Published online 16 November 2005
Published in Vadose Zone J 4:1048-1058 (2005)
DOI: 10.2136/vzj2004.0140
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
SPECIAL SECTION: SOIL WATER SENSING
Standardizing Characterization of Electromagnetic Water Content Sensors
Part 1. Methodology
S. B. Jonesa,*,
J. M. Blonquist, Jr.a,
D. A. Robinsona,
V. Philip Rasmussena and
D. Orb
a Dep. of Plants, Soils and Biometerology, Utah State University, Logan, Utah
b University of Connecticut, Dep. of Civil and Environmental Engineering, Storrs, CT
* Corresponding author (scott.jones{at}usu.edu)
Received 28 September 2004.
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ABSTRACT
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Performance differences in the growing number of electromagnetic (EM) sensors designed to estimate soil water content from a variety of indirect measurements (e.g., from measured travel time, capacitance, frequency shift) suggests the need for a standardized sensor characterization methodology. We suggest that characterization and evaluation of EM sensors, which currently lack citable standards, be performed in a homogeneous fluid of known permittivity rather than in a porous medium of unknown permittivity. Our objectives were to (i) develop a methodology for evaluating EM sensor measurement attributes referencing sensor-specific characteristics and targeted soil properties and (ii) suggest standards for characterization and comparison of sensors. Criteria for qualitative assessment of sensors include determination of effective measurement frequency; susceptibility to variations in salinity, dielectric relaxation, and temperature; and a look at spatial variation in sensor sampling area. Measurement frequencies for broadband sensors can be inferred from correlated network analyzer and sensor measurements or from manufacturer suggestions. Fluids were selected to provide surrogate soil-related effects such as relaxation occurring both within and outside of the effective measurement frequency range of common sensors. Test conditions included dielectrically relaxing (R) and nonrelaxing (NR) as well as electrically conducting (C) and nonconducting (NC) liquids and combinations thereof (e.g., NR-C). No suitable combination of relaxing and conducting (R-C) dielectric fluid was found in this study, but this remains a goal of future work because it represents a difficult and often common condition for EM sensor measurements in soils containing contributors to relaxation (e.g., clays, organic matter). Standards are based on fluids of known (based on Cole–Cole parameters) or measurable (using a network analyzer) frequency dependent permittivity that provide a reproducible homogeneous system for immersion of EM sensors. The methodology described here was applied using seven different EM sensing systems, and results are given in a companion paper.
Abbreviations: ATLCC, Arbitrary Transmission Line Calculator • C, conducting • EM, electromagnetic • NC, nonconducting • NR, nonrelaxing • R, relaxing • TDR, time domain reflectometry • TDT, time domain transmissometry
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INTRODUCTION
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ELECTROMAGNETIC SENSORS determine volumetric water content, 
v, and in some cases bulk electrical conductivity, 
b, by measuring EM sensor response in the medium under consideration. The strong dependence of EM signal properties on volumetric water content, v (m3 m–3), stems from the high permittivity of free water (
fw 
80). Electromagnetic estimates of soil v and b have gained popularity as technology has improved. These sensors, including TDR, TDT, frequency domain, and capacitance devices, are valuable field and laboratory techniques for monitoring water and in some cases salinity. However, it is sometimes the case that a new sensor is promoted and distributed only to be disapproved of years later due to poor measurement performance. The cost to users in unreliable experimental results or reduced productivity for growers ultimately falls back on the company in the form of a damaged reputation. These costs could be minimized or avoided by appropriate assessment of sensors and dissemination of standardized performance criteria. Studies evaluating EM sensor performance have typically evaluated permittivity determinations in a number of soils over a range of water contents (Evett et al., 2002; Leib et al., 2003; Seyfried and Murdock, 2004). These studies are useful in demonstrating the general water content measurement capability in specific soils. However, these results are often misleading and conflicting due to confounding effects arising from bound water or salinity that can be disguised by soil-specific calibrations showing improved apparent sensor performance. The question we ask is, "Does the sensor provide a unique and therefore reliable permittivity response (e.g., voltage, travel time) from water content changes when temperature, salinity, and even soil type are also varied?" Establishing standards for testing and characterization of EM sensors will provide users with a reference by which to judge sensor measurement capability and perhaps categorize sensors according to key criteria affecting permittivity determinations.
