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a Dep. of Water Resources Engineering, Lund University, Box 118, SE-221 00 Lund, Sweden
b Land Resources and Environmental Sciences, Montana State University, P.O. Box 173120, Bozeman, MT 59717-3120
* Corresponding author (magnus.persson{at}tvrl.lth.se)
Received 21 February 2002.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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a). Two SMP prototypes, 0.03 and 0.04 m long and having diameters of 0.006 m, were evaluated. The probes were calibrated in several fluids having different Ka and a. A primary advantage of the SMP is minimal physical probe length without sacrificing accuracy of Ka readings. Accuracy of Ka measurements for the new probes was similar to that of standard 0.20-m-long three-rod probes.
Abbreviations: PVC, polyvinyl chloride • SMP, shaft-mounted TDR probe • TDR, time domain reflectometry
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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) and bulk electrical conductivity (a). The TDR instrument sends a high frequency electromagnetic signal along a probe buried in the soil. The signal is reflected at the end of the probe and the travel time of the signal can be measured from the resulting waveform. The travel time can be related to dielectric constant (Ka), which in turn can be related to . Additionally, the attenuation of the reflected signal can be related to a. Each of these attributes and both in combination are useful in a variety of research and management applications (Jones et al., 2002).
Although TDR has been used for more than two decades, surprisingly little emphasis has been focused on TDR probe development. In most applications, TDR probes consisting of two or three metal rods, from a few centimeters up to 30 or 50 cm in length have been used. The accuracy of the Ka measurement depends on the travel time of the signal along the probe, and on the uncertainty in the calibration equation between and Ka. If the travel time is sufficiently long, the uncertainty of TDR measurements is generally <0.02 m3 m-3. Using a standard TDR instrument, the practical lower limit of probe length to maintain accuracy of measurement is generally considered as 0.10 to 0.15 m (Heimovaara, 1993). Shorter probes can also be used successfully if is consistently high, or with higher frequency TDR devices.
Time domain reflectometry probes having small physical size and spatial sensitivity are desirable for many applications. An efficient means of reducing the physical length of TDR probes without reducing the travel time (i.e., transmission line length) was presented by Nissen et al. (1998). They developed a miniature coil TDR probe only 15 mm long. Their design reduced the physical length of the probe by a factor of five, while maintaining adequate electromagnetic length, and hence without affecting measurement accuracy. Vaz and Hopmans (2001) constructed a shaft-mounted TDR probe (SMP). Their probe consisted of two parallel copper wires, 0.8 mm in diameter and 30 cm long, coiled around a 5-cm-long polyvinyl chloride (PVC) core with 3-mm wire separation along the core. Neither of these probes was capable of a measurement because of the lacquer or epoxy coating used to cover transmission wires.
The objective of this study was to develop and evaluate a compact TDR probe that is capable of measuring both Ka and a. We desired that the probe have accuracy similar to standard two- and three-rod probe designs. Furthermore, it was important that the resulting waveform traces be amenable to analysis using standard TDR software.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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a were calculated from the TDR trace using WinTDR99 software (Soil Physics Group, Utah State University, Logan, UT). Two standard three-rod probes, 0.20 m in length with a wire diameter of 0.003 m and a spacing of 0.05 m between the two outer rods (Soilmoisture Equipment Corp., Santa Barbara, CA), were used for reference Ka measurements. The reference TDR probes were calibrated using the approach suggested by Heimovaara (1993). Reference electrical conductivity measurements were made using a digital conductivity meter (Shott-Geräte, Hofheim, Germany).
Shaft-Mounted TDR Probe Design
The basic concept of the SMP is to coil the signal transmission wires around a cylindrical core, thus reducing the physical length of the probe without compromising the travel time of the electromagnetic wave. Plexiglas was selected as the core material, although it is rather brittle and sometimes shattered during SMP construction. Nissen et al. (1998) used PVC as core material for their coil probe, but we considered PVC as less suitable for our SMP since it lacks rigidity. An ideal core material should also have high Ka (Plexiglas and PVC have Ka of about 3) to maintain travel times as large as possible. Insignificant water absorption is also an important property of a suitable core material. The diameter of the SMP was chosen with consideration of Rothe et al. (1997), who showed that TDR probe installation can lead to compaction of the soil near the probe rods, producing significant measurement artifact for rod diameters greater than about 6 mm.
Two different SMP prototypes were manufactured, referred to as SMP1 and SMP2. The SMP1 probe consisted of a 6-mm Plexiglas rod with two 0.8-mm stainless-steel wires coiled around it. The ground and conductor wires were separated by 2 mm. The wired portion of the rod was 40 mm long, which meant that the ground and conductor wires were 190 mm long. The SMP2 was similar to SMP1, but 0.6-mm stainless-steel wires were used, with a 1.25-mm separation distance. The wired part was 30 mm long with a wire length of 225 mm.
