a calibration and temperature correction procedure for the water-content reflectometer

HYDROLOGICAL PROCESSESSCIENTIFIC BRIEFING

Hydrol. Process. 19, 3785–3793 (2005)Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hyp.6069

A calibration and temperature correction procedure for thewater-content reflectometer

Andrew W. Western1* andMark S. Seyfried2

1 Cooperative Research Centre forCatchment Hydrology and Centrefor Environmental AppliedHydrology, The University ofMelbourne, Melbourne,Victoria 3010, Australia2 USDA-Agricultural ResearchService, 800 Park Blvd, Boise,ID 83712, USA

*Correspondence to:Andrew W. Western, Centre forEnvironmental Applied Hydrologyand Cooperative Research Centrefor Catchment Hydrology,Department of Civil andEnvironmental Engineering,University of Melbourne,Melbourne, Victoria 3010,Australia.E-mail: [email protected]

Abstract

Calibration is required for most soil moisture sensors if accurate measure-ments are to be obtained. This can be time consuming and costly, especially iffield calibration is undertaken, but can be facilitated by a good understandingof the behaviour of the particular sensor being calibrated. We develop gen-eralized temperature correction and soil water calibration relationships forCampbell Scientific CS615 water-content reflectometer sensors. The tempera-ture correction is estimated as a function of the raw sensor measurement. Thecalibration relationship requires one soil-related parameter to be set. Theserelationships facilitate field calibration of these sensors to acceptable accura-cies with only a small number of samples. Copyright 2005 John Wiley &Sons, Ltd.

Key Words soil moisture; water content reflectometer; calibration

IntroductionSoil moisture (�) measurements can be achieved using a variety ofapproaches. A common approach is to measure changes in the soildielectric constant, which makes use of the contrast between the dielec-tric constant of air (1), soil mineral particles (3–7) and liquid water(approximately 80). Time-domain reflectometry (TDR) is widely usedto measure soil dielectric constant, from which � can be inferred. TDRcalibration relationships are quite stable to variations in soil type, andwell-known general calibration relationships exist, e.g. the Topp equation(Topp et al., 1980), although calibration relationships for soils with largeclay and or organic matter content can vary significantly from thesegeneral relationships (Hook and Livingston, 1996). TDR also has anadvantage in that it has a low sensitivity to soil temperature (Pepinet al., 1995).

TDR instruments are expensive and rely on analysis of measuredwaveforms, which may be problematic (Logsdon, 2000). A range ofcheaper devices relying on measuring a response to changes in thebulk soil dielectric constant have been developed in recent years. Theseinstruments generally operate at much lower frequencies (10–100 MHz)than TDR (700–1000 MHz) and, as a consequence, are more sensitiveto variations in soil properties and temperature (Seyfried and Murdock,2001, 2004). In fact, temperature sensitivity is a universal, sometimesvery large, problem for non-TDR dielectric sensors, and independently

Received 19 July 2005

Copyright 2005 John Wiley & Sons, Ltd. 3785 Accepted 12 September 2005

A. W. WESTERN AND M. S. SEYFRIED

tested correction approaches are rare or nonexistentin the literature. Also, it is generally necessary tocalibrate these sensors for specific soils if actual mea-surements of � are required, as opposed to someindication of soil water fluctuation over time. Thispaper summarizes temperature correction and calibra-tion methods developed and tested with one particularsensor, the Campbell Scientific CS615 water-contentreflectometer (Campbell Scientific Inc., 1996), whichis a transmission line oscillator that operates in thetime domain like TDR but at a lower frequency (Kel-leners et al., 2005).

The CS615 consists of a printed circuit boardconnected to two parallel stainless steel rods that actas wave guides. The rods are 3Ð2 mm in diameter,300 mm long and are separated by 32 mm. A robustversion of this sensor with rods 200 mm in length isalso available, but is less commonly used. The circuitforms a bistable vibrator producing pulses that travelalong the wave guides and reflect off the open end.The maximum incident wave frequency (propagatinginto the soil) is 45 MHz (Kelleners et al., 2005). Thisoscillation frequency of the circuit is sensitive to thedielectric constant and electrical conductivity (EC)of the bulk soil. The oscillation frequency signal isscaled down to about 1 kHz and the sensor output isa square wave with š2Ð5 V amplitude, the frequencyor period of which can be recorded with a datalogger. In this paper we follow Campbell ScientificInc. (1996) and Seyfried and Murdock (2001) and usemeasurements of the period produced by the CS615as the sensor signal.

