Published in Vadose Zone Journal 2:433-439 (2003)
© 2003 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
ORIGINAL RESEARCH PAPER
Measuring Water Content in Saline Sands Using Impulse Time Domain Transmission Techniques
R. Chawn Harlow*,
Eleanor J. Burke and
Ty P. A. Ferré
Department of Hydrology and Water Resources, University of Arizona, Tucson, AZ 85721
* Corresponding author (chawn{at}hwr.arizona.edu).
Received 21 March 2002.
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ABSTRACT
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This paper discusses two time domain transmission (TDT) electromagnetic methods for measuring soil water content in a sand and examines the impact of pore water salinity on the resulting measurements. The first technique calculates the time taken by an impulse traveling one way through the medium relative to its time taken in air. The second method converts this impulse to the frequency domain via a Fast Fourier Transform (FFT) and calculates the travel time from the difference in phase measured in air and that measured in the medium at each frequency, resulting in a measurement of the frequency-dependent travel time. The relationship between travel time and water content was determined for pore water electrical conductivities (EC) ranging from 0.5 to 40 dS m-1. At 0.5 dS m-1 the relationship was similar to that found by previous researchers using time domain reflectometry (TDR) measurements. At pore water EC 
5 dS m-1 the travel time was faster than that found for 0.5 dS m-1 at the same water content, contradicting traditional thinking based on transmission line theory and differing from results of TDR methods. In addition, for pore water EC 5 dS m-1, the relationship determined between travel time and water content was shown to be independent of pore water EC, to the precision of the TDT measurement technique. As a result, the impulse TDT method and this calibration relationship may improve our ability to measure soil water content under natural field conditions and may encourage further investigation of the impact of salinity on the spectral dielectric response of porous media.
Abbreviations: EC, electrical conductivity • FFT, Fast Fourier Transform • RMSE, root mean square error • TDR, time domain reflectometry • TDT, time domain transmission • VNA, vector network analyzer
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INTRODUCTION
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TIME DOMAIN ELECTROMAGNETIC measurement methods of soil water content are rapid and nondestructive techniques for determining volumetric water content in a wide variety of porous media. The most commonly used methods are based on TDR techniques, for which the two-way travel time of an electromagnetic signal along a transmission line is readily related to the volumetric soil water content (e.g., Topp et al., 1980). This paper demonstrates that TDT techniques can be used to measure the volumetric water content of soils in a similar manner by measuring the time taken for an electromagnetic pulse to travel one way along a transmission line.
For salt-tolerant agricultural operations, such as cotton (Gossypium hirsutum L.) farming, as well as for a variety of hydrogeologic investigations ranging from mine tailings studies to measurements in areas of evaporative salination, it is important to be able to measure the water content of media with very high pore water salinities. There are issues as to the applicability and accuracy of both TDT and reflection measurements in lossy media such as saline soils because of the large decrease in the amplitude of the measured signal information and loss of content (Weerts et al., 2001). While Hook et al. (1992) employed shorting diodes and the use of waveform subtraction techniques to extend the use of TDR to more saline soils (up to 50 dS m-1), the practical upper limit of salinity for standard time domain reflection measurements of soil water content is about 10 dS m-1 (Dalton and van Genuchten, 1986). Even if sufficient energy is retained in the pulse for analysis, the effects of increased salinity on measurements are still uncertain. Some investigators (Hook and Livingston 1995; Wyseure et al., 1997; Sun et al., 2000) suggest that travel time methods result in overestimates of the volumetric water content, while others show no observed dependence (Topp et al., 1980, 1988; Dalton et al., 1984; Kelly et al., 1995).
The objectives of this study were (i) to determine the dependence of the travel time of an electromagnetic wave, measured with two TDT methods, on the volumetric water content and pore water salinity of a sand and (ii) to compare these relationships with previously published results based on measurements made with TDR methods.