To manufacture the SMPs, the Plexiglas core was threaded with dual threads to serve as a guide for the transmission wires. The two stainless-steel wires were coiled around the core and glued in place with epoxy glue. After the glue had hardened, the core was machined down to a diameter of 6 mm to provide a smooth surface, leaving the partially milled bare wires in contact with the surrounding media. A small brass head was glued to the Plexiglas core at the distal end of the probe to facilitate insertion into soils. The stainless-steel wires were soldered to the conductor and ground of an RG58 coaxial cable, respectively. The cable lengths were 2.8 and 3.4 m for the SMP1 and SMP2, respectively. The solder joints and wire interface at the proximal probe end were covered by a 9.6-mm Plexiglas tube, which was filled with epoxy. The SMP2 probe design is shown in Fig. 1.
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a measurements are required. In dielectric mixing models, describing the contribution from x different compounds having different Ka values to the average Ka of the mixture, the contribution from the components is assumed constant if their geometric positions and volume fractions are constant within the applied electric field (Ferré et al., 1996). In the SMP four different materials will be present in the measurement volume: the lacquer coating, the epoxy, the Plexiglas shaft, and the surrounding media. Since the Ka of epoxy (3.6; Weast, 1986) and lacquer (2.8; Nissen et al., 1998) are close to the Ka of Plexiglas (2.7; Weast, 1986), and because they only occupy a small fraction of the total measurement volume, the contributions of epoxy and lacquer to the measured Ka can be neglected. Thus, it is possible to describe the contribution of these media using a two-phase dielectric mixing model
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To relate the Ka measured by SMP to Ka measured by the reference TDR probes, measurements were made in air and several fluids. The fluids used were rapeseed oil, ethyl acetate, syrup, ethanol, 75% ethanol mixed with 25% water (v/v), 50% ethanol in water, and water. Fifteen measurements were completed with replicate reference probes and SMPs in all fluids, and the means of measurements with the two reference probes were used as reference Ka values to optimize w and n for each SMP.
We also examined the variability of the SMP Ka measurements. This was done by using the measured Ka and the best-fit w and n parameters to calculate the Ksurr for each of the 15 measurements in each fluid. The measurement standard deviation was also calculated for the two reference probes (Fig. 3).
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a by comparing the measured RL with a measured by the reference electrical conductivity meter in salt solutions over a range of 0.0012 to 7.42 dS m-1. Twenty-two salt solutions with different a were used, with 10 SMP and 10 three-rod TDR probe measurements obtained in each solution. Similarly to Nissen et al. (1999) in calculating a for their printed circuit board TDR probes, we used the method suggested by Heimovaara et al. (1995)
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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The parameters w and n (Eq. [1]) obtained using nonlinear optimization of SMP and reference probe Ka are presented in Table 1. The fact that n is very close to 1 and that w is not far from 0.5 shows that the dielectric materials surrounding the probe rods are close to a parallel distribution with respect to the applied electromagnetic field. This is fortunate because the sample volume of the probe then can be expected to be only a weak function of Ksurr (Ferré et al., 2001). The Ksurr calculated from the SMP-measured Ka using Eq. [1] was in close agreement with Ka measured using the reference probes (Fig. 2). Both SMPs had similar parameter values, and Eq. [1] fit the data well (Table 1). Repeatability of Ka measurements using the SMPs was comparable to that of standard 0.20-m-long three-rod probes (Fig. 3). If the Ka is converted to using the Topp et al. (1980) equation, the average standard deviation of the estimation was about 0.003 m3 m-3 for all probes (data not shown).
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a as measured using SMPs and the electrical conductivity meter was excellent (Table 1). Calibrated probe constants (Kp) and cable resistances for both probes were similar. The standard deviations of the SMP-measured a were similar to those of the reference probes. The measurement volume geometry of the SMPs has not yet been characterized. However, if we assume that we have a parallel distribution of the dielectrics, the sampling volume can be estimated by using the definition of spatial sensitivity of Knight (1992) for a standard two-rod probe. On the basis of this analysis, we conclude that about 90% of the SMP sampling volume would be confined by a cylinder approximately 7 mm in radius, and 70% of the sampling volume by a cylinder with a radius of approximately 5 mm.
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CONCLUSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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a in salt solutions over a range of 0.0012 to 7.42 dS m-1 was also excellent.
As with the miniature coil probe presented by Nissen et al. (1998), spatial sensitivity of the SMPs are very small and only extend a few millimeters from the shaft. This would make the SMPs ideal for localized estimates of Ka and a, and will be an advantage for some measurement applications. However, careful installation of these (and other) miniature probes will be important since air gaps near the shaft would lead to significant errors.
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ACKNOWLEDGMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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