comparison of capacitance-based soil water probes in … bosch vadose zj v3... · 2004-11-30 ·...

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

David D. Bosch*

ABSTRACT structive by nature. In addition, the gravimetric watercontent (w, gm gm�1) determined through this methodSoil water influences infiltration and runoff and consequently watermust be related back to � through a measured or esti-quality. In situ measurements of soil water are critical for understand-

ing hydrologic and water quality processes. Many advances have re- mated sample volume to estimate water volume. The twocently been made in soil water measurement techniques. In particular, are related through the soil bulk density (�b, gm cm�3)instruments for estimating volumetric water content from measure- and the density of water (�w, gm cm�3):ments of soil electrical properties have become common. While theinstruments have been shown to be good indicators of relative changes

� � w�b

�w

[2]in soil water, questions remain regarding their ability to yield quantita-tive estimates. Most of these techniques rely on a limited set of calibra-tion equations obtained through laboratory analysis of homogeneous The water density is normally assumed equal to 1 gmsoil materials (i.e., sand, silt, and clay). The accuracy of two capaci- cm�3. The measurement or estimation of �b can intro-tance-based soil water probes was assessed for a range of Coastal Plain duce error into the estimate of � using the gravimet-soils. The probes measure capacitive and conductive soil properties ric method.and relate these to water content through calibration. Calibration curves Field-based indirect measurements of � are attractivefor three different Coastal Plain soils were developed. Laboratory tests

because of their relative ease and relatively nondestruc-indicate that the probes yield estimates of volumetric water contenttive nature. Some commonly used techniques includewithin �0.05 cm3 cm�3 of the observed values for these soils. Greaterthe neutron probe (Gardner et al., 2001), time domainvariability was observed in comparisons with field observations. Re-

sults indicate that improved equations can be developed through soil- reflectometry (TDR) (Robinson et al., 2003), and capac-specific laboratory calibration. The capacitance probes should prove itance methods (Paltineanu and Starr, 1997). Advancesto be useful tools for estimating volumetric water content in these soils. in electronics and data collection have made these meth-Additional work is required to quantify probe differences and the ods more attractive for measuring spatial and temporaleffects of soil conductivity on the measurements. changes in soil water. Extensive reviews of these tech-

niques have been conducted (Gardner et al., 2001; Rob-inson et al., 2003; Topp and Ferre, 2002).

Soil water content is an important soil characteristic The TDR and capacitance methods estimate � basedused to evaluate irrigation needs, runoff susceptibil- on an inferred measurement of soil dielectric (Topp

ity, and plant-available water. Volumetric water content and Ferre, 2002). The relative permittivity, or dielectricis defined as: constant, is the ratio of the dielectric of the material to

the dielectric of a vacuum. The dielectric constant of a� �

Vw

Vt

[1] soil describes its ability to store electrical energy byseparating opposite polarity charges in space. The com-

where � is the volumetric water content (cm3 cm�3), Vw plex dielectric of a soil can be divided into real andis the water volume (cm3), and Vt is the total volume of imaginary components (Topp et al., 1980). The real partsoil, water, and air (cm3). Methods commonly used to of the dielectric describes its ability to store energy inmeasure soil water include the gravimetric method, in- an applied electric field while the imaginary part relatesference from soil matric pressure and soil water release to energy losses. Energy losses increase with increasescurves, neutron probe, and indirect measurements based in soil conductivity (Saarenketo, 1998). If the losses areon electrical properties of the soil (Gardner, 1986; Gard- small the imaginary part can be neglected in the determi-ner et al., 2001; Topp and Ferre, 2002). Each of these nation of � and the dielectric becomes a function of soilmethods have strengths and shortcomings. While the constituents alone (Topp et al., 1980). Estimates of thegravimetric method, consisting of collecting the soil and real component of the dielectric are often referred tooven-drying, is considered the most reliable, it is de- as the apparent dielectric (Ka) because they neglect the

energy loss components.The capacitance method uses the soil as part of aUSDA-ARS, Southeast Watershed Research Laboratory, P.O. Box

748, Tifton, GA 31793. Contribution from the USDA-ARS, Southeast capacitor in which the permanent dipoles of water inWatershed Research Laboratory in cooperation with University of the dielectric medium are aligned by an electric fieldGeorgia Coastal Plain Experiment Station. All programs and services

and become polarized (Paltineanu and Starr, 1997;of the USDA are offered on a nondiscriminatory basis without regardGardner et al., 2001). These probes typically operate into race, color, national origin, religion, sex, age, marital status, or handi-

cap. Trade names and company names are included for the benefit the radio-frequency regime from 10 MHz up to severalof the reader and do not imply any endorsement or preferential treat- hundred MHz. Estimates of Ka obtained through thement of the products listed by USDA. Received 22 Jan. 2004. Original

capacitance methods may be different from those ob-Research Paper. *Corresponding author ([email protected]).

