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a Dep. of Soil and Water, China Agric. Univ. Beijing, China 100094
b Dep. of Agronomy, Iowa State Univ., Ames, IA 50011
* Corresponding author (rhorton{at}iastate.edu)
This journal paper of the Iowa Agric. and Home Econ. Exp. Stn., Ames, IA; Project No. 3287, is based on work supported by the National Science Foundation under Grant No. 0337553 and was also supported by Hatch Act and State of Iowa funds.
Received 29 September 2004.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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HP) was estimated from the heat capacity and water content relationship. For TDR measurements, the first reflection point on the waveform was determined by shorting the probe in air and the apparent probe length was determined from calibration in distilled water. The Topp equation was applied to convert the apparent relative permittivity to soil water content (TDR). The thermo-TDR probe is ideal for making the comparison between the heat pulse and TDR methods because the probe makes both measurements on nearly the same soil volume (approximate radius of 14 mm about the central heater for HP and approximate radius of 11 mm about the central cylinder for TDR). Experimental results on eight soils showed that both TDR and heat-pulse methods gave reliable soil water content data for repacked and undisturbed soil. Comparing with gravimetrically measured volumetric water content, the root mean square error (RMSE) of TDR measurements was 0.023 m3 m–3 for repacked soils and 0.018 m3 m–3 for undisturbed soils. The RMSE of HP measurements was 0.022 m3 m–3 for repacked soils and 0.021 m3 m–3 for undisturbed soils. The relatively large RMSE of the TDR measurements is attributed to the relatively short length (4-cm) of the thermo-TDR probe. The TDR method showed less sensitivity to spatial soil variability than did the heat-pulse method. The heat-pulse technique seemed better suited than TDR for water content measurements on soils with relatively high organic matter content.
Abbreviations: EC, electrical conductivity • RMSE, root mean square error • TDR, time domain reflectometry
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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) with excellent spatial resolution and minimum soil disturbance. Except for special cases, a single empirical calibration curve can be used for various soil types and conditions. Continuous, real-time measurements of have been in practice with automated and multiplexed TDR systems (Baker and Allmaras, 1990; Heimovaara and Bouten, 1990; Herkelrath et al., 1991).
The heat-pulse technique is also emerging as a valuable method for estimating . Laboratory and field studies indicate that the method offers the benefits of determining with minimal soil disturbance and automatic, frequent in situ readings (Bristow et al., 1993; Noborio et al., 1996; Tarara and Ham, 1997; Song et al., 1998; Ren et al., 1999; Basinger et al., 2003; Heitman et al., 2003). Since information of soil temperature (T) and soil thermal properties is obtained at the same time, this technique is especially useful for monitoring wetting or drying processes and studying coupled heat and water flow. A potential drawback of the heat-pulse technique is its small measuring volume. As a result, heterogeneity in soil structure and temperature profile may cause uncertainties in measurements. Furthermore, the measurements are sensitive to several factors such as probe-soil contact, sensor-to-heater spacing, T measurement accuracy, and axial heat loss (Kluitenberg et al., 1993, 1995; Basinger et al., 2003; Tarara and Ham, 1997; Ham and Benson, 2004).
The unsaturated soil zone is characterized by spatial heterogeneity and temporal variability. To understand energy transport mechanisms in soil, it is essential to continuously monitor the state variables and the thermal, hydraulic, and chemical properties of soil on an equal volume. Noborio et al. (1996) combined the TDR method and the heat-pulse method into a single unit, which allowed T, , electrical conductivity (EC) and thermal properties to be determined simultaneously in a similar volume. Water content results from TDR agreed well with gravimetrically measured values. However, the heat-pulse values from this sensor showed large deviation from the gravimetric measurements, which in part were attributed to needle deflection at probe insertion into the soil. Ren et al. (1999) reconsidered the probe design criteria and constructed an improved thermo-TDR probe. The new probe configuration not only produced promising results of T, , EC, and thermal properties, but also gave additional information such as soil bulk density (b), air-filled porosity, and degree of saturation (Ochsner et al., 2001; Ren et al., 2003a). Thermo-TDR probes provide an ideal opportunity to obtain comparison measurements because both heat pulse and TDR measurements can be made with each probe representing similar volumes of soil.
The objective of this study was to evaluate the performance of the thermo-TDR technique for measuring using the heat pulse method and the TDR method on repacked and undisturbed soil samples with a range of texture, organic matter content, and bulk density.
