Published in Soil Sci. Soc. Am. J. 68:1185-1190 (2004).
© 2004 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
DIVISION S-1—SOIL PHYSICS
On the Construction and Calibration of Dual-Probe Heat Capacity Sensors
J. M. Ham* and
E. J. Benson
Dep. of Agronomy, Kansas State University, Manhattan, KS 66506
* Corresponding author: (jayham{at}ksu.edu).
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ABSTRACT
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Dual-probe heat-capacity (DPHC) sensors can be used to measure soil heat capacity (C), water content, and temperature. Research was conducted to test design factors that affect sensor calibration, including: (i) calibration media, (ii) diameter and length of the needle probes, (iii) sensor body material, and (vi) duration and total power of the applied heat pulse. All sensors were calibrated in media with known C, including: agar (water), water-saturated glass beads, and dry glass beads. Calibration consisted of collecting heat pulse data in a given media and then calculating the apparent probe spacing (rapp, distance between heater and detector needles) that yielded correct value of C. An ideal sensor would have the same rapp regardless of media type. The rapp for all sensor designs increased as C decreased, on average changing by 6.7% between agar and dry beads. This undesirable result was consistent with previous studies that showed DPHC sensors calibrated in agar overestimated C in drier soils. Needle diameter (1.27 vs. 1.65 mm), sensor body material (urethane vs. high-conductivity epoxy), and shortening of the detector probe had a small effect on rapp. Sensors made with urethane bodies, 1.27-mm diam. needle probes, and shortened temperature probes showed less sensitivity to calibration media and are therefore recommended. The rapp for this design only increased by 2.6% between dry and water-saturated wet beads. Apparent probe spacing was not affected by changes in total applied power (400–1600 J m–1) or heat pulse duration (2–16 s) when the correct analytical model was used to compute C.
Abbreviations: AWG, American Wire Gauge • C, soil heat capacity • DPHC, dual probe heat capacity
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INTRODUCTION
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DUAL-PROBE HEAT capacity sensors are a promising heat-pulse technology for measuring soil thermal properties, soil water content, and soil temperature. Soil heat capacity is determined by applying a heat pulse to a line source and measuring the temperature increase about 6 mm from the heater (Campbell et al., 1991). Due to their small size and sample volume, DPHC sensors are particularly useful near the soil surface. A theoretical analysis by Kluitenberg and Philip (1999) showed DPHC sensors could be placed within 10 mm of the surface. Sensors are relatively inexpensive to build and can be readily automated using data acquisition systems to obtain near-continuous data. For example, DPHC sensors are ideal for monitoring heat storage in the soil layer above flux plates when measuring soil heat flux by the combination method (Ham, 2001). Because C is dependent on soil water content, DPHC sensors also can be used to monitor soil moisture (Bristow et al., 1993; Tarara and Ham, 1997; Basinger et al., 2003; Heitman et al., 2003; Ochsner et al., 2003) and plant water use (Song et al., 1998).
The DPHC sensor, as explained here, consists of two parallel hypodermic-tubing probes extending from a small sensor body (Fig. 1). Hereafter, probe will be used to describe the hypodermic tubing components while sensor will refer to the entire assembly. One probe contains a heater made of resistance wire and the other probe houses a thermistor. Once installed, the heat capacity of the soil surrounding the heater is determined by applying a short heat pulse (e.g., 8 s) and then measuring the subsequent temperature increase at the thermometer probe for about 60 s. As shown by Campbell et al. (1991), the heat capacity of the soil can be estimated as
 | [1] |
where C is heat capacity (J m–3 K–1), q is applied power per length of probe (J m–1), r is the distance between the hypodermic probes (m), and Tm is the maximum increase in temperature at the detector probe following the application of the heat pulse (°C). Equation [1] is a solution to the heat equation assuming an infinite line-source heater and an instantaneous heat pulse. Knight and Kluitenberg (2004) presented an improved heat capacity equation that considers the time interval of heating
 | [2] |
where 
is to/tm, to is the duration of the heat pulse (s), and tm is the time from the initiation of heating to the occurrence of the maximum temperature rise (s).