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THEORY
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In typical TDT applications, the travel time is defined as the time taken for an electromagnetic signal to travel one way along a transmission line. In practice, the measured travel time is the sum of the time taken to travel along the connecting cables and the transmission line. Two measurements are made to isolate the travel time through the sample. The first is the travel time along the connecting cables and the transmission line embedded in the medium of interest (tm). The second is the travel time along the connecting cables and the same transmission line in air (tair). The travel time through the connecting cables is the same for both measurements. For a transmission line of length, L, the travel time along the transmission line in air is L/c, where c is the speed of light in a vacuum. Therefore, the travel time through the medium (t) is thus given by
 | [1] |
This paper discusses the use of two different methods, both based on TDT measurements, to determine the travel time within a medium. The first technique calculates the travel time by examining the time difference between the peak of an impulse through the medium and that through air (tm - tair). The second method converts time domain measurements made in air and in the medium to the frequency domain via a FFT. Then, the travel time at each frequency is calculated from the difference in the phase measured in air and that measured in the medium.
For both TDR and TDT methods, the volumetric water content of the medium can be inferred from the measured travel time. In the case of a sand, Hook and Livingston (1996) showed that the volumetric water content (
) can be determined using
 | [2] |
where d is the distance traveled by the signal within the medium. For TDT measurements d is equal to L, and for TDR measurements d is 2L.
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MATERIALS AND METHODS
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Both methods for determination of travel time make use of an impulse sent along the transmission line that was generated using a vector network analyzer (VNA). A VNA is an instrument commonly used to measure the transmission and reflection properties of a transmission line in the frequency domain. It has a high signal/noise ratio that allows measurements in more highly attenuating environments than is possible with conventional TDR instruments. Sand with no clay fraction was chosen to minimize surface conductance and bound water effects that can complicate the interpretation of the water content in clay-rich soils (Brisco et al., 1992; Dasberg and Hopmans, 1992; Roth et al., 1992; Weitz et al., 1997; Wraith and Or, 1999).
Measurements were made in sand variably saturated with tap water (0.5 dS m-1) and NaCl solutions with pore water ECs (
w) of 5, 10, 15, 20, 25, and 40 dS m-1. In addition, three replicate measurements were made with tap water and at pore water ECs of 10, 25, and 40 dS m-1. Solution conductivities were measured with a conductivity meter at a temperature of 21°C. Solution conductivities before and after mixing with the sand were found to agree within 2%.
A 26-cm-tall, 10-cm-diameter column with a twin-rod transmission line installed vertically along its axis was used for the measurements (Fig. 1). The transmission line consisted of two 26-cm-long, 0.3-cm-diameter steel rods separated by 2.2 cm. Direct measurements showed that the sample volume of the probe did not extend far enough from the rods to include the column walls. Air-dried sand was poured into the top of the column to prepare the sample. The tap water and saline solutions were introduced through a tube at the bottom of the column. The volumetric water content was determined from the mass of water added, the mass of sand in the column, and the measured dry bulk density of the sand. Each end of the transmission line was connected to the VNA via coaxial connecting cables and terminal blocks. The VNA used in this study (HP 8752C Network Analyzer, Hewlett-Packard, Santa Rosa, CA) was set up to measure in transmission at 401 equally spaced points in the frequency range of 300 kHz to 1.5 GHz. The VNA measurements were made as the volumetric water content was increased. When measurements were complete and the sand was completely saturated, the sand was discarded and new sand and saline solution were added for the next run. Using new sand simulates the effects of variability due to localized packing around the rods that would occur in field measurements better than multiple flushings of a single packing (e.g., Sun et al., 2000). Further details of the experimental setup and techniques may be found in Harlow et al. (2003).
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Fig. 1. Schematic of measurement setup, showing connection of the transmission line in the column to the vector network analyzer (VNA).
