Published in Vadose Zone Journal 3:1146-1151 (2004)
© 2004 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
SPECIAL SECTION: HYDROGEOPHYSICS
Time-Domain Reflectometry Probe for Water Content and Electrical Conductivity Measurements in Saline Porous Media
Magnus Perssona,*,
David Bendzb and
Peter Flyhammara
a Department of Engineering Geology, Lund University, Box 118, 221 00 Lund, Sweden
b Swedish Geotechnical Institute, Hospitalsgatan 16A, 211 33 Malmö, Sweden
* Corresponding author (magnus.persson{at}tvrl.lth.se)
Received 30 March 2004.
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ABSTRACT
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A new coated time-domain reflectometry (TDR) probe design is described and evaluated. In contrast to previous coated TDR probes, our probe may be used to measure both the dielectric constant (Ka) and bulk electrical conductivity (
a) in saline porous media. This was made possible by attaching two coaxial cables to a 0.27-m three-rod probe with a coated central rod. The shield of the first cable was connected to one of the outer rods and the conductor was connected to the coated central rod. The conductor and shield of the other coaxial cable were connected to each of the two outer rods, respectively. Thus, our probe consists of two unbalanced, two-rod probes. The probe is called coated–uncoated probe (CUP). Four prototypes with two different coating materials (i.e., polyolefin and kynar heat-shrink tubes) were evaluated. The probes were calibrated in several fluids having different Ka and a. The Ka measurement of the coated part of the probe was successfully fitted to target Ka using a two-phase dielectric mixing model. Due to signal attenuation, measurements of Ka were not possible for a higher than 9 dS m–1 for the polyolefin-coated probes whereas the upper limits for the kynar-coated probes and the uncoated probe were 5 and 2.5 dS m–1, respectively. Measurements of a are only possible with the uncoated part. Measurements of Ka and a were also taken during three upward infiltration experiments in sand using soil solution electrical conductivities of 0.01, 6.31, and 12.03 dS m–1. For the uncoated part, Ka could not be measured when a was higher than about 2 dS m–1, whereas Ka measurements were possible using the coated part even when a was 3 dS m–1.
Abbreviations: CUP, coated–uncoated probe • TDR, time-domain reflectometry
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INTRODUCTION
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TIME-DOMAIN REFLECTOMETRY has become an important tool for measurement of soil water content (
) 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).
The dielectric constant of a salt solution (Kw) is dependent both on the temperature of the solution (T in °C) and the salt concentration (C, in mg L–1). Wentz and Meissner (2000) proposed the following relationship:
 | [1] |
This relationship was developed using measurements of the real part of the dielectric constant in saline solutions at frequencies in the range of 1.43 to 2.65 GHz. An increasing C leads to a decreasing Kw. On the other hand, the imaginary part of the dielectric constant is increasing with w. It is normally considered that the TDR-measured Ka represents the real part of the complex dielectric constant at the highest effective frequency of the TDR setup (Heimovaara et al., 1994); however, the imaginary part of the dielectric constant can also affect the TDR readings in certain cases. The effect of w on Kw is normally not considered for measurements in wet soil because it is very small at normal values of the w levels.
Many studies have reported that the is overestimated in highly saline soils due to Ka, as measured using TDR, increasing with w. Dalton (1992) observed an overestimation of at high w, but he concluded that this effect was only significant at w > 8 dS m–1. Sun et al. (2000) found the measurement to be overestimated at similar w in sand. Increasing with w in solute transport experiments in clayey soils has been observed by Campbell et al. (1999) and Persson et al. (2000). Nadler et al. (1999), however, presented a review of the effects of high a on the measurement. They concluded that high a values do not consistently imply overestimation. Wyseure et al. (1997) did a series of measurements with a 0.15-m-long three-rod TDR probe and found that the apparent value of Kw increased from 81 to 98 as w increased from 0 to 6 dS m–1. They concluded that this increase was due to the imaginary part of the dielectric permittivity, and hence Ka, increased as the conductivity increased.
