HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Figures Only Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Olmanson, O. K. Articles by Ochsner, T. E. Search for Related Content PubMed Articles by Olmanson, O. K. Articles by Ochsner, T. E. Agricola Articles by Olmanson, O. K. Articles by Ochsner, T. E. Related Collections Soil Methods/Instrumentation

SOIL PHYSICS

A Partial Cylindrical Thermo-Time Domain Reflectometry Sensor

^a Dep. of Soil, Water, and Climate, Univ. of Minnesota, St. Paul, MN 55108
^b USDA-ARS, Soil and Water Management Research Unit, St. Paul, MN 55108

^* Corresponding author (ochsner{at}umn.edu).

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX REFERENCES

 
Thermo-time domain reflectometry (T-TDR) sensors can be used to measure soil thermal properties and water content, and to obtain indirect estimates of bulk density and air-filled porosity; however, the small size and sensitivity to needle deflection of the conventional T-TDR sensor limit its accuracy, precision, and durability. The objective of this study is to change the size and geometry of this sensor to improve accuracy and precision and to better withstand the stress of field use. The new partial cylindrical design features opposing curved heaters with a central temperature-sensing needle and is more than double the size of conventional T-TDR sensors. The partial cylindrical design virtually eliminates sensitivity to needle deflection. Laboratory testing indicated that the new sensor was capable of accurately measuring soil water content and thermal properties. Comparison with literature values showed that this sensor performed as well as, or better than, conventional sensors in all areas except volumetric heat capacity estimates. Qualitative assessment indicated that this type of sensor should be less prone to distortion during field use.

Abbreviations: T-TDR, thermo-time domain reflectometry

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX REFERENCES

 
For more than 10 yr researchers have been using heat pulse theory and TDR technology in a single sensor to estimate a number of soil properties and state variables (Noborio et al., 1996; Ren et al., 1999). Chief among them are water content (), volumetric heat capacity (c), and thermal conductivity (). From these measurements, additional soil properties and state variables can be inferred, including bulk density (_b), air-filled porosity (n_a), and degree of saturation (Ren et al., 2003a). Accurate measurements of these soil properties are needed for a variety of purposes. Few data are more valuable to the agricultural industry than soil water content, especially when irrigation is involved. Furthermore, plant development and soil–atmosphere gas exchange are highly influenced by the air-filled porosity of the soil. In engineering contexts, backfill operations are deemed successful based on the results of moisture and density tests. In the research community, soil thermal properties are vital to the study of coupled heat transfer and water movement.

Since their introduction to common use, TDR sensors have been successful in reliably measuring soil water content (Dalton et al., 1984; Jones et al., 2005; Noborio et al., 1994). The performance of these sensors has been shown to be fairly consistent across a wide range of soil types and densities. Ren et al. (1999) found that the minimum length of a TDR sensor in dry soil is 0.023 m; however, Heimovaara (1993) showed that, using a sensor with a length <0.10 m, when the dielectric permittivity is low, there may be a mingling of the first and second reflections. It then becomes difficult to establish a sensor length in air during calibration, leading to poor calibration constants. Other researchers have suggested a sensor length between 0.15 and 0.30 m to provide adequate travel time measurement (Robinson et al., 2003). The 0.04-m waveguides of the conventional T-TDR sensor detract from the accuracy and precision of the sensor's TDR water content measurements.

The use of heat pulse sensors for measuring soil thermal properties has been widely studied and accepted. Bristow et al. (1994) reported that independent estimates of soil thermal properties compared well with values measured with a heat pulse sensor. Others have noted that heat pulse sensors are also capable of measuring soil water content (Ren et al., 2003b; Song et al., 1998). These sensors perform well under controlled settings but when put under physical stress, reliability can be compromised. Campbell et al. (1991) reported an "extreme sensitivity of this method to probe spacing." Later, others echoed the same sentiment: soil thermal property measurements are highly influenced by deflection of the sensor's needles (Bristow et al., 1994; Noborio et al., 1996; Ren et al., 2003a). The problem of deflection arises because of the sensor's physical design, which consists of two or three parallel needles typically 1.27 mm in diameter, 4 cm in length, spaced about 6 mm apart. When the needle spacing is altered during insertion into the soil, large errors in thermal property estimation can result.

