Soil texture and salinity effects on calibration of TDR300dielectric moisture sensor

George KargasA,C, Nikolaos NtoulasB, and Panayiotis A. NektariosB

ALaboratory of Agricultural Hydraulic, Department of Natural Resources Management and AgriculturalEngineering, Division of Water Resources Management, Agricultural University of Athens, Iera Odos 75,Athens 11855, Greece.

BLaboratory of Floriculture and Landscape Architecture, Department of Crop Science, Agricultural Universityof Athens, Iera Odos 75, Athens 11855, Greece.

CCorresponding author. Email: kargas@aua.gr

Abstract. Newly developed sensors have simplified real-time determination of soil water content (qm). Although theTDR300 is one of the most recent dielectric sensors, little is known with regard to the accuracy and dependency of itsmeasurements of soil type and other environmental factors. In this study, the performance of TDR300 was investigatedusing liquids of known dielectric properties and a set of porous media with textures ranging from sandy to clayey. Theexperiments were conducted in the laboratory by mixing different amounts of water with each soil to obtain a sufficientrange of soil water contents. For sand, the calculated permittivity values (er) correlated adequately with Topp’s equationderived for time domain reflectometry. However, for the remaining inorganic porous media, er values were overestimatedcompared with those resulting from Topp’s equation, especially for water contents exceeding 0.2 cm3/cm3. The resultssuggested that the relationship between qm andHer was strongly linear (0.953< r2 <0.998). The most accurate results wereprovided by soil-specific calibration equations, which were obtained by the multi-point calibration equation. However,two-point calibration equations determined water content in all tested soils reasonably well, except for clay soil. A linearregression equation was developed that correlated the slope of the relationship qm–Her with bulk soil electricalconductivity (EC). The regression slope was influenced more by soil EC than by soil texture. Also, TDR300response was investigated in bi-layered systems (liquid–air and saturated porous media–air). In a bi-layered sensingvolume characterised by strongly contrasting dielectric values, the appropriate bulk permittivity values for water and loamsoil were determined by arithmetic rather than refractive index averaging, while for butanol and sand these values remainedsomewhere between the two averaging schemes, indicating that the upward infiltration calibration technique isinappropriate for the TDR300 sensor. Soil solute EC, as determined by measurements conducted in liquids and sand,significantly affected permittivity values at much lower levels than the limit of EC <2 dS/m, as suggested by themanufacturer. However, the relationship qm–Her remained linear up to EC 2 dS/m, which corresponded to a bulk soil ECvalue of 0.6 dS/m. By contrast, for EC values >2 dS/m, the relationship qm–Her was not linear, and, thus theTDR300 device calibration became increasingly difficult. Therefore, rather than operating as a time domain device,TDR300 operates as a water content reflectometer type device.

Additional keywords: electrical conductivity, dielectric sensors, permittivity.

Received 8 January 2013, accepted 11 June 2013, published online 15 August 2013

Introduction

Soil water content determination constitutes a significantparameter for optimising the management of soil–plant–atmosphere and hydrological systems. Time domainreflectometry (TDR) is a reliable method for performingcontinuous, non-destructive measurements of soil watercontent. The TDR is based on measuring travel time of

electric pulses along a waveguide. Travel time is directlyrelated to soil dielectric permittivity (e). Water has a muchgreater value of dielectric permittivity (e= 80) than air (e= 1)or soil solids (e= 3–7); thus, permittivity is primarily a functionof porous media water content (Seyfried and Murdock 2004).

Soil relative permittivity is composed of a real component, adielectric constant, and an imaginary component (Eqn 1):

Abbreviations: TDR, Time domain reflectometry; er, relative apparent permittivity; q, soil/substrate water content; qs, saturatedwater content; qm, soil/substrate water content on a weight basis; RMSE, root mean square error; CALAL, calibration using allexperimental data points; CAL, two-point calibration.

Journal compilation � CSIRO 2013 www.publish.csiro.au/journals/sr

CSIRO PUBLISHING

Soil Research, 2013, 51, 330–340http://dx.doi.org/10.1071/SR13009

er ¼ e0r � je00r ð1Þwhere er is relative apparent permittivity, e0r is dielectric constant(the real part of relative permittivity), e00r is equivalent dielectricloss taking into consideration the conductive loss (imaginarypart of relative permittivity), and j=H–1. Relative imaginarypermittivity is the sum of a conduction term and a relaxationterm (Eqn 2):

e00r ¼ sb

we0þ e00rel ð2Þ

where sb is direct current bulk electrical conductivity (EC),e0 is permittivity of the free space (8.85� 10�12 F/m), e00rel isfrequency-dependent relative dielectric loss due to relaxation,and w is the angular frequency given as 2pf, with f being thefrequency.

