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Published online 16 May 2007
Published in Soil Sci Soc Am J 71:894-900 (2007)
DOI: 10.2136/sssaj2006.0420
© 2007 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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SOIL PHYSICS

Temperature-Dependent Scaled Frequency: Improved Accuracy of Multisensor Capacitance Probes

A. Faresa,*, H. Hamdhania and D. M. Jenkinsb

a Natural Resources & Environmental Management Dep., Univ. of Hawaii-Manoa, 1910 East West Rd., Honolulu, HI 96822
b Molecular Bioscience and Bioengineering Dep., Univ. of Hawaii at Manoa, 1955 East West Rd., Honolulu, HI 96822

* Corresponding author (AFares{at}Hawaii.edu).


   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 
The response of multisensor capacitance probes (MCPs) to water content depends on multiple soil properties including temperature. The goal of this study was to evaluate a new temperature-dependent scaled frequency algorithm to correct for the temperature effect on the performance of MCPs. Plastic columns with MCPs and thermocouples in the middle were filled with air, deionized water, or quartz sand at different water contents (0.0, 0.02, 0.04, 0.06, 0.08, 0.12 and 0.38 m3 m–3) and placed in a water bath with temperature varying between 5 and 45°C. Scaled frequency (SF) readings in saturated sand (0.38 m3 m–3) were negatively correlated with temperature. There were positive correlations observed, however, between isothermal SF readings and media temperature for air and unsaturated quartz sand. Temperature effects in the unsaturated sand decreased with increasing water content; observed SF for quartz sand at 0.0 and 0.12 m3 m–3 water contents increased 58 and 4%, respectively, when temperature increased from 5 to 45°C. A hysteretic temperature effect was observed in all tested media. A new temperature-dependent SF calibration methodology that we developed mitigated the increase in apparent water content caused by the use of the isothermal SF calibration equation. Our experimental data indicate that quartz sand temperature effects on apparent volumetric water content measured with MCPs can be mitigated using this new temperature-dependent SF methodology.

Abbreviations: MCP, multisensor capacitance probe • SF, scaled frequency


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
MATERIAL AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 
During the last two decades, capacitance soil water monitoring sensors have been gaining ground and have proved to be very popular as research and teaching tools with the scientific community, as well as for application in a wide range of agricultural, environmental, and engineering practices. Their widespread use has resulted partly from the simplicity, speed, and nondestructive nature of their measurement compared with the conventional gravimetric method.

Currently, capacitance sensors are commercialized as single and multisensor capacitance probes with different installation and monitoring techniques. Capacitance soil water sensors respond to the dielectric permittivity ({varepsilon}) of soil–water–air mixtures, and estimate soil water content from this response. The {varepsilon} of water (78.54 at 22°C) is large compared with those of the soil matrix (<10) and air (1), and thus dominates the {varepsilon} of the air–soil–water mixture. A change in soil water content will strongly influence the {varepsilon} of soil. The great spatial variability of soil minerals, soil organic matter content, and soil bulk electric conductivities, however, makes it necessary to calibrate these sensors for a particular soil and, if practical, for each soil horizon.

Despite their widespread use, several studies indicate that the capacitance method is influenced by soil physical properties such as temperature, bulk density, and salinity (Fares and Polyakov, 2006). Temperature in particular can have a large influence on water content measurement, especially under variable soil temperature conditions (Baumhardt et al., 2000; Evett et al., 2006). Studies investigating temperature effects on other electromagnetic methods, e.g., time domain reflectometry (TDR), have received ample attention (Pepin et al., 1995; Wraith and Or, 1999; Gong et al., 2003); however, few studies have been conducted on the effects of temperature and salinity on capacitance sensors and especially on these new MCPs.

