Closed‐Form Expressions for Water Retention and Conductivity Data

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 (Se) data.

[1]  J. W. Biggar,et al.  Simple field methods for estimating soil hydraulic conductivity. , 1980 .

[2]  Ken'ichirou Kosugi,et al.  Three‐parameter lognormal distribution model for soil water retention , 1994 .

[3]  Feike J. Leij,et al.  Analysis of Measured, Predicted, and Estimated Hydraulic Conductivity Using the RETC Computer Program , 1992 .

[4]  R. Zhang,et al.  NEW MODELS FOR UNSATURATED SOIL HYDRAULIC PROPERTIES , 1994 .

[5]  Keith Smettem,et al.  Describing soil hydraulic properties with sums of simple functions , 1993 .

[6]  John R. Nimmo,et al.  Modeling of soil water retention from saturation to oven dryness , 1994 .

[7]  L. A. Richards.  Capillary conduction of liquids through porous mediums , 1931 .

[8]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[9]  L. Ahuja,et al.  An Improved Form of Soil-Water Diffusivity Function , 1972 .

[10]  R. Carsel,et al.  Developing joint probability distributions of soil water retention characteristics , 1988 .

[11]  Gaylon S. Campbell,et al.  A SIMPLE METHOD FOR DETERMINING UNSATURATED CONDUCTIVITY FROM MOISTURE RETENTION DATA , 1974 .

[12]  W. M. Schuh,et al.  Effect of Soil Properties on Unsaturated Hydraulic Conductivity Pore-Interaction Factors , 1990 .

[13]  M. J. Fayer,et al.  Modified Soil Water Retention Functions for All Matric Suctions , 1995 .

[14]  Lynne Alexander,et al.  Predicting Unsaturated Hydraulic Conductivity from the Soil Water Characteristic , 1986 .

[15]  Y. Mualem.  A New Model for Predicting the Hydraulic Conductivity , 1976 .

[16]  W. Durner.  Hydraulic conductivity estimation for soils with heterogeneous pore structure , 1994 .

[17]  A. W. Warrick.  Correspondence of Hydraulic Functions for Unsaturated Soils , 1995 .

[18]  Bernd Diekkrüger,et al.  BIMODAL POROSITY AND UNSATURATED HYDRAULIC CONDUCTIVITY , 1991 .

[19]  W. R. Gardner.  SOME STEADY‐STATE SOLUTIONS OF THE UNSATURATED MOISTURE FLOW EQUATION WITH APPLICATION TO EVAPORATION FROM A WATER TABLE , 1958 .

[20]  Keith L. Bristow,et al.  Equation for extending water-retention curves to dryness , 1991 .

[21]  G. Lenhard.  THE DEHYDROGENASE ACTIVITY FOR THE STUDY OF SOILS AND RIVER DEPOSITS , 1966 .

[22]  H. Fujita.  The Exact Pattern of a Concentration-Dependent Diffusion in a Semi-infinite Medium, Part II , 1952 .

[23]  G. Hornberger,et al.  Empirical equations for some soil hydraulic properties , 1978 .

[24]  Lome G. Everett,et al.  A Comparison of Three Functional Forms for Representing Soil Moisture Characteristics , 1992 .

[25]  G. E. Laliberte,et al.  A MATHEMATICAL FUNCTION FOR DESCRIBING CAPILLARY PRESSURE-DESATURATION DATA , 1969 .

[26]  W. E. Larson,et al.  Modeling the pore structure of porous media , 1972 .

[27]  Wilfried Brutsaert,et al.  PROBABILITY LAWS FOR PORE-SIZE DISTRIBUTIONS , 1966 .

[28]  J. Hutson,et al.  A retentivity function for use in soil–water simulation models , 1987 .

[29]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[30]  David Russo,et al.  Determining soil hydraulic properties by parameter estimation: On the selection of a model for the hydraulic properties , 1988 .

[31]  D. R. Nielsen,et al.  On describing and predicting the hydraulic properties of unsaturated soils , 1985 .

[32]  Feike J. Leij,et al.  The RETC code for quantifying the hydraulic functions of unsaturated soils , 1992 .