In highly conductive media, the attenuation of the TDR pulse will cause the end reflection to disappear (Dalton and van Genuchten, 1986). Longer probes are more sensitive to signal attenuation. Dalton and van Genuchten (1986) derived a relationship between maximum rod length, , and soil water electrical conductivity w. The accuracy of the Ka measurement depends on the travel time of the signal along the probe, and thus on the probe length. Therefore, short probes are not desirable in applications where high accuracy is needed.
Two different solutions to the problem with high electrical conductivity have been presented: (i) waveform differencing using remote diode shorting (Hook et al., 1992) and (ii) the use of a coating material on the conductor wire of the TDR probe (Ferré et al., 1996). Nichol et al. (2002) examined the use of both remote shorting diodes and coated probes for measurements in highly saline salt solutions (up to 70 dS m–1). They showed that the coated probe design allowed for more accurate readings of Ka compared with remote diode shorting probes. Furthermore, the internal impedance of the diodes makes the remote shorting diode probe less suitable for Ka measurements in highly conductive media compared with the coated probe design.
There are, however, some disadvantages with a coated probe design. First, they are less sensitive than the uncoated probe type. Ferré et al. (1996) examined the sensitivity of different coated probe designs. They found that a thin coating material with a high Ka value would yield the highest accuracy of the Ka reading. Second, with the coated probe, a measurements are not possible.
The objective of the present study was to develop and test a coated TDR probe that allows for both a and Ka measurements. The basic concept was to use a three-rod probe with the (central) conductor rod covered with a coating material. One of the outer rods together with the coated rod were used for Ka measurements, whereas the two outer uncoated rods were used for Ka and a measurements. Thus, our probe actually consists of two unbalanced, two-rod probes with a common ground rod. Two different coating materials were tested. To test the performance of the new probe design, measurements of Ka and a were made in both salt solutions and in sand using three bromide solutions with different electrical conductivity.
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MATERIALS AND METHODS
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Coated–Uncoated Probe Design
The aim of this study was to construct a probe that combines the ability of an uncoated probe to measure a with the ability of a coated probe to take Ka measurements in highly saline media. Therefore, the probe is called a coated–uncoated probe (CUP). Our probe design is based on a three-rod TDR probe. The center rod, which was connected to the conductor of a coaxial cable, was coated with a heat-shrink tube. One of the outer rods was connected to the shield of the same cable. In addition, the conductor and shield of another coaxial cable were connected to each of the two outer rods. To prevent short circuiting, the shields of both cables were connected to the same rod. The basic probe design is shown in Fig. 1
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Fig. 1. Schematic design of the time-domain reflectometry (TDR) coated–uncoated probe (CUP). The total length of the stainless steel rods is 0.30 m and the separation distance between the other two rods is 0.04 m.
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The probe consisted of three 4-mm-diameter stainless steel rods, 0.3 m long. The rods had a separation of 0.02 m between each rod. After the two coaxial cables were soldered to the rods, a probe head was cast in epoxy resin to provide a constant rod separation and protect the solder joints. The probe head covered 0.03 m of the rods, leading to the total effective length of the probe being 0.27 m. An ideal coating material should be as thin as possible and have a relatively high Ka. Furthermore, it should be resistant to the chemical and physical stresses encountered and be easy to apply and get a perfect contact between the rod and the coating. Polyolefin heat-shrink tubes were used by Nichol et al. (2002) and were found to be a good coating material. Two types of heat-shrink tubes were used to construct the CUPs, polyolefin and kynar (polyvinylidene fluoride), which were 4.7 mm in diameter before shrinkage (Alpha Wire Company, Elizabeth, NJ). According to the product information, the kynar heat-shrink tube provides a thinner and more resistant coating. Four prototype CUPs were manufactured. Two of them had the polyolefin coating (CUP1 and CUP2) and two had the kynar coating (CUP3 and CUP4).
