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Published online 16 November 2005
Published in Vadose Zone J 4:1059-1069 (2005)
DOI: 10.2136/vzj2004.0141
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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SPECIAL SECTION: SOIL WATER SENSING

Standardizing Characterization of Electromagnetic Water Content Sensors

Part 2. Evaluation of Seven Sensing Systems

J. M. Blonquist, Jr.*, S. B. Jones and D. A. Robinson

Dep. of Plants, Soils and Biometeorology, Utah State University, 4820 Old Main Hill, Logan, UT, USA 84322-4820
* Corresponding author (jmarkb{at}cc.usu.edu)

Received 28 September 2004.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Transmission line-type electromagnetic (EM) methods for estimating soil volumetric water content ({theta}v) have advanced significantly in recent years, with many sensing systems now available. To estimate {theta}v, EM systems make use of the dependence of soil dielectric permittivity on {theta}v. However, a standard method for characterizing and comparing EM system measurement capability has not been established. Our objective was to evaluate the permittivity measurement ability of seven different EM sensing systems using readily available media. Sensing system outputs were converted to real permittivity ({epsilon}') values and compared with reference {epsilon}' values in lossless and lossy dielectric liquids under four different test conditions: nonrelaxing and nonconducting (NR-NC), relaxing and nonconducting (R-NC), nonrelaxing and electrically conducting (NR-C), and temperature variation in NR-NC. The higher frequency broadband sensing systems, consisting of two time domain reflectometry (TDR) systems and one time domain transmissometry (TDT) system, deviated from a network analyzer by less than ±2.94 {epsilon}' units across a {epsilon}' range of 12.7 to 78.5 in NR-NC media. Two lower frequency impedance sensing systems deviated from the network analyzer by less than ±3.94 {epsilon}' units across a {epsilon}' range of 12.7 to 36.5 in the same media. Measurement of {epsilon}' using higher frequency broadband sensing systems was impacted more by bulk electrical conductivity ({sigma}b) and temperature (T) than by dielectric relaxation. Imaginary permittivity values (due only to relaxation, {epsilon}''rel) of up to 14.5 in R-NC media resulted in {epsilon}' errors of ±0.511, whereas {sigma}b values ranging from 0 to 2 dS m–1 in NR-C media resulted in {epsilon}' errors of ±2.69 and T values ranging from 5 to 40°C resulted in {epsilon}' errors of ±4.89. Determination of {epsilon}' using lower frequency sensing systems—including one transmission line oscillator, two impedance probes, and one capacitance probe—was impacted more by {sigma}b than by T and {epsilon}''rel. For the lower frequency sensors (and the same ranges of {sigma}b, T, and {epsilon}rel), {sigma}b resulted in {epsilon}' errors of ±111, T resulted in {epsilon}' errors of ±6.59, and {epsilon}''rel resulted in {epsilon}' errors of ±3.28. The effects of {epsilon}''rel, {sigma}b, and T on permittivity measurement accuracy is to a large extent dependent on measurement frequency, with higher frequency broadband sensing systems generally yielding better measurements.

Abbreviations: EM, electromagnetic • NR-C, nonrelaxing and electrically conducting • NR-NC, nonrelaxing and nonconducting • R-C, relaxing and conducting • R-NC, relaxing and nonconducting • TDT, time domain transmissometry • TDR, time domain reflectometry


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
IT HAS BEEN ESTABLISHED that for many coarse-textured mineral soils there is a strong relationship between the dielectric permittivity ({epsilon}; all permittivity values discussed herein are relative to free space) determined with transmission line–type EM sensors and soil volumetric water content ({theta}v) (Topp et al., 1980; Malicki et al., 1996). This is due to the strong contrast between the permittivity of water ({epsilon} {approx} 80), mineral soil solids ({epsilon} {approx} 2–9), and air ({epsilon} {approx} 1). Two-step (i.e., relation of measured property to {epsilon} and {epsilon} to {theta}v) and direct calibrations (i.e., relation of measured property to {theta}v) are used in estimating {theta}v from EM signal measurements (e.g., travel time, impedance, capacitor charge time, oscillation frequency, frequency shift). For accurate {theta}v estimations, sensing systems must make accurate EM signal property measurements that can be accurately related to {theta}v. Fellner-Feldegg (1969) demonstrated that transmission line methods, specifically TDR, could be employed to measure {epsilon} of liquids. Topp et al. (1980) extended TDR measurements to soils and empirically related TDR-estimated {epsilon} to {theta}v. Estimates of {theta}v using TDR have been shown to be quite accurate, with the error reported at less than ±0.02 m3 m–3 in many coarse-textured mineral soils (Topp et al., 1980, 1982; Hook and Livingston, 1995).