Calibration equations, such as the empirical equation ofTopp et al. (1980), are widely used in coarse-grained mineralsoils for calculating volumetric water content from relativepermittivity using TDR. Roth et al. (1992) demonstrated that,due to their low bulk density, the relationship between er and qcould not be established for organic soils based on the Toppet al. (1980) equation, which is designated for mineral media.The relationship between water content and square root ofpermittivity can be described by a semi-theoretical linearequation (Ledieu et al. 1986; Heimovaara 1994). As wasshown by Topp and Reynolds (1998), the Topp et al. (1980)equation is equivalent to a linear equation between the squareroot of permittivity and water content:

q ¼ 0:115ffiffiffiffier

p � 0:176 ð3ÞFor TDR measurements, the slope of Eqn 3 incorporates the

effect of salts and clay content, while the constant term depictsthe effects of dry solids (Ferre and Topp 2002). Even thoughTDR constitutes a reliable and accurate method for determiningsoil and substrate water content, its increased cost has resulted inthe development of several other dielectric sensors that arecheaper and do not rely on complicated waveform analysis.These dielectric sensors operate at lower frequencies than TDRand are, therefore, prone to drawbacks. For instance, Evett andParkin (2005) illustrated that the response of electromagneticsensors is often dependent on soil type, especially when lowfrequencies (<200MHz) are utilised.

The occurrence of a linear equation between the square rootof permittivity and water content has been observed for severaldielectric sensors, mainly in relation to inorganic soils (Seyfriedet al. 2005; Kargas and Kerkides 2008; Kargas et al. 2011;Kargas and Soulis 2012). However, the linear relationshipparameters are significantly different between different soiltypes.

Manufacturer calibration studies for the TDR300 (SpectrumTechnologies Inc., Plainfield, IL) have related the sensor output(a time period (P) provided in ms) directly to soil water content.Such a one-step calibration may obscure important informationregarding sensor response to water content determination insoils that possess different electromagnetic properties (Kellenerset al. 2009). An in-depth understanding of TDR300 performanceand soil dielectric properties can be obtained by a two-step

calibration procedure (Robinson 2001). In this way, it may bepossible to determine the dielectric sensor operational frequencyeffect on porous medium dielectric properties (soil texture,organic matter content, and others).

Jones et al. (2005) recommend that two issues need to beaddressed regarding soil water sensor testing: (i) how accuratelythe instrument measures relative permittivity (er), and (ii) howeffectively relative permittivity is related to water content. Theformer issue is generally addressed using fluids of knownpermittivity values while the latter demands calibration.

Two different methodologies have been developed forcalibrating dielectric sensors. In the first, the relationshipbetween relative permittivity and water content is obtainedfrom soil samples having predetermined water content, whichis uniformly distributed in the soil mass. This method is time-consuming and can provide only a limited number ofexperimental points of water content (Seyfried et al. 2005).The second method, proposed by Young et al. (1997), is theupward-infiltration method, which is relatively fast and capableof obtaining several experimental points of water content. Theassumption underlying this method is that the sensor respondsto average water content within the sensing volume, as if it wereuniformly distributed, although a sharp wetting front separatesnearly saturated and dry soil. Thus, water content calculationcould provide different results compared with a uniform watercontent distribution (Seyfried et al. 2005; Kargas and Kerkides2009; Logsdon 2009; Kargas et al. 2011).

Other factors affecting permittivity values, such as bulkdensity, salinity level, bound water, organic matter content,and specific surface area have also been investigated.However, while the majority of these studies refer to thepioneer TDR devices, only limited research has beenconducted on recently developed devices such as theTDR300 (Seyfried and Murdock 2004; Kargas and Kerkides2008; Kizito et al. 2008; Kargas and Soulis 2012). Furthermore,it is frequently implied that dielectric sensors have similarbehaviour using TDR, which measures permittivity at relativehigh frequencies. Nevertheless, this concept is erroneous,especially concerning the effect of bulk soil EC (sb) on theer–q relationship, since its effect on the electromagnetic fieldattenuation has been proven to decrease as the operatingfrequency increases (Kelleners et al. 2009).

Another important issue relates to the performance ofdielectric sensors under non-uniform water regimes. TDRmeasurements in a non-uniform soil water regime wasinitially addressed by Topp et al. (1982) and subsequentlyfollowed by other researchers who contributed to this andsimilar subjects (Chan and Knight 1999, 2001; Schaap et al.2003; Robinson et al. 2005). More specifically, their analysis ofelectromagnetic wave velocity in media of differing permittivityshowed that the proper averaging scheme for the effective er ofa layered medium depends on the measurement frequency (f)relative to the thickness of the layer. When the measurementwavelength (l) is less than four times the layer thickness,averaging by the refractive index is expected to prevail (note:F= c/l, where c is the speed of light).