Probe Calibration
All TDR measurements were performed using a Tektronix (Beaverton, OR) 1502C cable tester with RS232 interface connected to a laptop computer. Estimates of Ka from the coated part of the CUP and Ka and a from the uncoated part were calculated from the TDR trace using WinTDR99 software (Soil Physics Group, Utah State University, Logan, UT). The TDR probes were connected to a SDMX50 multiplexer (Campbell Scientific, Logan, UT) controlled by the WinTDR99 software. Reference electrical conductivity measurements were made using a digital conductivity meter (WTW, Weilheim, Germany). To distinguish the different measurements from the CUPs, measurements from the coated part of the CUP are called Kc, and measurements from the uncoated part are called Ku.
Before coating the probes, measurements were taken in water and air to determine the effective length of the probe and the position of the start of the probe (see Heimovaara, 1993). Because the sample volume for the coated part of the CUP contains not only the medium of interest (i.e., the medium surrounding the probe), but also the coating itself, calibration of target media Ka and 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). Thus, it is possible to use a two-phase dielectric mixing model:
 | [2] |
where Kcoating is the dielectric constant of the coating material (this was set to 2.5 according to the product information), and w is a weighting factor describing the fractional contribution of the coating. The value of n is in the range of –1 to 1. These values represent a perfectly layered medium where the electric field is parallel (n = 1) or perpendicular (n = –1) to the layering. Thus, the n value summarizes the geometry of the medium in relation to the applied electric field. In the following sections we will refer to the Ka estimated from the Kc measurement using Eq. [2] to Kap and Kak for the polyolefin- and kynar-coated probes, respectively.
To determine the parameters of Eq. [2], measurements were made in air and several fluids. The fluids used were rapeseed oil, syrup, ethanol, 75% ethanol mixed with 25% water (v/v), 50% ethanol in water, 25% ethanol in water, and water. Fifteen measurements of Kc and Ku were completed with the CUPs in all fluids, and the means of measurements of Ku were used as reference Ka values to optimize w and n for each CUP. The standard deviation of all measurements was also calculated to study the variability of the Kc and Ku measurements.
The TDR software used in this study uses an approach similar to the one presented by Giese and Tiemann (1975) to calculate a:
 | [3] |
where Z0 is the characteristic probe impedance, Zu is the TDR cable tester load impedance (50 
), V0 is the incident pulse voltage, and Vinf is the return pulse voltage after multiple reflections have died out. The voltages V0 and Vinf are obtained from the TDR waveform.
Heimovaara et al. (1995) showed that for high a, Eq. [3] was not sufficient unless the series resistance was accounted for. They suggested the following relationship:
 | [4] |
where Kp is the probe cell constant, Rl is the resistive load, and Rcable is the contribution to Rl from the combined series resistances of the cable tester, cables, connectors, and the probe head. The Rl can be calculated by:
 | [5] |
To calibrate Kp and Rcable we used 20 KBr solutions covering a a range of 0.0028 to 11.63 dS m–1. In each solution, 15 measurements of Kc, Ku, and a were taken using all four CUPs.
Measurements in Sand
To test the CUP design, measurements were taken in uniform sand (0.0003–0.0006 m in diameter). The sand was packed into a cylinder, 0.125 m in diameter and 0.35 m long, to a dry bulk density of 1.5 g cm–3. One CUP of each type (CUP2 and CUP3) was inserted into the column. Measurements of Ka and a were taken during three upward infiltration experiments. This is an efficient method used to establish the relationship between Ka and and a and (Young et al., 1997; Persson and Haridy, 2003). An upward flux of 0.1 m h–1 was applied to the column using a peristaltic pump. Three different bromide solutions with w of 0.01, 6.31, and 12.03 dS m–1 were used during the upward infiltration experiments, used in that order. The initial for the first experiment was 0.05 m3 m–3 and the upward infiltration continued until the sample was saturated (0.38 m3 m–3). During the experiment, measurements of Kc, Ku, and a were taken every minute. When the sample was saturated, the sample was leached with water with a higher w until the effluent reached a stable w. Then the sample was drained at a suction of about 0.05 MPa. A new initial was calculated using the known volume of water applied and extracted. A new upward infiltration experiment was conducted and the leaching procedure was repeated. Finally, the third experiment was performed with the highest w level. A similar procedure has been described in detail in Hamed et al. (2003).
