Improved Calibration of Time Domain Reflectometry Soil Water Content Measurements

Abstract

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 m 2 g −1 and bulk densities ρ b = 0.55 to 1.65 g cm −3 . Topp yielded accurate ε(θ) values only for the four soils with ρ b > 1.30 g cm −3 , including illite ( S = 147 m 2 g −1 ). Maxwell‐De Loor gave similar accuracy for seven soils, including attapulgite ( S = 270 m 2 g −1 , ρ b = 0.55 g cm −3 ), assuming a monomolecular tightly bound water layer (thickness δ = 3 × 10 −10 m; θ bw = δ ρ b S), ε bw = 3.2, and ε s = 5.0. The ε(θ) curve of these soils had the same shape as Topp. Two gibbsite soils with dissimilar curves required ε bw = 3.2 and ε s = 16 to 18, and two smectite soil materials required ε bw = 30 to 50 and ε s = 5.0, to obtain good fits. Deviations from Topp appear generally due more to the lower ρ b 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 ε s , 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.