Since the Topp et al. (1980) seminal work in soils, much effort has focused on improving the {epsilon}–{theta}v relationship (Roth et al., 1990; Dirksen and Dasberg, 1993; Jacobsen and Schjonning, 1993; Whalley, 1993; Heimovaara et al., 1994; Malicki et al., 1996; Friedman, 1998; Ponizovsky et al., 1999). Work has also focused on evaluating EM sensing system performance in a number of soils at varying {theta}v ranges (Evett et al., 2002; Leib et al., 2003; Walker et al., 2004). However, EM signal measurements are sensitive to factors (e.g., dielectric relaxation, electrical conductivity, and temperature) beyond {theta}v, and signal measurements must be accurate before relation to {theta}v. For this reason Jones et al. (2005) proposed a standard method employing measurements in liquids to characterize and compare EM sensing system measurements. Liquids provide homogeneous backgrounds, as opposed to soils, which may enhance unwanted noise and uncertainty in the measurements because of secondary factors (Jones and Or, 2002, 2003). Liquids also eliminate contact problems between the medium and probe, which may occur in soils. Our objective was to demonstrate and test the proposed method of Jones et al. (2005) for characterizing and comparing EM signal measurement accuracy and range by applying it to seven different {theta}v sensing systems.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Sensing Systems Considered
The sensing systems considered are a TDR cable tester (1502B Metallic Cable Tester, Tektronix Inc., Beaverton, OR) connected to a custom three-rod probe with 0.15-m-long, 3.20-mm-diam. rods and 12.0-mm rod spacing; a second TDR instrument (TDR100, Campbell Scientific Inc., Logan, UT) connected to the same probe described above; a TDT system (Digital TDT Moisture Sensor, Acclima Inc., Meridian, ID); a transmission line oscillator (CS616 Water Content Reflectometer, Campbell Scientific Inc.); an impedance probe (Hydra Soil Moisture Probe, Stevens Water Monitoring Systems Inc., Beaverton, OR); a second impedance probe (Theta Probe type mL2x, Dynamax Inc., Houston, TX); and a capacitance probe (ECH2O Probe model EC-20, Decagon Devices Inc., Pullman, WA) (Table 1, Fig. 1) .


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  		Table 1. Principle of operation, required equipment, and cost breakdown for the sensing systems considered in the study.

 


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  		Fig. 1. Probes of the sensing systems considered in the study are from left to right: Acclima Digital TDT Sensor, three-rod TDR probe used with Tektronix TDR and TDR100 (0.15-m-long 3.20-mm-diam. rods, 12.0-mm rod spacing), CS616, ECH2O Probe, Hydra Probe, and Theta Probe.

 
The EM signal properties (i.e., travel time, period, impedance, and charge time) measured by the sensing systems listed are directly related to the {epsilon} of the medium in which they are embedded. The TDR and TDT sensing systems measure the travel time (t) of a broadband EM signal propagating along the probe and relate t to apparent permittivity (KTDR), which subsequently relates to {theta}v. Calculation of KTDR (= real permittivity, {epsilon}', in lossless media) from t (s) measurements is accomplished according to:

[1]
where c is the speed of light in vacuum (3 x 108 m s–1) and Le is electrical length of the probe (m). With TDR the signal is reflected at the end of the probe and the return signal is sampled. The factor 2 in the denominator of Eq. [1] accounts for the two-way (down and back) travel time of the signal. With TDT the signal travels the length of the probe once and the transmitted signal is sampled; thus the factor of 2 is omitted from Eq. [1]. It should be noted that both the Tektronix 1502B and the TDR100 account for the two-way travel time internally, and waveforms are output to display one-way travel. Thus, the factor of 2 is omitted from Eq. [1] for the TDR systems as well.

The waveforms measured with the Tektronix TDR were captured and interpreted for travel time with WinTDR waveform analysis software (Or et al., 2003) on a personal computer. The waveforms measured with the TDR100 were interpreted for travel time with PCTDR software (available with purchase of TDR100) on a personal computer. The waveforms measured with the Acclima TDT were captured and interpreted for travel time measurement via custom firmware developed by Acclima and contained in the sensor head. Custom software developed by Acclima (available with purchase of the Acclima system) was used to download data with the use of personal computer. Determination of the electrical length (Le) and travel time of the signal in the sensor head for the three-rod probe used with the Tektronix TDR and the TDR100, and the Acclima TDT, was conducted using measurements in air and deionized water according to the method described in Heimovaara (1993) and Robinson et al. (2003a). This procedure is outlined in Jones et al. (2005), and t values measured with the described software and firmware were adjusted based on this procedure. Further detail concerning TDR systems and measurements is given in Robinson et al. (2003b) and further detail concerning the Acclima TDT system is given in Blonquist et al. (2005).

