Evaluation of a capacitance probe freque

() R e p ro d u c e d f ro m V a d o s e Z o n e J o u rn a l P u b lis h e d b y S o il S c ie n c e S o c ie ty o f A m e ri c a A ll c o p y ri g h ts r e s e rv e d Evaluation of a Capacitance Pro[.]

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

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

TDR and Network Analyzer Measurements

D A Robinson,* T J Kelleners, J D Cooper, C M K Gardner,

P Wilson, I Lebron, and S Logsdon

trying to determine water content at a range of scales

Soils ranging in texture from sand to clay were used to compare

Many measurement methods have been reviewed by

permittivity measurements made using a Surface Capacitance

Inser-Gardner et al (2001) and Topp and Ferre (2002), among

tion Probe (SCIP) and time domain reflectometer (TDR)

Measure-others Two of the more commonly used

electromag-ments were made using the same electrodes embedded in each soil,

solutions Surface Capacitance Insertion Probe and TDR determined

Starr, 1997; Kelleners et al., 2004) A surface capacitance

permittivity values are similar for sandy soils but diverge for loam and

insertion probe (SCIP) (Robinson and Dean, 1993; Dean,

clay soils Using Topp’s values as a reference, the SCIP-determined

per-1994; Robinson et al., 1998) is used in this work

Capaci-mittivities for loams and clays lay close to the curve at water contents

tance probes such as the EnviroSCAN (Sentek, Stepney,

⬍0.25 m 3 m⫺3 , then often rose above the curve with increasing water

Australia) have become popular for irrigation

schedul-content Surface Capacitance Insertion Probe permittivity correction,

than expected real permittivity created by dielectric dispersion, (ii)

TDR and capacitance sensors attempt to measure the

a large contribution of the imaginary permittivity due to relaxation

permittivity of the soil medium Because they may not

processes assumed to be negligible, and (iii) poor model prediction

do so perfectly, the measurement yielded by the

instru-of permittivity due to excessive damping instru-of the oscillator circuit with

ment is termed the apparent permittivity.

high EC and dielectric losses Results from network analyzer

measure-Many calibration equations to relate apparent

permit-ments for one of the clay soils were used to aid data interpretation The

tivity to water content have been presented in the

litera-TDR measurements were much more consistent, producing apparent

equations are used interchangeably among different types of sensors Water content determination is a

two-The life-sustainingreservoir for plant and micro- step process—from sensor response to permittivity (Jones bial communities is soil water, a key component of et al., 2005; Blonquist et al., 2005), and from permittivity the hydrological cycle As such, knowledge of soil water to water content Errors or invalid assumptions in the content is required for using global circulation models first step will lead to difficulty in making interpretations

to estimate heat and vapor fluxes in what has been re- at the next step In this study we compared measure-ferred to as the “critical zone” (Committee on Basic Re- ments made using a surface capacitance insertion probe search Opportunities in the Earth Sciences, Board on and TDR in 12 soils The initial objective of this work

was to evaluate a calibration model developed for the Earth Sciences and Resources, National Research

Coun-SCIP This uses well-defined dielectric solutions and di-electric solutions with ionic conductivity to determine D.A Robinson and I Lebron, Dep of Plants, Soils and Biometeorol- whether accounting for EC measured at 1 kHz improves ogy, Utah State University, Logan, UT, USA; T.J Kelleners, George

permittivity measurement Solution electrical

conduc-E Brown Jr Salinity Lab USDA-ARS, Riverside CA, USA; J.D.

tivity changes by about 2% ⬚C⫺ 1and can have a strong im-Cooper, Instrument Section, Centre for Ecology and Hydrology,

Wall-ingford, Oxon, UK; C.M.K Gardner, IAHS Press, Centre for Ecology pact on the apparent permittivity measurement Elimi-and Hydrology, Wallingford, Oxon, UK; P Wilson, School of Environ- nating it from the apparent permittivity measurement mental Sciences, University of Ulster, Coleraine, Co Londonderry,

can considerably improve water content determination

N Ireland, UK; S Logsdon, National Soil Tilth Lab USDA-ARS,

The second objective was therefore to evaluate the model Ames/Ankeny, IA, USA Received 14 Sept 2004 *Corresponding

author (darearthscience@yahoo.com). permittivity predictions with and without accounting for

bulk soil EC to determine whether accounting for EC Published in Vadose Zone Journal 4:992–1003 (2005). could improve the permittivity and water content cali-Special Section: Soil Water Sensing

doi:10.2136/vzj2004.0131

 Soil Science Society of America Abbreviations: EC, electrical conductivity; SCIP, Surface Capacitance

Insertion Probe; TDR, time domain reflectometer.

