Frequency domain analysis of time domain reflectometry waveforms. 2. A four-component complex dielectric mixing model for soils

Although time domain reflectometry (TDR) is becoming, accepted as an important tool for the measurement of soil water content and bulk soil electrical conductivity, a major part of the method is based on empirical relationships. An improved understanding of dielectric measurements on soils may give more insight into soil properties other than soil water content and bulk soil electrical conductivity. Frequency domain analysis of TDR waveforms enables the measurement of the frequency dependent complex dielectric permittivity of soils. The frequency dependent complex dielectric permittivity of soils can be described with a four-component complex dielectric mixing model based on the volumetric mixing of the refractive indices of the soil components. The four soil components in the model are air, solids, bound water, and free water. Results indicate that the apparent dielectric permittivity obtained from the travel time of the TDR pulse in the soil is the dielectric permittivity at the highest measurement frequency of the cable tester, probe, and soil system. The model based on the volumetric mixing of real permittivities underestimates the measurements in situations with high values of the imaginary part of the dielectric permittivity. Because the model based on the mixing of the complex dielectric permittivities can describe the data, we conclude that the apparent dielectric permittivity is influenced by the imaginary parts in the dielectric permittivities of the soil components. Combination of the four-component complex dielectric mixing model with the complex dielectric permittivity obtained from the frequency domain analysis of TDR waveforms gives a tool for modeling the bulk soil electrical conductivity by separating the conductivity of the soil water into a bound water conductivity and a free water conductivity.