Soil Science Society of America Journal 64:54-61 (2000)
© 2000 Soil Science Society of America
DIVISION S-1-SOIL PHYSICS
Effect of Cable Length on Time Domain Reflectometry Calibration for High Surface Area Soils
S.D. Logsdona
a USDA-ARS, National Soil Tilth Laboratory, 2150 Pammel Dr., Ames, IA 50011 USA
logsdon{at}nstl.gov
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ABSTRACT
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Time domain reflectometry (TDR) has been used by soil scientists to determine soil water content (
). A waveform analysis determines an apparent dielectric number (
a) which can often be empirically related to . "Bound water" near colloid surfaces has different properties than free water. At the gigahertz frequencies used for TDR, free water has a negative temperature effect but bound water has a positive temperature effect on dielectric number. Long coaxial cables reduce the higher frequencies of the TDR equipment, which can influence the frequency dependent a of bound water. The objective of this study was to determine the effect of coaxial cable length and temperature on apparent dielectric properties for samples with and without large amounts of bound water. Two undisturbed columns of Okoboji mucky silty clay loam (fine, smectitic, mesic cumulic Endoaquoll) with a specific surface area of 286 m2 g-1 and two packed sand samples with calculated surface areas of 0.01 m2 g-1 were used for the experiment. The a was determined at four cable length combinations, three temperatures, and a range of . The temperature correction factors for Okoboji ranged from 0.008 to 0.012 /°C, depending on cable length. Long cables increased the rise time 41%, which decreased the frequency bandwidth. The Okoboji samples had a bulk electrical conductivity as high as 0.14 S m-1, which hampered determination of the final part of the waveform. In summary for Okoboji, cable length and temperature had a greater effect on a than did . High surface area samples should be calibrated using the same cable length used for measurements, and the temperature effect should be incorporated.
Abbreviations: a, apparent dielectric number, , soil water content • TDR, time domain reflectometry
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INTRODUCTION
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TIME DOMAIN REFLECTOMETRY can be used to measure dielectric properties from analysis of the reflected waveform (Topp et al., 1980) using apparent length or apparent travel time (Fig. 1) . The Tektronix 1502B cable tester (TDR system) has a short rise time (see Fig. 1), 
200 ps (Tektronix, 1991), which corresponds to a frequency (f) bandwidth around 1.75 GHz. In soil, water is expected to have a much higher dielectric number at these frequencies than any other soil component, which allows TDR to be used for determining by empirical calibration equations.
Waveform analysis (Fig. 1) determines the apparent length along the waveguide. The cable tester waveform analysis (Topp et al., 1980) measures the apparent dielectric number
 | (1) |
where c is the velocity of light, V is the propagation velocity, La is the apparent length of the waveguides, L is the actual length, a is the apparent dielectric number, 
dc is the zero-frequency electrical conductivity, o is the dielectric number for a vacuum, and ' and '' are the real and imaginary components of the complex dielectric.
As the frequency is increased, materials are no longer able to oscillate at the higher alternating frequency, which is manifested as a dielectric relaxation. Above the relaxation frequency for a material, the dielectric number is much lower. Pure water has a high dielectric relaxation (17 GHz), so below this frequency, water has a high dielectric number, and far below this frequency, the dielectric number does not change much as the frequency is reduced further (Stogryn, 1971; Hasted, 1973; Orr and Wraith, 1999). If the soil is dominated by sand or by colloids with low surface area and the bulk dc is small, then '' is usually much smaller than '. This allows simplification of Eq.[1] to
(Topp et al., 1980).