The objective of this study was to physically redesign the T-TDR sensor to minimize deflection and to reduce sensitivity to deflection while maintaining or improving TDR function. Toward this end, the new partial cylindrical T-TDR sensor was created. This sensor utilizes one central temperature-sensing needle between two parallel, opposed, curved heaters (Fig. 1 ). When compared with conventional two- or three-needle T-TDR sensors (Noborio et al., 1996; Ren et al., 1999), the partial cylindrical sensor has longer TDR waveguides, increased heater to temperature sensor spacing, and increased needle diameter. This sensor design was intended to limit physical deflection, to minimize the effects of deflection, to provide better resolution of the TDR waveform, and to sense a larger soil volume.

View larger version (14K): [in this window] [in a new window]   Fig. 1. The partial cylindrical thermo-time domain reflectometry sensor.

	THEORY

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX REFERENCES

[1]

where q (J m^–1) is the measured heat input to the line source, e is the base of the natural logarithm, and r (m) is the distance from the heater at which T_m is measured. For the partial cylindrical sensor (Fig. 1), we derived a similar equation by superposition of the infinite line source solution, again using the assumption of an instantaneous heat pulse:

[2]

where P (W) is the heating power, t₀ (s) is the small but finite pulse duration, a is the surface area of the heater (m²), and r' is the radius of the cylinder. (Note: the position of the central temperature sensing needle is r = 0 r'). Thermal diffusivity (m² s^–1) estimates can be obtained by

[3]

where t_m (s) is the time to the maximum temperature rise. The derivation of Eq. [2] and [3] can be found in the appendix.

	MATERIALS AND METHODS

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX REFERENCES

 
Sensor
The partial cylindrical sensor consisted of two opposing blades, 7.5 cm long, cut from one-fourth the circumference of a 3.175-cm-diameter aluminum tube with a wall thickness of 0.089 cm. One Kapton Thermfoil heater (Part no. HK5324R16.1L12A, 16.1 , Minco, Fridley, MN) was adhered to the outside of each blade with a manufacturer-supplied, pressure-sensitive adhesive. These heaters were wired in parallel to produce a total resistance of 8.05 . To reduce friction on the heaters during sensor insertion, the blades were milled to reduce the wall thickness by a fraction of a millimeter, except for a 2-mm length at the cutting edge (Fig. 1). This milling produced a protective lip behind which the heater was mounted. The 2-mm cutting tip at the end of the sensor was beveled on the outside to produce a sharp cutting edge. A 12-gauge hypodermic needle (0.279-cm diameter) was placed at the center with thermistors placed inside at two-thirds and one-third of the exposed length (10K3MCD1, BetaTHERM, Shrewsbury, MA). The needle was then filled with high-thermal-conductivity epoxy (Omegabond 101, Omega Engineering, Stamford, CT). For TDR functionality, the needle and the blades were soldered to a coaxial cable (RG6 Quad Shield, 15–1557, Radio Shack) and these served as the TDR lead and shields, respectively. A custom-built mold was then used to cast the sensor head with epoxy resin (CR-600, Micro-Mark, Berkeley Heights, NJ).

Data Acquisition System
The hardware used for data acquisition included a datalogger (CR23X) and a time domain reflectometer (TDR 100), both from Campbell Scientific, Logan, UT. Power for the 8-s heat pulse was provided by a 28-V rechargeable lithium ion battery (Milwaukee Electric Tool Co., Brookfield, WI) switched via a direct current relay. Heating power was measured with a 0.1 current-sensing resistor (PLV1, Precision Resistor Co., Largo, FL). Typical current draw for the sensor is about 2.9 A, resulting in a heating power of about 68 W. The resulting temperature rise at the needle was determined by measuring the resistance of the thermistors at a frequency of 1 Hz using the datalogger. The resistance was determined by applying a small excitation voltage and measuring the ratio of voltage drop across the thermistors to that across precision resistors (5 k ± 0.1%) wired in series with the thermistors.

