2-PARAMETER AND 3-PARAMETER CALIBRATIONS OF TIME-DOMAIN REFLECTOMETRYFOR 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 refineme nt is calibration to a specific soil but still using four parameters ( coefficients) from fitting a third-degree polynomial. Here we demonstr ate that a three-parameter expression, theta(upsilon) = aK(a)(alpha) b, fits as close as or more closely than the four-parameter polynomia l (where the three parameters a, b, and alpha are determined by fittin g water content theta(upsilon) to the dielectric coefficient K-a). Thi s form is consistent with the well-known mixing model. For an isotropi c soil with homogeneous water distribution this expression is further simplified to two parameters by taking alpha = 0.5. When alpha is 0.5, its calibration is equivalent to the linear calibration between theta (upsilon) and the travel time along the waveguide. In addition, the si mple 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 a lso conveys a physical connotation.