We should point out that the refractive index regime seemsto be the most appropriate for TDR devices, except in thefollowing two cases: (i) when operational frequency drops

Calibration of TDR300 dielectric moisture sensor Soil Research 331

below 100MHz, and (ii) when a multiplicity of thin layers isencountered. In those cases, the arithmetic averaging schememight be more suitable. Similar work, concerning the newdielectric devices which commonly operate in frequencies<100MHz, has been undertaken by several researchers(Seyfried et al. 2005; Kargas and Kerkides 2009; Kargaset al. 2011; Kargas and Soulis 2012). In addition, Logsdon(2009) reported that, using a CS616 dielectric sensor, the squareroot of apparent permittivity was greater in a column with wetand dry soil than in a uniformly wetted soil column. Thisresult was attributed to the fact that the electromagnetic fieldpreferentially responds to the wet zone.

However, it is important to emphasise that the above-mentioned issues have yet to be fully exploited for theTDR300 dielectric device. In the present work, we conducteda two-step calibration for the TDR300 using soil samples ofpredetermined water content and liquids of known permittivityin order to accomplish the following main objectives: (i)to develop a soil-specific calibration for the TDR300 and todetermine whether TDR300 calibration varied with differentsoils textures; (ii) to investigate the response of the TDR300 tochanges in bulk soil EC levels; and (iii) to determine theresponse of the TDR300 sensor in bi-layered systems(liquid–air and saturated porous media–air). It is our viewthat a detailed evaluation of the TDR300 device may lead toits better use in future field water-monitoring programs.

Materials and methods

The TDR300 Sensor

The TDR300 is equipped with two stainless steel rods that actas wave guides. The diameter of the rods is 0.5 cm and thespacing between the two rods is 3.3 cm. The electronicsembedded in the probe send a wave towards the rods. Thesignal travels through the whole rod length and is partiallyreflected when it reaches the interface between the rod tips andthe soil. The manufacturer does not provide the operatingfrequency of the TDR300 sensor, which is a particularlyimportant piece of information, especially given that thename of the device refers to TDR. Data output is providedas period (P, in ms), which is inversely related to the number ofreflections per second. The signal is transformed into a squarewave output with a frequency proportional to water content.The period of the TDR300 device increases according to theincrease of porous medium water content (SpectrumTechnologies, Inc. 2009). It is important to note here thatmost inexpensive sensors of this kind do not determine truetravel time. According to Evett et al. (2006), the Trime T3 tubeprobe (IMKO Micromodultechnik GmbH, Ettlingen, Germany;IMKO 2000) did not determine true travel time becausewaveform was not captured and tangent line analysis fortravel time was not performed.

The sampling volume is an elliptical cylinder that extends~3 cm out of the pair of rods, which can interchange between 3.8,7.5, 12, and 20 cm length. The TDR300 is equipped with internalcalibrations between water content and P only for standard andhigh-clay soil types. According to the manufacturer, internalcalibrations will work for a large number of soils, when EC is<2 dS/m (Spectrum Technologies, Inc. 2009). Moreover, for

maximum accuracy, it is advised by the manufacturer to performa soil-specific calibration through the establishment of arelationship between P and water content. In the presentstudy, the two-step calibration procedure was utilisedinvolving determination of the relationship between: (a)period and soil relative permittivity, and (b) soil relativepermittivity and gravimetric water content that wasdetermined independently. The length of the pair of rodsutilised in the study was 12 cm.

Measurements in liquids

Measurements in liquids with known dielectric properties wereperformed in order to determine the relationship between P andrelative permittivity. The liquids used included butanol, ethanol,and distilled water at 258C, which have a known permittivityvalue of 16.8, 24.3, and 80, respectively.

The aqueous solutions were employed to investigateTDR300 sensitivity to EC changes. Thus, using TDR300,P was determined in 25 different aqueous solutions of NaClthat ranged in EC from 0 to 10 dS/m.

In addition, measurements were performed in liquids(butanol and distilled water) to investigate the response of thesensor in bi-layered systems. In this case, the relativepermittivity given by a sensor is described either by therefractive index (Topp et al. 1982):

er-ref ¼ SNi¼1Li

ffiffiffiffiffieri

pSNi¼1Li

� �2

ð4Þ

or by simple arithmetic average:

er-arith ¼ SNi¼1LieriSNi¼1Li

ð5Þ

where er-ref denotes the apparent soil permittivity for refractiveindex averaging, er-arith denotes the apparent soil permittivityfor arithmetic averaging, Li is the ith layer thickness, eri is thepermittivity value of the ith layer, and N is the number oflayers. The sum, SN

i¼1Li, is the whole length of the layeredsystem.