Data collected from the heat pulse measurement included t_m, current, P, T_m, and a T_m that was corrected for ambient temperature drift. The drift rate was determined based on the change in ambient temperature during a 5-min period immediately before the heat pulse. The drift rate was assumed constant for the duration of the measurement. This correction was found to be significant in some cases and was therefore chosen when performing c calculations. Incremental temperature and time data were also collected for the purposes of plotting T curves.

Data output from the TDR mode consisted of the apparent length (m) for the total waveform, the probe calibration values, and a 251-point waveform. The resulting waves were processed in MATLAB using a fitting routine similar to that of Baker and Allmaras (1990), with tangents fit to the maximum slope of the falling and rising limbs of the waveform and horizontal intersecting lines extending from the local maximum and global minimum, respectively.

Calibration and Validation
The thermistors were validated by performing 50 measurements in a temperature-controlled water bath (Poly Science 9112, Niles, IL). Both thermistors measured water temperatures in agreement with the water bath settings to within ±0.15°C. The standard deviation for any set of readings was not greater than 0.040°C.

The apparent radius of the partial cylindrical sensor was calibrated by performing 10 measurements in saturated glass beads (0.425–0.600-mm diameter, Agsco Corp., Wheeling, IL). The thermal conductivity of the saturated glass beads (0.802 W m^–1 K^–1) was independently measured by the single heat probe method (Bristow, 2002). The volumetric heat capacity for the glass beads was calculated (Kluitenberg, 2002) based on the known bulk density (1.55 Mg m^–3), specific heat (794 J kg^–1 °C ^–1, Ham and Benson, 2004), and water content (0.351 m³ m^–3). Thermal diffusivity was then determined by = /c. The apparent radius was calculated by solving Eq. [3] for r' based on this independent measurement of diffusivity. Equation [2] was then used to calibrate the effective area of the heating surface (a). The apparent radius and effective area calibrations were validated by performing 10 heat pulse measurements in agar-stabilized water (6 g L^–1).

The TDR portion of the sensor was calibrated using air and water (Heimovaara, 1993) and was validated in acetone according to the following relationship for apparent dielectric permittivity (K_a):

[4]

where L_a is the apparent length of the sensor as determined from the TDR waveform, L_o is the travel distance within the sensor head, and L_e is the effective length of the exposed portion of the waveguides.

Packed Soil Tests
Lab tests were done in a silt loam soil (Ida series: fine-silty, mixed, superactive, calcareous, mesic Typic Udorthents) that had been air dried, passed through a soil grinder, and sieved through a 2-mm sieve. Particle size analysis by the hydrometer method gave 13% sand, 60% silt, and 27% clay. Soil organic matter determined by loss-on-ignition was 31 g kg^–1. The soil was wetted with a 10 mmol L^–1 solution of CaCl₂ and mixed to a predetermined gravimetric moisture content. Three different gravimetric moisture contents were used: 0.12, 0.16, and 0.21 kg kg^–1. The wetted soil was packed into a cylindrical mold 14.5 cm in diameter with a volume of 2 L to a predetermined density with a 1-kg vertical hammer. The soil was packed in eight equal lifts to enhance uniformity. The sensor was then inserted vertically into the soil, and heat pulse and TDR data were collected. After each test, the soil was removed, broken up, sampled for moisture verification by oven drying, rewetted as necessary, and repacked to the next highest density. For each gravimetric moisture content, four different bulk densities ranging from 1.05 to 1.35 Mg m^–3 were tested. Bulk densities were converted to volume fraction of solids assuming a particle density of 2.65 Mg m^–3. The result of increasing gravimetric moisture and density produced an incremental increase in volumetric moisture from 0.13 to 0.29 m³ m^–3. Initial testing showed negligible variability between successive, in situ readings; therefore, only one sensor reading was performed per volumetric moisture increment.

