A numerical analysis of the effects of coatings and gaps upon relative dielectric permittivity measurement with time domain reflectometry

Knight, J. H.; Ferré, T. P. A.; Rudolph, David L.; Kachanoski, R. G.

doi:10.1029/97wr00435

Cited by 87 publications

(81 citation statements)

References 9 publications

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“…The numerical analysis of Knight et al [1997] and the definition of spatial sensitivity of Knight [1992] provide a unique opportunity to define the sample area of conventional and alternative TDR probes. The results of this analysis serve as a guide for the appropriate choice of a TDR probe for specific sampling objectives, and as further advances are made in the design of alternative probes, probe configurations can be optimized Using this tool.…”

Section: Discussionmentioning

confidence: 99%

“…The numerical analysis of Knight et al [1997] defines the weighting function for each element in a finite element mesh for a representative cross section of any probe with a given distribution of relative dielectric permittivities in the surrounding porous medium. The weighting functions define the relative contribution per unit area of the medium located at each point in the plane.…”

Section: Definition Of the Sample Areamentioning

confidence: 99%

“…Therefore, unlike conventional rod probes, the sampling area of coated rods will be a function of both the probe geometry and the dielectric permittivities of the medium and of the coating. Knight et al [1997] showed numerically that the analytical solution of Annan [1977] closely approximates the apparent relative dielectric permittivity measured by rods with concentric coatings, demonstrating that concentric circular coatings can be considered to be in series with the soil. Similarly, thin coatings around three-rod probes approximately conform to the equipotentials shown in Figure 3, suggesting that the coatings on three-rod probes are approximately in series with the soil as well.…”

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confidence: 99%

“…Knight [1992] developed analytical descriptions of the spatial sensitivity in the plane perpendicular to the rods for several geometries of conventional rod probes surrounded by a homogeneous medium. The numerical analysis presented by Knight et al [1997] defines the apparent relative dielectric permittivity that would be measured by a representative cross section of any probe configuration regardless of the distribution of relative dielectric permittivities in the transverse plane.…”

Section: Introductionmentioning

confidence: 99%

“…We use the spatial weighting concept proposed by Knight [1992] and the numerical approach of Knight et al [1997] to define the area in the plane perpendicular to TDR rods that contributes significantly to the response of a TDR probe. Using this approach, we investigate the sample areas of conventional TDR rods, coated-rod probes, and alternative TDR probes designed to profile the soil water content [Hook et al, 1992;Redman and DeRyck, 1994] or to measure the soil water content at the ground surface [White and Zegelin, 1992; Selker et al, 1993].…”

Section: Introductionmentioning

confidence: 99%

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The sample areas of conventional and alternative time domain reflectometry probes

Ferré¹,

Knight²,

Rudolph³

et al. 1998

Water Resources Research

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168

152

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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...

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Section: Discussionmentioning

confidence: 99%

Section: Definition Of the Sample Areamentioning

confidence: 99%

mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The sample areas of conventional and alternative time domain reflectometry probes

Ferré¹,

Knight²,

Rudolph³

et al. 1998

Water Resources Research

Self Cite

168

152

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Preferential percolation quantified by large water content sensors with artifactual macroporous envelopes

et al. 2015

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For many scientific and practical tasks, it is important to estimate the soil–water percolation fluxes. This paper builds on measurements with large horizontal time‐domain reflectometry water content sensors in a loamy Mollisol. The sensors were installed into pre‐drilled holes and the gaps between them, and the soil was filled with a slurry of local soil with water. This gave rise to envelopes around them that contained artificial macropores. The sensors reacted to intensive rains by a rapid increase of their readings, often above the native soil's porosity, followed by an almost equally rapid decrease. The paper explores the feasibility of quantifying the rapid percolation, based on these anomalous water content peaks, and demonstrates that this is possible in principle, if the processes are simulated by a suitable model. A two‐dimensional dual porosity non‐equilibrium (mobile‐immobile) model was tried. The envelope around the sensor was modelled as an annulus with higher porosity and hydraulic conductivity, which attracts preferential flow and amplifies the percolation signal. With the model at hand, the flux hydrographs can be derived from model simulations and measured precipitation. For contrast, the Durner equilibrium dual porosity model was tried but was found little suitable. However, even the mobile‐immobile model did not perform perfectly. Simulated water contents were similar to the measured ones at some depths but not in the others, and the percolation fluxes were overestimated, compared to cumulative soil–water balance. Efforts to improve model performance were not successful. Hence, the model structure needs to be improved. Copyright © 2015 John Wiley & Sons, Ltd.

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The effects of soil bulk density, clay content and temperature on soil water content measurement using time‐domain reflectometry

Gong

Cao

Sun³

2003

Hydrological Processes

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Time-domain reflectometry (TDR) is increasingly used for field soil water estimation because the measurement is nondestructive and less affected by soil texture, bulk density and temperature. However, with the increase in instrument resolution, the influences of soil bulk density and temperature on TDR soil moisture measurements have been reported. The influence is primarily caused by changes in soil and water dielectric permittivity when soil compaction and temperature varies. The objective of this study is to quantify the influence of soil bulk density and temperature, and to provide the corresponding correction methods. Data collected from sand, sandy loam, loam and clay loam show a linear relationship between the square root of dielectric constant of dry soil and bulk density, and a bulk density correction formula has been developed. The dielectric permittivity of soil solids estimated using this formula is close to that of oxides of aluminium, silicon, magnesium and calcium. Data collection from sandy loam show a noticeable decrease in measured soil moisture with increase in temperature when the volumetric soil water content is above 0Ð30 m 3 m 3 . A temperature-correction equation has been developed, which could provide the corrected soil moisture based on soil temperature and TDR-measured moisture. The effect of clay content has been detected, but it is not statistically significant. High clay contents cause the underestimation of soil water content in the low moisture range and overestimation of soil water content in the high moisture range.

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A numerical analysis of the effects of coatings and gaps upon relative dielectric permittivity measurement with time domain reflectometry

Cited by 87 publications

References 9 publications

The sample areas of conventional and alternative time domain reflectometry probes

The sample areas of conventional and alternative time domain reflectometry probes

Preferential percolation quantified by large water content sensors with artifactual macroporous envelopes

The effects of soil bulk density, clay content and temperature on soil water content measurement using time‐domain reflectometry

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