The CS616 Water Content Reflectometer is a transmission line oscillator and operates similarly to TDR systems. Transmission line oscillators generate a voltage pulse inside the sensor head which propagates along the waveguide, with the arrival of the reflected pulse triggering the next pulse. The number of voltage pulse reflections over a certain time interval is recorded and a period (microseconds) that is inversely related to the number of reflections per second is output. The period is directly related to {theta}v via empirical calibration. Both a linear and a quadratic calibration equation relating period to {theta}v are reported (Campbell Scientific, Inc., 2002–2003). It should be noted that the actual frequency of the EM signal pulse generated by the CS616 is not reported. A more detailed treatment of measurements with water content reflectometers is presented in Seyfried and Murdock (2001) in which they test and compare six CS615s in air, ethanol, and four soils.

The Hydra Probe measures the ratio of reflected voltage to incident voltage of a 50-MHz signal, which is dependent on the impedance of the medium between the probe rods (Seyfried and Murdock, 2004). The Hydra Probe outputs four voltage values (V1, V2, V3, and V4) with V1, V2, and V3 characterizing the capacitive and conductive properties of the medium and V4 relating to temperature (Stevens Vitel, Inc., 1994). Custom software is employed to empirically calculate the real and imaginary parts of the permittivity and bulk electrical conductivity ({sigma}b) from the output voltage values (Stevens Vitel, Inc., 1994). Estimation of {theta}v is accomplished via the software using an empirical calibration with real permittivity as the input value. A more detailed treatment of the Hydra Probe is presented in Seyfried and Murdock (2004), in which they test and compare three Hydra Probes in several fluids and four soils, and in the article by Seyfried et al. (2005).

The Theta Probe measures the voltage amplitude difference (between the section of transmission line inside the sensor head and at the boundary between the sensor head and probe rods) of a 100-MHz signal, which is dependent on the impedance of the medium between the probe rods (Gaskin and Miller, 1996). The Theta Probe outputs a single voltage value that is related to permittivity (KTheta) via the following empirical relationship (Delta-T Devices Ltd., 1999):

[2]
where V is volts. To estimate {theta}v with the Theta Probe, media specific calibration with estimated KTheta values and known {theta}v values or use of established {theta}v prediction equations is required. A more detailed treatment of the Theta Probe is given in Gaskin and Miller (1996).

The ECH2O Probe measures the charge time of a capacitor that uses the medium surrounding the probe as the dielectric material (Decagon Devices, Inc., 2002). The ECH2O Probe outputs a single voltage value and directly relates this value to {theta}v via an empirical equation (Decagon Devices, Inc., 2002). It should be noted that the signal frequency at which the ECH2O Probe operates is not reported. McMichael and Lascano (2003) tested and compared four ECH2O Probes in water, two soils, and a potting medium.

For the CS616, Hydra Probe, Theta Probe, and ECH2O Probe power was supplied, measurements were triggered, and period or voltage was recorded via connection to a Campbell Scientific CR23X data logger connected to a personal computer. Each sensing system's principle of operation, the equipment required for operation, and cost comparisons of the systems (for single measurements and for simultaneous measurements with eight sensors) are summarized in Table 1.

Test Conditions
The measurements for the sensing system comparison were made under temperature controlled test conditions consisting of NR-NC media simulating nonsaline, sandy soils; R-NC media simulating lower conductivity, clayey soils; and NR-C media simulating saline, sandy soils. Temperature effects in the NR-NC media were also characterized by varying the temperature. With each sensing system, we made three repetitions of each measurement at each point under the different test conditions, and the three repetitions were averaged to yield the measurement value for the given point.

The NR-NC media were made using fractions of deionized water mixed into 2-isopropoxyethanol with the permittivity extremes ({epsilon}s = 12.7 and {epsilon}s = 78.5, where {epsilon}s is the static real part of the permittivity) coming from pure 2-isopropoxyethanol and pure deionized water, respectively. The NR-C media were made from two mixtures ({epsilon}s = 40.0 and {epsilon}s = 78.5) of these same fluids and dissolving pre-determined amounts of NaCl into the solutions to create {sigma}b ranging from 0.0 to 2.0 dS m–1. The R-NC media consisted of glycerol ({epsilon}s = 46.5), Brasso (Reckitt Benckiser, Slough, Berkshire, UK) ({epsilon}s = 28.0), and 1-propanol ({epsilon}s = 22.8). We attempted to synthesize a relaxing and conducting (R-C) media that simulated high conductivity, clayey soils by dissolving NaCl into the R-NC media, but were unable to reach {sigma}b levels above approximately 0.3 dS m–1. The test media, their associated properties, and the temperature ranges measured in the media during the sensor measurements are summarized in Table 2. Further detail concerning test conditions and media is provided in Jones et al. (2005).


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  		Table 2. Medium components, properties, and temperature (T) ranges for the different test conditions (NR-NC, nonrelaxing and nonconducting; NR-C, nonrelaxing and electrically conducting; R-NC, relaxing and nonconducting).