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RESULTS
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Time Separation Measurements of Impulse Travel Time
To simulate an impulse input, measurements made in the frequency domain using the VNA were convolved with a windows function (W) of the form
 | [3] |
where Np is the total number of discrete frequencies sampled by the VNA and n is the frequency sample index. The convolved response was then converted into the time domain via an inverse FFT. Figure 2 shows the transmission coefficient as a function of time for the 26-cm transmission line in air and for the same line immersed in sand at three different water contents and two different salinities. The time domain signal contains a series of peaks representing the transmitted and internally reflected responses of the transmission line and coaxial cable to an impulse signal. The highest peaks for each trace (at t = 152.5 ns for air and at t = 154.3 ns for sand on Fig. 2a) represent the energy that passes directly through the coaxial cables and the column with no internal reflections. Any secondary peaks after these first arrivals represent signals that have been multiply reflected from physical connections within the experimental setup.
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Fig. 2. Time domain separation of first arrivals with the transmission line immersed in air and in the variably saturated sand at specified average volumetric water contents and pore water electrical conductivity (w). The shaded regions in Fig. 2b represent the domains over which the gate is applied to the air (dark shading) and sand (light shading) signals.
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The difference in travel time is determined as the difference in time between the first arrival in air and the first arrival in sand. The travel time through sand is then determined from Eq. [1]. As expected, the travel time increases with increased water content. Also, the magnitude of the first arrival decreases with increased salinity (e.g., Fig. 2a and 2d) and with increased water content (e.g., Fig. 2a and 2b or Fig. 2c and 2d). The side lobes, which are particularly apparent to the left of the first arrival in Fig. 2d, are an artifact of using a finite bandwidth in the FFT. The side lobes are present for all of the synthesized time domain data. However, for low salinities the lobes are much smaller than the main peak. As the water content and salinity increase, the magnitude of the direct arrival decreases and approaches that of the side lobes. As with traditional TDR measurements, this results in an upper limit of the method's applicability which is controlled by the bulk electrical conductivity of the medium, by the measurement bandwidth, and by the rod length.
Figure 3 shows the relationship between travel time and volumetric water content for tap water (0.5 dS m-1) and for three selected pore water EC values (w): 10, 25, and 40 dS m-1. Three replicate measurements are shown for each value of w. The results are highly repeatable, particularly at the lower salinities, showing little influence of packing on the response. Hewlett-Packard states that all measurements resulting in losses >40 dB are unreliable (Hewlett-Packard, 1998). The gray symbols in Fig. 3 show the measured points for which the losses are greater than this 40 dB cutoff threshold.
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Fig. 3. Travel time as a function of water content for tap water (0.5 dS m-1) and three pore water electrical conductivity conditions (10, 25, and 40 dS m-1) calculated from the time separation of the first arrivals. The best fit for tap water is superimposed on the four plots.
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The best fit between the travel time and water content for the tap water is shown in Fig. 3a. The slope of the relationship is 0.0685 ns %-1 and the intercept is 1.4351 ns. This relationship agrees well with that reported by Hook and Livingston (1996), who showed a slope of 0.069 ns %-1 and an intercept of 1.52 ns. The root mean square error (RMSE) between the measurements and the fit for tap water is 0.009 cm3 cm-3. The RMSE between the measurements and the relationship suggested by Hook and Livingston (1996) is 0.016 cm3 cm-3. These results fall well within the expected accuracy of the TDR method (e.g., Topp et al., 1980). The best fit from Fig. 3a is superimposed on Fig. 3b, 3c, and 3d. Travel times measured under higher salinity conditions are faster than predicted by the relationship determined for tap water for any given water content. This result is unexpected, as TDR measurements have shown either no effect of salinity (Topp et al., 1980, 1988; Dalton et al., 1984; Kelly et al., 1995), or increases in dielectric permittivity, and therefore travel time, with increasing salinity (Sun et al., 2000; Dalton, 1992; Dalton et al., 1990). The results of this study imply that the permittivity of a variably saturated sand decreases with increasing salinity. This contradicts transmission line theory. However, a decreased permittivity for saturated saline sand has been confirmed by one of the reviewers of this paper. Further work is necessary to determine the cause of these measured discrepancies with TDR results and transmission line theory. If the relationship determined for tap water were used to evaluate the volumetric water content of saline soils, the RMSE between the predicted and measured water contents (not including those points with losses greater than the 40 dB cutoff threshold) would be 0.051, 0.038, and 0.023 cm3 cm-3 for w values of 10, 25, and 40 dS m-1, respectively. Further examination showed that the change in RMSE is due largely to the decrease in the number of points with losses greater than the threshold cutoff for higher salinities.
