Terrain slope calculation from waveform of airborne LiDAR

In this paper, a novel physical model and its mathematical expressions were advanced to estimate the average slope of land by using LVIS data, which was collected in mountain area, California, USA. The proposed expressions were related not only to the laser scan angle and the laser divergence, but also to the pulse delay and the pulse width. In order to calculate the time width of the echo waveform and the mean pulse delay, a new curve-fitting method was proposed to fit the echo waveforms using a non-Gaussian mathematical function named as `Extreme function´. Different from the slope estimation from the DEM, the method proposed in this paper can make a more average estimation for the local slope within laser footprint. It can be used to calculate the average slope of land and estimate the roughness roughly.