677 S Segoe Rd., Madison, WI 53711 USA

992

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

bration Predictions of permittivity are compared directly adaptable electrode configuration (Robinson et al., 1998;

Whalley et al., 1992)

with TDR measurements using the same electrodes and

also with some independent network analyzer measure- The capacitance of a pair of electrodes is a function

of the relative permittivity, εr, of the material in which ments As far as possible, we develop and use physical

principles and models to provide understanding of what the electrodes are embedded and the geometric

con-figuration of the electrodes:

is being measured By doing this we hope to identify

de-ficiencies in knowledge of what is being measured and

Cm⫽ gmεrεo [4] make recommendations for sensor improvements

where Cm is the capacitance, gm is a geometric factor, and εois defined previously The impedance, Z, of an

THEORY

inductance, L, and capacitance, C , in series is given by

Time Domain Reflectometry

Z ⫽ j␻L ⫹ 1

j␻C ⫽ j冢␻L ⫺ 1

The TDR method is a transmission line technique,

which determines an apparent TDR permittivity (Ka)

where j ⫽ 公⫺1, ␻ is the angular frequency (⫽ 2␲F, with

from the travel time of an electromagnetic wave that

prop-F being the frequency) At the resonance frequency, the agates along a transmission line, usually two or more

imaginary part of the impedance (Eq [6], from Eq [5]) parallel metal rods embedded in a dielectric (Topp and

is zero:

Ferre, 2002; Robinson et al., 2003) The propagation

ve-locity of a broadband (20 kHz–1.5 GHz) (Heimovaara,

1994) electromagnetic signal determined by fitting

tan-gent lines to the wave form is analogous to the phase

velocity, vp, of an electromagnetic plane wave through a which can be solved either for the angular frequency,

vp⫽ 1

√␮o␮rεoεr⫽

c

where c is the velocity of light in vacuo (3 ⫻ 108m s⫺ 1),

C ⫽ 1

εois the electric constant (8.854 pF m⫺ 1), εris the relative

permittivity, ␮ois the magnetic permeability of vacuum

The impedance of the SCIP oscillator circuit can be (1.257 ⫻ 10⫺ 6H m⫺ 1), and ␮ris the relative magnetic

per-written as (e.g., Dean, 1994; Dean et al., 1987) meability, which can be taken as unity in almost all soils

(Roth et al., 1992) The TDR signal propagates down

Z ⫽ j␻L ⫹ 1

j␻Cm⫹ j␻Cs

j␻Cb

[8] the transmission line and is reflected from its end; the

returning signal is sampled in the TDR device From

Eq [1], the velocity of the signal in a perfect, nonmag- where Cmis the capacitance of the electrodes, Csis a

capaci-tance of the circuit board Equation [8] can be written

v ⫽ 2l

t ⫽

c

Z ⫽ j(⫺␻2LCb[Cm⫹ Cs] ⫹ Cm⫹ Cs⫹ Cb)

where l is the length of the line and t is the time for a

At the resonance frequency, the imaginary part of round trip (back and forth) Rearranging Eq [2] gives

the impedance (Eq [10], from Eq [9]) is again zero:

the round trip propagation time (t ) of the wave as a

func-tion of both the length of the transmission line (l ) and ⫺␻2LCb[Cm⫹ Cs] ⫹ Cm⫹ Cs⫹ Cb⫽0 [10] the relative permittivity of the material:

The solution of Eq [10] for the angular frequency,

␻, and the electrode capacitance, Cm, is:

t ⫽ 2l√εr

␻ ⫽2␲F ⫽冪Cm⫹ Cs⫹ Cb

LCb(Cm⫹ Cs) [11]

Hence the permittivity can be determined by measuring

the time it takes the signal to traverse the probe

Cm⫽ Cs(␻2LCb⫺ 1) ⫺ Cb

Surface Capacitance Insertion Probe

The SCIP is a series resonance, frequency shift

capaci-tance probe operating between 70 and 150 MHz

(Rob-Complex Dielectric Permittivity

inson and Dean, 1993; Dean 1994; Robinson et al., 1998;

