An experiment to invert Seasat altimetry for the Mediterranean and Black Sea mean surfaces

Abstract

SUMMARY The high accuracy mapping of the mean sea surface (MSS) from satellite altimetry requires efficiency, flexibility and mathematical transparency from the data analysis. This paper argues that so does the least squares inverse method. Prior to the data inversion, models of covariance functions are constructed for the expected residual mean sea surface relative to a starting map and for the various error sources in the data including the radial orbit errors, instrument noise and sea height variability. The unique optimum solution is then restored from the data in a single step analysis, with formal error estimates and, possibly, local a posteriori covariances (‘resolving kernels’). Numerical experiments are performed to obtain the Mediterranean and Black Sea mean surfaces by an inversion of the Seasat altimeter data. In our present computational environment, the constraint raised by the cost of a run leads us to degrade the rigorous data analysis strategy. Owing to these limitations, and to the assumed covariance models and data coverage, the MSS is mapped with an accuracy of -12121x1 for wavelengths greater than 335 km. The supplementary error related to shorter scales is -70 cm. The inverse MSS solution is compared with another model computed at the Bureau Gravimetrique International in a classical way (crossing arc analysis plus data filtering) from Geos3 and Seasat. Then, neglecting the dynamic heights of the sea circulation, we invert the Seasat data set to map the equivalent free air gravity anomalies. The cross-covariance used is consistently derived from the a priori power spectrum of the MSS. The gravity anomalies are recovered with an accuracy of 1 mGal. Moreover, a large error of -25 mGal is expected from the smoothing of the shorter scales. An external comparison made with the gravimetric map of Torge, Weber & Wenzel (1983) broadly agrees with our formal error estimates. Several prospective specifications concerning the covariance models and the numerical procedure are drawn from these preliminary experiments and comparisons.