Estimation of lidar-based gridded DEM uncertainty with varying terrain roughness and point density

Light detection and ranging (lidar) scanning systems can be used to provide a point cloud with high quality and point density. Gridded digital elevation models (DEMs) interpolated from laser scanning point clouds are widely used due to their convenience, however, DEM uncertainty is rarely provided. This paper proposes an end-to-end workflow to quantify the uncertainty (i.e., standard deviation) of a gridded lidar-derived DEM. A benefit of the proposed approach is that it does not require independent validation data measured by alternative means. The input point cloud requires per point uncertainty which is derived from lidar system observational uncertainty. The propagated uncertainty caused by interpolation is then derived by the general law of propagation of variances (GLOPOV) with simultaneous consideration of both horizontal and vertical point cloud uncertainties. Finally, the interpolated uncertainty is then scaled by point density and a measure of terrain roughness to arrive at the final gridded DEM uncertainty. The proposed approach is tested with two lidar datasets measured in Waikoloa, Hawaii, and Sitka, Alaska. Triangulated irregular network (TIN) interpolation is chosen as the representative gridding approach. The results indicate estimated terrain roughness/point density scale factors ranging between 1 (in flat areas) and 7.6 (in high roughness areas), with a mean value of 2.3 for the Waikoloa dataset and between 1 and 9.2 with a mean value of 1.2 for the Sitka dataset. As a result, the final gridded DEM uncertainties are estimated between 0.059 m and 0.677 m with a mean value of 0.164 m for the Waikoloa dataset and between 0.059 m and 1.723 m with a mean value of 0.097 m for the Sitka dataset.