For pure water, as the dc is increased, '' increases, ' decreases (Stogryn, 1971) and tan 
increases. The bound water associated with colloids in the soil (clays and organic matter) has different properties than free water (Schwarz, 1962; Hasted, 1973; Arulanandan and Smith, 1973; White et al., 1994), and different properties than ice (de Loor, 1968; Calvet, 1975; Dobson et al., 1985). The dielectric relaxation(s) occurs at lower frequencies for bound water than for free water, but the relaxation frequencies for colloid-associated water are not well characterized, ranging between 106 and 1011 Hz, depending on (Calvet, 1972, 1975; Sposito and Prost, 1982). Many soils in the midwestern USA have a large cation exchange capacity (CEC) because of the large amount of negative charges associated with the soil colloids. This results in a high concentration near colloid surfaces, which contributes to a high electrical conductivity if there is continuity of water (White et al., 1994; Nadler, 1993, 1999). Calvet (1972, 1975) has shown that there are at least two dielectric relaxations in addition to bulk dc effects for water associated with smectites.
By means of the description of 2:1 smectites given by Prost et al. (1998), the water associated with internal and external surfaces is 1 to 1.5 layers per internal surface and 4 layers (1.3 nm) per external surface. If a quasi-crystal of smectite has 20 layers, the overall amount of colloid-associated water is 46 to 65 water layers (0.3-nm width) per quasi-crystal (40 surfaces). As the surface area of the soil is increased, the volume fraction of colloid-associated water increases to significant proportions.
As components are added to the 1502B cable tester, the higher frequencies are lost. This results in a bandwidth with the highest frequency lower than 1 GHz. Long cables and use of a transient suppressor have been shown to increase the impedance and reduce the high frequency components of the cable tester (Hook and Livingston, 1995; Reece, 1998). This high frequency loss may not be of much concern for soils dominated by free water of low solute level, since the dielectric relaxation is so much higher than the measurement frequency, and the dc influence would only be of concern at much lower frequencies. This high frequency loss could be of concern for soil with a large fraction of water associated with soil colloids (Arulanandan et al., 1973; Arulanandan and Smith, 1973; Saarenketo, 1998).
The dc depends strongly on temperature. In a mixture such as soil, dc depends on continuity and tortuosity of the conducting medium (i.e., water), so is affected by the soil structure and the water content (White et al., 1994). High bulk dc decreases the rebound of the reflected wave, often complicating waveform analysis (Zegelin et al., 1992; Persson and Berndtsson, 1998; Wraith and Orr, 1999). Long cables further complicate waveform analysis because of more rounded and less distinct waveforms (Hook et al., 1992; Heimovaara, 1994). The bulk dc is not only due to soil solution concentration but also to colloid-associated water effects, which may account for up to 90% of bulk dc (Nadler, 1991, 1993, 1998, 1999).
Use of TDR has been highly successful on soils with low surface area and low CEC, but many difficulties have been encountered on soils with high surface area and high CEC. Sometimes a separate calibration is enough to determine from the apparent dielectric number (Roth et al., 1992; Weitz et al., 1997), but often a simple calibration of
is not possible because of temperature effects on bulk dc (Bridge et al., 1996). Unpublished data (1999) of the author indicated that for some soil horizons with high surface area (>77 m2 g-1), high bulk dc (>0.09 S m-1 with temperatures around 12°C and around 0.3 m3 m-3), and long coaxial cables (30 m of RG8 and 8.2 m of RG58A), the a was more correlated with temperature than with . For horizons with similar cable lengths but higher surface areas (>200 m2 g-1) and bulk dc (>0.13 S m-1), waveform analysis was sometimes not possible in the summer months due to the small rebound for the reflections at the end of the waveguide.
Because the measurement frequency of the TDR is lower than the relaxation frequency of pure water, the temperature effect on dielectric of pure water is negative (dielectric increases as temperature decreases—de Loor, 1968; Stogryn, 1971). The measurement frequency is higher than the relaxation frequencies of colloid-associated water and of solute-associated water; therefore, the temperature effect is positive (dielectric increases as the temperature increases—de Loor, 1968). The combined effect for soil depends on bulk dc and on the proportion of the water that is associated with the soil colloids. Positive temperature effects have been reported by Hoekstra and Delaney (1974), Verstricht et al. (1994), Persson and Berndtsson (1998), and Wraith and Orr (1999). Net negative temperature effects were reported by Pepin et al. (1995), Hook and Livingston (1996), and Persson and Berndtsson (1998), but the negative effects were less than for free water.
