Comparison of Capacitance-Based Soil Water Probes in Coastal Plain ...

Comparison of Capacitance-Based Soil Water Probes in Coastal Plain Soils David D. Bosch*

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

ABSTRACT

structive by nature. In addition, the gravimetric water content (w, gm gm⫺1) determined through this method must be related back to ␪ through a measured or estimated sample volume to estimate water volume. The two are related through the soil bulk density (␳b, gm cm⫺3) and the density of water (␳w, gm cm⫺3):

Soil water influences infiltration and runoff and consequently water quality. In situ measurements of soil water are critical for understanding hydrologic and water quality processes. Many advances have recently been made in soil water measurement techniques. In particular, instruments for estimating volumetric water content from measurements of soil electrical properties have become common. While the instruments have been shown to be good indicators of relative changes in soil water, questions remain regarding their ability to yield quantitative estimates. Most of these techniques rely on a limited set of calibration equations obtained through laboratory analysis of homogeneous soil materials (i.e., sand, silt, and clay). The accuracy of two capacitance-based soil water probes was assessed for a range of Coastal Plain soils. The probes measure capacitive and conductive soil properties and relate these to water content through calibration. Calibration curves for three different Coastal Plain soils were developed. Laboratory tests indicate that the probes yield estimates of volumetric water content within ⫾0.05 cm3 cm⫺3 of the observed values for these soils. Greater variability was observed in comparisons with field observations. Results indicate that improved equations can be developed through soilspecific laboratory calibration. The capacitance probes should prove to be useful tools for estimating volumetric water content in these soils. Additional work is required to quantify probe differences and the effects of soil conductivity on the measurements.

␪⫽w

␳b ␳w

[2]

USDA-ARS, Southeast Watershed Research Laboratory, P.O. Box 748, Tifton, GA 31793. Contribution from the USDA-ARS, Southeast Watershed Research Laboratory in cooperation with University of Georgia Coastal Plain Experiment Station. All programs and services of the USDA are offered on a nondiscriminatory basis without regard to race, color, national origin, religion, sex, age, marital status, or handicap. Trade names and company names are included for the benefit of the reader and do not imply any endorsement or preferential treatment of the products listed by USDA. Received 22 Jan. 2004. Original Research Paper. *Corresponding author ([email protected]).

The water density is normally assumed equal to 1 gm cm⫺3. The measurement or estimation of ␳b can introduce error into the estimate of ␪ using the gravimetric method. Field-based indirect measurements of ␪ are attractive because of their relative ease and relatively nondestructive nature. Some commonly used techniques include the neutron probe (Gardner et al., 2001), time domain reflectometry (TDR) (Robinson et al., 2003), and capacitance methods (Paltineanu and Starr, 1997). Advances in electronics and data collection have made these methods more attractive for measuring spatial and temporal changes in soil water. Extensive reviews of these techniques have been conducted (Gardner et al., 2001; Robinson et al., 2003; Topp and Ferre, 2002). The TDR and capacitance methods estimate ␪ based on an inferred measurement of soil dielectric (Topp and Ferre, 2002). The relative permittivity, or dielectric constant, is the ratio of the dielectric of the material to the dielectric of a vacuum. The dielectric constant of a soil describes its ability to store electrical energy by separating opposite polarity charges in space. The complex dielectric of a soil can be divided into real and imaginary components (Topp et al., 1980). The real part of the dielectric describes its ability to store energy in an applied electric field while the imaginary part relates to energy losses. Energy losses increase with increases in soil conductivity (Saarenketo, 1998). If the losses are small the imaginary part can be neglected in the determination of ␪ and the dielectric becomes a function of soil constituents alone (Topp et al., 1980). Estimates of the real component of the dielectric are often referred to as the apparent dielectric (Ka) because they neglect the energy loss components. The capacitance method uses the soil as part of a capacitor in which the permanent dipoles of water in the dielectric medium are aligned by an electric field and become polarized (Paltineanu and Starr, 1997; Gardner et al., 2001). These probes typically operate in the radio-frequency regime from 10 MHz up to several hundred MHz. Estimates of Ka obtained through the capacitance methods may be different from those ob-

Published in Vadose Zone Journal 3:1380–1389 (2004). © Soil Science Society of America 677 S. Segoe Rd., Madison, WI 53711 USA

Abbreviations: MSE, mean square error; TDR, time domain reflectometry.