Published in Vadose Zone Journal 3:1380–1389 (2004).© Soil Science Society of America Abbreviations: MSE, mean square error; TDR, time domain reflec-

tometry.677 S. Segoe Rd., Madison, WI 53711 USA

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www.vadosezonejournal.org 1381

tained through TDR methods due differences in mea- which is then related to the water content through rela-tionships such as Eq. [3]. The Hydra probe capacitance-surement methods.

The dielectric constant for water at 20�C is 80, dry based sensor recently developed by Stevens-Vitel (Bea-verton, OR) yields estimates of volumetric water con-soil is from 4.5 to 10, while that for air is close to 1

(Robinson et al., 2003). Because of this large difference, tent, temperature, soil conductivity, and salinity. Theprobe is of interest to the scientific community due toa change in water content in the soil will change the

dielectric constant. The relationship between the water the soil properties it can be used to estimate. Stevens-Vitel lists three separate calibration equations for thecontent change and the dielectric of the medium de-

pends on temperature, soil type, sensor frequency, and Hydra probe based on primary soil type (Table 1).Decagon Devices (Pullman, WA) has also recentlychemical properties of the soil (Eller and Denoth, 1996;

Saarenketo, 1998; Robinson et al., 2003). Dielectric is developed a capacitance-based soil water probe, theEcho probe. The Echo probe is relatively small andinversely related to soil temperature (Weast, 1980). For

pure water, its dielectric constant would change from inexpensive, making it well suited for in situ measure-ments. The device measures the rate of change of a84 to 73 if the temperature were changed from 10 to

40�C (Weast, 1980). Considering no interactions in the voltage imposed on the soil by the probe. Equationsare given by the vendor to convert the measured voltagesoil, a decrease in temperature from 20 to 15�C at 20% �

will increase the dielectric constant by a value of 0.4 into volumetric water content. While both of theseprobes have features making them inviting for field re-(Jacobsen and Schjonning, 1993), or conversely, a differ-

ence in � of 0.7%. Thus, the effect of temperature in search, neither has undergone rigorous field testing.The objectives of this research were to:most cases would be expected to be small, as was found

by Topp et al. (1980) over a temperature range from • test the reliability of the Stevens-Vitel Hydra and10 to 36�C. Decagon Echo soil water probes based on factory-

Concentration of salts within soils increases their elec- supplied equations for a range of Coastal Plain soils,trical conductivity and dielectric losses. Robinson et al. • test other dielectric-based equations for the Ste-(1998) found that losses due to soil conductivity can be vens-Vitel Hydra probe, andneglected for conductivities less than 0.5 dS m�1. Thus, • develop improved equations for the probes if war-a measure of soil conductivity can be used to evaluate ranted by the results.whether or not the salinity will have an effect on thesoil water measurement via the capacitance method. METHODS

Estimates of Ka are often related to � through empiri-Tests were conducted to assess the accuracy of the Hydracal equations. Many of the relationships relating � to

and Echo probes. Laboratory studies were conducted to cali-Ka are written as cubic equations:brate the probes under controlled conditions. Field tests wereconducted to evaluate the factory equations in a setting where� � a � bKa � cK 2

a � dK 3a [3]

variability in climatic and geologic conditions can be expected.Several of these are outlined by Jacobsen and Schjon- The Topp and Eller–Denoth equations relating � to Ka were

ning (1995). The most frequently cited equation relating also examined (Table 1). In addition, a nonlinear regressionanalysis was conducted to develop soil-specific calibration� to Ka was developed by Topp et al. (1980). The Toppequations using the laboratory data.equation was based on analysis of four mineral soils,

ranging from a sandy loam to a clay. A calibration pre-Probe Descriptionssented by Roth et al. (1990) included the temperature

dependence of Ka in their calibration equation. Jacobsen The Stevens-Vitel Hydra probes perform electrical mea-and Schjonning (1993) included the dry bulk density, surements of the capacitive and conductive properties of soil

at a frequency of 50 MHz. These properties are then relatedpercent clay, and percent organic matter. However, forto the soil’s water and conductivity. The device consists ofthe 10 mineral soils examined by Jacobsen and Schjon-four 6-cm-long, 3-mm-diameter stainless steel tines, three inning (1993), including these parameters in addition to Kaa triangular fashion around the fourth tine in the center ofresulted in only a slight improvement over a relationshipthe triangle. The middle tine is used to measure temperature.without those parameters. Eller and Denoth (1996) de-The length of the entire device is 10 cm and the outsideveloped a quadratic equation that was listed as valid for diameter is 4 cm. The manufacturer reports that the effective

