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Published online 16 November 2005
Published in Vadose Zone J 4:992-1003 (2005)
DOI: 10.2136/vzj2004.0131
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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SPECIAL SECTION: SOIL WATER SENSING

Evaluation of a Capacitance Probe Frequency Response Model Accounting for Bulk Electrical Conductivity

Comparison with TDR and Network Analyzer Measurements

D. A. Robinsona,*, T. J. Kellenersb, J. D. Cooperc, C. M. K. Gardnerd, P. Wilsone, I. Lebrona and S. Logsdonf

a Dep. of Plants, Soils and Biometeorology, Utah State University, Logan, UT, USA
b George E. Brown Jr. Salinity Lab USDA-ARS, Riverside CA, USA
c Instrument Section, Centre for Ecology and Hydrology, Wallingford, Oxon, UK
d IAHS Press, Centre for Ecology and Hydrology, Wallingford, Oxon, UK
e School of Environmental Sciences, University of Ulster, Coleraine, Co. Londonderry, N. Ireland, UK
f National Soil Tilth Lab USDA-ARS, Ames/Ankeny, IA, USA
* Corresponding author (darearthscience{at}yahoo.com)

Received 14 September 2004.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
Soils ranging in texture from sand to clay were used to compare permittivity measurements made using a Surface Capacitance Insertion Probe (SCIP) and time domain reflectometer (TDR). Measurements were made using the same electrodes embedded in each soil, making the measurements directly comparable. The objective of the work was to test a model describing the frequency response of the SCIP to both permittivity and electrode conductance, and to compare results with TDR and network analyzer measurements. The model was tested using liquids of known permittivity and in saline, dielectric solutions. Surface Capacitance Insertion Probe and TDR determined permittivity values are similar for sandy soils but diverge for loam and clay soils. Using Topp's values as a reference, the SCIP-determined permittivities for loams and clays lay close to the curve at water contents <0.25 m3 m–3, then often rose above the curve with increasing water content. Surface Capacitance Insertion Probe permittivity correction, using electrical conductivity (EC) measured at 1 kHz, corrected the results in sands reasonably well but not enough in loams and clays for reliable calibration. We propose three possible reasons for the higher than expected permittivity values observed using the SCIP: (i) higher than expected real permittivity created by dielectric dispersion, (ii) a large contribution of the imaginary permittivity due to relaxation processes assumed to be negligible, and (iii) poor model prediction of permittivity due to excessive damping of the oscillator circuit with high EC and dielectric losses. Results from network analyzer measurements for one of the clay soils were used to aid data interpretation. The TDR measurements were much more consistent, producing apparent relative permittivity values below those of the Topp curve for the finer textured soils.

Abbreviations: EC, electrical conductivity • SCIP, Surface Capacitance Insertion Probe • TDR, time domain reflectometer


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
THE LIFE-SUSTAINING reservoir for plant and microbial communities is soil water, a key component of the hydrological cycle. As such, knowledge of soil water content is required for using global circulation models to estimate heat and vapor fluxes in what has been referred to as the "critical zone" (Committee on Basic Research Opportunities in the Earth Sciences, Board on Earth Sciences and Resources, National Research Council, 2001). A great deal of effort has been expended in trying to determine water content at a range of scales. Many measurement methods have been reviewed by Gardner et al. (2001) and Topp and Ferre (2002), among others. Two of the more commonly used electromagnetic methods for determining water content at the sample scale are the TDR method (Topp et al., 1980; Jones et al., 2002; Robinson et al., 2003) and the capacitance probe method (Wobschall, 1978; Dean et al., 1987; Bell et al., 1987; Evett and Steiner, 1995; Paltineanu and Starr, 1997; Kelleners et al., 2004). A surface capacitance insertion probe (SCIP) (Robinson and Dean, 1993; Dean, 1994; Robinson et al., 1998) is used in this work. Capacitance probes such as the EnviroSCAN (Sentek, Stepney, Australia) have become popular for irrigation scheduling (Evett and Steiner, 1995; Paltineanu and Starr, 1997; Kelleners et al. 2004). Hence, an understanding of the response of this instrument provides some insight into the operation and performance of similar sensors. Both TDR and capacitance sensors attempt to measure the permittivity of the soil medium. Because they may not do so perfectly, the measurement yielded by the instrument is termed the apparent permittivity.

