Published online 16 November 2005
Published in Vadose Zone J 4:1011-1019 (2005)
DOI: 10.2136/vzj2004.0108
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
SPECIAL SECTION: SOIL WATER SENSING
Time Domain Reflectometry Range of Accuracy for High Surface Area Soils
Sally Logsdon*
National Soil Tilth Laboratory, 2150 Pammel Dr., Ames, IA 50011
* Corresponding author (logsdon{at}nstl.gov)
1 Mention of specific equipment is for information only and does not constitute endorsement by the USDA. 
Received 15 July 2004.
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ABSTRACT
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Time domain reflectometry (TDR) is commonly used to determine water content. Many laboratory studies have shown accurate water determination across a wide range of soils, often with a unified calibration equation. Recent data has shown a strong temperature influence on some TDR data. The purpose of this study was to calibrate TDR for water content under both laboratory and field conditions for Mollisols. TDR waveguides and thermocouples were installed horizontally into the sides of pits at four sites and 9 or 10 depth positions on a 5% slope. Neutron access tubes were installed within 3.3 m of the TDR sites. After the field study, soil was collected around the waveguides and repacked into columns for laboratory calibration. The columns were progressively wetted and then dried over a few months. At each water content and at two or three temperatures, the waveforms, bulk electrical conductivity, and square root of apparent dielectric
were saved for the laboratory data, but memory limitations prevented saving waveforms from the field data. Much of the field calibration data were shifted to higher values for
a1/2 than for the laboratory data, apparently due to problems with internal waveform analysis. High bulk electrical conductivities (up to 0.13 S m1) were apparent for some of the sites and depths even though these are not saline soils. For the laboratory data, adding a temperature term to the calibration equation reduced the root mean square error (378 data points) from 0.54 to 0.34 m3 m3, and for the field data (939 points) reduced it from 0.78 to 0.54 m3 m3.
Abbreviations: TDR, time domain reflectometry
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INTRODUCTION
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TIME DOMAIN REFLECTOMETRY has been used extensively to determine soil water content, but several considerations affect the accuracy of the results. The TDR water content determinations are affected by factors such as waveform analysis, choice of waveguide geometry, long cables, numerous attachments, disturbed vs. undisturbed samples, air gaps, waveguide insertion (Ferré and Topp, 2002; Evett, 2003; Robinson et al., 2003a, 2003b). Many studies have shown response of TDR to temperature as well as water content. Wraith and Or (1999) showed diurnal temperature fluctuations of the square root of apparent dielectric (
a1/2). The
a1/2 increased as temperature increased for Brocko silt loam (coarse-silty, mixed, superactive, frigid Aridic Calciustept) which had specific surface area of 125 m2 g1. For Millville silt loam (coarse-silty, carbonatic, mesic Typic Haploxeroll) with specific surface area of 73 m2 g1,
a1/2 increased as temperature increased for water content of 0.3 g g1, but decreased as temperature increased for water content of 0.09 g g1. For Kidman fine sandy loam (coarse-loamy, mixed, superactive, mesic Calcic Haploxeroll) with specific surface area of 17 m2 g1,
a1/2 decreased as temperature increased at all water contents. For peat and montmorillonite, Persson and Berndtsson (1998) showed the positive temperature effect of
a1/2. For Okoboji silty clay (fine, smectitc, mesic Cumulic Vertic Endoaquoll) with specific surface area of 286 m2 g1, Logsdon (2000) showed a positive temperature effect on
a1/2 at all water contents.
Others have reported discrepancies for field determination of water content. Bridge et al. (1996) reported unpublished field TDR data for a Vertisol which showed no relation between water content and
a1/2 (converted to "water content" by Topp et al.'s equation, [1980]), with an overestimation of water content in most cases. Soil temperatures were not given. Nadler et al. (1999) compared TDR (converted to water content by the Topp equation) with neutron probedetermined water content. For a Psamment, the TDR soil water contents were less than neutron water content, but water contents were generally <0.1 m3 m3 and electrical conductivity of the water was <0.12 S m1. For a Calcic Palexeralf the TDR calculated water contents were greater than for neutron probe except early in the season. Soil temperatures were not reported, but probably influenced the seasonal effect since electrical conductivity increases with temperature.
