Spatial averaging of water content by time domain reflectometry: Implications for twin rod probes with and without dielectric coatings

The averaging of apparent relative dielectric permittivities by time domain reflectometry (TDR) is examined for properties varying along TDR waveguides and in the plane perpendicular to a TDR probe. A square root averaging model with uniform weighting factors describes the measured apparent relative dielectric permittivity for axially varying materials; variations in the transverse plane are described by an inverse averaging model with nonuniform spatial weighting. We define the sensitivity of a TDR probe as the change in the measured travel time for a given change in the average soil water content for rods of a fixed length. For rods with dielectric coatings, this sensitivity increases with the dielectric permittivity of the coating and the rod radius and decreases with the soil dielectric permittivity. Due to the dependence of the sensitivity on the soil water content, coated rods will not measure the actual average water content for conditions of axially variable water contents.