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Permittivity vs. Water Content Calibration of EM Sensors
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It is important to note that almost all EM sensors infer permittivity from indirect measurements of travel time, impedance, capacitance, resonant frequency, frequency shift, and other indirect means. For v determination, permittivity assessment is often an intermediate step that is bypassed by sensors whose output (e.g., voltage, time) does not lead directly to a calculation of permittivity. Such sensors can provide accurate water content determination based on empirical and often soil-specific calibrations. However, permittivity is the physical property giving rise to v determination, and it is much easier to provide a known permittivity in which to measure (e.g., using dielectric liquids) than to provide a known water content in soil (i.e., due to soil heterogeneity or hydrostatic water distribution). We therefore suggest assessment of sensor quality should refer to accurate permittivity determination. Liquids serve as "ideal" dielectric media because of their well-defined dielectric properties, such as temperature dependence (Wohlfarth, 2004), sample homogeneity, consistency, and ease of acquisition. Liquids also lack the complications associated with soil, such as air gaps near conductors and density variations. Dielectric fluids such as air and distilled water have been used for calibration of EM sensors and verification of accurate permittivity determinations (Kaatze et al., 1996; Robinson et al., 2003b). These two extreme values of permittivity form bounds around most of the permittivities one expects to find in nature. Beyond permittivity calibration there is the need for calibration for v determination. Where the soil is coarse or medium textured in nature, the empirical relationship of Topp et al. (1980) is commonly employed to infer v from permittivity determinations. A physically based approach may also be taken using dielectric mixing models to derive the permittivity–v relationship (Friedman, 1998; Jones and Friedman, 2000). However, EM sensors that do not measure permittivity directly or that employ modifications such as rod coatings require additional soil dependent permittivity calibrations because of their nonlinear output. For end users the investment in time and resources to generate new soil-specific calibrations can be unappealing and difficult. Numerous references addressing the permittivity–v relationship and related factors affecting this relationship have been identified (Ferre et al., 1996; Heimovaara et al., 1996; Hilhorst, 1998; Jones et al., 2002; Or and Wraith, 1999; Robinson et al., 2003a; Topp et al., 1980). We will focus our presentation on characterization and calibration of sensors used for permittivity determination, avoiding further discussion regarding water content determination.
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Sensor Permittivity Calibration
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Travel-Time Measurement
Permittivity can be derived from measurement of the travel time of an EM signal propagating along a transmission line embedded in a medium. The propagation velocity (vp) of the signal transmitted by the sensing system is a function of the EM properties of the medium according to:
 | [1] |
where c is the speed of light in free space (3 x 108 m s–1), and and µ are the dielectric permittivity and magnetic permeability of the medium relative to free space. Most soils are nonmagnetic; thus, µ is equal to one and determines vp. We distinguish between the apparent sensor determined permittivity, Ka, and the permittivity of the medium of interest, . By rearranging Eq. [1] we solve for , which is assumed equal to Ka in soil that does not exhibit dielectric loss (i.e., lossless media). In Eq. [1] vp = Le/t, where t is travel time in the sample (s), and Le is the electrical length of the probe (i.e., length of conductor "seen" by the EM signal).
Travel time sensing systems require accurate determination of Le, which should be calibrated with deionized water and air because these two media bound the entire soil permittivity range (e.g., 2 < Ka < 60) in which measurements will take place. For travel time sensors this can be accomplished using the method of (Heimovaara, 1993) and (Robinson et al., 2003b). This method involves deriving a signal travel time correction factor (t0), accounting for signal travel in the sensor head, and Le from measurements in air and water. The following pair of equations (Robinson et al., 2003b) is solved for the unknown t0 and Le values:
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 | [3] |
where tp is the total travel time (s) of the signal and is a combination of t0 and travel time in the sample (ts), air is 1 for air permittivity and fw is temperature dependent free water permittivity calculated by the following equation (Weast, 1986):
 | [4] |
where T is temperature measured (°C). Subsequent Ka measurements are made by rearranging Eq. [2] to solve for Ka (replacing air) of the medium being measured and using the determined electrical length and measured travel time (ts = tp – t0) in the sample according to the following (Heimovaara and Bouten, 1990):
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Here the 2 accounts for a "reflection" measurement as in time domain reflectometry (TDR), and is omitted for one-way travel measurements used in time domain transmissometry (TDT). For consideration of the effect of dielectric loss Robinson et al. (2003a) suggested the following relation:
 | [6] |
where ' is the relative real part of the permittivity, ''rel is the imaginary part of the permittivity caused by relaxation losses, dc is the dc frequency electrical conductivity (S m–1), f is frequency (Hz), and 0 is the permittivity of free space (8.854 x 10–12 F m–1).
Other Sensors
Theoretically, for impedance or capacitance sensors permittivity is derived from measurement of the impedance (Z) of the probe embedded in a medium (Campbell, 1990):
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or the capacitance (C) of a circuit which uses the medium surrounding the probe as the dielectric material (Kelleners et al., 2005):
 | [8] |
where j = (–1)1/2, g is a geometric factor (m) associated with probe configuration, and the other variables are as described. Generally, impedance and capacitance sensors measure oscillation frequency or frequency shift, which is related to signal resistance, impedance, and capacitance. For this type of sensor, measurement output should be correlated with independently measured permittivity because the output response varies and is sensor dependent. Additional effects on permittivity determination include salinity and temperature. These effects would not be evident when performing soil-specific water content calibrations unless b and temperature were included in the measurement.