Recently, Campbell Scientific has released an up-dated version of this sensor, the CS616. Although thespecific relationships developed in this paper are notapplicable to this new sensor, we believe the approachis applicable because the CS616 uses the same oper-ating principle, but at a somewhat higher measure-ment frequency (maximum measurement frequencyapproximately 175 MHz compared with 44 MHz;Kelleners et al., 2005). Like the CS615, the CS616also shows marked sensitivity to soil type and temper-ature. Thus, although some recalibration or refittingof the equations would be necessary to apply theapproach to the CS616, we believe that the benefits interms of facilitating easier field calibration will alsoexist for the new sensor.

The sensitivity of the CS615 calibration to soil typeand temperature relative to TDR is largely explained

by the differing measurement frequencies. The CS615measured period is a function of KŁ, the complexdielectric constant of the soil:

KŁ D K0 � iK00 �1�

where K0 and K00 are the real and imaginary compo-nents respectively of the complex dielectric constant.The K0 values of pure water, soil solids and air areinsensitive to measurement frequency in the 10 to1000 MHz range. However, any mixture of these mayshow dielectric dispersion (complex dielectric con-stant changes with frequency), especially if there areions in the soil water (which is usually the case). Forthis reason the instrument response of low-frequencyinstruments, such as the CS615, is similar to that ofTDR in soils with negligible K00 (Seyfried and Mur-dock, 2001, 2004). Temperature effects in these soilsare dominated by the effect of temperature on purewater, for which the dielectric constant declines from88 at 0 °C to 72 at 45 °C, which results in a slightnegative temperature effect.

The imaginary component is related to soil solutionionic composition and concentration, properties ofadsorbed ions and the degree of interaction betweensoil water and solids at the solid–liquid interface.These properties vary considerably with soil type. Itappears that K00 is dominated by EC at the measure-ment frequencies of the CS615 (Campbell, 1990). Theeffect of EC on K00 is inversely proportional to themeasurement frequency, so that TDR is less sensi-tive to individual soil properties than the CS615 andother low-frequency measurements and KŁ tends to begreater when measured at low frequencies. In addi-tion, EC is strongly temperature dependent. The ECof aqueous solutions increases about 2% per degreeCelsius. The result is a strong positive temperatureeffect, which may be as great as that of soil watercontent, on all field soils we have measured.

Whereas field or laboratory calibration will gen-erally give the best results for most soil moistureinstruments, this process can be made efficient byunderstanding and generalizing either the overall sen-sor response or components of it so that the numberof samples required can be minimized. Based on twosets of laboratory experiments, we provide a gen-eral calibration relationship that relates raw sensoroutput to a temperature-corrected soil water content.The approach requires independent measurements of

Copyright 2005 John Wiley & Sons, Ltd. 3786 Hydrol. Process. 19, 3785–3793 (2005)

SCIENTIFIC BRIEFING

� to determine the value of a single, soil-specific cal-ibration parameter. It facilitates field calibration ofthe sensor because it requires relatively few measure-ments to determine the parameter value.

Materials and MethodsThe results provided are based on two sets of experi-mental data. The first is that of Seyfried and Murdock(2001) from soils of the Reynolds Creek watershed inthe USA and the second is a set of laboratory mea-surements for a variety of soils from Australia andNew Zealand. Both studies used similar, but not iden-tical, laboratory measurement approaches centred onmeasurements of the sensor response as a function oftemperature and � using repacked cores in the labo-ratory.

Seyfried and Murdock (2001) performed their mea-surements on four soil types: Sheep Creek, Summit,Foothill, and sand. The sand was construction sandrather than a natural soil. Table I provides sand andclay percentages, bulk density (from volumetric sam-ples collected in the field) and EC measurements forthese soils. Twelve soil horizons from seven soil typeswere included in the Australian and New Zealandsoils measurements. Textures range from sand toheavy clay and all are natural soils. It should be

noted that the EC data provided by Seyfried and Mur-dock (2001) are measured on saturation paste extracts,whereas those for the Australian and New Zealandsoils are measured on 1 : 5 (soil : water by mass) sus-pensions. The 1 : 5 dilution tests typically result inan EC that is substantially smaller than that obtainedfor saturation paste extracts (Slavich and Petterson,1993). Nevertheless, the Australian and New Zealandsoils have a lower EC (salinity) than the ReynoldsCreek soils.

