The sea surface pressure formulation of rigid lid models. Implications for altimetric data assimilation studies

The sea surface pressure formulation of the rigid lid primitive equation oceanic problem is reviewed and clarified. The geostrophic limit for the sea surface pressure equation is then considered and a new diagnostic relationship is found that relates the surface pressure to the barotropic and baroclinic components of the subsurface flow field. We demonstrate that a direct insertion in the model equations of sea surface information, such as that provided by satellite altimetry, does not produce changes in the subsurface dynamics due to the divergenceless nature of the barotropic flow field. The geostrophic limit of the sea surface pressure field computed from a standard general circulation model of the world ocean is presented and the barotropic/baroclinic components of the absolute dynamic topography of the global general circulation are discussed.