Unfortunately most of the explanations ignored the frequency-dependent dielectric properties of soil water at frequencies <1 GHz (Campbell, 1990; Ishida et al., 2000; Dudley et al., 2003; Logsdon and Laird, 2004). De Loor (1983) explained that dielectric properties will increase as temperature increases when most of the frequency-dependent dielectric properties occur at frequencies below the measurement frequency. Conversely the dielectric properties will increase as temperature decreases if most of the frequency-dependent dielectric properties are at frequencies higher than measurement frequency. Sun and Young (2001) and Robinson et al. (2003a) showed that dielectric dispersion lowers the effective measurement frequency, but this topic requires more study to verify. This lowered effective frequency is in addition to the loss of high frequencies due to long cables and numerous attachments (Logsdon, 2000).
High bulk electrical conductivities (
b) increase as temperature increases, and
b increase dielectric properties at low frequencies. If attachments lower the effective frequency range, then
b can increase the TDR-determined water content. Wyseure et al. (1997) added varied amounts of NaCl to soils (sand to clay loam texture) to achieve
b up to 0.65 S m1 and showed an increase in apparent dielectric as
b increased, more so for
b > 0.25 S m1.
Including temperature in TDR calibration of water content might improve accuracy of field data. The objective of this study was to calibrate TDR for soil water content across a range of temperatures under both laboratory and field conditions, and to compare the results.
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METHODS
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Field Study
The location has a 5% slope, and variations in soil properties were apparent for the four sites on the hill (Table 1, Fig. 1) . The soils at Sites 1, 2, and 3 are Clarion (fine-loamy, mixed, superactive, mesic Typic Hapludoll), and at the toeslope position (Site 4) is Webster (fine-loamy, mixed, superactive, mesic Typic Endoaquoll). A Tektronix 1502B cable tester (Beaverton, OR) was used.1 In 1995 TDR waveguides were installed in the field horizontally from the side of pits for four positions on a hill and 9 or 10 depths with two probes for the 15-cm depth (Table 2). The parallel waveguides with 1:1 balun (Spaans and Baker, 1993) were 0.3 m long, 50 mm apart, and 3.2 mm in diameter (Midwest Special Services, Inc.; no longer available). Thermocouples (copper-constantine) were installed at the same depths as TDR to measure soil temperature. The TDR and thermocouples were hooked to separate Campbell Scientific (Logan, UT) data loggers and accessories, collected, and averaged every one-half hour.
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Table 1. Site positions and general characteristics. The elevation at the top of the hill was arbitrarily set to 10 m.
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The field TDR data were collected automatically every hour on a data logger because there was no source of electricity in the field to collect on a computer. The data logger had memory limitations that prevented saving the waveforms. The waveforms were periodically examined in an attempt to improve the setup (initial start point needed for internal waveform analysis). Also the Campbell Scientific equipment at that time could only collect
a1/2 or apparent bulk electrical conductivity,
b, but both could not be collected in automated mode at the same time. An additional coaxial multiplexer was used for the bottom four or five depths of the TDR. All the TDR cables and attachments are listed in Table 3. Connecting cables were buried (
40 cm) except for connection with aboveground attachments.
During installation (and removal in 2000) of TDR, undisturbed cores (76 mm long and 73 mm in diameter) were taken to determine bulk density and disturbed samples for particle size analysis (hydrometer method, Gee and Bauder, 1986) and hygroscopic water content (equilibration in humidity chamber over MgNO3 for relative humidity of 56% after equilibration over distilled water for relative humidity close to 99%, Logsdon, 2000). This was converted to specific surface area assuming a monolayer of water of 0.3-nm thickness on the surfaces. Horizontal undisturbed samples were taken by bracing a hydraulic jack against the back wall of the pit to push the cylinders into soil. The cores were capped, returned to the laboratory, and stored at 5°C until time of analysis.
