Abstract The relative hydraulic conductivity curve Kr(h) = K/Ks is a key variable in soil modeling. This study proposes a model to represent Kr(h), the so-called Gardner dual (GD) model, which extends the classical Gardner exponential model to h values greater than ho, the suction value at the inflection point of the Kr(h) curve in the log-log scale. The goodness of fit of GD using experimental data from UNSODA was compared to that of the MVG [two-parameter (Kro, L) Mualem-van Genuchten] model and a corresponding modified MVG model (MVGm). In 77 soils without evidence of macropore flow, GD reduced the RMSE errors by 64% (0.525 to 0.191) and 29% (0.269 to 0.193) in relation to MVG and MVGm, respectively. In the remaining 76 soils, GD generally was less accurate than MVG and MVGm, since most of these soils presented evidence of macropore flow (dual permeability). GD has three parameters and two degrees of freedom, like MVG. Two of them allow the calculation of the macroscopic capillary length, a parameter from the infiltration literature. The three parameters are highly dependent on the Kr(h) data measurement in a short wet suction range around ho, which is an experimental advantage.

中文翻译：

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Gardner 指数方程的扩展以表示水力传导率曲线

摘要 相对导水率曲线Kr(h) = K/Ks 是土壤建模中的一个关键变量。本研究提出了一个代表 Kr(h) 的模型，即所谓的 Gardner 对偶 (GD) 模型，它将经典的 Gardner 指数模型扩展到大于 ho 的 h 值，即 Kr(h) 拐点处的吸力值对数-对数标度中的曲线。使用来自 UNSODA 的实验数据的 GD 拟合优度与 MVG [双参数 (Kro, L) Mualem-van Genuchten] 模型和相应的修正 MVG 模型 (MVGm) 的拟合优度进行了比较。在 77 种没有大孔隙流动证据的土壤中，GD 相对于 MVG 和 MVGm 分别将 RMSE 误差降低了 64%（0.525 至 0.191）和 29%（0.269 至 0.193）。在剩余的 76 个土壤中，GD 的准确度通常低于 MVG 和 MVGm，因为这些土壤中的大多数都呈现出大孔隙流动（双渗透性）的证据。GD 与 MVG 一样，具有三个参数和两个自由度。其中两个允许计算宏观毛细管长度，这是渗透文献中的一个参数。这三个参数高度依赖于在 ho 附近的短湿吸范围内的 Kr(h) 数据测量，这是一个实验优势。