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MATERIALS AND METHODS |
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m–1, Pelican Wire Co., Naples, FL) through the cylinder four times. The resistance of each completed heater is 820 m–1. The thermocouples, placed at the center (0.02 m from the base) of the cylinders, are chromel and constantan (Type E). When the heaters and thermocouples are placed in position, high-thermal-conductivity epoxy glue (Omegabond 101, Omega Engineering, Stanford, CT) is drawn into the cylinders to provide a water-resistant, electrically insulated probe. For the TDR part of the probe, the center conductor of a coaxial cable (RG187 A/U, 75 , Newark Electronics, Omaha, NE) is soldered to the center cylinder and the shield of the cable is split and soldered to the outer two cylinders. Finally, the three cylinders are positioned in a mold that is then filled with epoxy (RBC-4300 and A-121 hardener, RBC industries, Warwick, RI).
For heat-pulse measurement using the thermo-TDR probe, a datalogger (Model CR23X, Campbell Scientific, Logan, UT) was used to control the heat pulse and collect temperature data from the outer cylinders. A DC power supply, which was controlled by a relay through the datalogger, was used to supply direct current to the central heater for 15 s. The heating power was inferred from the voltage drop measured across a 1- precise resistor placed in series with the heater. Temperature as a function of time in the two outer cylinders was measured at 1-s intervals for 300 s. The TDR measurements were made using a Tektronix 1502 cable tester (Tektronix Inc., Beaverton, OR). For waveform analysis, the first reflection point was set at the calibration value (see next section for a description of the calibration procedure) and the second reflection point was found by using the WinTDR package (Or et al., 1998).
Probe Calibration
The apparent spacing (ra), the distance between the central heater and the thermocouple in the outer cylinder, was calibrated in a temperature-regulated room (20 ± 1°C) with the probe immersed in agar-immobilized water (6 g agar L–1). The heat pulse length was 15 s and the applied DC was 0.28 A. The heat capacity of the agar solution was taken as 4.18 MJ m–3 C–1 (Campbell et al., 1991; Ochsner et al., 2003). A nonlinear regression method (Welch et al., 1996) was used to estimate the spacing by fitting the temperature increase as a function of time. The calibration process was repeated 12 times for each probe with a 60-min interval, and ra was calculated as the mean of the 12 measurements.
The apparent length (La) of the thermo-TDR probe was obtained following the procedures of Robinson et al. (2003b). The first reflection position (L0) was located by shorting the three cylinders in air with a blade at the cylinder base. The end reflection point (Lw) was determined by analyzing the TDR waveforms in distilled water using the WinTDR software (Or et al., 1998). Figure 1
shows the waveforms collected in air, in water, and shorted at the cylinder base in air. Then La was calculated from the following relationship:
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with the thermo-TDR probe are based on different theories and therefore, values from the two methods may represent different soil volumes. Two simple experiments were performed to determine the approximate sampling volumes of the heat-pulse and TDR methods using the thermo-TDR probe. In the first experiment, we placed agar gel (6 g L–1) in a glass container (12-cm long, 6-cm wide and 6-cm tall) at room temperature (20 ± 1°C). A thermo-TDR probe was inserted vertically into the surface of the agar gel several times. At each insertion the plane of the cylinders was parallel to the same glass wall, and the distance between the central heater cylinder and the glass wall was varied, for example, 2, 4, 8, 10, 12, 14 mm between the central cylinder (the heating cylinder) and the container wall. Heat pulse measurements were made each time that the probe position was changed. For reference, probe measurements in the bulk agar solution were also made in the center of a large container of the bulk agar solution.
In the second experiment, we used distilled water as a medium to test the water content detecting range of the TDR part of the thermo-TDR probe. The probe was positioned in the center of a 1-L glass beaker in such a way that all the three cylinders were perpendicular to the beaker wall, and the outer cylinders were above and below the central cylinder. Water was added to the beaker so that the water level was just over the central cylinder. Then more water was added in 1-mm increments and TDR waveforms were collected with each addition of water. The procedure was continued until the value of relative dielectric permittivity did not change with water level.
Soil Samples and Measurements
The experiment was conducted on samples of eight soils collected from different regions of China. Clay content of the soils ranged from 11.7 to 36.7% and organic matter content ranged from 0.7 to 7.2%. Table 1 lists the details of selected soil properties. Particle size analysis was performed using the hydrometer method (Gee and Bauder, 1986), particle density was determined using the pycnometer method (Blake and Hartge, 1986), and organic matter content of the soil was measured using the Walkley-Black titration method (Nelson and Sommers, 1982).
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b were determined by oven drying each sample at 105°C.
