Sensitivity of time domain reflectometry measurements to lateral variations in soil water content

Abstract

The spatial responses of two types of time domain reflectometry (TDR) probes used for measuring the water content of soils and other porous materials are examined. We investigate the effect of spatial variation in the water content of the sample on the measured value of the water content for both the coaxial cylinders probe and the two parallel wires probe. The response of the instrument to water content distributions that are perturbed slightly from a uniform distribution is calculated, using the conventional electrostatic treatment of electromagnetic wave propagation in the transverse electro‐magnetic (TEM) mode. Under this small perturbation assumption, we show that the spatial weighting function is approximately proportional to the distribution of electromagnetic energy between the electrodes for uniform water content, calculated from a solution of Laplace's equation for each probe type. For coaxial probes, most of the energy (and hence most of the measurement sensitivity) is concentrated around the inner cylinder in a “skin effect” if the ratio of the radii of the inner and outer cylinders is too small. For parallel wire probes, most of the measurement sensitivity is close to the wires if the wire diameter is too small compared to the spacing between them. This can cause significant errors if there is an air gap close to the wires or soil around the wires has been compacted by the process of inserting them into the soil.