The effect of soil temperature on capacitive systems has been reported for some soil types. Baumhardt et al. (2000), in a diurnal soil temperature fluctuation experiment in Olson soil, reported a temperature effect on a specific MCP type. They found a positive relationship between the capacitance sensor reading and the monitored soil temperature. Paltineanu and Starr (1997) reported that temperature effects on capacitance sensors might be negligible within the temperature range of 10 to 30°C. Seyfried and Murdock (2001) showed that there were no identified temperature effects on the measured values of volumetric soil water content for sand, while for various other soils the effect was strongly positive, resulting in a large apparent water content variation across a 40°C temperature change. Using an MCP, Polyakov et al. (2005) reported 15 and 10% overestimation of soil water content due to temperature effects using a manufacturer's default calibration for Ewa silty clay loam and silica sand, respectively. Correction of temperature effects might be implemented with a calibration equation, if soil temperature were measured along with water content.

Seyfried and Murdock (2001) reported relatively smaller temperature effects on readings of their reflectometer in four different soils. Evett et al. (2006) reported variable sensitivity of different electromagnetic soil water content sensors. Two capacitance sensors, EnviroSCAN and Diviner 2000 (Sentek Sensor Technologies, Stepney, SA, Australia), were moderately sensitive to temperature at the saturated end; however, the Delta-T PR1/6 (Delta-T Devices, Cambridge, UK) and Trime T3 (IMKO Micromodultechnik GmbH, Ettlingen, Germany), a capacitance and a TDR sensor, respectively, were quite sensitive to temperature fluctuations. Polyakov et al. (2005) suggested that an integrated temperature and capacitance sensor would be able to detect temperature changes in the surrounding soil and achieve dependable water content measurement.

Based on an electric circuit theory study, Kelleners et al. (2004) reported that the dependence of the capacitance sensor on ionic conductivity implies that the sensor is sensitive to changes in media temperature. Also, a small decrease of resonant frequency of the capacitive probes, which is associated with an apparent increase in water content, may be attributed to temperature effects on the sensor's circuitry (Dean et al., 1987).

The objectives of this study were: (i) to evaluate the effects of media temperature on the apparent water content measured with an MCP, and (ii) to correct quartz sand temperature effects using a temperature-dependent scaled frequency.


   MATERIAL AND METHODS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 
This study was conducted at the Watershed Hydrology Laboratory, Natural Resources and Environmental Management Department, College of Tropical Agriculture and Human Resources, University of Hawai'i at Manoa.

Multisensor Capacitance Probe
The principles of operation and design of the MCP were described by Fares and Polyakov (2006), and the manufacturer's calibration manual (Sentek Pty Ltd, 2001). The MCP system enables the user to operate up to 32 sensors (e.g, eight probes with four sensors each) simultaneously. A single probe consists of a printed circuit board, four pairs of electrodes as capacitance sensors, and a polyvinyl chloride (PVC) access tube. Sensors are set at 10, 20, 30, and 50 cm from the soil surface. During installation, a single probe is inserted into a 60-cm-long access tube with internal and external diameters of 28 and 32 mm, respectively. The capacitive electrodes are interfaced with the printed circuit board to form an oscillator with an on-board inductor. A time-varying electric field is generated between the two electrodes and extends beyond the access tube wall into the soil medium. The capacitance sensors are designed to resonate in excess of 100 MHz inside the access tube in free air.

The resonant frequency of an oscillator circuit that includes the soil can be represented as follows (Kelleners et al., 2004):

Formula 1[1]
where Cm, Cp, and Cs are the capacitances (in Farads [F]) of the medium, plastic access tube, and capacitance due to stray electric fields, respectively. The observed frequency is then used to determine a SF, defined as

Formula 2[2]
where Fa, Fw, and Fs are the frequency readings of the sensor (inside the PVC tube) in air, water, and soil, respectively, at room temperature (22°C).

The value of the SF varies between 0 and 1 depending on the air/water ratio of the medium, with SF positively correlated with water content. The scaled frequency is then used in a calibration equation to estimate the corresponding soil water content. Under the default setting, volumetric water content ({theta}v) can be calculated using the following factory-supplied calibration, which was established based on calibration in a variety of soils:

Formula 3[3]

Correction of Temperature Effect
The following temperature-dependent SF was used to replace the manufacturer's isothermal SF equation:

Formula 4[4]
where SF(T) is the scaled frequency at temperature T, Fa(T), Fw(T), and Fs(T) are the frequencies of the sensor at temperature T in air, water, and the medium (i.e., sand or soil), respectively. Thus, for a given temperature, the corresponding frequencies of the sensor in air, soil, and water were used.