To determine the bulk specific heat of soil solids (cs), we conducted heat-pulse measurements of volumetric heat capacity (C) for the eight soils on oven-dried samples (105°C and 24 h) packed to the corresponding appropriate bulk densities. From the measured C values and known b values, cs was calculated from the relationship C = bcs (Ren et al., 2003a, 2003b).
Soil Water Content Calculation
Volumetric heat capacity of the soils was calculated from the measured temperature change as a function of time using the HPC code (Welch et al., 1996). The heat-pulse soil water content (HP) was obtained from the C-HP relationship (Campbell et al., 1991),
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The relative dielectric permitivity (Ka) of the soil samples was calculated from the measurements of initial and end reflection points L1 and L2, using the following relationship,
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We then applied the Topp equation (Topp et al., 1980) to estimate TDR soil water content (TDR) from the Ka results.
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RESULTS AND DISCUSSION |
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TDR for a soil with 0.10 m3 m–3 water content.
Sampling Volume of the Heat-Pulse Method
The heat-pulse method for soil thermal property measurement is based on the heat conduction of a line heat source in an infinite homogeneous medium. Any heterogeneity in a soil sample will affect the heat transfer process and therefore distort the temperature vs. time curve. For the current study, if the probe sampling range falls beyond the agar gel boundary, then the temperature vs. time curve will differ from the curves obtained within the bulk agar gel. Figure 2
shows the temperature vs. time curves measured at a sensor cylinder when the thermo-TDR probe is placed at various distances from the container wall. Because the glass has smaller C than water, the closer the heater cylinder is to the container wall, the greater the maximum temperature rise. At the distance of 14 mm, the temperature vs. time curve overlaps the temperature vs. time curve obtained from the bulk agar solution, and the maximum temperature rise (0.851°C) is very close to the value obtained in the bulk agar solution (0.848°C). Therefore, under these experimental conditions, the measurement boundary of the thermo-TDR probe for soil thermal property and HP measurements is within a cylinder of 14 mm in radius, 2.3 times the ra value. Our conclusion confirms the theoretical analysis of Campbell et al. (1991) that the outer boundary of the heat pulse method is about 2.37 times the value of ra, assuming that the maximum temperature change at the outer boundary is 1% of the maximum temperature increase at ra. It should be noted that the above analysis is based on our experience that a maximum temperature increase of 0.8 to 0.9°C will ensure sufficient temperature measurement accuracy for determination of soil thermal properties and HP. We expect the sampling range of the heat pulse method will expand if heating power (and consequently the maximum temperature change at ra) is further increased. This is not recommended since large heat production in the soil sample results in increasing convective heat transfer, and possible changes of soil thermal properties.
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TDR) and heat-pulse water contents (HP) with the volumetric water contents (G) determined gravimetrically for the six repacked soils are shown in Fig. 4A and 4B . In general, both TDR and HP agree well with the G values, as indicated by the random distribution of the data along the 1:1 line. Comparing with G, the RMSE was 0.023 m3 m–3 for TDR and 0.022 m3 m–3 for HP. Linear regression analysis with the pooled data of the six soils produced equations having intercepts close to 0 and slopes near 1. The slope of the heat pulse relationship was slightly larger than that for the TDR relationship.
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HP data of the same soil, on the other hand, showed excellent agreement with G values (Fig. 4B). Therefore, the heat-pulse method seemed to have some advantage over the TDR method for measuring water content in higher OM soils. In the middle water content range (0.10–0.21 m3 m–3) of the clay loam soil, the heat pulse method underestimated water content by 0.019 to 0.047 m3 m–3 (Fig. 4B). We speculate that this underestimation is a result of the b variation in the soil column, as we experienced difficulties in packing this higher clay content soil in the middle water content range.
Soil Water Content of Undisturbed Soils
The combined results of TDR and HP vs. G for the two undisturbed soils are presented in Fig. 5A and 5B
. Both the TDR and HP values agreed well with the G values. Comparing with G, the RMSE was 0.018 m3 m–3 for TDR and 0.021 m3 m–3 for HP. For the TDR vs. G data, linear regression analysis yielded a line with an intercept of 0.0035 m3 m–3, a slope of 1.003, and an r2 of 0.9138. For the HP vs. G data, the intercept, slope and r2 were-0.0011, 0.9985, and 0.8754, respectively. Compared to the TDR data, the heat-pulse data showed slightly greater scatter and a lower r2 value. The reason for the larger scatter may be because the heat-pulse measurements are relatively more sensitive to cylinder-soil contact. Spatial variability in soil b and structure formations (e.g., cracks and earthworm holes) associated with undisturbed soils may have larger impacts on the accuracy of the heat-pulse method than on the TDR method.
