Relaxing the Boussinesq Approximation in Ocean Circulation Models

Abstract

There is a growing need for ocean circulation models that conserve mass rather than volume (as in traditional Boussinesq models). One reason is bottom pressure data expected to flow from satellite-mounted gravity-measuring instruments, and another is to provide a complete interpretation of data from satellite altimeters such as TOPEX/Poseidon. In this paper, it is shown that existing, hydrostatic Boussinesq ocean model codes can easily be modified, with only a modest increase in the CPU requirement, to integrate the hydrostatic, non-Boussinesq equations. The method can be used to integrate both coarse-resolution and eddy-resolving non-Boussinesq models. The basic equations can also be used to formulate a fully nonhydrostatic, non-Boussinesq model. The method is illustrated for the case of the Parallel Ocean Program (POP), the parallel version of the Bryan?Cox?Semtner code developed at Los Alamos National Laboratory. A comparison of eddy-permitting model solutions under double-gyre wind forcing shows that the error in making the Boussinesq approximation is, reassuringly, only a few percent. The authors also consider a coarse-resolution global ocean model under seasonal forcing. The non-Boussinesq model shows a seasonal variation in global mean sea surface height (SSH) with a range of about 3 cm, attributable mostly to changes in the mass of the ocean due to the freshwater flux forcing, but with a roughly 25% contribution from the steric expansion effect. The seasonal cycles of model-computed SSH are also compared with TOPEX/Poseidon data from the South Pacific and South Atlantic Oceans. It is shown that the seasonal cycle in global mean SSH contributes to the model-computed seasonal cycle, and improves the model performance compared to the data. It is found that the difference between the seasonal cycles in the Boussinesq and non-Boussinesq models is almost entirely accounted for by the seasonal cycle in global mean SSH. On the other hand, on longer timescales the difference field between the non-Boussinesq and Boussinesq models shows spatial variability of several centimeters that is not accounted for by a globally uniform correction to the Boussinesq model.