� � 3% for a wide variety of soils. The coefficients for sensing volume for the probe as a cylinder is approximatelythe Topp and Eller–Denoth equations in the form of 2.5 cm in diameter and 6 cm in length, bounded on the outsideEq. [3] are shown in Table 1. by the three outer tines, and on the ends by the probe head

Capacitance-based probes measure the apparent di- and the free end of the tines. The probe wiring is sealed in aPVC case.electric constant of the soil surrounding the sensor,

Table 1. Coefficients for various cubic equations in the form of Eq. [3] relating the volumetric water content to apparent dielectric.

Equation a b c d

Topp �0.0530 2.920 10�2 �5.500 10�5 4.300 10�6

Eller–Denoth �0.0033 1.484 10�2 6.000 10�5 0Hydra probe for sand �0.0863 3.251 10�2 �9.751 10�4 1.632 10�5

Hydra probe for silt �0.1304 3.861 10�2 �9.331 10�4 7.587 10�6

Hydra probe for clay �0.2093 6.625 10�2 �2.519 10�3 3.350 10�5

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1382 VADOSE ZONE J., VOL. 3, NOVEMBER 2004

Table 2. Physical characteristics of the validation soils.The Hydra probe requires an excitation voltage between 7and 30 V DC. Its output consists of four voltages, one from Average packing Average soileach of the four tines. The Hydra probes come with software Sample Sand Silt Clay bulk density conductivityprovided by the manufacturer to convert measured voltages

% gm cm�3 dS m�1

into temperature-corrected estimates of the complex dielec-Tifton Ap 87 7 6 1.54 0.07

tric, which can then be used to determine the capacitive (real) Tifton Bt 60 9 31 1.51 0.10and the conductive (imaginary) parts of the soil’s response. Fuquay Ap 90 7 3 1.57 0.04The capacitive part of the response reflects the water contentwhile the conductive part reflects predominantly soil conduc-

2). The Tifton loamy sand is one of the most prevalent soiltivity (Gardner et al., 2001). Temperature is determined fromtypes and the dominant agricultural soil in the region. Thea thermistor in the probe. Both the real (Ka) and imaginarysecond soil sample was collected from the Bt horizon of thedielectric vary with temperature. To compensate for this aTifton loamy sand from approximately 25 to 40 cm deep. Thetemperature correction is applied using the measured soil tem-Bt horizon has a higher clay content than the Ap horizonperature. The temperature correction amounts to calculating(Table 2). The third soil sample was collected from the Apwhat the constants should be at 25�C. The calculated soil waterhorizon (top 10 cm) of a Fuquay loamy sand (loamy, kaolinitic,is based on the temperature-corrected real dielectric constantthermic Arenic Plinthic Kandiudult). The Fuquay Ap has awhile the soil conductivity, soil salinity, and temperature-cor-slightly higher sand fraction than the Tifton Ap (Table 2).rected soil conductivity are all based on both the temperature-The sandy loam is a common surface texture throughout thecorrected real and imaginary dielectric constants.southeastern United States and is the soil of the greatest inter-The manufacturer reports that the accuracy of the real andest for application of the soil water probes in the region.imaginary dielectric constants are typically �1% or 0.5, which-The Tifton and Fuquay soils are both upland soils used forever is greater. The readings reportedly become less reliableagricultural production. All samples were collected from tilledas soil conductivity levels increase and as temperature variesagricultural fields in the spring before any application of fertil-from 25�C. The soil temperature measurement the Hydraizer. The Fuquay Ap provides a contrast to the Tifton Ap andprobe makes is used to remove most of the temperature ef-a means of testing the probes’ response for different soils.fects. The typical accuracies reported by the manufacturer areThe Tifton Bt provided a test for applications in deeper soil�3% for soil water, �0.0014 S m�1 for soil conductivity, �20%horizons with greater clay contents.for salinity, and �1�C for temperature. The response of the

