Published online 18 June 2008
Published in Soil Sci Soc Am J 72:1000-1005 (2008)
DOI: 10.2136/sssaj2007.0332
© 2008 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
SOIL PHYSICS
Determination of Soil Bulk Density with Thermo-Time Domain Reflectometry Sensors
Xiaona Liua,
Tusheng Rena,* and
Robert Hortonb
a Dep. of Soil and Water, China Agriculture Univ., Beijing, China 100094
b Dep. of Agronomy, Iowa State Univ., Ames, IA 50011
* Corresponding author (tsren{at}cau.edu.cn).
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ABSTRACT
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Surface soil bulk density varies with time and location. In most cases, destructive soil sampling has been used to monitor soil bulk density, 
b. Recently the thermo-time domain reflectometry (TDR) technique was shown in principle to be able to estimate b. Thermo-TDR sensors can measure soil volumetric heat capacity (c) and soil water content (
). Since c depends on and b, measurements of c and can be used to estimate b. Previous studies indicated, however, that there were large deviations between thermo-TDR estimates and gravimetric measures of b. Deviations were attributed mainly to the change of thermo-TDR needle-to-needle spacing during sensor insertion into the soil. The objective of this study was to improve the thermo-TDR sensor design to improve estimation of b. The ability of three new prototype thermo-TDR sensors, along with an existing thermo-TDR sensor, to estimate b was investigated. Evaluation results indicated that a three-needle sensor design with 2-mm needle diameter, 40-mm needle length, and 8-mm needle-to-needle spacing provided the most accurate estimation of soil b. For this sensor, the RMSEs of b estimates compared with gravimetric measures of b in laboratory evaluations were 0.055, 0.051, and 0.046 Mg m–3 for a silt loam, a clay loam, and a sand soil, respectively, and was 0.095 Mg m–3 in a field evaluation. In terms of relative error, this specific design was generally within 5% under laboratory conditions and within 10% under field conditions. The improved thermo-TDR sensor provides an opportunity for obtaining accurate, nondestructive, repeated estimates of soil b.
Abbreviations: OM, organic matter • RE, relative error • TDR, time domain reflectometry
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INTRODUCTION
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Knowledge of soil bulk density (b) is required for estimating soil water and nutrient status and for studying soil physical, chemical, and biological processes in both natural and agricultural ecosystems. Measuring spatial and temporal dynamics of b can be challenging. The core method, the most commonly used technique for measuring b directly, has the advantages of being simple and precise, but it is tedious and destructive (Grossman and Reinsch, 2002). The technique of gamma ray attenuation is rapid and nondestructive, and has the option of repeated measurements at the same site, but site-specific calibration is required, it depends on an independent determination of volumetric water content (), and the unavoidable radiation hazard limits its extensive application (Grossman and Reinsch, 2002).
Ochsner et al. (2001) and Ren et al. (2003a) introduced the thermo-time domain reflectometry (thermo-TDR) technique to determine b indirectly. The thermo-TDR combines heat pulse technology and TDR technology. Soil is estimated by the TDR method, and soil volumetric heat capacity (c) is estimated by the heat-pulse method (Ren et al., 1999). Knowing and c, b can be determined from the relationship between c and . Since the thermo-TDR method produces minimal soil disturbance, and is able to make rapid and repeated in situ measurements, it provides a valuable tool for monitoring the dynamics of b in the vadose zone. Ren et al. (2003a) showed that the thermo-TDR was able to predict the actual b values, but the agreement between thermo-TDR estimates and gravimetric values was relatively low. Across all six soils tested, the correlation coefficient was 0.426 and the standard error of estimation was 0.134 Mg m–3. Ren et al. (2003a) suggested that the major error in thermo-TDR-measured b was from the change in needle spacing at sensor insertion into the soil.
The objective of this study was to improve the thermo-TDR technique for b determination. New thermo-TDR sensor designs were developed, and their performance was evaluated under both laboratory and field conditions.
