Time-Domain Reflectometry (TDR) Technique for the Estimation of Soil Permittivity

Time Domain Reflectometry (TDR) has been initially developed as a remote sensing electrical measurement tool and it has been widely used to detect cable faults and discontinuities of signal lines (Somlo & Hollway, 1969). Recently, TDR has been widely applied to soil science, hydrology and agronomy to estimate the electrical properties of soils (Courtney, 1998; Evett & Parkin, 2005; Nozaki & Bose, 1990; Robinson et al., 2003; Topp & Ferre’, 2002). The two major features of TDR waveforms are the travel time and the response ’late’ time amplitude: they are directly related to the apparent dielectric constant Ka and to the soil electrical conductivity γ (Robinson et al., 2005). If the assumption is made that the imaginary part of the complex electrical permittivity is small compared to the real part, only the real part of permittivity changes with soil water content, and if the real part is close to the apparent dielectric permittivity Ka (effective bulk permittivity), then water content can be evaluated by means of empirical formulas based on known value of Ka (Evett et al., 2005; Topp et al., 1980). Evaluation of the dielectric permittivity of a medium from its reflection response is an inverse problem in which the medium propagation behavior is used to infer its constitutive relations (Feng et al., 1999; Heimovaara, 1994; Lin, 2003; Oswald et al., 2006). Owing to this application, over the past twenty years great efforts have been spent on the calibration of the TDR system, i.e. the relationship between apparent dielectric permittivity and soil water content (Hansson & Lundin, 2006; Roth et al., 1990; Topp et al., 1980), on the design and testing of various type of probes (Canone et al., 2009; Evett et al., 2006; Robinson et al., 2005); and on the methods to solve the inverse problem of estimating permittivity from reflection responses (Heimovaara, 1994; Oswald et al., 2006). Regardless of the inversion method used, the model of the measurement system (relating measured waveforms to the unknown permittivity to be estimated) is the instrument enabling the permittivity estimation from the reflection response. The modeling of the TDR measurement system received, therefore, a great deal of attention in the past (Heimovaara, 1994; Lin, 2003). In spite of the advances in modeling of the TDR setup and in evaluation of permittivity from the TDR response, the intrinsic limitations introduced by the TDR 18