Mapping of the Topography of Continental Ice by Inversion of Satellite-altimeter Data

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.

Brief communication "Importance of slope-induced error correction in volume change estimates from radar altimetry"

“…The second method, the relocation method, corrects R to R c , where R c is now the range to the point closest to the satellite (now R cos(α)), and displaces the location by R sin(α). The intermediate method, finally, finds the location where R = R c , and relocates the measurement to that point (Remy et al, 1989). When one is interested in elevation changes, errors in the vertical cancel out, but measurements are still located at the wrong locations.…”

Antarctic Ice Sheet and Radar Altimetry: A Review

“…This error, pointed out by Brooks et al [17] or Brenner et al [18] depends on the square of the surface slope so that, near the coast of Antarctica, the restitution of a precise topography in such places is complicated. The correction can be done either directly on the height at the nadir or by relocating the impact point in the upslope direction [18][19][20][21]. The limitation is due to the lack of knowledge of the 2-D surface slope that can be derived from an external base [22] or by iteration from an a priori DEM obtaining by fitting a bi-quadratic form over the local area [21].…”

“…The correction can be done either directly on the height at the nadir or by relocating the impact point in the upslope direction [18][19][20][21]. The limitation is due to the lack of knowledge of the 2-D surface slope that can be derived from an external base [22] or by iteration from an a priori DEM obtaining by fitting a bi-quadratic form over the local area [21]. Nevertheless, data processing can be developed to correct for (or minimize) these errors so that altimeter measurements reach a very good accuracy.…”

Assessment of CryoSat-2 interferometric and non-interferometric SAR altimetry over ice sheets

“…With their capacity to resolve changes at the scale of individual glacier basins, they have tracked signals of ice imbalance in Antarctica (Shepherd et al, 2001;Flament and Rémy, 2012;McMillan et al, 2014a;Wouters et al, 2015), Greenland (Zwally et al, 2005;Sørensen et al, 2015;McMillan et al, 2016) and the Arctic (McMillan et al, 2014b;Gray et al, 2015). They have also provided detailed topographic information (Remy et al, 1989;Bamber and Bindschadler, 1997;Bamber et al, 2009;Helm et al, 2014), which provides a boundary condition for numerical ice sheet models.…”