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MATERIALS AND METHODS
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Sensor Design
For the design of a thermo-TDR sensor, needle length, needle diameter, needle length/diameter ratio, and needle-to-needle spacing are the major factors that require attention (Ren et al., 1999). The uncertainties of soil water content measurement with TDR are increased with shorter sensors (Zegelin et al., 1992; Heimovaara, 1993; Evett and Parkin, 2005). Since the heat-pulse technique is based on the "line source" heater theory, soil thermal property determination also favors longer needles. Needle deflection during sensor insertion, however, affects the heat-pulse results. Needle deflection has been shown theoretically and experimentally to be the key factor that influences the accuracy of the heat-pulse technique (Bristow et al., 1994; Kluitenberg et al., 1995; Noborio et al., 1996; Ren et al., 2003a; Ham and Bension, 2004). In this study, our modification to the Ren et al. (1999) thermo-TDR sensor focused on three aspects: using relative larger diameter needles to reduce needle deflection during sensor insertion, increasing the needle length to improve the accuracies in TDR-measured , and using needles with pointed tips to minimize soil disturbance and improve the ease of sensor insertion. Accordingly, the needle-to-needle spacing was also altered to meet the approximate line heat source requirement (Ren et al., 1999). Four prototype three-needle sensors were considered in our investigation: Sensor 1, the Ren et al. (1999) sensor with needle diameter (d) of 1.3 mm, length (L) of 40 mm, and needle-to-needle spacing (S) of 6 mm; Sensor 2, with d = 2 mm, L = 40 mm, and S = 8 mm; Sensor 3, with d = 2 mm, L = 50 mm, and S = 8 mm; and Sensor 4, with d = 2 mm, L = 60 mm, and S = 9 mm. In addition, Sensors 2, 3, and 4 had pointed tips. A schematic view of Sensors 1 and 2 is shown in Fig. 1
. Sensors 3 and 4 had designs similar to Sensor 2, except for different needle length and needle-to-needle spacing.
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Fig. 1. Schematic view of (a) Sensor 1 and (b) Sensor 2. Sensors 3 and 4 have similar designs as Sensor 2 except that Sensor 3 has a needle length of 50 mm and Sensor 4 has a needle length of 60 mm and a needle-to-needle spacing of 9 mm. The drawings are in millimeters but not to scale.
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The outer needles of the thermo-TDR sensor enclosed chromel-constantan thermocouples (40 AWG) at the midpoint, and the central needle enclosed the resistance heater made of two loops of 38-gauge Nichrome 80 wire. The heat wire and thermocouples were kept in place with high-thermal-conductivity epoxy, which also served to provide water resistance and electrical insulation. A coaxial cable was connected to the sensor by soldering the inner conductor to the central needle and the shield to the two outer needles. A two-part casting resin was used for the sensor head (CR-600, Micro-Mark, Berkeley Heights, NJ). One sensor of each type was constructed and used for all the laboratory and field measurements.
Sensor Calibration
The distance between the central heater and the thermocouple (r) in the outer needles was calibrated using agar-immobilized water (5 g L–1), assuming that the volumetric heat capacity of the agar–water solution was equal to the volumetric heat capacity of water (4.18 MJ m–3 C–1) (Campbell et al., 1991; Ren et al., 2003a). The heat pulse was generated by a direct-current power supply for 15 s. A datalogger (Model CR23X, Campbell Scientific, Logan, UT) controlled the heat input and measured the temperatures of the thermocouples. The value of r was calculated to fit the temperature increase as a function of time using a nonlinear regression method (Welch et al., 1996). The measurements were repeated 10 times at 60-min intervals, and the mean of the 10 measurements was used for thermal property calculation. To reduce the uncertainties caused by spacing changes, the r values were recalibrated in agar-immobilized water after 8 to 10 measurements (insertions) on soil samples.
The electrical length (La) of the thermo-TDR sensor was obtained using a Tektronix 1502C cable tester (Tektronix, Beaverton, OR). The first reflection position (L0) of the TDR waveform (the transition point from the sensor head to the exposed waveguides) was located by shorting the three needles in air with a blade at the needle base (Robinson et al., 2003). The end reflection point (Lw) was determined by analyzing the TDR waveforms in distilled water using the WinTDR software (Or et al., 2001). The value of La was then calculated from the following relationship:
 | [1] |
where Vp was set to 0.99 to achieve the maximum measuring resolution of the instrument and K is the relative dielectric permittivity of water at the measurement temperature. For Sensors 1, 2, 3, and 4, the estimated La values were 40.7, 44.9, 53.7, and 64.9 mm, respectively.