In order to investigate the response of the TDR300 sensor inbi-layered systems, butanol–air and water–air systems wereemployed. The sensor was gradually inserted vertically into acylindrical vessel containing either butanol or water at aconstant temperature of 258C. At each depth of immersion(D), sensor output readings (P) were recorded and thecorresponding relative permittivity values were calculatedaccording to the previously determined equation usingliquids of known permittivity values. Moreover, assumingthat air has a relative permittivity of er= 1, thecorresponding relative permittivity values were estimatedaccording to either the refractive or the arithmetic averagingscheme (Eqns 4 and 5) and were compared with the relativepermittivity of the TDR300 sensor for each depth (D).

Measurements in porous media

Porous media with uniform water contentOur evaluation included seven disturbed porous media

(sand, sandy loam, clay loam, loam, clay, peat, and perlite).

332 Soil Research G. Kargas et al.

Themechanical analysis of porous media inorganic components,dry bulk density (rj), cation exchange capacity (CEC), and bulkEC at saturation (sb) for each soil texture are presented inTable 1.

Porous media with uniform water contentIn the present study, the method of independent samples with

predetermined volumetric water content was employed. The air-dried soil samples were placed in a bucket, and each time aspecific amount of deionised water was added to obtainpredetermined water content. At each level of water content,the samples were continuously turned over and thoroughlymixed until they were completely homogenised concerningtheir water content.

After their complete homogenisation, the samples wereplaced in containers (10 cm by 10 cm by 15 cm) and soilwater content readings along with the period measurementswere obtained using the TDR300 device. Each soil waspacked to a consistent, yet different, bulk density, which wasdetermined at the end of each measurement given the knownweight of the oven-dry soil and the container volume.

The calculation of actual water content was performedindependently using gravimetric water content and bulkdensity. In addition, the period was determined in an oven-dried soil sample (q= 0 cm3/cm3). As a result, soil water contentranged from completely dry to saturation.

For two porous media (loam and clay), permittivity was alsodetermined with a second dielectric sensor operating at 100MHz(ThetaProbe ML2x User manual; Delta-T Devices Ltd 1999);moreover, the dielectric sensor WET-2 (Delta-T Devices Ltd2005) was employed to determine soil bulk EC (sb) (Regaladoet al. 2007).

Porous media with non-uniform water contentIn order to investigate the response of the TDR300 sensor to

porous media with non-uniform water content, a similarapproach to butanol or water–air bi-layered system wasutilised. More specifically, air-dried porous media samples(sandy and loamy soils) were placed in cylindrical plasticvessels having a vertical length approximately equal to thesensor’s rods (12 cm). The vessels containing the soil sampleswere saturated from below, and following that, the sensor rodswere gradually inserted vertically into the saturated soil. At eachimmersion depth (D), the TDR300 output readings (P) wererecorded. The corresponding permittivity (er) values were

estimated using the equation developed from liquids withknown permittivity values. Moreover, permittivity valueswere estimated according to either the refractive or thearithmetic averaging scheme (Eqns 4 and 5), assuming thatair er= 1. Permittivity values for saturated soils were obtained byfully inserting the TDR300 sensor into the saturated soils.Through this procedure, it was possible to plot permittivity v.immersion depth (D).

Salinity effects in sand

The impact of salinity on the accuracy of TDR300measurements was investigated by manipulating sand toobtain different levels of bulk EC. Due to the capacity ofsand both to leach and to easily dispose of any saltaccumulation, it was ensured that EC within the mediumpores was identical to that in the administered solution. Byinitiating measurements from completely dry sand, thepredetermined water content was obtained by employing sixdifferent NaCl solutions with increasing EC levels of 0.5, 1, 1.5,2, 2.5, and 5 dS/m. The homogenisation of water within eachsand sample was performed in the manner described above. Intotal, 48 sand samples having different water content and soilbulk EC were examined.

Statistical analyses

For each substrate and water content, three measurements wereperformed in different sample locations. For each soil, thecalibration equation was derived by regression of the plotteddata. Regression was performed using JMP Version 8 statisticalsoftware (SAS Institute Inc., Cary, NC). The evaluation of theefficiency of calibration methodologies was determined usingroot mean square error (RMSE) for two-point (CAL calibration)and total data points (CALAL calibration).

Results and discussion

Determination of the relationship between periodof time and permittivity in liquids of known permittivityvalues

The relationship between P and er for a pair of 12-cm long rods ispresented in Fig. 1. More specifically, it was shown that therelationship between er and P is described by a quadraticequation (Eqn 6). The relationship between er and P for rodswith a 12-cm length used for the calculation of porous media

Table 1. Mechanical analysis, dry bulk density (rw), cation exchange capacity (CEC), and bulk electrical conductivityat saturation (sb) of the porous media

Soil texture Clay Silt Sand rj (g/cm3) CEC (mmol/kg) sb (dS/m)

Sand Fine 1.68 0.0 0.04Sandy loam 13.2 8.0 78.8 1.39 4.3 0.15Loam 23.8 35.6 40.6 1.15 13.2 0.32Clay loam–silty clay loam 31.0 49.0 20.0 1.11 18.2 0.44Clay 55.0 20.5 24.5 1.16 35.0 0.59Peat 0.17 0.43Perlite 0.18 0.02

