Assimilation of altimeter data in a two-layer primitive equation model of the Gulf Stream

A two-layer finite depth, primitive equation model of the Gulf Stream region is used to study the effect of updating the model with simulated altimeter data as observations. In this study both a complete field of sea surface height (SSH) and SSH sampled along satellite tracks are used as "observations." A simulated 17-day repeat orbit corresponding to the Geosat-ERM and a 10-day repeat period corresponding to Topex/Poseidon are used. Satellite observations give only information about the sea surface height but previous studies have shown that it is important to transfer the surface information to the lower layer as fast as possible in order for the model to have a realistic evolution. A statistical inference technique is therefore used to update the lower-layer pressure field. The velocity fields in both layers are updated using a geostrophic correction calculated from the change in the pressure fields. It is shown that updating the velocities is important for the assimilation to be successful. When complete fields of sea surface heights from an identical twin experiment are assimilated the rms error between the model solution and the "true" ocean for the upper-layer pressure field is reduced to less than 5% after six weeks of assimilation. Assimilation of simulated observations along Geosat-ERM and Topex/Poseidon tracks show that both satellites give similar levels of rms error at the end of the assimilation period. The effect of assimilating altimeter data from two satellites is also discussed. The results show there can be a reduction in the rms error of up to 40% with the addition of a second satellite with appropriate orbital characteristics.