Parameter Estimation for Soil Hydraulic Properties Using Zero-Offset Borehole Radar: Analytical Method

ity and the van Genuchten . In this study, we apply this approach to measurements of wetting front advance Inverse methods to obtain soil hydraulic parameters are becoming made under simulated field conditions. increasingly popular, due to their more rapid, complete, and robust estimations of hydraulic parameters compared with traditional direct Standard methods typically determine the hydraulic methods. We present a method to infer hydraulic parameters based on parameters for small disturbed soil samples. It can be first arrival travel time measurements made with zero-offset borehole difficult to make quantitative use of these measurements ground penetrating radar (BGPR). Borehole ground penetrating rato characterize flow and transport in a heterogeneous dar offers many advantages for field-scale monitoring of transient field site (Wang et al., 2003). Existing field methods are processes including the ability to measure rapidly, over relatively large intrusive and/or disruptive of the flow system under soil volumes, with high temporal resolution and to great depths. The study (Inoue et al., 1998) and are often limited to near BGPR measurements are used to infer the position of the wetting surface measurement (Perroux and White, 1988). It would front during infiltration. The analysis makes use of critical refraction be advantageous to infer the hydraulic properties at the at the edge of the wetting front, which gives rise to a linear increase field scale with a method that causes minimal disturin BGPR travel time with time as the wetting front passes beneath the antennae. The slope of this response is used directly to calculate bance to the medium in which the measurements are the hydraulic conductivity. We demonstrate that unique determination made. Ideally, this method would allow for profiling of the van Genuchten and n parameter is not possible with BGPR and mapping of the hydraulic properties. data alone; at least one pressure head measurement in the dry range Many geophysical methods are nonintrusive (mea(early time) is required. We employ a nonlinear least squares paramsurements made at the ground surface) or minimally eter estimation code to obtain the optimal and n parameters for intrusive (measurements made within a borehole). As synthetic data. The method could potentially be applied to areas a result, these methods are good candidates for obof artificial recharge in an infiltration basin, natural recharge in an taining the measurements needed to infer hydraulic ephemeral stream, or agricultural settings where the surface is flooded properties (e.g., Binley et al., 2002; Hubbard et al., 1998; with irrigated water. Yeh et al., 2002). In addition, many of these methods are rapid and measure over scales of interest that are more representative for field scale characterization of S hydraulic functions, such as those that describe vadose zone processes. Finally, borehole methods can the unsaturated hydraulic conductivity, soil-water offer high resolution profiling of hydrologic properties retention, and soil-water diffusivity as functions of presto great depths, which may lead to the ability to profile sure head, partially govern the movement of water in soil hydraulic properties. High frequency electromagan unsaturated soil during absorption, infiltration, and netic techniques, such as ground penetrating radar (GPR) drainage. Modeling of a wetting front during infiltration, and time domain reflectometry (TDR), provide robust for example, requires knowledge of these parameters indirect measurements of the volumetric water content to solve the Richards’ equation (Richards, 1931) of unwithin their sample volume through the empirical corresaturated water flow in porous media. With traditional lations with the dielectric permittivity (e.g., Topp et al., direct laboratory methods, the parameters are time-con1980). Low frequency or direct current electrical methsuming to measure and require restrictive initial and ods can also provide information regarding the volumetboundary conditions (Hopmans and Simunek, 1999; ric water content through correlation with the electrical Lambot et al., 2002). Several researchers have presented conductivity (Archie, 1942). However, this correlation improved methods to infer soil hydraulic properties is less unique than the correlation between dielectric through inverse procedures, for example, Warrick (1993) permittivity and volumetric water content, because elecand Inoue et al. (1998). We adopt the method of Warrick tric conductivity also depends on tortuosity, electrical (1993) in which the forward model uses the simplified conductivity of the soil matrix and electrical conductivanalytical representation of water flow given in Warrick ity of the pore water (de Lima and Niwas, 2000). et al. (1985). Warrick (1993) discusses how measureRucker and Ferré (2004b) demonstrated that BGPR ments of the wetting front position with time made in the in zero-offset profiling (ZOP) mode could be used to laboratory, together with an assumed van Genuchten n monitor the advance of a wetting front. They showed can be used to deduce the saturated hydraulic conductivthat when critical refraction of the electromagnetic waves is considered, the volumetric water content proD.F. Rucker and T.P.A. Ferré, Dep. of Hydrology and Water Refile could be determined from first arrival BGPR travel sources, Univ. of Arizona, Harshbarger Bldg. 11, P.O. Box 210011, times on a radargram. High temporal and spatial resoluTucson, AZ 85721. Received 17 Oct. 2003. *Corresponding author ([email protected]). Abbreviations: BGPR, borehole ground penetrating radar; bgs, below ground surface; EM, electromagnetic; TDR, time domain reflectomPublished in Soil Sci. Soc. Am. J. 68:1560–1567 (2004).  Soil Science Society of America etry; WCAC, Western Campus Agricultural Center; ZOP, zero-offset profiling. 677 S. Segoe Rd., Madison, WI 53711 USA