Application of dispersion theory to time domain reflectometry in soils

With time domain reflectometry (TDR) two dispersive parameters, the dielectric constant, , and the electrical conductivity, can be measured. Both parameters are nonlinear functions of the volume fractions in soil. Because the volume function of water (_w) can change widely in the same soil, empirical equations have been derived to describe these relations. In this paper, a theoretical model is proposed based upon the theory of dispersive behaviour. This is compared with the empirical equations. The agreement between the empirical and theoretical aproaches was highly significant: the (_w) relation of Topp et al. had a coefficient of determination r² = 0.996 and the (_u) relation of Smith and Tice, for the unfrozen water content, _u, at temperatures below 0°C, had an r² = 0.997. To obtain (_w) relations, calibration measurements were performed on two soils: Caledon sand and Guelph silt loam. For both soils, an r² = 0.983 was obtained between the theoretical model and the measured values. The correct relations are especially important at low water contents, where the interaction between water molecules and soil particles is strong.