A Mathematical Model for Soil-Water Characteristic Curve by Weibull Distribution

The soil-water characteristic curve (SWCC) plays a crucial role in unsaturated soil behavior. However, none of the models are fully applicable to all soil classes. Therefore, it is necessary to come up with more different models to best-fit the measured SWCC data. In this paper, a mathematical model (that is, Weibull model) for the soil-water characteristic curve was proposed based on two-parameters Weibull distribution. It only contains two parameters a and n, the effects of which on the SWCC are independent. The Brutsaert, van Genutchen, Boltzman and Weibull models were fitted to 24 SWCC data sets from UNSODA 2.0. The quality of fit for these models was compared. Results showed that Weibull model was desirably accurate to fit data from a variety of soil classes with 0.999 for R2 and 0.010 for RMSE. Taking into account the \(\overline {{{R^2}}}\), RMSE and ∑Ri criteria, it is therefore suggested that the exponential-based Weibull model had a higher fitting accuracy and performed marginally better than the Brutsaert and VG models. As respect to the criteria of AICc, the Weibull and Brutsaert models performed almost equally well but both had a better performance than VG model. The VG model had the largest average number of iterations, as such, it was relatively difficult to fit. However, the Boltzman model had a lower fitting accuracy and less flexibility in comparison with the other models. Consequently, the Weibull model could be used as an alternative to the soil-water characteristic curve models.