黄土高原土壤侵蚀严重、地形地貌破碎复杂，精细量化土壤侵蚀过程对区域土壤侵蚀机理研究、侵蚀模型构建以及侵蚀防治意义重大。激光雷达获取的密集点云数据可准确描述三维地形信息，为土壤侵蚀精细量化提供了可能，然而基于点云数据的复杂地形区变化监测算法匮乏，阻碍了激光雷达技术在土壤侵蚀研究中的应用。鉴于此，本研究以黄土丘陵沟壑区辛店沟和桥沟（二支沟）流域为研究区，提出了适用于坡面尺度地形变化监测的Slice Contraction Change Detection（SCCD）算法，以及适用于小流域尺度地形变化监测的SCCD-Watershed（SCCD-W）算法。然后，基于辛店沟原位坡面小区（A、B两小区）冲刷试验获取的实测产沙数据和地基激光雷达获取的地形点云序列，对比分析了SCCD算法与已有地形变化监测算法（3D-Multiscale Model-to-Model Cloud Comparison（3D-M3C2）和DEM of Difference （DoD））在复杂三维地形场景下的监测性能，评估了SCCD算法监测精度。最后，利用无人机激光雷达技术获取桥沟二支沟地面点云数据，以M3C2-GRID算法监测结果为基准值，对比了SCCD和SCCD-W算法的监测结果，评估了SCCD-W的监测精度。算法原理及评估结果如下：

（1）所提出算法首先对地面点云进行切片，利用余切权重拉普拉斯矩阵对点云切片进行收缩，准确提取地面点云切片轮廓。然后依次对点云切片无序轮廓点进行降采样和排序，利用面积微分方法计算切片面积。最后将切片面积与切片厚度相乘得到地形变化体积。结合坡面/小流域尺度地面点云特点，分别给出了使用固定厚度投影切片与统一Level of Detection（LoD）的SCCD算法，以及使用自适应厚度投影切片与空间分布式LoD的SCCD-W算法。

（2）坡面小区的监测算法对比结果表明，在复杂三维地形场景下，SCCD与3D-M3C2算法监测精度相当（A、B小区的平均相对误差分别为13.32%和10.37%，10.07%和10.84%），DoD算法监测精度最低（35.30%和27.23%），相对误差的标准差分别为5.79，8.29和10.18。当点云密度发生变化时（1.0×10⁴ points m^-2降至1.0×10³ points m^-2），三种算法对点云密度变化的敏感性排序为：3D-M3C2 > SCCD > DoD，A、B小区的平均相对误差范围分别为10.07~18.59%和10.84~13.62%，13.32%~16.83%和10.37%~15.50%，35.30%~38.33%和26.52%~27.26%。当点云形态差异增大时，SCCD和DoD算法的监测精度升高或保持稳定，A、B小区的相对误差分别为20.04%~9.95%和5.54%~7.96%，42.49%~11.94%和3.89%~4.96%，而3D-M3C2算法对点云形态变化高度敏感，A、B小区的相对误差变化分别为10.87~93.77%和30.76~167.89%。

（3）桥沟二支沟的算法评估结果显示，SCCD算法的相对误差为318.42%，绝对误差为732.55 m³，Kappa系数为0.033，均方根误差（Root Mean Square Error, RMSE）为0.081 m，平均绝对误差（Mean Absolute Error, MAE）为0.021 m。相较于SCCD算法，使用自适应厚度投影和空间分布式LoD的SCCD-W算法监测精度进一步提高（相对误差为12.74%，绝对误差为29.31 m³，Kappa系数为0.493，RMSE为0.011 m，MAE为0.006 m），模拟产沙体积和侵蚀沉积空间分布结果与基准值差异最小。

