General scaling rules of the hysteretic water retention function based on Mualem’s domain theory

Abstract

Based on the domain theory of hysteresis, the present study rigorously derives a unified scaling transformation for predicting the wetting scanning retention function, y w (c), following any sequence of wetting and drying processes, from the measured main wetting curve. It is proved theoretically that a shape-similarity exists among the different wetting curves of a given soil. Each wetting scanning curve and the main wetting curve are described by the same normalized equation, over the common interval of c values. This shape-similarity is a direct result of the Mualem domain theory. On this basis, a general unique equation is formulated for prediction of all wetting scanning curves, of all orders, which is compatible with the Mualem dependent, as well as independent, domain theory. On the same theoretical basis, it is proved that no similarity exists among the drying scanning curves. Thus, the use of the scaling transformation for prediction of the drying scans is subjected to inconsistency with the physical principles underlying the dependent domain theory. As a result, scaling in this case would inevitably lead to inaccuracies in the calculated drying curves. A significant step forward has been made in the present study, from Mualem's dependent domain model (1984) with its implicit predictive formulae of the drying scanning curves. A unique explicit equation was theoretically derived, applicable for describing the drying scanning curves of all orders. This unique equation of the drying scanning curves, together with the general single equation of the wetting scanning curves, provided closure of all theoretical wetting and drying scans within the main hysteresis loop. Consequently, the retention function following any sequence of successive wetting and drying processes can be predicted by these two equations determined by the measured boundary curves.

Conceptual and Parametric Representation of Soil Hydraulic Properties: A Review

“…9, using data reported by Huang et al (2005). The different approaches that have been applied to the modeling of hysteresis in WRC include empirical expressions, invasion–percolation theory, and independent and dependent domains theory, as reviewed by Pham and Barbour (2005) and Mualem and Beriozkin (2009).…”

“…Comparison between the performances of the different approaches and models can be found in Viaene et al (1994), Pham and Barbour (2005), and Mualem and Beriozkin (2009). The test performed by Viaene et al (1994) using 10 soils indicated that models calibrated by both branches of the main hysteresis loop performed better than those calibrated by a single main branch.…”

Infiltration into soils: Conceptual approaches and solutions

“…Temporal variability of intensity within the same rainfall event could induce drainage and redistribution to occur simultaneously in the same soil profile. Consequently, hysteresis in the () relationship [Haines, 1930;Everett, 1955;Poulovassilis, 1962;Topp, 1971;Mualem, 1974;Mualem and Dagan, 1975;Parlange, 1976;Hogarth et al, 1988;Nimmo, 1992;Huang et al, 2005;Mualem and Beriozkin, 2009] would play a crucial role in the accurate description of the flow processes within that soil profile [Ibrahim and Brutsaert, 1968;Hanks et al, 1969;Scott et al, 1983;Glass et al, 1989]. The capability to describe the ensemble of scanning curves within the hysteresis loop is necessary to achieve any reliable quantitative treatment of the flow process.…”

Infiltration from the Pedon to Global Grid Scales: An Overview and Outlook for Land Surface Modeling

“…The resulting desorption–sorption curves are generally not identical because equilibrium soil water content is greater at a given suction during drying than during wetting. The relationship of actual water content and matrix potential has been extensively studied by Haines (1930), Everett (1955), Poulovassilis (1962), Topp (1971), Mualem (1974), Mualem and Dagan (1975), Parlange (1976), Hogarth et al (1988), Nimmo (1992), Bachmann and van der Ploeg (2002), Huang et al (2005), and Mualem and Beriozkin (2009).…”