Thirteen laboratory tests were conducted with the Hydraprobe varies with soil type. Separate calibration equations areprobes. Four of these tests were conducted using the Tiftonprovided by the manufacturer for three different soil types:Ap, five with the Tifton Bt, and four with the Fuquay Ap.sand, silt, and clay (Table 1). The manufacturer indicates thatEight laboratory tests were conducted with the Echo probes,the accuracy of the � measurement can be improved with soilfour with the Tifton Ap, and four with the Fuquay Ap. Thetype information.Echo probes were only tested for the Ap horizons becauseThe second probe examined was the Decagon Echo dielec-they were only being considered for applications at the soiltric aquameter. Two probe lengths were available, a longersurface. Two of the shorter Echo probes (10 cm) were alsoprobe with a measuring length of 20 cm and a shorter probetested and compared with results for the longer Echo probeswith a measuring length of 10 cm. The probe itself is approxi-(20 cm).mately 5 cm longer than the measuring length, 3 cm wide, and

Following collection, the soils were sieved through a 10-mm1.5 mm thick. The probe requires an excitation voltage ofsieve to remove large rocks and organic particles, and then2.5 to 5 V. The probe outputs a voltage proportional to thepacked at uniform densities into plastic cylindrical containers.dielectric properties of the soil. The manufacturer reports thatThe containers were 19 cm in diameter and 25 cm deep. Thethe output is effected by soil temperature, texture, and salinity.containers provided approximately 8 cm of soil between theSimilar to the Hydra probe, the accuracy of the Echo probecontainer sidewalls and the probes. The containers were inter-decreases with increasing soil conductivity. Reported soil wa-mittently tamped during packing to assure uniformity and toter accuracies are �3% without or �1% with calibration. Theremove air voids. When a 10-cm layer had been placed in thestandard calibration equation given by Decagon for the 20-cmbottom of the container the probes were inserted verticallyEcho probe is:into the soil with minimal soil compaction. The remainder ofthe core was then packed until the soil was 2.5 cm from the� � �0.29 � 0.000695mV [4]top of the container. The volume of soil and the entire mass

where mV is the millivolt output of the probe with a 2.5-V of the container were then measured. The mass of the sampleexcitation. The factory equation provided and used for 10-cm probe and the container were measured before packing andprobes was different from that provided for the 20-cm probes. were used to determine the soil mass by difference.The intercept for the 10-cm probes is �0.0376 while the slope A 300-g sample of the soils used in the initial packing wasis 9.36 10�4. collected at the same time the containers were packed, weighed,

The Hydra and Echo probes were controlled and read with dried, and reweighed for determination of the initial gravimet-a Campbell Scientific (Logan, UT) CR10X data logger. Power ric water content. All samples were oven-dried at 105�C forwas supplied at 12 V for the Hydra probes and 2.5 V for the 24 h. The gravimetric water content and the volume of theEcho probes. The Type A Hydra Probes were used, which soil in the container were used to determine the dry bulkare specially designed for the Campbell data loggers. density at packing (Table 2). The packing densities obtained

are similar to field observations for the soils. At the end ofthe test the soil was removed from the container and oven-Laboratory Calibrationdried, and the final gravimetric water content was determined.

Three different soils were used for the laboratory calibra- A final bulk density and volumetric water content were deter-tion study. The first sample was collected from the Ap horizon mined and compared with the values estimated from the oven-(top 10 cm) of a Tifton loamy sand (fine-loamy, kaolinitic, dried sample at the beginning of the study. Differences be-

tween the measured dry soil mass and the estimate obtainedthermic Plinthic Kandiudult), with a high sand content (Table

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from the initial measurement of water content were small(1%).

The cores were saturated from the bottom up followingpacking. The cores were allowed to soak for 2 d and thengravity-drained for 1 d. Initial readings were taken at satura-tion. The cores were then allowed to air-dry over a period of2 mo. Measurements of the sample mass, soil volume, andprobe readings were made daily. A final probe reading wastaken in the oven-dried soil, which was assumed to be at zeromoisture. The observed volumetric water content (�o) wascalculated by determining the amount of water lost betweenreadings from the reduction in mass, and back-calculatingfrom the final observation of �o, which was determined throughoven-drying of the entire sample.

For the Hydra probes, estimates of Ka, soil conductivity,estimated volumetric water content (�e), and temperaturewere determined from the factory equations (Eq. [3], Table1). For the Echo probes, estimates of �e were made directlyfrom the factory equation (Eq. [4]). The Decagon softwaredoes not yield Ka directly. Average measured soil conductivityfor these soils varied from 0.1 dS —1 for the Tifton Bt to 0.04for the Fuquay Ap dS m�1 (Table 2). Temperatures remainedfairly constant throughout the laboratory study (approxi-mately 22�C). The Hydra probe factory equations for eachsoil type were examined. Comparisons were made between�e obtained using published equations (Table 1) relating �e

to Ka. Nonlinear regression analysis was used to determinecalibration equations for �e in the form of a third-order polyno-mial (Eq. [3]).