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Fig. 1. Diagram of a dual-probe heat capacity sensor. For some sensors, the length of the temperature probe was reduced to 18 mm.
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Calibration of a DPHC sensor requires precise determination of r, the only empirical sensor-specific parameter in the calculation of C. Probe spacing is estimated by collecting heat pulse data in a media of known C and then rearranging Eq. [1] or [2] to solve for apparent probe spacing, hereafter noted as rapp. The calculation of C is very sensitive to r; for example, a 2% error in r causes a 4% error in C (Campbell et al., 1991). Therefore, for a sensor with 6-mm probe spacing, rapp must be determined to within 0.3 mm to measure C to within 10%. In theory, rapp should not change if a sensor is calibrated in media with different heat capacities. However, at lower water contents, data suggest rapp increases when C decreases which causes a progressively increasing overestimate of C and soil water content as the soil dries (Tarara and Ham, 1997; Song et al., 1998; Basinger et al., 2003). This response indicates model errors (i.e., Eq. [1] or [2] do not accurately represent sensor physics) or instrumentation errors (i.e., inaccurate measurement of q, Tm, or tm) are changing as a function of water content. An added concern is that r may be altered during installation in the soil (probe deflection). It might be advantageous to use larger diameter or shorter needle probes that are more rigid (Kluitenberg et al., 1993).
The objectives of our research were to calibrate DPHC sensors of various designs by measuring rapp in media with different heat capacities and water contents. Sensors having a better design and operated in the most optimal manner should have a more similar rapp across all media. Tests were conducted to examine the effect of: (i) calibration media, (ii) needle-probe diameter and length, (iii) sensor body material, and (iv) duration and total power of the applied heat pulse. Also provided is a description of fabrication methods suitable for building large numbers of DPHC sensors.
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MATERIALS AND METHODS
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The basic template for the DPHC sensors was a modified version of the design proposed by Campbell et al. (1991) and similar to that used by Tarara and Ham (1997) and Basinger et al., (2003). Each sensor consisted of two needle probes, made from 1.27- or 1.65-mm diam. (16 or 18 American wire gauge [AWG]) hypodermic tubing, mounted in a cylindrical body (Fig. 1). Hypodermic tubing was custom cut to 36 mm, deburred, and flanged on one end (Small Parts Inc., Miami Lakes, FL). The temperature-sensing probe contained a thermistor (10K3MCD1, Betatherm Corp., Shrewsbury, MA) positioned halfway between the sensor body and the tip of the tubing. Heater probes were made from two loops (four strands total) of enameled resistance wire (205 ohm m–1, Nichrome 80, Pelican Wire Co., Naples, FL) resulting in an overall heater resistance of 820 ohms m–1. The resistance of the heater wire was measured in the laboratory and was slightly different from the manufacturer's rating. Once the thermistors and heater wires were in place, the hypodermic tubing was filled with high-conductivity epoxy (Omegabond 101, Omega Engineering, Stamford, CT). Epoxy was loaded into a syringe and injected into the bore of the hypodermic tubing using a flexible tube. Wires exiting the back of the heater and thermistor probes were spliced to an extension cable (9L28024-H100-8, Belden Wire and Cable, Richmond, IN), four conductors to the thermistor and two conductors to the heater (Fig. 1). Splices from the heater wire and thermistor to the copper extension wire were made using 7% silver solder (Kapp Alloy and Wire Co., Oil City, PA).