Calibration equations were used to convert the SF(T) reading of the MCP into volumetric water content (m3 m–3). Two- (Morgan et al., 1999; Paltineanu and Starr, 1997) and three-parameter (Fares et al., 2004; Baumhardt et al., 2000) power models have been used as calibration models for MCPs. The latter models were proven to be superior (Fares et al., 2004; Polyakov et al., 2005). Thus, a three-parameter power model was used in this study to relate SF and {theta}v as follows:

Formula 5[5]
where A, B, and C are fitted coefficients. Consequently, nine temperature-dependent calibration equations were developed, using a 5°C temperature increment, for the temperature range of 5 to 45°C. These new calibration equations are referred to as adjusted calibration equations. We then conducted three regression analyses to quantify the relationship between the fitted coefficients (A, B, and C) of the nine adjusted calibration equations (Eq. [5]) and the sand temperature across the range of 5 to 45°C. Thus, for a given sand temperature, we can use the corresponding fitted coefficients (A, B, and C) for the temperature-adjusted calibration equation (Eq. [5]) across the range of 5 to 45°C.

Experimental Procedure
Deionized Water and Air Measurements
The MCP system used in this study was a Sentek EasyAg 50 (Sentek Pty Ltd, South Australia). The MCPs were tested in deionized water and air. During the testing, MCP sensors were subjected to heating and cooling cycles between 5 and 45°C. This temperature testing range should help in identifying sensor sensitivity in extreme soil temperature. Testing the response of the sensors to air temperature enabled us to establish the response of the sensor's circuitry to temperature changes independent from media effects because the dielectric constant of air does not vary appreciably with temperature.

Quartz Sand Measurements
The MCP readings were logged in quartz sand at seven different water contents ranging from dry to saturation (0.00, 0.02, 0.04, 0.06, 0.08, 0.12 and 0.38 m3 m–3). Starting from oven-dried sand for each treatment, water was added to obtain 0.02, 0.04, 0.06, 0.08, 0.12 and 0.38 m3 m–3 water content and then packed into PVC columns (32-cm height and 15 cm in diameter) with the access tube inserted in the middle of each soil column. To ensure uniform water content, sand and water were mixed to obtain a homogeneous mixture within 2 min; precautions were taken to reduce water losses during the mixing. Homogeneous bulk density was ensured throughout the soil columns by adding the sand and compacting it in small increments. The quartz sand in the columns was compacted uniformly to the targeted bulk density of 1.45 g cm–3. The top of the column was tightly covered with a lid to prevent water losses from the surface.

Heating and Cooling Treatments
The plastic columns with MCPs in the middle were placed in a 30- by 30- by 52-cm insulated plastic cooler used as a water bath for heating and cooling cycles. During the heating cycle, the temperature of water in the bath was increased from 5 to 45°C using regular submerged aquarium water heaters. The cooling cycle from 45 to 5°C was achieved by adding iced water incrementally. A fish-tank submerged pump was used to circulate water to obtain homogeneous temperatures throughout the water bath.

The MCPs were logged at 1-min intervals using the system's data logger, RT6. The temperature of the medium inside the column, of the MCP sensors inside the access tube, and of the water bath were continuously monitored using calibrated thermocouples connected to a CR10 data logger (Campbell Scientific, Logan, UT) at the same time interval (1 min) as the MCPs. The thermocouples were placed inside, 1 cm away from the access tube wall, in the core zone of influence of the proposed sensors (Fig. 1).


Figure 1
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  		Fig. 1. Schematic of the experimental setup. The multisensor capacitance probe (MCP) is inserted in the soil column, which is placed in the water bath.

