Constraints on the Repetitivity of the Orbit of an Altimetric Satellite: Estimation of the Cross-Track Slope

Abstract

The effect of a poorly constrained repetitivity of the orbit of an altimetric satellite is analyzed. From existing data, 35% of the marine geoid slopes are found to excess 1.5 cm km?1. This may be due either to short-distance-scale features (seamounts, fracture, and subduction zones) or to the large-scale geoid (in the Indian and North Atlantic oceans). A geoid cross-track slope (CTS) can be calculated locally from the tracks inside the repetitivity band. Assuming that the various measurement errors and ocean variability signals are decorrelated, it has a precision of 0.2?2 cm km?1, depending on the orbit cycle (which constrains the number of repeal passes per year) and on the width of the band (from 1 to 10 km in thew calculations). This can be used as a correction but increases the noise level by at least 50%. Alternatively, the CTS can be derived from a mean sea surface. This adequately corrects for the large-wale signals but, with present mean sea surfaces, it is inadequate for the short-distance-scale features. Future high-density altimetric samplings such as that of the ERS-1 176-day orbit should improve this precision to about ±0.1?0.2 cm km?1. Above continental ice, larger than 0.3% along-track slopes were encountered for more than 10% of the time above an altitude of 500 m. These slopes result mostly from undulations of the ice topography. Over one year, a median height profile inside the repetitivity band can be derived at 8?16-cm precision, depending on the number of tracks used and assuming that the measurement noise is 50 cm. From one yew to the next, a CTS correction needs to be applied to compare the yearly median height profiles. The latter can be estimated at a 13?130 cm km?1 precision, depending on the repetitivity (from 0.5 to 2.5 km at a latitude of 70°) and the number of tracks. In each case, the precision is comparable with the expected signals (e.g., mesoscale variability of the dynamic topography or climatic variation of the snow accumulation rate). These signals can, however, be recovered by space-time analysis of the data. A more elaborate analysis of the covariances of these corrections is thus required.