Field Testing

Hydra probes were installed at four different sites nearTifton, GA, centered at two depths, 5 and 13 cm. The sitesselected consisted of loamy sand soils, with light-texturedsandy surfaces and clay subsurfaces. The clay content of thissoil increases at 30 cm. The soils were similar in texture tothe Tifton Ap and the Fuquay Ap samples tested in the labora-tory. The probes were installed at least 2 mo before conductingthe tests. The observations were conducted from June to Julyof 2001 and again from June to August of 2002. Normal fluctu-ations in water content and temperatures were observed forthat period in southern Georgia. Soil temperatures variedfrom 15 to 33�C. The average measured soil conductivity atthe sites varied from 3.91 to 1.11 dS m�1.

Biweekly readings were made with the field probes andcompared with gravimetric samples collected at each site. Thegravimetric samples were collected within 3 m of the probeinstallation site. Samples were not collected immediately nextto the probe to prevent introducing water pathways into thesubsurface and soil disturbance. Five-centimeter-diameter cy-lindrical samples were collected from intervals from 2.5 to 7.5and 10.2 to 15.2 cm. The gravimetric water content of eachsample was determined by oven-drying. The sample was cutto 5 cm in length. The volume of the soil sample was used to Fig. 1. Example results of the Stevens-Vitel Hydra probe laboratorycalculate bulk density, which was then used to determine �o tests comparing the observed data with the predicted values using

the factory-provided equations for the different soil types.(Eq. [2]). These measurements of �o were assumed to be abest approximation of the volumetric water content at theprobe site. Because of natural spatial variability in all soils, of Ka along with �e and temperature. Comparisons were madesome variation in soil water over space can be expected. In between the goodness of fit of the various estimates of �e.addition, some error was anticipated from converting gravi-metric to volumetric water content due to some inaccuracy in Error Analysisthe sample volume. Where problems were experienced collect-ing the fixed volume sample, an average bulk density for the The mean square error (MSE) was used as a measure ofsite was used. the accuracy of the estimates of �e, calculated for each data

set as (Ott, 1984):The probe readings were used to determine the estimates

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Table 3. Accuracy assessments of the Hydra probe volumetric water content predictions based on correlation coefficients and meansquare error (MSE) obtained through comparison with the observed data.

Stevens-Vitel factoryequation for sands Topp Eller–Denoth Calibration equation

Soil r 2 MSE r 2 MSE r 2 MSE r 2 MSE

Tifton Ap 0.96 3.94 10�4 0.96 9.98 10�4 0.95 4.09 10�4 0.96 3.10 10�4

Tifton Bt 0.93 8.76 10�4 0.93 9.46 10�4 0.92 7.43 10�4 0.94 4.73 10�4

Fuquay Ap 0.98 4.00 10�4 0.98 6.92 10�4 0.95 6.60 10�4 0.98 1.86 10�4

mined through this analysis are shown in Table 4. TheseMSE �

� (�o � �e)2

n � 2[5] differed slightly from previously published relationships

(Table 1).where n is the number of observations. The MSE provides a The calculated MSEs along with the correlation coef-measure for comparing the accuracy of the different probes for ficients resulting from linear regression between thethe different soil types examined and a means for comparing predicted values of �e and �o for each tested soil horizonalternative equations. are shown in Table 3. The Topp and Eller–Denoth equa-

tions (Eq. [3], Table 1) were also used to evaluate �e

using the Hydra estimate of temperature-corrected Ka.RESULTS AND DISCUSSIONOther equations including two relating volumetric water

Laboratory Calibration—Hydra Probes content to the square root of Ka (Yu et al., 1997; Alharthiand Lange, 1987) were examined as well. In most cases,Soil water contents for the Hydra probes were calcu-the equations provided by the vendor were better pre-lated using the factory-provided calibration equationsdictors of volumetric water content than were previouslyand compared with values observed in the laboratorypublished equations. The Eller–Denoth equation pro-tests. Results were variable, but in general indicated duced slightly lower MSE than did the Stevens-Vitelgood agreement between predicted and observed soil equation for the Tifton Bt. The Hydra predictions fol-

water. Calculations of �e from Ka using the equations lowed the same trend as the observed water contentprovided by Stevens-Vitel were made. For all cases, the over the entire observed range (Fig. 2). The deviationssoil conductivity for the laboratory soils remained low throughout the observed range were less than �0.05(0.2 dS m�1) as did the imaginary dielectric. Thus, soil cm3 cm�3. The Topp equation was more inaccurate atconductivity effects should have been negligible. Values higher water contents (Fig. 2).of temperature-corrected Ka were always twice those Because they each use different coefficients to relatecalculated for the temperature-corrected imaginary di- water content to Ka, the estimates of water content ob-electric, a stipulation provided by the Hydra probe man- tained from the various equations in the literature (Ta-ufacturer for better accuracy of the Ka estimate. ble 1) vary considerably (Fig. 3). In most cases, the