 
Relationship between the Temperature of the Multisensor Capacitance Probe Sensors and the Temperature of the Media
To quantify the relationship between the temperature of MCP sensors inside the access tube and that of its surrounding medium (sand, air, or water), three MCP access tubes were inserted in the middle of three PVC columns, as described above, filled with air, deionized water, or sand at 0.04 m3 m–3 water content. These columns were inserted in the water bath. The temperature of the water bath was increased from 5 to 45°C and decreased back to 5°C using the same procedure described above. For each MCP access tube, we installed two thermocouples at the same depth, one inside the MCP access tube and one outside of it, approximately 1 cm away of its external wall and inside the medium (sand, air, or water). Thermocouples inside and outside the access tubes were monitored (at 1-min intervals) using a CR10 data logger.


   RESULTS AND DISCUSSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSION
CONCLUSION
 REFERENCES
 
The temperature inside the MCP access tube was correlated with that of the surrounding medium (air, water, or sand) using a linear regression equation of the form: Tinside = ATmedium, where A, Tinside, and Tmedium are the slope of the regression, and the temperature inside the MCP access tube and that in the medium (air, water, or sand), respectively. Results of these regressions proved that there was, at most, a 1% difference between temperatures inside the access tube and that of the surrounding medium as the slopes of these regressions were 1.012, 0.996, and 1.007 for air, water, and sand, respectively. These regression models were almost perfect, as their correlation coefficients were 0.998, 0.999, and 0.999 for air, water, and sand, respectively. It is clear that the temperature of the media within 1 cm of the wall of the access tube was the same as that of the MCP sensor inside the access tube. In the rest of the experiment, we monitored the temperature of the media using thermocouples placed 1 cm away from the wall of the access tubes and across the MCP sensors.

Effect of Media Temperature
Heating and Cooling Cycle Effect
A hysteretic effect was observed in the deionized water treatments (Fig. 2). A paired t-test was performed to check for differences in heating and cooling cycle readings in the deionized water. This test indicated a significant difference at P < 0.05 between the two. We observed an approximately constant difference of 0.0006 SF across the temperature range from 5 to 45°C.


Figure 2
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  		Fig. 2. Capacitance sensor scaled frequencies (SF) in deionized water treatment at varying temperatures of heating and cooling.

 
A more distinct hysteretic effect was observed in the air treatment (Fig. 3), again at P ≤ 0.05. In this treatment, differences between the SF readings due to hysteresis were larger at smaller temperatures, with observed differences of 0.023 and 0.015 at 5 and 45°C, respectively. A similar hysteretic effect was also observed in all water content treatments in quartz sand. The readings during heating and cooling cycles at each water content level were compared and found to be statistically different, based on a t-test, which gave a value of P < 0.05 at all water content levels. The hysteretic effect for sand at 0.02 m3 m–3 water content during a heating and cooling cycle is illustrated in Fig. 4. There was no specific consistent pattern of the hysteretic magnitude related to the quartz sand water content levels, however. A similar hysteretic effect was also observed by McMichael and Lascano (2003) with a different type of capacitance probe.


Figure 3
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  		Fig. 3. Capacitance sensor scaled frequencies (SF) in air treatment at varying temperatures of heating and cooling.

 

Figure 4
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  		Fig. 4. Hysteretic effect of the multisensor capacitance probe (MCP) output in the quartz sand treatment under heating and cooling cycles for a range of temperatures between 5 and 45°C.

 
Temperature Effects in Deionized Water
The sensor readings in deionized water showed a negative temperature effect. The regression models suggested that at least 99.6% of apparent water content variation can be explained by the variation of deionized water temperature during heating and cooling cycles. The sensitivity of the SF to temperature was –6.0 · 10–4 °C–1 during both heating and cooling. The calculated apparent volumetric water content data using the manufacturer's default calibration equation against the corresponding temperature showed that the slope was similar to that of the SF against the corresponding temperature (data not shown).

The negative relationship between temperature and apparent water content and SF is consistent with changes in the {varepsilon} of free water with temperature, as explained by Weast (1986). A similar negative temperature correlation in water was also observed by Pepin et al. (1995) using a different type of dielectric permittivity probe.

