通过对不同期数字高程模型（DEM，digital elevation model）的相减计算，可以获得侵蚀和淤积的空间分布及泥沙负载估算值，为了度量泥沙负载量估算的不确定性，提高野外切沟泥沙负载量的估算精度，该文提出了一种修正泥沙负载量估算值的方法，通过对大样本点云数据的统计抽样，得到了对应 DEM 差值结果不同坡度位置的误差δz，使得DEM误差具有一定的空间可变性，根据δz和DEM差值结果，通过t检验，建立了侵蚀和沉积发生的先验概率；再以侵蚀和沉积发生的空间相关性为基础，建立了一个由权重因子构成的概率修正滤波器，用来计算侵蚀和沉积发生的条件概率，最后，通过Bayesian推理方法，计算侵蚀和沉积发生的后验概率，用来更新和修正泥沙负载量估算值。经在甘肃天水桥子沟切沟应用，使用该文方法计算得到的侵蚀/沉积变化量相比未经处理的DEM差值结果和用Brasington和Lane方法修正的DEM差值结果估算的净负载量，在95%的置信水平下分别下降了13.13%和7.53%，经与天水水保站实际径流泥沙观测资料对照，与实际观测净负载量相差2%；该文同时还探讨了切沟坡度、点云点密度、地表粗糙度与侵蚀/沉积不确定性的关系，研究结果为提高黄土沟壑区侵蚀沟侵蚀量的估算精度提供了参考依据。%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 δz which was the error between the observed and calculated elevations, as the individual error, then the individual errors in DEMs can be propagated intoδcutfil 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.
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