Wet-range physical realism in a model of soil water retention

Most models of soil water retention represent the wettest range simplistically, reflecting a high priority on facilitating computation without recognition of the active physical processes. Commonly the wet range is misleadingly represented by a straight line of zero slope, or by default using the same formulation as for the middle range, even though the mechanisms of water retention are different for the wet and middle portions of the range. Though adequate for some purposes, such treatment causes problems for applications that are sensitive to wet-range processes. It prevents accurate prediction of critical but challenging wet-range phenomena such as domain exchange between preferential flow paths and soil matrix. It limits the choices available for quantifying flow problems, for example a blowing-up of derivatives on approach to saturation prohibits the use of diffusivity-based formulations.

A new model addresses these issues for the important case where the medium is soil matrix material exclusive of macropores, thus having a well-defined air-entry value, and the moisture dynamics are the typical wet and dry cycling that achieves maximum wetness at field saturation, with a presence of trapped air at zero matric potential. The range between the air-entry value and field saturation is dominated by trapped air expansion in response to pressure change, as well as a process that increases the sensitivity to changing matric pressure. This enhanced sensitivity may be related in part to a collapse of liquid bridges between air pockets as they expand. For this wet range, the new model incorporates the Boyles’ law inverse-proportionality of trapped air volume and pressure, amplified by an empirical factor to account for the additional processes. To cover the full range of possible moisture, this wet-range formula is supplemented by two others. The middle range of capillary advance/retreat and Haines jumps is represented by a new adaptation of the lognormal distribution function. The adsorption-dominated dry range is represented by a logarithmic relation used in earlier models. Joined together with a continuous first-derivative constraint, the overall formulation recognizes the dominant processes within three segments of the full range. Optimization of five parameters can fit the model to a full data set.

Tests have demonstrated excellent fits, using measured data that have many closely spaced points in the wet and middle ranges. With their basis in process, the model’s parameters have a strong physical interpretation, and potentially can be assigned values without fitting, from knowledge of fundamental relationships or individual measurements. This basis in process also may permit accommodation of hysteresis by a systematic adjustment of the relation between the wet and middle ranges, and with minimal additional data may serve to facilitate estimation of other properties such as hydraulic conductivity, diffusivity, and sorptivity.