Abstract. We define the sample area in the plane perpendicular to the long axis of conventional and alternative time domain reflectometry (TDR) probes based on the finite element numerical analysis of Knight et al. [1997] and the definition of spatial sensitivity of Knight [1992]. The sample area of conventional two-and three-rod probes is controlled by the rod separation. Two-rod probes have a much larger sample area than three-rod designs. Low dielectric permittivity coatings on TDR rods greatly decrease the sample area. The sample area of coated rod probes decreases as the relative dielectric permittivity of the surrounding medium increases. Two alternative profiling probes were analyzed. The separation of the metal rods of Hook et al. [1992] probes controls the size of the sample area. Reducing the height or width of the rods improves the distribution of sensitivity within the sample area. The relative dielectric permittivity of the probe body does not affect the sample size. The sample size of the Redman and DeRyck [1994] In addition to the ability to accurately measure a soil property, the volume of porous medium sampled is an important characteristic of any sampling method. We use the spatial In addition, we examine the influence of changes in both the probe design and the relative dielectric permittivity of the surrounding medium on the sample areas of these probes.
Definition of the Spatial Weighting FunctionIt was shown by Knight [1992] that the spatial weighting function Wo(X, y) for a TDR probe surrounded by a medium with a near-uniform distribution of relative dielectric permittivity, K(x, y), is given by Wo(x,y) = .The weighting function has the property that ff•wo(x,y) dA=l.The electrostatic potential distribution, •o(X, y), corresponds to a uniform value of K o of the relative dielectric permittivity in the region, 1•, surrounding the probe. Knight [1992] showed that when K is not uniform, the weighting function, w(x, y), depends on the distribution of the relative dielectric permittivity, K(x, y), and is given by w(x,y) = , Knight et al. [1997] showed that the weighting factor, w(x, y), can be determined for any given distribution of dielectric permittivities in the transverse plane. In brief, the method followed is to determine numerically the potential distribution, •o(X, y), for the metallic rods forming a probe with none of the nonmetallic probe components present if those rods were placed in a homogeneous porous medium. Then the potential distribution, •(x, y), is determined numerically for the same geometry with all of the probe components present. The gradients of these potential distributions are used in (3) to define the spatial weighting factors throughout the transverse plane for each probe design.
Heterogeneous K DistributionsA number of probe designs incorporate nonmetallic probe components of known K that lie within the sampling volume of the probe. To compare the performance of probes and to optimize their designs, it is important to know how these materials affect the spati...