Soils are composed of wide-ranged grains and grain size distribution (GSD) is the fundamental characteristic determining the physical and hydraulic properties. Previously we have proposed a GSD function for various soils. However, the remarkable discrepancy in the distribution occurs in some soils, which not only limits the applicability of the function but also raises doubt as to the possibility of a universal GSD function. In this study we modify the GSD function to a general form of P(D) ~ D^−μexp(−D/D_c)ⁿ, which introduces a new exponent n for the grain size scale. It turns out that this modification has eliminated the discrepancies and universally applies to a great variety of soils from around the world (hence to be a universal GSD function, UGSD). The exponent n is proved to be a scaling factor of grain size in log-scale and divides soils into three categories of n < 1 n > 1, and n = 1. Furthermore, soils of surface processes (e.g., erosion, tillage, desertification, landslides, avalanches, deposition, and sediment transportation) remain in the same category and preserve the UGSD function. Thus, the UGSD not only provides parameters μ and D_c as synthetic indices for soil properties (e.g., as indices for spatial heterogeneity or variables for pedotransfer functions), but also describes texture changes in dynamic processes. The UGSD function represents a ‘conservative law’ underlying soil genesis and processes, which fills the knowledge gaps related to the lack of universally applicable indices for soil properties, and thus has universal applications in soil classification, spatial variability, as well as dynamical processes.

中文翻译：

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一种具有标度不变性的通用土壤粒度分布

土壤由范围广泛的颗粒组成，粒度分布 (GSD) 是决定物理和水力特性的基本特征。之前我们已经提出了针对各种土壤的 GSD 函数。然而，在某些土壤中出现了显着的分布差异，这不仅限制了该函数的适用性，而且对通用 GSD 函数的可能性提出了质疑。在本研究中，我们将 GSD 函数修改为P ( D ) ~  D ^{− μ} exp(− D / D _c ) ⁿ的一般形式，它引入了一个新的指数n为粒度尺度。事实证明，这种修改消除了差异并普遍适用于来自世界各地的多种土壤（因此成为通用 GSD 函数，UGSD）。指数n被证明是对数尺度上粒度大小的比例因子，将土壤分为n  < 1 n  > 1 和n = 1三类。 此外，表层过程（如侵蚀、耕作、荒漠化）的土壤、滑坡、雪崩、沉积和沉积物输送）仍属于同一类别并保留了 UGSD 功能。因此，UGSD 不仅提供参数μ和D _c作为土壤特性的综合指数（例如，作为空间异质性指数或土壤传递函数的变量），但也描述了动态过程中的质地变化。UGSD 函数代表了土壤发生和过程的“守恒律”，它填补了与缺乏普遍适用的土壤特性指标相关的知识空白，因此在土壤分类、空间变异性和动力过程中具有普遍的应用。