Application of the “proportionate partitioning” method suggested by Poulovassilis and Kargas (2000) for determination of the domain distribution function

Abstract

The soil water hysteresis model proposed by Poulovassilis and Kargas (Soil Sci. Soc. Am. J. 64:1947–1950, 2000) is considered in the present study. According to this model, the bivariate domain density distribution function f can be derived by partitioning the slopes of either of two main curves proportionally to the slopes of another. Accordingly, there are two possible ways of deriving function f. The basic claim of Poulovassilis and Kargas is that both possibilities lead to the same resultant function f, which can be evaluated using integral equation presented by them. The present study shows that the above two ways of determining function f actually lead to two incompatible partitioning models yielding different domain density distribution functions. Moreover, none of these two partitioning models can reproduce the measured hysteresis loop used for calibration. Whether the partitioning of the main wetting curve slopes proportionally to the main drying curve slopes or vice versa is applied, most of the predicted primary scanning curves deviate considerably from the measured ones, cross out the measured boundary loop and do not converge at an appropriate edge of the loop. The present study reveals that the above-mentioned integral equation, presented by Poulovassilis and Kargas, appears to be at variance with both partitioning models. It is shown herein that this integral equation unambiguously follows from Mualem (Water Resour. Res. 9:1324–1331, 1973) similarity hypothesis and, accordingly, the correspondent domain density distribution function derived as the unique analytical solution of this equation is evidently identical to that obtained by Mualem (1973). The predicted curves presented by Poulovassilis and Kargas are not obtained when any of the two partitioning models is applied, but when using the integral equation of Mualem’s (1973) model.