Once the heater- and temperature-probe assemblies were completed, they were then clamped into a custom-built stainless steel mold, which was used to hold the needles 6 mm apart and parallel. Two different molds were used for all fabrication, one each for the 1.27- and 1.67-mm probe diameters. A release agent (MS122DF, Miller-Stephenson Chemical Co., Danbury, CT) was sprayed on the molds before use. Cylindrical sensor bodies (32 mm long, 13 mm diam.) were cast using either of two epoxies: RBC4300 (RBC Industries, Inc., Warwick, RI) or CR600 (MicroMark, Berkeley Heights, NJ). Thermal properties of the hardened epoxies were measured using DPHC sensors. RBC4300 is a thermally conductive, black epoxy with a thermal conductivity of 0.6 W m–1 K–1 and a heat capacity of 2.9 MJ m–3 K–1, whereas CR600 is a nonconductive white urethane epoxy with a thermal conductivity of 0.2 W m–1 K–1 and a heat capacity of 1.7 MJ m–3 K–1. Thermal conductivity of the RBC4300 was about half the value stated by the manufacturer. Epoxies with two different thermal conductivities were chosen to determine if heat transfer in or near the sensor body might affect results. Of the two casting materials tested, the CR600 urethane was easier to use because the hardener and epoxy mixture was easier to prepare, cured rapidly at room temperature (e.g., 75 min), and was easier to remove from the mold.
All sensors were fabricated in the same manner but certain aspects of the design were modified. As mentioned earlier, sensors were built with two different hypodermic probe diameters, two different body materials, and two different temperature probe lengths. Sensor designs used for testing included: (i) urethane body with 1.27-mm diam. probes, (ii) urethane body with 1.65-mm diam. probes, and (iii) RBC4300 body with 1.27-mm diam. probes. After all testing had been completed with the original sensors, the length of the temperature probes was shortened to 18 mm by removing the tips with a precision cutting wheel, leaving the thermistor 4 mm from end (Fig. 1). Heater probes remained 28 mm long. All tests were then repeated with the modified probes. In all, six different sensor configurations were tested. In addition to changing sensor design, sensors were calibrated using different levels of q (400–1600 J m–1) and different heat pulse lengths (2–16 s). Duration of the heat pulses was verified by measuring the heater voltage at 10 Hz using a CR23X datalogger (Campbell Scientific, Logan, UT). One special sensor was constructed (1.27-mm diam., 18-mm long temperature probe, urethane body) that had fine-wire thermocouples (Type-T, 0.08-mm diam.) both inside and cemented to the surface of the heater probe 14 mm from the sensor body. Thermocouples also were attached to the surface of the temperature probe at 4 and 14 mm from the sensor body.
Sensors were calibrated by collecting heat pulse data in media of known heat capacities and calculating rapp using Eq. [1] or [2]. For conditions used in this study, sample calculations showed that the difference between Eq. [1] and [2] is <0.5% except for very long pulse lengths (e.g., 16 s). Thus, Eq. [1] was used for all calculations except when Eq. [1] and [2] were explicitly compared to study the effect of heat pulse length. Media included agar, water-saturated glass beads, and dry glass beads with heat capacities of 4.18, 2.82, and 1.23 MJ m–3 K–1, respectively. The heat capacity of agar (6 g L–1) was assumed equal to that of water. The glass beads (0.43- to 0.60-mm diam., Agsco Corp., Wheeling, IL) had a specific heat of 794 J kg–1 K–1 at 23°C as determined by differential scanning calorimetry at the Thermal Physical Properties Research Laboratory, Inc., West Lafayette, IN. Heat capacities of the wet and dry beads were calculated on a volumetric basis in the manner used by DeVries (1963). Bulk density of the glass bead media was found to be 1530 kg m–3 (Basinger, 1999). Calibration data were collected in the laboratory using a CR10X data logger and two AM416 multiplexers (Campbell Scientific, Logan, UT). Current flowing through the heater circuit was measured with a four-leg shunt resistor (SM155-4, 1 ohm, 0.1%, Precision Resistor Co., Largo, FL). After a heat pulse, thermistors were sampled at 2 or 4 Hz for 75 s using a four-wire half bridge with a 0.1%, 5000-ohm reference resistor. The thermistor circuit provided a resolution of 0.0008°C, which was about 10 times better than that achieved with a Type-T thermocouple. Once sensors were installed in a given media and the data collection system configured for specific heat pulse length and q, measurements were collected hourly for 1 to 2 d. The last 20 heat-pulse measurements from each test were used for analysis. In addition to the indirect determinations of rapp, the actual spacing between the heater and detector probes (center to center) for each sensor was measured with a digital caliper.
