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a Inst. of Geographic Sci. and Natural Resources Research, Chinese Academy of Sci., Beijing, China 100101
b Dep. of Agronomy, Iowa State Univ., Ames, IA 50011
* Corresponding author (rhorton{at}iastate.edu).
Journal paper of the Iowa Agriculture and Home Economics Exp. Stn., Ames, IA, Project No. 3287. Supported by the Knowledge Innovation Program of CAS (KZCX2-411, U871), Natural Science Foundation of China (40025106), and Agronomy Dep. Endowment Funds, Hatch Act, and the State of Iowa.
Received 14 March 2003.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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), temperature (T), electrical conductivity (EC), thermal conductivity (
), thermal diffusivity (
), and volumetric heat capacity (
c) at the same sampling positions simultaneously. Furthermore, other soil physical parameters, such as bulk density (b), air-filled porosity (na), and degree of saturation (S), can be determined from their relationships with c and . We examined the performance of the thermo-TDR using both published data and laboratory measurements on packed columns and intact cores from six soils of varying texture. The results show that the thermo-TDR provides reliable measurements of , EC, c, , na, and S, but relatively large errors exist in b. The average standard error between thermo-TDR measurements and gravimetric measurements is 0.026 m3 m-3 for , 0.050 m3 m-3 for na, 0.069 for S, and 0.134 Mg m-3 for b. The standard error between thermo-TDR measurements and theoretical predictions of c is 0.134 MJ m-3 K-1. These promising findings coupled with the characteristics of small probe size and easy automation make the thermo-TDR sensor an ideal tool for studying coupled flow processes in the vadose zone. Further improvements in probe design, waveform interpretation, and determination of effective probe length are also noted as steps toward improving accuracy and precision of future thermo-TDR measurements.
Abbreviations: EC, electrical conductivity • TDR, time domain reflectometry
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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, bulk EC, and other thermal and hydraulic properties continuously and nondestructively.
The rapid development of TDR and dual-probe heat-pulse techniques provide opportunities for improved understanding of the dynamics of T, , EC, and soil thermal properties. The TDR technology, which relates to soil dielectric constant (Ka) and EC to the attenuation of electromagnetic waves in soil, is capable of monitoring and EC accurately in both space and time (Topp et al., 1980; Dalton et al., 1984; Herkelrath et al., 1991). With improvements in operating range, probe design, multiplexing, and automated data collection, TDR is becoming a powerful tool for characterizing soil water and solute transport (Topp and Reynolds, 1998). The heat-pulse technique, which measures soil temperature change at a given distance from a pulsed heat source, was first introduced to acquire c of soil (Campbell et al., 1991), and further developed to simultaneously determine , , c (Bristow et al., 1994; Bilskie et al., 1998), (Bristow et al., 1993; Tarara and Ham, 1997; Song et al., 1998; Campbell et al., 2002), soil water flux, and pore water velocity (Ren et al., 2000). The heat-pulse technique is capable of automatically providing in situ readings with minimal soil disturbance.
Measurements by separate TDR and heat-pulse probes occur at separate positions in the soil, and when applying the measurements to coupled flow studies of heat, water and solutes, the results are subject to errors from soil heterogeneity and spatio-temporal variability of T, , and soil physical properties. To overcome these problems, some investigators have combined TDR and thermal technologies into a single probe. Baker and Goodrich (1987) developed a two-pronged TDR-thermal conductivity probe to measure from dry to saturation. The values > 8% were related to Ka from TDR and values < 8% were calculated from the – relationship. Since the empirical – relation was soil-dependent, it was impractical to use this probe in laboratory or field conditions. Noborio et al. (1996) combined the functional capabilities of a TDR probe and a heat-pulse probe into one unit. Transient T was measured with thermocouples, thermal properties were determined with the heat-pulse method, and and EC were obtained from the TDR. Laboratory results showed that the values obtained from TDR agreed well with gravimetric values, but measured and c showed considerable deviations from the de Vries model (de Vries, 1963). Ren et al. (1999) reexamined the design criteria for TDR and heat-pulse probes and developed an improved thermo-TDR probe based on the Noborio et al. (1996) work. The new probe configuration produced promising information of T, , EC, , , and c (Ren et al., 1999; Ochsner et al., 2001a). A multineedle heat-pulse probe built by Bristow et al. (2001) measured T, , , and c using the heat-pulse techniques and EC applying the four-electrode theory, and was calculated indirectly from c measurements. The validity and application of the equipment requires further tests under various laboratory and field conditions (Bristow et al., 2001).