 
Network analyzer (Hewlett-Packard, Beaverton, OR, model 8752C network analyzer connected to model 85070B dielectric probe) measurements of the frequency dependent real ({epsilon}') and imaginary parts ({epsilon}'') of the permittivity of the described NR-NC and R-NC media were modeled with the Cole–Cole model (Hasted, 1973; Heimovaara, 1994; Eq. [9] in Jones et al., 2005). The Cole–Cole model was fit to the measured network analyzer data to provide media dependent parameter values and frequency dependent {epsilon}' and {epsilon}'' values for the range of operating frequencies of the sensing systems considered in the study. The network analyzer covers a frequency range of 300 kHz to 6 GHz, spanning the frequency ranges of the sensing systems. The network analyzer measurements and Cole–Cole model are described in further detail and the models and parameter values are shown in Jones et al. (2005).

Frequency Determination, Response Modeling, and Accuracy Assessment
Sensing system frequencies were determined to produce response models as explained in Jones et al. (2005). The maximum passable frequency (fmax) was determined for the two TDRs connected to a 0.15-m-long three-rod probe (fmax is probe dependent) and the Acclima TDT in NR-NC media (ranging from {epsilon}s = 12.7 to {epsilon}s = 62.8) by matching KTDR (= {epsilon}' in NR-NC media) data from the sensing systems to frequency dependent {epsilon}' from the network analyzer and averaging the results (Table 3). The fmax is the highest frequency component of the broadband signal and is the frequency at which measurements are made when tangent line fitting is used to determine permittivity from travel time. Greater detail concerning fmax determination for the two TDRs and TDT is found in Blonquist et al. (2005) and Jones et al. (2005). Frequencies for the Hydra Probe and Theta Probe (Table 3) are the reported frequencies (Stevens Vitel, Inc., 1994; Delta-T Devices Ltd., 1999; respectively). Frequencies for the CS616 and ECH2O Probe (Table 3) were approximated from rise times of the incident voltage pulse of 2 ns (Campbell Scientific, personal communication, 2004) and 8 ns (Decagon Devices, personal communication, 2004), respectively, according to (Bogart et al., 2004):

[3]
where f is the frequency (Hz) of the signal corresponding to a measurement in air ({approx} fmax in NR-NC media) and tr is rise time (s). Equation [3] is often used in electrical engineering to describe the frequency characteristics of a low-pass filter and is only accurate when the voltage signal energy is equally distributed across the frequency bandwidth. This is not necessarily the case for the CS616 and ECH2O Probe; therefore, the frequencies calculated with Eq. [3] are only estimates. Additionally, the frequency estimates from Eq. [3] are for the EM signal before it passes from the sensor head into the medium; the signal frequency likely changes (decreases) in the medium. However, in NR-NC media the frequency change is likely small, and knowing an exact frequency at which the lower frequency sensing systems operate is not essential when deriving a response model due to the minimal dispersion observed in NR-NC media below a frequency of approximately 500 MHz (Jones et al., 2005).


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  		Table 3. Response models used to predict real permittivity ({epsilon}') values from output travel time, period or voltage for each sensing system.

 
Responses in NR-NC media for each sensing system were produced by plotting network analyzer {epsilon}' data, taken at the frequency determined (Table 3) for each sensing system, as a function of the sensing system outputs (i.e., travel time, period, voltage) as explained in Jones et al. (2005). Response models (Table 3) for each sensing system were produced by fitting an equation to the {epsilon}' vs. output data. Root mean squared error (RMSE) values were calculated to indicate how well the response models fit the data. The response models were used as {epsilon}' prediction equations for all subsequent tests. The same response model is used for the two TDRs and Acclima TDT and is derived from Eq. [1] omitting the factor of 2 and setting Le = 0.15 m. It should be noted that the travel times for the Acclima TDT are divided by a factor of 4 to account for the longer probe length (0.60 m). The response models for the lower frequency sensing systems are empirical equations fit to the data using TableCurve (Jandel Scientific, San Rafael, CA).

The outputs of the sensing systems (excluding the CS616 and ECH2O Probe; whose manufacturers do not provide information for calculating permittivity from sensor output) from the NR-NC media test were converted to {epsilon}' values using Eq. [1] for the two TDRs and Acclima TDT, custom software for the Hydra Probe and Eq. [2] for the Theta Probe. The outputs from the R-NC media, NR-C media, and temperature varying NR-NC media tests were input into the derived response models to produce a predicted sensor {epsilon}' value (for the Hydra Probe the {epsilon}' calculated by the custom software was used). The measurement accuracy of each sensing system under the different test conditions is inferred by calculating a residual value for each measurement in each test. The residual value is the difference between the reference and {epsilon}' predicted by the sensing system being considered, and from these residual values, RMSE values are computed (Eq. [15] in Jones et al., 2005). For the NR-NC media (including the temperature variation test) and R-NC media, the Cole–Cole models fit to the network analyzer measurements (Jones et al., 2005) serve as the reference. For NR-C media the {epsilon}' value predicted by the given sensing system when medium {sigma}b = 0.0 dS m–1 serves as the reference.