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RESULTS AND DISCUSSION
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Calibration Media
Regardless of sensor design, rapp increased significantly as C of the calibration media decreased (Table 1, Fig. 2). On average, rapp for the full-length probes increased from 5.70 mm in agar to 6.08 mm in dry beads, a 6.7% increase. These results are consistent with field and laboratory analyses that indicate DPHC sensors calibrated in agar tend to overestimate C and soil water content under dry conditions (Tarara and Ham, 1997; Song et al., 1998; Basinger et al., 2003). Of all sensor designs tested, the urethane bodies with shortened 1.27-mm diam. temperature probes showed the least sensitivity to calibration media. Changing from agar to dry beads with this sensor resulted in a 4.4% increase in rapp (Table 1). Overall, rapp in wet beads was closest to the caliper measurements.
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Table 1. Mean apparent probe spacing (rapp) of different sensor designs in three calibration media. Also included are measurements of probe spacing as determined with a digital caliper.
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Fig. 2. Effect of calibration media on the estimate of rapp. Shown are data from sensors with (a) full-length, 28 mm, temperature probes and (b) shortened, 18 mm, temperature probes. Comparisons are made among sensors constructed from 1.27- and 1.67-mm diam. stainless steel needles mounted in bodies fabricated from high thermal conductivity (HTC) RBC4300 epoxy and low thermal conductivity (LTC) urethane epoxy. Different letters indicate rapp is statistically different within a given media type (P < 0.10).
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The dependence of rapp on C indicates there was some form of error that changed with media thermal properties. Most likely, there are measurement errors in Tm, or Eq. [1] and [2] are not accounting for some form of heat flow affecting Tm (i.e., model error). Greater contact resistance between temperature probe and media in the dry beads may cause an underestimation of Tm. Another possible problem is that heat flow into the sensor body distorts the temperature regime around the temperature probe, a process not considered by the infinite line source model. Data from the sensor equipped with thermocouples on the probe exterior suggests the sensor body is a heat sink in dry beads (Fig. 3). In dry beads, there was a 0.25°C temperature difference between the thermocouples at 4 and 14 mm at the time of maximum temperature increase. Conversely, there is almost no longitudinal gradient along the temperature probe in wet beads. Initially, the different response in wet and dry beads was attributed to the magnitude of the temperature increase itself (1.2 vs. 2.4°C). However, as will be shown later, changing the applied power and the magnitude of Tm had no effect on the estimate of rapp. The sensor body was probably absorbing a larger fraction of the heat pulse in the dry case because the thermal conductivity of the sensor body was 0.2 W m–2 K–1, which was almost equal to that of the dry beads (0.18 W m–1 K–1). Furthermore, the low diffusivity of the dry beads, 1.5 x 10–7 m2 s–1, creates a slower moving pulse providing more opportunity for heat flow into the sensor body. In wet beads, with a thermal conductivity of 0.87 W m–1 K–1 and a diffusivity of 3.1 x 10–7 m2 s–1, the pulse moved more rapidly and the temperature gradient between the media and sensor body was smaller. While this analysis is somewhat circumstantial, results suggest sensor performance is affected by the difference in thermal properties between the sensor body and the soil.
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Fig. 3. Temperature increase at the temperature probe following an 8-s, 858-J m–1 heat pulse in water-saturated and dry glass beads. Data are from an experimental sensor (1.27-mm probes, urethane body) with fine-wire thermocouples attached 4 and 14 mm from the sensor body. Arrows depict the time of maximum temperature increase.
