Comparative analysis of the apparent saturation hysteresis approach and the domain theory of hysteresis in respect of prediction of scanning curves and air entrapment

This study theoretically analyzes the concept of apparent saturation hysteresis, combined with the Scott et al. (1983) scaling approach, as suggested by Parker and Lenhard (1987), to account for the effect of air entrapment and release on the soil water hysteresis. We found that the theory of Parker and Lenhard (1987) is comprised of some mutually canceling mathematical operations, and when cleared of the superfluous intermediate calculations, their model reduces to the original Scott et al.’s (1983) scaling method, supplemented with the requirement of closure of scanning loops. Our analysis reveals that actually there is no effect of their technique of accounting for the entrapped air on the final prediction of the effective saturation (or water content) scanning curves. Our consideration indicates that the use of the Land (1968) formula for assessing the amount of entrapped air is in disaccord with the apparent saturation concept as introduced by Parker and Lenhard (1987). In this paper, a proper routine is suggested for predicting hysteretic scanning curves of any order, given the two measured main curves, in the complete hysteretic domain and some verification tests are carried out versus measured results. Accordingly, explicit closed-form formulae for direct prediction (with no need of intermediate calculation) of scanning curves up to the third order are derived to sustain our analysis.