An In-Depth Examination of the Philip Equation for Cataloging Infiltration Characteristics in Rangeland Environments

Abstract

The objective of this study was to investigate the use of Philip's equation coefficients (which have, in theory, direct physical meaning) to characterize infiltration on rangelands. It was found that a least squares regression approach to estimating Philip equation parameters (S and A) essentially reduces A, and perhaps S, to empirical coefficients. However, the Philip equation does provide a model that fits infiltrometer data reasonably well and reflects signiflcant differences between infiltration curves. The effects of land management and temporal variables (e.g., soil moisture, season) may be associated with changes in S and A for particular sites. Indexing of inflltration curves by model coefficients allows for infiltrometer data from different researchers to be pooled and provides a basis for simulation modeling of infiltration and runoff on small watersheds. Coefficients are tabulated for a variety of rangeland plant communities for easy reference by practicing rangeland hydrologists. Researchers who present infiltration data in the future are urged to represent their data, at least in part, in the form of S and A coefficients to expand results tabulated from this study. Authors are graduate research assistant and professor, respectively, Watershed Science Unit, College of Natural Resources, Utah State University, Logan. Mr. Jaynes is currently attending law school at the University of Utah. This work was supported jointly by the Utah Agricultural Experiment Station (Proj. 749) and the United States Department of the Interior, Office of Water Research and Technology, Project No. E143-Utah, Agreement No. 14-34-0001-7193, as authorized under the Water Resources Research Act of 1964, as amended. Technical paper No. 2483, Utah Agricultural Experiment Station, Logan, 84322. Thanks are due Dr. Will Blackburn, Texas A&M University, for use of data relative to Nevada plant communities. Manuscript received November 14, 1979. Water movement through the soil-air interface (or infiltration) may be regarded as one of the most important processes on rangeland watersheds. Indeed, in an environment where convective rainstorms produce the majority of watershed runoff and erosion events, infiltration characteristics are key factors in determining the extent of soil loss, gully formation, and stream sedimentation. Since soil moisture on rangelands is often the most limiting resource for plant growth, the occurrence of surface runoff inhibits storm precipitation from promoting on-site forage production. In many instances, the main goal of rangeland watershed management is to simply prevent overland flow. Therefore, the variability in infiltration characteristics among plant communities and as a consequence of land management becomes an important item of study. The ability to understand and predict infiltration characteristics and runoff events on rangeland watersheds (where extensive rainfall-runoff data rarely exists) is of great value to watershed hydrologists. There exists a variety of empirical techniques which are intended to simulate individual processes as well as the overall infiltration phenomenon. The development of infiltration models based on physically meaningful quantitative theories may well provide rangeland hydrologists with infiltration and runoff indexes which are more interpretable. Such models present the opportunity of utilizing infiltration characteristics of individual plant communities to predict watershed runoff events. The two major objectives of this study were: (1) to investigate utilizing the well-known Philip infiltration model to index infiltration characteristics of rangeland communities (i.e., spatial variability both within and among different soil-plant complexes), and (2) JOURNAL OF RANGE MANAGEMENT 34(4), July 1981 285 This content downloaded from 207.46.13.48 on Wed, 12 Oct 2016 05:48:34 UTC All use subject to http://about.jstor.org/terms to determine what magnitude of change (or +) must be experienced in equation coefficients before temporal changes affecting community infiltration characteristics are deemed significant (e.g., the effects of land management, season, and antecedent soil moisture). The Philip Equation: Philip's infiltration equation is: I(t) = St 12 + A T (1) where: I(t) is cumulative infiltration at a given time (t) (cm), S is (cm/ hr1/2), and A is a permeability coefficient or gravity term (cm/hr). Chapter 7 of Kirkham and Powers(1972)containsa detailed analysis of the mathematics of the Philip equation. The first term of equation (1) describes the uptake of water by porous media via forces and dominates infiltration when time is small (Philip 1957a, b). This term contains a coefficient S, or (cm/hr1/2 ), which bears resemblance to the terms permeability, capillary conductivity, and absorptivity. The term sorptivity is preferred by Philip (1 957b) because it embraces both the concepts of absorption and desorption (i.e., the ability of the soil pores to absorb and release water by capillarity). Sorptivity may also be discussed in terms of pore-liquid geometry (Philip 1957b). Although the parameter is not a directly measurable soil attribute, it may be derived from actual soil properties (Hanks and Ashcroft 1976). The differential form of equation (1) is: