Analysis of Errors Due to Polynomial Adjustment of Altimeter Profiles

Abstract

Among the various sources of error on altimetric sea surface height variability, the orbit error has the largest amplitude. However, since orbit error is mostly at long wavelengths, it can theoretically be distinguished from the mesoscale signal, characterized by wavelengths of a few hundred kilometers. The most commonly used technique to subtract this long-wavelength error is polynomial adjustment (zero, first or second degree) over distances of a few thousand kilometers. This paper examines the error on estimating the polynomial, which directly impacts the mesoscale signal obtained after the adjustment. We demonstrate how it can be estimated in theory and how it varies according to the spatial and energetic mesoscale characteristics (variability level, nonhomogeneities). These results are checked against simulated data and validated using actual Geosat data. The error is far from negligible: for a first-degree fit over 1500 km or a second-degree fit over 2500 km, its amplitude is typically 30% to 50% of the total mesoscale signal amplitude at the profile center and ends, respectively. In certain cases, where nonhomogeneity is significant, it can be greater than the total signal amplitude. We show that in such cases, a polynomial adjustment that takes amount of the statistics of mesoscale signal is a considerably better method. However, in the longer term, more global techniques such as inverse methods should be used so that the mesoscale signal can be extracted with the fewest possible errors.