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TDR results from Eq. [3] were usually less than G in the lower water content range and larger than G in the higher water content range. As a result, a special calibration equation for the thermo-TDR probe was recommended (Ren et al., 2003a). The results presented here for both repacked and undisturbed soil measurements indicated that with probe calibration, Eq. [3] (Topp equation) could be used safely for estimating soil water content with the thermo-TDR probe.
Reports in the literature regarding the HP accuracy from the heat-pulse method are inconsistent. Campbell et al. (1991) showed that the C values from heat-pulse method were 10 to 15% larger than the values given by de Vries (1963). While some studies gave unbiased HP from the heat-pulse method (Campbell et al., 2002, Mori et al., 2003), other laboratory and field studies concluded that the heat-pulse method tended to overestimate C and HP (Bristow et al., 1993; Tarara and Ham, 1997; Song et al., 1998; Bristow et al., 2001; Basinger et al., 2003; Ren et al., 2003a; Heitman et al., 2003). Campbell et al. (1991) indicated that high clay content soils retained some water at oven-dry conditions and therefore had larger specific heat than expected. Bristow (1998) also showed that errors of >10% could occur in HP when inaccurate values of cs were used. A recent study by Ham and Benson (2004) showed the importance of probe construction and calibration in reducing the errors in HP. Error analysis by Basinger et al. (2003) and Heitman et al. (2003), however, pointed out that HP errors of the heat-pulse method were not caused by a single input parameter, but could be the result of a combination of biased parameters (e.g., b, cs, ra, heating power, and maximum temperature change at ra). Consequently, Basinger et al. (2003) established an empirical relationship to correct the bias of HP. Although currently there are no conclusive explanations on the HP bias, this study and the work of Ren et al. (2003a)( 2003b) prove that it is possible to obtain accurate HP data by using oven-dried soil cs values obtained from heat-pulse measurements with the thermo-TDR technique.
A potential error in L1 may arise when making TDR measurements at temperatures different (e.g., under field conditions) from the original temperature at which L0 is established. For the probes used in this study, the first reflection point shifts to the right with decreasing ambient temperature and to the left with increasing ambient temperature. This is mainly caused by the reduction in dielectric permittivity of the coaxial cable with increasing temperature. Our experience with the thermo-TDR probe under field conditions indicated that the WinTDR software was able to locate the L1 position without causing significant error in TDR.
When applying the thermo-TDR method in field studies, another practical question is how to determine bcs without having to remove a soil sample at the measurement site. Since bcs is essentially the volumetric heat capacity of soil at TDR = 0, it can be determined with TDR and C measurements obtained simultaneously using the combined TDR and heat-pulse capabilities of the thermo-TDR technique. With the thermo-TDR method, one can obtain pairs of TDR and C values at different soil water contents. The intercept from linear regression of C vs. TDR will then give an estimate of bcs.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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TDR) geometrically. In this study, we determined L0 of the thermo-TDR probe by shorting the cylinders in air and then obtained La by calibrating the probe in distilled water. Laboratory measurements on both repacked and undisturbed soils showed that the calibration procedure was helpful for the TDR measurements made with the thermo-TDR probe, and that the common –Ka equation (Eq. [3]) could be applied to the thermo-TDR probe. We experimentally investigated the soil water content sampling volumes of the heat-pulse and TDR methods of the thermo-TDR probe. The results indicated that the sampling radius of the heat-pulse method was approximately 14 mm about the central heater, and the TDR method had an approximate sampling radius of 11 mm about the central cylinder.
Many factors influence the accuracy of the heat-pulse method for C and HP measurements. Our results on eight soils proved that accurate HP data could be obtained with the thermo-TDR probe when cs values determined from heat-pulse measurements on oven-dried soil samples were applied.
With careful calibration of the thermo-TDR probe, both TDR and heat-pulse methods gave reliable soil water content data. Due to the relatively short cylinder length, the RMSE of the thermo-TDR probe was probably larger than the RMSE would be for a longer conventional TDR probe. It appeared that the TDR method was less sensitive to soil spatial variability than the heat-pulse method. On the other hand, the heat-pulse technique was better suited to water content measurements on high OM soils where the TDR method tended to underestimate soil water content.
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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T) at a sensor cylinder as related to the position of the heater cylinder. The numerical values indicate the distance of the heater cylinder to the wall of the glass container.