Laboratory Evaluation
A laboratory experiment was conducted to compare the new thermo-TDR sensors with the original design on three soils: a sand, a silt loam, and a clay loam (Table 1
). The sand was collected from a reservoir bed (0–30 cm) nearby Beijing, China; the clay loam soil was sampled from the 200- to 220-cm soil horizon at the experimental farm of China Agricultural University, Beijing, China; and the silt loam soil was sampled from the surface layer (0–15 cm) of a tillage study plot in the Luancheng Agricultural Ecosystem Experimental Station, located in Hebei Province of China. Soil samples were air dried, ground, sieved through a 2-mm screen, moistened with distilled water, mixed thoroughly, and then packed into polyvinyl chloride cylinders (100 mm in diameter and 80 mm in height) with different water contents and bulk densities. The number of columns for the sand, silt loam, and clay loam soils was 16, 17, and 13, respectively. Table 1 lists the bulk density and water content ranges of the packed soil columns.
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Table 1. Particle-size distributions, organic matter (OM) content, bulk density (b) range, water content () range, and specific heat capacity (cs) of the laboratory soils. The cs values were determined from heat-pulse measurements on oven-dried soil samples.
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The packed columns were covered tightly and placed in a temperature-regulated room (20 ± 1°C) for 24 h before obtaining measurements. For c and measurements, the thermo-TDR sensor was inserted into the soil columns vertically. The heat pulse (15 s) in the central needle was generated by a direct current supply. The datalogger controlled the heat input, monitored the temperatures of thermocouples every second, and recorded the voltage drop across a precision resistor that was used to determine the heat input to the central needle. The magnitude of the heating power was adjusted manually to maintain the temperature increases in the outer needles in the range of 0.6 to 0.9°C. For a given soil column, the measurements were repeated three times at 60-min intervals. Meanwhile, the cable tester was connected and the two reflection points were manually recorded. The process was repeated for each of the four sensors. Finally, the gravimetric water content and bulk density of the soil column was determined by oven drying the soil sample for 24 h at 105°C.
Field Evaluation
The performances of the four thermo-TDR sensors were evaluated on a long-term tillage experimental site at the Luancheng Agricultural Ecosystem Experimental Station of the Chinese Academy of Sciences, located in Hebei Province of China. The soil was the same silt loam as listed in Table 1. The study, initiated in 2001, included three tillage treatments under winter wheat (Triticum aestivum L.): conventional tillage, rotary tillage, and zero tillage.
Field measurement of soil bulk density was conducted in the summer of 2007 after winter wheat harvest. Sensors were installed in trenches about 300 mm long, 200 mm wide, and 200 mm deep. The sensors were pushed into the soil horizontally at 50-mm depth, with about 100-mm spacing between neighboring sensors. Heat-pulse and TDR measurements were then completed following the same procedure as in the laboratory except that a 12-V battery was used to produce the heating power, and the heat pulse length for Sensor 1 was reduced from 15 to 8 s to maintain a temperature increase at the outer needles of <0.9°C. When heat-pulse and TDR measurements were completed, undisturbed soil samples were collected using ring samplers (50 mm long and 50-mm diameter), pushed in horizontally at each location where thermo-TDR sensors were installed. The core samples were used to determine soil bulk density and water content gravimetrically. The same procedure was repeated at the 150-mm depth. Four replicated measurements were made for each tillage treatment.
Calculation
Soil c was calculated by applying the HPC code to fit the measured temperature change as a function of time (Welch et al., 1996). As a sensor had two temperature-measuring needles, each heat-pulse measurement produced two c data. Thus, for a specific laboratory column, each sensor was inserted and three repeated heat-pulse measurements were taken at 60-min intervals, creating six c data for each sensor. For the field study, four trenches were excavated in each tillage treatment. The four sensors were inserted at the first depth in a trench and heat-pulse measurement was conducted once for each sensor. The same was done at the second depth. This generated eight c data at each depth from a specific sensor. We used the mean of the six data for laboratory study results and the mean of the eight data for field study results. Consequently, each data point reported here represents an average of multiple heat-pulse measurements. The Topp equation was used to calculate from TDR-measured dielectric permittivity (Topp et al., 1980).
