Development and evaluation of closed‐form expressions for hysteretic soil hydraulic properties

A concise representation of hysteretic soil hydraulic properties is given based on a combination of M. T. van Genuchten's (1980) parametric K ‐ θ ‐ h model and P. S. Scott et al.'s (1983) empirical hysteresis model modified to account for air entrapment. The resulting model yields compact closed‐form expressions for the hysteretic water retention curve θ ( h ) and soil water capacity C( h ), as well as for the hydraulic conductivity function K ( h ). Depending on the degree of simplification involved, the model entails a total of 6–9 parameters which can be calibrated from direct measurements of θ ( h ) and saturated conductivity or by an inverse solution approach from transient flow experiments. Comparison of model‐predicted and measured K ‐ θ ‐ h relations for eight soils revealed one case in which model predictions were very poor. Model accuracy was judged to be acceptably good in the other cases. Mualern's modified (Y. Mualem, 1984) dependent domain model was found to be more accurate for soils with very narrow pore size distributions. Use of a simplified version of the proposed model with two parameters eliminated provided overall accuracy very similar to that of the more complex model. Numerical simulations of flow during transient infiltration and drainage using the proposed model and a variant of Y. Mualem's (1984) modified dependent domain model did not differ greatly and agreed reasonably well with experimental water content distributions, even when scanning curves were not described very accurately. By contrast, simulations without consideration of hysteresis produced highly unacceptable results. It is concluded that the proposed model provides a convenient and simple means of incorporating hysteretic effects into numerical flow models to provide significant improvement in prediction accuracy with little additional effort and with minimal data requirements.