It is known that colloid-associated water in soil might contribute to a large bulk dc even for non saline soils. In some cases, this bound water has large changes in a for a small change in frequency. It is known that long cables and high electrical conductivity interfere with waveform analysis. The hypothesis of this study is that long cables and use of a transient suppressor will reduce the measurement frequency into a range that is influenced by water associated with colloids. The objective of this study is to examine how varied coaxial cable lengths and temperature influence the apparent dielectric number for samples with and without a large amount of colloid-associated water. A detailed mechanistic study of colloid-associated water is beyond the scope of this study, but is continuing in further studies.
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Materials and methods
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Two undisturbed soil cores were taken by the procedure of Logsdon (1994) from Okobji mucky silty clay loam. The stove pipe cylinders were 0.1-m diam and 0.43 m long. The lengths of the soil in the cylinders were 0.38 m (Sample A) and 0.34 m (Sample B). The specific surface area was determined by humidifying the soil over Mg(NO3)2 (Newman, 1983; Laird, 1999; Quirk and Murray, 1999) and correcting to a Ca-saturated bentonite standard (750 m2 g-1). Two additional cores were filled with coarse sand and watered to settle. The settled length of sand samples were 0.34 m for Sample C and 0.33 m for Sample D. The lengths of the samples were 30 to 80 mm longer than the 0.3-m waveguides. The 1:1 parallel waveguides (Spaans and Baker, 1993) were inserted horizontally, and the cylinders remained horizontal throughout the study.
Samples were covered with plastic on the bottom, then wetted up with 0.005 M CaSO4 before covering the top with plastic. Campbell Scientific, Inc.1
equipment (21X data logger with TDR proms or control chips, and one or two coaxial multiplexers) was used with a Tektronix cable tester (1502B) to collect internal data for La/L and reflection coefficient quotient (for solute analysis). In addition, each waveform was collected with distance/division set to 1 m (for a total apparent distance of 10 m for the 251 points). To achieve a range of , the samples were dried slowly over time, taking measurements initially three times a week, gradually reducing the frequency of measurement down to once every two weeks. The unconsolidated sand samples dried rapidly and needed to be rewetted during the drying cycle to prevent the samples from falling apart.
For two of the levels, cable length effect on La/L and bulk dc was examined for 12 cable length combinations ranging from 6.3 to 49.5 m (Fig. 2
, Table 1)
. For the other levels, I only examined three or four cable length combinations but included measurements at two or three temperatures for each cable length. The samples as well as cables and multiplexers were equilibrated at the appropriate temperature; only the cable tester and a short length of cable connected to the cable tester remained at room temperature for the lower temperatures tested. Thus possible effects of temperature on the cable were included but possible effects of temperature on the cable tester were not included. Thermometers were used to measure the temperatures.
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Fig. 2 Diagram of the setup for cable tester, multiplexers, cables and accessories. Waveguide cables were attached to either the first level multiplexer or the second level multiplexer, but not both at the same time. The lengths of cables between the transient suppressor and the two multiplexers varied as described in Table 1
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Table 1 Equipment setup showing length of coaxial cables between the cable tester (CT), transient suppressor (TS), first multiplexer (M1), second multiplexer (M2), and waveguide in the soil core (WG)
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The cable length effect on resistance was corrected as described by Reece (1998), and the observed cable resistance was 0.005 and 0.02 
/m cable for RG8 and RG58A cables, respectively. These are smaller cable resistances than Reece (1998) observed, perhaps because of a longer time to determine final reflection. The resistance of a coaxial multiplexer was negligible.
Analysis of variance was used separately for the Okoboji soil and for the sand to assess significant effects of the four major cable length combinations and the three temperatures on
, and bulk dc. The temperature correction factor (Persson and Berndtsson, 1998) for
was determined for four main cable length combinations (Table 1, top) for each of the four samples.