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Frequency-Dependence of Permittivity Determination
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Recent research has focused on frequency dependent permittivity determinations (e.g., using network analyzer) for greater information retrieval and improved v determination (Hook et al., 2004; Huisman et al., 2004; Logsdon and Laird, 2004; Starr et al., 2000). High end instruments such as network or impedance analyzers can be used to accurately determine frequency dependent complex permittivity of homogeneous systems such as liquids and powders. Dielectric probes having geometries that allow high frequency signal passage interface with network analyzers to measure intrinsic electrical properties of these materials and relate them to complex permittivity and loss tangent. However, the instruments are expensive, have limited measurement frequency ranges and often require precision probe geometries for permittivity determinations. The need for frequency dependent permittivity determinations is illustrated in Fig. 1
using bentonite clay, quartz sand, and talc at different water contents. The wet bentonite clay exhibits strong dielectric relaxation revealed in the large change in permittivity as a function of network analyzer measured frequency. This relaxation is related to a reduction in the apparent energy storage capacity of the system as sources of this energy storage such as molecular rotation and ion migration (e.g., Maxwell-Wagner effect) are unable to respond to the faster cycling of the electrical field, resulting in reduced permittivity at higher frequency. Very little relaxation is exhibited by most dry materials and even by some wet materials with low surface area, such as the sand and talc. This suggests that sensors measuring at different frequencies in dispersive porous media may predict vastly different v, assuming a standard calibration equation relating permittivity to v (Topp et al., 1980).
There are a number of factors that also influence the bulk permittivity determination that are worthy of consideration. The geometry and spacing of the electrodes along which the signal travels in the medium dictate the resulting electric field from which the permittivity determination is derived. Sensor design, including probe geometry, can have a significant impact on the permittivity determination (Pettinellia et al., 2002). Other effects include the influence of temperature and electrical conductivity on both the medium's permittivity and on the sensor output.
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Temperature Dependence of Permittivity Determination
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Temperature effects arise both from the temperature dependence of the medium (e.g., water, soil) and from the temperature dependent response of the sensor itself. The temperature effect on sensor performance can be characterized and potentially included in calibrations to account for soil temperature fluctuations. These effects can be significant under field conditions where daily diurnal temperatures fluctuate significantly, with maximum changes occurring near the surface and decreasing with depth. These effects should ideally be separated, but the physical connection between conductors and sensor circuitry in many instances makes this a difficult task. Information on sensor measurement accuracy and effective measurement frequency coupled with the frequency dependence of the medium being measured add to the difficulty of separating these two temperature effects.
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Soil-Specific Factors Affecting Permittivity Determination
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In many cases, poor sensor performance can be attributed to a sensor's inability to provide a unique permittivity–v relationship response (e.g., salinity or temperature changes modify this relationship or cause measurement frequency shifts) in soils that are often also poorly correlated to Topp et al.'s (1980) Ka–v relation, which many users assume as a default calibration. Properties of the soil, such as surface area, particle shape, and constituent configuration (layering) (Jones and Friedman, 2000; Jones and Or, 2002; Robinson and Friedman, 2001; Robinson et al., 2002), contribute to permittivity determination errors and ultimately erroneous v determination. Electrical conductivity of the soil solution can modify the permittivity, especially when measured at frequencies in the tens of megahertz range or less, due to Maxwell-Wagner effects associated with charge migration and build up at interfaces (Hilhorst, 1998). These effects can be amplified or even disguised by changes in temperature due to the temperature dependence of electrical conductivity and to the permittivity of the various forms of water (Or and Wraith, 1999). These confounding effects associated with soil, including gaps around sensor rods and other heterogeneities, should ideally be avoided when evaluating the sensor performance. Ultimately, the quality of EM sensor v(Ka) predictions depends largely on the sensor's ability to accurately determine water content on the basis of permittivity, and this ability should be quantified using a standard approach for the benefit of users.
The objectives of this research were to (i) develop a methodology for evaluating EM sensor measurement attributes based on sensor-specific characteristics (e.g., frequency- and temperature-dependence) and targeted soil properties (i.e., related to losses) and (ii) suggest standards for evaluation of sensor measurement performance. Four specific measurement conditions are suggested to be representative of most soils addressing the frequency band where many EM sensors operate and including effects of electrical conductivity, which when large enough can completely attenuate the measurement signal. The four target conditions created from dielectric liquids with the following designations are proposed: (i) NR-NC for nonrelaxing and nonconducting (e.g., sandy soil) conditions to provide unambiguous testing of sensors where permittivity is independent of frequency, (ii) R-NC for dielectrically relaxing and nonelectrically conducting conditions (e.g., low conductivity clayey and organic soils) to evaluate effects of dielectric relaxation on permittivity determination, (iii) NR-C for dielectrically nonrelaxing and electrically conducting conditions (e.g., saline sand) for evaluating effects of electrical conductivity on permittivity determination, and (iv) R-C for dielectrically relaxing and electrically conducting conditions (e.g., many fine-textured soils) for evaluating these combined effects which are commonly found in natural soils.