Many calibration equations to relate apparent permittivity to water content have been presented in the literature (Topp et al., 1980; Roth et al., 1992; Jacobsen and Schjonning, 1993; Malicki et al., 1996). Many of these equations are used interchangeably among different types of sensors. Water content determination is a two-step process—from sensor response to permittivity (Jones et al., 2005; Blonquist et al., 2005), and from permittivity to water content. Errors or invalid assumptions in the first step will lead to difficulty in making interpretations at the next step. In this study we compared measurements made using a surface capacitance insertion probe and TDR in 12 soils. The initial objective of this work was to evaluate a calibration model developed for the SCIP. This uses well-defined dielectric solutions and dielectric solutions with ionic conductivity to determine whether accounting for EC measured at 1 kHz improves permittivity measurement. Solution electrical conductivity changes by about 2% °C–1 and can have a strong impact on the apparent permittivity measurement. Eliminating it from the apparent permittivity measurement can considerably improve water content determination. The second objective was therefore to evaluate the model permittivity predictions with and without accounting for bulk soil EC to determine whether accounting for EC could improve the permittivity and water content calibration. Predictions of permittivity are compared directly with TDR measurements using the same electrodes and also with some independent network analyzer measurements. As far as possible, we develop and use physical principles and models to provide understanding of what is being measured. By doing this we hope to identify deficiencies in knowledge of what is being measured and make recommendations for sensor improvements.


   THEORY
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
Time Domain Reflectometry
The TDR method is a transmission line technique, which determines an apparent TDR permittivity (Ka) from the travel time of an electromagnetic wave that propagates along a transmission line, usually two or more parallel metal rods embedded in a dielectric (Topp and Ferre, 2002; Robinson et al., 2003). The propagation velocity of a broadband (20 kHz–1.5 GHz) (Heimovaara, 1994) electromagnetic signal determined by fitting tangent lines to the wave form is analogous to the phase velocity, vp, of an electromagnetic plane wave through a dielectric material:

[1]
where c is the velocity of light in vacuo (3 x 108 m s–1), {epsilon}o is the electric constant (8.854 pF m–1), {epsilon}r is the relative permittivity, µo is the magnetic permeability of vacuum (1.257 x 10–6 H m–1), and µr is the relative magnetic permeability, which can be taken as unity in almost all soils (Roth et al., 1992). The TDR signal propagates down the transmission line and is reflected from its end; the returning signal is sampled in the TDR device. From Eq. [1], the velocity of the signal in a perfect, nonmagnetic dielectric is

[2]
where l is the length of the line and t is the time for a round trip (back and forth). Rearranging Eq. [2] gives the round trip propagation time (t) of the wave as a function of both the length of the transmission line (l) and the relative permittivity of the material:

[3]
Hence the permittivity can be determined by measuring the time it takes the signal to traverse the probe.

Surface Capacitance Insertion Probe
The SCIP is a series resonance, frequency shift capacitance probe operating between 70 and 150 MHz (Robinson and Dean, 1993; Dean 1994; Robinson et al., 1998; Gardner et al., 1998). The frequency response is a function of the electrode capacitance; from this, an apparent soil permittivity (KSCIP) is obtained. The most attractive features of capacitance probes are their simplicity of concept and use compared with the TDR, and their more adaptable electrode configuration (Robinson et al., 1998; Whalley et al., 1992).

The capacitance of a pair of electrodes is a function of the relative permittivity, {epsilon}r, of the material in which the electrodes are embedded and the geometric configuration of the electrodes:

[4]
where Cm is the capacitance, gm is a geometric factor, and {epsilon}o is defined previously. The impedance, Z, of an inductance, L, and capacitance, C, in series is given by

[5]
where j = {surd}–1, {omega} is the angular frequency (= 2{pi}F, with F being the frequency). At the resonance frequency, the imaginary part of the impedance (Eq. [6], from Eq. [5]) is zero:

[6]
which can be solved either for the angular frequency, {omega}, or the total circuit capacitance C:

[7a]

[7b]

The impedance of the SCIP oscillator circuit can be written as (e.g., Dean, 1994; Dean et al., 1987)

