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

Abstract

Many empirical formulas relating TDR‐measured permittivity (Ka) to volumetric water content (θ) have been presented owing to the lack of a robust and accurate physically derived model describing this relationship across a range of soils. Soil‐specific calibrations are often infeasible due to the time‐consuming gravimetric sampling required for adequate calibration. In this work we propose a sample scale model for the Ka–θ relationship in coarse‐grained media using physically based pore‐scale, or calibrated two‐point, anchoring. Materials tested include mono‐size glass spheres and quartz sand grains in addition to two sandy soils. The performance of the model was comparable with the empirical models of Topp et al. (1980) for the different media. The model accounts for particle shape and bulk density using a two‐phase pore‐scale mixing model and refers to a wetting or draining profile with a sharp wetting or drying front. Our measurements indicate the absence of dielectric hysteresis for the narrow size distribution materials studied. An alternate calibration approach only requires the measured soil effective permittivities for dry (εdry) and saturated (εsat) conditions (i.e., two‐phase mixtures) and knowledge of the bulk density. We recommend a general value of 2.8 for εdry in soils with predominantly quartz mineralogy; the model then requiring only the εsat to develop a soil specific calibration. The results provide insight into the appropriate ‘refractive index’ modeling of layered (wetting/drying) soil profiles with the grain‐scale modeled two‐phase permittivity providing bounds for the sample‐scale three‐phase porous medium.