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. . 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.
ASJC Scopus subject areas
- Water Science and Technology