A Physically Derived Water Content/Permittivity Calibration Model for Coarse-Textured, Layered Soils

to try and ascertain the relative importance of different soil properties for calibration. This approach has good Many empirical formulas relating TDR-measured permittivity (Ka) utility for finding simple and practical equations that can to volumetric water content ( ) have been presented owing to the lack of a robust and accurate physically derived model describing this be used to estimate . However, the limitation of such an relationship across a range of soils. Soil-specific calibrations are often approach is set by the required input parameters deinfeasible due to the time-consuming gravimetric sampling required scribing the soil attributes used in the analysis. for adequate calibration. In this work we propose a sample scale model An alternative approach to understand the permittivfor the Ka– relationship in coarse-grained media using physically ity response of unsaturated porous media is the ‘bottombased pore-scale, or calibrated two-point, anchoring. Materials tested up’ approach. This approach begins at the grain-scale include mono-size glass spheres and quartz sand grains in addition to and endeavors to reconstruct the sample-scale response two sandy soils. The performance of the model was comparable with based on the grain-scale properties. Maxwell (1881) dethe empirical models of Topp et al. (1980) for the different media. veloped a mixing model approach relevant for describThe model accounts for particle shape and bulk density using a twoing the electrical conductivity of heterogeneous sands. phase pore-scale mixing model and refers to a wetting or draining profile with a sharp wetting or drying front. Our measurements indicate Since then many dielectric-mixing models have been the absence of dielectric hysteresis for the narrow size distribution maproposed for different applications and geometries (Looterials studied. An alternate calibration approach only requires the yenga, 1965; de Loor, 1968; Dobson et al., 1985; Hilfer, measured soil effective permittivities for dry (εdry) and saturated (εsat) 1991; Heimovaara et al., 1994; Friedman, 1997; Friedconditions (i.e., two-phase mixtures) and knowledge of the bulk denman, 1998; Hilhorst et al., 2000). This approach has been sity. We recommend a general value of 2.8 for εdry in soils with preused extensively in the geophysics literature where satudominantly quartz mineralogy; the model then requiring only the εsat rated rocks present the simpler case of a two-phase meto develop a soil specific calibration. The results provide insight into dium (Sen et al., 1981; Kenyon, 1984). The extension the appropriate ‘refractive index’ modeling of layered (wetting/drying) of these methods to the problem of three-phase, unsatusoil profiles with the grain-scale modeled two-phase permittivity prorated soils presents a difficult conceptual and mathematviding bounds for the sample-scale three-phase porous medium. ical problem. Friedman (1998) applied an effective medium approach using two types of configurations for the air, water, and solid phases with some success. In that T et al. (1980) proposed a sample-scale empirical work, the modeled three-phase Ka– relationship is very calibration between apparent permittivity (Ka) measensitive to the solid/water/air geometrical configuration. sured using time domain reflectometry (TDR) and soil We analyze a less complex situation where the wetvolumetric water content ( ): ting/draining of the material leads to distinct, almost sat( 530 292Ka 5.5K a 0.043K a) 10 4 [1] urated and unsaturated layers as is commonly encountered in soils. The aim of the work is to determine if a This so-called ‘universal calibration’ equation obtained modeling approach requiring easily measurable paramfrom a fit to four mineral soils is widely used in coarse eters can be used to successfully describe the sampleand medium-textured soils and has proved very successscale dielectric response of the coarse grained layered maful. However, in some soils containing clays (Bridge et al., terial. The modeling approach capitalizes on previously 1996) and organic matter (Schaap et al., 1996), or in agacquired insight into the grain-scale dielectric phenomgregated (Miyamoto et al., 2003) or anisotropic porous ena for the prediction of the sample-scale response, and media (Jones and Friedman, 2000), this equation doesn’t can be applied as a new field calibration, especially in describe the lower permittivity values often measured. conditions where a TDR probe is inserted vertically (i.e., Many other empirical equations have been presented perpendicular to the wetting–drying front in a coarsethat seek to incorporate the effects of soil texture and textured soil). It also serves for exploring how we can density to overcome this (Roth et al., 1992; Malicki et al., better understand sample-scale dielectric measurements 1996; Yu et al., 1997). Complex learning algorithms such in soils. The limitations of the model are that it is develas neural networks have been used (Persson et al., 2002) oped for coarse-grained media and does not account for the presence of bound water. D.A. Robinson, S.B. Jones, and J.M. Blonquist Jr., Dep. of Plants, Soils and Biometeorology, Utah State Univ., Logan, UT 84322-4820; S.P. Friedman, The Institute of Soil, Water and Environmental SciMATERIALS AND METHODS ences, (ARO) The Volcani Center, Bet Dagan 50250, Israel. Received 24 Nov. 2004. *Corresponding author ([email protected]). Granular Materials and Soils Published in Soil Sci. Soc. Am. J. 69:1372–1378 (2005). In our first experiment three coarse-grained media were Soil Physics used to fill TDR cells, two types of 500m glass beads (Mo-Sci doi:10.2136/sssaj2004.0366 © Soil Science Society of America 677 S. Segoe Rd., Madison, WI 53711 USA Abbreviations: TDR, time domain reflectometry. 1372 Published online August 4, 2005