The unique characteristic of the thermo-TDR probe is that the TDR and heat-pulse measurements are made at identical sampling positions, and therefore the effect of soil heterogeneity on the results is minimized. Furthermore, the dynamics of other soil properties (e.g., na, S, and b) can be extracted indirectly from the thermo-TDR measurements (Ochsner et al., 2001a). Therefore, the technique is especially useful for studying the coupled flow of heat, water, and solute in the vadose zone. The objectives of this paper are to present the principles and procedures of the thermo-TDR sensor, and to describe the application of the thermo-TDR for T, , EC, , , c, na, S, and b determinations. This paper combines new thermo-TDR measurements with data from the literature to provide a thorough analysis of the thermo-TDR method.
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THEORY |
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and EC measurements. Basically, a fast rise-time voltage pulse is propagated (as an electromagnetic wave) down and reflected back from the transmission line in the soil. Since the propagation velocity of the electromagnetic wave is governed by Ka and its attenuation is determined by EC, analysis of the waveform provides the information of Ka and EC (Topp et al., 1980; Dalton, 1992):
 | [1] |
 | [2] |
), and 
is the reflection coefficient after all possible multiple reflections of the pulse have taken place. The K is experimentally determined by immersing the probe in solutions of known EC (Heimovaara et al., 1995). The can be calculated from the formula = (V - V0)/V0, where V0 is the amplitude of the signal from the TDR instrument and V is the amplitude where the multiple reflections have ceased.
Once Ka is determined, may be calculated from a widely-accepted empirical –Ka relationship established by Topp et al. (1980), or from a dielectric mixing model (Roth et al., 1990; Dirksen and Dasberg, 1993; Hook and Livingston, 1995; Malicki et al., 1996) that requires additional soil parameters. The Topp et al. (1980) equation is expressed as
 | [3] |
This relationship, however, needs adjustment for soils with higher organic matter, peat, or clay contents (Herkelrath et al., 1991; Pepin et al., 1992; Bridge et al., 1996), or where greater accuracy is required. Kelly et al. (1995) showed that for short TDR probes (<0.075 m), from Eq. [3] deviated significantly from gravimetric data. Ren et al. (1999) found that when Eq. [3] was used, there was a slight discrepancy between gravimetrically determined and the thermo-TDR measured for several soils. They developed the following polynomial equation to represent the –Ka relationship in the range of 0.03 m3 m-3 < < 0.4 m3 m-3 for their thermo-TDR probe:
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Thermal Properties
The heat pulse method is based on theory of radial heat conduction of a short-duration heat-pulse from an infinite line source. In an infinite medium, the temperature change as a function of time at a radial distance from the heat pulse source is given by (de Vries, 1952; Kluitenberg et al., 1993),
 | [5] |
T is the temperature change (°C), t is time (s), t0 is the heat pulse length (s), r is the radial distance (m), and –Ei (–x) is the exponential integral. The source strength is defined as Q = q/c, where q is the rate of heat liberation per unit length of probe (W m-1). On the basis of Eq. [5], soil thermal properties can be expressed analytically as (Kluitenberg et al., 1993; Bristow et al., 1994):
 | [6] |
 | [7] |
 | [8] |
Tm is the maximum temperature change (°C).
When making thermal property measurements, the heat pulse is generated by applying constant current to a heater cylinder from a power supply. A datalogger controls the heat input and records the heating power and the temperature changes in the sensing cylinders a short distance from the heater. Once the T(r, t) data are available, , c, and are calculated from Eq. [6]–[ 8] using the single point method (Bristow et al., 1994), or by means of nonlinear curve fitting of Eq. [5] to the measured data (Bristow et al., 1995; Welch et al., 1996).
The apparent spacing between the heater and the thermocouples located in the sensing cylinder, r, is often obtained through calibrating the probe in agar-stabilized water (5–6 g agar L-1). The c of the agar gel is assumed to equal to the c of water (4.17 MJ m-3 K-1 at 20°C; Weast, 1978).
