Complex Permittivity Model for Time Domain Reflectometry Soil Water Content Sensing: I. Theory

Despite numerous applications of time-domain reflectometry (TDR), serious difficulties remain in estimating accurate soil water contents under field conditions, especially in fine-textured soils. We developed a physically based calibration model to predict the frequency- and temperature-dependent complex dielectric response of soils. The model was used to predict frequency-dependent attenuation and a single "effective" frequency approximation of apparent permittivity of the soil. Effective frequency was predicted to decline from 450 to 160 MHz as water contents increased from air dry to saturation. Predicted frequency decline was small for an input bandwidth of 130 MHz, reflecting that modeled polarization mechanisms associated with relaxation frequencies above 100 MHz were responsible for most of the frequency-dependent attenuation. For specific surface areas ranging from 150 to 300 m 2 g -1 , simulations indicate that ignoring dielectric and conductive losses or the associated decline in effective frequency results in a 5 to 22% underestimation of the apparent permittivity. Both the power-law and de Loor-Dobson mixing models gave a reasonable approximation to the measured apparent permittivity for a silty clay loam (34% clay) across the entire water content range. Moreover, the models were able to describe the behavior of apparent permittivity in response to temperature for two soils with contrasting bulk electrical conductivity contributions to losses. These results demonstrate that loss mechanisms and declines in effective frequency need to be considered to accurately predict the soil water content of fine-textured soils.

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