A Novel Model for Terrain Slope Estimation Using ICESat/GLAS Waveform Data

The accurate estimation of terrain slope is very important for accurately monitoring the elevation and mass changes of glacier using laser altimeter. In this paper, a novel physical model was proposed for accurately estimating within-footprint terrain slope. The new proposed model was built based on overlapping footprints of the geoscience laser altimeter system (GLAS) data, namely, using altitude angle, footprint size, shape, orientation, terrain aspect, and ground extent. Ground extent estimation models were established on the basis of linear regression analyses between: 1) GLAS-derived waveform extent and airborne topographic mapper (ATM)-derived ground extent and 2) GLAS-derived waveform width and ATM-derived ground extent, respectively. In addition, the terrain slopes estimated from the overlapping footprints were validated by ATM data and compared with the slopes calculated from surface elevations, i.e., from ASTER global digital elevation model (DEM) (GDEM) and GLAS elevation. Results showed that the accuracy of waveform width-predicted ground extents ( $R^{2} = 0.868$ , RMSE = 0.686 m, $n = 20$ , and $p$ -value $R^{{\mathbf {2}}} = 0.776$ , RMSE = 0.824 m, $n = 20$ , and $p$ -value < 0.0001), which indicated that waveform width is more suitable for estimating ground extent. Slopes estimated from the new proposed model have a strong consistency with those calculated from ATM data (Corrcoef = 0.786, bias = 0.654°, SD = 1.368°, and RMSE = 1.452°). Additionally, results also indicated that the new proposed model performs much better than the methods based on ASTER GDEM and the GLAS surface elevation in estimating within-footprint terrain slope due to higher correlation, lower bias, standard deviation, and RMSE.