The response of CS615 output period to � andsoil temperature was measured for each soil usingthe following procedure. First, an appropriate massof oven dry soil was thoroughly mixed with anappropriate volume of de-ionized water and packedinto a PVC cylinder of known volume (Table II) toachieve a target bulk density (field value) and �.The cylinder was then sealed to prevent changes in� during the experiment. Bulk density and � weredetermined gravimetrically after each set of measure-ments was completed. Target � values were basedon expected field values given the soil texture toachieve a wide range of � while avoiding redistri-bution in the soil column during the experiment.The CS615 sensors and thermocouples for measur-ing the soil temperature were then inserted into thesoil columns.

Table I. Soils used for laboratory calibrations

Country Soil sample site andhorizon (i.e. A or B horizon)

Sand(%)

Clay(%)

Bulk density(t m�3)

ECa

(S m�1)

NZ Carran’s A 27 35 1Ð37 0Ð05NZ Carran’s B 14 54 1Ð26 0Ð04NZ Clayden’s A 18 43 1Ð21 0Ð05NZ Clayden’s B 14 49 1Ð25 0Ð04NZ Satellite Station Hillslope A 22 27 1Ð55 0Ð03NZ Satellite Station Hillslope B 21 30 1Ð45 0Ð02NZ Satellite Station Valley A 8 59 1Ð03 0Ð06NZ Marine Rd A 16 56 1Ð12 0Ð05NZ Marine Rd B 17 53 1Ð13 0Ð03Aust Tarrawarra A 4 25 1Ð35 0Ð03Aust Tarrawarra B 3 50 1Ð5 0Ð02Aust Point Nepean A 99 1Ð47 0Ð02USA Foothill 31 29 1Ð5 0Ð145USA Sheep Creek 23 19 1Ð3 0Ð774USA Summit 69 5 1Ð7 0Ð25USA Sand 97 <0Ð1 1Ð52 0Ð00006

a Soil ECs were determined from natural samples using a 1 : 5 dilution test for Australian and New Zealand soils and using asaturation paste extract test for the USA soils. The bulk density is the in situ value.



Table II. Summary of experimental setup

ReynoldsCreekdata

Australian andNew Zealand

data

Cylinder diameter (cm) 10Ð16 15Ð35Cylinder length (cm) 33 33Ð5Target temperatures (°C) 5, 15, 25,35, 45 5, 20, 25,35

The soil columns were allowed to come to ther-mal equilibrium in a controlled temperature chamber.Soil temperature and CS615 output period were thenrecorded using a data logger. Air temperature waschanged progressively so that each target tempera-ture (Table II) was attained and the measurementswere repeated. Seyfried and Murdock (2001) mea-sured three replicates for each � combination. Onlyone replicate was used for each � combination for theAustralian and New Zealand soils, unless subsequentdata analysis showed anomalies in either the tempera-ture response or the � calibration curve, in which casemeasurements were repeated to resolve the anomalousresults.

ResultsThe results were analysed in two steps, starting withthe behaviour for individual soils and then moving todeveloping generalized relationships. For the individ-ual soils, the temperature effects were analysed firstfollowed by the � calibration relationship.

0.0

0.5

1.0

1.5

2.0

2.5

40

P (m

s)

SM=0.1 9 SM=0.2 9 SM=0.3 5 SM=0.4 8

0 10 20 30

T ( C)

Figure 1. The effect of temperature on sensor output for four mois-ture contents for the Clayden A-horizon soil

The temperature response for each � combinationwas determined by plotting the measured CS615 out-put period Pobs against measured soil temperatureT. Typically, increasing T results in a roughly lin-ear increase in Pobs with the slope increasing with� �m3 m�3� (Figure 1). A linear regression was fittedto the Pobs, T data pairs for each soil–� combination.The slope of the regression relationship CT is effec-tively a temperature correction coefficient and can beused to calculate a P value corrected to 25 °C using

P25 D Pobs � CT �T � 25� �2�

The second step was to examine relationshipsbetween � and P25 (Figure 2). Clearly, there aremarked differences in the calibration relationship

0.5

1.0

1.5

2.0

2.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6Volumetric Soil Moisture (m /m ) 3 3

P

(m

s)25

Pt Nepean A

Sat. Stn. Hill A

Tarrawarra A

Sat. Stn. Hill B

Carran A/B

Clayden A

Clayden B

Marine Rd A

Tarrawarra B

Sat. Stn. Valley A

Marine Rd B

Foothill

Sheep CreekSummit

Sand

Figure 2. Comparison of measured volumetric soil moisture and the CS615 period at 25 °C. The manufacturer’s calibration relationships forlow EC (solid line) and 0Ð3 S m�1 EC (dashed line) soils are shown