[8]
where Cm is the capacitance of the electrodes, Cs is a capacitance due to stray electric fields, and Cb is the capacitance of the circuit board. Equation [8] can be written

[9]

At the resonance frequency, the imaginary part of the impedance (Eq. [10], from Eq. [9]) is again zero:

[10]

The solution of Eq. [10] for the angular frequency, {omega}, and the electrode capacitance, Cm, is:

[11]

[12]

Complex Dielectric Permittivity
Many materials, including soils, do not constitute a perfect dielectric. Energy losses arising from dielectric relaxation and ionic conductivity need to be taken into account. The relative permittivity of the material should then be represented by a complex quantity {epsilon}r* with a real part {epsilon}r' describing energy storage and an imaginary part {epsilon}r'' describing energy losses:

[13]

The {epsilon}r'' term in Eq. [13] is the sum of a conductivity term and a relaxation term:

[14]
where {sigma} is the ionic conductivity and {epsilon}''r,rel is the loss due to dielectric relaxation. The electrode capacitance, Cm, is now also a complex quantity:

[15]
where Cm* is the complex electrode capacitance, Cm' is the real part of the material capacitance, and gm was previously defined. Multiplication of both sides of Eq. [15] with j{omega} gives

[16]
where G = gm{sigma} + gm{omega}{epsilon}''r,rel{epsilon}o. The impedance of the SCIP oscillator circuit for a material with a complex permittivity is written as

[17]

Separating the real and imaginary parts gives

[18]
As before, the imaginary part of the impedance is zero at the resonance frequency:

[19]

This is a quadratic equation in both {omega}2 and C'm, with solutions (see Appendix).


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
Sample Description and Collection
Soils were collected for this project from 12 locations across Northern Ireland and Southern England. They represent a broad spectrum of soil textural classes. The Northern Ireland soils are derived mainly from drift deposits overlying diverse bedrock. The mixing and outcropping of different strata has led to the development of a wide variety of soils, from diatomaceous earths to Fe-rich clays (Cruickshank, 1997). Details of the soils are contained in Table 1. All soil samples were taken from between 10 and 30 cm depth below the soil surface, thereby sampling topsoil below the root mat if present.


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  		Table 1. Soil sites, description, and texture with soil horizon and classification according to the N. Irish soil survey (Cruickshank, 1997), Soil Survey of England and Wales (Avery, 1980). Texture classification according to U.S. Soil Taxonomy (Soil Survey Staff, 1975).

 
Soil samples were collected to develop a comprehensive data set of repacked soils. Approximately 5 kg of soil was collected from each location. Once in the laboratory, the soil was sieved onto large plastic trays. A 5-mm sieve was used to remove any large stones, while partially maintaining the natural ped structure; it also homogenized the soil. The soils were left for 6 wk to air dry in the laboratory. Subsamples were removed for physical and chemical characterization.

Soil Characterization
Particle size analysis was performed using the standard sieving and pipette method (Klute, 1986; Loveland and Whalley, 1991) (Table 1). After passing the samples through a 2-mm sieve, all the soil samples were pretreated with dilute acid to remove carbonates and then boiled with hydrogen peroxide to remove the organics (Gee and Bauder, 1986). Soil chemical and mineralogical analyses are presented in Table 2. Soil mineralogy was determined using semi quantitative mineral X-ray diffraction analysis. Subsamples of the sand and silt fraction and the clay fraction were analyzed semiquantitatively. Soils 10 and 11 contained notably high values of oxide minerals that may be overestimated slightly because they were determined semiquantitatively from X-ray diffraction data, but Soil 10 was formed on a weathered Fe-rich band within the underlying basalt. These soils were classified as sandy silt loam (10) and clay (11). However, the iron oxides were not removed during pretreatment and were observed to be cementing the soil. Our belief is that both these soils would be more appropriately classified as clays. The loss-on-ignition technique (Davies, 1974) was used to determine the percentage of organic matter. Soil pH was measured using a soil/water ratio of 1:2.5 (Rowell, 1994). The soil solution electrical conductivity was measured using a standard 1:5 soil/water extract (Landon, 1991). The EC meter (Jenway EC sensor, Jenway, Felsted, Dunmow, England) automatically temperature compensated the readings to 25°C.


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  		Table 2. Soil mineralogy and chemical properties.