Sensor Measurement Weighting and Sampling Volume
The approximate sampling volume of each probe was estimated according to the method presented in Jones et al. (2005). Briefly, this method employs the use of a computer program, the Arbitrary Transmission Line Calculator (ATLC) (Kirkby, 1996; 2003), which numerically calculates EM energy density distributions surrounding a specific transmission line geometry; and a Matlab (Mathworks, Natick, MA) function (Humphries, 2004), which calculates the cross-sectional area within a specified minimum EM energy density contour. For our calculations we used a 10% EM energy density contour; thus, the cross-sectional area contains all the values of EM energy density that are >10% of the maximum value. The sampling volume is calculated by multiplying the cross-sectional area by the physical length of the probe. The CV within the cross-sectional area is calculated by dividing the standard deviation of the EM energy density by the mean. The CV indicates the uniformity of the EM energy density surrounding the probe and is referred to as the measurement weighting.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
NR-NC Media
The maximum residuals and RMSE values for the NR-NC media (Table 4) indicate the accuracy of each sensing system in such media. The results indicate that, compared with the modeled {epsilon}' values, the higher frequency broadband and lower frequency sensing systems both estimate {epsilon}' values reasonably well (Fig. 2 and 3) . The network analyzer dielectric probe error is reported as ±4 {epsilon}' units within the frequency ranges or at the operating frequencies of the sensing systems considered. The Tektronix TDR, TDR100, Acclima TDT, Hydra Probe, and Theta Probe all estimate {epsilon}' within this range (Table 4), with the Theta Probe deviating the least and the Hydra Probe deviating the most from the modeled {epsilon}' data. It should be noted that the CS616 and ECH2O Probe were excluded in the NR-NC test (Table 4, Fig. 3) because the manufacturers do not provide information for permittivity determination.


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  		Table 4. Maximum residual (reference – prediction) of real permittivity ({epsilon}') and RMSE values for each sensing system.

 


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  		Fig. 4. Response models fit to the NR-NC media data for the (a) higher frequency broadband sensing systems (model is Eq. [1] fit to the data using an electrical length, Le, of 0.15 m and where the travel times measured with the Acclima TDT are divided by a factor of four to account for 0.60-m waveguide length), (b) CS616, (c) Hydra Probe (response model was not derived for the Hydra Probe because it uses three output voltage values to derive permittivity and the details concerning how this is accomplished were not available from the manufacturer), (d) Theta Probe and ECH2O Probe. The models for the CS616, Theta Probe, and ECH2O Probe are empirical equations fit to the data with TableCurve (Jandel Scientific, San Rafael, CA).

 


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  		Fig. 2. Deviation of higher frequency broadband sensing system {epsilon}' predictions from the modeled network analyzer {epsilon}' measurements (reference) in nonrelaxing and nonconducting (NR-NC) media. The frequencies from which the reference {epsilon}' measurements were taken are in parentheses and are maximum passable frequencies (fmax).

 


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  		Fig. 3. Deviation of the lower frequency sensing system (excluding CS616 and ECH2O Probe) {epsilon}' predictions from the modeled network analyzer {epsilon}' measurements (reference) in nonrelaxing and nonconducting (NR-NC) media. The frequencies from which the reference {epsilon}' measurements were taken are in parentheses and are reported sensor frequencies. The x axis ranges from 0 to 80 to indicate the measurement range compared with the higher frequency broadband sensing systems (Fig. 2). Note that the CS616 and ECH2O Probe are excluded because the manufacturers do not provide information for permittivity determination.

 
In relation to accurate EM signal property measurements, {theta}v prediction depends on a particular sensing system's ability to measure contrast as {theta}v changes. The response models (Fig. 4a–4d) show that it is possible to detect {epsilon}' differences over the entire range of permittivity covered in NR-NC media. However, there is much greater travel time (Fig. 4a) and period contrast (Fig. 4b) than there is output voltage contrast (Fig. 4c and 4d) above {epsilon}' {approx} 40 ({epsilon}' {approx} 25 for the ECH2O Probe; Fig. 4d). The Tektronix TDR, TDR100, Acclima TDT, and CS616 showed good contrast for the entire permittivity range, allowing the potential for accurate {theta}v prediction for the entire permittivity range found in soils ({epsilon}' {approx} 2–60). The Hydra Probe, Theta Probe, and ECH2O Probe showed minimal output voltage contrast in the permittivity range of {epsilon}' {approx} 40 to {epsilon}' {approx} 80. This implies that {theta}v prediction with these sensing systems in media with {epsilon}' >40 will be difficult to perform with high accuracy. While it is likely that most soils have {epsilon}' values within the 2 to 40 range, soils with high clay and/or organic matter contents and high porosity artificial growth media can have {epsilon}' values within the 40 to 80 range. In practice, media specific calibrations are often required due to the significant variation of dielectric properties among different porous media over the {theta}v range from saturated to oven dry. The response models give good indication of the approximate {epsilon}' ranges and limits that the sensing systems considered should be used within.

