The sample areas of conventional and alternative time domain reflectometry probes

Abstract

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...

A column system for modeling bentonite slurry infiltration in sands

“…The influence zone of the probe is 20 to 30 mm around the rod, and the accuracy of the measured dielectric constant is ±1% (Ferré et al, 1998). The TDR measurement device is a Campbell Scientific TDR100 (Campbell Scientific, Inc., USA).…”

Experimental Study on Sample Size for Laboratory Calibration Tests of Commercial Dielectric Soil Water Sensors

“…Ferré et al 4 demonstrated that the sensor sampling area increases with both diameter and rod spacing and that two-rod probes have a much larger sampling area than tree-rod designs. Therefore, this large difference in the necessary sample size between the TRIME-EZ and TDR100 with CS605 is attributable to the differing number of rods between these probes 4 . Further, the smaller sample sizes required for the CS615 and CS616 compared with the TRIME-EZ were due to differences in the diameter and spacing of the rods 4 ( Table 1).…”

“…Similarly, Petersen et al 10 reported that the effective sensor sampling area should contain approximately 95% of the electromagnetic energy. However, the distribution of the electromagnetic energy changes greatly depending on the probe designs 4 . Because there is no evidence regarding the effect of changes in the dielectric constant outside the soil sample on the measurement, the ability of these approaches to specify an appropriate sample size for each type of dielectric soil water sensor remains uncertainty.…”

“…To clarify this, Knight 5 and Knight et al 6 proposed numerical solutions to analyze the spatial sensitivity of TDR probes associated with the two-dimensional electromagnetic energy distribution in the plane perpendicular to the longitudinal axis of the TDR probe rods. Ferré et al 4 applied these analysis results to determine the sampling area in the plane perpendicular to TDR probes with various designs. Baker and Lascano 1 experimentally visualized a three-dimensional measurement sensitivity distribution around a two-rod TDR probe.…”

“…However, the sample size used when the calibration equations are determined in a laboratory is of great concern, because the dielectric properties of the materials surrounding soil samples subject to the test might affect the measurement, resulting in a critical error during in-situ monitoring of the soil water dynamics. Ferré et al 4 defined the sensor sampling volume (i.e. the necessary sample size) as the region of the porous medium that contributes to the measurement, namely; "changes in the properties of the porous medium outside this volume have no significant influence on the response of the instrument".…”