Bv. Sanchez et Nk. Pavlis, ESTIMATION OF MAIN TIDAL CONSTITUENTS FROM TOPEX ALTIMETRY USING A PROUDMAN FUNCTION EXPANSION, J GEO RES-O, 100(C12), 1995, pp. 25229-25248
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.