Improved Calibration of Time Domain Reflectometry Soil Water Content Measurements

Abstract

Time domain reflectometry (TDR) is becoming a widely used method to determine volumetric soil water content, θ, from measured effective relative dielectric constant (permittivity), ε, using the empirical θ(ε) Topp-Davis-Annan calibration equation. This equation is not adequate for all soils. The purpose of this study was to compare the Topp calibration equation with a theoretical (Maxwell-De Loor) and an empiricial (fitting exponent α) mixing model for the four components: solid phase (s), tightly bound water (bw), free water, and air. Water content permittivity were measured, gravimetrically and by TDR, on packed columns of 11 soils ranging from loess to pure bentonite. Measured specific surfaces were S = 25 to 665 m2 g−1 and bulk densities ρb = 0.55 to 1.65 g cm−3. Topp yielded accurate ε(θ) values only for the four soils with ρb > 1.30 g cm−3, including illite (S = 147 m2 g−1). Maxwell-De Loor gave similar accuracy for seven soils, including attapulgite (S = 270 m2 g−1, ρb = 0.55 g cm−3), assuming a monomolecular tightly bound water layer (thickness δ = 3 × 10−10 m; θbw = δ ρbS), εbw = 3.2, and εs = 5.0. The ε(θ) curve of these soils had the same shape as Topp. Two gibbsite soils with dissimilar curves required εbw = 3.2 and εs = 16 to 18, and two smectite soil materials required εbw = 30 to 50 and εs = 5.0, to obtain good fits. Deviations from Topp appear generally due more to the lower ρb and thus higher air volume fraction at the same θ associated with fine-textured soils than to tightly bound water with low ε. Both effects, as well as apparent anomalous behavior such as decreasing effective ε with increasing εs, can be accomodated by the Maxwell-De Loor equation. This makes it a better calibration equation than Topp. The empirical α model is sensitive to the unpredictable value of α and cannot accomodate anomalous behavior.