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Published online 9 April 2007
Published in Vadose Zone J 6:244-254 (2007)
DOI: 10.2136/vzj2006.0138
© 2007 Soil Science Society of America
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ORIGINAL RESEARCH

Performance of the Commercial WET Capacitance Sensor as Compared with Time Domain Reflectometry in Volcanic Soils

Carlos M. Regalado*, Axel Ritter and Rosa M. Rodríguez-González

Instituto Canario de Investigaciones Agrarias (ICIA), Dep. Suelos y Riegos, Apdo. 60, La Laguna, 38200 Tenerife, Spain. The mention of trade or manufacturer names is made for information only and does not imply an endorsement, recommendation, or exclusion by ICIA-Agricultural Research Institute
* Corresponding author (cregalad{at}icia.es).

All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.


Received 21 September 2006.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 Theory
 Materials and Methods
 Results and Discussion
 Conclusions
 REFERENCES
 
Among different alternatives, dielectric capacitance sensors may provide simultaneous readings of the volumetric water content and the soil solution electrical conductivity in the same sample volume at low cost. Reliability of capacitive sensors may be questioned, however, due to the low signal frequency at which they work, and also because of soil electrical conductivity effects on the water content estimation. In this study we evaluated the commercial capacitive WET Sensor (Delta-T Devices Ltd., Burwell, UK) compared with time domain reflectometry (TDR) in three volcanic soils with different textures. Although the WET Sensor uses internally the Hilhorst approach for describing the relationship between soil moisture and bulk and pore water electrical conductivity, results suggest that the Vogeler model is a better choice for the soils studied. The sensor provides good estimation of the bulk electrical conductivity, but determination of soil water content is biased. Thus, we propose an alternative empirical equation to determine the volumetric water content from the WET Sensor readings, the soil bulk density, and an estimate of the sensor's effective frequency.

Abbreviations: AIC, Akaike information criterion • EC, electrical conductivity • TDR, time domain reflectometry.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
Theory
 Materials and Methods
 Results and Discussion
 Conclusions
 REFERENCES
 
Capacitive dielectric sensors are a low-disturbance technique, inexpensive and nonhazardous, that provides instantaneous readings of volumetric water content, {theta} (m3 m–3). As a result, some capacitance sensors have become an alternative to the more expensive TDR technique (Dean et al., 1987; Dean, 1994; Evett and Steiner, 1995; Paltineanu and Starr, 1997; Robinson et al., 1998; Seyfried and Murdock, 2001; Kelleners et al., 2004). No waveform analysis algorithms are required for data interpretation of capacitive sensors, and these can be connected to most commercial dataloggers. On the other hand, capacitive sensor readings may strongly depend on the electric field frequency used by the system (Kelleners et al., 2005) and the electrical conductivity of the material (Campbell, 2002; Seyfried and Murdock, 2004). In addition, some capacitive sensors have been developed for determining both {theta} and the soil bulk electrical conductivity, {sigma} (S m–1) simultaneously and in the same sample volume.

The WET Sensor (Delta-T Devices Ltd., Burwell, UK) is a commercial capacitive dielectric sensor designed at the Institute of Agricultural and Environmental Engineering (Wageningen, the Netherlands), which estimates both the volumetric water content and the soil solution electrical conductivity in the same soil volume. The WET Sensor was developed from an upgrade of the Sigma probe type EC1 pore water conductivity meter now out of production. Although operating at a slightly higher frequency, the theory behind the Sigma probe (30 MHz) is the same as for the WET Sensor (20 MHz) (Hilhorst, 2000). The WET Sensor readings are based on independently measuring both components of the composite permittivity ({varepsilon}) of a material. The composite permittivity of the soil is a physical quantity that describes the response of the soil to an applied electric field. It is a complex number ({varepsilon} = {varepsilon}' – j{varepsilon}''), where the real part, {varepsilon}', represents the stored energy and the imaginary part, {varepsilon}'', accounts for the total energy absorption or loss. The real part of {varepsilon}, known as the dielectric constant, provides a surrogate measure of soil water content, while the imaginary component of the permittivity depends on the soil {sigma} and frequency of measurement, such that

Formula 1[1]
where {varepsilon}mr'' is the permittivity component due to molecular relaxation, f is the effective frequency (Hz) of the applied electric field, and {varepsilon}0 is the permittivity for free space ({varepsilon}0 = 8.854 x 10–12 F m–1). While the dependence of {varepsilon}'' on the effective frequency shown in Eq. [1] is well known (Kraszewski, 1996; Kelleners et al., 2005), the real part of the permittivity can also show a significant f dependence. This is referred to as the Maxwell–Wagner effect (Wagner, 1914; Campbell, 1990). Recently, Kelleners et al. (2005) studied this effect in a medium with severe dielectric dispersion, such as bentonite. They reported a strong dependence of the real part of the permittivity when frequency was below 500 MHz, and recommended improving the capacitance technique by using an electrical field with a frequency above this value. In fine-textured soils containing clay minerals, such frequency dependence can be particularly significant (Kelleners et al., 2005). According to Campbell (2002), electrical conductivity may bias permittivity measurements in saline media ({sigma} ≥ 10 dS m–1) even at frequencies of 1 GHz.