 
Table 3 presents the soil physical properties. The bulk density is the average for each of the repacked soils. Repacked bulk density values were generally lower than bulk density values found in undisturbed field samples. The hygroscopic water content of the soils is given for two values of relative humidity. Samples were oven dried at 105°C and then allowed to equilibrate at the respective humidity. Values for the sands (Soils 1, 2, and 3) were all <0.001%. The hygroscopic water content is given as a volumetric percentage based on the average bulk density. The external surface area of the soil was measured using nitrogen adsorption (Newman, 1987), with a Gemini III 2375 surface area analyzer (Micrometrics, Londonderry, NH).


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  		Table 3. Soil physical properties.

 
Sample Repacking and Wetting
The use of repacked soil samples for permittivity measurement followed the approach of Gardner et al. (1998); similar methods having been used by others (Malicki et al., 1996). Repacking of soil allows measurements to be performed over a wide range of water content and dry bulk density. A plastic cylinder, with 0.103-m inside diameter, capped at one end, was packed with air-dried soil to a height of 0.14 m to give a prepared sample 1167 cm3 in volume. This was weighed on a balance accurate to 0.1 g. A pair of stainless-steel electrodes, 0.1 m in length, was fully inserted vertically into the center of the sample. Measurements were taken by TDR and then the SCIP. After the measurements, the sample in its core was reweighed and then a temperature probe inserted into the soil to measure soil temperature. All work was conducted in a laboratory, whose temperature was maintained at 20 ± 1°C. A 10-g subsample of soil was removed and oven dried so that the gravimetric water content could be determined. The soil was then removed from the cylinder and mixed with the remainder of the soil. The cylinder was then repacked with soil to a slightly greater bulk density than previously. This procedure was repeated for repacked soil at five bulk densities with the same gravimetric water content. Volumetric water content and bulk density were calculated from the gravimetric water content and the wet mass of the repacked mixture contained in the known volume of the cylinder following the same procedure as Gardner et al. (1998). To obtain measurements for a range of water contents, the above procedure was repeated with progressively wetter soil, each time adding 80 to 100 g of deionized water to the soil using an atomizer spray gun while continually mixing. This process was repeated until a volumetric water content range from air dry to saturation was achieved.

Instrumentation, TDR, SCIP, and Network Analyzer
Measurements were made with both TDR and SCIP using the same electrodes. These were stainless steel, 6 mm in diameter and 100 mm in length, with a 25-mm center spacing; they were inserted vertically into the soil. They had female sockets in the upper end, which mated with male connectors, so that each instrument could be used to make measurements in the soil without disturbing the electrodes. EC was measured across the electrodes using a 1-kHz bridge (ESI Inc., Portland, OR). The sensor measurements were calibrated for conductivity ({sigma}) in solutions of potassium chloride. A cell constant (gm) of 0.1246 m was determined by comparison with measurements using a conductivity bridge (Robinson et al., 1998).

The SCIP was described in more detail by Dean (1994) and Robinson et al. (1998). Normally, the instrument has two 100-mm stainless-steel electrodes secured in a 30-mm-thick plastic housing at the base of the probe body. The circuitry is contained above the electrodes inside the main body of the instrument. The oscillation frequency of the instrument is displayed on an LCD screen at the top of the instrument. The whole instrument weighs less than 1.5 kg and is housed in a robust, water resistant, plastic casing. The 30-mm-thick plastic electrode-mounting block of this experimental SCIP was cut in half and the main body was fitted with two male connectors. These could be inserted into the female connectors in the detachable electrodes. The instrument was calibrated in air and water following the procedure developed by Robinson et al. (1998). The value of Cb was fixed at 15 pF, and Cm was determined according to Cm = gm{epsilon}o{epsilon}r (Dean, 1994). The values L and Cs were 0.3794 µH and 2.566 pF respectively, determined using Eq. [11]. The response of the SCIP was tested in a range of dielectric liquids at 25°C (white paraffin, 2.2; hexanol, 13.3; 2-propanol, 18.3; 1-propanol, 20.1; acetone, 20.7; methanol, 32.6; glycol, 37.7; glycerol, 42.5) and in dielectric liquids containing potassium chloride within the EC range of 0 to 2.8 dS m–1.