Calculations
The sensors were used to estimate volumetric heat capacity, Eq. [2], and thermal diffusivity, Eq. [3], using the heat pulse method and volumetric water content by the TDR method. These values were then used to estimate thermal conductivity, the volume fraction of solids (v_s), and air-filled porosity (n_a). Water content was calculated by

[5]

where K_s is the dielectric permittivity of the oven-dry soil and K_w is the dielectric permittivity of water (Pepin et al., 1995). We chose this equation because it has a physically meaningful, soil-specific calibration parameter and because it is linear. Once water content was determined, the volume fraction of solids was estimated by solving

[6]

where _s, _a, and _w are the thermal conductivities of the soil solids, air (0.024 W m^–1 °C ^–1), and water (0.60 W m^–1 °C^–1), respectively (Cosenza et al., 2003). Since we had no independent measurement of K_s or _s, we used a spreadsheet solver tool to optimize these parameters by minimizing the root mean square difference between the measured and modeled and between measured and modeled . Once and v_s are determined, air-filled porosity is simply their complement.

	RESULTS AND DISCUSSION

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX REFERENCES

 
Deflection Sensitivity
The choice to use curved heating blades for this sensor was mainly for structural reasons. The curved surface is much more resistant to deflection than a thin needle. This shape has an added advantage of reducing the effects of deflection of the temperature-sensing needle, should it occur. Figure 2 shows relative T_m vs. relative deflection for a dual-probe heat pulse sensor and for the partial cylindrical sensor. These results were obtained by integration of Eq. [A2] using Mathcad (Parametric Technology Corp., Needham, MA). It is clear that the partial cylindrical sensor is much less sensitive to needle deflection. A needle deflection of –25% from the center produces a relative error of <4% of T_m for the partial cylindrical sensor, whereas a 25% deflection of the temperature-sensing needle toward the heater of a dual-probe heat pulse sensor yields a relative T_m error 78%. The deflection sensitivity would be reduced even further if we were to use a full cylindrical heater with a single central needle, a possibility we did investigate. More severe problems resulted, however; when the cylinder was inserted in the soil, friction between the soil and the cylinder walls caused the soil inside the cylinder to compress. This compression altered the soil properties enough to render the resulting data unrepresentative of the surrounding soil.

View larger version (13K): [in this window] [in a new window]   Fig. 2. Relative maximum temperature rise vs. relative deflection of the temperature sensing needle from initial position for dual-probe (solid line) and partial cylindrical heat pulse sensors (dashed lines). The inset denotes heater position and radial orientation of transects for the partial cylindrical sensor. The heater is positioned at –1 for the two-needle sensor.

The calibration results presented in Table 1 are very encouraging. Calibrated values for r' are about 0.09 cm smaller than the radius measured to the outer edge of the blade. This is acceptable because the discrepancy is equal to the wall thickness of the aluminum blade. This suggests that the heat pulse is transferred through the blades nearly instantaneously and that the calibrated radius could be taken as the distance from the center to the inner edge of the blade. Calibrated heater areas are about 6% larger than the manufacturer's specified area of the heaters. A larger calibrated heater area indicates that T_m is low, possibly due to the thermal mass of the sensor components.

Validation Media
The validation results presented in Table 2 show excellent agreement between the reference and sensor-estimated values for c, , and K. The discrepancies are all <1.5%. The precision of the estimates for these parameters is also very good, with coefficients of variation <0.8%.

View this table: [in this window] [in a new window]   Table 2. Results of sensor validation, where c is volumetric heat capacity, is thermal conductivity, and K is the dielectric permittivity.

The adherence of the data to Eq. [A3] further increased our confidence in the validation. Figure 3 shows the mean of the data from the upper and lower thermistors from a single heat pulse measurement plotted with the theoretical predictions from Eq. [A3]. For these predictions, we used the independent reference values for c and (Table 2), and we used the mean of the upper and lower thermistor calibration values for r' and a. An R² value of 0.998 indicates that this sensor behaves precisely as the model predicts.

