Terrain slope estimation within footprint from ICESat/GLAS waveform: Model and method

Terrain slope of Greenland is usually calculated from surface elevation on a large scale. Novel physical models were established to estimate the terrain slope within laser footprints on a smaller scale. Based on the time-stamped waveforms of ice, clouds, and land elevation satellite/geoscience laser altimeter system (ICESat/GLAS), the physical models for calculating the slopes were established in two cases: zero attitude angles and non-zero attitude angles, respectively. The expressions of waveform slopes are related not only to the waveform width and the mean pulse delay of the time-stamped waveform, both in nanoseconds, but also to the attitude of the satellite and the laser divergence angle. In order to calculate the waveform width and the mean pulse delay, a non-Gaussian mathematical function was proposed to curve-fit the waveforms. The slopes estimated from the waveforms were compared with the slopes calculated from surface elevations. Results show that the two methods generate almost identical slope estimations for the same terrain. Calculation results also indicate that the method for slope estimation proposed in this paper performs better for extreme sloping terrain than for gentle sloping terrain.