Journal of Glaciology, Vol. 35, No. 119, 1989 MAPPING OF THE TOPOGRAPHY OF CONTINENTAL ICE BY INVERSION OF SATELLITE-ALTIMETER DATA By F. REMY, P. MAZZEGA,S. HOURY,C. BROSSIER,and J.F. MINSTER (UM39, Groupe de Recherche de Geodesie Spatiale, 18 avenue Edouard-Belin, F-31055 Toulouse Cedex, France) 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 Adelie 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. INTRODUCTION The use of Geos-3, Seasat, or Geosat altimeter measurements over Antarctica and Greenland give major information for use in glaciological studies. From the three classical altimetric parameters (transit time, width of the leading edge of the radar wave forms, and total intensity of the received energy), such different geophysical parameters are provided as topography (e.g. Brooks and others, 1978; Zwally and others, 1983), or wind intensity (Remy and others, in press). Here, we will study the altimetric height as given by the Seasat altimeter over East Antarctica. The topography of continental ice is useful for models of ice-sheet flow, for climatic surveys, or for undulation studies. Ice-sheet topographies have been derived from Geos-3, Seasat, and Geosat data (Brooks and others, 1982, 1983; Zwally and others, 1983, 1987). The error estimation is as important as the topographic map itself. Up to now, the error has been estimated, mostly from internal con- sistency checks, at around I m. These estimates do not adequately take into account the error in the orbit nor the errors introduced by the slope of the ice surface. The objective of the present note is to propose, implement, and test a technique to derive reproducible ice-sheet topo- graphies and their error estimates. We will show that precision of less than I m is achievable with Seasat data. It is therefore suggested that the long-term evolution of ice- sheet topographies can indeed by estimated from satellite data. In the first section we discuss the various sources of error in satellite-altimeter measurements. The second section explains how unbiased estimates of the topography and its error can be obtained by an inverse technique. It relies on a priori covariances of the expected parameters and realistic estimates of the measurement errors which are described in section 3. The slope-error correction is further discussed in section 4 and an optimized technique to correct this error is 98 proposed. The method is then tested on small parts of the Antarctic ice sheet, and applied to Terre Adelie, using Seasat data (section 5). Further possible improvements and the consequences of the results are then discussed in sections 6 and 7. 1. THE ERRORS OF SATELLITE-ALTIMETER MEASUREMENTS OVER ICE SHEETS A radar altimeter transmits pulses toward the sub- satellite point and receives the returned signal, after reflection at the surface (see, for example, MacArthur, 1978). The transit time of the signal will provide the altimetric height. Three kinds of distinct errors affect its estimation. a. The measurement error This is the error in the distance between the satellite and the nearest point of the ice surface. The main difficulty arises from a correct estimation of the first return time of the signal, because return wave forms cannot be accurately described by a simple analytical model such as Brown's (1977). Also, as the distance to the surface varies quickly, the tracking system (which pre-positions the receiving window based on previous measurements) cannot follow the variations in height, and consequently (in the case of Seasat) the on-board estimate of height is inaccurate. A re-estimation of this height, named "retracking" must be applied. Brooks and others (1983) proposed to estimate the return time of the signal as the time when the received energy is 50% of the maximum return power. Martin and others (1983) fitted a functional, derived from Brown's model, to the altimeter wave form for retracking. Remy and others (in press) deduced the position of the middle of the leading edge from the total energy. The last method, tested on repeat profiles of the Seasat altimeter data, provides a reproducibility of 50 em Lm.S. This method, which is easier than that of Martin and others and more reproducible than that of Brooks and others, will be used here. Ridley and Partington (1988) recently suggested that volume retrodiffusion from the ice affects the wave forms of a radar altimeter. In this case, the height, with any retracking technique, would not correspond to the ice surface but to a level somewhat below (of the order of I m). This effect still requires further studies. In addition to the estimate of the transi t time of the signal, effects of propagation through the atmosphere should be considered. As the troposphere above continental ice is very dry (less than I g/cm 2 of water vapor), the so-called wet tropospheric corrections can be neglected (see, for example, Tapley and others, 1985). On the other hand, a dry tropospheric correction should be applied, related to the pressure at the surface. This correction, for an altitude varying from 1000 to Downloaded from https://www.cambridge.org/core. 02 Jan 2022 at 12:10:07, subject to the Cambridge Core terms of use.