Gardner et al., 1998) The frequency response is a func- Many materials, including soils, do not constitute a

per-fect dielectric Energy losses arising from dielectric relax-tion of the electrode capacitance; from this, an apparent

soil permittivity (KSCIP) is obtained The most attractive ation and ionic conductivity need to be taken into

ac-count The relative permittivity of the material should features of capacitance probes are their simplicity of

con-cept and use compared with the TDR, and their more then be represented by a complex quantity ε* with a

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

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

N Irish Soil Survey/

%

broad spectrum of soil textural classes The Northern Ireland

real part εr⬘describing energy storage and an imaginary

soils are derived mainly from drift deposits overlying diverse

part εr″ describing energy losses:

bedrock The mixing and outcropping of different strata has

εr* ⫽ εr⬘ ⫺ jεr″ [13] led to the development of a wide variety of soils, from

diato-maceous earths to Fe-rich clays (Cruickshank, 1997) Details

The εr″ term in Eq [13] is the sum of a conductivity

of the soils are contained in Table 1 All soil samples were

thereby sampling topsoil below the root mat if present

εr″ ⫽ ␴

␻εo

set of repacked soils Approximately 5 kg of soil was collected from each location Once in the laboratory, the soil was sieved

where ␴ is the ionic conductivity and ε″r,relis the loss due

onto large plastic trays A 5-mm sieve was used to remove any

to dielectric relaxation The electrode capacitance, Cm,

large stones, while partially maintaining the natural ped

struc-is now also a complex quantity:

ture; it also homogenized the soil The soils were left for 6 wk to air dry in the laboratory Subsamples were removed for physical

C*m⫽ C ⬘m⫺ j冢gm␴

␻ ⫹ gmε″r,relεo冣 [15] and chemical characterization.

where Cm* is the complex electrode capacitance, Cm⬘ is Soil Characterization

the real part of the material capacitance, and gmwas

pre-Particle size analysis was performed using the standard

siev-viously defined Multiplication of both sides of Eq [15]

ing and pipette method (Klute, 1986; Loveland and Whalley,

sieve, all the soil samples were pretreated with dilute acid to

remove carbonates and then boiled with hydrogen peroxide

where G ⫽ gm␴ ⫹ gm␻ε″r,relεo The impedance of the SCIP to remove the organics (Gee and Bauder, 1986) Soil chemical oscillator circuit for a material with a complex permittiv- and mineralogical analyses are presented in Table 2 Soil

diffraction analysis Subsamples of the sand and silt fraction and the clay fraction were analyzed semiquantitatively Soils

j␻C ⬘m⫹ G ⫹ j␻Cs

j␻Cb

[17]

10 and 11 contained notably high values of oxide minerals that may be overestimated slightly because they were determined

Separating the real and imaginary parts gives

semiquantitatively from X-ray diffraction data, but Soil 10 was formed on a weathered Fe-rich band within the underlying

Z ⫽ ⫺␻CbG ⫺ j[␻ 4LCb(C ⬘m⫹ Cs ) 2 ⫹ ␻ 2LCbG2 ⫺ ␻ 2Cb(C ⬘m⫹ Cs ) ⫺ ␻ 2(C ⬘m⫹ Cs ) 2⫺ G2 ]

␻Cb [⫺␻ 2(C ⬘m⫹ Cs ) 2⫺ G2 ] basalt These soils were classified as sandy silt loam (10) and

[18] clay (11) However, the iron oxides were not removed during

pretreatment and were observed to be cementing the soil Our

As before, the imaginary part of the impedance is

belief is that both these soils would be more appropriately

clas-zero at the resonance frequency: sified as clays The loss-on-ignition technique (Davies, 1974)

was used to determine the percentage of organic matter Soil pH

␻4LCb(C ⬘m⫹ Cs)2⫹ ␻2LCbG2⫺ ␻2Cb(C ⬘m⫹ Cs) ⫺

was measured using a soil/water ratio of 1:2.5 (Rowell, 1994)

␻2(C ⬘m⫹ Cs)2⫺ G2⫽0 [19] The soil solution electrical conductivity was measured using

a standard 1:5 soil/water extract (Landon, 1991) The EC meter

This is a quadratic equation in both ␻2and C ⬘m, with

(Jenway EC sensor, Jenway, Felsted, Dunmow, England)

auto-solutions (see Appendix)

matically temperature compensated the readings to 25⬚C Table 3 presents the soil physical properties The bulk

bulk density values were generally lower than bulk density

val-Sample Description and Collection ues found in undisturbed field samples The hygroscopic water

content of the soils is given for two values of relative humidity Soils were collected for this project from 12 locations across

