Scaling Parameter to Predict the Soil Water Characteristic from Particle-Size Distribution Data

The Arya-Paris model is an indirect method to estimate the soil water characteristic from particle-size data. The scaling parameter, a, in the original model was assumed constant for all soil textures. In this study, a is defined as a, = (logJV//log«,-), where n, is the number of spherical particles in the ith particle-size fraction (determined by the fraction solid mass, wh and mean particle radius, R,) and /V/ is the number of spherical particles of radius R, required to trace the pore length generated by the same solid mass in a natural structure soil matrix. An estimate for log A',was obtained by either relating log A', to log n, using a logistic growth equation or by relating log A', linearly to log (w,IR}) based on the similarity principle. For any given texture, both approaches showed that a was not constant but decreased with increasing particle size, especially for the coarse fractions. In addition, a was also calculated as a single-value average for a given textural class. The three formulations of a were evaluated on 23 soils that represented a range in particle-size distribution, bulk density, and organic matter content. The average a consistently predicted higher pressure heads in the wet range and lower pressure heads in the dry range. The formulation based on the similarity principle resulted in bias similar to that of the constant a approach, whereas no bias was observed for the logistic growth equation. The logistic growth equation implicitly accounted for bias in experimental procedures, because it was fitted to log N, values computed from experimental soil water characteristic data. The formulation based on the similarity principle is independent of bias that might be inherent in experimental data. T is AMPLE JUSTIFICATION for indirect methods of estimating soil hydraulic properties from routinely available taxonomic data (e.g., Bouma and van Lanen, 1987; van Genuchten and Leij, 1992). The effects of texture, bulk density, and organic matter on soil water retention and hydraulic conductivity have long been recognized. However, an explicit formulation of the relationship between texture and hydraulic properties of the soil remains a challenge because of the very complex pore-particle geometry. Hence, empirical approaches to predicting hydraulic properties at specific points of the water content-pressure-hydraulic conductivity curves from texture, bulk density, mineralogy, and organic matter content by using multiple regression techniques or neural network analyses remain popular (e.g., Rajkai and Varallyay, 1992; Tietje and Hennings, 1995). Mathematical representations of the water content-pressurehydraulic conductivity curves as a continuous function (Brooks and Corey, 1964; Mualem, 1976; and van Genuchten, 1980) require one or more fitting parameters, which are normally evaluated from the basic soil properties through regression (Kool et al., 1987; Rajkai et Lalit M. Arya, Feike J. Leij, Martinus Th. van Genuchten, and Peter J. Shouse, USDA-ARS, U.S. Salinity Lab., 450 W. Big Springs Rd., Riverside, CA 92507. Received 1 April 1998. *Corresponding author ([email protected]). Published in Soil Sci. Soc. Am. J. 63:510-519 (1999). al., 1996) or neural network techniques (Schaap and Bouten, 1996). Because the soil water retention curve is essentially a pore-size distribution curve, it is required as the primary input in models of the hydraulic conductivity based on pore-size distribution (e.g., Marshall, 1958; Millington and Quirk, 1961; Mualem, 1976). Thus, accurate water retention curves are of great importance. The first attempt to directly translate the particle-size distribution into a soil water characteristic was made by Arya and Paris (1981). The basis for their model is a close similarity between the shapes of the particle-size distribution and the water retention curve. In the model, the pore size that is associated with a pore volume is determined by scaling the pore length. Since particle size is normally expressed in terms of equivalent spheres, Arya and Paris (1981) estimated pore lengths for the various fractions of the particle-size distribution curve by summing the diameters of spherical particles in the fraction. Pore lengths based on spherical particles were scaled to natural pore lengths using a scaling parameter, a, with an average value of 1.38. A similar model was later proposed by Haverkamp and Parlange (1986) and tested on a coarse-textured sand. Tyler and Wheatcraft (1989) interpreted a. as being the fractal dimension of a tortuous pore. Since then, there has been a growing interest in the use of fractals to predict hydraulic properties from particle-size distributions (e.g., Rieu and Sposito, 1991; Tyler and Wheatcraft, 1992; Shepard, 1993). However, it should be noted that fractal scaling, inasmuch as it is concerned with the nature of fragmentation, accounts only for the effects of tortuosity of pore lengths, but not for other factors that influence water retention, such as packing density, chemical characteristics of solid surfaces, organic matter content, fluid properties, and air entrapment. Later investigations by Arya et al. (1982) showed that the average a varied among textural classes and ranged in value from 1.1 for finer textures to 2.5 for coarsetextured materials. A similar range of values was reported by Tyler and Wheatcraft (1989) for the fractal dimension. Yoshida et al. (1985) also reported higher values of a for coarse-textured materials. Several researchers (e.g., Schuh et al., 1988; Mishra et al., 1989; Gupta and Ewing 1992; Jonasson, 1992; Basile and D'Urso, 1997; Nimmo, 1997) have suggested that predictions of water retention curves would improve if a were formulated such that it varies over the range of particle sizes. The single values of a in the original study of Arya and Paris (1981) were obtained by minimizing the sum of squares of deviations between the measured and calculated pressures. The objective of the present study is to investigate of relationships between a and the particle-size distribution.