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THEORETICAL AND EXPERIMENTAL CONSIDERATIONS
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Measurement and Modeling of Frequency-Dependent Permittivity
Frequency dependent permittivities can be determined using network or impedance analyzers (e.g., Hewlett-Packard, Beaverton, OR, model 8752C) and dielectric probes (e.g., Hewlett-Packard, model 85070B). Temperature dependent permittivities of liquids may be measured in a nonmetallic (e.g., glass) container surrounded by a circulating water-filled radiator where temperature of the circulating water is adjustable.
For dielectrics exhibiting relaxation within the effective measurement frequency of the sensor, the Cole and Cole (1941) model describes the real and imaginary permittivity response of fluids with permanent electric dipole moments (Sihvola, 1999). The Cole–Cole model can be fitted to the frequency dependent permittivity data obtained with a network analyzer, providing complex permittivity parameters describing liquids and some porous materials. Fitting algorithms are common in mathematical software and in spreadsheets using optimization of model parameters (Weerts et al., 2001; Wraith and Or, 1998). The Cole–Cole model (Hasted, 1973; Heimovaara et al., 1994) can also be used to describe frequency dependent real (') and imaginary components ('') of permittivity from the complex expression:
 | [9] |
where s is the static permittivity, 
is the infinite (i.e., high frequency) permittivity, f is frequency (Hz), frel is the relaxation frequency (Hz), and 
is a parameter that corresponds to the dispersion in the relaxation frequency range. Permittivity is described as a complex number containing both real and imaginary parts. The real component (') of complex permittivity (*) is dependent on dielectric material energy storage, and the imaginary component ('') of complex permittivity is dependent on energy loss arising from electrical conductivity and heat dissipation arising from dielectric relaxation phenomena (Robinson et al., 2003a):
 | [10] |
where the term in parentheses is the combined imaginary component (''). The permittivity estimated by EM sensors, Ka, is some combination of ' and '', the magnitude of each being dependent on the sensor circuit design. Figure 1b illustrates network analyzer measured ' and '' in bentonite clay at 30% volumetric water content and modeled *, ', and '' results. In this case the imaginary losses 
are significant. For lossless media ('' negligible), we assume Ka approximates '. For this condition, the Cole–Cole model is fit to measured network analyzer data to facilitate determination of what we refer to as the maximum passable frequency, fmax. The modeling reduces noise in the network analyzer measurements and describes these data as a continuous function. The determination of fmax is achieved by correlating the frequency associated with the intersection of Ka on the ' curve described by the Cole–Cole model, described in the following.
Maximum Passable Frequency (fmax) Determination
Evaluation of sensor permittivity determination performance is based on the dielectrically relaxing or electrically conducting conditions described in the introduction. Determining sensor effective measurement frequency is critical to understanding and characterizing the permittivity determination performance, especially in frequency dependent dielectrics. For the NR-NC condition (i.e., Ka = '), the effective measurement frequency for TDR has been suggested to correspond to the intersection of the TDR measured Ka and the network analyzer measured real permittivity, '(f), as illustrated in Fig. 2
(Or and Rasmussen, 1999; Robinson et al., 2003a). Robinson et al. (2003a) termed this the maximum passable frequency (fmax) related to the highest "unfiltered" frequency being reflected back to the TDR. This approach is only applicable to nonrelaxing media because relaxation effects tend to shift the effective frequency to reduced values associated more with the signal group velocity (Robinson et al., 2005). For travel time measurements (TDR, TDT), the mean maximum passable frequency can be derived from averaging multiple determinations of fmax in NR-NC liquids of varied permittivity. The coefficient of variation of fmax is the standard deviation divided by the average frequency.
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Fig. 2. Example of sensor measurement frequency determination by relating TDR measured permittivity (Ka) to the Cole–Cole modeled network analyzer data (symbols), yielding what is termed the maximum passable frequency for travel time instruments.
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Test Conditions
Sensor evaluation criteria are related to the four soil related effects discussed above, which are associated with relaxation and electrical conductivity. Liquids that were evaluated and tested are listed under each of the four conditions shown here:
NR-NC.
