Modeling of soil water retention from saturation to oven dryness

Most analytical formulas used to model moisture retention in unsaturated porous media have been developed for the wet range and are unsuitable for applications in which low water contents are important. We have developed two models that fit the entire range from saturation to oven dryness in a practical and physically realistic way with smooth, continuous functions that have few parameters. Both models incorporate a power law and a logarithmic dependence of water content on suction, differing in how these two components are combined. In one model, functions are added together (model “sum”); in the other they are joined smoothly together at a discrete point (model “junction”). Both models also incorporate recent developments that assure a continuous derivative and force the function to reach zero water content at a finite value of suction that corresponds to oven dryness. The models have been tested with seven sets of water retention data that each cover nearly the entire range. The three-parameter sum model fits all data well and is useful for extrapolation into the dry range when data for it are unavailable. The two-parameter junction model fits most data sets almost as well as the sum model and has the advantage of being analytically integrable for convenient use with capillary-bundle models to obtain the unsaturated hydraulic conductivity.