Global nondynamic orbit improvement for altimetric satellites

Abstract

The largest source of error in satellite altimetry is in the radial position of the satellite. Radial orbit errors of more than a few decimeters prohibit basin‐scale studies of sea surface height variability. We explore nondynamic techniques for reducing this error. Sea surface height differences at intersections of satellite altimeter profiles (crossover data) provide a strong constraint on radial orbit error but do not uniquely define it. The portion of orbit error that is a function of latitude and longitude only produces no crossover differences and therefore cannot be recovered with crossover data. Using mathematics (inclination functions) originally developed for satellite dynamics, we determine the entire class of orbit error functions not recoverable with crossover data. These functions are mappings of surface spherical harmonics into the orbit plane. For example, the l = 1, m = 0 surface harmonic maps into sinusoidal orbit error with a frequency of once per orbit. Nonzonal harmonics map into linear combinations of three or more frequencies that are linked by the inclination functions. Between frequencies of 0 and 2.2 cycles per orbit there are nine orbit error components that cannot be recovered using crossover data. These components are uniquely defined, however, by nine globally distributed radial tracking points. Fewer tracking points are sufficient if a smoothness criteria is applied to the orbit correction curve. Our findings suggest that radial orbit error can be significantly reduced by including a few globally distributed radar reflectors (or transponders) in the tracking network.