2-Isopropoxyethanol (99%, Aldrich Chemical, St. Louis, MO) and deionized water solutions can be used to ascertain sensor performance in NR-NC media. The solutions are prepared by measuring the desired volumes of each liquid and thoroughly mixing them together before permittivity determinations are conducted (frequent mixing is required to avoid separation). For further detail concerning the described solutions the reader is referred to (Kaatze et al., 1996).
NR-C.
Sodium chloride (100%) was mixed with different solutions listed in Table 1 to generate electrically conductive mixtures, both nonrelaxing and relaxing. The amounts were varied depending on the solution where lower dielectric solutions exhibited reduced NaCl solubility. Periodic mixing was found to be important to assure spatially uniform concentrations. For the NR-C condition, 2-isopropoxyethanol and deionized water solutions and pure deionized water were mixed with NaCl according to Table 2. Linear regression was used to obtain the following two equations describing the amount of NaCl required to obtain solution electrical conductivity, b, (Orion conductivity meter model 150A and Conductivity Cell 013005D; Thermo Orion, Beverly, MA) in a 60% 2-isopropoxyethanol:water solution
 | [11] |
and in deionized water
 | [12] |
where CNaCl is grams of sodium chloride in 1 L of solution.
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Table 1. Cole–Cole parameters (Eq. [9] fitted to network analyzer measurements in nonrelaxing mixtures of 2-isopropoxyethanol and water and in relaxing dielectric liquids shown.)
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R-NC.
Network analyzer measured and Cole–Cole modeled permittivities were derived for glycerol (100%, Mallinckrodt Baker Inc., Paris, KY), Brasso (Reckitt Brenckiser, Inc., Wayne, NJ), 1-propanol (Class 1B, HPCL grade, Fisher Scientific, Fair Lawn, NJ), castor oil (Cumberland Swan, Smyrna, TN), and Carbowax (Polyethylene Glycol 300; Dow Chemical Company, Midland, MI), which were initially selected as candidate liquids to ascertain sensor performance in R-NC media.
R-C.
A number of the relaxing fluids (i.e., glycerol, 1-propanol) and mixtures containing suspended solids (Brasso) were evaluated by attempting to dissolve NaCl for increased electrical conductivity up to 2 dS m–1 to obtain a R-C system. Clay suspensions have potential to provide both relaxing and conductive conditions, but obtaining a standard reference would be questionable, and suspensions tend to exhibit multiple relaxation phenomena including Maxwell-Wagner effects which show relaxation at relatively low frequencies (e.g., 1 MHz; Dudley et al., 2003; Ishida et al., 2000).
Temperature Variation
Using controlled fluid temperature and knowing or measuring (with network analyzer) the temperature dependence of the fluid permittivity allows examination of the sensor's temperature dependence. Temperature dependent Cole–Cole (1941) parameters (s) were fit to network analyzer measurements in two permittivity ranges. Permittivity values near 80 (water) and 40 (a 0.6 volume fraction mixture of 2-isopropoxyethanol in water) were chosen to represent two upper values found in solution and in soil, respectively. Using these reference permittivity determinations in nonrelaxing solutions, the static permittivity is taken as reference against which sensor measured permittivities are compared.
Modeling Sensor Sampling Volume
The sample volume in which the electromagnetic energy is most dense will contribute the greatest weight to the permittivity determination (Ferre et al., 1998). Knight (1992) related the EM energy storage density distribution surrounding TDR probes to the sampling volume in a homogeneous isotropic dielectric medium. The EM energy storage density distribution can be calculated using finite difference modeling to infer the sampling volume and measurement weighting of a given sensor. The Arbitrary Transmission Line Calculator (ATLC) (Kirkby, 1996) is a computer software program that employs a finite difference approach to calculate characteristic impedances of prescribed geometries assumed to function as transmission lines (Kirkby, 2003). ATLC uses transmission line theory to calculate EM parameters (i.e., EM energy density, electric field intensity, and voltage distributions based on conductor geometry) from the impedance data. Robinson et al. (2003a) described the theoretical basis for relating the porous medium sample permittivity to the electric potential (
), electric field intensity (
), and energy storage density [()2]. The computation of energy storage density for a coaxial cell geometry of radius, r, includes the electric charge per unit length, Q, and permittivity of material in the cell, .
 | [13] |
The binary ATLC output data was normalized and converted to numerical output using a Matlab (Mathworks, Natick, MA) function (Humphries, 2004). The function also calculates the cross-sectional area within a specified minimum EM energy density contour (i.e., the sample area that contains all the EM energy density values within the specified minimum value). The mean and standard deviation ()2 values within the specified minimum area are also computed. The sampling volume is calculated by multiplying the cross-sectional area within the specified area by the physical probe length. Technically, the sampling volume should include the volume beyond the end of the probes that influences the measurement, but because of the difficulties inherent in determining the distance that the signal reaches beyond the probe's end, the physical length is used. The coefficient of variation (CV) within the specified area is calculated by dividing the ()2 standard deviation by the mean.
