顾及DEM误差空间自相关的地形变化检测方法

传统的地形变化检测方法忽略了DEM误差的空间自相关性，针对此问题，本文提出了顾及DEM误差空间自相关的地形变化检测方法。首先，通过2期DEM相减得到差值DEM（DoD），并通过蒙特卡罗方法评估DEM的误差空间分布；其次，基于DEM误差空间分布图，通过误差传播公式计算DoD误差，并使用半变异函数分析其空间自相关程度；最后，在误差空间自相关分析和显著性检测的基础上计算地形变化量（体积）和对应的误差限。本文在4个黄土小流域进行了实验，结果表明：无人机摄影测量DEM的高程误差存在一定程度的空间自相关，通过光束平差蒙特卡罗方法可以模拟无人机摄影测量DEM的误差空间分布；在进行地形变化检测时，使用误差空间分布代替中误差进行地形变化检测有效降低了检测结果对显著性阈值的敏感性；显著性阈值从68%提高到95%时，使用误差空间分布的检测结果损失的观测值比使用中误差低5.39%~6.75%。顾及空间自相关的地形变化检测方法能够更加科学、精确地量化地形变化特征，也可有效地应用于地表变形监测、流域侵蚀监测、输沙量评估等领域。

Topographic Change Detection that Considers the Spatial Autocorrelation of DEM Errors

Traditional topographic change detection methods often ignore the spatial autocorrelation of DEM errors. To solve this problem, a topographic change detection method that considers the spatial autocorrelation of DEM errors is proposed in this paper. Firstly, the DEM of Difference (DoD) is obtained from two original DEMs, and the spatial distribution of DEM errors is evaluated by the Monte Carlo method. Secondly, based on spatially distributed DEM errors, DoD errors are calculated by error propagation and their spatial autocorrelation degree is analyzed using the semi-variance function. Finally, topographic changes (erosion, deposition, and net changes) are calculated based on the spatial autocorrelation analysis and significance detection. The results in four small catchments show that the elevation errors of UAV-photogrammetry DEM are spatially autocorrelated, which can be simulated by the Monte Carlo method. The use of spatially distributed error instead of RMSE for topographic change detection effectively reduces the sensitivity of the detection results to the significance threshold. When the significance threshold is increased from 68% to 95%, the loss of observations using the spatially distributed error is 5.39%~6.75% lower than that using the RMSE. The proposed method can be effectively used in the fields of surface deformation monitoring, erosion monitoring, sediment transport assessment, and so on.