Northern Ireland and Southern England They represent a Samples were oven dried at 105⬚C and then allowed to

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

Table 2 Soil mineralogy and chemical properties.

mineralogy

brate at the respective humidity Values for the sands (Soils (1998) To obtain measurements for a range of water contents,

the above procedure was repeated with progressively wetter

1, 2, and 3) were all ⬍0.001% The hygroscopic water content

is given as a volumetric percentage based on the average bulk soil, each time adding 80 to 100 g of deionized water to the soil

using an atomizer spray gun while continually mixing This density The external surface area of the soil was measured using

nitrogen adsorption (Newman, 1987), with a Gemini III 2375 process was repeated until a volumetric water content range

from air dry to saturation was achieved

surface area analyzer (Micrometrics, Londonderry, NH)

The use of repacked soil samples for permittivity measure- Measurements were made with both TDR and SCIP using ment followed the approach of Gardner et al (1998); similar the same electrodes These were stainless steel, 6 mm in diame-methods having been used by others (Malicki et al., 1996) ter and 100 mm in length, with a 25-mm center spacing; they Repacking of soil allows measurements to be performed over were inserted vertically into the soil They had female sockets

a wide range of water content and dry bulk density A plastic in the upper end, which mated with male connectors, so that cylinder, with 0.103-m inside diameter, capped at one end, was each instrument could be used to make measurements in the packed with air-dried soil to a height of 0.14 m to give a pre- soil without disturbing the electrodes EC was measured across pared sample 1167 cm3in volume This was weighed on a bal- the electrodes using a 1-kHz bridge (ESI Inc., Portland, OR). ance accurate to 0.1 g A pair of stainless-steel electrodes, 0.1 m The sensor measurements were calibrated for conductivity

in length, was fully inserted vertically into the center of the (␴) in solutions of potassium chloride A cell constant (g

m) of sample Measurements were taken by TDR and then the SCIP 0.1246 m was determined by comparison with measurements After the measurements, the sample in its core was reweighed using a conductivity bridge (Robinson et al., 1998).

and then a temperature probe inserted into the soil to measure The SCIP was described in more detail by Dean (1994) soil temperature All work was conducted in a laboratory, whose and Robinson et al (1998) Normally, the instrument has two temperature was maintained at 20 ⫾ 1⬚C A 10-g subsample of 100-mm stainless-steel electrodes secured in a 30-mm-thick soil was removed and oven dried so that the gravimetric water plastic housing at the base of the probe body The circuitry content could be determined The soil was then removed from is contained above the electrodes inside the main body of the cylinder and mixed with the remainder of the soil The cyl- the instrument The oscillation frequency of the instrument is inder was then repacked with soil to a slightly greater bulk displayed on an LCD screen at the top of the instrument The density than previously This procedure was repeated for re- whole instrument weighs less than 1.5 kg and is housed in a packed soil at five bulk densities with the same gravimetric robust, water resistant, plastic casing The 30-mm-thick plastic water content Volumetric water content and bulk density electrode-mounting block of this experimental SCIP was cut were calculated from the gravimetric water content and the wet in half and the main body was fitted with two male connectors. mass of the repacked mixture contained in the known volume These could be inserted into the female connectors in the

de-of the cylinder following the same procedure as Gardner et al tachable electrodes The instrument was calibrated in air and

water following the procedure developed by Robinson et al

deter-mined according to Cm⫽ gmεoεr(Dean, 1994) The values L and

Hygroscopic water

Eq [11] The response of the SCIP was tested in a range of

dielectric liquids at 25⬚C (white paraffin, 2.2; hexanol, 13.3;

taining potassium chloride within the EC range of 0 to 2.8

dS m⫺ 1

connected to the electrodes, which in this case formed the

probe, by a 1-m length of coaxial cable The TDR was used to

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

demonstrates the damping of the frequency response that occurs

permit-tivity measured by both the TDR and SCIP were the same,

form was downloaded to a PC and interpreted using this

the small triangles representing the TDR data should fall

software

inside the large open circles These circles represent the

Measurements were also made using a dielectric probe

(Hew-SCIP-derived permittivity corrected for the effects of

lett-Packard 85070B, Hewlett-Packard, Palo Alto, CA) attached

electrical conductivity In the first three of the figures

to a network analyzer (Hewlett-Packard 8753B) The network

analyzer measures the real (ε ⬘r) and imaginary (ε ″r, Eq [14]) this is the case; one or two points lie outside, which may