Time domain reflectometer measurements were made using a Tektronix 1502C system (Tektronix, Beaverton, OR). It was connected to the electrodes, which in this case formed the probe, by a 1-m length of coaxial cable. The TDR was used to measure apparent relative permittivity (Ka) using software developed by Heimovaara and de Water (1993). Each waveform was downloaded to a PC and interpreted using this software.

Measurements were also made using a dielectric probe (Hewlett-Packard 85070B, Hewlett-Packard, Palo Alto, CA) attached to a network analyzer (Hewlett-Packard 8753B). The network analyzer measures the real and imaginary ({epsilon}''r, Eq. [14]) permittivity independently between 10 MHz and 3 GHz using the dielectric probe. Samples of Soil 10 (Giants Causeway a) were wetted and repacked into a 3.17-cm3 sample holder mounted on top of the dielectric probe. The low frequency electrical conductivity was measured across the sample using a 1-kHz bridge (ESI Inc.) and found to correspond with measurements made with the TDR.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
SCIP Model Calibration in Dielectric Fluids
A comparison of the frequency response of the SCIP predicted by Eq. [A2] in the appendix and the measured data is presented in Fig. 1 and shows excellent agreement. The response of the SCIP in electrically conducting solutions is also presented to demonstrate how bulk EC reduces the frequency response of the instrument. The frequency response for electrical conductivity >2.0 dS m–1 becomes very flat and suggests that permittivity measurement will be difficult in conductive soils. Figure 2 shows the frequency response to changes in electrical conductivity of saline (KCl) dielectric solutions; the lines indicate the modeled response. Again the model and data are in excellent agreement.



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  		Fig. 1. Frequency response of the SCIP modeled according to Eq. [19]. Closed circles represent measurements in dielectric solutions and show excellent agreement with the model. The sequence of lines demonstrates the damping of the frequency response that occurs as salinity increases.

 


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  		Fig. 2. Measured frequency response of the SCIP in four dielectric fluids with potassium chloride used to raise the EC. The lines represent the modeled response using Eq. [19].

 
Measured Apparent Permittivity in Soils
Measurements for the sandy soils are presented in Fig. 3 . Three of these soils had very low values of bulk EC, generally below 0.1 dS m–1. The fourth, from Herringswell, had a bulk EC that rose to 0.45 dS m–1 at high water content. Topp's curve for mineral soils (Topp et al., 1980) provides the reference in Fig. 3, and the data follow it closely as expected and previously presented (Robinson et al., 1999). If the apparent relative permittivity measured by both the TDR and SCIP were the same, the small triangles representing the TDR data should fall inside the large open circles. These circles represent the SCIP-derived permittivity corrected for the effects of electrical conductivity. In the first three of the figures this is the case; one or two points lie outside, which may be due to experimental error, but there is no consistent deviation. The data demonstrate that in sandy soils with low bulk EC (<0.1 dS m–1), permittivity measurements from both sensors correspond and that there was negligible correction to the SCIP measurements for electrical conductivity. In the case of the Herringswell soil, the bulk EC has a significant impact on the apparent permittivity measured by the SCIP. The model corrections for EC reduce the apparent permittivity from 23 to 18 at saturation. After correction, the SCIP permittivity values are closer to those obtained with the TDR. The data clearly indicate the requirement for correction to retrieve permittivity from capacitance sensors in soils where bulk soil EC interferes with the determination of the apparent soil permittivity.



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  		Fig. 3. The permittivity, bulk electrical conductivity, and bulk density for four coarse soils. Symbols (first column): SCIP apparent permittivity (solid circles), SCIP apparent permittivity corrected for EC (open circles) TDR apparent permittivity (solid triangles).

 
Results for the loamy soils are presented in Fig. 4 . These soils had lower average bulk density than the sandy soils (0.73–0.96 g cm–3). The soils also offered a range of bulk EC at saturation, ranging from 0.1 dS m–1 for the soil from Glenwherry to 1.3 dS m–1 for the Wallingford soil. This time, clear divergence between the measurements can be observed for all four soils. Electrical conductivity is observed to influence the SCIP measurements from White Park Bay, Portstewart, and Wallingford. After correction for EC, the SCIP-determined permittivity still exceeds the TDR results at the higher water contents. Permittivity measurements from the Glenwherry soil also deviate similarly at higher water contents, but it is clear that electrical conductivity plays no role in this as the uncorrected permittivity values (solid circles) lie inside the corrected values (open circles). The apparent permittivity estimates from the TDR lie consistently below those predicted by Topp's curve for all the soils. This is most probably a density effect; the Glenwherry soil is high in organic matter content and has an average bulk density of 0.73 g cm–3 (Table 3) and gives the lowest permittivity values.