Within 3.3 m of the TDR sites, but at similar relative elevations (Table 1), stainless-steel neutron probe access tubes were installed to 2.5 m depth. The access tubes were 50-mm-diameter steel tubes, installed with a hydraulic auger. Bentonite was filled in around the top 0.2 m to prevent water flow down the side of the tube. Neutron probe measurements were usually made once weekly during the growing season and less frequently in the winter. Soil water content was determined every 20 cm starting at 30 cm. Unless the ground was frozen, a volumetric soil sampler was used for taking gravimetric samples to 30 cm, and then subdivided every 10 cm. Gravimetric water content samples deeper than 30 cm were only collected a couple times. Neutron probe calibration for each site and depth was additionally modified (adjusted intercept, occasionally slope if necessary) based on bulk density measurements for each depth and expected ranges of water content (not more than total porosity, not less than air dry water content).
To show seasonal field trends for 1996 through 1998, daily means of
a1/2 and temperature were calculated after removing obviously incorrect TDR data. For comparison with neutron probe at different depths, the neutron data was interpolated to the same depth as the TDR waveguides. This combination provides triplet water content,
a1/2, and temperature (from thermocouples) values.
Laboratory TDR Study
Because of data logger limitations for the field study, soil was collected for further analysis in the laboratory. In the fall of 2000, pits were dug to remove the TDR waveguides. Rocks prevented collection of large undisturbed samples around the waveguides, so instead disturbed soil was collected around each waveguide.
In the laboratory after removing large stones, the soil was packed into plastic or PVC pipes. An attempt was made to achieve bulk densities similar to the undisturbed cores, but most of the bulk densities were slightly less than field density (Fig. 2) . The pipe inner diameters were either 70 or 76 mm, and the length of soil in each pipe ranged from 305 to 365 mm, slightly longer than the waveguides to reduce fringing. TDR waveguides were inserted into each reconstructed sample, and hooked up with all the associated multiplexer, cables, and transient suppressor that had been used in the field. To obtain a range of water contents, water was incrementally added to the columns, and the TDR measurements were made 2 or 3 d after adding the water. Then soil columns slowly dried at both ends over a few months with periodic TDR measurements. Between the measurements, the columns were placed horizontally. At each water content in addition to weighing the column, measurements included
a1/2,
b, and the 251 point waveform. The
b was corrected for cable and attachments as described by Reece (1998) and Logsdon (2000). In some cases the waveform was accidentally not saved. Also some of the TDR waveguides did not survive the movement from field to laboratory and installation, so data were not useful for all soildepth combinations. Soil temperature was also measured at each water content using a laboratory thermometer. Temperatures ranged between 3 and 30°C for the laboratory study. At the end of the study, subsamples were oven dried to determine water content by mass. Then the rest of the mass water contents at each step were back-calculated and all were converted to volumetric water content. Waveforms were examined manually to see if the automated analysis was approximately correct. The
a1/2 values that were obviously in error were omitted from analysis (i.e., around 1 or 13, for instance), but the automated values were not corrected further.

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Fig. 2. Comparison of bulk densities for field sites and corresponding repacked laboratory calibration.
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Laboratory and Field Comparison
To compare laboratory and field calibration for each soildepth combination, the mean
a1/2 values and the difference between the two means (field and laboratory) were calculated when both were available. These means for laboratory, field, and difference were examined for correlations with total porosity, specific surface area, sand, silt, clay, and effective cable length. The length of the low loss cable was divided by four because the resistance was only about one-fourth as much (Logsdon, 2000). Also stepwise linear regression for these means (laboratory, field, or difference) was calculated as a function of the independent variables listed above. Note that the clay fraction in this study was mostly smectite, so the results would only be applicable to similar soils, not to soils dominated by other clay minerals.
Calibration
For calibration, the field data for each soil-depth combination were neutron probe soil water contents interpolated to the depth of the TDR waveguides, and daily means on corresponding days of
a1/2 and temperature. The laboratory data were the measured soil water contents from column weights, temperature, and TDR-measured
a1/2. Calibration for laboratory and field data was based on a simple empirical equation:
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in which T is temperature, a is an empirical constant, and b is set equal to 0.115 (Topp and Reynolds, 1998) to reduce the number of fitted parameters. Individual sites and depths were calibrated separately both for the laboratory data and for the field data. This calibration was compared with the site- or depth-specific calibration without the temperature term by examining the 95% confidence interval of the difference between measured and calculated water content for both the laboratory and the field data. In addition, the root mean square error was calculated with and without the temperature term for both laboratory and field data. Measured and calculated water contents were compared with and without the temperature correction, and compared with Topp's (1980) equation.