View larger version (8K): [in this window] [in a new window]   Fig. 3. Measured temperature curve for the partial cylindrical sensor in water and theoretical model (Eq. [A3]). The model predictions are based on independent reference values for the thermal properties of water (Table 2) and sensor parameters calibrated in saturated glass beads.

View larger version (9K): [in this window] [in a new window]   Fig. 4. Measured vs. theoretical heat capacity for the partial cylindrical sensor in Ida silt loam.

View larger version (9K): [in this window] [in a new window]   Fig. 5. Thermal conductivity measurements from the partial cylindrical sensor in Ida silt loam vs. measured air-filled porosity. Thermal conductivity data for a similar soil from Ochsner et al. (2001a) are shown for comparison.

View larger version (9K): [in this window] [in a new window]   Fig. 6. Sensor estimates vs. measured values for volume fractions of water, solids, and air from laboratory packing experiment with Ida silt loam.

View this table: [in this window] [in a new window]   Table 3. Linear regression statistics for comparisons between sensor estimates of volume fractions in Ida silt loam soil and measured values, where is volumetric water content, na is air-filled porosity, and vs is the volume fraction of solids.

Spatial variation in the soil columns may be a leading cause for differences between the sensor estimates and the measured volume fractions. The sensor volume was only 5% of the total soil volume so it is quite possible that soil conditions within the vicinity of the sensor were not representative of the soil volume as a whole.

Measurements of the thermal properties could also be affected by axial heat flow. Figure 7 shows the heat pulse curves in agar-stabilized water, in saturated glass beads, and in Ida silt loam. The upper thermistor shows a larger temperature increase in the agar, while the lower thermistor shows a larger temperature increase in the Ida silt loam. In the saturated glass beads, there is no difference between thermistor positions. This may be related to the heat capacity of the materials with water > saturated glass beads > Ida silt loam. If axial heat flow is significant, there could be a problem with the assumption that the heaters are infinitely long; however, this seems unlikely. Kluitenberg et al. (1993, 1995) have shown that the error introduced by this assumption depends on the ratio of heater half length to needle spacing. For the partial cylindrical sensor, this ratio is 2.36, which is nearly identical to the ratio of 2.33 for the widely used dual-probe heat pulse sensors (e.g., Ham and Benson, 2004). Therefore, the theoretical error due to finite heater length is equal or less with the partial cylindrical sensor than with dual-probe heat pulse sensors.

View larger version (18K): [in this window] [in a new window]   Fig. 7. Measured heat pulse curves in soil, saturated glass beads, and agar-stabilized water showing discrepancies between the upper and lower thermistors.

Previously, v_s has been estimated from its influence on heat capacity rather that thermal conductivity (Ochsner et al., 2001b; Ren et al., 2003a). The volumetric heat capacity of water is about double that of soil solids, however, so resolution of v_s has been limited. In contrast, the thermal conductivity of water is much less than that of typical soil solids, so v_s may have a relatively greater effect on thermal conductivity than on heat capacity. This was the rationale behind using thermal conductivity to estimate v_s.

As with most sensors, proper soil–sensor contact is critical. Improper sensor insertion into the soil could lead to soil displacement, resulting in air gaps between the sensor and the soil. These situations could degrade the performance of both the TDR and heat pulse modes of the sensor.

Durability
One of the objectives when developing this sensor was to improve the durability of the sensor. While we have no quantitative evidence to show that this partial cylindrical sensor is more robust, there is qualitative evidence. Commonly while using a conventional T-TDR sensor in dense soil, the user must realign the individual needles between tests because of deformation. With the partial cylindrical T-TDR sensor, no such maintenance was needed. Our experiences suggest that the curved heaters and thicker central needle of the partial cylindrical sensor will withstand the stresses of repeated insertions in dense soil better than the smaller needles of the conventional T-TDR.