Gated Time Domain Measurements of Impulse Travel Time
The gated TDT method is discussed in detail in Harlow et al. (2003) and is summarized only briefly here. The time domain response of the signal shown in Fig. 2 was gated to select only the first arrival while removing the influences of internal reflections. The gate was defined and applied in the frequency domain, although its impact on the complex transmission coefficient was examined in the time domain. The gate (G) is of the form (Ifeachor and Jervis, 1993, p. 288–295):
 | [4] |
where Np is the total number of discrete frequencies sampled by the VNA, n is the frequency sample number, and 
is given by
 | [5] |
where 
t is the gate width in the time domain (ns); f is the frequency (GHz), and fc is the central frequency of the bandwidth. The frequency increment is defined by Np equal steps in the value of f over the bandwidth of interest. The Fourier Transform of the function [sin()]/ is a step function of finite width. Therefore, the gate can be applied in the frequency domain with prior knowledge of its effects in the time domain.
Figure 2b shows an example of the region of application of the gate (shaded) in the time domain. Within this region the gate maintains the shape of the arrival; outside of this region the signal is filtered to zero. It should be noted that the experimental setup is not ideal for filtering out the secondary arrivals because the time separation between the first and secondary arrivals in air is not as long as that recommended by Harlow et al. (2003). However, to increase this travel time would entail the use of a longer column. This would increase the attenuation, reducing the range of water contents and salinities for which sufficient signal is preserved and measurements are possible. The experimental setup discussed here is a compromise between the ideal solution for the gating technique and that for measurements in lossy soils.
A FFT was used to convert the gated time domain response to the frequency domain. As for the peak travel time method described above, the travel time through the medium is calculated based on the difference between the travel time of the signal through an air-filled column and that through the column containing the sample. The time taken in air, tair (ns), can be calculated from the phase of a pulse that has traveled along the transmission line through air, 
air, as
 | [6] |
where 
is the angular frequency (rad s-1). The travel time of the transverse electromagnetic wave (t) propagating in the medium is then given by
 | [7] |
where is the difference between the phase of a pulse transmitted through air and that through the sample.
Figure 4 shows the gated frequency-dependent travel time for sand that is variably saturated with tap water. The travel time through the sand when partially saturated with a 25 dS m-1 solution is shown as well. As a result of the gating, the frequency-dependent travel time cannot be determined for the entire range of frequencies measured (Harlow et al., 2003). The shaded area in Fig. 4 denotes the unacceptable frequency range. The relationship between the travel time at a frequency of 0.75 GHz (dotted black line in Fig. 4) determined from the gated time domain response and volumetric water content is very similar to that shown in Fig. 3. (The frequency of 0.75 GHz was chosen somewhat arbitrarily but primarily because it is the midpoint of the acceptable frequency range in a region where the gate is flat, as suggested by Harlow et al. [2003]). In this case the slope of the relationship for tap water is 0.0678 ns %-1, and the intercept is 1.5142 ns. The RMSE between this best fit and the measured volumetric water contents is 0.009 cm3 cm-3. The RMSE between the measurements and the relationship suggested by Hook and Livingston (1996) is 0.01 cm3 cm-3. Again these results fall well within the expected accuracy of TDR methods (e.g., Topp et al., 1980). Also, as seen for the measurements made with the pulse travel time method, travel times measured under higher salinity conditions are faster than predicted with the tap water calibration for any given volumetric water content. The range of conditions for which the water content can be measured is very similar to that found for the pulse travel time method (Fig. 3).
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Fig. 4. Travel time as a function of frequency for tap water with the sand at four different water contents and a pore water electrical conductivity of 25 dS m-1 at one of the previously specified water contents calculated using the gated time domain method. The dotted vertical black line indicates the frequency at which further analyses were performed (0.75 GHz).
