Materials and Methods
THE ELECTRICAL CONDUCTIVITY RESPONSE OF A PROFILING TIMEDOMAIN REFLECTOMETRY PROBE
Experiments were conducted on a field site on Canadian Forces Base Borden, ON, Canada. The site material is a homogeneous well-sorted fine- to medium-grained sand with no significant clay fraction (MacFarlane et al., 1983). Two profiling probe access tubes were installed as described by Ferre´ et al. (1998). Two 140-cm long metal rods were driven into the ground adjacent to the access tubes to form a vertical tworod TDR probe. Two 3 by 3 m drip-line irrigation systems were placed on the ground surface. One irrigation system applied municipal water (EC ⫽ 0.040 S m⫺1) and the other applied a 0.67 g L KCl tracer (EC ⫽ 0.142 S m⫺1). Each system applied water at a rate of 0.0036 cm s⫺1. Initially, the site was flushed with municipal water. After 3 h of infiltration, the waveforms collected with the 140-cm long continuous-rod probe were constant in time, indicating that steady-state conditions had been reached to the 140-cm depth. Then, the municipal water gallery was turned off, and a 45-min duration pulse of the 0.67 g L KCl tracer was applied at the same infiltration rate. Finally, the tracer gallery was turned off and infiltration of the municipal water was resumed. A prototype-profiling probe was inserted into a pair of access tubes with 20-cm long target rods centered at the 90-cm depth.
T. P. A. Ferre´,* D. L. Rudolph, and R. G. Kachanoski Abstract Direct measurements of changes in the electrical conductivity (EC) are made using the profiling time domain reflectometry (TDR) probe described in a previous work. This is the first demonstration of the ability of a TDR probe to measure EC through coatings or access tubes. Based on the ability of this probe to profile the water content, this suggests that a single instrument may be able to profile changes in water content and electrolytic solute concentration during transient flow through the unsaturated zone.
F
erre´ et al. (1998) presented an alternative TDR probe that is designed to profile the water content with depth. The profiling probe is comprised of two identical rods that are lowered within parallel polyvinyl chloride (PVC) access tubes. Each rod includes two sections: a small diameter coated wire that is connected to the pulse generator through a balancing transformer (balun); and a short larger diameter target rod that is connected to the end of the small diameter wire. The design of one of these rods is shown on Fig. 1. Full construction details are available in Ferre´ et al. (1998). The profiling probe is capable of measuring changes in the water content of the medium between the access tubes over the length of the target rods. In addition, it is not sensitive to the properties of the medium between the access tubes over the length of the small diameter wire. Therefore, like a neutron probe, the profiling probe measures over a limited depth interval. Furthermore, the target rods of the profiling TDR probe can be lowered to any depth within the access tubes, allowing for high resolution profiling. Finally, the target rods can be removed from the access tubes and replaced with target rods of a different length, allowing the user to tailor the sample size of the instrument. Ferre´ et al. (1998) showed that the profiling probe could monitor the advance of a wetting front with accuracy comparable with that of a neutron probe. We present the results of a field experiment designed to test whether this probe design offers the possibility to profile the solute concentration as well as the water content.
Results and Discussion Selected waveforms collected during the experiment are shown in Fig. 2. Ferre´ et al. (1998) demonstrated that the water content within the depth interval spanned by the target rods could be determined from the elapsed time between characteristic reflections on the waveform. This water-content measurement window is identified on the waveforms on Fig. 2. We hypothesize that, as with standard TDR probes, changes in the EC of the medium between the target rods could be inferred from changes in the waveform amplitudes. Direct observation of the waveforms shows qualitatively that the waveform amplitudes are affected by changes in the EC of the medium. Specifically, there is very little change in the amplitudes of the waveforms collected for 90 min following the beginning of tracer application. Then there is a measurable decrease in the waveform amplitudes reaching a maximum change after 143 min. Waveforms collected after 200 min were indistinguishable from those collected immediately after application of the tracer pulse, demonstrating complete displacement of the tracer pulse within the measurement interval (not shown). The timing of the observed changes in the waveforms is consistent with the estimated time of arrival of the solute pulse based on the known infiltration rate and the measured volumetric water content behind the wetting front (0.255 cm3 cm⫺3). The electromagnetic field that propagates along the target rods interacts with both the medium and the nonmetallic probe components (i.e., water-filled gaps and PVC access tubes). These probe components insulate the target rods from the medium, leading to greatly reduced absolute changes in waveform amplitude com-
T.P.A. Ferre, Dep. of Hydrology and Water Resources, University of Arizona, Tucson, AZ 85721; D.L. Rudolph, Dep. of Earth Science, University of Waterloo, Waterloo, ON, N2L 3G1 Canada; R.G. Kachanoski, Dean of Graduate Studies, University of Saskatchewan, Saskatoon, SK, S7N 5A4 Canada. Received 19 Apr. 1999. *Corresponding author (
[email protected]).
Abbreviations: EC, electrical conductivity; PVC, polyvinyl chloride; TDR, time domain reflectometry.
Published in Soil Sci. Soc. Am. J. 67:494–496 (2003).
