Applications of Geostatistics in Optimal Design of Satellite Altimetry Orbits and Measurement Configurations

Abstract

The Geoscience Laser Altimeter System (GLAS) aboard NASA’s Ice, Cloud and land Elevation Satellite (ICESat) is a pulse-limited laser that records measurements in a geophysical track-line ground pattern of single discrete points along a sub-satellite track. Spacing between tracks depends on latitude and repeat cycle. Derivation of digital elevation models (DEMs) of the ice surface from GLAS data requires interpolation, which due to the spatial data distribution is mathematically an extrapolation problem, best solved using a form of geostatistical estimation. In this article, we investigate the relationships between observing ice surface elevations with single-beam and multi-beam altimetry, regional coverage and spatial resolution, orbit ground track design and repeat-track spacing, analysis with ordinary and advanced universal Kriging algorithms and resultant DEM accuracy. The study is a contribution to the ICESat-2 ad-hoc Science Definition Team tasks and analyzes GLAS data and several potential multi-beam configurations proposed for the ICESat-2 instrumentation. Measurement of elevation change at the accuracy required by the U.S. National Research Council (2007) “Decadal Survey” recommendations requires understanding the effects of spatial variability of the elevation measurement, in particular for complex, rough or steep natural surfaces. This problem, which is important to correctly assess the cryosphere’s contribution to sea-level rise, is treated using scale-dependent simulation. Results indicate that multi-beam laser measurements are needed and provide a solution to the trade-off problem between repeat-mission and geodetical coverage. More generally, the article demonstrates links between space mission planning, orbit design, spatial distribution of measurements from future instrumentation and improved mathematical data processing algorithms.