Topography complicates the illumination distribution over rugged terrains and hinders the applications of surface reflectance data over mountainous areas. Topographic correction is an essential process to remove the topographic effects in surface reflectance data. This study proposed a Physical model and image Simulation-based topographic Correction method (PSC) for atmospherically corrected surface reflectance images. In contrast with traditional methods, the proposed approach explicitly estimates the illumination distribution over rugged terrains based on image information and then corrects the topographic effects following physical laws. The proposed method was validated and compared with existing well-performed topographic correction methods, including path length correction (PLC), sun-canopy-sensor correction with c factor (SCSC), C correction (CC), and statistical empirical correction (SE). Simulated and satellite data obtained at different times and geolocations are used for evaluation and comparison. The results demonstrated that most existing methods face challenges in removing the biases induced by topography in surface reflectance images. The PLC method failed to obtain reasonable results for faint illumination conditions when the sun zenith angle is high. SE showed relatively poor performance in terms of physical consistency and outlier percentage. Besides, all the traditional methods failed in the correction of cast shadow regions. Comparably, our method consistently demonstrated superior performance in physical consistency, cast shadow correction, and outlier percentage across various regions, encompassing different sun zenith angles and illumination conditions. The proposed method offers an effective and physically consistent approach for the topographic correction of surface reflectance images, facilitating multi-temporal applications over mountainous areas.

中文翻译：

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集成物理模型和图像模拟来校正地形对表面反射率的影响

地形使崎岖地形的照度分布变得复杂，并阻碍了山区表面反射率数据的应用。地形校正是消除表面反射率数据中地形影响的重要过程。本研究提出了一种基于物理模型和图像模拟的地形校正方法（PSC），用于大气校正的表面反射率图像。与传统方法相比，该方法根据图像信息明确估计崎岖地形上的光照分布，然后根据物理定律校正地形效应。所提出的方法经过验证，并与现有的性能良好的地形校正方法进行了比较，包括路径长度校正（PLC）、带 c 因子的太阳冠传感器校正（SCSC）、C 校正（CC）和统计经验校正（SE） 。在不同时间和地理位置获得的模拟数据和卫星数据用于评估和比较。结果表明，大多数现有方法在消除表面反射图像中地形引起的偏差方面面临挑战。当太阳天顶角较高时，PLC 方法无法在微弱光照条件下获得合理的结果。 SE 在物理一致性和异常值百分比方面表现相对较差。此外，所有传统方法都无法对投射阴影区域进行校正。相比之下，我们的方法在物理一致性、投射阴影校正和不同区域的异常值百分比（涵盖不同的太阳天顶角和照明条件）方面始终表现出卓越的性能。该方法为表面反射图像的地形校正提供了一种有效且物理一致的方法，促进了山区的多时相应用。