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  		Fig. 4. The permittivity, bulk electrical conductivity and bulk density for 4 medium textured soils. Symbols (first column): SCIP apparent permittivity (solid circles), SCIP apparent permittivity corrected for EC (open circles) TDR apparent permittivity (solid triangles).

 
Results for the four fine textured soils are presented in Fig. 5 . Again, these soils represent a range of bulk density (0.51–1.02 g cm–3) and bulk EC at saturation (0.4–2.7 dS m–1). The geometry of the Toombebridge soil is fascinating—it is composed of silica tubes that are the remains of diatoms (Fig. 6) . As a result, the soil has a particularly low bulk density. Bulk EC has little impact on the permittivity measurements in this soil. All the measurements, from both TDR and SCIP, lie below Topp's curve, probably because of the low bulk density. However, at the higher water contents, the SCIP measurements become higher than those found using TDR. The two soils from the Giants Causeway both had high bulk electrical conductivity near saturation. After accounting for this in the SCIP measurement, relative permittivity values as high as 275 and 70 were obtained at saturation for Soils a and b, respectively. Measurements from Soil a lie above those of Topp's curve; above a water content of 0.25 m3 m–3, the apparent permittivity increases dramatically. Soil b measurements follow Topp's curve to a water content of about 0.25 m3 m–3 and then diverge upward in a similar but less sharp manner. The TDR results for these soils both lie below Topp's curve; however, at the higher water contents the permittivity values for Soil a rise above Topp's curve. This is similar to the observations of Dirksen and Dasberg (1993) for TDR measurements in montmorillonite. The heavy clay soil from Wytham also shows deviation between the TDR measurements and the corrected SCIP measurements, the highest relative permittivity value from the SCIP being 43, and from the TDR being 20.



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  		Fig. 5. The permittivity, bulk electrical conductivity and bulk density for 4 heavy textured soils. Symbols (first column): SCIP apparent permittivity (solid circles), SCIP apparent permittivity corrected for EC (open circles) TDR apparent permittivity (solid triangles).

 


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  		Fig. 6. Scanning electron micrograph image of the Toombebridge diatomaceous silty soil. The tubes are about 10 µm in diameter.

 
These results indicate good correspondence between measurements made in sandy soils using both instruments. However, in the wetter clay soils, deviation between the values of permittivity is very pronounced. In the next section we examine some explanations for this observed deviation.

Frequency Domain Results
We obtained preliminary data using the network analyzer to try to gain further insight into the measurements made in the Giants Causeway a. This soil produced SCIP measurements that differed the most from the TDR results. Network analyzer measurements are helpful because the real and imaginary permittivities are measured separately. It provides separate measurements of both the real and imaginary permittivity, against which apparent permittivity from other instruments can be compared and interpreted. Measurements for the Giants Causeway a are presented in Fig. 7 for water contents of 0.08 and 0.46 and bulk density of approximately 1.0 g cm–3. This bulk density and the water content of 0.46 closely resemble the final measurement in Fig. 5 (Giants Causeway a). This soil is clearly a dispersive dielectric; that is, its dielectric properties change with frequency. Dispersion of this nature has been reported for clay minerals and heavy textured clay soils (Saarenketo, 1998; Logsdon and Laird, 2002). At a water content of 0.46, the relative permittivity measured at about 68 MHz corresponds to a value of 52. This is much lower than the value of 277 obtained with the SCIP, which seems to be improbably high. The corresponding imaginary relative permittivity due to relaxation is about 14. Inclusion of this value of imaginary permittivity does not improve the estimate of the real permittivity. One of the major problems is that the oscillation frequency of the SCIP has been damped so much by the EC and imaginary permittivity that a small inaccuracy in the measurements may give a very high (or low) real permittivity estimate. This is demonstrated in Fig. 1 for an EC of 4 dS m–1; at this EC the frequency response of the SCIP is almost flat (i.e., it does not change as a function of the permittivity).