Calibration of TDR300 dielectric moisture sensor Soil Research 333

relative apparent permittivity for each water content level wasgiven by Eqn 6:

er ¼ 11:169P2 � 31:389P þ 19:124 ð6ÞSoil specific TDR300 Sensor calibration

Figure 2 illustrates the relationship between relative apparentpermittivity, as determined by the TDR300, and actual watercontent for the seven porous media under study. The apparentpermittivity of the TDR300 was calculated from P acquired bythe sensor and was based on Eqn 6. Water content valuesresulting from factory calibration of inorganic porous mediaand clayey soil are also presented. Our results indicated thatfactory calibration in sand underestimated actual water content,whereas with loam and clay loam soils, there was anoverestimation of high water contents. More specifically withregard to clay soil factory calibration, underestimation of actualwater content ranged from 0 to 35%, whereas there was anoverestimation in relation to higher water contents. Reliableresults were obtained only with sandy loam soil. Topp’scalibration equation served as a reference point for theinorganic porous media (Topp et al. 1980). As can beobserved in Fig. 2, only with sand were relative apparentpermittivity values close to the predicted ones based onTopp’s calibration equation. For the remaining inorganicporous media, the deviation between calculated apparentpermittivity values based on TDR300 measurements andTopp’s calibration equation increased depending on both claycontent and bulk soil EC of the porous media (Table 1). Thedifferent responses compared with Topp’s equationdemonstrated the need for individual calibration equations foreach porous medium. A similar phenomenon of increasedapparent permittivity was also observed by Kelleners et al.(2005) using the CS615 device (Campbell Scientific Inc.,Logan, UT; Campbell Scientific Inc. 1996), which operated atmuch lower frequencies (44MHz) than the TDR. These resultsshow that the TDR300 sensor does not operate similarly to atime domain device, but rather as a water content reflectometertype device.

The above-mentioned phenomenon may be due to theinfluence of dielectric dispersion and EC of soil solution.Dielectric dispersion can occur in soils containing clay, wherefor a given actual water content, apparent permittivity increasesas the operating frequency of the device is reduced. Soil EC canalso affect the devices operating at low frequencies in twodifferent ways. First, soil EC increases the imaginary part ofpermittivity, and it therefore increases apparent permittivity.Typically, this effect is ignored, but it can become significantin case of saline media combined with increased water content.In addition, such effects might become significant in soils withappreciable quantities of active clay exhibiting high values ofbulk EC, which is known to vary in accordance with watercontent and soil temperature. Second, increased EC can have adetrimental effect on P and its corresponding apparentpermittivity for a given actual water content.

The above-mentioned reasons may explain the fact thatTDR300 values approximated those predicted according toTopp’s equation only for sand, where clay does not exist andbulk EC is minimal (sb = 0.04 dS/m). By contrast, in saturatedclay soil with a clay content of 55% and a bulk soil EC of0.59 dS/m, the deviation between TDR300 and predicted valuesfrom Topp’s equation was significant and reached 31 units inapparent permittivity. A similar divergence in permittivityvalues was also observed with regard to the clay loam porousmedium. For the remaining porous media, with intermediateclay content and bulk EC, the differences between measured andpredicted permittivity values were smaller. In an attempt toexplain the behaviour of the TDR300, additional measurementswere performed in loam and clay soils with the ML2 ThetaProbedielectric sensor, which operates at a frequency of 100MHz(Fig. 3). The results demonstrated that apparent permittivityvalues resulting from the Topp et al. (1980) equation werealmost identical to those obtained by the ML2 ThetaProbesensor (Fig. 3). These results further confirmed the fact thatthe TDR300 sensor does not function similarly to a TDRdevice.

The behaviour of clay and loam soils is in agreement with thedescription of measurements in dispersive media. These resultsindirectly indicate that the TDR300 operating frequency is smalland <100MHz. However, such increased differences, especiallyfor clay, cannot be attributed mainly to dielectric dispersion,since the predominant clay minerals were illite and chlorite.Saarenketo (1998) observed that, when the dominant claymineral was smectite, the dielectric constant was reducedfrom 65 to 28 units when the operating frequency increasedfrom 50MHz to 1.01GHz, respectively. Thus, ionicconductivity of clay and loam soils can also affect TDR300readings. From the current data, we are unable to determine towhat extent dielectric dispersion and bulk soil EC contributed tothe phenomenon of increased apparent permittivity.