S

oil water content is an important soil characteristic used to evaluate irrigation needs, runoff susceptibility, and plant-available water. Volumetric water content is defined as: ␪⫽

Vw Vt

[1]

where ␪ is the volumetric water content (cm3 cm⫺3), Vw is the water volume (cm3), and Vt is the total volume of soil, water, and air (cm3). Methods commonly used to measure soil water include the gravimetric method, inference from soil matric pressure and soil water release curves, neutron probe, and indirect measurements based on electrical properties of the soil (Gardner, 1986; Gardner et al., 2001; Topp and Ferre, 2002). Each of these methods have strengths and shortcomings. While the gravimetric method, consisting of collecting the soil and oven-drying, is considered the most reliable, it is de-

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tained through TDR methods due differences in measurement methods. The dielectric constant for water at 20⬚C is 80, dry soil is from 4.5 to 10, while that for air is close to 1 (Robinson et al., 2003). Because of this large difference, a change in water content in the soil will change the dielectric constant. The relationship between the water content change and the dielectric of the medium depends on temperature, soil type, sensor frequency, and chemical properties of the soil (Eller and Denoth, 1996; Saarenketo, 1998; Robinson et al., 2003). Dielectric is inversely related to soil temperature (Weast, 1980). For pure water, its dielectric constant would change from 84 to 73 if the temperature were changed from 10 to 40⬚C (Weast, 1980). Considering no interactions in the soil, a decrease in temperature from 20 to 15⬚C at 20% ␪ will increase the dielectric constant by a value of 0.4 (Jacobsen and Schjonning, 1993), or conversely, a difference in ␪ of 0.7%. Thus, the effect of temperature in most cases would be expected to be small, as was found by Topp et al. (1980) over a temperature range from 10 to 36⬚C. Concentration of salts within soils increases their electrical conductivity and dielectric losses. Robinson et al. (1998) found that losses due to soil conductivity can be neglected for conductivities less than 0.5 dS m⫺1. Thus, a measure of soil conductivity can be used to evaluate whether or not the salinity will have an effect on the soil water measurement via the capacitance method. Estimates of Ka are often related to ␪ through empirical equations. Many of the relationships relating ␪ to Ka are written as cubic equations: ␪ ⫽ a ⫹ bKa ⫹ cK 2a ⫹ dK 3a

which is then related to the water content through relationships such as Eq. [3]. The Hydra probe capacitancebased sensor recently developed by Stevens-Vitel (Beaverton, OR) yields estimates of volumetric water content, temperature, soil conductivity, and salinity. The probe is of interest to the scientific community due to the soil properties it can be used to estimate. StevensVitel lists three separate calibration equations for the Hydra probe based on primary soil type (Table 1). Decagon Devices (Pullman, WA) has also recently developed a capacitance-based soil water probe, the Echo probe. The Echo probe is relatively small and inexpensive, making it well suited for in situ measurements. The device measures the rate of change of a voltage imposed on the soil by the probe. Equations are given by the vendor to convert the measured voltage into volumetric water content. While both of these probes have features making them inviting for field research, neither has undergone rigorous field testing. The objectives of this research were to: • test the reliability of the Stevens-Vitel Hydra and Decagon Echo soil water probes based on factorysupplied equations for a range of Coastal Plain soils, • test other dielectric-based equations for the Stevens-Vitel Hydra probe, and • develop improved equations for the probes if warranted by the results. METHODS Tests were conducted to assess the accuracy of the Hydra and Echo probes. Laboratory studies were conducted to calibrate the probes under controlled conditions. Field tests were conducted to evaluate the factory equations in a setting where variability in climatic and geologic conditions can be expected. The Topp and Eller–Denoth equations relating ␪ to Ka were also examined (Table 1). In addition, a nonlinear regression analysis was conducted to develop soil-specific calibration equations using the laboratory data.

[3]

Several of these are outlined by Jacobsen and Schjonning (1995). The most frequently cited equation relating ␪ to Ka was developed by Topp et al. (1980). The Topp equation was based on analysis of four mineral soils, ranging from a sandy loam to a clay. A calibration presented by Roth et al. (1990) included the temperature dependence of Ka in their calibration equation. Jacobsen and Schjonning (1993) included the dry bulk density, percent clay, and percent organic matter. However, for the 10 mineral soils examined by Jacobsen and Schjonning (1993), including these parameters in addition to Ka resulted in only a slight improvement over a relationship without those parameters. Eller and Denoth (1996) developed a quadratic equation that was listed as valid for ␪ ⱖ 3% for a wide variety of soils. The coefficients for the Topp and Eller–Denoth equations in the form of Eq. [3] are shown in Table 1. Capacitance-based probes measure the apparent dielectric constant of the soil surrounding the sensor,

Probe Descriptions The Stevens-Vitel Hydra probes perform electrical measurements of the capacitive and conductive properties of soil at a frequency of 50 MHz. These properties are then related to the soil’s water and conductivity. The device consists of four 6-cm-long, 3-mm-diameter stainless steel tines, three in a triangular fashion around the fourth tine in the center of the triangle. The middle tine is used to measure temperature. The length of the entire device is 10 cm and the outside diameter is 4 cm. The manufacturer reports that the effective sensing volume for the probe as a cylinder is approximately 2.5 cm in diameter and 6 cm in length, bounded on the outside by the three outer tines, and on the ends by the probe head and the free end of the tines. The probe wiring is sealed in a PVC case.

