A COMPARISON OF 3 FUNCTIONAL FORMS FOR REPRESENTING SOIL-MOISTURE CHARACTERISTICS

Three functional forms relating capillary pressure to soil saturation (the Brooks and Corey equation, the Boltzmann distribution, and the Fermi distribution) were evaluated and compared by matching each form to soil moisture characteristic data for 12 different soil types. Out of 113 data sets, the Boltzmann distribution and the Brooks and Corey equation performed very well-and almost equally well-in matching the soil moisture data. Only 10 data sets were significantly better matched by the Boltzmann distribution, and only nine data sets were significantly better matched by the Brooks and Corey equation. The Fermi distribution did not achieve as high a rate of success, although unlike the other two functional forms, it was able to match data in all regions of the curve, including the capillary fringe. Considering that the Brooks and Corey equation and the Boltzmann distribution performed almost equally well, the Boltzmann distribution has an additional advantage: it is amenable to an analytic solution to the governing differential equation for flow in unsaturated media. Based on the results of this study, the authors recommend use of the Boltzmann distribution.