Two- and three-parameter calibrations of time domain reflectometry for soil moisture measurement

Time domain reflectometry (TDR) is widely used to measure and monitor soil water. The commonly used calibration curve is the third-degree 'universal polynomial' of Topp et al. [1980]. The most common refinement is calibration to a specific soil but still using four parameters (coefficients)from fitting a third-degree polynomial. Here we demonstrate that a three-parameter expression, θ(v) = aK(a)/α + b, fits as close as or more closely than the four-parameter polynomial (where the three parameters a, b, and α are determined by fitting water content θ(v) to the dielectric coefficient K(a)). This form is consistent with the well-known mixing model. For an isotropic soil with homogeneous water distribution this expression is further simplified to two parameters by taking α = 0.5. When α is 0.5, its calibration is equivalent to the linear calibration between θ(v) and the travel time along the waveguide. In addition, the simple three-parameter expression can be easily inverted without losing accuracy with regard to the original calibration. The TDR calibration expressed in a three-parameter form not only achieves a good fit but also conveys a physical connotation.