of a (very expensive) Green's function convolution at each time step. SAL effects produce a perturbation of typically about 10% of the computed ocean bottom pressure, but much more in places, for both tidal and atmospherically forced motions. An investigation into simple parameterizations of these effects by means of a term proportional to local bottom pressure reveals the following results: For tides, the best coefficient is systematically dependent on depth, ranging from less than 0.08 in shallow water to about 0.12 in the deepest water, and incorporating this effect improves the parameterization. For atmospherically forced motions, there is still some effect of depth but more an effect of latitude (increasingly so for longer periods), regional variation is greater, and correlation between the SAL effect and bottom pressure is weaker. Parameterization with a constant coefficient of 0.1 reduces errors due to failing to include SAL by about 30%. To do better than this, a proper scale-dependent representation of SAL must be used.