Rise time is the portion of the waveform before that used for apparent length determination. Rise time was determined from the waveform (Tektronix, 1991), and changes in the slope were verified from slope(time) of the waveform. In addition, the risetimes from waveforms in air were verified from shorted waveforms. The frequency bandwidth (BW) was related to the risetime (t) using the equation given by Tektronix,
. The frequency bandwidth is affected not only by the cable and accessories, but also by the capacitance of the sample (Tektronix, 1991).
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Results and discussion
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Soil Properties
The bulk densities of the undisturbed Okoboji samples (A and B) were 1.25 and 1.27 Mg/m3. The specific surface area was 286 m2 g-1, which would be equivalent to a bound water fraction between 0.123 and 0.177 m3 m-3, depending on . The Okoboji had 5.0% organic carbon, and 12.9, 49.9, and 37.2% sand, silt, and clay, respectively. The bulk densities of the packed sand samples (C and D) were 1.74 and 1.83 Mg/m3, and the particle-size distribution was 3.7% very coarse sand, 16.6% coarse, 48.1% medium, 30.8% fine, 0.7% very fine sand, and 0.1% coarse silt. Specific surface area was not determined directly for the sand samples but was calculated to be 0.01 m2 g-1 based on round particles and mean diameters for each fraction. Such a low surface area would result in an insignificant bound water fraction for the sand samples.
Dielectric Properties as Affected by Cable Length and Temperature
For the Okoboji soil,
was significantly affected by cable length combination, temperatures, and the cable length by temperature interaction. Each of the cable length combinations (Table 1) was significantly different from the others with mean
values of 6.05, 6.53, 6.56, and 7.32 for the 6.4 + 0, 4.6 + 20, 16.9 + 0, and 4.6 + 45 m combinations of RG58A and RG8, respectively (averaged across temperatures, , and replicate). Each of the temperature means was significantly different from the others with mean
values of 5.82, 6.69, and 7.23 for 6.5, 16.6, and 23.5°C, respectively (averaged across cable length combinations, , and replicate). For the sand,
was significantly affected by cable length combination, but not by temperature. The longest cable length combination had a significantly greater (2.6%)
(3.61) than the other cable length combinations (3.51), which were not significantly different from each other. Because of the large effects of cable length and temperature for the Okoboji samples, the standard deviation for
as a function of (averaged across temperatures and cable length combinations) was ten times greater than for the sand samples (Table 2)
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Table 2 Apparent dielectric number as a function of water content, averaged across temperature and cable length combinations
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Both temperature and cable length had large effects on the simple regression functions (Ledieu et al., 1986) of
for Okoboji Sample A (Fig. 3)
. (Okoboji Sample B was similar, but is not included to save space.) In contrast, neither temperature nor cable length had more effect on the simple regression functions for the sand Sample D (Fig. 4)
, each of which could be easily described by a single regression equation. (Sand Sample C was similar, but is not included to save space.)
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Fig. 3 Water content as a function of the square root of apparent dielectric number for two temperatures, and four cable length combinations for Okoboji Sample A
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Fig. 4 Water content as a function of the square root of apparent dielectric number for two temperatures, and four cable length combinations for sand Sample D
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By comparison, Hook et al. (1992) observed a 5.6% increase
for sand at a of 0.215 as RG6 cable length was increased from 2 to 100 m. Likewise for water, Heimovaara (1993) showed a 6.0% increase in
for an increase in cable length from 2.4 to 51 m.
Cable Length Effect on Temperature Correction Factor
For the sand samples (C and D), the temperature effect was smaller than the variation in the data, so no temperature correction was needed for the sand (temperature coefficient of 0 /°C). The temperature correction factors for the Okoboji samples were all positive. For the measurements at 6.4 m RG58A, the temperature correction factors were 0.008 and 0.0078 /°C for the A and B samples, respectively. Likewise for the 16.9 m of RG58A, the temperature correction factors were 0.0097 and 0.0083 /°C for the A and B samples. For the cable combinations of 4.6 m of RG58A and 20 m of RG8, the temperature correction factors were 0.0109 and 0.0116 /°C for Samples A and B. For the cable combinations of 4.6 m of RG58A and 45 m of RG8, the temperature correction factors were 0.0122 and 0.0118 /°C for Samples A and B. Much of the temperature correction factor was due to bulk dc as Persson and Berndtsson (1998) showed, but this data would suggest an additional temperature coefficient of 8.3 x 10-5 /°C/m of RG58A cable, and 18.1 x 10-5 /°C/m of RG8 cable.
