No abstract

Satellite-altimeter data over ice sheets provide the best tool for mapping their topography and its possible climatic variations. However, these data are affected by measurement errors, orbit errors, and slope errors. We develop here a three-step inversion technique which accommodates the a priori information on the expected topography and correctly handles and propagates the data errors: it estimates first a large-scale reference surface, then maps the residuals related to undulations, and finally iteratively corrects the slope error. The method is tested on overlapping small fragments of the Antarctic ice sheet, using a sub-set of Seasat data. Finally, a topographic map of Terre Adélie is produced. Over areas of small slopes, the a posteriori error should be of the order of 0.4 m. Using ERS-I data, it is therefore expected that climatic variations in the ice-sheet topography since the introduction of Seasat will be observable.

Geosat profiles_ of the Exact Repeat Mission have been averaged over a 1-year period and high-pass-filtered using inverse method techniques. The geoid surface constructed with both ascending and descending profiles shows at medium wavelengths band-shaped anomalies preferentially elongated in the east-west direction. These anomalies have an average amplitude of ~30 cm and dominant wavelengths of 750 krn and 1100 km. We have performed numerous tests to show that the lineations are not artefacts created by the filtering process. Moreover, two-dimensional (2-D) filtering with the inverse method applied on a regional basis over the Pacific gives essentially similar results, indicating that the filtered geoid is not affected by directional bias. Seafloor topography in the Pacific filtered by 2-D inverse method also shows east-west trending depth anomalies positively correlated to medium-wavelength geoid lineations. Along the East Pacific Rise, there is a clear correlation between geoid lineations and regional variations in axial depth. Cross-spectral analysis carried_out on geoid and topography data over the Pacific area gives coherence maxima at 750-km and 1100-km wavelengths and admittance values of 2-3 m/km. Observed admittance matches the magnitude and shape of admittance predicted by lithospheric cooling models, suggesting that the lineations are related to regional variations in the plate cooling process. Convection models produce much higher admittances than observed unless a low-viscosity layer is assumed so that dynamical support cannot be completely discarded. In most instances, however, the position and direction of the lineations seem to be controlled by major fractures zones which is in favor of a lithospheric origin. In the south central Pacific where the lineations appear parallel to absolute plate motion, there may be a combination of both lithospheric and sublithospheric processes.

S U M M A R YThe 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.

Using the altimeter data from the Geosat Exact Repeat Mission, we have produced yearly averaged mean profiles and a global mean sea surface. The radial error of each 6‐day orbital arc computed with the GEM‐T2 geopotential was first estimated by calculating the amplitude and phase of the nine dominant frequencies of the difference between the altimetric profiles and the mean sea surface obtained when adding the permanent sea surface topography (computed from the Levitus' Climatological Atlas) to the GEM‐T2 geoid. We show that this operation is little affected by the choice of the geoid or by its formal error. The resulting correction has been subtracted from each individual arc. Yearly mean profiles were then obtained by averaging the corrected altimetric data of each repeat cycle on a yearly basis. Their noise level is 1 to 2 cm and their resolution is 20 km, but the differences of the altimetric heights at crossovers of ascending and descending tracks are still 30 cm nns. The latter can be reduced to 7 cm rms by a crossover analysis. In addition to the mean values, standard deviations were computed at each point of the repeat cycle. This “yearly along‐track variability” is of the order of 10 cm rms and is dominated by the ocean mesoscale variability. A global yearly mean sea surface has been derived by bilinear interpolation. Its resolution ranges approximately from 160 km to 80 km, depending on the latitude. It is shown to be much less noisy than those deduced from GEOS 3 and Seasat data.