Accurate soil moisture determinations are unlikely if both the real and imaginary components of the permittivity are comparable (i.e., when f is low), such that when the electrical conductivity of the medium is high, soil moisture values will be overestimated (Dalton, 1992). Correction of water content estimations may be possible, however, if soil electrical conductivity, texture, density, and temperature are taken into account (Campbell, 2002). Some capacitive dielectric systems, such as the WET Sensor, are expected to suffer from these effects because they use a low operating frequency (20 MHz). Conversely, these frequencies can be achieved with simpler electronics that translate into lower cost sensors. Thus, when using such capacitive sensors, correcting soil moisture readings is desirable.

The three rods, 6.5 cm long, of the WET Sensor probe are spaced 1.5 cm apart, representing the two electrodes of a lossy capacitor. Sensor readings may be obtained with the HH2 moisture meter, which generates an incident oscillatory signal, a 20-MHz electromagnetic wave, which translates into an electric field between the rods. The dielectric and ionic behavior of the material between the center and outer rods produces changes in the incident 20-MHz wave. According to these changes, the sensor determines the capacitance Cc and the conductance Gc, thus providing the corresponding values of the real part of the apparent permittivity ({varepsilon}a') and {sigma}. In addition, temperature is measured with a miniature sensor built into the central rod such that the electrical conductivity can be referred to 25°C ({sigma}25).

The working principle of the WET Sensor is based on considering that a dielectric material between two electrodes (such as soil between the probe parallel rods) acts as a lossy medium, so that the electromagnetic wave impedance, Z ({Omega}), across the soil may be expressed as

Formula 2[2]
where {omega} = 2{pi}f is the angular frequency (rad s–1), {varepsilon} is the soil permittivity, and k (m) is a geometric factor determined by the distance between the electrodes and the area in contact with the soil, such that contact problems between the soil and the sensor rods will be reflected in this factor. A lossy capacitor can be represented by a capacitance, Cc, connected in parallel to an electrical resistance with a conductance, Gc. The conductance represents the loss energy and is related to {sigma} and {omega}. The capacitance represents the soil's capacity to store energy and is related to {varepsilon}', the real part of the soil permittivity. The WET Sensor estimates the soil {theta} from

Formula 3[3]
where b0 = {surd}({varepsilon}'{theta}{approx}0). A soil-specific calibration is recommended to estimate parameters b0 and b1, but in case this is not possible; values for b0 and b1 for different soil types (mineral, organic, sandy, and clayey) can be found in the sensor's user manual (Delta-T Devices, 2002). Equation [3] corresponds to the three-phase Birchack refractive index model (Birchack et al., 1974). From Yu et al. (1999),

Formula 4[4]

Thus, the parameters b0 and b1 gain physical meaning in terms of the soil porosity, {eta}, and the dielectric constants of the soil components. As an illustrative example, for a sandy soil with {eta} = 0.5, Eq. [4] yields b0 = 1.6 and b1 = 8.0, which are fairly close to the values presented in the sensor's user manual, i.e., b0 = 1.4 and b1 = 8.4, and to those reported by Alharti and Lange (1987) for TDR measurements in sandy soils at 23°C, i.e., b0 = 1.6 and b1 = 7.8. Notice that in Eq. [3], the soil bulk electrical conductivity, {sigma}, and the sensor's frequency, {omega}, are not considered. There is a need to include them explicitly in a calibration model for any electromagnetic soil water sensor, particularly for the WET Sensor that uses relatively small frequencies such that the quantity {sigma}/{omega} becomes large.

After Hilhorst (2000), the soil solution electrical conductivity, {sigma}w (S m–1), is estimated from {varepsilon}a' and {sigma} as

Formula 5[5]
where, as above, {varepsilon}w' is the dielectric constant of the soil solution, usually assumed to be equal to that of pure water (80.4 at 20°C). The {varepsilon}'{sigma}=0 in Eq. [5] is a soil-specific parameter with a default value of 4.1, representing the polarizability of the dry material. Values between 1.9 and 7.6 have been reported for {varepsilon}'{sigma}=0 (Hilhorst, 2000). These values are dependent on particle density, texture, and sensor pin-type configuration. Rearranging Eq. [5] such that

Formula 6[6]
the offset {varepsilon}'{sigma}=0 may be graphically estimated from a plot of {varepsilon}a' vs. {sigma}.

Hilhorst (2000) claimed finding good agreement between the Sigma probe {sigma}w readings and a laboratory four-electrode conductivity meter in seven different porous media. In fact, WET Sensor's user manual is based on Hilhorst's (2000) results (Delta-T Devices, 2002); however, Hamed et al. (2003) compared the Sigma probe with the TDR technique using nine different soil types, and observed a larger variability of Sigma probe soil-specific calibration parameters than originally predicted by Hilhorst (2000). More recently, Hamed et al. (2006) evaluated the WET Sensor compared with TDR. Their results revealed that the WET Sensor dielectric constant and consequent water content determinations were affected by the electrical conductivity of the moistening solution.