R-NC and NR-C Media and Temperature Effects in NR-NC Media
Sensing system accuracy is also dependent on contrast caused by effects (i.e., relaxation, {sigma}b, temperature) other than {theta}v changes. Relaxation has minimal effects on the high frequency broadband sensing system {epsilon}' estimates (Table 3), with errors increasing slightly as {epsilon}''rel increases (Fig. 5) . However, the fmax decreases from the reported values (Table 3) to approximately 500 MHz for the two TDRs and 200 MHz for the Acclima TDT, owing to filtering of the higher frequency signal components brought about by energy dissipation during relaxation (Robinson et al., 2003b). In contrast, {epsilon}''rel has greater effects on the Hydra Probe and Theta Probe (Table 4), causing both overprediction and underprediction of {epsilon}' values as {epsilon}''rel increases (Fig. 6) . It should be noted that the CS616 and ECH2O Probe were excluded in the R-NC test (Table 4, Fig. 6) because their measurement frequencies in R-NC media cannot be estimated from Eq. [3] or network analyzer data because the manufacturers do not provide information for permittivity determination.



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  		Fig. 5. Deviation of higher frequency broadband sensing system {epsilon}' predictions (from response model) from modeled network analyzer {epsilon}' measurements (reference) in relaxing and nonconducting (R-NC) (Table 2) media as relaxation increases. The frequencies from which the reference network analyzer {epsilon}' measurements were taken are the individual maximum passable frequencies (fmax) of the sensing systems in the three R-NC media samples (glycerol, Brasso, and 1-propanol). It should be noted that the fmax values in R-NC media are reduced by approximately 1 GHz compared with the nonrelaxing and nonconducting (NR-NC) media.

 


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  		Fig. 6. Deviation of lower frequency sensing system (excluding the CS616 and ECH2O Probe) {epsilon}' predictions (from software for Hydra Probe and response model for Theta Probe) from modeled network analyzer {epsilon}' measurements (reference) in relaxing and nonconducting (R-NC) media (Table 2) as relaxation increases. Note that the CS616 and ECH2O Probe are excluded because their measurement frequencies in R-NC media and cannot be estimated from Eq. [3] or inferred from network analyzer data (manufacturers do not provide information for permittivity determination).

 
Electrical conductivity ({sigma}b) affects the higher frequency broadband sensing systems to a greater extent than {epsilon}''rel (Table 4), with {epsilon}' being underpredicted by the Tektronix TDR and overpredicted by the TDR100 and Acclima TDT as {sigma}b increases (Fig. 7 and 8) . The effects of {sigma}b are more pronounced in the lower permittivity media ({epsilon}s = 40.0) (Fig. 7) compared with the higher permittivity media ({epsilon}s = 78.5) (Fig. 8). The reason is inferred from the transmission line equation for a sinusoidal wave used as an analogy for transmission of a TDR signal (Eq. [6] in Jones et al., 2005). As {epsilon}' decreases, the ratio of the losses (i.e., {epsilon}''rel and {sigma}dc, where {sigma}dc = {sigma}b and is the dc frequency electrical conductivity) to {epsilon}' increases, thus modifying estimated permittivity to a greater extent. This phenomenon is demonstrated in Fig. 5 of Robinson et al. (2003b).



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  		Fig. 7. Deviation of higher frequency broadband sensing system {epsilon}' predictions from the {epsilon}' prediction where electrical conductivity ({sigma}b) = 0.0 dS m–1 (reference) as nonrelaxing and conducting (NR-C) sample {sigma}b increases from 0.0 to 2.0 dS m–1. The NR-C sample used here has a {epsilon}s = 40.0 (Table 2).

 


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  		Fig. 8. Deviation of higher frequency broadband sensing system {epsilon}' predictions from the {epsilon}' prediction where electrical conductivity ({sigma}b) = 0.0 dS m–1 (reference) as nonrelaxing and conducting (NR-C) sample {sigma}b increases from 0.0 to 2.0 dS m–1. The NR-C sample used here has a {epsilon}s = 78.5 (Table 2).