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  		Fig. 7. Frequency domain analysis of Soil 9 (Giants Causeway a) for two water contents, 0.08 and 0.46. This is a dielectrically dispersive soil, the real permittivity changes with frequency. The real permittivity and imaginary permittivity due to EC and due to relaxation are all separated.

 
In Fig. 8 , results from the network analyzer for the real permittivity are plotted along with the TDR results (Fig. 8A), for different frequencies from the network analyzer (Fig. 8B), and adjusted SCIP permittivity (Fig. 8C). Dielectric spectra, like the ones in Fig. 7, were obtained for the soil at six water contents repacked to a bulk density close to 0.75 g cm–3. Results are also shown in Fig. 8A and 8C for two higher water contents with the soil repacked to a bulk density of about 1.0 g cm–3. The real permittivity was extracted from the spectra at three frequencies for comparison with the TDR, 3.00, 1.01, and 0.26 GHz (Fig. 8A), and three frequencies for the SCIP, 1.01, 0.10, and 0.07 GHz (Fig. 8C).



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  		Fig. 8. (A) TDR results and network analyzer results of the real part of the permittivity as a function of water content for the Giants Causeway a soil. Measurements at six water contents are presented and three of frequency. (8B) Frequency domain data for the same soil with the air-dry water content of 0.09 subtracted; this demonstrates that the real permittivity at this bulk density follows a Topp shaped curve but rises above Topp as the frequency becomes lower. (8C) Data for the same soil for the SCIP and network analyzer results for three frequencies.

 
In Fig. 8A, the network analyzer results are compared with the TDR results. At water contents above 0.3 the TDR apparent permittivity values increase markedly. Dirksen and Dasberg (1993) also observed similar behavior for repacked samples of montmorillonite. Our interpretation of this is that the real permittivity increases not only because of higher water content, but also because there is a further polarization mechanism that contributes and is itself dependent on bulk density. This is over and above the expected increase in permittivity resulting from the reduction in air-filled porosity caused by increasing solid and water. Reasonable agreement is found between the TDR measurements and the network analyzer real permittivity for a bulk density around 0.75 g cm–3 up to a water content of 0.3; above this water content, the data diverge, with the TDR permittivity rising above Topp's curve and the network analyzer data remaining below it. From Fig. 5 (Giants Causeway a, bulk density) one can observe that at water contents higher than this, the bulk density in the packed column is correspondingly greater. Network analyzer measurements packed to 1.0 g cm–3 in Fig. 8A also demonstrate that the real permittivity rises above Topp's curve for more densely packed samples. This may indicate that the increase in permittivity measured by the TDR is simply a function of the increased bulk density. The permittivity measured by the TDR appears to correspond well with the real permittivity measured by the network analyzer for a frequency of around 1.0 GHz. The change of shape of the calibration curve can be ascribed to the change of bulk density involved in repacking the soils. This suggests that in clay soils there is a polarization mechanism that is a function of the bulk density that can significantly affect the real permittivity. As this occurs at saturation, a possible physical mechanism explaining it might be that the geometry confines the ions more effectively and their confinement enhances charge storage, that is, the real permittivity. Mechanisms such as the Maxwell-Wagner effect (e.g., Hasted, 1973; Sen, 1984; Haslund, 1996) have been described for low frequencies <100 MHz, but this data indicate that a further mechanism occurs above 100 MHz.

The network analyzer data for the real permittivity and for a uniform bulk density are presented in Fig. 8B. The gravimetric water content for the air-dry sample is subtracted from all the values. The purpose of this is to demonstrate that for a uniform bulk density at a range of frequency values (0.05, 0.10, 0.26, and 1.01 GHz) the data give a Topp shaped curve for the high frequencies (1 GHz), and permittivity increases as the frequency reduces. These data support the interpretation of the TDR data that the change observed in the shape of the calibration (Fig. 8A) is a consequence of the changing bulk density. For the bulk density of 0.75 g cm–3 measured using the network analyzer at 1.01 GHz, the shape of the water content–permittivity relationship is consistent with the shape of Topp's curve, but offset by the presence of hygroscopic water.