For the TDR300, the relationship qm–Her was linear for alltested porous media (Table 2). The coefficient r2 ranged between0.953 and 0.998; linear regression slope (parameter A) andintercept are presented in Table 2 for each porous medium.In addition, the accuracy of the two-point calibration method(complete dry porous medium [qm= 0] and at saturation[qm= qs]) was investigated. Accordingly, two methods wereinvestigated for their accuracy of the TDR300 specific

1.5 2.0 2.5 3.0 3.5 4.0 4.50

10

20

30

40

50

60

70

80

90

Rel

ativ

e ap

pare

nt p

erm

ittiv

ity

Period (msec)

y = 11 169x2 – 31 389x + 19 124

R2 = 1

Fig. 1. Relationship between the period and relative apparent permittivity(er) for TDR300 with 12-cm-long rods. Values are the mean of threereplications.

334 Soil Research G. Kargas et al.

calibration. The first method used all experimental data (multi-point calibration, CALAL), while the second used the two mostextreme values of water content (two-point calibration, CAL).

The ensuing differences between the two predictions of thespecific calibration equations (CALAL or CAL) compared withthe actual water content (qm) proved the significant impact ofsoil-specific calibration. To quantify this comparison, thecorresponding RMSE values were calculated based on Eqn 7:

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiSni¼1ðq̂i � qmiÞ2

n

sð7Þ

where q̂i is ith predicted q value, qmi is actual q value, and n isnumber of couples (qm, q̂). The calculated RMSE valuescomparing the accuracy of the two methods (multi-point

calibration method, CALAL; two-point calibration method,CAL) are presented in Table 3. Note that specific calibrationequations of the porous media (CAL and CALAL) performedbetter than the manufacturer’s calibration equation in all cases.Furthermore, the multi-point calibration method (CALAL)performed better than the two-point calibration method(CAL). Obviously, the multi-point calibration methodrequires more experimental data and for that reason, it istime-consuming. However, taking into consideration therelatively small RMSE values for the CAL method (Table 3),the two-point calibration method was considered to determinewater content reasonably well, except in the case of clay soil.The maximum water content differences that were observedusing the CAL method in the various porous media (sand, sandyloam, loam, clay loam, clay, peat, and perlite) were 0.008, 0.025,

0.0 0.1 0.2 0.3 0.40

5

10

15

20

25

0.0 0.1 0.2 0.3 0.4

5

10

15

20

25

0.0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

0.0 0.1 0.2 0.3 0.4 0.5 0.60

10

20

30

40

50

60

0.0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

50

60

0.0 0.1 0.2 0.3 0.4 0.5 0.60

10

20

30

40

0.00 0.05 0.10 0.15 0.20 0.250

2

4

6

8

10

Water content (cm3/cm3)

Rel

ativ

e ap

pare

nt p

erm

ittiv

ity

Experimental

Topp

Factory calibration

Sand Sandy loam

Loam Clay loam

Clay Peat

Perlite

Fig. 2. Relationship between apparent permittivity and actual water content for TDR300 (&) for allporous media (sand, sandy loam, clay loam, loam, clay, peat and perlite). Actual water content (qm) wascalculated independently by gravimetrical method. Relationship between er and q from Topp et al. (1980)equation (solid line) and TDR300 sensor factory calibration (dashed line) for inorganic porous media(sand, sandy loam, clay loam, loam and clay) are also presented. Values are the mean of three replications.

Calibration of TDR300 dielectric moisture sensor Soil Research 335

0.05, 0.028, 0.083, 0.024, and 0.026 cm3/cm3, respectively. Ifaccuracy must be obtained with a deviation of �0.03 cm3/cm3,then the CAL method cannot provide reliable results in clay soil,while in loamy soil it fails with regard to intermediate valuesof q.

From the data analysed (Table 2), for both CALAL and CALcalibration methods, the value of slope (parameter A) in inorganicmedia (except for sand) was less than the value indicated by Ferreand Topp (2002) (A=0.115). This was due to the increased valuesof apparent permittivity provided by the TDR300 compared withthe TDR (Table 2). Both calibration methods (CALAL and CAL)provided similar slopes for all inorganic porous media, althoughthe intercepts differed.

The effect of soil texture and bulk soil EC on the TDR300linear relationship slope was further investigated in more detail.Figure 4a shows the relationship between parameter A and bulksoil EC at saturation, while Fig. 4b presents the relationshipbetween parameter A and clay content of the porous media. Theresults show that bulk soil EC had a significant (a= 0.05) effecton the slope, and the relationship was relatively strong(r2 = 0.776) for the five inorganic porous media. Thus, theslope of the linear relationship was significantly influenced bybulk soil EC. This influence might be due to soil particle-ionpolarisations, which become an important factor at lowfrequencies, as this is a mechanism through which bulk soilEC can increase apparent permittivity and concomitantlydecrease parameter A (Kelleners et al. 2009). Evett et al.(2005) also reported alternative mechanisms that might alsocontribute to such a phenomenon. By contrast, no significanteffect (a= 0.05) of clay content was observed on parameter A,and the relationship had lower r2 = 0.646 (Fig. 4b). However,this should be further investigated for the effect of otherinorganic porous media as well for the effect of clay type onthe above relationship. Two factors are known to affect soildielectric properties, ion exchange capacity and specific surfacearea, both of which vary according to clay type mineralogy; thelatter may suggest that texture alone is not an effective way tocategorise soils in relation to their water content calibration.