Bulk Density, Air-filled Porosity, and Degree of Saturation
The determination of b with the thermo-TDR sensor follows the theory that c is the sum of the heat capacities of soil water, solids, and air (de Vries, 1963). The contribution of soil air to the soil heat capacity is negligible and c can be approximated as the sum of heat capacities of soil water and solids (Campbell et al., 1991):
 | [9] |
w (kg m-3) and cw (kJ kg-1 K-1) are the specific heat and density of water, respectively. The value of cs can be obtained from the literature (de Vries, 1963; Campbell, 1985) or determined experimentally (Campbell et al., 1991; Ren et al., 2003).
Once c is determined with the heat-pulse part of the thermal-TDR and is measured with the TDR part of the thermo-TDR, b can be calculated by the following equation (Ochsner et al., 2001a):
 | [10] |
By definition, the solid fraction (vs), the air-filled porosity (na), and degree of saturation (S) of soil are, respectively
 | [11] |
 | [12] |
 | [13] |
s (kg m-3) is the particle density of soil solids, which is approximately 2.65 Mg m-3 for mineral soils (Campbell, 1985). For improved accuracy, s may be determined experimentally (Blake and Hartge, 1986). |
MATERIALS AND METHODS |
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b and were determined gravimetrically.
Heat-pulse measurements were also performed on separate oven-dried samples of the silty clay loam, silt loam, and sand to determine cs. The cs values were then calculated from the relationship c = bcs (Table 1). The cs values of the clay loam and sandy loam were taken from Ochsner et al. (2001b). For the silt loam soil with intact cores, the same cs value as the disturbed silt loam soil was used. The cs values estimated in this manner were then used in Eq. [10] to calculate b for the other samples of each soil. Particle density (Table 1) was measured using the pycnometer method (Blake and Hartge, 1986).
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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was compared with the gravimetric values (Fig. 2A and 2B). Despite soil texture variation from sand to silty clay loam, all of the six soils showed a consistent trend. This indicates that soil texture had no measurable effect on the Ka results of the thermo-TDR probe. However, it appears that Eq. [4] (Ren et al., 1999) produces more accurate results than Eq. [3] (Topp et al., 1980). For example, when Eq. [3] was applied to convert Ka to , the thermo-TDR was slightly lower than the gravimetric values in the range 0.10 to 0.27 m3 m-3, and tended to be higher than the gravimetric values at > 0.27 m3 m-3. A similar trend was also shown by Noborio et al. (1996) with a different probe design. When Eq. [4] was used, the thermo-TDR agreed well with gravimetric values. Correlation analysis for thermo-TDR vs. the gravimetric values showed that the results from Eq. [4] had a higher coefficient of determination (r2), an intercept closer to zero, and a slope closer to 1 than the results from Eq. [3] (Fig. 2). The standard errors for the thermo-TDR values were 0.028 m3 m-3 for Eq. [3] and 0.026 m3 m-3 for Eq. [4]. Similar results were also reported by other investigators who used relatively short TDR probes (Kelly et al., 1995; Hudson et al., 1996). Therefore, we conclude that for accurate information, a separate calibration is necessary for a thermo-TDR probe.
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An important issue is the determination of the effective probe length. It is clear from Eq. [1] that any error with L is transferred to Ka (and consequently to ). This kind of error may become serious with a thermo-TDR probe because of its small size. Therefore, instead of taking L as the physical length of the probe, it is recommended to determine the effective probe length. The effective length of a probe can be determined by making measurements in a medium (e.g., in air or distilled water) with known Ka (Heimovaara, 1993). For the probes used in this study, the effective length ranged from 3.91 to 4.13 cm when calibrated in distilled water.
