Refinement of the short arc satellite altimetry adjustment model

The short arc adjustment mode makes a determination of the geoid surface possible without the requirement of highly precise reference orbits. In this mode, the state vector components are subject to adjustment and represent in fact a set of independent weighted parameters. In a most elementary approach, the radial distance to a satellite point is differentiated with respect to these parameters and a radial distance to the geoid (r) is differentiated with respect to the earth potential coefficients. The observed satellite altimetry value (H) is approximately equal to the difference between these two radial distances. In the present study, a correction is introduced that makes it possible to express the mathematical model for H as accurately as practicable, good to a few centimeters. With regard to the partial differentiation, it is argued that r, in addition to being differentiated with respect to the potential coefficients, has to be differentiated also with respect to the state vector components. This gives rise to a second type of correction. It is shown that for most practical purposes, the ellipsoidal approximation to the geoid used to compute the above two kinds of corrections is satisfactory. The final results indicate that actual computation of these corrections is a very simple matter; an eventual upgrading of satellite altimetry computer programs can thus be accomplished with almost no additional effort. A practical benefit of the presented analysis is faster convergence in the adjustment which, in some cases, may remove the need for iterated solutions altogether.