Table 1. Coefficients for various cubic equations in the form of Eq. [3] relating the volumetric water content to apparent dielectric. Equation Topp Eller–Denoth Hydra probe for sand Hydra probe for silt Hydra probe for clay

a ⫺0.0530 ⫺0.0033 ⫺0.0863 ⫺0.1304 ⫺0.2093

b 2.920 1.484 3.251 3.861 6.625

⫻ ⫻ ⫻ ⫻ ⫻

c 10⫺2 10⫺2 10⫺2 10⫺2 10⫺2

⫺5.500 6.000 ⫺9.751 ⫺9.331 ⫺2.519

⫻ ⫻ ⫻ ⫻ ⫻

d 10⫺5

10⫺5 10⫺4 10⫺4 10⫺3

4.300 ⫻ 0 1.632 ⫻ 7.587 ⫻ 3.350 ⫻

10⫺6 10⫺5 10⫺6 10⫺5


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The Hydra probe requires an excitation voltage between 7 and 30 V DC. Its output consists of four voltages, one from each of the four tines. The Hydra probes come with software provided by the manufacturer to convert measured voltages into temperature-corrected estimates of the complex dielectric, which can then be used to determine the capacitive (real) and the conductive (imaginary) parts of the soil’s response. The capacitive part of the response reflects the water content while the conductive part reflects predominantly soil conductivity (Gardner et al., 2001). Temperature is determined from a thermistor in the probe. Both the real (Ka) and imaginary dielectric vary with temperature. To compensate for this a temperature correction is applied using the measured soil temperature. The temperature correction amounts to calculating what the constants should be at 25⬚C. The calculated soil water is based on the temperature-corrected real dielectric constant while the soil conductivity, soil salinity, and temperature-corrected soil conductivity are all based on both the temperaturecorrected real and imaginary dielectric constants. The manufacturer reports that the accuracy of the real and imaginary dielectric constants are typically ⫾1% or 0.5, whichever is greater. The readings reportedly become less reliable as soil conductivity levels increase and as temperature varies from 25⬚C. The soil temperature measurement the Hydra probe makes is used to remove most of the temperature effects. The typical accuracies reported by the manufacturer are ⫾3% for soil water, ⫾0.0014 S m⫺1 for soil conductivity, ⫾20% for salinity, and ⫾1⬚C for temperature. The response of the probe varies with soil type. Separate calibration equations are provided by the manufacturer for three different soil types: sand, silt, and clay (Table 1). The manufacturer indicates that the accuracy of the ␪ measurement can be improved with soil type information. The second probe examined was the Decagon Echo dielectric aquameter. Two probe lengths were available, a longer probe with a measuring length of 20 cm and a shorter probe with a measuring length of 10 cm. The probe itself is approximately 5 cm longer than the measuring length, 3 cm wide, and 1.5 mm thick. The probe requires an excitation voltage of 2.5 to 5 V. The probe outputs a voltage proportional to the dielectric properties of the soil. The manufacturer reports that the output is effected by soil temperature, texture, and salinity. Similar to the Hydra probe, the accuracy of the Echo probe decreases with increasing soil conductivity. Reported soil water accuracies are ⫾3% without or ⫾1% with calibration. The standard calibration equation given by Decagon for the 20-cm Echo probe is:

␪ ⫽ ⫺0.29 ⫹ 0.000695mV

[4]

where mV is the millivolt output of the probe with a 2.5-V excitation. The factory equation provided and used for 10-cm probes was different from that provided for the 20-cm probes. The intercept for the 10-cm probes is ⫺0.0376 while the slope is 9.36 ⫻ 10⫺4. The Hydra and Echo probes were controlled and read with a Campbell Scientific (Logan, UT) CR10X data logger. Power was supplied at 12 V for the Hydra probes and 2.5 V for the Echo probes. The Type A Hydra Probes were used, which are specially designed for the Campbell data loggers.

