Conversion of soil water retention and conductivity parameters from van Genuchten–Mualem to Groenevelt and Grant model

Abstract

The van Genuchten–Mualem (VGM) model is used largely to represent the relative soil hydraulic conductivity and soil water retention functions [Kr(Θ) and Θ(h)]. Alternative equations proposed by Groenevelt and Grant (GRT) present advantages regarding mathematical versatility. Considering the VGM model cannot be analytically converted into the GRT model, this study empirically related parameters n and α (VGM) to parameters p and k (GRT). We used 90 value combinations of n and α and minimised the sum of squared differences between VGM and GRT models. Linear equations were fitted and validated using soil samples from the UNSODA database. A singular equation of p as a function of n was fitted, while a two-step procedure was required to correlate k and α. All fits resulted in very high precision (r ≥ 0.999) and accuracy (RMSD ≤ 0.025 m3 m−3) for the water retention function and very high precision (r ≥ 0.994) for the hydraulic conductivity function. The accuracy for the Kr(Θ) function was high (RMSD ≤ 0.50) for 34 of the 40 tested soils. The derived empirical equations can be used to convert the equation parameters for Θ(h) regardless of soil type, and for Kr(Θ) with some restrictions upon parameter combinations.