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RESULTS
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Network Analyzer Measured Permittivity of Reference Fluids
For generation of permittivity standards between those of water and air, the 2-isopropoxyethanol/water mixture used by (Kaatze et al., 1996) provides fluids with a wide permittivity range between 10 and 80 whose relaxation occurs at frequencies >1 GHz. (Debye, 1929) or Cole–Cole (1941) model parameters describing isopropoxyethanol (Kaatze et al., 1996) and other liquids (Bao et al., 1996; Friel and Or, 1999) are available in the literature where access to a network analyzer is unavailable. We used a dozen different 2-isopropoxyethanol/water fluid combinations for network analyzer measurements and fit the Cole–Cole model to these data generating the parameters listed in Table 1. Other liquids were examined relative to their reduced relaxation frequency, which was targeted to lie between 1 and 1000 MHz, with permittivities between 5 and 40. Table 1 also lists the Cole–Cole model parameters fit to these measured data with lower relaxation liquids, including glycerol, Brasso, 1-propanol, 300C Carbowax, and castor oil.
Nonrelaxing-Nonconducting Condition
A comparison of our Cole–Cole fitted static permittivities for the NR-NC 2-isopropoxyethanol/water mixture and those of Kaatze et al. (1996) are plotted in Fig. 3
, given as a function of volume fraction of 2-isopropoxyethanol, Xiso. A second-order polynomial equation was fit as a function of Xiso to the static permittivities given in Table 1 (24.2 ± 0.5°C).
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Fig. 3. Measured and fitted static permittivity (obtained from s in Eq. [9]) of water–2-isopropoxyethanol mixtures as a function of volume fraction of the latter. Data from Kaatze et al. (1996) are compared with our network analyzer (NA) measurements. A polynomial equation was fit to the network analyzer (N.A. Measured) data and is presented in the text as Eq. [14].
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 | [14] |
The relaxation occurring beyond 1 GHz in the 2-isopropoxyethanol/water mixture is illustrated in Fig. 4a and 4b
showing Cole–Cole modeled real and imaginary permittivities as a function of frequency. The relaxation frequency migrates gradually from that of water at around 18 GHz to pure 2-isopropoxyethanol with a relaxation frequency of around 3 GHz. These mixtures provide reliable lossless frequency dependent permittivity data for calibration and probe characterization between 1 and 1000 MHz. Neither of these liquids shows significant dielectric relaxation below a frequency of about 2 GHz, which is the approximate upper frequency limit of many transmission line EM sensors. While the frequency range of a sensor can be characterized (e.g., Heimovaara et al. [1994] reported a Tektronix TDR frequency band between 20 kHz and 1.5 GHz), it is much more difficult to characterize the effective measurement frequency range that can vary with dielectric. The difference between the network analyzer ' at the sensor's average maximum passable frequency and the sensor measured Ka value represents the residual permittivity of the sensor. If several measurements are made over a given permittivity range as suggested here, then the residual permittivity values can be used to calculate the RMSE as follows:
 | [15] |
where n is the number of measurements, mr is the reference permittivity determination (i.e., network analyzer), and ms is the sensor permittivity determination. The RMSE value indicates the total deviation from the network analyzer, which serves as the permittivity reference. The NR-NC solution is the proposed condition for manufacturer testing and calibration of EM sensor batch variability. Drawbacks of the use of volatile fluids include the potential for permittivity variation with time from evaporative loss of fluid mass, and the potential for alcohols to absorb water, with a resulting increase in permittivity.
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Fig. 4. Modeled (Eq. [9]) real and imaginary permittivities of various dielectric liquids and mixtures thereof (numbers in Part a indicate volume fraction of 2-isopropoxyethanol–water). In the left-hand panels (real) and (imaginary), relaxation occurs beyond 1 GHz, outside the frequency range of many EM sensors. On the right, relaxations occur within the megahertz frequency range where EM sensors operate. The broader relaxation spectrum of Brasso (polishing compound) is due to its complex liquid makeup and mixture of fine suspended solids.
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Relaxing-Nonconducting Condition
Standards for probe characterization using R-NC conditions were considered using a number of different liquids in which effects of relaxation are observed. As with the measurements in NR-NC media, a RMSE value can be calculated for the sensor measurements in R-NC media where again, the network analyzer measurements are used as the reference. Where dielectric relaxation occurs within the sensor measurement range, it tends to reduce the effective measurement frequency for broadband sensors as illustrated in Fig. 2 (Robinson et al., 2005). This frequency shift is also tied to the impedance mismatch that results from changes in the permittivity of the dielectric medium reduced by relaxation. The dielectric relaxation provides greater contrast for estimating the approximate effective measurement frequency from network analyzer data than do NR-NC liquids. This condition is further restricted to cases where the sensor-measured permittivity lies within the frequency dependent permittivity range of the network analyzer or other reference being used.