SCIENTIFIC BRIEFING

between soils. Measured periods are smallest for theconstruction sand, intermediate for the soils fromAustralia and New Zealand, and greatest for the nat-ural soils from Reynolds Creek for a given �. This isin line with the general salinity (EC) levels increasingfrom the construction sand to the Australian and NewZealand soils, with the Reynolds Creek soils beingthe most saline. It is also clear that there is a generalconsistency between the two data sets in terms of theshapes and locations of the curves, which appear toform a family of relationships with a similar y-axisintercept. The spread in calibration relationships ismuch larger than suggested by the manufacturer.

Generalized RelationshipsThe next step was to develop generalized relation-ships for both the temperature dependence of the sen-sor and the �–P25 calibration relationship. To collapsethe � response data (i.e. the family of relationships inFigure 2) onto a single curve, we calculate a normal-ized period N:

N D P25 � P0Ð0P0Ð4 � P0Ð0

�3�

where P0Ð0 and P0Ð4 are the periods (temperature cor-rected to 25 °C) for � of 0Ð0 m3 m�3 and 0Ð4 m3 m�3

respectively. This normalization was chosen becausethe relationships in Figure 2 appear to have similar yintercepts and shapes, but the curves appear to scalevertically relative to the intercept. Thus, choosing toscale the period responses relative to the interceptor zero moisture response and by the period response

over a fixed � range should provide an efficient meansof unifying the data. The value of P0Ð0 is set equalto 0Ð76 ms, which is the average value observed bySeyfried and Murdock (2001) for oven-dry soil. P0Ð4is the free parameter that is set when applying thegeneral calibration curve to a specific soil. We foundthat the power function relationship

� D 0Ð4Nˇ �4�

is a good representation of the relationship between� and N. The coefficient is set to 0Ð4 to be consistentwith the definition of P0Ð4.

To fit the combination of Equations (3) and (4), wejointly optimized ˇ and P0Ð4 using a nonlinear quasi-Newton optimization procedure with the objective ofminimizing the sum of squared errors in estimated� for all the experimental data simultaneously. Thisresulted in ˇ D 0Ð70, which is taken as a constantapplicable across all soils. Fitted values of P0Ð4 forthe experimental soils vary between 1Ð34 and 2Ð29,with an average of 1Ð69. Figure 3 shows the resultingrelationship between normalized periods for each soiland �, along with the generalized calibration curve.The root-mean-squared error (RMSE) of the � esti-mate for this fit is 0Ð025 m3 m�3. It is worth notingthat, while the q value chosen for the wet end of thenormalisation (i.e. q D 0.4) is well above the largestq observed in many coarser textured soils, the gen-eral calibration curve still performs well for such soils(see Point Nepean and sand in Figure 3).

In an attempt to generalize the observed relation-ships further, we analysed the relationships between

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.5 1.0 1.5

N

Pt Nepean A

Sat. Stn. Hill A

Tarrawarra A

Sat. Stn. Hill B

Carran A/B

Clayden A

Clayden B

Marine Rd A

Tarrawarra B

Sat. Stn. Valley A

Marine Rd B

Foothill

Sheep Creek

SummitSand

θ (m

3 /m3 )

Figure 3. Comparison of normalized period N and volumetric soil moisture. The generalized calibration relationship is also shown



P0Ð4 and soil texture, bulk density and EC. To makethe EC measurements for the two data sets com-parable, the 1 : 5 dilution test results for the Aus-tralian and New Zealand data were multiplied by 6Ð4,as recommended by Lovejoy (1974). P0Ð4 is weaklyrelated to EC (r2 D 0Ð14), clay content (r2 D 0Ð09)and bulk density (r2 D 0Ð11). If the two sandy soilsare excluded, then these r2 values improve to 0Ð27,0Ð40 and 0Ð21 respectively. Only the clay content isstatistically significant, and using the fitted relation-ship (to clay content) to predict P0Ð4 resulted in adoubling of the RMSE to 0Ð049 m3 m�3. Using themean of the fitted P0Ð4 values resulted in a furtherdegradation of the RMSE to 0Ð063 m3 m�3. On thebasis of the current data set, it must be concluded thatit is necessary to calibrate P0Ð4 for each soil type.

