Uncertainty of gully sediment budgets based on laser point cloud data

Abstract: Gully erosion has been recognized as one of the important processes in sediment production and land degradation in a wide range of environments. Soil loss rates by gully erosion represent from minimal 10% up to 94% of total sediment yield caused by water erosion. The recent advances in LIDAR provide the rapid acquisition method of topographic data at spatial resolutions. These advances make monitoring gully geomorphic changes and estimating sediment budgets through DEM (digital elevation model) differences, a tractable, affordable approach for monitoring applications in both research and practice.In order to reduce the uncertainty of the estimated gully morphological sediment loading produced by the DEM difference, a new method was presented in this paper, which allowed for more robust estimation of DEM uncertainties and propagated this forward to the estimation of morphological sediment loading. The method allowed for probabilistic representation of uncertainty and thresholding of the sediment loading at a user-specified confidence interval. 1000 times sampling were carried out by Matlab through the Bootstrap method to achieve which was the error between the observed and calculated elevations, as the individual error, then the individual errors in DEMs can be propagated into δcutfill as a priori probability. On this basis, the difference between the initial detection threshold values of DEM for preliminary screening was determined; then, the new approach modified this estimate on the spatial correlation of erosion and deposition units, which was based on a convolution filter creating a moving window of 5 × 5 cell size of DEM for calculating erosion/deposition conditional probability; finally, according to the prior probability, conditional probability and confidence level (95%), the minimum detection threshold value was established for the final corrected morphological sediment loading. Compared with those resulted from DEM difference without correction and from DEM difference corrected by Brasington and Lane method, the variable quantity of erosion and deposition estimated by this new method applied in typical gully in Qiaozigou, Tianshui, Gansu Province, decreased by 13.13% and 7.53% respectively at a 95% confidence interval. Moreover, the estimation value was only about 2% error with the observed sediment loading provided by the Water Conservation Station. Besides, the relations between the gully slope, point cloud density, surface roughness and the uncertainty of erosion/deposition were as followed: the greater the gully bank's slope, the greater the uncertainty of erosion/deposition; when the point density was in the range of 0~140 points/m2, the erosion/deposition showed a decreasing trend with the point density increasing, while, when the point density was more than 140 points/m2, erosion/deposition density had little change; the greater the gully surface roughness, the greater the erosion/deposition uncertainty, the greater the slope of the gully bank. Tests show that the new method provides a scientific basis for the monitoring of the Loess gully erosion morphological change and accurate estimation of erosion.