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Probe Length, Probe Diameter, and Body Material
A paired t test showed that shortening the temperature probes from 28 to 18 mm caused a small but statistically significant 0.4 and 1.0% decrease in rapp in the wet and dry beads, respectively (Table 1, Fig. 2). Heat transfer near the tip of the heater probe will be different than that of an infinite line source, a fact not accounted for in Eq. [1] and [2]. Thus, in the full-length sensors (i.e., 28 mm), the tip of the temperature probe may not rise to the same temperature as the rest of the needle after a heat pulse. This would cause longitudinal heat flow toward the tip of the temperature probe, moving heat away from the thermistor located in the center of the probe (14 mm). Indeed, Tm was slightly lower in the full-length probes resulting in a larger rapp. Also, rapp of the shortened probes was less sensitive to the changes from wet to dry beads, regardless of the elements of sensor design. Finally, a shorter temperature probe is less likely to deflect during insertion into soil. It is recommended that the temperature probe be about 10 mm shorter than the heater probe in future designs.
Probe diameter was evaluated using sensors with urethane bodies only. In wet glass beads and agar, the diameter of the hypodermic tubing did not cause a significant difference in rapp (Table 1, Fig 2). In dry beads; however, rapp was 2.5% larger for the 1.67-mm diam. probes. Also, sensors made from the 1.67-mm diam. probes showed a greater sensitivity to changing the calibration media from wet to dry beads (Table 1). Averaging over all sensors tested, switching from wet to dry beads caused a 3.1 and 5.6% increase in rapp in the 1.27- and 1.67-mm diam. probes, respectively. Using larger diameter probes could reduce deflection when sensors are installed in soil, thus minimizing errors in r. However, results shown here suggest larger diameter probes may exacerbate the problem of increasing C at lower soil water contents. It is recommended that a probe diameter of 1.27 mm or less be used for fabrication.
The effect of sensor body material was tested using 1.27-mm diam. probes only, all of which were cast from the same mold. Body material did not significantly affect calibration in agar or wet beads. However, in dry beads, rapp was significantly larger (P = 0.1) in sensors made from the RBC4300 epoxy for both full length and shortened probes. The RBC4300 epoxy has a relatively high conductivity and heat capacity; thus, it can act as a strong heat sink during a heat pulse. As mentioned previously, it is probable that some of the heat generated in the heater probe was conducted into the sensor body, effectively reducing q and Tm. Because the effect of the sensor body on q is not accounted for in the model, the result is larger rapp. When using casting epoxies, it appears that products with lower thermal conductivities and heat capacities (e.g., urethane) are superior.
Total Applied Power, Heat Pulse Length, and Probe Temperatures
The effect of applied power, q, was examined by using input voltages of 9.2, 13.0, and 18.4 V, which for 8-s pulses corresponded to heating of 400, 800, and 1600 J m–1, respectively. For all sensor designs and all calibration media, changing q had no statistically significant affect on rapp (not shown).
Heat pulse length was varied between 4 and 16 s while the input voltage was adjusted between 9.2 and 18.4 V, respectively. This procedure kept q almost constant (approximately 850 J m–1). Figure 4 shows rapp for full length and shortened sensors in wet beads as calculated using the instantaneous pulse model (Eq. [1]) and the finite pulse model (Eq. [2]). Heat pulse length had no statistical effect on rapp when calculated using either equation. However, there was a trend for rapp to increase with pulse length when using Eq. [1], albeit the effect was very small. For the 1.27-mm urethane sensor, rapp increased by 0.9% between 4- and 16-s pulses. Conversely, the finite pulse model (Eq. [2]) showed no trends as a function of pulse length. Although the differences between Eq. [1] and [2] are small, Eq. [2] is recommended because there is both empirical and theoretical evidence that it is a better heat flow model for DPHC sensors.