Errors also arise from the waveform analysis method that is used to determine the travel time t. To extract t from the TDR waveform, a frequently applied technique is to find the intersection of two tangent lines (Heimovaara and Bouten, 1990). The accuracy of this method, however, depends on the noise in the waveform and the slope and amplitude of the reflections. The time it takes the TDR signal to reach equilibrium depends on the rise time of the signal arriving at the cable-probe interface. Coaxial cable length, coaxial switches, and other connectors can increase the signal rise time. Short probes used in combination with long cables can result in erroneous measurements, as the increased rise time leads to an increased mingling of reflections. For example, the cable length of a TDR probe of 0.05 cm should not be longer than 3.2 m (Heimovaara, 1993). We have kept the cable length of our thermo-TDR probes within 2.0 m.
Additional errors in water content measurement may also be introduced during thermo-TDR probe installation and handling. Because of the relatively small thermo-TDR probe size, the air gap problem may become serious, and therefore probe-soil contact is important (Annan, 1977; Whalley, 1993). A slight movement of a probe that is embedded in the soil can cause air gaps to occur around the probe, which in turn decrease the measurements of Ka.
Making multiple measurements is important to reduce uncertainties during the measurement process. Taking the mean of multiple measurements will not only reduce the standard error of water content measurement, but also translate into smaller errors in calculations that utilize the measured water content.
The technique of frequency domain analysis overcomes some disadvantages of time domain analysis for TDR probes of shorter rod length, and may serve to improve the measurement accuracy of soil water content using the thermo-TDR probe. Jones and Or (2001) successfully used a TDR probe of 3-cm rod length to determine soil dielectric permitivity by transforming TDR waveform from time domain to frequency domain. Numerical analysis by Lin (2003) also showed that the frequency domain analysis, which gives the actual frequency-dependent dielectric permitivity, could be performed using a short probe.
Ren et al. (1999) compared EC measurements by the thermo-TDR probe with measurements from a four-electrode probe. Results from the two methods showed excellent agreement on a saturated clay loam soil. They also showed that the reflection point of the thermo-TDR waveform could be clearly defined at EC of 6.06 dS m-1. Furthermore, determination of EC by the thermo-TDR probe appeared to be insensitive to cylinder-to-soil contact while it was difficult to obtain good estimates by the four-electrode probe at low water contents. Further laboratory and field evaluation is necessary to test the application of the thermo-TDR for EC and solute transport studies.
Thermal Properties
The performance of the thermal-TDR technique for soil thermal property determination was tested by comparing measured c and against theoretical values (Fig. 3A and Fig. 3B). The theoretical c values were calculated with Eq. [9], where soil specific cs values were as listed in Table 1 and values were determined by the thermal-TDR technique. The widely accepted de Vries model (de Vries, 1963) was used to calculate the theoretical with the computerized approach of Tarnawski and Wagner (1992).
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c and estimated c (Fig 3A). The data are randomly distributed along the 1:1 line and the six soils of different textures show a consistent trend. A least-squares fit of a straight line through all of the data has a slope of 0.961, an intercept of 0.054 MJ m-3 K-1, an r2 of 0.918, and a standard error of estimate of 0.134 MJ m-3 K-1. Therefore, the thermo-TDR sensor provides accurate c results. This conclusion has important implications because other soil parameters are determined indirectly from the c data.
The comparison between measured values and theoretical values of is somewhat complicated (Fig. 3b). For three of the six soils (the silty clay loam, the silt loam, and the sandy loam), thermo-TDR measured agrees reasonably well with de Vries model estimates of . For the sand and the clay loam soils, the thermo-TDR measurements and de Vries model predictions agree well for lower than 1.0 W m-1 K-1. For larger values of , however, the measured data are greater than the predicted values for the clay loam, and less than the predicted values for the sand. Hopmans and Dane (1986) also reported that at higher water contents, the predicted thermal conductivity from the de Vries model was lower than the measured values using the line-source heat probe method. The measurements on the undisturbed silt loam soil are consistently larger than the predicted values. One possible explanation for this observation is that heat conduction in soil may be enhanced by soil structure. Kaune et al. (1993) obtained soil thermal diffusivity and thermal conductivity using the harmonic method on both disturbed and undisturbed soils. They concluded that the development of soil structure from disturbed soils led to an increase in the apparent thermal conductivity.