Temperature Effects in Air
There was a positive linear temperature effect on MCP SF readings in air (Fig. 3). In the heating and cooling treatments, approximately 92 and 95%, respectively, of the variability in measured SF were explained by temperature variation. The regression model indicates that the sensitivities of the SF to temperature were 6.0 x 10–4 and 4.0 x 10–4 °C–1 for heating and cooling, respectively. This positive correlation agrees with data reported by Campbell (2002) in a temperature response study using a different type of capacitance sensor. Since the dielectric constant of air is not affected by temperature, MCP response to changes in air temperature shows the response of the sensor's electronics to temperature changes. This is an important test for any field instrument that may be subjected to a wide range of temperatures.

Temperature Effects in Quartz Sand
Only the temperature effect in quartz sand in the cold to hot (heating) treatment is presented and discussed. A positive temperature effect on MCP readings was observed in the unsaturated quartz sand with the following treatments: 0.0, 0.02, 0.04, 0.08, and 0.12 m3 m–3 (Fig. 5). A two-parameter linear model was used to describe the temperature effect on the apparent water content of quartz sand for each water content using the following general equation:

Formula 5
[6]


Figure 5
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  		Fig. 5. Capacitance sensor output in (A) unsaturated and (B) saturated quartz sand based on the manufacturer's default calibration within the temperature range from 5 to 45°C.

 
where {alpha} and ß are fitting parameters and T is the media temperature (in °C). These linear models describe the effect of temperature on apparent water contents very well, with the lowest observed correlation coefficient of 0.96 (Table 1). The sensitivity of apparent water content to temperature was 3 x 10–4 m3 m–3 °C–1 across the temperature range of 5 to 45°C for low water contents (≤0.06 m3 m–3). Sensitivity decreased to 2 x 10–4 m3 m–3 °C–1 for the 0.08 m3 m–3 treatment, however, and further to just 1 x 10–4 m3 m–3 °C–1 for the 0.12 m3 m–3 treatment. In the saturated quartz sand, the apparent water content was negatively correlated with temperature (–8 x 10–4 m3 m–3 °C–1). This value is similar to the MCP dependence on deionized water temperature. Polyakov et al. (2005) reported 15% overestimation of the actual water content for silty clay loam soil at 0.26 m3 m–3 actual water content and 10% for quartz sand at 0.09 m3 m–3 water content across a 45°C temperature interval.


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  		Table 1. Coefficients of the linear relationship of quartz sand temperature (T) and apparent water content ({theta}v) at different water content levels in the cold to hot treatment, according to the equation is {theta}v(T) = {alpha}T + ß.

 
Working with a clayey soil and an EnviroSCAN MCP system, manufactured by the same manufacturer as the EasyAg system used in this study, Baumhardt et al. (2000) showed even larger temperature effects in nearly saturated soil than those in air-dried soil under diurnal air and soil temperature fluctuations. Evett et al. (2006) reported that water content determined with several TDR and capacitance devices, using both factory calibrations and their own calibrations, was linearly regressed vs. temperature for both air-dry and saturated endpoints at constant water content. They also added that soil type did not influence the relationship between reported water content and soil temperature of the EnviroSCAN system. It is important to notice that the range of the temperature used in the study of Evett et al. (2006) was 16°C, compared with 40°C used in this study.

Nine calibration equations, based on a 5°C increment for the test temperature range of 5 to 45°C, were developed for both temperature-adjusted (Eq. [4]) and unadjusted (Eq. [3]) data. Differences between the data of these two calibration methods at the boundary temperatures (5 and 45°C) are shown in Fig. 6A and 6B, respectively. The adjusted and unadjusted calibrations at 5°C show that using the default calibration equation (Eq. [3]), the capacitance sensor overestimates water content at water content <0.12 and >0.23 m3 m–3. At 45°C, the manufacturer's default calibration equation overestimates the water content reading for sand water content <0.16 m3 m–3 and underestimates it for water content larger than that. These results clearly illustrate the response of the MCP reading to quartz sand temperature and demonstrate the need for a temperature-dependent calibration equation.