Persson and Berndtsson (1998) gave d/dT values ranging from -0.0007 to +.0079 for soils or mixtures with bulk dc ranging from 0 to 0.049 S m-1. For bulk dc from 0.12 to 0.17 S m-1, they used coated waveguides so they could not determine d/dT except to say it was positive.
Electrical Conductivity
For both the Qkoboji soil and the sand, the bulk dc was significantly affected by and temperature, but not by cable length, since cable length effect had already been corrected for using the technique of Reece (1998). The bulk dc increased as a function of and temperature (Fig. 5)
. The relationship of bulk dc() was not linear for the Okoboji but appeared to level off between of 0.4 and 0.45 m3 m-3, increasing after 0.45 m3 m-3. A similar stepwise trend was noticed by Saarenketo (1998) for bulk dc of Beaumont soil.
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Fig. 5 Bulk DC electrical conductivity as a function of water content and temperature for the Okoboji and sand samples
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The Okoboji soil was not saline, but the high bulk dc was due to colloid effects (high CEC contributing to high surface conductivity). Electrical conductivity influences the imaginary component of dielectric inversely as a function of frequency (Eq. [1]). White et al. (1994) suggest that increased merely serves to connect the higher conductivity components (in this case, water associated with colloids).
Frequency Bandwidth
The rise time increased and the frequency bandwidth decreased as cable length increased (Table 3)
. The effect was more pronounced for the sand than for the Okoboji soil. By comparison Hook and Livingston (1995) observed rise times of 4.72 ns for 30.5 m of RG58 cable and 0.89 ns for 30.5 m of RG8 cable in sand. Heimovaara (1993) observed rise times ranging from 0.08 to 0.14 ns for different probes in air or water connected to 3.2 m cable.
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Table 3 The 90% rise time and frequency bandwidth as a function of cable length combination for Okoboji soil and for sand
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Although the change in bandwidth was greater for sand than for Okoboji (Table 3), the bandwidth did not affect the dielectric properties of the sand (Fig. 6)
. For the Okoboji,
increased more than the noise level below a frequency of 0.4 GHz. Similarly Saarenketo (1998) for Beaumont and Houston soils observed increases in a below frequencies of 0.4 GHz. Orr and Wraith (1999) mention that the frequency-dependent ' converges to the travel time determined a as the frequency approaches 1 GHz, meaning that the high frequency components are the measurement frequency for a determined from waveform analysis.
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Fig. 6 Square root of the apparent dielectric number as a function of the frequency bandwidth for the two Okoboji and two sand samples each at two different water contents
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Waveform Analysis Effects on Dielectric
Waveform analysis could potentially be influenced by difficulties assessing either or both the first and second point of the apparent length. Since I used 300-mm-long waveguides with 1:1 balans, the first point of waveform analysis for the longest cable length combination was still 63% of the shortest cable length combination (Fig. 7)
. Hook et al. (1992) observed for long cables, much greater attentuation of the first point peak for three wire probes with no balan. Waveform analysis of the Okoboji soil in this study was far more affected by difficulty in determining the second point because the high bulk dc reduced the rebound after the second point for all cable length combinations at the highest and temperature (Fig. 7). The rounded waveforms for long cable lengths presented additional difficulties for waveform analysis.