In general, good agreements were observed between shape of the curves follow a curve similar to the Hydrathe Hydra estimates and the observed values for individ- probe sand conversion (Fig. 3). All of our observationsual probes (Fig. 1). Trends in the prediction followed were at water contents less than 40%, or conversely Kaclosely with those observed. Some probes produced less than 20. In this range, considerable variation existsgreater error than did others. It was not clear whether between the Topp equation and the Hydra sand equa-this was due to measurement error or probe differences. tion. For our soils, the Hydra equation with the sand

conversion yielded a more accurate estimate of �e thanSome measurement error is expected due to inaccura-did other published equations. However, �e increasescies in the estimation of bulk density. Because it wouldrapidly as Ka increases above 30 for the Hydra sandbe impractical to separately calibrate each probe, dataequation. Thus, it would be important to evaluate thefor particular soils were combined for further analysis.suitability of this equation for heavier-textured soils,The Hydra probe equations for sand, silt, and claywhich would reach higher water contents.were each examined relative to their accuracy for pre-

The calibration equations provided the best fit to thedicting volumetric water content using temperature-cor-observed data (Table 3). The errors observed using therected Ka. The results obtained using the factory conver-calibration equations were fairly well distributed aboutsion provided for a clay soil were not as accurate aszero (Fig. 4). Similar results were obtained using thethose obtained using the equation for either the sandTopp and the Hydra sand equations. The majority ofor the silt. This included the Tifton Bt, which has 31%

clay and 60% sand. The best results, based on the MSE Table 4. Coefficients for the third-order polynomial (Eq. [3])obtained by fitting Ka to the observed volumetric water content(Table 3), obtained using equations provided by Ste-for each soil horizon examined in the laboratory analysis.vens-Vitel were those using the coefficients for sand

(Table 1). A slight improvement was obtained through Equation a b c d

calibration by determining soil-specific coefficients for Tifton Ap �0.0775 3.578 10�2 �1.627 10�3 4.012 10�5

Tifton Bt �0.1719 6.876 10�2 �4.599 10�3 1.207 10�4each soil type using nonlinear regression analysis (TableFuquay Ap �0.1176 4.785 10�2 �2.293 10�3 4.865 10�5

3). The coefficients for the third-order polynomial deter-

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to be related to individual probe differences rather thaninaccuracies in the equation, indicating that a scaling ofthe soil water estimate for each probe may be an neces-sary to improve the accuracy of the results.

Laboratory Calibration—Echo ProbesSoil water contents for the Echo probe readings were

calculated using the factory-provided equations andcompared with values observed in the laboratory tests.Soil water estimates from the Echo probes were consis-tently less than the observed values (Fig. 5). However,the Echo predictions followed the same trends as thoseof the observed data, indicating that with recalibrationthe Echo probes would yield good results for these soils.Similar results were observed between the different soiltypes and the different probe lengths examined (Fig. 5).For both the Hydra and Echo probes, the predictedvalues that fall below zero are a consequence of theequations used and can be corrected by setting a lowerlimit of zero to the predictions.

While the absolute estimates obtained through theequations provided for the Echo probes were consider-ably lower than the observed values, the difference be-tween the predicted and observed soil water for theEcho probes was very uniform. Improved equations forthe different soils were developed through linear regres-sion between the voltage reading and the observed soilwater (Table 5) in the same form as Eq. [4]. Theseequations represent statistically significant (p � 0.05)improvements over the factory equations for the 20- and10-cm probes. The equations for the Tifton Ap and theFuquay Ap were also found to be statistically different(p � 0.05), indicating a need for different equations fordifferent soil types. Results of the fit obtained with theregression equations and the errors are shown in Fig.6. Errors were consistently less than �0.05 cm3 cm�3.

Field TestingComparisons of the field data were made between �o

and �e obtained using the factory-provided equationsfor the Hydra probes (Fig. 7). In general, good agree-ment was observed. Some deviation can be anticipatedbecause of errors in estimating bulk density and naturalvariability, which can be expected over fairly small areasin the landscape. Warrick and Nielsen (1980) reportedcoefficients of variation for the water content from 10to 50% depending on the degree of saturation. Greatervariability can be expected at lower saturations (War-rick and Nielsen, 1980). Thus, a certain amount of scat-ter around the 1:1 line can be expected.