With respect to volcanic soils, previous studies have revealed that their permittivity varies with both water content (Weitz et al., 1997; Tomer et al., 1999; Miyamoto et al., 2001; Regalado et al., 2003) and electrical conductivity (Vogeler et al., 1996; Muñoz-Carpena et al., 2005) in ways that are soil specific, and that TDR standard calibration equations developed for montmorillonitic or kaolinitic soils are not applicable in soils of volcanic origin.

Thus, the specific objectives of this study were (i) to study the possible dependence of the WET Sensor's dielectric constant reading on the electrical conductivity in both liquid and porous media, (ii) to compare the WET Sensor's measurements in three different volcanic soils with those obtained with a widely accepted dielectric technique (TDR), (iii) to test pore water conductivity models, and finally, (iv) to derive an alternative empirical model for predicting {theta} from the WET Sensor's readings in the soils studied.


   Theory
TOP
 ABSTRACT
 INTRODUCTION
 Theory
Materials and Methods
 Results and Discussion
 Conclusions
 REFERENCES
 
Current Models for Estimating Solution Electrical Conductivity and Electrical Conductivity
To estimate the bulk electrical conductivity, {sigma}, from changes in the voltage amplitude of a TDR multireflection wave, several methods have been proposed (for a review, see Muñoz-Carpena et al., 2005). Of those, the approach of Nadler et al. (1991) considers that {sigma} is related to the soil's bulk impedance, Z ({Omega}), as follows:

Formula 7[7]
where Kcc is the cell constant of the TDR probe (m–1), and ft is a temperature correction factor (ft = 1 at 25°C). To account for cable losses and the presence of connectors, the multiplexer, or other discontinuities in the transmission line, Castiglione and Shouse (2003) suggested calculating Z as

Formula 8[8]
where Z0 is the characteristic impedance of the coaxial cable ({Omega}), {rho}0 is the sample reflection coefficient, and {rho}air and {rho}sc are the reflection coefficients measured in air and in the shorted circuit, respectively. Recently, Castiglione (as reported by Evett et al., 2006) derived a theoretical equation for the cell constant of a three-rod TDR probe of length L (m), such that

Formula 9[9]
where dp is the ratio of the rod radius, and the center-to-center rod interspacing. The need for calibrating the TDR probe in air and short circuited is thus eliminated.

Once {sigma} is computed with any of the aforementioned methods, the soil solution electrical conductivity, {sigma}w, may be obtained using different models. Rhoades et al. (1976) proposed the following relationship between {sigma} and {sigma}w:

Formula 10[10]
where {alpha} and ß are fitting parameters, and {sigma}s (S m–1) accounts for the surface conductance of the soil matrix. Several researchers (Rhoades et al., 1989; Mallants et al., 1996; Nadler, 1997) observed, however, that for low-salinity conditions, {sigma}s cannot be assumed to be constant, and thus the free term in Eq. [10] may be substituted by {delta}{sigma}s, where {delta} is a function of both {theta} and {sigma}s, i.e., {delta} = {delta}({theta},{sigma}s). For example, Rhoades et al. (1989) proposed the following model, where the {delta} factor includes the effect of solute distribution in the soil's mobile water fraction:

Formula 11[11]
with {chi} and {phi} being fitting parameters, and where {theta}sol = {rho}/{rho}s (m3 m–3) represents the volumetric solid content in the soil, calculated as the ratio between the soil's bulk ({rho}) and specific ({rho}s) densities.

In contradistinction to the above physical models, Vogeler et al. (1996) introduced an empirical relationship between {sigma} and {sigma}w for volcanic soils of New Zealand of the form

Formula 12[12]
where {nu}i are fitting parameters. More recently Muñoz-Carpena et al. (2005) developed an alternative model to describe the {sigma}–{sigma}w relationship observed in a volcanic soil of the Canary Islands:

Formula 13[13]
with a smaller number of fitting parameters, ci, than the Vogeler et al. (1996) approach.

Combining Eq. [3] and Eq. [5] and rearranging terms, we arrive at

Formula 14[14]
Hence, comparing the previous models with Eq. [14], one may notice that the Hilhorst (2000) approach lacks a free term, {sigma}s (S m–1), independent of {sigma}w, which accounts for the surface conductance of the soil matrix, for example, {sigma}s = c3{theta}2 in Eq. [13]. Furthermore, comparing Eq. [14] with the Rhoades et al. (1976) model, Eq. [10] and Eq. [14] are equivalent provided the following equalities hold:

Formula 15[15]

23.2 Calibration Models for the WET Sensor
As discussed above, due to the low operating frequency of the WET Sensor, dielectric constant readings may be affected by salinity, so that {theta} estimations based on Eq. [3] may become unreliable. Water content estimation with the WET Sensor may succeed, however, if the salinity dependence of {varepsilon}a' is taken into account. Several models have been proposed to correct the effect of bulk electrical conductivity (EC) on the soil dielectric constant (Wyseure et al., 1997; Robinson et al., 1999), such that

Formula 16[16]
where a, b, and c (<0) are fitting parameters.