Two other studies of the calibration of the CS615water-content reflectometer shed some light on thegenerality of the calibration curves presented above.Stenger et al. (2005) studied four soil types with sam-ples from three depths for each soil type. Comparisonof their fitted curves with our generalized relationshipsuggests that our relationship is a close approximationfor most of their soils. However, two gley soils standout as having the opposite curvature and their Allo-phanic soil shows an inflection not captured either byour relationship or their quadratic fit. This indicatesthat caution needs to be taken when generalizing fromour results. Kim and Benson (2002) studied a varietyof soils from the USA. They used linear and quadraticcalibration fits and found that the slope was stronglydependent on bulk soil EC, which is also consistent

with our data. Their data do not allow detailed com-parison of calibration relationship shapes.

For the temperature correction, we use an approachwhere the raw sensor measurement is corrected priorto calculating �. This is different to the approachtaken by Seyfried and Murdock (2001) and alsoto that recommended by the sensor manufacturer(Campbell Scientific Inc., 1996), in that they bothestimate a � value that is then temperature corrected.We did this because it allows a general temperaturecorrection determined from the raw sensor responseto be estimated.

Figure 4 shows a strong linear relationship betweenCT and P25; however, the behaviour of the con-struction sand (which has an extremely low EC; seeTable I) is clearly different from the natural soils. Thenegative slope apparent in the construction sand dataindicates that the temperature effect is being domi-nated by the reduction in the real part of the dielectricconstant of water with temperature. The positive slopefor all other soils suggests that the temperature effecton soil EC (affecting the dielectric dispersion or imag-inary component of the dielectric constant) dominates.The relationship between P25 and CT is likely to arisefrom the strong links between these two parametersand the bulk soil EC (not necessarily the extract EC).Thus, both P25 and CT respond as either the soilmoisture or the soil specific properties influencing ECchange, leading to the strong correlation observed.The solid line is the fit to all the data, excluding theconstruction sand (r2 D 0Ð89). When combined withEquation (2), the fit to the overall data results in an

-0.005

0.000

0.005

0.010

0.015

0.020

0.5 1.0 1.5 2.0 2.5

P (ms)

C

Pt Nepean A

Sat. Stn. Hill A

Tarrawarra A

Sat. Stn. Hill B

Carran A/B

Clayden A

Clayden B

Marine Rd A

Tarrawarra B

Sat. Stn. Valley A

Marine Rd B

Foothill

Sheep Creek

Summit

Sand

T

25

Figure 4. Comparison of the temperature correction coefficient and the CS615 signal at 25 °C. The fit to all the data (excluding the washedsand) is also shown (solid line)


SCIENTIFIC BRIEFING

empirical temperature correction equation:

P25 D Pobs C 0Ð0114�T � 25�

1 C 0Ð0134�T � 25��5�

There is some difference between the fitted relation-ship and relationships evident for individual soils(Figure 4), as well as some scatter. To give an ideaof the practical significance of the variation betweenthe relationships we calculate the difference in esti-mated � for a 10 °C temperature correction (from 15to 25 °C) with the temperature correction calculatedusing linear regression fits to each soil individuallyand to the whole data set (solid line in Figure 4).Figure 5 shows this difference as a function of � forall the soils. Two things are clear. First, the error intro-duced is small (generally less than 0Ð02 m3 m�3),compared with the practical accuracy expected in thefield. Second, the error is a function of � and changesrapidly and nonlinearly for small � and then moregradually and linearly for greater �.

It should be noted that CT tends to be smaller forthree soils: the B horizon soils for each of Tarrawarra,Satellite Station hillslopes and Marine Road. Thereason for this is unclear.

Application to Field Measurements

The University of Melbourne is operating a soil mois-ture monitoring network in the Murrumbidgee basinas part of the Murray Darling Basin Water BalanceProject, which is a GEWEX (Global Energy and

Water Balance Experiment) catchment-scale experi-ment (Western et al., 2002). To illustrate the appli-cation of the approaches described above we havecompared field TDR measurements with CS615 mea-surements. The CS615 period measurements weretemperature corrected to 25 °C using Equation (5) andthe measured temperature. To calibrate the value ofP0Ð4 for each site and soil layer the first two availableTDR measurements were used and the RMSE wasminimized. Subsequent TDR measurements (5 and 6at Adelong, 3 at Kyeamba) were used for validation.Figure 6 shows the validation TDR measurements of� at three depths for two monitoring sites, along withthe CS615 normalized periods. The general calibra-tion curve (Equation (4)) is the solid line shown andit relates the normalized period to the predicted �.Hence, vertical scatter about the curve shows thecombination of the CS615 and TDR moisture mea-surement error. The RMSE for the validation pointsvaries between 0Ð005 and 0Ð026 m3 m�3. There areonly a small number of measurements at each soildepth, but they cover a reasonable range of � and areindependent of the measurements used to estimateP0Ð4. It is apparent that the generalized calibrationapproach developed in this paper works well, with theresiduals all being small and the shape of the generalrelationship fitting the data well.

