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

Knight, J. H.

doi:10.1029/92wr00747

Cited by 215 publications

(215 citation statements)

References 13 publications

(6 reference statements)

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“…The resulting equipotentials for this heterogeneous medium also conform to Zegelin et al [1989] introduced the three-rod TDR probe and derived an approximate analytical expression for the voltage distribution in the transverse plane for probes with one central rod and a number of rods arranged in a circle around it. Knight [1992] showed the importance of the spatial energy distribution in the transverse plane and analyzed the response of some TDR probes to small lateral perturbations of the relative dielectric permittivity about a uniform value. Knight et al [1994] gave an approximate expression for the energy distribution around the multiwire probes of Zegelin et al [1989].…”

Section: Introductionmentioning

confidence: 99%

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

Knight¹,

Ferré²,

Rudolph³

et al. 1997

Water Resources Research

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Abstract. Fluid-filled gaps or dielectric coatings around parallel-wire transmission lines affect the ability of time domain reflectometry (TDR) to measure the water content of soils and other porous materials. We use a steady state, two-dimensional, finite element numerical solution of Laplace's equation to analyze these effects. We prove that the numerically determined electrostatic potential distribution and boundary fluxes can be used to calculate the equivalent relative dielectric permittivity measured by TDR by comparing the results of the numerical model with those obtained using existing analytical solutions for special cases. We then analyze the effects of fluid-filled concentric gaps that completely or partially surround TDR rods. The results show that an analytical solution due to Annan [1977b] for nonconcentric gaps can be used as a good approximation to predict the effect of concentric gaps or coatings that completely surround the rods. Coatings or gaps filled with low relative dielectric permittivity materials have a greater impact on the measured relative dielectric permittivity than those filled with high dielectric media. An increase in the thickness of the gap or coating for given rod diameters and separations increases the impact of the coating. To a lesser degree, the impact of a coating of a given thickness decreases with an increase in the ratio of the rod diameter to the rod separation. A gap or coating of a given thickness and relative dielectric permittivity will have a greater impact on the response of a three-rod probe than on that of a two-rod probe with the same rod diameter and separation of the outermost rods. Partial air gaps surrounding less than 30 ø of the rod circumference are not likely to affect the probe response significantly.

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Section: Introductionmentioning

confidence: 99%

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

Knight¹,

Ferré²,

Rudolph³

et al. 1997

Water Resources Research

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“…Oliver [1990] used a perturbation approach to calculate the weighting function for permeability estimates derived from the semilog plot of drawdown versus time for nonsteady pump test data. Weighting functions have been developed according to theoretical means for a number of other problems, including measurement of porosity by flow-through borehole tests using a radioactive tracer [Moltyaner, 1989], measurement of liquid phase porosity by 'nuclear magnetic resonance imaging [Maneval et al, 1990], and measurement of soil water content by time domain reflectomerry [Knight, 1992].…”

mentioning

confidence: 99%

What does an instrument measure? Empirical spatial weighting functions calculated from permeability data sets measured on multiple sample supports

Tidwell¹,

Gutjahr²,

Wilson³

1999

Water Resources Research

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Abstract. With the aid of linear filter theory we analyze 13,824 permeability measurements to empirically address the question, What does an instrument measure? By measure we mean the sample support or sample volume associated with an instrument, as well as how the instrument spatially weights the heterogeneities comprising that sample support. Although the theoretical aspects of linear filter analysis are well documented, physical data for testing the filtering behavior of an instrument, particularly in the context of porous media flow, are rare to nonexistent. Our exploration makes use of permeability data measured with a minipermeameter on a block of Berea sandstone. Data were collected according to a uniform grid that was resampled with tip seals of increasing size (i.e., increasing sample support). Spatial weighting (filter) functions characterizing the minipermeameter measurements were then calculated directly from the permeability data sets. In this paper we limit our presentation to one of the six rock faces, consisting of 2304 measurements, as the general results for each rock face are similar. We found that the empirical weighting functions are consistent with the basic physics of the minipermeameter measurement. They decay as a nonlinear function of radial distance from the center of the tip seal, consistent with the divergent flow geometry imposed by the minipermeameter. The magnitude of the weighting function decreases while its breadth increases with increasing tip seal size, reflecting the increasing sample support. We further demonstrate, both empirically and theoretically, that nonadditive properties like permeability are amenable to linear filter analysis under certain limiting conditions (i.e., small variances). Specifically, the weighting function is independent of the power average employed in its calculation (e.g., arithmetic versus harmonic average). Finally, we examine the implications of these results for other instruments commonly employed in hydraulic testing (e.g., slug and pump tests). Introduction Questions concerning what is actually measured by an in-In this way, the weighting function 13mo explicitly accounts for the influence of the measurement process on the value of k m.