Additionally, Malicki et al. (1996) showed that the {varepsilon}a'–{theta} relationship in mineral and organic soils may be scaled by taking into account the soil porosity. This was also observed by Bartoli et al. (2007) in volcanic soils. We may thus propose an alternative empirical equation for computing {theta} from the measured {varepsilon}a' and {sigma} values such that

Formula 17[17]
where d is an extra fitting parameter and {rho} (Mg m–3) is the soil bulk density.

Finally, Evett et al. (2005) found that the inclusion of the effective frequency, f, may improve the above model predictions such that the following equation may be introduced:

Formula 18[18]

and if both the effect of bulk density and frequency are taken into account, then

Formula 19[19]


   Materials and Methods
TOP
 ABSTRACT
 INTRODUCTION
 Theory
 Materials and Methods
Results and Discussion
 Conclusions
 REFERENCES
 
WET Sensor's Performance in Liquid Media
Jones et al. (2005) recommended characterization of water content sensors in fluids with known properties as a strategy for standardization. Hence, the WET Sensor (type WET-1/d) was tested in different reference solutions. First, the sensor was used to measure the electrical conductivity in a set of KBr aqueous solutions (0.0, 1.0, 2.0, 3.3, 7.3, and 10.0 dS m–1). These were compared with those obtained with a laboratory Crison 525 EC meter (Crison Instruments SA, Alella, Spain). Second, permittivity measurements were performed in reference fluids with known dielectric constant (Table 1). Finally, dielectric constants were measured in a set of KBr–ethanol/water (2:1) and aqueous KBr solutions with electrical conductivities of 0.0, 0.5, 1.1, 1.8, 2.7, 3.9, 4.6, 5.8, 6.3, 7.7, 8.5, and 9.2 dS m–1.


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  		TABLE 1. Dielectric constants ({varepsilon}a') of different reference fluids used for the WET Sensor validation.

 
Experiments in Saturated Porous Media
Three natural forest soils from Tenerife, Canary Islands (northernmost 28, southernmost 27, easternmost 16, westernmost 17), of volcanic origin (denoted as Soils A, B, and C) were used in this study (Table 2). These were air dried, sieved (<0.002 m), and packed at field bulk density in polyvinyl chloride (PVC) cylinders (0.106 m i.d. by 0.22 m). Thirty columns were prepared for each volcanic soil (A, B, and C) resulting from the combination of five different water contents expressed as porosity ({eta}) fractions (0.5{eta} to 0.9{eta} in 0.1{eta} steps) and six different KBr moistening solutions (0, 1, 2, 4, 6.5, and 9 dS m–1). Since for Soil C the columns with water content corresponding to soil moisture 0.8{eta} and 0.9{eta} presented a supernatant that was not homogeneously mixed with the soil, these samples were rejected and an additional column with {theta} = 0.4{eta} was prepared. In each cylinder {varepsilon}a', {sigma}, and temperature readings were taken with the WET Sensor. To compare these readings with independent measurements, {varepsilon}a' and {sigma} were also estimated with a TDR Trase System I 6050X1 (Soilmoisture, Santa Barbara, CA). For computing {sigma} with the TDR technique, the procedure described in Muñoz-Carpena et al. (2005) was followed. Soil bulk impedance ({Omega}) was calculated with Eq. [8]. Volumetric water content was determined by gravimetry, while {sigma}w was measured with the laboratory EC meter in soil solution samples. These were obtained with Rhizon extractors (Eijkelkamp, Giesbeek, the Netherlands) as described in Regalado et al. (2005).


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  		TABLE 2. Physical and chemical properties of the volcanic soils used in the study (S. Armas Espinel, unpublished data, 2005).

 
Soil Water Content Calibration
Soil water content vs. {varepsilon}a' calibrations were performed in soil cylinders of dimensions 0.106 m i.d. by 0.22 m for TDR and 0.076 m i.d. by 0.076 m for the WET Sensor. The soil samples were saturated from bottom to top, to overcome air entrapment, with a 0.005 M CaCl2 solution to minimize clay dissagregation, while thymol was added to serve as a microbial inhibitor. Water content was determined by gravimetry simultaneously with dielectric constant readings. In early stages the soil columns, initially saturated, were left to drain freely. Then weights and both TDR and WET readings were recorded while the columns were first dried at room temperature, then oven dried at 50 to 70°C, and finally at 105°C until constant weight. In all instances, the soil columns were left to reach room temperature before readings to diminish possible temperature effects on the dielectric constant of water and to allow homogenization and stabilization of the moisture content.