Application ProcedureTo apply the calibration procedure described aboverequires estimation of the P0Ð4 parameter, which inturn requires:

)D

iffe

renc

e in

soi

l moi

stur

e (m

/m33

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

0.0 0.1 0.2 0.3 0.4 0.5

Soil Moisture (m /m )33

Figure 5. Difference between temperature-corrected (to 25 °C) soil moisture based on the fit to the data for each soil individually and the fitto all the data collectively (Figure 4) assuming a 15 °C measurement temperature



N

Soil

Moi

stur

e (m

/m

)3

3

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.2 0.4 0.6 0.8 1.0

A0-30cm A30-60cm A60-90cmK0-30cm K30-60cm K60-90cm

Figure 6. Comparison of CS615 normalized period N with TDR soil moisture estimates for Adelong and Kyeamba Creek soil moisturestations. P0Ð4 has been optimized using these data. The solid line is the generalized calibration relationship (Equation (3))

1. Independent soil moisture measurements �obs.These will preferably be field measurements obtai-ned using volumetric soil samples and gravimetricdetermination of bulk density and �.

2. Corresponding measurements of CS615period measurements Pobs and soil temperature T(probably from the monitoring record for the sta-tion).

3. Temperature correction of Pobs to P25 using Equa-tion (5).

4. Finally, nonlinear optimization of P0Ð4 to minimizethe sum of squared differences between �obs and�, where � is obtained from the combination ofEquations (3) and (4) with ˇ set to 0Ð7 and P0Ð0 setto 0Ð76 ms.

Although it is theoretically possible to estimateP0Ð4 from one soil moisture measurement, we rec-ommend an absolute minimum of three measure-ments spread across the whole operating soil moisturerange for the monitoring site. This at least allows forsome checking of residuals between the fitted calibra-tion and the sample data to identify any issues withthe samples or applicability of the calibration rela-tionship. Once the value of P0Ð4 is determined, therecord of Pobs for the station can then be system-atically temperature corrected (using Equation (5))and converted to � estimates (using Equations (3)and (4)).

SummaryGeneralized temperature correction and soil-watercalibration relationships for Campbell ScientificCS615 water-content reflectometer sensors have beendeveloped and are described. To use the approach,measurements of soil temperature and the sensor out-put from the CS615 are required. In addition, severalindependent measurements of � are required to setthe one soil-related parameter in the � calibrationcurve. This parameter (and thus the calibration rela-tionship) is sensitive to soil characteristics, includingEC, texture and bulk density. These vary betweensoils and over time (except texture). The between-soil variability is captured by variation in P0Ð4. Thetemporal variability is a source of uncertainty in themeasurement of �. Although our data do not allow usto quantify this directly, our field applications (aboveand others) suggest that this is not a major sourceof error. With good-quality measurements, accuracyapproaching that of TDR sensors can be achievedwith this sensor. These relationships facilitate fieldcalibration of these sensors to acceptable accuracieswith only a small number of samples.

AcknowledgementsMark Murdock was responsible for laboratory mea-surement and instrument design for the ReynoldsCreek data. The work in Australia was undertaken


SCIENTIFIC BRIEFING

as part of projects funded by the Australian ResearchCouncil, National Institute of Water and AtmosphericResearch New Zealand, and the Cooperative ResearchCentre for Catchment Hydrology. Assistance withlaboratory measurements in Melbourne was providedby Julian Thompson, Chris Olszak and Tom Ander-son. Robert Pipunic assisted with data preparation.Rodger Grayson provided valuable comments on thework. We wish to thank Jim Buttle and the anony-mous reviewers of this paper for their valuable com-ments.

Mention of manufacturers is for the convenienceof the reader only and implies no endorsement on thepart of the authors, The University of Melbourne orthe USDA.

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a calibration and temperature correction procedure for the water-content reflectometer

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