permittivity independently between 10 MHz and 3 GHz using be due to experimental error, but there is no consistent

the dielectric probe Samples of Soil 10 (Giants Causeway a ) deviation The data demonstrate that in sandy soils with

were wetted and repacked into a 3.17-cm3 sample holder low bulk EC (⬍0.1 dS m⫺ 1), permittivity measurements

mounted on top of the dielectric probe The low frequency from both sensors correspond and that there was

negligi-electrical conductivity was measured across the sample using ble correction to the SCIP measurements for electrical

a 1-kHz bridge (ESI Inc.) and found to correspond with

mea-conductivity In the case of the Herringswell soil, the bulk

surements made with the TDR

EC has a significant impact on the apparent permittivity measured by the SCIP The model corrections for EC

satura-tion After correction, the SCIP permittivity values are

SCIP Model Calibration in Dielectric Fluids

closer to those obtained with the TDR The data clearly

A comparison of the frequency response of the SCIP indicate the requirement for correction to retrieve per-predicted by Eq [A2] in the appendix and the measured mittivity from capacitance sensors in soils where bulk data is presented in Fig 1 and shows excellent agree- soil EC interferes with the determination of the appar-ment The response of the SCIP in electrically conduct- ent soil permittivity.

ing solutions is also presented to demonstrate how bulk Results for the loamy soils are presented in Fig 4.

EC reduces the frequency response of the instrument The These soils had lower average bulk density than the sandy frequency response for electrical conductivity ⬎2.0 dS m⫺ 1

soils (0.73–0.96 g cm⫺ 3) The soils also offered a range becomes very flat and suggests that permittivity mea- of bulk EC at saturation, ranging from 0.1 dS m⫺ 1 for surement will be difficult in conductive soils Figure 2 the soil from Glenwherry to 1.3 dS m⫺ 1for the Walling-shows the frequency response to changes in electrical ford soil This time, clear divergence between the mea-conductivity of saline (KCl) dielectric solutions; the lines surements can be observed for all four soils Electrical indicate the modeled response Again the model and conductivity is observed to influence the SCIP

Walling-ford After correction for EC, the SCIP-determined

contents Permittivity measurements from the Glen-Measurements for the sandy soils are presented in

Fig 3 Three of these soils had very low values of bulk wherry soil also deviate similarly at higher water

con-tents, but it is clear that electrical conductivity plays no

EC, generally below 0.1 dS m⫺ 1 The fourth, from

Her-ringswell, had a bulk EC that rose to 0.45 dS m⫺ 1 at role in this as the uncorrected permittivity values (solid

circles) lie inside the corrected values (open circles) high water content Topp’s curve for mineral soils (Topp

et al., 1980) provides the reference in Fig 3, and the data The apparent permittivity estimates from the TDR lie

consistently below those predicted by Topp’s curve for follow it closely as expected and previously presented

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

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

all the soils This is most probably a density effect; the are the remains of diatoms (Fig 6) As a result, the soil

has a particularly low bulk density Bulk EC has little Glenwherry soil is high in organic matter content and has

an average bulk density of 0.73 g cm⫺ 3(Table 3) and impact on the permittivity measurements in this soil

All the measurements, from both TDR and SCIP, lie gives the lowest permittivity values

Results for the four fine textured soils are presented below Topp’s curve, probably because of the low bulk

density However, at the higher water contents, the SCIP

in Fig 5 Again, these soils represent a range of bulk

density (0.51–1.02 g cm⫺ 3) and bulk EC at saturation measurements become higher than those found using

TDR The two soils from the Giants Causeway both had (0.4–2.7 dS m⫺ 1) The geometry of the Toombebridge

soil is fascinating—it is composed of silica tubes that high bulk electrical conductivity near saturation After

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

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

accounting for this in the SCIP measurement, relative mittivity values for Soil a rise above Topp’s curve This

is similar to the observations of Dirksen and Dasberg permittivity values as high as 275 and 70 were obtained

at saturation for Soils a and b, respectively Measure- (1993) for TDR measurements in montmorillonite The

heavy clay soil from Wytham also shows deviation

be-ments from Soil a lie above those of Topp’s curve; above

a water content of 0.25 m3m⫺ 3, the apparent permittiv- tween the TDR measurements and the corrected SCIP

measurements, the highest relative permittivity value

ity increases dramatically Soil b measurements follow

Topp’s curve to a water content of about 0.25 m3m⫺ 3and from the SCIP being 43, and from the TDR being 20

