Tidal models for the main diurnal and semidiurnal constituents have been computed from TOPEX altimeter data and a set of Proudman functions computed numerically in the space defined by the ocean basins. The surface height field due to any tidal constituent can be expanded in terms of the eigenfunctions of the velocity potential (Proudman functions) with coefficients estimated in a least squares sense from a field of discrete data points obtained from altimetry, tide gauges, bottom pressure sensors, etc. The data field used in this study consisted of approximately 15 months of TOPEX altimetry in the form of collinear differences.

The quasi-stationary sea surface topography (QSST) and associated oceanic circulation was determined by means of a characteristic function technique. The data field was provided by the first year of altimeter data from the TOPEX/POSEIDON mission. The method requires the numerical determination of the eigenfunctions spanning the streamfunction field and the associated characteristic functions from the balance equation. The former yields the flow field and the latter the surface height distribution, or QSST.