Mathematical Simulation‐Based Evaluation of Measurement Error Impacts on Topographic Change Detection

ABSTRACT Topographic change detection is widely applied in fields such as geological hazard early warning, environmental monitoring, and geographic process analysis. However, measurement errors—such as random and systematic errors—are inevitable during the acquisition of topographic data, and their propagation and accumulation can significantly increase the uncertainty of change detection results. This study aims to analyze the impacts of different types of measurement errors on topographic change detection and to assess whether appropriate detection methods can reduce these impacts. First, mathematical terrain surfaces were simulated, and three types of measurement errors, namely pure random error, spatially autocorrelated random error, and systematic error, were artificially introduced into the simulated point clouds. Then, three change detection methods—the Differencing of Digital Elevation Models (DoD), the Multiscale Model to Model Cloud Comparison using a vertically projected distance (M3C2‐V), and the M3C2 using a normal vector projected distance (M3C2‐N)—were applied to perform change detection under different error conditions. Finally, mean error (ME), standard deviation (STD), root mean square error (RMSE), mean absolute error (MAE), and Moran's I were used to evaluate the effects of error type and magnitude on topographic change detection. The results showed that pure random and spatially autocorrelated random errors caused only approximately 0.5%–3% volumetric deviations, whereas systematic error produced deviations exceeding 10% in some cases. For elevation‐change detection, pure random error had the weakest influence, spatially autocorrelated random error most strongly enhanced residual spatial clustering, and systematic error caused the greatest residual dispersion. Although the absolute ME values were small, STD increased by 9.21%–30.22% and 52.76%–172.82% under spatially autocorrelated random error and systematic error, respectively. The influence of measurement errors can be reduced by selecting an appropriate change detection method; DoD produced the smallest overall bias but was highly sensitive to error type, whereas M3C2‐V exhibited the greatest stability across different error types. These findings demonstrate that selecting an appropriate method can reduce the influence of measurement errors on topographic change detection.