Orthonormal function approach for Geosat determination of sea surface topography

Abstract

A set of orthonormal (ON) functions were employed to represent the sea surface topography (SST) in a joint model of satellite altimetry where radial orbit errors, the sea surface topography, and the geoid are recovered simultaneously. For comparison, the spherical harmonic representation was also used in another solution. A linear orbit theory was used to model the orbit error. Both solutions used 32 days of Geosat/ ERM data, and the parameters were conditioned using a‐priori information from the GEM‐T2 covariance and hydrographic data. The ON function approach yields ocean currents that have better behavior at the land/ocean boundary as compared results using the spherical harmonic approach. The two Geosat SST models show high correlation with the Levitus SST and the SST derived from I year of TOPEXIPOSEIDON altimetry at low ON degrees. The ON error spectrum of the oceanic geoid was obtained using a transformation technique, thus allowing comparison of the SST and the geoid just over the oceans. The error analysis using the ON spectra shows that the accuracy of the low‐frequency geoidal components is consistent with that from GEM‐T2 and at a resolution of 2,00011,330 km the SST has an average error of 9.7110.7 cm, while the oceanic geoid has an average error of 6.4/7.9 cm. With the Geosat data used and the GEM‐T2 orbits, we concluded that the cutoff frequency of the SST is about ON degree 15. In both solutions the root‐mean‐square crossovers of the Geosat GEM‐T2 orbits were reduced from 35 cm before adjustment to 20 cm.

Keywords:

• Geosat altimetry
• orthonormal functions
• radial orbit error
• sea surface topography