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RESULTS AND DISCUSSION
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Probe Calibration
The best-fit parameters of Eq. [2] obtained for the four different CUPs are presented in Table 1. As expected, the n value was close to –1, the value for the case where the electrical field is perpendicular to the layering. During optimizing it was found that the best-fit value of n was slightly lower than the theoretical limit –1 (–1.1 and –1.08 for CUP3 and CUP4, respectively); however, –1 was within the 95% confidence interval of the estimated n. The n value was set to –1 for these probes because we chose to restrict the n value to be in the range –1 to 1. The w values were very low, especially for CUP3 and CUP4. The coating was indeed thin, approximately 0.3 mm for the polyolefin and 0.1 mm for the kynar heat-shrink tubes. The best-fit values of Rcable and Kp are also presented in Table 1.
In the salt solutions, Ku measurements were only possible when a was lower than 2.5 dS m–1. For higher a levels, the end reflection disappeared and made Ku measurements impossible. The limit where Ka measurements are possible depends on the probe length. Based on our experience, using 0.20-m probes, Ka measurements can be made at a up to 5 dS m–1 and using 0.08-m probes at least up to 6 dS m–1. There was also a significant increasing trend in the Ku measurements as a increased. Even though the reflection after a long time of the TDR trace for CUP3 and CUP4 remained unaffected (i.e., Vinf remained constant), the reflection of the end of the probe changed its shape (the slope decreased and the reflection became more and more flat) as a increased (Fig. 2)
. The Kc measurements were impossible for a higher than about 5 dS m–1. For CUP1 and CUP2, however, Kc measurements were possible at all encountered a; however, the Kc increased to unrealistically high values for a higher than about 9 dS m–1. This increase is probably related more to wave analysis problems than a real increase in Ka (see Fig. 2).
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Fig. 2. Time-domain reflectometry (TDR) waveforms collected during the measurements in the KBr solutions using two coated–uncoated probes (CUP2 and CUP3). The waveforms are taken at three different levels of electrical conductivity: (a) 0.015, (b) 2.00, and (c) 8.95 dS m–1. The + signs indicate the end reflection of the probe estimated by the wave analysis software.
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In Fig. 3
the measured Kap, Kak, and Ku in the salt solutions are presented together with the calculated Kw using Eq. [1]. In the figure, the Kap from CUP1 and CUP2, the Kak from CUP3 and CUP4, and the Ku from all CUPs were averaged to improved clarity and because the variation between them was low. In the range 0.0028 to 0.1 dS m–1 (n = 5) the Ka measurements for all probes and the modeled Kw value are all identical. In the range 0.1 to 2 dS m–1 the Ku increased from 80.5 to 85.7, whereas the Kap and Kak decreased from 81 to 78. Before the reflection of the end of the probe deteriorated completely, the measured Ku and the Kak increased significantly. Our results show that the TDR-measured Kw will change with w. This change is different for different probe types and probably also for the algorithm used to estimate Ka from the TDR trace (see Wraith and Or, 1999).
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Fig. 3. The measured dielectric constant from the coated part of CUP1 and CUP2 (Kap), CUP3 and CUP4 (Kak), and from the uncoated part of all CUPs (Ku) plotted against the electrical conductivity of the KBr solutions. The solid line represents the predicted Kw according to Eq. [1]. CUP, coated–uncoated probe.
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The average standard deviation of the Ku measurements was about 0.07 and did show a slightly increasing trend with a. For the Kap and Kak measurements the standard deviation remained constant with a. The average standard deviation of the Kap was about 0.18 and 0.15 for Kak.
Measurements in Sand
The Kap–, Kak–, and Ku– relationships during the upward infiltration experiments are presented in Fig. 4
. For comparison, the best-fit, third-order polynomial relationship between Ka and was added to the graphs. When optimizing the parameter to this relationship, only the Ka measurements at the lowest w were considered.