The thermo-TDR technique for determining the bulk density follows the theory that the volumetric heat capacity of the soil can be calculated by summing the heat capacities of the solids, water, and air (de Vries, 1963). Since the density and specific heat capacity of air are very small relative to the other terms, the contribution of soil air is negligible (Campbell et al., 1991):
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Then b can be estimated by (Ochsner et al., 2001)
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where w (1.0 Mg m–3) and cw (4.18 kJ kg–1 K–1) are the density and the specific heat capacity of water, respectively, and cs (kJ kg–1 K–1) is the specific heat capacity of the soil solids. Because cs is related to soil texture and organic matter content, the accuracy of c can be improved using specific c values determined from heat-pulse measurements on dry soils (Ren et al., 2003b). In this study, the cs values were measured on oven-dried soil samples and the results are presented in Table 1.
Sensor performance was evaluated by RMSE and relative error (RE) of soil bulk density estimates:
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where T-TDR is the thermo-TDR-estimated bulk density value, grav is the gravimetrically determined bulk density value, and n is the number of the data points.
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RESULTS AND DISCUSSION
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Soil Bulk Density Measurements
Soil bulk density estimates from the thermo-TDR sensors were compared with gravimetrically determined bulk density values for the laboratory soil samples (Fig. 2
). For all of the sensors, b data were distributed randomly along the 1:1 lines, indicating that the thermo-TDR technique was able to capture the trend of the gravimetric soil bulk density. Comparing the four sensors, Sensor 2 gave results that showed the highest degree of agreement with gravimetric values, followed by Sensors 3 and 4. The largest discrepancy was associated with Sensor 1. The RMSE of thermo-TDR b values was 0.125, 0.051, 0.097, and 0.097 Mg m–3 for Sensors 1, 2, 3, and 4, respectively. On the silt loam, clay loam, and sand soils, the RMSE of b estimates from Sensor 2 compared with gravimetric measures of b were 0.055, 0.051, and 0.046 Mg m–3, respectively. Our analysis also indicated that the b errors of Sensors 1, 3, and 4 were generally within 10% of the gravimetric b, but some data points had errors >15% of the gravimetric b. For Sensor 2, except for one data point, the relative errors of thermo-TDR b values were <5%.
The sensors were able to capture the gravimetric bulk density trends in the field experiment (Fig. 3
). Compared with the laboratory results, however, there was a relatively larger scattering of data for all of the field sensors. For example, the RMSE of thermo-TDR-estimated b was 0.152, 0.095, 0.137, and 0.117 Mg m–3 for Sensors 1, 2, 3, and 4, respectively. The relative b errors of Sensor 2 were mostly within 10% of the gravimetric values, but many b values of Sensors 1, 3, and 4 had errors >10% of the gravimetric values.
The performance of the four thermo-TDR sensors on laboratory and field studies indicates that although extension of needle length improves the measurement accuracy of thermo-TDR-determined b, the most effective improvement comes from increasing the needle diameter.
Influence of Water Content Measurement Error
Equation [3] indicates that the errors of thermo-TDR-estimated b are associated with the accuracies of TDR and heat-pulse c, assuming w, cw, and cs are constants. Therefore we examined the data from the thermo-TDR sensors (Fig. 4
). The RMSE values of Sensors 1, 2, 3, and 4 were 0.016, 0.016, 0.013, and 0.011 m3 m–3, respectively, indicating that the accuracy of values from the thermo-TDR technique increased with increasing needle length. Even though Sensor 4, the sensor with the longest needles, provided the most accurate values, all of the thermo-TDR sensors provided relatively accurate values. Even for Sensor 1, the worst case, the relative errors of thermo-TDR were generally within 10% of the gravimetric values.