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RESULTS AND DISCUSSION
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The results of the laboratory study are discussed first to show the effects of surface area, electrical conductivity, and many cable attachments on water content determination. Then the field data are discussed to demonstrate cases where soil water content determination was possible, and where it was not. Also the discrepancies between the laboratory and field data are discussed.
The major soil differences were high specific surface area for soils at Site 4 between 0.35 and 1.14 m depth (Fig. 1.) Bulk densities for Sites 1, 2, and 3 ranged from 1.52 to 1.74 and for Site 4 from 1.44 to 1.56 Mg m3. Across all the sitedepth combinations, sand fraction ranged from 0.39 to 0.66 g g1.
Laboratory Data
Comparing waveforms from a sample lower in clay (Fig. 3a)
with a wetter sample higher in clay and organic matter (Fig. 3b) showed the expected difficulty in waveform analysis for the second soil because of highly attenuated second reflection. Note that the soil was not saline, but the
b was due to charges associated with the smectite clay and organic matter. Wraith and Or (1999) showed that different methods of determining the second point in the waveform can result in large discrepancies in calculated water content. The parallel waveguide probe has an impedance in air around 360
(Reece, 1998), which caused the large rise in the first point. This effective probe impedance should be reduced for high water content and high
b (Spaans and Baker, 1993); however, the mismatch occurs within the head instead of the soil (Robinson et al., 2003a) and will always result in a large rise of the first point.

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Fig. 3. Laboratory waveforms for (a) Site 3, 43-cm depth, 0.326 m3 m3 and for (b) Site 4, 96-cm depth, 0.379 m3 m3.
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Extensive attachments increase rise time and decrease the effective frequency bandwidth (Topp et al., 2000; Logsdon, 2000; Robinson et al., 2003a). At these lower frequencies, dielectric dispersion affected both the real and imaginary component of permittivity, and electrical conductivity affected the imaginary component of permittivity. The
a1/2 increased due to increase in the imaginary component of permittivity as well as to increases in the real component of permittivity. The increase of
b as temperature increased resulted in an increase in
a1/2 as temperature increased. Logsdon (2000) and Lin (2003) have shown that larger
b increases
a1/2.
Field Data
First examine the raw data for Site 3, 35-cm depth (Fig. 4)
with the shorter cable (Table 3). For this sandy loam soil, the seasonal TDR data followed the neutron probe water content trend for all years (only 1996 is shown). Only early and late in the season was there any discrepancy. Contrast this with the soil for Site 1, at the 58-cm depth (Fig. 5)
with a longer cable, which showed noisy data and, at best, fair agreement with seasonal neutron probe data. Similar or worse responses were apparent for most other sitedepth combinations and years (not shown).
Even if both TDR and neutron attenuation methods are working properly with adequate calibration, differences are expected. The parallel TDR waveguide measures a much smaller soil volume (Ferré and Topp, 2002; Nissen et al., 2003) than the neutron probe (Hignett and Evett, 2002), and the neutron probe sampling volume varies with water content. Also the neutron probe water content measurements were affected somewhat by soil shrinkage in dry years (1997).
Comparison of Laboratory and Field Data
For Site 3 at the 35-cm depth, the laboratory raw
a1/2 data used for calibration showed similar trends with the field raw data used for calibration, except at low water contents (Fig. 6a) . At each water content of the laboratory data, the two or three points represent the different temperatures, and the cooler temperatures had smaller
a1/2. The laboratory calibration might have been affected by nonuniform water content during incremental wetting followed by drying at both ends, though no sharp gradients would be expected. The field calibration might have been affected by spatial variability in water content at the neutron probe site and TDR site, as well as differences in sample volume and uncertainties in neutron probe calibration.