Laboratory Calibration Three different soils were used for the laboratory calibration study. The first sample was collected from the Ap horizon (top 10 cm) of a Tifton loamy sand (fine-loamy, kaolinitic, thermic Plinthic Kandiudult), with a high sand content (Table

Table 2. Physical characteristics of the validation soils. Sample Tifton Ap Tifton Bt Fuquay Ap

Sand

Silt

Clay

Average packing bulk density

Average soil conductivity

87 60 90

% 7 9 7

6 31 3

gm cm⫺3 1.54 1.51 1.57

dS m⫺1 0.07 0.10 0.04

2). The Tifton loamy sand is one of the most prevalent soil types and the dominant agricultural soil in the region. The second soil sample was collected from the Bt horizon of the Tifton loamy sand from approximately 25 to 40 cm deep. The Bt horizon has a higher clay content than the Ap horizon (Table 2). The third soil sample was collected from the Ap horizon (top 10 cm) of a Fuquay loamy sand (loamy, kaolinitic, thermic Arenic Plinthic Kandiudult). The Fuquay Ap has a slightly higher sand fraction than the Tifton Ap (Table 2). The sandy loam is a common surface texture throughout the southeastern United States and is the soil of the greatest interest for application of the soil water probes in the region. The Tifton and Fuquay soils are both upland soils used for agricultural production. All samples were collected from tilled agricultural fields in the spring before any application of fertilizer. The Fuquay Ap provides a contrast to the Tifton Ap and a means of testing the probes’ response for different soils. The Tifton Bt provided a test for applications in deeper soil horizons with greater clay contents. Thirteen laboratory tests were conducted with the Hydra probes. Four of these tests were conducted using the Tifton Ap, five with the Tifton Bt, and four with the Fuquay Ap. Eight laboratory tests were conducted with the Echo probes, four with the Tifton Ap, and four with the Fuquay Ap. The Echo probes were only tested for the Ap horizons because they were only being considered for applications at the soil surface. Two of the shorter Echo probes (10 cm) were also tested and compared with results for the longer Echo probes (20 cm). Following collection, the soils were sieved through a 10-mm sieve to remove large rocks and organic particles, and then packed at uniform densities into plastic cylindrical containers. The containers were 19 cm in diameter and 25 cm deep. The containers provided approximately 8 cm of soil between the container sidewalls and the probes. The containers were intermittently tamped during packing to assure uniformity and to remove air voids. When a 10-cm layer had been placed in the bottom of the container the probes were inserted vertically into the soil with minimal soil compaction. The remainder of the core was then packed until the soil was 2.5 cm from the top of the container. The volume of soil and the entire mass of the container were then measured. The mass of the sample probe and the container were measured before packing and were used to determine the soil mass by difference. A 300-g sample of the soils used in the initial packing was collected at the same time the containers were packed, weighed, dried, and reweighed for determination of the initial gravimetric water content. All samples were oven-dried at 105⬚C for 24 h. The gravimetric water content and the volume of the soil in the container were used to determine the dry bulk density at packing (Table 2). The packing densities obtained are similar to field observations for the soils. At the end of the test the soil was removed from the container and ovendried, and the final gravimetric water content was determined. A final bulk density and volumetric water content were determined and compared with the values estimated from the ovendried sample at the beginning of the study. Differences between the measured dry soil mass and the estimate obtained

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from the initial measurement of water content were small (⬍1%). The cores were saturated from the bottom up following packing. The cores were allowed to soak for 2 d and then gravity-drained for 1 d. Initial readings were taken at saturation. The cores were then allowed to air-dry over a period of 2 mo. Measurements of the sample mass, soil volume, and probe readings were made daily. A final probe reading was taken in the oven-dried soil, which was assumed to be at zero moisture. The observed volumetric water content (␪o) was calculated by determining the amount of water lost between readings from the reduction in mass, and back-calculating from the final observation of ␪o, which was determined through oven-drying of the entire sample. For the Hydra probes, estimates of Ka, soil conductivity, estimated volumetric water content (␪e), and temperature were determined from the factory equations (Eq. [3], Table 1). For the Echo probes, estimates of ␪e were made directly from the factory equation (Eq. [4]). The Decagon software does not yield Ka directly. Average measured soil conductivity for these soils varied from 0.1 dS —1 for the Tifton Bt to 0.04 for the Fuquay Ap dS m⫺1 (Table 2). Temperatures remained fairly constant throughout the laboratory study (approximately 22⬚C). The Hydra probe factory equations for each soil type were examined. Comparisons were made between ␪e obtained using published equations (Table 1) relating ␪e to Ka. Nonlinear regression analysis was used to determine calibration equations for ␪e in the form of a third-order polynomial (Eq. [3]).