Apparent permittivity of completely dry inorganic media(qm= 0) varies between 2 and 5. In the present study,permittivity values of completely dry media were 2.44, 2.61,2.30, 2.93, and 2.15 for sand, sandy loam, loam, clay loam, andclay, respectively. Moreover, permittivity of peat and perlitewas <2 (1.43 and 1.85, respectively) due to their reduced bulkdensity. This phenomenon has been observed in organic porousmedia and in media with low bulk densities (Roth et al. 1992).For perlite, the relationship between apparent permittivity andwater content was almost identical to that determined for sand.By contrast, at water contents >0.2 cm3/cm3, the deviation inapparent permittivity values between peat and sand increased.The observed relationship between apparent permittivity andwater content in perlite could be explained due to the absenceof clay and the negligible maximum bulk EC (0.02 dS/m).

0.0 0.1 0.2 0.3 0.4 0.5

0

5

10

15

20

25

30

0.0 0.1 0.2 0.3 0.4 0.5

Rel

ativ

e ap

pare

nt p

erm

ittiv

ity

Actual water content (cm3/cm3)

Topp

ML2

Loam Clay

Fig. 3. Relationship between apparent permittivity and actual water content (er–q), either based on Topp’sequation (solid line) or using the ML2x ThetaProbe (*) for loam kai clay soils. Values are the mean ofthree replications.

Table 2. Slope, intercept, and correlation coeficient (r2) values of linearregression (q=AHer+B) between water content (qm) and square root ofapparent permittivity (er) following the multi-point calibration method

(CALAL)Slope and intercept values using the two-point calibration method (CAL) are

also presented

CALAL CALSlope Intercept r2 Slope Intercept

Sand 0.124 –0.176 0.998 0.125 –0.177Sandy loam 0.095 –0.171 0.988 0.095 –0.153Loam 0.078 –0.105 0.977 0.074 –0.112Clay loam 0.062 –0.103 0.982 0.063 –0.109Clay 0.072 –0.083 0.953 0.066 –0.097Peat 0.099 –0.104 0.997 0.099 –0.118Perlite 0.112 –0.140 0.979 0.114 –0.155Topp et al. (1980) 0.115 –0.176

Table 3. Root mean square error values (RMSE) for TDR300 specificcalibration using two methodologies (multi-point calibration method,

CALAL; two-point calibration method, CAL)

Sand Sandy loam Loam Clay loam Clay Peat Perlite

CAL 0.004 0.018 0.027 0.016 0.050 0.014 0.015CALAL 0.004 0.010 0.015 0.015 0.030 0.008 0.010

336 Soil Research G. Kargas et al.

However, in the case of peat, the results contradicted existingliterature, in that when water content is at the same level for bothpeat and sand, based on its larger fraction of bound water, theapparent permittivity value of peat should be smaller than that ofsand (Anisko et al. 1994; Da Silva et al. 1998). This particularbehaviour of the TDR300 could be explained based on bulk ECof peat, which was 0.43 dS/m. For the clay loam soil, such a levelof bulk EC was observed to impose a major influence onapparent permittivity (Fig. 2). Therefore, it could be assumedthat the increased bulk EC of peat increased the permittivityvalues, thus resulting in increased deviation in larger watercontents, since the impact of bound water was relativelysmall. The particular case of peat calibration proved onceagain the major effect of bulk EC on the increase of apparentpermittivity values.

Sensor response in layered systems

Sensor response in water or butanol–air systems

In Fig. 5, apparent permittivity values obtained by partiallyinserting the TDR300 sensor in water and butanol were plottedagainst immersion depth (D), together with estimatedpermittivity values according to the refractive and arithmeticaveraging schemes (Eqns 4 and 5). Permittivity values obtainedby the TDR300 sensor for water were shown to follow thearithmetic averaging scheme, while those for butanol rangedbetween the two averaging schemes (Fig. 5).

Sensor response in air over saturated porous mediasystem

Plots of apparent and estimated permittivity againstimmersion depth were obtained for saturated porous media(sand and loam soils) in a similar manner as described abovefor liquids (Fig. 5). It was observed that for loam soil apparentpermittivity values obtained by the sensor followed thearithmetic averaging scheme, while those for sand rangedbetween the two averaging schemes. The latter results are inagreement with those reported by Robinson et al. (2005), whoproposed that the correct averaging scheme would probablyhave to be experimentally determined and might lie somewhere

between the refractive index and arithmetic averaging schemes,since the effects of layered media on permittivity are frequency-dependent. The observed arithmetic averaging of ermeasurements in water and loam soil is in contrast topreviously reported results from TDR, but are consistent withthose obtained by sensors operating at a relatively low frequency(Chan and Knight 2001); it also provided additional support forthe conviction that the operating frequency of the TDR300 isrelatively small.

