ESTIMATION OF MAIN TIDAL CONSTITUENTS FROM TOPEX ALTIMETRY USING A PROUDMAN FUNCTION EXPANSION

Tidal models for the main diurnal and semidiurnal constituents have be en computed from TOPEX altimeter data and a set of Proudman functions computed numerically in the space defined by the ocean basins. The acc urate modeling of the ocean tides is necessary in order to interpret t he height measurements of the ocean surface obtained from satellite al timeters. It is also an interesting dynamical problem in its own right . The surface height field due to any tidal constituent can be expande d in terms of the eigenfunctions of the velocity potential (Proudman f unctions) with coefficients estimated in a least squares sense from a field of discrete data points obtained from altimetry, tide gauges, bo ttom pressure sensors, etc. The Proudman functions constitute a mass c onserving orthogonal basis; their computation does not require any ass umption concerning friction or energy dissipation, only a numerical gr id expressing the shape of coastline and the bathymetry of the ocean b asins. They have the space structure of standing waves and can be iden tified as the zero-rotation gravitational normal modes. They have to b e evaluated numerically only once for each particular grid resolution. In this investigation the Proudman functions were computed by means o f finite differences in spherical coordinates over a 2 degrees x2 degr ees grid covering most of the world's oceans for a total of 8608 degre es of freedom. The data field used in this study consists of approxima tely 15 months of TOPEX altimetry in the form of collinear differences . Results for the major semidiurnal and diurnal constituents (M(2), S- 2, N-2, K-2, K-1, O-1, P-1, and Q(1)) have been obtained in terms of c orrections to a priori values obtained by fitting Schwiderski's (1980) models. The new models (Goddard Space Flight Center (GSFC94A)) are te sted at a set of ''ground truth'' data points. These tests indicate su bstantial improvement for most of the constituents as compared with Sc hwiderski's solutions. Use of GSFC94A results in a 7.8-cm reduction in the rms overlap difference of 15.5 cm. The GSFC94A model yielded a me an rms sea surface variability of 7.9 cm, compared with the 9.4 cm obt ained when using Schwiderski's model.