Field Testing Hydra probes were installed at four different sites near Tifton, GA, centered at two depths, 5 and 13 cm. The sites selected consisted of loamy sand soils, with light-textured sandy surfaces and clay subsurfaces. The clay content of this soil increases at 30 cm. The soils were similar in texture to the Tifton Ap and the Fuquay Ap samples tested in the laboratory. The probes were installed at least 2 mo before conducting the tests. The observations were conducted from June to July of 2001 and again from June to August of 2002. Normal fluctuations in water content and temperatures were observed for that period in southern Georgia. Soil temperatures varied from 15 to 33⬚C. The average measured soil conductivity at the sites varied from 3.91 to 1.11 dS m⫺1. Biweekly readings were made with the field probes and compared with gravimetric samples collected at each site. The gravimetric samples were collected within 3 m of the probe installation site. Samples were not collected immediately next to the probe to prevent introducing water pathways into the subsurface and soil disturbance. Five-centimeter-diameter cylindrical samples were collected from intervals from 2.5 to 7.5 and 10.2 to 15.2 cm. The gravimetric water content of each sample was determined by oven-drying. The sample was cut to 5 cm in length. The volume of the soil sample was used to calculate bulk density, which was then used to determine ␪o (Eq. [2]). These measurements of ␪o were assumed to be a best approximation of the volumetric water content at the probe site. Because of natural spatial variability in all soils, some variation in soil water over space can be expected. In addition, some error was anticipated from converting gravimetric to volumetric water content due to some inaccuracy in the sample volume. Where problems were experienced collecting the fixed volume sample, an average bulk density for the site was used. The probe readings were used to determine the estimates

Fig. 1. Example results of the Stevens-Vitel Hydra probe laboratory tests comparing the observed data with the predicted values using the factory-provided equations for the different soil types.

of Ka along with ␪e and temperature. Comparisons were made between the goodness of fit of the various estimates of ␪e.

Error Analysis The mean square error (MSE) was used as a measure of the accuracy of the estimates of ␪e, calculated for each data set as (Ott, 1984):

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Table 3. Accuracy assessments of the Hydra probe volumetric water content predictions based on correlation coefficients and mean square error (MSE) obtained through comparison with the observed data. Stevens-Vitel factory equation for sands


Soil

r

Tifton Ap Tifton Bt Fuquay Ap

2

0.96 0.93 0.98

MSE ⫽

Topp 2

MSE

r

3.94 ⫻ 10⫺4 8.76 ⫻ 10⫺4 4.00 ⫻ 10⫺4

0.96 0.93 0.98

兺 (␪o ⫺ ␪e)2 n⫺2

Eller–Denoth 2

MSE

r

9.98 ⫻ 10⫺4 9.46 ⫻ 10⫺4 6.92 ⫻ 10⫺4

0.95 0.92 0.95

[5]

where n is the number of observations. The MSE provides a measure for comparing the accuracy of the different probes for the different soil types examined and a means for comparing alternative equations.

RESULTS AND DISCUSSION Laboratory Calibration—Hydra Probes Soil water contents for the Hydra probes were calculated using the factory-provided calibration equations and compared with values observed in the laboratory tests. Results were variable, but in general indicated good agreement between predicted and observed soil water. Calculations of ␪e from Ka using the equations provided by Stevens-Vitel were made. For all cases, the soil conductivity for the laboratory soils remained low (⬍0.2 dS m⫺1) as did the imaginary dielectric. Thus, soil conductivity effects should have been negligible. Values of temperature-corrected Ka were always twice those calculated for the temperature-corrected imaginary dielectric, a stipulation provided by the Hydra probe manufacturer for better accuracy of the Ka estimate. In general, good agreements were observed between the Hydra estimates and the observed values for individual probes (Fig. 1). Trends in the prediction followed closely with those observed. Some probes produced greater error than did others. It was not clear whether this was due to measurement error or probe differences. Some measurement error is expected due to inaccuracies in the estimation of bulk density. Because it would be impractical to separately calibrate each probe, data for particular soils were combined for further analysis. The Hydra probe equations for sand, silt, and clay were each examined relative to their accuracy for predicting volumetric water content using temperature-corrected Ka. The results obtained using the factory conversion provided for a clay soil were not as accurate as those obtained using the equation for either the sand or the silt. This included the Tifton Bt, which has 31% clay and 60% sand. The best results, based on the MSE (Table 3), obtained using equations provided by Stevens-Vitel were those using the coefficients for sand (Table 1). A slight improvement was obtained through calibration by determining soil-specific coefficients for each soil type using nonlinear regression analysis (Table 3). The coefficients for the third-order polynomial deter-

