Soil Water Retention Curve (SWRC) provides crucial information for understanding soil moisture retention, essential for agriculture, hydrology, engineering and environmental science applications. Many SWRC fitting models in the literature are based on empirical equations without a direct physical meaning. However, SWRC data is physically related to the soil’s porous structure and its interactions with the wetting fluid. Hence, the curve’s behavior reflects the porous complexity. Non-physical model equations might even be able to fit the data to be used in several applications; however, the search for physically fitting models representing the SWRC data as a smooth continuous distribution function can reflect new insights and information about this heterogeneous porous media. In this regard, the well-established physically-based Kosugi model is based on the assumption of lognormal pore size distributions. However, a general approach for any modality and distribution shape could be interesting. This paper proposes applying the mathematical method known as “” (ILT) to fit the Soil Water Retention Curve using a weighted superposition of exponential decays. This multi-exponential approach involves working with two physically related parameters, the amplitude and its respective characteristic matric potential, which are physically interpreted as the amount of pores that empty at that suction head. The ILT-EXP method proposed was implemented in Python software to fit the curves, and it is now available in an online web app. The evaluation of the ILT-EXP model to fit SWRC data is discussed, presenting its potential to estimate soil pore size distribution of multimodal samples. One advantage of ILT-EXP over other multimodal models is that it does not need to know how many modal components are present in the SWRC data, being automatically determined by the method. Finally, a statistical fitting comparison of 439 SWRC data, with six other classical models is discussed. The results indicate that fitting with the ILT-EXP model demonstrates strong potential, making it a powerful method for handling multimodal curves. This approach represents a novel and robust method for estimating a smooth, continuous soil pore size distribution.

中文翻译：

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拉普拉斯逆变换拟合土壤保水曲线并估计孔径分布


土壤保水曲线 (SWRC) 提供了了解土壤保水性的重要信息，这对于农业、水文学、工程和环境科学应用至关重要。文献中的许多 SWRC 拟合模型都是基于经验方程，没有直接的物理意义。然而，SWRC 数据在物理上与土壤的多孔结构及其与润湿流体的相互作用有关。因此，曲线的行为反映了多孔的复杂性。非物理模型方程甚至可以拟合在多种应用中使用的数据；然而，寻找将 SWRC 数据表示为平滑连续分布函数的物理拟合模型可以反映有关这种异质多孔介质的新见解和信息。在这方面，完善的基于物理的小杉模型是基于对数正态孔径分布的假设。然而，适用于任何形态和分布形状的通用方法可能会很有趣。本文建议应用称为“”（ILT）的数学方法，利用指数衰减的加权叠加来拟合土壤保水曲线。这种多指数方法涉及两个物理相关参数，即振幅及其各自的特征矩阵势，它们在物理上被解释为在该吸力头处排空的孔隙量。提出的 ILT-EXP 方法是在 Python 软件中实现的，以拟合曲线，现在可以在在线 Web 应用程序中使用。讨论了 ILT-EXP 模型拟合 SWRC 数据的评估，展示了其估计多模态样品土壤孔径分布的潜力。 与其他多模态模型相比，ILT-EXP 的优点之一是它不需要知道 SWRC 数据中存在多少模态分量，而是由该方法自动确定。最后，讨论了 439 个 SWRC 数据与其他六种经典模型的统计拟合比较。结果表明，ILT-EXP 模型的拟合显示出强大的潜力，使其成为处理多峰曲线的强大方法。这种方法代表了一种新颖且稳健的方法，用于估计平滑、连续的土壤孔径分布。