 
The lower frequency sensors are much more sensitive to {sigma}b than {epsilon}''rel (Table 4), except for the Hydra Probe, which showed similar sensitivities to {sigma}b and {epsilon}''rel. Excluding the Hydra Probe, the lower frequency sensors are much more sensitive to {sigma}b than the higher frequency broadband sensors (Table 4). Increasing {sigma}b causes {epsilon}' overprediction with the CS616 and ECH2O Probe and {epsilon}' underprediction with the Hydra Probe and Theta Probe in the lower permittivity ({epsilon}s = 40.0) media (Fig. 9 and 10 ; note the scale differences between these two figures and between Fig. 7 and 8). As stated above, the Hydra Probe estimates {sigma}b from the output voltage values and likely corrects {epsilon}' based on {sigma}b estimates, yielding accuracies similar to the higher frequency broadband sensing systems in NR-C media. In the higher permittivity ({epsilon}s = 78.5) NR-C media the CS616 overpredicts {epsilon}' (graphical data not shown). It should be noted that NR-C media data for the Hydra, Theta, and ECH2O Probes in the higher permittivity media are not shown because {epsilon}s = 78.5 is beyond the measurement range of these sensors (Fig. 4c–4e).



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  		Fig. 9. Deviation of lower frequency sensing system (excluding ECH2O Probe; see Fig. 10) {epsilon}' predictions from the {epsilon}' prediction where electrical conductivity ({sigma}b) = 0.0 dS m–1 (reference) as nonrelaxing and conducting (NR-C) sample {sigma}b increases from 0.0 to 2.0 dS m–1. The NR-C sample used here has a {epsilon}s = 40.0 (Table 2).

 


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  		Fig. 10. Deviation of ECH2O Probe {epsilon}' predictions from the {epsilon}' prediction where electrical conductivity ({sigma}b) = 0.0 dS m–1 (reference) as nonrelaxing and conducting (NR-C) sample {sigma}b increases from 0.0 to 2.0 dS m–1. The NR-C sample used here has a {epsilon}s = 40.0 (Table 2).

 
Temperature (T) affects {epsilon}' predictions of the higher frequency broadband sensing systems to about the same magnitude as {sigma}b (Table 4). Temperature <35°C causes {epsilon}' overprediction and T >35°C generally causes {epsilon}' underprediction in the lower permittivity ({epsilon}s = 40.0) media (Fig. 11) . The trend is reversed in the higher permittivity ({epsilon}s = 78.5) media; T < 25°C causes {epsilon}' underprediction and T > 25°C causes {epsilon}' overprediction (Fig. 12) . The observed trend reversal may be due in part to the relative temperature independence of the NR-NC media ({epsilon}s = 40.0) between approximately 1 and 2 GHz caused by a temperature dependent shift in relaxation. For the lower frequency sensing systems, the temperature effects in the lower permittivity media are similar to those observed for the higher frequency broadband sensing systems (Table 4). Temperature <25°C generally causes {epsilon}' overprediction and T > 25°C generally causes {epsilon}' underprediction, except for the CS616 where overprediction was observed across the entire range (Fig. 13) . In the higher permittivity media, T effects cause underprediction of {epsilon}' at T < 25°C and slight overprediction at T > 25°C for the CS616 (graphical data not shown). Why the higher frequency broadband sensing systems and the CS616 {epsilon}' predictions do not fall near the reference at 25°C in the lower permittivity media is unknown (Fig. 11 and 13). The T range for the measurements in NR-NC media used to derive the response models is near 25°C (Table 2), and thus {epsilon}' predictions in the temperature varying NR-NC media test should be near the reference at 25°C. It should be noted that data for T variation in NR-NC media for the Hydra, Theta, and ECH2O Probes in the higher permittivity media are not shown for the same reason given above for the higher permittivity NR-C media.



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  		Fig. 11. Deviation of higher frequency broadband sensing system {epsilon}' predictions from modeled network analyzer {epsilon}' measurements in nonrelaxing and nonconducting (NR-NC) media with a temperature (T) range of 5.38 to 39.5°C (Table 2). The NR-NC sample used here has a {epsilon}s = 38.5 to 41.3 (Table 2).

 


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  		Fig. 12. Deviation of higher frequency broadband sensing system {epsilon}' predictions from modeled network analyzer {epsilon}' measurements in nonrelaxing and nonconducting (NR-NC) media with a temperature range of 5.05 to 40.0°C (Table 2). The NR-NC sample used here has a {epsilon}s = 73.4 to 86.1 (Table 2).

 


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  		Fig. 13. Deviation of lower frequency sensing system {epsilon}' predictions from modeled network analyzer {epsilon}' measurements in nonrelaxing and nonconducting (NR-NC) media with a temperature (T) range of 5.38 to 39.5°C (Table 2). The NR-NC sample used here has a {epsilon}s = 38.5 to 41.3 (Table 2).

 
The observed differences between the Tektronix TDR and TDR100 {epsilon}' predictions (Table 4) are likely software related. The waveforms measured by the two TDR systems are nearly identical; thus, the maximum residuals and RMSE values for the Tektronix TDR (Table 4) indicate that WinTDR software is superior to PCTDR software in interpreting measured waveforms. It is possible to interpret waveforms measured with each TDR sensing system with the same software (TACQ; Evett, 2000a, 2000b), but we considered software developed for use with certain systems (i.e., WinTDR for Tektronix TDRs and PCTDR for TDR100) as part of the sensing system.