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Fig. 2. Waveforms collected with a profiling probe with 20-cm long target rods centered at a 90-cm depth during the advance of a 0.67 g L⫺1 KCl tracer step (electrical conductivity [EC] ⫽ 0.142 S m⫺1) applied at a rate of 0.0036 cm s⫺1 following steady-state infiltration with municipal water (EC ⫽ 0.040 S m⫺1). Waveforms are labeled with the elapsed time since the beginning of application of the tracer step. Fig. 1. Schematic diagram of one of the pair of profiling time domain reflectometry (TDR) rods and access tubes.
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related directly to changes in the EC of the pore water. We found a linear dependence of the EC of the tracer solution on the tracer concentration. For these conditions, changes in the measured EC of the medium are linearly related to changes in the tracer concentration in the pore water. Ward et al. (1994) demonstrated that, under these conditions, the electrical conductivity measured with horizontally installed TDR rods could be calibrated to return the resident solute mass by numerical integration of the probe responses during the advance of a tracer pulse of known total mass. Mallants et al. (1996) found that this method produced the most accurate probe calibrations for a homogeneous soil. We applied this method to relate the solute concentration to the soil EC inferred from the profiling probe responses. The inferred tracer concentration is shown as a function of elapsed time since the beginning of tracer application in Fig. 3. The breakthrough curve shows the arrival of solute mass after approximately 90 min. The solute concentration rises smoothly to a maximum value equal to 65% of the input concentration after 130 min. Greater dispersion is evident during displacement than
The constant, a, describes the reduced sensitivity of the probe to the EC of the medium because of the insulating effects of the probe materials. The constant, b, is a function of both the probe sensitivity and the electrical properties of the probe materials. The cable that connected the profiling probe to the cable tester was unchanged for all of our measurements. Therefore, we made no attempt to consider directly any electrical losses through the connecting cables. Rather, the constants, a and b, include any effects of cable loss. A series of measurements were made to confirm that the EC response of the probe was well described by this model (not shown). The duration of the water-content measurement window was unchanged throughout the experiment (Fig. 2), indicating that the water content within the sample volume of the profiling probe was constant. Given that the water content did not change with time, any observed changes in the EC of the medium with time could be
Fig. 3. The solute concentration inferred from the electrical conductivity response of a profiling probe during the advance of a 0.67 g L⫺1 KCl tracer step (points) calibrated using the solute pulse numerical integration method of Ward et al. (1994). The calculated breakthrough curve of a nondispersed solute pulse is shown as a solid line. Results are presented as a function of elapsed time since the beginning of application of the tracer step.
pared with those that would be measured with uncoated rod probes under the same conditions. Quantitative interpretation of the EC response of the profiling probe requires the development of an expression relating the probe response to the EC of the surrounding medium. Following Nadler et al. (1991), we defined the EC response of the profiling probe, TDR, as the inverse of the maximum amplitude (ohms at cursor) of the waveform. To minimize the effects of inductive losses in the balun, the waveforms were truncated after 55 ns. Ferre´ et al. (1998) developed an expression to predict the dielectric permittivity response of a coated-rod probe based on its geometry, the dielectric properties of the probe materials, and the soil dielectric permittivity. We postulate that the EC response of the profiling probe, TDR, will follow a similar harmonic dependence on the EC of the medium, m: 1 a ⫽ ⫹ b. TDR m
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during the arrival of the solute pulse. Finally, the solute pulse was displaced completely after approximately 180 min. For comparison, a breakthrough curve was calculated for a 45-min duration, nondispersed step pulse. The pore water velocity was calculated using the applied flux rate and the average measured water content of 0.255. The travel time of the center of mass calculated from the measured breakthrough curve of 134 min is in good agreement with the 129-min time predicted for the nondispersed step pulse. The results shown here offer compelling qualitative evidence that the profiling probe and other coated rod TDR probes can be used to monitor both the water content and the EC of soils. The profiling probe can be used to monitor solute transport over discrete depth intervals under steady-state flow conditions. Further work is necessary to account for the effects of changing
water contents on the measured EC to extend the use of this probe to transient flow conditions. REFERENCES Ferre´, P.A., D.L. Rudolph, and R.G. Kachanoski. 1998. The water content response of a profiling time domain reflectometry probe. Soil Sci. Soc. Am. J. 62:865–873. MacFarlane, D.S., J.A. Cherry, R.W. Gillham, and E.A. Sudicky. 1983. Migration of contaminants in groundwater at a landfill: A case study. 1. Groundwater flow and plume delineation. J. Hydrol. (Amsterdam) 63:1–29. Mallants, D., M. Vanclooster, N. Toride, J. Vanderborght, M.Th. van Genuchten, and J. Feyen. 1996. Comparison of three methods to calibrate TDR for monitoring solute movement in undisturbed soil. Soil Sci. Soc. Am. J. 60:747–754. Nadler, A., S. Dasberg, and I. Lapid. 1991. Time domain reflectometry measurements of water content and electrical conductivity of layered soil columns. Soil Sci. Soc. Am. J. 55:938–943. Ward, A.L., R.G. Kachanoski, and D.E. Elrick. 1994. Laboratory measurements of solute transport using time domain reflectometry. Soil Sci. Soc. Am. J. 58:1031–1039.
