Tidal estimation in the pacific with application to SEASAT altimetry

Abstract

The techniques for computing the eigenfunctions of the velocity potential (Proudman functions) set out in Sanchez et al. (1986) in relation to the Atlantic‐Indian Ocean are here applied to the Pacific Ocean, using a 6° × 6° grid of 510 points (455 points for the associated stream functions). Normal modes are computed from the first 150 Proudman functions and have natural periods from 43.9 hours downwards. Tidal syntheses are derived from these modes by direct application of the (frictionless) dynamic equations and by least‐squares fitting of Proudman functions to the dynamically interpolated tide‐gauge data of Schwiderski (1983). The modes contributing most energy to the principal harmonic tidal constituents are different in the two computations; their natural periods are typically in the range of 9–16 hours for semidiurnal, 14–43 hours for diurnal tides. The RMS of fit for Proudman functions is in all cases better than the corresponding value for the same number of spherical harmonics.

Before fitting the Proudman functions to the altimetry from the 3‐day repeat cycle of Seasat, the data are processed by novel methods. The geoid component is eliminated by taking collinear differences at a fixed time‐lag of two repeat cycles. Orbit errors are reduced by extracting the 1 rev⁻¹ component at every ascending node; this component varies slowly and nonlinearly in time. The spatial fitting process includes M₂ and O₁ frequencies, both of which emerge with significant and realistic tidal mapping, but residual noise in the data limits the number of Proudman functions to about 50–60 before showing signs of “over‐fitting.”; Fitting the same data by spherical harmonics gives marginally lower predicted variance for the same number of parameters.