Influence of Heat Capacity Data on Soil Bulk Density
We also examined the c data measured from the thermo-TDR sensors. The data were compared with values calculated from Eq. [2], where gravimetrically determined and b values were used, and the soil cs was taken from Table 1. A positive linear relationship existed between thermo-TDR c data and theoretical values, but the degree of scattering differed dramatically among the four sensors (Fig. 5
). For Sensors 1, 2, 3, and 4, the RMSE values were 0.112, 0.047, 0.088, and 0.092 Mg m–3, respectively, in the laboratory study, and 0.169, 0.077, 0.148, and 0.120 Mg m–3, respectively, in the field study. It was evident that the newly designed thermo-TDR sensors performed better than the Ren et al. (1999) sensor, and Sensor 2 gave the most accurate data. These results concur with the estimated b data, demonstrating that the major error in thermo-TDR-estimated b stems from the inaccuracies in c measurement. Furthermore, the smaller errors in Sensor 2 compared with Sensors 3 and 4 lead to the conclusion that needle diameter, not needle length, is the key to reducing the uncertainties in thermo-TDR-measured c and b. This may be caused by the fact that the change in needle-to-needle spacing at sensor insertion is the major source of error in heat-pulse-measured c (Kluitenberg et al., 1993, 1995; Ren et al., 2003a; Ham and Benson, 2004).
Other Sources of Error
Some differences between thermo-TDR-estimated b and gravimetric b may be due to the sampling volume difference between the thermo-TDR technique and the gravimetric method. According to the analysis of Campbell et al. (1991), the outer boundary of the heat-pulse method is about 2.37 times the value of r, the spacing between heater needle and sensor needle, assuming that the maximum temperature change at the outer boundary is 1% of the maximum temperature change at r. Laboratory investigation by Ren et al. (2005) confirmed that for the Ren et al. (1999) thermo-TDR sensor (Sensor 1), the outer boundary was within 14 and 11 mm for heat-pulse and TDR measurements, respectively. These analyses indicated that the outer boundary of our thermo-TDR sensors was <30 mm (Sensor 1) or 40 mm (Sensors 2, 3, and 4). In the laboratory study, the gravimetric b data were obtained from measurements on the whole soil column, which was much larger than the outer boundary of the thermo-TDR sensor. Since the columns were packed carefully, we did not expect variation in sampling volume to cause major errors in the b data. For the field study, the collecting volume of the ring sampler was a cylinder with a diameter of 50 mm, slightly larger than that of the thermo-TDR sensor. As a result, b data from the thermo-TDR might not completely represent the actual b value that is usually characterized by field spatial heterogeneity. This may partly explain why the data in Fig. 3 show a greater degree of scatter than the data in Fig. 2.
Another source of error may come from the ring sampler method. For the current work, we took the gravimetrically determined b as "actual b" to evaluate the thermo-TDR estimates. Although we followed the standard procedures carefully, some operative error during the sampling and drying processes is unavoidable. Soil compaction leading to overestimation of the "actual b" was a possibility during sampling. Furthermore, it was common to find plant roots in the undisturbed soil cores. Because roots and other soil organic materials decompose during the oven-drying process, the ring sampler method might at times underestimate the "actual b." In this regard, the estimates from the thermo-TDR technique seem to be quite representative of the actual field bulk density.
The HPC code applies a nonlinear fitting procedure to calculate soil c from the temperature increase in the outer needles (Welch et al., 1996). This procedure is sensitive to measurement accuracy in soil temperature. In our field study, due to the difference in sensor dimensions, the 12-V battery produced various temperature increases in the outer needles: 0.7 to 0.8°C for Sensors 1 and 2, 0.5 to 0.6°C for Sensor 3, and 0.3 to 0.4°C for Sensor 4. Compared with the other sensors, the c data from Sensor 4 might include relatively larger errors because of temperature measurement noise.
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CONCLUSIONS
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The linear relationship between c and has been applied for estimating soil b using the thermo-TDR technology. We evaluated the performance of four types of thermo-TDR sensors for measuring b. Experimental results from laboratory and field studies indicated that the new prototype sensors (Sensors 2, 3, and 4) increased the accuracy of b estimates; however, results from the sensor with a needle diameter of 2 mm, needle length of 40 mm, and needle-to-needle spacing of 8 mm showed the closest match with gravimetric data. The relative error of the estimated b from this specific design was within 5 and 10% of measured b under laboratory and field conditions, respectively. The b errors from the thermo-TDR were attributed mainly to the uncertainties in c data, a consequence of the changes in needle-to-needle spacing at sensor insertion into the soils. The thermo-TDR technique provides a valuable tool for obtaining soil temperature, water content, thermal properties, and bulk density, as it allows in situ, direct, rapid, and automated measurements.
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NOTES
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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 September 11, 2007.
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ABSTRACT
INTRODUCTION