Statistical Methods
Each model's goodness of fit was quantified with the coefficient of efficiency, Ceff, also known as the Nash–Sutcliffe coefficient (Nash and Sutcliffe, 1970). This is defined as the ratio of the mean square error to the variance of the observed data, subtracted from unity. The coefficient of efficiency compares the variance about the 1:1 line (perfect agreement) to the variance of the observed data. It ranges from –{infty} to 1, where more positive values indicate a better agreement. Notice that for nonregression models, the Ceff does not represent the proportion of sum of squares (i.e., deviation of the observed values to their mean) explained by the model. It represents an improvement over R2 (0 ≤ R2 ≤ 1, given as the square of the Pearson's product-moment correlation coefficient), because it is sensitive to differences in the observed and model-predicted means and variances. This is not the case with R2, which is limited in that it standardizes for differences between observed and predicted means and variances (Legates and McCabe, 1999).

Model overparameterization and parameter correlation is also an issue to take into account when discerning between models. The Akaike information criterion (AIC) may help to decide whether an increment in the number of parameters, q, is justified, such that the preferred model is that with the most negative AIC. The AIC is defined as

Formula 20[20]
where n is the number of observations and RSS is the residual sum of squares (Akaike, 1974).


   Results and Discussion
TOP
 ABSTRACT
 INTRODUCTION
 Theory
 Materials and Methods
 Results and Discussion
Conclusions
 REFERENCES
 
Determination of Electrical Conductivity at 25°C and Dielectric Constant in Fluids
Figure 1a shows the good performance of the WET Sensor for measuring {sigma}25 in fluids. The near-perfect agreement between the WET Sensor's {sigma}25 measurements and those obtained with the laboratory EC meter rendered a high Ceff (0.999) and a low RMSE (0.09 dS m–1). Also, Fig. 1b indicates that the sensor accurately estimated the dielectric constant in nonsaline reference fluids (Ceff = 0.992, RMSE = 2.49). These errors are within the specified accuracy of ±2.5 for {varepsilon}a' and ±0.1 dS m–1 for {sigma} (Delta-T Devices, 2002). However, {varepsilon}a' readings became inaccurate when the electrical conductivity of the fluid was increased (Fig. 1c). Although, the sensor's user manual (Delta-T Devices, 2002) extends the interval for accurate stable reading up to 6 dS m–1, from Fig. 1c it follows that this upper limit reduces to 3 dS m–1. The real part of the dielectric constant of an electrolyte solution at low frequencies, {varepsilon}w', decreases linearly with increasing electrical conductivity such that (Robinson and Stokes, 1959)

Formula 21[21]
where {varepsilon}'H2O is the dielectric constant for pure water, C is the ion concentration (mol dm–1), and the slope (dielectric decrement), {tau}, depends on the type of electrolyte. In general, the decrease in {varepsilon}w' predicted by Eq. [21] is small within the usual range of salinity in soils ({sigma}w < 1 S m–1). Permittivity reduction may not be negligible in the diffusive double layer near the soil minerals however, due to a higher cation concentration (Friedman et al., 2006). Thus Fig. 1c shows that, far from being linear, the WET Sensor {varepsilon}a' readings decreased more steeply than expected from Eq. [21], rendering even negative physically unrealistic {varepsilon}a' values. This has an additional implication: if one wishes to include corrections to {varepsilon}w' in Eq. [5] to account for the decrease in {varepsilon}w' due to increased EC, this cannot be done from WET Sensor readings in reference electrolyte solutions, but one must use Eq. [21] with tabulated values of {tau}. Overall, these results show that an increased EC has a significant undesirable effect on the WET Sensor real permittivity determination.


Figure 1
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  		FIG. 1. The WET Sensor's performance (a) to measure electrical conductivity (EC) at 25°C ({sigma}25) in solutions with known EC, and to determine (b) dielectric constant ({varepsilon}a') in nonsaline reference fluids, and (c) the influence of EC on the WET Sensor's dielectric constant reading in two saline solutions (Ceff is the coefficient of efficiency).

 
Determination of Bulk Electrical Conductivity in the Volcanic Soils
Figure 2 shows that the bulk electrical conductivity measured with the WET Sensor and the TDR {sigma} estimate agreed in the three studied volcanic soils (Ceff > 0.93, RMSE ≤ 0.07 dS m–1). In this case, the cheaper WET Sensor is preferred to the more expensive TDR, because it gives an instant {sigma} measure without the need for a wave analysis implementation.


Figure 2
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  		FIG. 2. Comparison between electrical conductivity ({sigma}) readings obtained with the WET Sensor and the time domain reflectometry (TDR) Trase System in Soils A, B, and C (Ceff is the coefficient of efficiency).