The standardized residuals, the difference between �eFig. 2. Comparison between the predicted values of soil water from and �o divided by �o, were calculated and plotted versusthe Stevens-Vitel factory equation for sands, the Topp equation,�o (Fig. 8). Observed errors for the field data rangedand the Ellor–Denoth equation for the observed soil water for the

examined soil samples. between �75%. The figure clearly shows a bias to theprediction equation. At lower water contents (0.10)the equation generally overpredicts � while at higherwater contents it underpredicts. This may be a functionthe observations (�95%) were within �0.04 cm3 cm�3

of the observed water content. The greatest deviations of underestimating the bulk density at low water con-tents and overestimating it at higher water contents.were observed for the Tifton Bt soil. Trends appeared

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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 Topp equation using the Hydra probe estimates for Ka

contents leading to inadvertently collecting larger vol- (Fig. 9). The best fit using the calibration equationsumes and also more soil mass. Greater error in the was obtained using the relationship developed for themeasurement of Ka and thus �e is also expected because Fuquay Ap soil in the laboratory. The surface textureof the higher soil conductivities of the field soils. Aver- of the field soils was similar to that of the Fuquay Ap.age soil conductivities for these soils were consistently The MSE for the Fuquay Ap calibration predictionsabove 0.5 dS —1, the values at which Robinson et al. was 0.00128, and 0.00131 for the Topp predictions. The(1998) found that losses due to soil conductivity begin MSE calculated using the Stevens-Vitel factory equa-to significantly affect the estimation of Ka. The under- tion for sands was 0.00186. Estimates obtained fromestimation of soil water at higher water contents is con- these equations were more evenly distributed aroundtrary to the findings of Mead et al. (1995) who found the 1:1 line than were those obtained using the Stevens-that capacitance probes tend to overestimate soil water Vitel factory equation for sands (Fig. 7). However, cal-in wet soils with higher electrical conductivity. culation of the residuals and the standardized residuals

Soil water was also calculated using the calibration indicated a bias to these equations as well (Fig. 10).equations developed in the laboratory analysis and the Overall, errors were less, but these equations also over-

predicted the lower soil water and underpredicted thehigher soil water. In addition, larger errors were ob-served at lower water contents (� 0.10), similar totrends observed with the laboratory data (Fig. 3).

CONCLUSIONSLaboratory and field comparisons of the Hydra and

Echo capacitance-based soil water probes indicatepromise for applications in sandy-loam soils such asthose studied here. While large deviations from fieldmeasurements of true soil water were observed (up to75%), the probe predictions followed the trends of theobserved data well. Laboratory results indicated a betterfit (within 0.05 cm3 cm�3 of �o), indicating that the largeerrors may have been due to inaccurate estimates ofFig. 4. Deviation from the observed soil water for the Tifton Apbulk density, natural variability, and soil conductivity.laboratory sample obtained using the calibration equation for

that soil. The higher conductivities of the field soils would typi-

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Fig. 6. Deviation from the observed soil water from the Echo probepredictions calculated using the calibration equations determinedthrough linear regression for the Tifton Ap and Fuquay Ap soils.

Fig. 7. Comparison between the predicted values of soil water fromFig. 5. Example results of the Echo probe laboratory tests comparing the Hydra probe factory equation for sands and the observed soilthe observed data with the predicted values using the factory- water for the field data.provided equations for the different soil types and probe lengths.

Table 5. Linear equations developed for the Echo probes for the different soil and probe types.

Factory equation Linear regression

Soil type Probe MSE† Slope Intercept r2 MSE

cmTifton Ap 20 3.53 10�3 8.07 10�4 �0.296 0.94 4.62 10�4

Fuquay Ap 10 7.61 10�3 1.18 10�3 �0.413 0.98 2.88 10�4

Fuquay Ap 20 7.31 10�3 9.25 10�4 �0.344 0.99 1.21 10�4

† Mean square error.

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

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

similar accuracy to those studies. Estimates can be fur-ther improved with soil-specific calibrations.

The Topp equation performed very well for the soilsexamined. Based on the errors between �o and �e, theTopp equation produced a better estimate of observedfield soil water than did the soil-specific Hydra factorycalibration equations. However, under the more con-trolled laboratory settings the Hydra factory equationsyielded better results.