Calibration equation 2

MSE

r

4.09 ⫻ 10⫺4 7.43 ⫻ 10⫺4 6.60 ⫻ 10⫺4

0.96 0.94 0.98

MSE 3.10 ⫻ 10⫺4 4.73 ⫻ 10⫺4 1.86 ⫻ 10⫺4

mined through this analysis are shown in Table 4. These differed slightly from previously published relationships (Table 1). The calculated MSEs along with the correlation coefficients resulting from linear regression between the predicted values of ␪e and ␪o for each tested soil horizon are shown in Table 3. The Topp and Eller–Denoth equations (Eq. [3], Table 1) were also used to evaluate ␪e using the Hydra estimate of temperature-corrected Ka. Other equations including two relating volumetric water content to the square root of Ka (Yu et al., 1997; Alharthi and Lange, 1987) were examined as well. In most cases, the equations provided by the vendor were better predictors of volumetric water content than were previously published equations. The Eller–Denoth equation produced slightly lower MSE than did the Stevens-Vitel equation for the Tifton Bt. The Hydra predictions followed the same trend as the observed water content over the entire observed range (Fig. 2). The deviations throughout the observed range were less than ⫾0.05 cm3 cm⫺3. The Topp equation was more inaccurate at higher water contents (Fig. 2). Because they each use different coefficients to relate water content to Ka, the estimates of water content obtained from the various equations in the literature (Table 1) vary considerably (Fig. 3). In most cases, the shape of the curves follow a curve similar to the Hydra probe sand conversion (Fig. 3). All of our observations were at water contents less than 40%, or conversely Ka less than 20. In this range, considerable variation exists between the Topp equation and the Hydra sand equation. For our soils, the Hydra equation with the sand conversion yielded a more accurate estimate of ␪e than did other published equations. However, ␪e increases rapidly as Ka increases above 30 for the Hydra sand equation. Thus, it would be important to evaluate the suitability of this equation for heavier-textured soils, which would reach higher water contents. The calibration equations provided the best fit to the observed data (Table 3). The errors observed using the calibration equations were fairly well distributed about zero (Fig. 4). Similar results were obtained using the Topp and the Hydra sand equations. The majority of Table 4. Coefficients for the third-order polynomial (Eq. [3]) obtained by fitting Ka to the observed volumetric water content for each soil horizon examined in the laboratory analysis. Equation Tifton Ap Tifton Bt Fuquay Ap

a

b

c

d

⫺0.0775 ⫺0.1719 ⫺0.1176

3.578 ⫻ 10⫺2 6.876 ⫻ 10⫺2 4.785 ⫻ 10⫺2

⫺1.627 ⫻ 10⫺3 ⫺4.599 ⫻ 10⫺3 ⫺2.293 ⫻ 10⫺3

4.012 ⫻ 10⫺5 1.207 ⫻ 10⫺4 4.865 ⫻ 10⫺5

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to be related to individual probe differences rather than inaccuracies in the equation, indicating that a scaling of the soil water estimate for each probe may be an necessary to improve the accuracy of the results.


Laboratory Calibration—Echo Probes Soil water contents for the Echo probe readings were calculated using the factory-provided equations and compared with values observed in the laboratory tests. Soil water estimates from the Echo probes were consistently less than the observed values (Fig. 5). However, the Echo predictions followed the same trends as those of the observed data, indicating that with recalibration the Echo probes would yield good results for these soils. Similar results were observed between the different soil types and the different probe lengths examined (Fig. 5). For both the Hydra and Echo probes, the predicted values that fall below zero are a consequence of the equations used and can be corrected by setting a lower limit of zero to the predictions. While the absolute estimates obtained through the equations provided for the Echo probes were considerably lower than the observed values, the difference between the predicted and observed soil water for the Echo probes was very uniform. Improved equations for the different soils were developed through linear regression between the voltage reading and the observed soil water (Table 5) in the same form as Eq. [4]. These equations represent statistically significant (p ⫽ 0.05) improvements over the factory equations for the 20- and 10-cm probes. The equations for the Tifton Ap and the Fuquay Ap were also found to be statistically different (p ⫽ 0.05), indicating a need for different equations for different soil types. Results of the fit obtained with the regression equations and the errors are shown in Fig. 6. Errors were consistently less than ⫾0.05 cm3 cm⫺3.

Field Testing

Fig. 2. Comparison between the predicted values of soil water from the Stevens-Vitel factory equation for sands, the Topp equation, and the Ellor–Denoth equation for the observed soil water for the examined soil samples.

the observations (⬎95%) were within ⫾0.04 cm3 cm⫺3 of the observed water content. The greatest deviations were observed for the Tifton Bt soil. Trends appeared

Comparisons of the field data were made between ␪o and ␪e obtained using the factory-provided equations for the Hydra probes (Fig. 7). In general, good agreement was observed. Some deviation can be anticipated because of errors in estimating bulk density and natural variability, which can be expected over fairly small areas in the landscape. Warrick and Nielsen (1980) reported coefficients of variation for the water content from 10 to 50% depending on the degree of saturation. Greater variability can be expected at lower saturations (Warrick and Nielsen, 1980). Thus, a certain amount of scatter around the 1:1 line can be expected. The standardized residuals, the difference between ␪e and ␪o divided by ␪o, were calculated and plotted versus ␪o (Fig. 8). Observed errors for the field data ranged between ⫾75%. The figure clearly shows a bias to the prediction equation. At lower water contents (⬍0.10) the equation generally overpredicts ␪ while at higher water contents it underpredicts. This may be a function of underestimating the bulk density at low water contents and overestimating it at higher water contents.