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Fig. 4. Effect of pulse length on the estimate of rapp. Shown are data from sensors with (a) full-length, 28 mm, temperature probes and (b) shortened, 18 mm, temperature probes. Comparisons are made among sensors constructed from 1.27- and 1.67-mm diam. stainless steel needles mounted in bodies fabricated from high thermal conductivity (HTC) RBC4300 epoxy and low thermal conductivity (LTC) urethane epoxy. Results from the instantaneous pulse (Eq. [1]) and finite pulse (Eq. [2]) models are shown.
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Given that applied power and pulse length have negligible effects on sensor performance, these parameters should be selected to avoid thermally induced water flow, prolong the life of the sensors, and maximize the precision of data acquisition. Table 2 shows maximum internal and external heater temperatures as recorded by thermocouples imbedded in or mounted on the surface of the experimental sensor (1.27-mm probes with urethane body). Voltage was adjusted inversely to the pulse length so q was 848 ± 15 J m–1 for all tests. At the end of the 2-s pulse in dry beads, internal and external temperatures were 179.4 and 102.9°C, respectively. Thus, in drier soils, high temperatures resulting from short heat pulses might cause moisture movement near the heater. Furthermore, the high temperatures inside the heater could damage the enamel on the resistance wire and eventually cause an electrical short. Increasing the heat pulse length to 8 s caused a 62°C reduction in internal and a 22°C reduction in external temperatures. Heat pulse lengths of 8 s or greater with a q near 850 J m–1 are recommended. For the sensors described here, this protocol would result in an easily measured value of Tm between 1.1°C in wet soils and 2.2°C in dry soils.
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Table 2. Internal and external heater temperatures immediately after the heat pulse as recorded by thermocouples imbedded in or mounted on the surface of an experimental sensor (1.27-mm probes with urethane body). Temperatures represent the average of five measurements at each pulse length in water-saturated and dry glass beads. Voltage was adjusted inversely to the pulse length so q was 848 ± 15 J m–1 for all tests.
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Sampling Frequency
In most cases, DPHC sensors are used to collect data on an hourly or daily basis. However, there could be cases where more frequent sampling is required. For example, if used in an automated irrigation control system, the sensors would need to detect the movement of a wetting front at different depths in the soil profile (Bremer and Ham, 2003). Figure 5 shows the effect of repeatedly sampling sensors at different intervals (4, 8, 16, 32, and 60 min). When the interval between repeated samples was <16 min, rapp began to increase in both wet and dry beads, although the impact was more pronounced in the dry case. This indicates that heat from the previous heat pulse was affecting the determination of Tm. Thus, the fastest allowable sampling interval for DPHC sensors was about 15 min.
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CONCLUSIONS
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General recommendations from this study are: the diameter of the needle probes should be 1.27 mm or less; the length of the temperature probe should be shorter than the heater probe; sensor bodies should be made from materials with low thermal conductivities and heat capacities (e.g., urethane); applied power should be 800 ± 100 J m–1; heat pulse lengths should be 8 ± 2 s; the model of Knight and Kluitenberg (2004) should be used for both calibration of rapp and the field measurements of C; and repeated sampling of the same sensor should occur at intervals of 15 min or longer.
Apparent probe spacing of the recommended sensor design (1.27-mm diam. probes, urethane body, shortened temperature probe) will still have some sensitivity to soil water content. Sample calculations were performed to emulate the drying of a silt loam soil from 0.4 to 0.1 m3 m–3 (Tarara and Ham, 1997). At 0.1 m3 m–3, representing the worst case, a sensor calibrated in wet beads would overestimate C by 4.2% and predict a water content of 0.115 m3 m–3. The difference between 10 and 11.5% water content is probably negligible in most studies. Furthermore, other sources of error would likely have a larger impact on accuracy, including probe deflection upon insertion, uncertainty in soil specific heat, spatial variability in soil properties, and poor probe-soil contact caused by shrinking and swelling. After installation in the field, it is strongly recommended that sensor results be compared with independent estimates of C. Volumetric samples can be collected at the same depth as the sensors and C approximated from gravimetric analysis (Basinger, 1999; Heitman et al., 2003). Although some variation is expected, this procedure will provide assurance that the laboratory calibrations are valid.
