Published online 3 October 2006
Published in Vadose Zone J 5:1071-1072 (2006)
DOI: 10.2136/vzj2005.0150
© 2006 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
COMMENTS
Comments on "Time Domain Reflectometry Laboratory Calibration in Travel Time, Bulk Electrical Conductivity, and Effective Frequency"
Johan A. Huisman and
Harry Vereecken
Institute of Chemistry and Dynamics of the Geosphere, Institute IV: Agrosphere, Forschungszentrum Jülich, 52425 Jülich, Germany
s.huisman{at}fz-juelich.de
Accurate calibration is key to obtaining successful time domain reflectometry (TDR) measurements of soil water content and soil bulk electrical conductivity. The article by Evett et al. (2005) contains many useful suggestions regarding further improvements of the accuracy of TDR measurements. We would like to use this comment to improve one of these suggestions. In their Fig. 6, Evett et al. (2005) showed that the probe impedance is a function of the cable length attached to the probe, which would imply that calibration procedures for accurate bulk electrical conductivity measurements need to be revised. In this comment, we will illustrate that this apparent relation between probe impedance and cable length might be the result of a widely accepted but inappropriate method for calculating the probe impedance.
The bulk electrical conductivity, 
soil (S m–1) is typically calculated from TDR measurements using
 | [1] |
where Kp is the probe constant and RL is the load resistance (
). The load resistance is calculated from the reflection coefficient at long times, 
:
 | [2] |
where Zcable is the impedance of the cable (50 ). The probe constant can be calculated from
 | [3] |
where c is the speed of light (3 x 108 m s–1), L is the length of the probe (m), Z0 is the characteristic impedance of the probe (), and 
0 is the dielectric permittivity of free space (8.854 x 10–12 F m–1). As suggested by Zegelin et al. (1989), Wraith (2002), and Evett et al. (2005), the probe impedance, Z0, can be calculated from
 | [4] |
where ref is the permittivity of a reference material with known dielectric properties and ref is the minimum reflection coefficient in the probe waveform measured in the reference material (see arrows in Fig. 1 and Vmin in Fig. 1 of Evett et al., 2005). It is generally recommended to use Eq. [4] only for lossless media (Heimovaara, 1992), such as demineralized water used by Evett et al. (2005). In this comment we investigate whether Eq. [4] is valid in the presence of significant cable losses, as implied in Fig. 6 of Evett et al. (2005).
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Fig. 1. Time domain reflectometry waveforms simulated with the same system parameters (L = 0.20 m and Z0 = 225 ) but different input signals based on measurements of six different open-ended TDR cables 1, 5, 10, 15, 20, and 25 m long. Arrows indicate the minimum reflection coefficient used to calculate the probe impedance in Eq. [4].
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To test the appropriateness of Eq. [4] for different cable lengths, we simulated six TDR waveforms with the multiscatter function of Feng et al. (1999). This function describes how an input signal is modified by the TDR probe. The model assumes ideal TEM mode wave propagation and does not distinguish between two-, three-, or multi-wire TDR probes. To simulate the effect of different cable lengths, we used measurements of open-ended cables (RG58 C/U) of different lengths as input signal. The TDR measurements were made with the cables attached directly to a TDR100 cable tester (Campbell Scientific Inc., Logan, UT). The multiscatter function requires specification of two system parameters (Z0 and L). In all subsequent simulations, Z0 was specified as 225 . Please note that this value corresponds to different probe designs in case of two-, three-, or multi-wire probes. We chose Z0 = 225 to obtain probe impedances in the range of those measured by Evett et al. (2005). To test the effect of different probe lengths, a set of TDR waveforms was simulated for L = 0.10, 0.20, and 0.50 m. The simulated TDR waveforms with L = 0.20 m are shown in Fig. 1.
Figure 1 shows that significant changes occur in the shape of the TDR waveform when the cable length increases. These changes are related to changes in the frequency content of the input signal since the cables act as a low-pass filter due to dispersion and skin resistance effects. Figure 1 also shows that the minimum reflection coefficient, ref, increases with increasing cable length due to the different frequency content. This implies that the use of Eq. [4] will lead to an apparent increase in probe impedance with increasing cable length, as shown in Fig. 2 for the simulated waveforms and in Fig. 6 of Evett et al. (2005) for actual measurements. Figure 2 illustrates that the actual probe impedance of 225 is approached for short cable lengths, but that significant deviations between the results of Eq. [4] and the actual probe impedance occur for cable lengths relevant for field and laboratory TDR experiments. Figure 2 also shows that the deviations are larger for shorter probe lengths.
