Closed‐Form Expressions for Water Retention and Conductivity Data

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Abstract
Closed‐form expressions for quantifying the unsaturated soil hydraulic properties are widely used in computer programs to model subsurface flow and transport in porous media and to investigate indirect methods for estimating these properties. For example, water retention data, which relate soil‐water pressure head (h) and effective water saturation (Se), are frequently used to predict the unsaturated hydraulic conductivity (K). However, the suitability of different functions to describe unsaturated hydraulic data has rarely been investigated comprehensively. We attempted to fit 14 retention and 11 conductivity functions to 903 sets of water retention and hydraulic conductivity data measured on soil and rock samples or horizons reported in the unsaturated hydraulic database UNSODA. Some of the best mean values for r2 and MSE for fitting Se(h) data were obtained with the retention functions reported by van Genuchten (1980), Globus (1987), and Hutson and Cass (1987). A function reported by Gardner (1958) could describe K (h) data quite well whereas functions reported by Brooks and Corey (1964) and van Genuchten (1980), which are respectively based on the conductivity models by Burdine and Mualem, yielded a relatively good description of K(SC) data.