Sampling Volume and Measurement Weighting
The Acclima TDT probe has a much larger estimated sampling volume than the other probes, while the ECH2O Probe has the smallest estimated sampling volume (Table 5). The coefficient of variation of the EM energy density (CV E{rho} in Table 5) is the measurement weighting of each probe. The lower the CV E{rho} value, the more uniform the EM energy, which should yield a more uniformly weighted measurement. In contrast, a higher CV E{rho} value indicates more EM energy concentrated near the probe rods (i.e., "skin" effect) and a measurement more heavily weighted to the media immediately surrounding the rods. The Acclima TDT shows the most uniform energy density while the Theta Probe shows the least uniform. The probe used with the two TDRs, the Hydra Probe, and the CS616 all have similar uniformity. The CV E{rho} value reported for the ECH2O Probe does not account for the plastic material surrounding the probe and is likely higher than what is reported. Those probes that display increased measurement weighting near the probe rods (high CV E{rho}) increase the possibility for measurement error because soil near the rod surfaces is subject to greater disturbance during insertion, or nonuniform packing around the rods can occur if the medium is excavated to embed the probe.


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  		Table 5. Sampling volume and measurement weighting within a 10% electromagnetic energy density contour for each sensor.

 

   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
A standard methodology for characterizing and comparing transmission line-type EM sensors designed for estimating soil volumetric water content ({theta}v) was proposed by Jones et al. (2005). We demonstrated and tested this methodology by comparing seven sensing systems according to their measurement capabilities in media simulating conditions often observed in soils. The conditions included accuracy and range testing in NR-NC media simulating nonsaline, sandy soils and the effects of dielectric relaxation in R-NC media simulating low conductivity, clayey soils and electrical conductivity in NR-C media simulating saline, sandy soils. The effects of temperature varying conditions in NR-NC media were also tested. Attempts were made to produce R-C media simulating high conductivity, clayey soils in which the combined effects that these two phenomena have on measurements could be characterized. For reasons detailed in Jones et al. (2005) we were unable to produce R-C media.

Under NR-NC test conditions (including temperature variation), the higher frequency broadband sensing systems (two TDR systems and one TDT system) and the lower frequency sensing systems (one transmission line oscillator, two impedance probes, and one capacitance probe) showed similar measurement accuracy, with the TDRs, TDT, and transmission line oscillator covering a larger real permittivity ({epsilon}') range (1–80) than the others. The results from the R-NC, NR-C, and temperature varying NR-NC test conditions indicate that for higher frequency systems, electrical conductivity ({sigma}b) and varying temperature (T) have similar and greater effects on {epsilon}' predictions than does relaxation . The results indicate that for lower frequency sensing systems {sigma}b has the greatest effect on {epsilon}' predictions, while varying T and {epsilon}rel'' have similar effects. Compared with the higher frequency systems, the lower frequency systems were generally limited in the {epsilon}' range (<40) in which they can measure and were generally more sensitive to {sigma}b and {epsilon}rel'', especially {sigma}b, under which condition all but one of the lower frequency sensing systems were extremely sensitive. This indicates that the frequency at which measurements are made is essential to accuracy in these media.

Calibration of EM sensors to estimate {theta}v is often a two-step process involving first relating the measured EM signal property to {epsilon}' and second relating {epsilon}' to {theta}v. Conversely, some sensing systems employ a calibration from the measured signal property directly to {theta}v. With either two-step or direct calibration, the measured signal property is sensitive in some degree to {epsilon}rel'', {sigma}b, and T, leading to potential errors in {theta}v prediction if conditions vary from the calibration conditions. In addition, the permittivity determined is often sensor dependent and represents an apparent permittivity dependent on both {epsilon}' and imaginary permittivity ({epsilon}''). Based on the findings herein we suggest that more attention should be given to separation of {epsilon}' and {epsilon}'' because it is {epsilon}' that directly relates to {theta}v. We also suggest that the measurement frequency should be increased because measurements are more sensitive to {epsilon}rel'' and {sigma}b at lower frequencies.


   ACKNOWLEDGMENTS
 
This project was supported by National Research Initiative Competitive Grant no. 2002-35107-12507 from the USDA Cooperative State Research, Education, and Extension Service and by the Utah Agricultural Experiment Station, Utah State University, Logan, UT 84322-4810. The authors extend special thanks to Bill Mace, Seth Humphries, and Robert Heinse for their help in setting up the experiment and making the measurements and to Scott Anderson and Dr. Jim Ayers for technical assistance. The authors also extend special thanks to the guest editor Dr. Steve Evett, Dr. Thijs Kelleners, and two anonymous reviewers for carefully reviewing the manuscript and providing many helpful comments and insights.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 




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