Interestingly, the SCIP data in Fig. 8C also begin to show dramatic divergence from a Topp-shaped curve at a slightly lower water content of 0.26. The similar response for both the TDR and SCIP around this water content gives more weight to the suggestion of a significant change in the soil dielectric properties at this water content. The apparent permittivity from the SCIP measurements, however, rises much more abruptly than those from TDR, and even though the real permittivity measured with the network analyzer is higher at a frequency of 70 MHz, it is not enough to account for the SCIP response.


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
CONCLUSIONS
 APPENDIX
 REFERENCES
 
An important objective of this study was to discover if incorporating EC into SCIP calibration was enough to improve water content determination. The results from the sandy Herringswell soil are encouraging. However, the results from the other medium and heavy textured soils indicate that the use of low frequency EC measurements is not sufficient by itself to produce results close to real permittivity, as measured by a network analyzer or a calibration curve similar to those of Topp et al. (1980). As discussed for fine textured soils (Fig. 5), there appears to be a critical range of water content from about 0.20 to 0.25 m3 m–3 at which the SCIP permittivity results change abruptly. This is also the point at which the electrical conductivity increases steeply, perhaps indicating an electrical percolation threshold. We propose three explanations that could account for the high values of permittivity obtained with the SCIP measurements:

The first two have some impact, but they do not sufficiently account for the high permittivity values obtained with the SCIP based on the network analyzer results. This suggests that the third possibility is the case and that the circuit model can no longer predict accurate permittivity values with such heavy damping of the oscillator response. This further suggests that reliable, accurate water content determination using this type of capacitance probe will be limited to soils with low EC and low dielectric relaxation.

This work demonstrates the need for several improvements in measurements to determine water content from permittivity measurements. With so many sensors now available, all purporting to measure permittivity, it is important to develop a standard methodology that can be used to determine the ability of a sensor to measure the real permittivity, especially in dispersive and/or conductive dielectrics. One way to do this is to use dielectric liquids as in this work with the SCIP and as presented in Jones et al. (2005) and Blonquist et al. (2005) for seven sensors. A further important contribution is the need for "truth." This means we need to understand permittivity behavior in the frequency domain and particularly how geometry and hygroscopic water affect measurements. In our opinion this should be based on measurements with a network analyzer to measure the real permittivity. Huisman et al. (2004) indicated that the network analyzer results are much better than equivalent measurements with TDR. Although some work has been done on the effect of dielectric dispersion on TDR (Lin, 2003), it is far from being fully understood.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
APPENDIX
 REFERENCES
 
The capacitance probe circuit model was found to give an excellent prediction of instrument response in dielectric solutions and dielectric solutions with salts added. The circuit model gives a reasonable permittivity correction in an electrically conductive sandy soil. However, in clay soils the inclusion of the bulk soil EC, measured at 1 kHz, improved measurements of the permittivity only marginally. We suggest three possible reasons for this: (i) higher than expected real permittivity created by dielectric dispersion, (ii) a large contribution of the imaginary permittivity due to relaxation processes assumed to be negligible, and (iii) poor model prediction of permittivity due to excessive damping of the oscillator circuit. In the non-lossy sandy soils, the TDR and SCIP measurements compared very well. Because the measurements obtained as input for the SCIP model were unable to compensate fully for the dielectric losses in the heavier soils, the results from the SCIP and TDR did not compare well. We believe that the damping of the oscillator brought about by values of bulk EC above 2 dS m–1 accounts for a major portion of the discrepancy.


   APPENDIX
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 APPENDIX
REFERENCES
 
Equation [19] solved for the angular frequency results in

[A1]
with:

Equation [19] solved for the real material capacitance Cm' results in

[A2]
with

Hence, the real permittivity is determined according to

[A3]


   ACKNOWLEDGMENTS
 
The authors would like to acknowledge funding provided in part by the Department of Education for Northern Ireland (C.A.S.T., Ph.D. award), the Institute of Hydrology 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. Approved as journal paper no. 7733. Thanks are due to those landowners (Royal Portrush Golf Club, The National Trust, Mr. D. Black and Dep. Ag. N. Ireland, Upton Suffolk Farms) who allowed access to their property to collect soils. Guidance on the soils of N. Ireland was provided by Dr. J. Cruickshank and Mr. A. Higgins, without whom we wouldn't have found such interesting soils.


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




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