Figure 6
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  		Fig. 6. The apparent water contents before and after adjustment using temperature-dependent scaled frequency calibration of multisensor capacitance probes in quartz sand at (A) 5 and (B) 45°C.

 
Results of the three regression analyses quantifying the relationship between the fitted coefficients (A, B, and C) for the calibration equation (Eq. [5]) and the sand temperature across the range of 5 to 45°C are shown in Fig. 7A, 7B, and 7C. The regression between the first two fitted coefficients A and B was linear; however, the regression between the third fitted coefficient, C, and sand temperature was nonlinear. For all three cases, the lowest regression coefficient was equal to 0.98, indicating that at least 98% of the variations of the fitted coefficients are due to sand temperature. Thus, if sand temperature is monitored, temperature-dependent fitted calibration coefficients can be determined based on the regression equations shown in Fig. 7A, 7B, and 7C and, consequently, the temperature effect on sensor readings will be mitigated.


Figure 7
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  		Fig. 7. Regression correlations describing the relationship between the values of the fitted calibration parameters for the multisensor capacitance probes and quartz sand temperature for the range of 5 to 45°C. The calibration equation is in the following form: water content = A + B(scaled frequency)C.

 
The use of temperature-dependant SF (Eq. [4]) and calibration (Eq. [5]) equations mitigated the effect of temperature on MCP readings (Fig. 8). Thus, the water contents estimated from the MCP outputs using the new method were nearly constant across the test temperature range (5–45°C) at all water content levels. Using the new method, the temperature effect was reduced by at least 92% to a complete elimination (Table 2). As this method was proven effective in mitigating the temperature effect of a cold to hot temperature change, the same approach could be applicable for the opposite temperature change (hot to cold). It is not likely, however, that calibration equations done for hot-to-cold transitions will work for cold-to-hot transitions. The use of temperature-dependent SF calibration equations is a successful method to mitigate the effect of the tested medium (quartz sand) temperature on the type of MCP tested in this work. This method needs to be further tested in different soil types with variable contents of clay and organic matter to test its universality. Adding a temperature sensor inside the access tube of these MCP systems might be worth further investigation.


Figure 8
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  		Fig. 8. Capacitance sensor output at (A) unsaturated and (B) saturated quartz sand after the temperature-dependant scaled frequency calibration was applied within the temperature range from 5 to 45°C.

 

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  		Table 2. Slope of the correlation between soil temperature and water content as determined by multisensor capacitance probes using the default calibration equation (before) and the calibration equation based on the temperature-dependent scaled frequency (after).

 

   CONCLUSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSION
REFERENCES
 
Media temperature influenced the apparent water content measured with MCPs for the tested temperature range (5–45°C). Temperature effects on both media (quartz sand and deionized water) were consistent with results reported in the literature. In unsaturated sand, apparent water content increased with increasing sand temperature; however, temperature effects were negative for deionized water and saturated quartz sand. The magnitude of the temperature effect decreased with increasing water content.

The use of a new temperature-dependent SF and calibration model was successful in eliminating the temperature effect by at least 92.3%. This new method allows the user of an MCP to improve the accuracy of their data. Our experimental data clearly indicate that ignoring media temperature during measurements of volumetric water content with an MCP can lead to substantial errors, particularly at low water content.


   ACKNOWLEDGMENTS
 
The project was supported by a grant from the USDA, Cooperative State Research, Education and Extension Service Grant no. 2005-34135-15974. We wish to thank Mohammad Safeeq and Samira Fares from the College of Tropical Agriculture and Human Resources at the University of Hawaii-Manoa for their assistance in preparing this manuscript.


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSION
 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 December 3, 2006.


   REFERENCES
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 




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T. Saito, H. Fujimaki, H. Yasuda, and M. Inoue
Empirical Temperature Calibration of Capacitance Probes to Measure Soil Water
Soil Sci. Soc. Am. J., October 21, 2009; 73(6): 1931 - 1937.
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