The oceanographic and geoidal components of sea surface topography
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Altimetric, gravimetric and oceanographic data over the North Atlantic are combined -using techniques of optimum estimation- to infer the surface expression of the time averaged circulation (ζ) and to estimate the marine geoid (γ), both in the wavelength band 100 km-2000 km. Optimum inverse methods in geophysics are reviewed. They are then used to analyze the estimation of the geoid from gravity data, emphasizing the wavenumber spectrum of resolution functions. It is found that accurate bandpassed versions of the geoid can be recovered from restricted data sets. The accuracy and distribution of publicly available gravity data are shown to define an estimate γ whose expected errors, σγ, range between 30 and 260 cm, assuming the Wagner and Colombo (1978) spectrum describes the average geoid behaviour. The σγ underestimate the actual differences between 'y and an altimetric surface (s) derived from Seasat, but the spatial variation of σγ follows closely the differences s-γ. The discrepancy is attributable to a partial failure of the spectral model at short wavelengths. The differences s-γ are dominated by geoid error that masks much of the signal ζ. The main North Atlantic gyre emerges clearly only after the σγ and the simplest model for ζ -as a spatially uncorrelated process with (30 cm)2 variance- are taken into account. To obtain a corrected geoid, a hydrographic estimate of ζ is combined with sand γ, and their expected errors.
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February, 1983
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