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Fig. 6. Fairly good agreements between laboratory and field raw data for (a) Site 3, 35-cm depth, but field data were offset to higher values for (b) Site 4, 35-cm depth. The laboratory excludes data points with incorrect internal waveform analysis, and only the good field data were included in the calibration.
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The laboratory and field raw data of Site 4, 35-cm depth, showed that the field data was offset to higher
a1/2 (Fig. 6b) than the laboratory data. Similar offset trends were apparent for most sitedepth combinations, except upper depths at Site 3 (not shown). The laboratory data readily showed the temperature effect because of the greater spread in
a1/2 at each water content. The field data were affected by additional factors beyond what contributed to the laboratory data variability. Perhaps the waveform analysis of field data had problems beyond that seen in laboratory data, but this could not be verified since we were unable to save the waveforms from the field data. In the laboratory only the soil, waveguide, and part of the cable were at the applied temperature; perhaps the field digression was due to cable tester, transient suppressor, and multiplexers being at ambient temperature. Of course in the field, the neutron probe measurement site was displaced from the TDR site, and the volume of influence was much larger. Uncertainties in the neutron probe calibration added to uncertainties in the field TDR calibration, but would not have been enough to explain the great discrepancies.
If the input total initial length had been set too long, the first point in the waveform analysis would be missed. Robinson et al. (2003b) showed that cooler and drier conditions could delay the start point, more so for longer cables and multiple attachments. Hence wetter and warmer conditions could result in the first point being earlier, increasing the chance it might be missed in the internal waveform analysis. This variation would not have showed up in the laboratory analysis since the cable tester, cables, and attachments were at room temperature, for the most part. In the field the buried cable and aboveground attachments would be at soil or ambient air temperatures.
Simple correlation analysis (Table 4) showed that the laboratory mean square root of apparent dielectric for each sample was positively correlated with sample specific surface area, silt and clay fractions, and apparent cable length. The field means of each sample were positively correlated with sample specific surface area, clay fraction, and effective length, and negatively correlated with sand fraction. The difference between these means was only positively correlated with specific surface area and apparent cable length, although the number of samples was small. The stepwise regression for the laboratory means resulted in the equation
The field data resulted in the equation
The difference between the means resulted in the equation
These factors together only partly explained the variability in the data (Table 5). The overall observation was that the site-specific, temperature-corrected laboratory calibration usually could not be used for the field TDR data because of this difference, even though the same cables and attachments were used in both cases.
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Table 4. Correlation (r2) of square root of apparent dielectric with soil property, and sample number (in parentheses).
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Table 5. Stepwise regression for mean square root of apparent dielectric for the calibrations in laboratory, field, or field minus laboratory (difference) as a function of effective cable length (in which low loss = 1/4 high loss length in m, lg), specific surface area (m2 g1, su), and fraction (g g1) of sand (sa).
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Calibration
Since the
a1/2 was positively correlated with temperature, the temperature terms were negative (i.e., subtract out the temperature effect). The negative terms ranged from 0.0001 to 0.008 for the laboratory data and from 0.00006 to 0.0124 for the field data. Persson and Berndtsson (1998) recorded change in water divided by change in temperature of 0.00795 for montmorillonite, 0.00179 for a clayey moraine soil, and 0.00086 for a mixture of montmorillonite and sand to which KCl was added. The rest of their sand or sandy mixture samples showed a negative correlation between water content and temperature.
When each depth of each site was calibrated separately, including a temperature term decreased the difference between measured and calculated water content somewhat. Of the 21 sitedepth combinations with enough data available for the laboratory calibration, 17 had significant regressions from Eq. [1] (Fig. 7)
. Combining all the laboratory data that had significant correlations (378 points), the 95% confidence interval of the difference between measured and calculated water content was 0.0027 to 0.0042 m3 m3 without a temperature term and 0.0018 to 0.0034 m3 m3 with a temperature term. The total range of the difference was 0.227 to 0.111 m3 m3 without a temperature term and 0.099 to 0.119 m3 m3 with a temperature term. For the laboratory data, by including a temperature term in the calibration the correlation coefficient was increased from 0.89 to 0.94, and the root mean square error was reduced from 0.542 to 0.340 m3 m3. For the laboratory data (Fig. 7), Topp's equation would not have been too bad except for one sample (Site 4, 0.96 m).

