Accuracy Assessment of Widely Used Orbit Error Approximations in Satellite Altimetry

Abstract

Orbit error simulations have shown that the orbit error can be assumed to be a slowly varying sine wave with a predominant wavelength comparable to the earth's circumference. Thus, one can derive analytically the error committed in representing the orbit error along a segment of the satellite ground track by a bias; by a bias and a tilt (linear approximation); or by a bias, tilt and curvature (quadratic approximation). The result clearly agrees with what is obvious intuitively; i.e., 1) the fit is better with more parameters, 2) as the length of the segment increases, the approximation gets worse. But more importantly, it provides a quantitative basis to evaluate the accuracy of past results and, in the future, to select the best approximation according, to the required precision and the efficiency of various approximations. Furthermore, the same formulas can determine the percentage of oceanic signal at each spatial scale that could be mistakenly removed by a particular orbit error representation in an orbit error removal procedure. Depending on the problem on hand, one can make an intelligent choice among the many orbit error representations based on the accuracy, efficiency, and signal preserving properties of that representation.