Approximation of van Genuchten Parameter Ranges from Hydraulic Conductivity Data

The use of retention function and relative conductivity function is essential for the calculation of flow in a variably saturated media using the Richards equation. A widely used mathematical model for this is the Mualem-van Genuchten model which requires the shape parameters $\alpha$ and $n$. These, however, are difficult to obtain. When data is scarce, $\alpha$ and $n$ are often taken from literature and may deviate largely from actual values. The current study presents a novel mathematical model for the approximation of $\alpha$ and $n$ and for the further estimation of realistic value ranges, which may be used as parameter space, for example, for the calibration of a numerical model. The model was developed for cases where data is scarce and only values of saturated hydraulic conductivity are available. It is based on a large data set from literature and it is demonstrated that the model estimates mean values from that data set with a good accuracy. In order to show the applicability of the model, a second data set has been compiled anew (provided as Supporting Information). The model is incorporated into the current version of the freeware computer program HYPAGS, which enables easy usage.