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“…Empirical investigations (Baker & Lascano, 1989;Zegelin et al, 1992) and theoretical considerations (Knight, 1992;Ferré et al, 1996) agree that a sensitivity perpendicular to the TDR probes decreases exponentially with the distance from the transmission line elements. Furthermore, the volume evaluated by the propagation of the electromagnetic waves from TDR probes presents a quasi-elliptical form around the transmission with two rods, but a limited sensitivity extends much farther (Baker & Lascano, 1989;Zegelin et al, 1989;Knight et al, 1992;.…”

Section: Probe Orientation and Soil Volume Evaluated By Tdrmentioning

confidence: 87%

“…The presence of air gaps may cause discontinuities in the propagation of electromagnetic waves and thus considerably increase estimation errors (Knight, 1992;Ferré et al, 1996). This is probably one explanation for the greater deviation in the evaluations of θ TDR (Table 2) at the surface, where macropores are frequently found, caused by dead roots and macrofauna activity.…”

Section: Soil Characteristicsmentioning

confidence: 99%

“…Furthermore, the volume evaluated by the propagation of the electromagnetic waves from TDR probes presents a quasi-elliptical form around the transmission with two rods, but a limited sensitivity extends much farther (Baker & Lascano, 1989;Zegelin et al, 1989;Knight et al, 1992;. The radii of measured soil volume around the TDR rods were calculated for the probes used in this study by Knight's model.…”

Section: Probe Orientation and Soil Volume Evaluated By Tdrmentioning

confidence: 99%

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Sampling and TDR probe insertion in the determination of the volumetric soil water content

Teixeira

Schroth

Marques

et al. 2003

Rev. Bras. Ciênc. Solo

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Volumetric soil water content (theta) can be evaluated in the field by direct or indirect methods. Among the direct, the gravimetric method is regarded as highly reliable and thus often preferred. Its main disadvantages are that sampling and laboratory procedures are labor intensive, and that the method is destructive, which makes resampling of a same point impossible. Recently, the time domain reflectometry (TDR) technique has become a widely used indirect, non-destructive method to evaluate theta. In this study, evaluations of the apparent dielectric number of soils (epsilon) and samplings for the gravimetrical determination of the volumetric soil water content (thetaGrav) were carried out at four sites of a Xanthic Ferralsol in Manaus - Brazil. With the obtained epsilon values, theta was estimated using empirical equations (thetaTDR), and compared with thetaGrav derived from disturbed and undisturbed samples. The main objective of this study was the comparison of thetaTDR estimates of horizontally as well as vertically inserted probes with the thetaGrav values determined by disturbed and undisturbed samples. Results showed that thetaTDR estimates of vertically inserted probes and the average of horizontally measured layers were only slightly and insignificantly different. However, significant differences were found between the thetaTDR estimates of different equations and between disturbed and undisturbed samples in the thetaGrav determinations. The use of the theoretical Knight et al. model, which permits an evaluation of the soil volume assessed by TDR probes, is also discussed. It was concluded that the TDR technique, when properly calibrated, permits in situ, nondestructive measurements of q in Xanthic Ferralsols of similar accuracy as the gravimetric method.

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

Cited by 215 publications

References 13 publications

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

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

What does an instrument measure? Empirical spatial weighting functions calculated from permeability data sets measured on multiple sample supports

Sampling and TDR probe insertion in the determination of the volumetric soil water content

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