While the absolute errors observed for the Echoprobe estimates of � were quite large, analysis of thedata indicated that the factory-provided equation couldbe improved to yield very accurate estimates (�0.05cm3 cm�3). Further analysis is necessary to verify thisfor additional soil types.

Fig. 9. Comparison between the predicted values of soil water from The laboratory analysis indicated that there may bethe (a) Topp equation and (b) calibration equation for the Fuquay considerable variability between individual HydraAp soil and the observed soil water for the field data.

probes. While some probes yielded very accurate re-sults, other probes used on the same soil type did not.cally lead to greater energy losses and greater error inWhile it is possible that there was some variability be-the estimate of volumetric water content (Saarenketo,tween the studied soils, it is unlikely. Further analysis1998). In addition, the larger variations in soil tempera-is necessary to examine these probe differences andture that occurred at the field sites would also changethose of soil conductivity.the expected accuracy of the water content estimates.

Overall, errors observed in the field data were greaterREFERENCESthan those observed in similar studies with TDR-type

probes (Jacobsen and Schjonning, 1993, 1995; Eller and Alharthi, A., and J. Lange. 1987. Soil water saturation: Dielectricdetermination. Water Resour. Res. 23:591–595.Denoth, 1996). However, the laboratory studies yielded

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Gardner, C.M.K., D.A. Robinson, K. Blyth, and J.D. Cooper. 2001. model. Hydrol. Earth Syst. Sci. 2:83–92.Robinson, D.A., S.B. Jones, J.M. Wraith, D. Or, and S.P. Friedman.Soil water content measurement. p. 1–64. In K. Smith and C. Mul-

lins (ed.) Soil and environmental analysis: Physical methods. 2nd 2003. Advances in dielectric and electrical conductivity measure-ment using time domain reflectometry: Simultaneous measuremented. Marcel Dekker, New York.

Gardner, W.H. 1986. Water content. p. 493–544. In A. Klute (ed.) of water content and bulk electrical conductivity in soils and porousmedia. Vadose Zone J. 2:444–475.Methods of soil analysis. Part 1. 2nd ed. Agron. Monogr. 9. ASA

and SSSA, Madison, WI. Roth, K., R. Schulin, H. Fluhler, and W. Attinger. 1990. Calibrationof time domain reflectometry for water content measurement usingJacobsen, O.H., and P. Schjonning. 1993. A laboratory calibration of

time domain reflectometry for soil water measurement including a composite dielectric approach. Water Resour. Res. 26:2267–2273.Saarenketo, T. 1998. Electrical properties of water in clay and siltyeffects of bulk density and texture. J. Hydrol. (Amsterdam) 151:

147–157. soils. J. Appl. Geophys. 40:73–88.Topp, G.C., J.L. Davis, and A.P. Annan. 1980. Electromagnetic deter-Jacobsen, O.H., and P. Schjonning. 1995. Comparison of TDR calibra-

tion functions for soil water determination. p. 25–33. In L.W. Pet- mination of soil water content: Measurements in coaxial transmis-sion lines. Water Resour. Res. 16:574–582.ersen and O.H. Jacobsen (ed.) Proc. Symp. Time-Domain Reflec-

tometry Applications in Soil Science, Tjele, Denmark. 16 Sept. 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. SSSA1994. Danish Inst. of Plant and Soil Sci., Tjele.

Mead, R.M., J.E. Ayars, and J. Liu. 1995. Evaluating the influence Book Ser. 5. SSSA, Madison, WI.Warrick, A.W., and D.R. Nielsen. 1980. Spatial variability of soilof soil texture, bulk density, and soil water salinity on a capacitance

probe calibration. ASAE Paper 953264. Am. Soc. Agric. Eng., St. physical properties in the field. p. 319–344. In D. Hillel (ed.) Appli-cations in soil physics. Academic Press, New York.Joseph, MI.

Ott, L. 1984. An introduction to statistical methods and data analysis. Weast, R.C. (ed.) 1980. Handbook of chemistry and physics. 61st ed.CRC Press, Boca Raton, FL.PWS Publ., Boston.

Paltineanu, I.C., and J.L. Starr. 1997. Real-time soil water dynamics Yu, C., A.W. Warrick, M.H. Conklin, M.H. Young, and M. Zreda.1997. Two- and three-parameter calibrations of time domain reflec-using multisensor capacitance probes: Laboratory calibration. Soil

Sci. Soc. Am. J. 61:1576–1585. tometry for soil moisture measurement. Water Resour. Res. 33:2417–2421.Robinson, D.A., C.M.K. Gardner, J. Evans, J.D. Cooper, M.G. Hod-

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