Relaxation peaks may be useful for emphasizing relaxation loss effects within a given sensor's frequency response or to mimic a soil's relaxation. For example, the relaxation exhibited by glycerol occurs in the 100-MHz frequency range that is common to some EM sensors (Fig. 4c and 4d). Relaxations of Brasso and Carbowax (i.e., polyethyleneglycol) are spread over a wider frequency band than the pure molecular liquids due to their having suspended solids and long-chain molecular structure of varied length, respectively. For standardized testing and repeatability, we recommend pure molecular liquids (glycerol, 1-propanol) rather than liquids that often vary among manufacturers and from lot to lot in composition and purity (Brasso, polyethyleneglycols, oils).
Nonrelaxing-Conducting Condition
Measurements in NR-C media can be made in deionized water and in mixtures of 2-isopropoxyethanol and deionized water with increasing amounts of salt added to increase electrical conductivity. Deionized water and mixtures of 2-isopropoxyethanol and deionized water were used because neither shows significant dielectric relaxation below 1 GHz, and significant amounts of salt can be dissolved in both. The same solution covering a range of electrical conductivity values should be used to ascertain the effects of electrical conductivity on the permittivity determination. The electrical conductivity range evaluated should equal a known range or determine the range of the sensor being considered if unknown. The amount of salt (e.g., NaCl) required for approximating these electrical conductivities is listed in Table 2 for the two solutions described. It should be noted that other volume fractions of deionized water and 2-isopropoxyethanol could be used, but as the permittivity of the solution gets lower it becomes more difficult to dissolve the desired amount of salt (i.e., six times more NaCl for a solution with one-half the permittivity).
The Cole–Cole model (Eq. [9]) describes real and imaginary permittivities of nonconducting solutions and in theory small additions of ions to a solution have little effect on the permittivity within the range of b typical of nonsaline and even moderately saline conditions. However, at extremely high electrical conductivity ion presence has a marked effect on ' (Hasted, 1973). In our measurements of conducting solutions only minor differences in ' were noted among network analyzer measurements in different levels of conductivity, but substantial differences in '' were observed at lower frequencies for increasing w (Fig. 5)
. Because of the difficulty in relating measurements of ' and '' to sensor determination of Ka, we did not fit Cole–Cole model parameters to conducting solutions nor use network analyzer measurements of complex permittivity as a reference for NR-C conditions. The modest range of electrical conductivities where EM sensors operate (i.e., 0–2 dS m–1) can lead to substantial changes in sensor measured permittivity and are worthy of consideration and characterization. We propose using each sensor's measurement in solution at 0.0 dS m–1 as the reference from which to track effects of conductivity on sensor measurements followed by estimation of the RMSE for NR-C media.
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Fig. 5. Network analyzer measured real and imaginary permittivities measured in a 0.6 fraction mixture of 2-isopropoxyethanol and water as a function of solution electrical conductivity. The effect of salinity on the imaginary component is two to three times greater at 0.1 GHz as compared with data at 1 GHz.
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Relaxing-Conducting Condition
Probably the most common test condition relative to natural soils is one where an element of relaxation and electrical conductivity is present as in clay soils. Unfortunately, this condition is also the most difficult to generate using liquids. As stated above, the solubility of salts in dielectric liquids is proportional to the magnitude of permittivity. Upper bounds on solution electrical conductivity are limited by the reduced solubility in the lowest dielectric fluid. For the NR-C condition using 0.6 2-isopropoxyethanol/water mixture where s = 40.0, the low solubility of the 2-isopropoxyethanol limited the maximum value of electrical conductivity. Attempts were made to synthesize a relaxing and conducting medium via dissolving NaCl in the R-NC solutions described above. Each attempt failed due to the inability to dissolve a significant amount of NaCl. For Brasso and 1-propanol the failure was likely due to the low static permittivity values (28.0 and 22.8, respectively) of the solutions. Using 10% water and 1-propanol, a maximum electrical conductivity of only 0.25 dS m–1 was obtained. For glycerol and 10% water, the maximum electrical conductivity reached was 0.35 dS m–1. This failure underscores the difficulty of obtaining an R-C system providing electrical conductivities sufficient to test sensor performance (i.e., dc > 0.5 dS m–1). We anticipate there are other liquids not tested here that may provide a more suitable R-C system that would provide electrical conductivities on the order of 2 dS m–1, which we propose as a test solution in our sensor evaluation and characterization protocol.