These results indicate good correspondence between then diverge upward in a similar but less sharp manner

The TDR results for these soils both lie below Topp’s measurements made in sandy soils using both

instru-ments However, in the wetter clay soils, deviation be-curve; however, at the higher water contents the

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

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

tween the values of permittivity is very pronounced In measurements that differed the most from the TDR

results Network analyzer measurements are helpful be-the next section we examine some explanations for this

cause the real and imaginary permittivities are measured observed deviation

separately It provides separate measurements of both the real and imaginary permittivity, against which

ap-Frequency Domain Results

parent permittivity from other instruments can be

com-We obtained preliminary data using the network ana- pared and interpreted Measurements for the Giants lyzer to try to gain further insight into the measurements Causeway a are presented in Fig 7 for water contents

of 0.08 and 0.46 and bulk density of approximately 1.0 g

made in the Giants Causeway a This soil produced SCIP

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

Fig 6 Scanning electron micrograph image of the Toombebridge

dia-tomaceous silty soil The tubes are about 10 ␮m in diameter.

Fig 7 Frequency domain analysis of Soil 9 (Giants Causeway a ) for

two water contents, 0.08 and 0.46 This is a dielectrically dispersive soil, the real permittivity changes with frequency The real

per-cm⫺ 3 This bulk density and the water content of 0.46

mittivity and imaginary permittivity due to EC and due to

relax-closely resemble the final measurement in Fig 5 (Giants ation are all separated.

Causeway a ) This soil is clearly a dispersive dielectric;

that is, its dielectric properties change with frequency cause there is a further polarization mechanism that con-Dispersion of this nature has been reported for clay min- tributes and is itself dependent on bulk density This is erals and heavy textured clay soils (Saarenketo, 1998; over and above the expected increase in permittivity re-Logsdon and Laird, 2002) At a water content of 0.46, sulting from the reduction in air-filled porosity caused the relative permittivity measured at about 68 MHz cor- by increasing solid and water Reasonable agreement is responds to a value of 52 This is much lower than the found between the TDR measurements and the net-value of 277 obtained with the SCIP, which seems to be work analyzer real permittivity for a bulk density around improbably high The corresponding imaginary relative 0.75 g cm⫺ 3 up to a water content of 0.3; above this permittivity due to relaxation is about 14 Inclusion of water content, the data diverge, with the TDR permit-this value of imaginary permittivity does not improve the tivity rising above Topp’s curve and the network analyzer estimate of the real permittivity One of the major prob- data remaining below it From Fig 5 (Giants Causeway a, lems is that the oscillation frequency of the SCIP has been bulk density) one can observe that at water contents higher damped so much by the EC and imaginary permittivity than this, the bulk density in the packed column is corre-that a small inaccuracy in the measurements may give spondingly greater Network analyzer measurements

a very high (or low) real permittivity estimate This is packed to 1.0 g cm⫺ 3in Fig 8A also demonstrate that demonstrated in Fig 1 for an EC of 4 dS m⫺ 1; at this the real permittivity rises above Topp’s curve for more

EC the frequency response of the SCIP is almost flat densely packed samples This may indicate that the in-(i.e., it does not change as a function of the permittivity) crease in permittivity measured by the TDR is simply a

In Fig 8, results from the network analyzer for the function of the increased bulk density The permittivity real permittivity are plotted along with the TDR results measured by the TDR appears to correspond well with (Fig 8A), for different frequencies from the network the real permittivity measured by the network analyzer analyzer (Fig 8B), and adjusted SCIP permittivity (Fig for a frequency of around 1.0 GHz The change of shape 8C) Dielectric spectra, like the ones in Fig 7, were ob- of the calibration curve can be ascribed to the change of tained for the soil at six water contents repacked to a bulk density involved in repacking the soils This sug-bulk density close to 0.75 g cm⫺ 3 Results are also shown gests that in clay soils there is a polarization mechanism

in Fig 8A and 8C for two higher water contents with that is a function of the bulk density that can significantly the soil repacked to a bulk density of about 1.0 g cm⫺ 3 affect the real permittivity As this occurs at saturation, The real permittivity was extracted from the spectra at a possible physical mechanism explaining it might be three frequencies for comparison with the TDR, 3.00, that the geometry confines the ions more effectively and 1.01, and 0.26 GHz (Fig 8A), and three frequencies for their confinement enhances charge storage, that is, the the SCIP, 1.01, 0.10, and 0.07 GHz (Fig 8C) real permittivity Mechanisms such as the

