The non‐Lambertian surface features varying particle size and discrete distribution, resulting in reflectance to be unevenly distributed in different directions. Mine soil with a high content of coarse particles and non‐uniform particle distribution exhibits significant non‐Lambertian properties on its surface. Consequently, not only vertical observation of the reflectance spectra but also multi‐angle reflectance spectra are related to the physical and chemical properties (e.g. soil organic carbon, moisture content and particle size) of mine soil. Understanding the bidirectional reflectance distribution of mine soil with various particle sizes is essential for accurately estimating soil properties using spectroscopy. Current estimations of soil properties using spectroscopy mainly focus on vertical observations, overlooking the bidirectional reflectance characteristics. This study reports the bidirectional reflectance distribution of mine soil with various particle sizes. Furthermore, the performance of different bidirectional reflectance distribution function (BRDF) models in simulating the bidirectional reflectance of mine soil with various particle sizes was evaluated. Soil samples from three typical mine areas were collected and sieved into seven particle sizes ranging from 25 to 3500 μm. The bidirectional reflectance in the Vis–NIR wavelength region was measured in a laboratory using the Northeastern University bidirectional reflectance measurement system. The performance of five BRDF models (isotropic multiple scattering approximation, anisotropic multiple scattering approximation, H2008, H2012 and SOILSPECT) in modelling the bidirectional reflectance distribution of mine soil with different particle sizes was compared. Sobol's sensitivity indices were used to quantify the contributions of the parameters in the BRDF models. The results showed that (1) small mine soil particles (25 μm) exhibited greater reflectance than large particles (3500 μm). Large particles (3500 μm) exhibited backward scattering, whereas small particles (25 μm) exhibited extremely forward scattering characteristics because of the high silicon dioxide content; (2) the SOILSPECT model outperformed the other BRDF models in simulating the bidirectional reflectance of mine soil and had the smallest root mean square error (0.004–0.04); (3) the single‐scattering albedo (ɷ) parameter had the greatest contribution in the SOILSPECT model. Four parameters in the phase function (b, b′, c and c′) effectively indicated the scattering behaviour of mine soil with different particle sizes. These findings improve our understanding of the scattering characteristics of mine soil with various particle sizes and can be used to improve the accuracy of extracting particle size and other soil properties from mine soil.

中文翻译：

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使用物理模型定量表征矿土的双向反射率分布


非朗伯表面具有不同的粒径和离散分布，导致反射率在不同方向上分布不均匀。粗颗粒含量高且颗粒分布不均匀的矿土在其表面表现出显著的非朗伯特性。因此，不仅反射光谱的垂直观察，而且多角度反射光谱都与矿井土壤的物理和化学性质（例如土壤有机碳、水分含量和粒径）有关。了解各种粒径的矿土的双向反射率分布对于使用光谱学准确估计土壤特性至关重要。目前使用光谱学对土壤特性的估计主要集中在垂直观察上，而忽略了双向反射特性。本研究报告了不同粒径的矿土的双向反射率分布。此外，还评估了不同双向反射率分布函数 （BRDF） 模型在模拟不同粒径矿土双向反射率方面的性能。收集来自三个典型矿区的土壤样品，并将其筛分为 25 至 3500 μm 的 7 种粒径。Vis-NIR 波长区域的双向反射率是在实验室中使用东北大学双向反射测量系统测量的。比较了 5 种 BRDF 模型（各向同性多重散射近似、各向异性多重散射近似、H2008、H2012 和 SOILSPECT）对不同粒径矿土双向反射率分布进行建模的性能。 Sobol 的敏感性指数用于量化 BRDF 模型中参数的贡献。结果表明：（1） 小矿土颗粒 （25 μm） 的反射率高于大颗粒 （3500 μm）。大颗粒 （3500 μm） 表现出后向散射，而小颗粒 （25 μm） 由于二氧化硅含量高，表现出极强的前向散射特性;（2） SOILSPECT 模型在模拟矿土的双向反射率方面优于其他 BRDF 模型，并且具有最小的均方根误差 （0.004-0.04）;（3） 单散射反照率 （ɷ） 参数在 SOILSPECT 模型中的贡献最大。相函数中的 4 个参数 （b、b′、c 和 c′） 有效地表明了不同粒径矿土的散射行为。这些发现提高了我们对各种粒径矿土散射特性的理解，可用于提高从矿井土壤中提取粒径和其他土壤特性的准确性。