Soil water sustains life on Earth, and how to quantify water equilibrium and kinetics in soil remains a challenge for over a century despite significant efforts. For example, various models were proposed to interpret non-Darcian flow in saturated soils, but none of them can capture the full range of non-Darcian flow. To unify the different models into one overall framework and improve them if needed, this technical note proposes a theory based on the tempered stable density (TSD) assumption for the soil-hydraulic property distribution, recognizing that the underlying hydrologic processes all occur in the same, albeit very complex and not measurable at all the relevant scales, soil-water system. The TSD assumption forms a unified fractional-derivative equation (FDE) using subordination. Preliminary applications show that simplified FDEs, with proposed hydrological interpretations and TSD distributed properties, effectively capture core equilibrium and kinetic water processes, spanning non-Darcian flow, water retention, moisture movement, infiltration, and wetting/drying, in the soil-water system with various degrees and scales of system heterogeneity. Model comparisons and evaluations suggest that the TSD may serve as a unified density for the properties of a broad range of soil-water systems, driving multi-rate mass, momentum, and energy equilibrium/kinetic processes often oversimplified by classical models as single-rate processes.

中文翻译：

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统一的唯象模型捕捉土壤中的水平衡和动力学过程

土壤水维持着地球上的生命，尽管付出了巨大的努力，如何量化土壤中的水平衡和动力学仍然是一个多世纪以来的挑战。例如，人们提出了各种模型来解释饱和土壤中的非达西流，但没有一个模型能够捕获非达西流的全部范围。为了将不同的模型统一到一个整体框架中并在需要时对其进行改进，本技术说明提出了一种基于土壤水力特性分布的调和稳定密度（TSD）假设的理论，认识到潜在的水文过程都发生在同一区域中。 ，尽管非常复杂并且无法在所有相关尺度上测量土壤-水系统。TSD 假设使用从属关系形成统一的分数阶微分方程 (FDE)。初步应用表明，简化的 FDE 以及提出的水文解释和 TSD 分布特性，可以有效捕获土壤-水系统中的核心平衡和动态水过程，涵盖非达西流、保水、水分运动、渗透和润湿/干燥具有不同程度和规模的系统异质性。模型比较和评估表明，TSD 可以作为各种土壤-水系统特性的统一密度，驱动多速率质量、动量和能量平衡/动力学过程，而经典模型通常将其过度简化为单速率流程。