	CONCLUSIONS

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX REFERENCES

 
This partial cylindrical T-TDR sensor is a viable means for measuring soil water content and thermal properties. The new geometry facilitated the successful development of a sensor more than double the size of previous T-TDR sensors. Calibration and validation data show that it adheres well to the theoretical models associated with it. In addition, the new geometry exhibits minimal sensitivity to needle deflection, a serious problem for prior types of heat pulse sensors. The data show that the new sensor performs better than or equal to conventional T-TDR sensors in most areas, but improvements in heat capacity estimates would be beneficial.

	APPENDIX

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX REFERENCES

 
We want to develop the analytical solution for transient heat conduction about the partial cylindrical source shown in Fig. 1. We begin with the solution for an instantaneous cylindrical surface source at t = 0, of strength Q2r' and radius r', and with axis along the axis of z. That solution is (Carslaw and Jaeger, 1959)

[A1]

where T is temperature rise (°C), r is radial position (m), t is time (s), is the thermal diffusivity of the medium (m² s^–1), e is the base of the natural logarithm, and the integral is evaluated for angles from 0 to 2 radians, i.e., all the way around the cylinder. To obtain the solution for the partial cylindrical source we simply alter the path of integration, yielding

[A2]

Notice that the solution now depends on the angle ; the solution is no longer completely symmetrical.

At the center of the partial cylinder, r = 0, Eq. [A2] simplifies to

[A3]

The time to the maximum temperature rise at the center occurs at the time t_m, given by

[A4]

This result is found by taking the partial derivative of Eq. [A3] with respect to t, setting the partial derivative equal to 0, and solving for t. The value of the maximum temperature rise, T_m, is found by substituting Eq. [A4] into [A3]. The result is

[A5]

Now Q is equal to the product of the heating power, P (W), and the heating duration, t₀ (s), divided by the area, a (m²), of the heated portion of the cylinder and the volumetric heat capacity of the medium, c (J m^–3 °C ^–1), so Eq. [A5] can be written as

[A6]

If T_m, t_m, and P are measured and t₀, a, and r' are known, then Eq. [A4] and [A6] permit determination of the thermal properties of the medium, and c.

	ACKNOWLEDGMENTS

 
Dr. John Nieber, Dep. of Bioproducts and Biosystems Engineering, University of Minnesota, provided helpful results from two-dimensional numerical heat transfer modeling of earlier sensor prototypes. We are thankful for his assistance and insight.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX REFERENCES

 
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.

Received for publication February 26, 2007.

	REFERENCES

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS APPENDIX REFERENCES

 