The Chinese Loess Plateau suffers from severe soil erosion and features fragmented and complex terrain. Precisely quantifying soil erosion processes is crucial for understanding erosion mechanisms, constructing erosion models, and implementing erosion control measures in this region. Light Detection and Ranging (LiDAR) technology provides accurate description of three-dimensional terrain information through dense point cloud data . However, monitoring algorithms for complex terrain changes based on point cloud data have been severely lacking, which hindered the application of LiDAR technology in soil erosion research. In this study, taking the Xindiangou and Qiaogou watershed as study areas, we developed the Slice Contraction Change Detection (SCCD) algorithm for slope-scale terrain change monitoring and the SCCD-Watershed algorithm (SCCD-W) for small watershed-scale terrain change monitoring. Using sediment yield measurements collected from runoff scouring experiments conducted on two erosion plots (plots A and B) constructed on natural slopes of the Xindiangou watershed, along with ground point cloud sequences obtained using terrestrial laser scanning, we compared the SCCD algorithm with existing algorithms for terrain change monitoring (3D-Multiscale Model-to-Model Cloud Comparison (3D-M3C2) and DEM of Difference (DoD)). We comprehensively evaluated the monitoring performance of these algorithms in complex three-dimensional terrain circumstance and validated the monitoring accuracy of the SCCD algorithm. Finally, using ground point cloud data acquired from unmanned aerial vehicle LiDAR, we compared the monitoring results of the SCCD and SCCD-W algorithms and also evaluated the monitoring accuracy of the SCCD-W algorithm, through taking the result of M3C2-GRID algorithm as a benchmark. The main results are as follows:

(1) The proposed algorithm firstly sliced the ground point cloud and employed a cotangent weight Laplacian matrix to contract the point cloud slices, accurately extracting the contour of the ground point cloud slices. Secondly, the unordered contour points of the point cloud slices were downsampled and sorted, and the area differential method was used to calculate the slice area, which was then multiplied by the slice thickness to obtain the terrain change volume. Considering the characteristics of slope-scale and small watershed-scale ground point clouds, two algorithms were finally developed, including the SCCD and SCCD-W algorithms. The former was based on fixed thickness projection slices and a unified Level of Detection (LoD), while the latter employed adaptive thickness projection slices and spatially distributed LoD.

(2) The comparison of three algorithms on the plots indicated that in complex three-dimensional terrain, the monitoring accuracy of SCCD was comparable to that of the 3D-M3C2 algorithm (average relative errors of plots A and B were 13.32% and 10.37%, 10.07% and 10.84%), while the DoD algorithm showed the lowest monitoring accuracy (35.30% and 27.23%). The standard deviations of relative errors for the SCCD, 3D-M3C2, and DoD algorithms were 5.79, 8.29, and 10.18, respectively. When the point cloud density changed from 1.0×10⁴ points m^-2 to 1.0×10³ points m^-2, the sensitivity of the three algorithms to changes in point cloud density were ranked as follows: 3D-M3C2 > SCCD > DoD. The average relative error ranges for plots A and B were 10.07%-18.59% and 10.84%-13.62%, 13.32%-16.83% and 10.37%-15.50%, 35.30%-38.33% and 26.52%-27.26%, respectively. As the differences in ground point cloud morphology increased, the monitoring accuracy of the SCCD and DoD algorithms either increased or remained stable. The relative error changes for plots A and B were 20.04%-9.95% and 5.54%-7.96%, 42.49%-11.94% and 3.89%-4.96%, respectively. However, the 3D-M3C2 algorithm was highly sensitive to differences in point cloud morphology. The relative error changes for plots A and B were 10.87%-93.77% and 30.76%-167.89%, respectively.

(3) The evaluation of the algorithmfor the Qiaogou watershed (Second Branch) indicated that the relative error of the SCCD algorithm reached 318.42%, with an absolute error of 732.55 m³, a Kappa coefficient of 0.033, a Root Mean Square Error (RMSE) of 0.081 m, and a Mean Absolute Error (MAE) of 0.021 m. Compared to the SCCD algorithm, the SCCD-W algorithm, which utilized the adaptive thickness projection and spatial distributed LoD, further improved monitoring accuracy (relative error of 12.74%, absolute error of 29.31 m³, Kappa coefficient of 0.493, RMSE of 0.011 m, MAE of 0.006 m), with the derived sediment yield and spatial pattern of erosion / deposition showing the smallest differences from the reference values.

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