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Fig. 3. Observed and predicted soil water for the Tifton Ap laboratory analysis sample versus temperature-corrected real dielectric.

Soil samples tend to hold together better at higher water contents leading to inadvertently collecting larger volumes and also more soil mass. Greater error in the measurement of Ka and thus ␪e is also expected because of the higher soil conductivities of the field soils. Average soil conductivities for these soils were consistently above 0.5 dS —1, the values at which Robinson et al. (1998) found that losses due to soil conductivity begin to significantly affect the estimation of Ka. The underestimation of soil water at higher water contents is contrary to the findings of Mead et al. (1995) who found that capacitance probes tend to overestimate soil water in wet soils with higher electrical conductivity. Soil water was also calculated using the calibration equations developed in the laboratory analysis and the

Topp equation using the Hydra probe estimates for Ka (Fig. 9). The best fit using the calibration equations was obtained using the relationship developed for the Fuquay Ap soil in the laboratory. The surface texture of the field soils was similar to that of the Fuquay Ap. The MSE for the Fuquay Ap calibration predictions was 0.00128, and 0.00131 for the Topp predictions. The MSE calculated using the Stevens-Vitel factory equation for sands was 0.00186. Estimates obtained from these equations were more evenly distributed around the 1:1 line than were those obtained using the StevensVitel factory equation for sands (Fig. 7). However, calculation of the residuals and the standardized residuals indicated a bias to these equations as well (Fig. 10). Overall, errors were less, but these equations also overpredicted the lower soil water and underpredicted the higher soil water. In addition, larger errors were observed at lower water contents (␪ ⬍ 0.10), similar to trends observed with the laboratory data (Fig. 3).

CONCLUSIONS

Fig. 4. Deviation from the observed soil water for the Tifton Ap laboratory sample obtained using the calibration equation for that soil.

Laboratory and field comparisons of the Hydra and Echo capacitance-based soil water probes indicate promise for applications in sandy-loam soils such as those studied here. While large deviations from field measurements of true soil water were observed (up to 75%), the probe predictions followed the trends of the observed data well. Laboratory results indicated a better fit (within 0.05 cm3 cm⫺3 of ␪o), indicating that the large errors may have been due to inaccurate estimates of bulk density, natural variability, and soil conductivity. The higher conductivities of the field soils would typi-

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Fig. 6. Deviation from the observed soil water from the Echo probe predictions calculated using the calibration equations determined through linear regression for the Tifton Ap and Fuquay Ap soils.

Fig. 5. Example results of the Echo probe laboratory tests comparing the observed data with the predicted values using the factoryprovided equations for the different soil types and probe lengths.

Fig. 7. Comparison between the predicted values of soil water from the Hydra probe factory equation for sands and the observed soil water for the field data.

Table 5. Linear equations developed for the Echo probes for the different soil and probe types. Factory equation Soil type Tifton Ap Fuquay Ap Fuquay Ap † Mean square error.

Linear regression

Probe

MSE†

Slope

Intercept

r2

MSE

cm 20 10 20

3.53 ⫻ 10⫺3 7.61 ⫻ 10⫺3 7.31 ⫻ 10⫺3

8.07 ⫻ 10⫺4 1.18 ⫻ 10⫺3 9.25 ⫻ 10⫺4

⫺0.296 ⫺0.413 ⫺0.344

0.94 0.98 0.99

4.62 ⫻ 10⫺4 2.88 ⫻ 10⫺4 1.21 ⫻ 10⫺4


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Fig. 8. Standardized residuals (residual divided by the observed soil water content) for the Hydra probe factory predictions of soil water for the field data.

Fig. 10. Standardized residuals (residual divided by the observed soil water content) for the (a) Topp equation and (b) calibration equations for the Fuquay Ap soil for the field data.

