Estimation of main tidal constituents from TOPEX altimetry using a Proudman function expansion

Abstract

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 accurate modeling of the ocean tides is necessary in order to interpret the height measurements of the ocean surface obtained from satellite altimeters. It is also an interesting dynamical problem in its own right. 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 Proudman functions constitute a mass conserving orthogonal basis; their computation does not require any assumption concerning friction or energy dissipation, only a numerical grid expressing the shape of coastline and the bathymetry of the ocean basins. They have the space structure of standing waves and can be identified as the zero‐rotation gravitational normal modes. They have to be evaluated numerically only once for each particular grid resolution. In this investigation the Proudman functions were computed by means of finite differences in spherical coordinates over a 2°×2° grid covering most of the world's oceans for a total of 8608 degrees of freedom. The data field used in this study consists of approximately 15 months of TOPEX altimetry in the form of collinear differences. Results for the major semidiurnal and diurnal constituents (M2,S2, N2, K2, K1, O1, P1, and Q1) have been obtained in terms of corrections to a priori values obtained by fitting Schwiderski's (1980) models. The new models (Goddard Space Flight Center (GSFC94A)) are tested at a set of “ground truth” data points. These tests indicate substantial improvement for most of the constituents as compared with Schwiderski'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 mean rms sea surface variability of 7.9 cm, compared with the 9.4 cm obtained when using Schwiderski's model.