Temperature
Temperature dependent standards provide a reference for comparing sensor-related temperature effects and potentially calibrating against these effects for the case where sensors measure temperature. The two proposed NR-NC liquids, water and a mixture of water and 2-isopropoxyethanol, both exhibit well-defined (T) relationships (Fig. 6)
. The 0.6 2-isopropoxyethanol:water mixture is described by the linear equation, (T) = –0.083T + 41.765 (R2 = 0.999). Complete immersion of sensors in liquid and adequate time for sensor electronics to come to temperature equilibrium is required. By varying liquid temperature using an external heating/cooling source or circulating water bath, the effects of temperature on sensor performance and potential corrections for instrument offset should lead to improved permittivity determination.
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Fig. 6. Temperature dependent permittivities of pure water and a 0.6 mixture of 2-isopropoxyethanol and water. A linear equation was fit to the measured mixture permittivities shown.
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Modeling Probe Sampling Volume
The method for determining probe sampling volume using the ALTC program and Matlab code was described above. For the example shown in Fig. 7a
, the dielectric of the background was set to a value of 1 and the simulation was rerun using a background of 10, yielding the same distribution of the field regardless of the background permittivity value for the homogeneous case. For a layered background with permittivity contrast, the resulting field varies depending on the contrast (Ferre et al., 1998, 2001; Robinson et al., 2003a). In Fig. 7b, the horizontal layering case is shown consisting of a background permittivity above the conductors of 10 and a value of 1 below. This order-of-magnitude contrast results in greater field penetration within the higher permittivity region, which significantly modifies the electric field density and therefore the probe sampling volume.
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Fig. 7. Cross section of the modeled sampling area of a 2-conductor, looped TDT sensor (Acclima TDT, Blonquist et al., 2005). The electromagnetic energy storage density was modeled using the ATLC model of (Kirkby, 1996) with normalized contour lines ranging from 0 to 1 at increments of 0.1. The two center rods are connected and the two outer rods form a separate connection. In (a) the energy storage density is independent of background permittivity, while in (b) there is an order of magnitude difference between the background permittivity of the top and bottom half of the cross section resulting in a significantly different distribution.
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Evaluations of sampling volume should focus on the homogeneous background case for consistency. The cross-sectional area of the region multiplied by the probe length yields the approximate sampling volume of the probe (i.e., volume containing 90% of the maximum EM energy used here). The coefficient of variation of the EM energy density (CV
) values within this area provides a statistic indicating the uniformity of the EM energy density distribution within the approximated sampling area and volume. Probe geometries exhibiting lower CV values theoretically provide a more uniform weighting or representative measure of the average permittivity (water content) within the sampling volume.
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CONCLUSIONS
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Electromagnetic sensor evaluation and characterization criteria have been developed for the purpose of giving users and manufacturers a much needed standard approach for comparison, testing, and calibration. The primary consideration should be specification of or determination of the sensor effective measurement frequency, which is not always specified or readily determinable. The effective measurement frequency is a key factor in permittivity determination due to the frequency dependence of many dielectrics (e.g., soil), and this frequency can shift when using broadband EM sensors, especially where losses due to dielectric and conductive loss mechanisms cause filtering of higher frequencies. Sensor permittivity determination comparisons based on network analyzer referenced permittivity spectra provide a standard for determination of effective sensor measurement frequency (i.e., maximum passable frequency for travel time–based sensors). Even without a network analyzer, Cole–Cole model parameters, presented here and elsewhere, describe the complex fluid dielectric character and can be used for sensor calibration and evaluation. Other sensor evaluation criteria include examining effects of dielectric relaxation within or outside of the sensor's effective measurement frequency as well as electrically conducting and non-conducting conditions. The lossless conditions, nonrelaxing and nonconducting, are useful for evaluating the sensor's permittivity determination range capability as well as permittivity determination calibration. The relaxing and conducting conditions (i.e., R-NC, NR-C, and R-C) apply to measurements in soil exhibiting dielectric or electrically conductive losses and a combination thereof. These effects are perhaps the most important to consider given the difficulties of determining water content in clayey and saline soils. Effects of temperature on sensor measurement performance can also be evaluated using dielectric liquids of known permittivity described here. The influence of sensor conductor geometry relative to permittivity determination sampling volume can be modeled using the ATLC program or other EM modeling software. In this study no suitable combination of relaxing and sufficiently conducting (dc > 0.35 dS m–1) solution was found because of lower salt solubility associated with a reduced dielectric constant. Application of these performance criteria are presented in a companion paper (Blonquist et al., 2005).
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ACKNOWLEDGMENTS
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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 the guest editor, Steve Evett, and two anonymous reviewers for carefully reviewing the manuscript and providing many helpful comments and insights. The authors extend special thanks to Scott Anderson and Acclima Inc. for technical assistance and student financial support and to Seth Humphries for assistance in this work.
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TOP
ABSTRACT
INTRODUCTION