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ACKNOWLEDGMENTS
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This material is based upon work supported by the Cooperative State Research, Education, and Extension Service, USDA, under Agreement No. 2001-38700-11092. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the view of the USDA. Technical support was provided by F.W. Caldwell. G.K. Kluitenberg made many helpful suggestions on the first version of the manuscript.
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NOTES
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Contribution no. 04-189-J from the Kansas Agric. Exp. Stn., Manhattan, KS.
Received for publication November 20, 2003.
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REFERENCES
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- Basinger, J.M. 1999. Laboratory and field evaluation of the dual-probe heat-pulse method for measuring soil water content. M.S. Thesis. Kansas State Univ., Manhattan.
- Basinger, J.M., G.J. Kluitenberg, J.M. Ham, J.M. Frank, P.L. Barnes, and M.B. Kirkham. 2003. Laboratory evaluation of the dual-probe heat-pulse method for measuring soil water content. Vadose Zone J. 2:389–399.[Abstract/Free Full Text]
- Bremer, D.J., and J.M. Ham. 2003. Soil moisture sensors can help regulate irrigation. Golfdom. June. 49–54.
- Bristow, K.L., G.S. Campbell, and K. Calissendorff. 1993. Test of a heat-pulse probe for measuring changes in soil water content. Soil Sci. Soc. Am. J. 57:930–934.[Abstract/Free Full Text]
- Campbell, G.S., K. Calissendorff, and J.H. Williams. 1991. Probe for measuring soil specific heat using a heat-pulse method. Soil Sci. Soc. Am. J. 55:291–293.[Abstract/Free Full Text]
- DeVries, D.A. 1963. Thermal physical properties of soil. p. 210–235. In W.R. van Wijk (ed.) Physics of the plant environment. John Wiley and Sons, New York.
- Ham, J.M. 2001. On the measurement of soil heat flux to improve estimates of energy balance closure. Eos Trans. AGU, 82(47), Fall Meet. Suppl., Abstract B51A–0183. American Geophysical Union, Washington, DC.
- Heitman, J.L., J.M. Basinger, G.J. Kluitenberg, J.M. Ham, J.M. Frank, and P.L. Barnes. 2003. Field evaluation of the dual-probe heat-pulse method for measuring soil water content. Vadose Zone J. 2:552–560.[Abstract/Free Full Text]
- Kluitenberg, G.J., J.M. Ham, and K.L. Bristow. 1993. Error analysis of the heat pulse method for measuring soil volumetric heat capacity. Soil Sci. Soc. Am. J. 57:1444–1451.[Abstract/Free Full Text]
- Kluitenberg, G.J., and J.R. Philip. 1999. Dual thermal probes near plane interfaces. Soil Sci. Soc. Am. J. 63:1585–1591.[Abstract/Free Full Text]
- Knight, J.H., and G.J. Kluitenberg. 2004. Simplified computational approach for dual-probe heat-pulse method. Soil Sci. Soc. Am. J. 68:447–449.[Abstract/Free Full Text]
- Ochsner, T.E., R. Horton, and T. Ren. 2003. Use of the dual-probe heat-pulse technique to monitor soil water content in the vadose zone. Vadose Zone J. 2:572–579.[Abstract/Free Full Text]
- Song, Y., J.M. Ham, M.B. Kirkham, and G.J. Kluitenberg. 1998. Measuring soil water content under turfgrass using the dual-probe heat-pulse technique. J. Am. Soc. Hortic. Sci. 123:937–941.[Abstract/Free Full Text]
- Tarara, J.M., and J.M. Ham. 1997. Measuring soil water content in the laboratory and field with dual-probe heat-capacity sensors. Agron. J. 89:535–542.[Abstract/Free Full Text]
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TOP
ABSTRACT
INTRODUCTION