 
Determination of the Soil Solution Electrical Conductivity
The WET Sensor uses Eq. [5] to estimate the soil solution conductivity, {sigma}w. One preliminary step is to compute {varepsilon}'{sigma}=0 as an offset from the plot of {varepsilon}a' vs. {sigma} (Eq. [6]). Figure 3 shows data from an experiment where a soil initially saturated with a 0.005 M CaCl2 + thymol solution was dried from saturation to oven dry. For Soils A and C, we observed that the {varepsilon}a' vs. {sigma} data may be closely linear, and thus Eq. [6] renders {varepsilon}'{sigma}=0 = 3.15 (Soil A) and {varepsilon}'{sigma}=0 = 4.83 (Soil C) by linear fitting. By contrast, for Soil B as {sigma} -> 0, the {varepsilon}a'–{sigma} relationship curved downward. Hamed et al. (2003) also reported a nonlinear {varepsilon}a'–{sigma} relationship for their Värpinge topsoil. Notice that for computing the {varepsilon}'{sigma}=0 offset, linearity of the {varepsilon}a'–{sigma} relationship was not required. In our case, if a polynomial rather than a linear fitting is performed for Soil B, a value of {varepsilon}'{sigma}=0 = 4.75 (closer to the default 4.1) instead of 8.27 is obtained.


Figure 3
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  		FIG. 3. Relationship between dielectric constant ({varepsilon}a') and electrical conductivity ({sigma}) measured with the WET Sensor for determining the offset {varepsilon}'{sigma}=0.

 
We tested Eq. [14] for the WET Sensor using {sigma}w experimental data (referenced to the same temperature as {sigma}), and the gravimetrically determined {theta} values (Fig. 4 ). Fitted b1 values were: 8.93 (Soil A), 6.04 (Soil B), and 5.97 (Soil C). Some agreement was observed for low conductivity in Soils B and C, but in general predicted values departed from the 1:1 line. The bad performance of the Hilhorst (2000) model is not surprising, taking into account the following. As we have shown in Eq. [15], constraining {varepsilon}'{theta}{approx}0 {approx} {varepsilon}'{sigma}=0, reduces the Hilhorst (2000) model to a particular case of the Rhoades et al. (1976) model with negligible surface conductance of the soil matrix ({sigma}s = 0). In our case, such an approximation holds (Soil A: {varepsilon}'{theta}{approx}0 = 3.1, {varepsilon}'{sigma}=0 = 3.15; Soil B: {varepsilon}'{theta}{approx}0 = 3.4, {varepsilon}'{sigma}=0 = 4.75; and Soil C: {varepsilon}'{theta}{approx}0 = 3.7, {varepsilon}'{sigma}=0 = 4.83), given that a 30% reduction in the above {varepsilon}'{sigma}=0 parameter values leads to a change in {sigma}w within the specified ±0.1 dS m–1 accuracy of the WET Sensor (Delta-T Devices, 2002).


Figure 4
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  		FIG. 4. Correlation between electrical conductivity of the soil solution ({sigma}w) observed in the Rhizon extractor samples and {sigma}w predicted using Eq. [14], {sigma} measured with the WET Sensor, and the soil water content {theta} determined by gravimetry (Ceff is the coefficient of efficiency).

 
The above results bring into question the validity of Eq. [5] (see also Hamed et al., 2003). Alternatively, one may estimate {sigma}w using the models described in Rhoades et al. (1976), Rhoades et al. (1989), Vogeler et al. (1996), and Muñoz-Carpena et al. (2005) (Eq. [10–13]GoGoGo). The two last models have been shown to be the most appropriate for volcanic soils (Muñoz-Carpena et al., 2005). For the three volcanic soils investigated here, the Vogeler et al. (1996) model yielded a better fit, although the Muñoz-Carpena et al. (2005) approach has fewer parameters, q (Table 3). In our case a smaller moisture content was explored, since the extraction technique used here (Regalado et al., 2005) allowed extraction of soil solution held up to –600 kPa, in contrast to the –70 kPa reported by Muñoz-Carpena et al. (2005). Thus the results presented in this study broaden the applicability of the Muñoz-Carpena et al. (2005) model in volcanic soils for a wider moisture range. According to the computed AIC, the Vogeler et al. (1996) model is a slightly better choice than the one proposed by Muñoz-Carpena et al. (2005) (Table 3). In light of the wide range of coefficient values in Table 3, the WET Sensor remains as an alternative for determining the soil solution conductivity, provided an appropriate soil specific calibration is performed beforehand.


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  		TABLE 3. Estimation of electrical conductivity ({sigma}) from electrical conductivity of the soil solution ({sigma}w) and volumetric water content ({theta}) for the soils studied, using the Vogeler et al. (1996) and the Muñoz-Carpena et al. (2005) models and either the WET Sensor or time domain reflectometry (TDR).