Maxwell-In Fig 8A, the network analyzer results are compared Wagner effect (e.g., Hasted, 1973; Sen, 1984; Haslund, with the TDR results At water contents above 0.3 the 1996) have been described for low frequencies ⬍100 TDR apparent permittivity values increase markedly MHz, but this data indicate that a further mechanism Dirksen and Dasberg (1993) also observed similar be- occurs above 100 MHz

havior for repacked samples of montmorillonite Our The network analyzer data for the real permittivity interpretation of this is that the real permittivity increases and for a uniform bulk density are presented in Fig 8B

The gravimetric water content for the air-dry sample is not only because of higher water content, but also

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

cant change in the soil dielectric properties at this water content The apparent permittivity from the SCIP mea-surements, however, rises much more abruptly than those from TDR, and even though the real permittivity measured with the network analyzer is higher at a fre-quency of 70 MHz, it is not enough to account for the SCIP response

DISCUSSION

An important objective of this study was to discover

if incorporating EC into SCIP calibration was enough to improve water content determination The results from the sandy Herringswell soil are encouraging However, the results from the other medium and heavy textured soils indicate that the use of low frequency EC measure-ments is not sufficient by itself to produce results close

to real permittivity, as measured by a network analyzer

or a calibration curve similar to those of Topp et al (1980)

As discussed for fine textured soils (Fig 5), there ap-pears to be a critical range of water content from about 0.20 to 0.25 m3m⫺ 3at which the SCIP permittivity results change abruptly This is also the point at which the electrical conductivity increases steeply, perhaps indi-cating an electrical percolation threshold We propose three explanations that could account for the high values

of permittivity obtained with the SCIP measurements:

• higher than expected real permittivity created by dielectric dispersion

• a large contribution to the imaginary permittivity

by relaxation processes assumed to be negligible

• failure of the circuit model to provide reliable per-mittivity determination with such significant oscil-lator damping

suffi-ciently account for the high permittivity values obtained

Causeway a soil Measurements at six water contents are presented

with the SCIP based on the network analyzer results This

and three of frequency (8B) Frequency domain data for the same

permittiv-shaped curve but rises above Topp as the frequency becomes lower.

ity values with such heavy damping of the oscillator

re-(8C) Data for the same soil for the SCIP and network analyzer

sponse This further suggests that reliable, accurate water

results for three frequencies.

content determination using this type of capacitance probe will be limited to soils with low EC and low dielectric subtracted from all the values The purpose of this is to

demonstrate that for a uniform bulk density at a range relaxation

This work demonstrates the need for several

improve-of frequency values (0.05, 0.10, 0.26, and 1.01 GHz) the

data give a Topp shaped curve for the high frequencies ments in measurements to determine water content from

permittivity measurements With so many sensors now (1 GHz), and permittivity increases as the frequency

reduces These data support the interpretation of the available, all purporting to measure permittivity, it is

important to develop a standard methodology that can TDR data that the change observed in the shape of the

calibration (Fig 8A) is a consequence of the changing be used to determine the ability of a sensor to measure

the real permittivity, especially in dispersive and/or con-bulk density For the con-bulk density of 0.75 g cm⫺ 3

mea-sured using the network analyzer at 1.01 GHz, the shape ductive dielectrics One way to do this is to use dielectric

liquids as in this work with the SCIP and as presented

of the water content–permittivity relationship is

con-sistent with the shape of Topp’s curve, but offset by the in Jones et al (2005) and Blonquist et al (2005) for seven

sensors A further important contribution is the need for presence of hygroscopic water

Interestingly, the SCIP data in Fig 8C also begin to “truth.” This means we need to understand permittivity

behavior in the frequency domain and particularly how show dramatic divergence from a Topp-shaped curve

at a slightly lower water content of 0.26 The similar geometry and hygroscopic water affect measurements

In our opinion this should be based on measurements response for both the TDR and SCIP around this water

content gives more weight to the suggestion of a signifi- with a network analyzer to measure the real permittivity