Local crossover analysis of exactly repeating satellite altimeter data

Abstract

The crossover adjustment plays a central role in the processing of satellite altimeter measurements. The usual procedure is to form sea surface height differences at crossover points, solve for the radial orbit error (with due attention to the singular nature of the estimation problem) and then to construct altimetric sea-level maps using the mean sea surface heights at the crossover points. Our approach is very different, to make direct use of measurements at crossover points without differencing and to estimate simultaneously orbit parameters, mean sea surface height and sea surface height variability in a single, unified adjustment. The technique is suited for repeat data over an area small enough that adjoining passes may be considered to be parallel and to permit the solution of a set of linear equations of dimension equal to the number of crossover points. The size of the numerical problem is almost independent of the number of repeat cycles of the altimeter mission. Explicit recognition is given to the rank defect of the least-squares estimation problem; we show that, for an orbit model with r parameters, the rank defect of the local crossover problem is exactly r2. The defect may be overcome by choosing an appropriate set of constraints – either giving a best fit of mean sea surface heights to a reference surface, or minimising orbit parameters, or a minimum norm solution in which both mean sea surface heights and orbit parameters are minimised. There is no need to choose a reference pass, all passes are treated equally and data gaps are easily accommodated. Numerical results are presented for the south-western Indian Ocean, based on the first 2 years of altimeter data from the Geosat Exact Repeat Mission.