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Fig. 2. Apparent probe impedance calculated with Eq. [4] from simulated waveforms with different cable and probe lengths. The actual probe impedance was held constant at 225 during all simulations.
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To illustrate the error caused by using the apparent probe impedance instead of the actual probe impedance, we simulated six additional TDR waveforms with L = 0.20 m and varying bulk electrical conductivity (0, 0.02, 0.04, 0.06, 0.08, and 0.10 S m–1). The probe impedance remained unchanged, and the TDR measurement for the 10-m open-ended coaxial cable was used as the input function. Figure 3 shows that the results of the conductivity estimation with Eq. [1]
to [3] are very close to the actual conductivity, as would be expected for model simulations. Figure 3 also shows that a relative error of approximately 18% will be present when the apparent probe impedance is used instead of the actual probe impedance because the use of Eq. [4] overestimates the probe constant by approximately 18% for a cable length of 10 m. This value of 18% is an estimate of the maximum error in the experiments of Evett et al. (2005) and should be lower for smaller cable lengths.
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Fig. 3. Bulk conductivity estimates based on Eq. [1] to [3] and the apparent or true probe impedance for a 0.2-m TDR probe for simulated TDR waveforms with varying bulk conductivity (input function based on TDR measurements using a 10-m-long open-ended cable).
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We hope that this small exercise has illustrated that the probe impedance should not be estimated directly from the minimum reflection coefficient. The conclusion of Heimovaara (1992) that Eq. [4] is only valid for lossless media should be extended to only valid for lossless systems, which renders the equation useless for most practical applications. For accurate bulk electrical conductivity measurements in soils, proper calibration of the probe constant (and therewith the probe impedance) using solutions with different electrical conductivities according to the procedures of Castiglione and Shouse (2003) seems unavoidable. The conclusions of this comment have minor implications for the results presented in Evett et al. (2005). We are confident that the general conclusions of their contribution are still valid since the relative variation in probe impedance is only 4% due to the small range of cable lengths in their study. Nevertheless, it would be interesting to see to what degree the calibrations presented in their Table 7 would change if more appropriate methods for the bulk electrical conductivity determination were used.
REFERENCES
- Castiglione, P., and P.J. Shouse. 2003. The effect of ohmic cable losses on time domain reflectometry measurements of electrical conductivity. Soil Sci. Soc. Am. J. 67:414–424.[Abstract/Free Full Text]
- Evett, S.R., J.A. Tolk, and T.A. Howell. 2005. Time domain reflectometry laboratory calibration in travel time, bulk electrical conductivity, and effective frequency. Available at www.vadosezonejournal.org. Vadose Zone J. 4:1020–1029 [erratum: 5:513].[Abstract/Free Full Text]
- Feng, W., C.P. Lin, R.J. Deschamps, and V.P. Drnevich. 1999. Theoretical model of a multisection time domain reflectometry measurement system. Water Resour. Res. 35:2321–2331.[CrossRef]
- Heimovaara, T.J. 1992. Comments on "Time domain reflectometry measurements of water content and electrical conductivity of layered soil columns." Soil Sci. Soc. Am. J. 56:1657–1658.[Web of Science]
- Wraith, J.M. 2002. Time domain reflectometry. p. 1289–1296. In J.H. Dane and G.C. Topp (ed.) Methods of soil analysis. Part 4. SSSA Book Ser. 5. SSSA, Madison, WI.
- Zegelin, S.J., I. White, and D.R. Jenkins. 1989. Improved field probes for soil water content and electrical conductivity measurements using time domain reflectometry. Water Resour. Res. 25:2367–2376.
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J. A. Huisman, C. P. Lin, L. Weihermuller, and H. Vereecken
Accuracy of Bulk Electrical Conductivity Measurements with Time Domain Reflectometry
Vadose Zone J.,
April 14, 2008;
7(2):
426 - 433.
[Abstract]
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