Bulk Density
Figure 4A shows the thermo-TDR determined b vs. the gravimetrically determined b. For three of the six soils (the silty clay loam, the clay loam, and the sand), the data depart from the 1:1 line considerably, and thermo-TDR determined values are greater than the gravimetric measurements at small b and less than gravimetric measurements at large b. The thermo-TDR determined b and the gravimetric b agree well for the silt loam soil where the data are randomly spread along the 1:1 line and the differences are mostly within 0.1 Mg m-3. A similar trend of agreement also appears for the sandy loam soil, but there is some scatter at higher b. For the intact cores of the silt loam soil, thermo-TDR b show larger variation than the gravimetric b. Across all six soils, the average standard error of estimation for b is 0.134 Mg m-3.
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b depends on the accuracy of thermo-TDR measured c, cs, and (Eq. [10]). To examine the influence of on b, Eq. [10] was used to recalculate b with the gravimetrically measured data, and the results are shown in Fig. 4B. Comparing with the data in Fig. 4A, the variation of thermo-TDR b from the intact cores is reduced substantially. The least-squares straight line in Fig. 4B had a smaller intercept, a larger slope, and a larger r2 than the line in Fig. 4A, indicating that error in did contribute to the inaccuracy of b. The inaccuracies in c and cs also contributed to the errors in b, as the standard error between thermo-TDR data and gravimetric values in Fig. 4B was similar to that in Fig. 4A. As has been indicated by other studies, any change in cylinder spacing during probe insertion can be a key factor that affects the accuracy of c determination (Campbell et al., 1991; Bristow et al., 1993; Kluitenberg et al., 1993, 1995; Tarara and Ham, 1997). To avoid changes in cylinder spacing and to increase the accuracy in b measurement, further improvements in the thermo-TDR probe design (e.g., increased rigidity of the cylinders) are necessary.
Air-filled Porosity and Degree of Saturation
On the basis of thermo-TDR measurements, na and S were calculated indirectly for the six soils, and the combined results are presented vs. the gravimetric values in Fig. 5A and 5B. The thermo-TDR data agree well with the gravimetric measurements. For na, a linear correlation of the data yields a line with an intercept of 0.028 m3 m-3, a slope of 0.918, and an r2 of 0.870. For S, the intercept, slope, and r2 are 0.011, 0.965, and 0.941, respectively. The r2 values for na and S are higher than the r2 value for b (0.480, Fig. 4). These higher r2 values suggest that the thermo-TDR estimates of na and S are less sensitive to measurement errors in c and than are the thermo-TDR estimates of b. Similarly, Ochsner et al. (2001a) reported that the error in na is less than the error in vs. The standard error of estimation is 0.050 m3 m-3 for na and 0.069 for S. The results here from the six soils of varying textures lead us to conclude that the thermo-TDR can give reliable measurements of soil air fraction and degree of saturation of the soil.
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CONCLUSION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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), electrical (EC), and thermal (T, , c, and ) properties, as well as other physical parameters (b, na, and S). Thermo-TDR measured , EC, c, , na, and S agree well with the results from theoretical models and gravimetric measurements. Relatively larger errors exist in the thermo-TDR b determination. To further increase the measurement accuracy of thermo-TDR, additional efforts are required to improve the probe design, waveform interpretation, and effective probe length determination. With the thermo-TDR sensor, TDR and heat-pulse measurements are made at identical sampling positions and at the same time. Therefore, the temporal features of soil physical properties are captured and the effects of soil heterogeneity on the results are minimized. The thermo-TDR sensor provides new opportunities for observational studies of coupled flow of heat, water, and solute, and for other transfer processes in the vadose zone.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONREFERENCES |
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hler, and W. Attinger. 1990. Calibration of time domain reflectometry for water content measurement using a composite dielectric approach. Water Resour. Res. 26:2267–2273.This article has been cited by other articles:
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O. K. Olmanson and T. E. Ochsner A Partial Cylindrical Thermo-Time Domain Reflectometry Sensor Soil Sci. Soc. Am. J., May 1, 2008; 72(3): 571 - 577. [Abstract] [Full Text] [PDF]
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J. L. Heitman, R. Horton, T. Ren, and T. E. Ochsner An Improved Approach for Measurement of Coupled Heat and Water Transfer in Soil Cells Soil Sci. Soc. Am. J., May 16, 2007; 71(3): 872 - 880. [Abstract] [Full Text] [PDF]
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