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Fig. 7. Comparison of measured and calculated water content for laboratory data showing each site-depth regression (overlapping) without and with a temperature correction, and compared with Topp's (1980) equation.
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Likewise of the 41 sitedepth combinations with enough data available for the field calibration, 28 had significant regressions from Eq. [1] (Fig. 8)
. Combining all the field data that had significant correlations (939 points), the 95% confidence interval for the difference between measured and calculated water content was 0.0015 to 0.0022 m3 m3 without a temperature term, and 0.0012 to 0.0019 m3 m3 with a temperature term. The overall range of the difference was from 0.098 to 0.084 m3 m3 without a temperature term, and 0.090 to 0.083 m3 m3 with a temperature term. For the field data the correlation coefficient was increased from 0.84 to 0.89, and the root mean square error was reduced from 0.776 to 0.536 m3 m3 by adding a temperature term. Thirteen sitedepth combinations of the field data did not have significant calibration regressions. These were mainly the high surface area depths at Site 4 (Fig. 1), as well as some of the deeper depths at Sites 1 and 2, due to small variation in water contents and/or inadequate reliable data points. For the field data (Fig. 8), the Topp equation seriously overpredicted water content.

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Fig. 8. Comparison of measured and calculated water content for field data showing each sitedepth regression (overlapping) without and with a temperature correction, and compared with Topp's (1980) equation.
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Even though the 95% confidence interval error was small, some of the field-calculated water content data were still inadequate (Fig. 911)
. Adding a temperature term improved the data that already tended to follow the seasonal water content pattern (Fig. 9). Including a temperature term resulted in calculated drier soils in the mid season when soil temperatures were warmer, and wetter soils in the early and late season when soil temperatures were cooler. The noisier data set was still noisy after calculation with a temperature term (Fig. 10). Although the seasonal pattern was better than without including a temperature term, the pattern still missed some of the cooler and wetter data.

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Fig. 9. Calculated water content from TDR, with and without a temperature term, and water content from neutron probe for 1996, Site 3, 35-cm depth.
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Fig. 11. Calculated water content from TDR, with and without a temperature term, and water content from neutron probe for 1997, Site 1, 58-cm depth.
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Fig. 10. Calculated water content from TDR, with and without a temperature term, and water content from neutron probe for 1996, Site 1, 58-cm depth.
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Uncertainty in neutron probe calibration added to the uncertainty in TDR calibration. This was especially evident in a dry year (Fig. 11). Both with and without a temperature term, the TDR water content data followed the seasonal trend shown by neutron probe (Fig. 10), but neutron probe water content was drier. In dry years for some sites and depths, the neutron probe data were affected by shrinkage away from the access tube and inaccurate linear neutron calibration. As mentioned above, about one-third of the field sitedepth combinations did not have significant regression equations, and data were not improved by including a temperature term.
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CONCLUSIONS
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In summary, even with long cables and numerous attachments, the water content determined by TDR was accurate for a few soils when a site-specific, field calibration that included a temperature term was used. For other soils, including a temperature term improved the field calibration, but not to a point that the data were reliable across a range of water contents. Soils with high
b often resulted in unusable TDR data during the summer because of difficult internal waveform analysis, and no calibration was possible for these soils. Field calibration usually was offset to higher
a1/2 than laboratory calibration, and inaccurate internal waveform analysis appeared to be the reason for the difference. Mean values of
a1/2 were correlated with soil specific surface area for data from laboratory, field, and the difference between laboratory and field.
To increase the chance of success in obtaining water content by TDR in the field, the waveforms should be saved for postprocessing, if at all possible. If memory restrictions are a problem, it would be better to collect data from fewer sites and/or less frequently to ensure that waveforms could be saved. Reducing cable length and number of attachments would also increase the chance of success. It might be better to use a separate cable tester at each site instead of using long cables (even if low loss cables). Because cable testers are expensive, monitoring fewer sites might make sense. It would be better to get a smaller data set of usable data than a large data set in which only some of the data are useful. It is always a good idea to measure soil temperature at the same depths that water content is measured so a temperature correction can be made, if necessary.
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