Scaling of Infiltration and Redistribution of Water across Soil Textural Classes

known (Tillotson and Nielsen, 1984): (1) the dimensional analysis technique, which is based on the existence of Results with an empirically based one-parameter model showed physical similarity in the system; and (2) the empirical that the pore-size distribution index ( ) described in the Brooks and Corey formulation of soil hydraulic properties can scale the soil–water method, called functional normalization, which is based retention curves below the air-entry pressure head ( b) values across on regression analysis. The similar-media scaling of Miller dissimilar soils. It is shown here that b and saturated hydraulic conand Miller (1956) and the fractal-based approaches of ductivity (Ks) are also strongly related to , and thus all hydraulic Tyler and Wheatcraft (1990), Rieu and Sposito (1991), parameters may be estimated from . The major objective here was and Hunt and Gee (2002a, 2002b) are examples of the to examine how these relationships to lead to relationships for first method. Most of the scaling work cited above has infiltration and soil water contents during redistribution across soil extended the similar-media scaling concept to field soils textural classes. The Root Zone Water Quality Model simulated infilthat are generally “non-similar” by invoking additional tration for four rainfall intensities and two initial pressure head condiempirical assumptions and using a regression method. tions and redistribution for four initial wetting depths and two initial pressure head conditions in 11 textural class mean soils. All infiltration Very limited research has been done on relating soil results across textural classes were scaled quite well by using the hydraulic properties across widely dissimilar soil tex-derived normalization variables based on the dimensional analysis tural classes. Gregson et al. (1987) showed that the slope of the Green–Ampt model. Thus, if infiltration for one soil ( ) is and intercept of the commonly used Brooks and Corey known, infiltration for other soils ( s) can be estimated. Additionally, (1964) log–log relationship for soil matric potential verwe present infiltration, as well as redistribution, as explicit functions sus water content, below the air-entry value, was highly of . These functions can be used to approximately estimate infiltracorrelated across 41 Australian and British soil classes. tion and soil water contents across soil types for other soils and This formed the basis for their one-parameter model conditions by interpolation. This study enhances our understanding of for estimating the soil water retention curve in any soil. the soil–water relationships among soil textural classes, and hopefully, provides a basis of further studies under field conditions for (i) estimatIn a recent book chapter, Williams and Ahuja (2003) ing spatial variability of soil water for site-specific management and showed that: (1) there was a strong relationship between (ii) for scaling up results in modeling from plots to fields to watersheds. the intercepts and slopes of textural class mean water retention curves (obtained using the geometric mean Brooks–Corey parameters) for 11 U.S. soil classes from S has been used as a tool for approximately sand to clay (Rawls et al., 1982); and (2) these curves describing field spatial variability of soil hydraulic could be scaled very well (brought together closely) using properties, specifically the matric potential and unsatutheir slopes as scaling factors. As a part of this study we rated hydraulic conductivity as a function of soil water found that Ks and the air-entry or bubbling pressures of content (e.g., Warrick et al., 1977; Simmons et al., 1979; these textural class mean curves also had a strong logaRusso and Bresler, 1980) as well as characteristics derithmic relation with their slopes. The air-entry value on rived from these, such as infiltration (Sharma et al., the log–log water retention curve defined by the slope– 1980). The frequency distribution and spatial–correlation intercept relation also determines the saturated soil structure of scaling factors describe variability in the water content. field, thus resulting in considerable simplicity and enFurther, if we accept the assumption that the unsatuhanced understanding as well as convenience in modelrated hydraulic conductivity curve can be estimated from ing a heterogeneous watershed for its hydrologic rethe known water retention curve, and Ks value, as estabsponses (Pachepsky et al., 2003; Nielsen et al., 1998; Peck lished by numerous investigations (See Green et al., et al., 1977; Sharma and Luxmoore, 1979; Warrick and 1982; Campbell, 1974) and used commonly by modelers, Amoozegar-Fard, 1979; Ahuja et al., 1984). Inversely, the slope of the log–log water retention curve, , can scaling can also be used to estimate soil hydraulic propbe used to estimate the conductivity curve as well. Thus, erties at different locations in a watershed from meathe slope of the water retention curve determines the surement of these properties at one representative locasoil hydraulic properties instrumental in infiltration and tion and limited data at other locations (Ahuja et al., soil water redistribution. 1985; Williams and Ahuja, 1991). The above relationships between and soil hydraulic Two methods to derive the scaling factors are wellproperties were derived through empirical means. Part of these relationships and correlations may be explained USDA-ARS, Great Plains Systems Research Unit, 2150 Centre Ave., through physical–statistical approaches, such as the fracBuilding D, Suite 200, Fort Collins, CO 80526. Received 2 Mar. 2004. tal theory (Tyler and Wheatcraft, 1990; Hunt and Gee, Soil Physics. *Corresponding author ([email protected]. 2002a, 2002b; Rieu and Sposito, 1991). However, real gov). soil systems are more complex, and these approaches Published in Soil Sci. Soc. Am. J. 69:816–827 (2005). have yet to explain the above relationships across soil doi:10.2136/sssaj2004.0085 textural classes. Further research to establish these rela© Soil Science Society of America 677 S. Segoe Rd., Madison, WI 53711 USA tions is a challenge for the future. 816 Published online May 6, 2005