 
Effects of Salinity on the Estimation of the Dielectric Constant
As we have just discussed above, the WET Sensor computes {sigma}w from Eq. [5], making use of {varepsilon}a' instead of {theta}. Figure 5 shows the observed values of pore water conductivity vs. those predicted using Eq. [5] and real permittivity values determined using the WET Sensor and TDR. Two conclusions may be drawn. Some agreement is observed for low salinity values (<1 dS m–1) for Soils B and C, but in general data diverge from the 1:1 line, more so for the WET Sensor. Thus, we may conclude that at least for the soils here investigated, the Hilhorst (2000) model is not valid, and that this is especially true for the WET Sensor, where {varepsilon}a' is biased. If instead of {varepsilon}a', one uses the gravimetrically determined {theta} according to Eq. [14], goodness of fit improves (cf. Fig. 4 and 5). This is only so in appearance because the fitted b1 compensates for both the bias in {varepsilon}a' and the reduced performance of Eq. [5] (from Eq. [4], the expected b1 = 8.4). In any case, either the Vogeler et al. (1996) or the Muñoz-Carpena et al. (2005) models are a better alternative, as we have already shown above (Table 3).


Figure 5
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  		FIG. 5. Comparison between electrical conductivity of the soil solution ({sigma}w) measured in the Rhizon extractor samples (observed) and {sigma}w estimated using the Hilhorst (2000) model (Eq. [5]; predicted). Goodness of fit criteria given for the WET Sensor only (Ceff is the coefficient of efficiency).

 
The low effective frequency of the WET Sensor makes {varepsilon}a' unreliable as salinity increases. This was already detected in fluids (Fig. 1c) and is here further confirmed in volcanic soils. Although such salinity values would not presumably affect the TDR readings (operating at a much higher frequency, i.e., >500 MHz), however, still Eq. [5] fails to predict {sigma}w (Fig. 5).

Relationship between Soil Water Content and the Dielectric Constant
Experiments showed differences between TDR and WET Sensor {varepsilon}a' measurements, such that in general {varepsilon}a' was larger for the WET Sensor than for the TDR for similar {theta} (Fig. 6 ). The larger dielectric constant rendered by the WET Sensor may be explained in terms of the frequency dependence of the real permittivity {varepsilon}a' for f <500 MHz. An increase of stored energy due to polarization of the clay particle diffuse electrical double layer, and the Maxwell–Wagner effect, raises the permittivity due to charge accumulation in clay surfaces resulting in an increase of soil polarizability. Additionally, capacitance sensor frequency decreases as permittivity increases (Dean et al., 1987). At a base frequency of the incident wave of 20 MHz, the change in the resultant oscillation frequency may be large in proportion to 20 MHz, exacerbating the confounding effect of the frequency dependence of permittivity. This is a common problem for capacitance type sensors, but the confounding of these two effects (frequency change due to water content variation and permittivity dependency on frequency) is often overlooked.


Figure 6
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  		FIG. 6. Relationship between volumetric water content ({theta}) and dielectric constant ({varepsilon}a') observed with the WET Sensor and time domain reflectometry (TDR) in the volcanic soils studied. Solid lines indicate slope changes in the {varepsilon}a'–{theta} trend at certain {theta} values, {theta}dc (arrows).

 
The dielectric constant, {varepsilon}a', obtained with the TDR was also less affected by saline conditions than it was for the WET Sensor. This was confirmed by computing the mean {varepsilon}a' standard deviations, SD, for varying {sigma}w at different water contents: SDWET – 2 vs. SDTDR – 1.2 (Soil A); SDWET – 4.6 vs. SDTDR – 0.7 (Soil B); and SDWET – 4.1 vs. SDTDR – 0.7 (Soil C).

Differences in {varepsilon}a' between TDR and the WET Sensor were more pronounced for {theta} > 0.3 m3 m–3 (Fig. 6). A similar result was obtained by Campbell (1990) and Kelleners et al. (2005), who suggested the existence of a percolation threshold at which the water phase becomes connected because air is replaced by water. Such a percolation threshold would depend on bulk density (Kelleners et al., 2005). Additionally, the role of phase configuration would be very important in producing the complex dielectric response depicted in Fig. 6 observed with both TDR and the WET Sensor (Chen and Or, 2006). From an interfacial point of view, the number of interfaces and degree of fragmentation (contributing to the Maxwell–Wagner effect) would be much larger at the low water content; in contrast, the largest difference between the two measurements is manifested at intermediate water contents, which points toward the possible role of phase configuration. According to Chen and Or (2006), the initial concave rise in effective permittivity observed in Fig. 6 at low saturation may be explained by an AWS configuration (air entrapped in water shell inclusions embedded in a background of solid matrix), while the steep convex increase at medium saturation would be captured by an SWA configuration (solid grains coated with water placed in a background of air).

A change in slope in the {varepsilon}a'–{theta} curve may be observed around 0.3 m3 m–3 in Fig. 6. Blonquist et al. (2006) have recently pointed out that in aggregated porous media, the water content where the slope of the {varepsilon}a'–{theta} curve changes (denoted as {theta}dc) does not simply occur after the interaggregate pores have drained and before the water content at which intraaggregate pores have emptied (denoted as {theta}hc), but this is a function of the connectivity ratio, 1 – {theta}dc/{theta}hc. Volcanic soils exhibit a strong microaggregation of particles, and the different {theta}dc depicted in Fig. 6 might be explained based on the ideas of Blonquist et al. (2006). An additional change of slope in the {varepsilon}a'–{theta} curve may be also observed at 0.5 m3 m–3 (Soil A), 0.6 m3 m–3 (Soil B), and 0.65 m3 m–3 (Soil C) (Fig. 6). Soil water retention curves suggest that such {theta} values may be related to a certain decrease in water content from saturation (results not shown).

