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Sea surface elevation and bottom pressure anomalies due to thermohaline forcing are examined through analytical and numerical models, including Boussinesq and non-Boussinesq models. It is shown that Boussinesq approximations can introduce noticeable errors, depending on the spatial and temporal scales of the perturbations. According to the theory of geostrophic adjustment, when the initial perturbations have horizontal scales com- parable to the barotropic radius of deformation, the initial pressure perturbations will be basically retained through the adjustment. On the other hand, if the initial perturbations have horizontal scales much smaller than the barotropic radius of deformation, the initial pressure perturbations will be largely lost. Precipitation has horizontal scales on the order of 10-100 km, much smaller than the barotropic radius of deformation. Thus, for timescales longer than days, the contribution from individual precipitation events to the local free surface elevation and bottom pressure is small and is difficult to identify from satellite data. On the other hand, thermal forcing has horizontal scales comparable to the barotropic radius of deformation, so its long-term contribution to sea surface height anomaly is noticeable and is easily identified from satellite data. Because Boussinesq models induce faulty sea surface height and bottom pressure signals, the errors introduced by these models are noticeable for anomalies in large-scale (O(1000 km)) thermohaline forcing.

Sea Surface Elevation and Bottom Pressure Anomalies due to Thermohaline Forcing. Part I: Isolated Perturbations*