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.

Revisiting hydraulic hysteresis based on long‐term monitoring of hydraulic states in lysimeters

“…Although both models are founded on the dependent‐domain concept, the different assumptions of Mualem [] and Poulovassilis and Kargas [] lead to generally different model structures. The corresponding discussion between the authors about suitability and superiority of the different models did not result in a common agreement [ Kargas and Kerkides , ; Mualem and Beriozkin , ; Poulovassilis et al ., ].…”

Comments on the Paper “Application of the “Proportionate Partitioning” Method Suggested by Poulovassilis and Kargas (2000) for Determination of the Domain Distribution Function” by Mualem and Beriozkin (2008)

“…The three values of f thus obtained may not be identical. A final comment concerns the conclusion (number 5) (Mualem and Beriozkin 2008) about the zero values of F on the diagonal AB (Fig. 1).…”

“…The procedure for determining the latter values is described in detail in the above-mentioned paper of Poulovassilis and Kargas. Mualem and Beriozkin (2008) do not take into consideration Eqs. 5 and 6 of Poulovassilis and Kargas (2000) but, using as an excuse a general introductory statement contained in the paper of Poulovassilis and Kargas, they embarked in formulating a "theory" under the name of "proportionate partitioning," and applied it for drawing primary scanning curves shown in their Figures 3, 4, and 5 where there are compared with experimental ones presented by Poulovassilis (1970).…”