Fig. 9. Comparison between the predicted values of soil water from the (a) Topp equation and (b) calibration equation for the Fuquay Ap soil and the observed soil water for the field data.

cally lead to greater energy losses and greater error in the estimate of volumetric water content (Saarenketo, 1998). In addition, the larger variations in soil temperature that occurred at the field sites would also change the expected accuracy of the water content estimates. Overall, errors observed in the field data were greater than those observed in similar studies with TDR-type probes (Jacobsen and Schjonning, 1993, 1995; Eller and Denoth, 1996). However, the laboratory studies yielded

similar accuracy to those studies. Estimates can be further improved with soil-specific calibrations. The Topp equation performed very well for the soils examined. Based on the errors between ␪o and ␪e, the Topp equation produced a better estimate of observed field soil water than did the soil-specific Hydra factory calibration equations. However, under the more controlled laboratory settings the Hydra factory equations yielded better results. While the absolute errors observed for the Echo probe estimates of ␪ were quite large, analysis of the data indicated that the factory-provided equation could be improved to yield very accurate estimates (⫾0.05 cm3 cm⫺3). Further analysis is necessary to verify this for additional soil types. The laboratory analysis indicated that there may be considerable variability between individual Hydra probes. While some probes yielded very accurate results, other probes used on the same soil type did not. While it is possible that there was some variability between the studied soils, it is unlikely. Further analysis is necessary to examine these probe differences and those of soil conductivity. REFERENCES Alharthi, A., and J. Lange. 1987. Soil water saturation: Dielectric determination. Water Resour. Res. 23:591–595.



Eller, H., and A. Denoth. 1996. A capacitive soil moisture sensor. J. Hydrol. (Amsterdam) 185:137–146. Gardner, C.M.K., D.A. Robinson, K. Blyth, and J.D. Cooper. 2001. Soil water content measurement. p. 1–64. In K. Smith and C. Mullins (ed.) Soil and environmental analysis: Physical methods. 2nd ed. Marcel Dekker, New York. Gardner, W.H. 1986. Water content. p. 493–544. In A. Klute (ed.) Methods of soil analysis. Part 1. 2nd ed. Agron. Monogr. 9. ASA and SSSA, Madison, WI. Jacobsen, O.H., and P. Schjonning. 1993. A laboratory calibration of time domain reflectometry for soil water measurement including effects of bulk density and texture. J. Hydrol. (Amsterdam) 151: 147–157. Jacobsen, O.H., and P. Schjonning. 1995. Comparison of TDR calibration functions for soil water determination. p. 25–33. In L.W. Petersen and O.H. Jacobsen (ed.) Proc. Symp. Time-Domain Reflectometry Applications in Soil Science, Tjele, Denmark. 16 Sept. 1994. Danish Inst. of Plant and Soil Sci., Tjele. Mead, R.M., J.E. Ayars, and J. Liu. 1995. Evaluating the influence of soil texture, bulk density, and soil water salinity on a capacitance probe calibration. ASAE Paper 953264. Am. Soc. Agric. Eng., St. Joseph, MI. Ott, L. 1984. An introduction to statistical methods and data analysis. PWS Publ., Boston. Paltineanu, I.C., and J.L. Starr. 1997. Real-time soil water dynamics using multisensor capacitance probes: Laboratory calibration. Soil Sci. Soc. Am. J. 61:1576–1585. Robinson, D.A., C.M.K. Gardner, J. Evans, J.D. Cooper, M.G. Hod-

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nett, and J.P. Bell. 1998. The dielectric calibration of capacitance probes for soil hydrology using an oscillation frequency response model. Hydrol. Earth Syst. Sci. 2:83–92. Robinson, D.A., S.B. Jones, J.M. Wraith, D. Or, and S.P. Friedman. 2003. Advances in dielectric and electrical conductivity measurement using time domain reflectometry: Simultaneous measurement of water content and bulk electrical conductivity in soils and porous media. Vadose Zone J. 2:444–475. Roth, K., R. Schulin, H. Fluhler, and W. Attinger. 1990. Calibration of time domain reflectometry for water content measurement using a composite dielectric approach. Water Resour. Res. 26:2267–2273. Saarenketo, T. 1998. Electrical properties of water in clay and silty soils. J. Appl. Geophys. 40:73–88. Topp, G.C., J.L. Davis, and A.P. Annan. 1980. Electromagnetic determination of soil water content: Measurements in coaxial transmission lines. Water Resour. Res. 16:574–582. Topp, G.C., and P.A. Ferre. 2002. Water content. p. 417–421. In J.H. Dane and G.C. Topp (ed.) Methods of soil analysis. Part 4. SSSA Book Ser. 5. SSSA, Madison, WI. Warrick, A.W., and D.R. Nielsen. 1980. Spatial variability of soil physical properties in the field. p. 319–344. In D. Hillel (ed.) Applications in soil physics. Academic Press, New York. Weast, R.C. (ed.) 1980. Handbook of chemistry and physics. 61st ed. CRC Press, Boca Raton, FL. Yu, C., A.W. Warrick, M.H. Conklin, M.H. Young, and M. Zreda. 1997. Two- and three-parameter calibrations of time domain reflectometry for soil moisture measurement. Water Resour. Res. 33: 2417–2421.