Alternative Model for Predicting Volumetric Water Content from the WET Sensor Readings
Parameter values and goodness of fit criteria for the alternative models for predicting {theta} from the measured {varepsilon}a' and {sigma} values (Eq. [16–19]GoGoGo) are summarized in Table 4. We have found that the inclusion of the bulk density, {rho} (Mg m–3), results in a model that is valid for the three different volcanic soils here investigated. Ignoring the effect of bulk density not only reduces goodness of fit considerably, but also the AIC is worsened and not all parameter values are significant (Table 4). To investigate the effect of including the sensor's effective frequency (Eq. [18–19]Go), we have computed f values from the {theta} determined by gravimetry using the power law {theta} {propto} SFe proposed by Paltineanu and Starr (1997), where SF is a linearly scaled f and the power e ~ 2, such that f decreases with increasing {theta} (see also Evett et al., 2005). Based on the goodness-of-fit criteria (Table 4), Eq. [19] results in an improvement of soil moisture predictions even though no additional parameters were fitted compared with Eq. [17]. This is also the case when no bulk density term is included, such that the goodness of fit of both individual soil data and all soils together is improved by taking into account f in the calibration equation (cf. results for Eq. [16] and [18] in Table 4). The results in Table 4, however, also show that the inclusion of f alone is not sufficient to describe the effects of bulk density (cf. goodness of fit and AIC criteria for all soils in Eq. [17–18]Go). Notice the significance of the negative values of the coefficients c in Table 4. They are negative for the four models, as they should be if the apparent permittivity, {varepsilon}a, is inflated by a contribution from the imaginary part ({sigma}/f) such that {varepsilon}a needs to be corrected to properly reflect only the contribution due to free water in the soil. Finally, Fig. 7 shows the match between observed water content and {theta} calculated using Eq. [19].


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  		TABLE 4. Parameters and goodness-of-fit criteria for the alternative models considered for determining volumetric water content ({theta}) from dielectric constant ({varepsilon}a') and electrical conductivity ({sigma}) (Eq. [16–19]GoGoGo). Parameters are significant (P ≤ 0.0001) unless otherwise indicated.

 

Figure 7
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  		FIG. 7. Comparison between observed volumetric water content ({theta}, determined by gravimetry) and predicted soil water content using Eq. [19].

 

   Conclusions
TOP
 ABSTRACT
 INTRODUCTION
 Theory
 Materials and Methods
 Results and Discussion
 Conclusions
REFERENCES
 
A series of laboratory experiments was conducted with the capacitive dielectric WET Sensor to evaluate its performance in volcanic soils. The WET Sensor's measurements were compared to those obtained with a TDR system. Experiments on different reference liquids with known properties showed that the WET Sensor provided highly accurate readings of the apparent dielectric constant ({varepsilon}a') when salinity was low, but these became inaccurate when the electrical conductivity of the liquid increased above 3 dS m–1. With respect to bulk electrical conductivity, {sigma}, this was measured satisfactorily in both the volcanic soils and in liquid media. Therefore, due to the simplicity of the measurement, the WET Sensor was considered a preferred alternative to TDR for determining {sigma}. The WET Sensor predicts the pore water electrical conductivity ({sigma}w) from the {varepsilon}a' and {sigma} readings based on the Hilhorst (2000) model; however, we showed that this model was not valid for the soils here investigated for either the WET Sensor or TDR, and that this is especially true for the former, where {varepsilon}a' is biased. In general, differences in {varepsilon}a' between TDR and the WET Sensor were more pronounced as soil moisture increased. The results revealed also that the relationship between {sigma}, {sigma}w, and soil water status was better described with the Vogeler et al. (1996) model. Finally, although the WET Sensor's {varepsilon}a' readings were biased, soil moisture predictions succeeded using an alternative empirical equation proposed here that takes into account the salinity dependence of {varepsilon}a', the soil bulk density, and an estimate of the sensor's effective frequency. Further developments of the WET Sensor may consider displaying the effective frequency to improve soil moisture determination.


   ACKNOWLEDGMENTS
 
We would like to thank A.R. Socorro (ICIA) for her help with the laboratory instrumentation, and S. Armas Espinel (University of La Laguna, Spain) for the determination of the soil properties in Table 2. The work was financed with funds of the INIA–Programa Nacional de Recursos y Tecnologías Agroalimentarias (Projects RTA-2005-205 and RTA-2005-228).


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 Theory
 Materials and Methods
 Results and Discussion
 Conclusions
 REFERENCES
 





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