• Baker, J.M., and R.R. Allmaras. 1990. System for automating and multiplexing soil moisture measurement by time-domain reflectometry. Soil Sci. Soc. Am. J. 54 :1–6.[Abstract/Free Full Text]
• Bristow, K.L. 2002. Thermal conductivity. p. 1209–1226. In J.H. Dane and G.C. Topp (ed.) Methods of soil analysis. Part 4. SSSA Book Ser. 5. SSSA, Madison, WI.
• Bristow, K.L., G.J. Kluitenberg, and R. Horton. 1994. Measurement of soil thermal properties with a dual-probe heat-pulse technique. Soil Sci. Soc. Am. J. 58 :1288–1294.[Abstract/Free Full Text]
• Campbell, G.S., C. 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]
• Carslaw, H.S., and J.C. Jaeger. 1959. Conduction of heat in solids. 2nd ed. Oxford Univ. Press, Oxford, UK.
• Cosenza, P., R. Guerin, and A. Tabbagh. 2003. Relationship between thermal conductivity and water content of soils using numerical modelling. Eur. J. Soil Sci. 54 :581–587.[CrossRef]
• Dalton, F.N., W.N. Herkelrath, D.S. Rawlins, and J.D. Rhoades. 1984. Time-domain reflectometry: Simultaneous measurement of soil water content and electrical conductivity with a single probe. Science 224 :989–990.[Abstract/Free Full Text]
• de Vries, D.A. 1963. Thermal properties of soils. p. 210–235. In W.R. van Wijk (ed.) Physics of plant environment. North-Holland Publ. Co., Amsterdam.
• Ham, J.M., and E.J. Benson. 2004. On the construction and calibration of dual-probe heat capacity sensors. Soil Sci. Soc. Am. J. 68 :1185–1190.[Abstract/Free Full Text]
• Heimovaara, T.J. 1993. Design of triple-wire time domain reflectometry probes in practice and theory. Soil Sci. Soc. Am. J. 57 :1410–1417.[Abstract/Free Full Text]
• Jones, S.B., R.W. Mace, and D. Or. 2005. A time domain reflectometry coaxial cell for manipulation and monitoring of water content and electrical conductivity in variably saturated porous media. Vadose Zone J. 4 :977–982.[Abstract/Free Full Text]
• Kluitenberg, G.J. 2002. Heat capacity and specific heat. p. 1201–1208. In J.H. Dane and G.C. Topp (ed.) Methods of soil analysis. Part 4. SSSA Book Ser. 5. SSSA, Madison, WI.
• Kluitenberg, G.J., K.L. Bristow, and B.S. Das. 1995. Error analysis of heat pulse method for measuring soil heat capacity, diffusivity, and conductivity. Soil Sci. Soc. Am. J. 59 :719–726.[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]
• Lide, D.R. (ed.). 2003. CRC handbook of chemistry and physics. CRC Press, Boca Raton, FL.
• Noborio, K., K.J. McInnes, and J.L. Heilman. 1994. Field measurements of soil electrical conductivity and water content by time-domain reflectometry. Comput. Electron. Agric. 11 :131–142.[CrossRef]
• Noborio, K., K.J. McInnes, and J.L. Heilman. 1996. Measurement of soil water content, heat capacity, and thermal conductivity with a single TDR probe. Soil Sci. 161 :22–28.[CrossRef]
• Ochsner, T.E., R. Horton, and T. Ren. 2001a. A new perspective on soil thermal properties. Soil Sci. Soc. Am. J. 65 :1641–1647.[Abstract/Free Full Text]
• Ochsner, T.E., R. Horton, and T. Ren. 2001b. Simultaneous water content, bulk density, and air-filled porosity measurements with thermo-time domain reflectometry. Soil Sci. Soc. Am. J. 65 :1618–1622.[Abstract/Free Full Text]
• Pepin, S., N.J. Livingston, and W.R. Hook. 1995. Temperature-dependent measurement errors in time domain reflectometry determinations of soil water. Soil Sci. Soc. Am. J. 59 :38–43.[Abstract/Free Full Text]
• Ren, T., K. Noborio, and R. Horton. 1999. Measuring soil water content, electrical conductivity, and thermal properties with a thermo-time domain reflectometry probe. Soil Sci. Soc. Am. J. 63 :450–457.[Abstract/Free Full Text]
• Ren, T., T.E. Ochsner, and R. Horton. 2003a. Development of thermo-time domain reflectometry for vadose zone measurements. Vadose Zone J. 2 :544–551.[Abstract/Free Full Text]
• Ren, T., T.E. Ochsner, R. Horton, and Z. Ju. 2003b. Heat-pulse method for soil water content measurement: Influence of the specific heat of the soil solids. Soil Sci. Soc. Am. J. 67 :1631–1634.[Abstract/Free Full Text]
• Robinson, D.A., S.B. Jones, J.M. Wraith, D. Or, and S.P. Friedman. 2003. A review of advances in dielectric and electrical conductivity measurements in soils using time domain reflectometry. Vadose Zone J. 2 :444–475.[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.

This article has been cited by other articles:

				T. Kamai, G. J. Kluitenberg, and J. W. Hopmans Design and Numerical Analysis of a Button Heat Pulse Probe for Soil Water Content Measurement Vadose Zone J., March 5, 2009; 8(1): 167 - 173. [Abstract] [Full Text] [PDF]

This Article Abstract Figures Only Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Olmanson, O. K. Articles by Ochsner, T. E. Search for Related Content PubMed Articles by Olmanson, O. K. Articles by Ochsner, T. E. Agricola Articles by Olmanson, O. K. Articles by Ochsner, T. E. Related Collections Soil Methods/Instrumentation