It should be noted that the upward infiltration method is based on the assumption that the Ka measurements can be directly related to the length-averaged along the TDR probe. This is only true for uncoated probes (Ferré et al., 1996). For coated probes the length-averaged is not generally a linear function with the measured Ka. This effect will increase as the thickness of the coating increases. Our probes have thin coatings and the w parameter in Eq. [2] is small. This means that within the encountered range of Ka found in the upward infiltration experiment, the relationship between Ku and Kc is close to linear. Thus, we assume that the measured Kc represents the length-averaged .
At the lowest a, all probes gave almost identical Ka measurements except for some values close to saturation. When using the highest w, Ku measurements were not possible when a was higher then about 2 dS m–1. A small deviation between the Ku for w = 0.01 and 6.31 dS m–1 could also be noted. For the w = 6.31 dS m–1 experiment, the Ku was slightly higher at saturation. This effect was not noted using the uncoated part of the probe, so this was probably an effect of the higher a (a was around 1.5 dS m–1 at saturation). The Kap and Kak also increased close to saturation when the w was 12.03 dS m–1. At this point, a was about 3 dS m–1. Thus, the highest a values when measurements were not affected were lower for measurements in sand compared with the measurements in the salt solutions. This means that both Ka and a will determine the limits of Ka estimations.
Measurements of a were also made during the upward infiltration experiments using the uncoated parts of the probes. The results are presented in Fig. 5
.
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CONCLUSIONS
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A new TDR probe design was presented and evaluated. In contrast to previous probe designs, our probe is capable of taking both Ka and a readings in highly saline porous media. Two different coating materials were tested, polyolefin and kynar heat-shrink tubes. The Kc measurement of the coated part of the probe was successfully fitted to target Ka using a two-phase dielectric mixing model. We refer the Ka estimated from the Kc measurement using Eq. [2] to Kap and Kak for the polyolefin- and kynar-coated probes, respectively. Measurements of Kak were only possible if a was lower than 5 dS m–1; however, Kap was possible for a as high as 9 dS m–1. Using the uncoated part of the CUP, Ka measurements were not possible for a higher than 2.5 dS m–1. On the other hand, a measurements are only possible with the uncoated part.
Three upward infiltration experiments were conducted in sand using bromide solutions with w of 0.01, 6.31, and 12.03 dS m–1. Using uncoated probes, Ku measurements were not possible for a higher than about 2 dS m–1, whereas Ka measurements were possible using the coated part even when a was 3 dS m–1. Although not the purpose of this study, we also noted that when a was higher than 1.5 dS m–1, Ku was slightly overestimated (corresponding to an error up to about 0.01 m3 m–3 at saturation) whereas the Kap and Kak measurements were unaffected. Because the waveform of the uncoated part is more affected by high a, the overestimation is likely to be an effect of the waveform analysis rather than a real increase in the Ka. The Kap and Kak also increased close to saturation when a was about 3 dS m–1. Thus, the highest a values when measurements were not affected were lower for measurements in sand compared with the measurements in the salt solutions. This means that both Ka and a will determine the limits of Ka estimations.
The polyolefin coating was thicker than the kynar coating and consequently, the Ka readings were slightly less sensitive to changes in Ka. However, Ka measurements were possible for higher a levels compared with the kynar-coated probe. The kynar proved to be a more resistant coating material because the polyolefin coating can peel off when inserting the probe into soil repeatedly.
Normally, the sampling volumes for the Ka and a measurements are the same. Our CUPs, however, have partially different sampling volumes for Ka and a measurements. An alternative CUP design could share the middle rod (connected to the ground wires) and have one of the outer rods coated. Then both the coated and uncoated part would have the same rod spacing. However, for this probe, the measurement volumes of the Ka and a measurements would be different and not overlap, which could lead to problems in soils displaying high spatial heterogeneity.
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ACKNOWLEDGMENTS
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This study was funded by the Swedish Research Council and the Swedish Road Administration.
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ABSTRACT
INTRODUCTION
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