To attempt separating effects due to inadequate waveform analysis from effects due to soil colloids, I utilized data from Saarenketo (1998). He had data for complex as a function of frequency determined from a network analyzer for several samples including two vertisols, Houston black clay (very fine, smectitic, thermic Oxyaquic Hapludert) and Beaumont clay (fine, smectitic, hyperthermic Chromic Dystraquert). At high temperature and high , the bulk dc was 0.19 S m-1 for the Beaumont clay, but was not given for the Houston black clay. The CEC was 38 and 36 cmolc kg-1 for the Beaumont clay and Houston black clay, respectively; whereas, the clay content was 38% for the Beaumont clay and 35% for the Houston black clay. Since the Okoboji is also smectitic with 37% clay and CEC around 36 cmolc kg-1, the frequency dependent ' and '' of the Beaumont and Houston soils were used as relative indicators of possible trends for the Okoboji soils. For the Beaumont soil at of 0.48 and frequency of 0.5 GHz, ' was 33 and '' was 18, whereas at 0.3 GHz, ' was 36 and '' was 27. By means of Eq. [1], this would result in
of 5.9 and 6.4, respectively, for 0.5 and 0.3 GHz frequency. Similarly for the Houston soil at of 0.47 and frequency of 0.5 GHz, ' was 25 and '' was 15; and for 0.3 GHz frequency, ' was 28 and '' was 23. This resulted in
of 5.2 and 5.8, respectively for 0.5 and 0.3 GHz. This was an average 9% increase in
as the frequency was lowered from 0.5 to 0.3 GHz. Since the change in frequency bandwidth encountered in this study on Okoboji was only 0.12 GHz (Table 3), the equivalent expected change in
would be only 5%. The measured change in
was 6.9 to 8.9 for Sample A and 6.7 to 8.7 for Sample B, or about 30% change. Using these crude estimates, around 5% of the increase in
was due to colloid effects, the other 25% being due to difficulties in waveform analysis.
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Conclusions
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The
for the Okoboji soil with high surface area was more influenced by length of coaxial cable and temperature (positive response) than by . In contrast, the
of sand with low surface area was not significantly affected by temperature, and only influenced by the longest cable length. Most soils encountered would fall somewhere between these extremes. The nonsaline Okoboji soil was strongly influenced by high bulk dc. Techniques to improve waveform analysis in the presence of high bulk dc include remote diode shorting (Hook et al., 1992; Hook and Livingston, 1995), or coated waveguides (Persson and Berndtsson, 1998).
Practically speaking for high surface area soils, the TDR calibration of (
, temperature) should be carried out with the coaxial cable length and equipment combination that will be used on site, or calibration should be done on site. Anticipate that high surface area soils will probably have high bulk dc even for nonsaline soils. This might lead to considerable measurement variability or even impossible waveform analysis. The high dc will require a temperature term correction specific for each soil/cable length combination, but further calibration as a function of cable length should not be necessary. Failure to subtract out the positive temperature effect could result in data reflecting seasonal temperature trends more than seasonal trends. These concerns are only true for soils with a high bound water content (high in smectites, organic matter, some volcanic ash soils). There should not be a problem for sandy soils or for soils with the clay fraction dominated by kaolinite and oxides.
Smectites are not rare minerals in the soil, and are dominant in nearly all Vertisols, and prominent in many Aridisols and Mollisols, comprising over 2.35 x 106 km2 of soils (Borchardt, 1989). The poorly crystalline minerals in Andisols also often have high surface area and form complexes with organic matter. Organic matter is obviously high in Histisols, and also in Mollisols. Add to these soils the saline soils of the Aridisols, and together close to 1/3 of the world's soils could present potential problems for TDR analysis unless precautions are taken.
Future studies will emphasize development of more physically based mixing models to describe the dependence of
on bulk dc, temperature, bound water fraction, frequency, as well as total .
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ACKNOWLEDGMENTS
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Thanks to Andrea Thede for conducting much of the laboratory work, and to the USDA-Agricultural Research Service for funding the research apprentice program.
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NOTES
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1 Mention of specific equipment is for information only and does not constitute endorsement by the USDA. 
Received for publication January 25, 1999.
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