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DISCUSSION
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The relationship between travel time and volumetric water content in saline soils is different than that for sand containing pore water with low EC (Fig. 3). Figure 5 shows one replicate set of results for pore water EC ranging from 5 to 40 dS m-1. Measurements that had unacceptably high losses (gray points in Fig. 3) have been excluded. There is no discernable effect of the pore water EC on the relationship between travel time and water content for either of the measurement methods discussed. However, the travel times are slightly slower and show more scatter when determined by the gated time domain method than when measured using the time of separation of the first arrivals. The increased scatter and break in slope may be due to incomplete separation of the first peak from the reflections by the gate. This is probably the result of using rods that are a compromise between optimal rod length for time separation and that needed to minimize signal losses. This effect can be seen in Fig. 2a, where there is not a large separation in time between the first and second peaks for the reference line.
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Fig. 5. Travel time as a function of water content for pore water electrical conductivity of 5, 10, 15, 20, 25, and 40 dS m-1 calculated using both methods: the time separation of first arrival and the gated time domain transmission (TDT) method. The best fit for each method is shown (solid black line) along with the relationship suggested by Hook and Livingston (1996).
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Using a similar format for the relationship between travel time and soil water content as that of Hook and Livingston (1996), the following equations are obtained for the time separation measurements and for the gated time domain measurements, respectively:
 | [8] |
 | [9] |
The intercepts of these relationships are very similar to those for the tap water (0.5 dS m-1) and those found by Hook and Livingston (1996). The differences between these slopes and the slope found for tap water suggest a different sensitivity of the bulk dielectric permittivity to changes in the water content. This may have further implications for monitoring the advance of saline solutions into a medium initially containing low EC pore water.
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CONCLUSIONS
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Two methods of determining the one-way travel time of an electromagnetic wave along a transmission line are examined. The first method calculates the time separation of an impulse with the transmission lines buried in the medium compared with that measured with the same line in air. This is a very simple method that uses information from all transmitted frequencies to determine a single effective travel time. The second method uses only the information contained in the first arrival. This information is converted to the frequency domain using a FFT. Then the difference in the phase measured with the transmission line in air and that measured through the sample is used to determine the travel time. This results in a frequency-dependent travel time over a limited frequency band. Both methods produce similar and highly repeatable relationships between travel time and measured volumetric water content. However, there is slightly less scatter in the measurements made using the time separation method for the experimental conditions examined in this study.
There are three key findings regarding the dependence of the travel time measured with these transmission measurements on the pore water salinity. First, the relationship between travel time and the volumetric water content of sand agrees well with that suggested by Hook and Livingston (1996) for sand containing low salinity (0.5 dS m-1) tap water. Second, the travel time is independent of the pore water salinity if the pore water salinity is 5 dS m-1 and 
40 dS m-1. Third, the travel times measured through more saline sands are smaller than those measured through the same sand containing tap water at the same water content.
The first finding demonstrates that there are no significant errors in the methods under low loss conditions. The pore water electrical conductivity can be relatively high under many natural settings. Therefore, the second finding suggests that these TDT methods may allow for measurement of volumetric water content in soil without regard for the pore water EC as long as a measurable signal can be transmitted. The third finding differs from results found by previous researchers using TDR methods. Further investigation is required to explain this discrepancy.
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ACKNOWLEDGMENTS
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Primary support for Dr. Eleanor Burke while preparing this paper came from NOAA project NA96GP0412. During the preliminary work for this paper, Chawn Harlow and Dr. Eleanor Burke were visiting scientists at ESSC, the University of Reading, UK. This material is based on work supported by SAHRA (Sustainability of semi-Arid Hydrology and Riparian Areas) under the STC program of the National Science Foundation, Agreement no. EAR-9876800.
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S. B. Jones and D. Or
Frequency Domain Analysis for Extending Time Domain Reflectometry Water Content Measurement in Highly Saline Soils
Soil Sci. Soc. Am. J.,
September 1, 2004;
68(5):
1568 - 1577.
[Abstract]
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ABSTRACT
INTRODUCTION