Based on the above findings the vertical placement of theTDR300 sensor into the surface soil layer, which is subjected tosuccessive drying–wetting cycles, is not the most appropriate,since the water profile is non-uniform and the use of the linearqm–Her relationship may lead to large errors in water contentmeasurements. For the most common uses of the TDR300sensor, that is, involving the pair of rods inserted horizontallywithin the soil, the assumption of uniform soil water contentwithin the measurement volume appears to be more appropriate,and in that case, the suggested specific calibration equationscould be employed.

Salinity effects in liquid solution and sand

From Fig. 6, it appears that P measured by the TDR300 sensorincreased as the EC of aqueous solution exceeded 0.2 dS/m.Consequently, for an EC of 0 dS/m the value of P was only3600ms, whereas for 10 dS/m it reached 6000ms, which mightconstitute the upper limit of the TDR300’s measuring capacity.These results demonstrated that the TDR300 sensor isparticularly sensitive to solution EC even at low levels.According to the manufacturer, when using a 12-cm-long rodsthe sensor must indicate a water content of 70–75% in waterwith an EC of 0 dS/m. Certainly, the water content obtainedby submersing the 12-cm-long rods in water of EC 0 dS/m was73.1%. However, when the same rods were submersed insolution with EC 10 dS/m, the value of the water content was195%. The latter implies that EC severely affects P providedby the TDR300 device and causes a substantial increase inpermittivity and concomitantly in the calculated water content.Despite the fact that temperature effects were not investigatedin the current study, given the well-documented temperature

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0 10 20 30 40 50 60

(a) (b)

A = –0.0957sb + 0.1155R2 = 0.7764

Par

amet

er A

Bulk soil saturated EC (dS/m)

Clay (%)

A = –0.0009 Clay (%) + 0.1089

R2 = 0.6466

Fig. 4. Relationship between the slope (parameter A) and (a) bulk soil saturated electrical conductivity(EC) and (b) clay content of the porous media. Values are the mean of three replications.

Calibration of TDR300 dielectric moisture sensor Soil Research 337

dependence of EC, it is highly likely that a strong temperatureeffect might interfere with TDR300 measurements due to itsincreased sensitivity to EC. It should be pointed out that this hasbeen substantiated for other highly temperature-sensitivedielectric sensors, such as the CS615 (Seyfried and Murdock2001).

For sand, the EC effect on the relationship qm–Her initiated atparticularly small values (Fig. 7), since it was affected even at asolution EC of 0.5 dS/m. Nonetheless, the relationship betweensquare root of apparent permittivity and actual water contentremained linear up to EC 2 dS/m, which corresponded to a bulkEC of 0.56 dS/m, as measured by another sensor (WET-2). Thus,

the manufacturer’s claim that the TDR300 sensor is not affectedup to an EC of 2 dS/m does not hold. As an example, at a watercontent of 0.3 cm3/cm3 and for a solution EC of either 0 or 2 dS/m, the corresponding permittivity values of 14.9 and 22.1 wereobtained. Obviously, the use of the factory calibration with apermittivity value of 22.1 would result in a large increase of thecalculated water content.

It is noteworthy that for EC values >2 dS/m, permittivityincreased at a much faster rate along with an increasing EC level.In addition, at EC >2 dS/m, the relationship qm–Her ceased to be

0

20

40

60

80

0

5

10

15

20

0 20 40 60 80 100 120 1400

5

10

15

20

0 20 40 60 80 100 120 1400

10

20

30

40

50

Immersion depth (mm)

Rel

ativ

e ap

pare

nt p

erm

ittiv

ity

ARITHREFTDR300

Water Boutanol

Sand Loam

Fig. 5. Apparent permittivity values predicted by TDR300 sensor (*) or estimated according torefractive (REF, dashed line; Eqn 4) or arithmetic (ARITH, solid line; Eqn 5) averaging schemes v.immersion depth (D), for the case of the bi-layered systems of air–water, air–butanol, and air–saturatedporous media (sand and loam).

0 2 4 6 8 10 120

1000

2000

3000

4000

5000

6000

7000

Rod length 12 cm

Per

iod

(µse

c)

Electrical conductivity (dS/m)

Fig. 6. Relation between electrical conductivity and period for the aqueoussolution as determined by TDR300 device.

0.0 0.1 0.2 0.3 0.40

2

4

6

8

10

Squ

are

root

of p

erm

ittiv

ity

Actual water content (cm3/cm3)

0.0 dS/m 0.5 1.0 1.5 2.0 2.5 5.0

Fig. 7. Relationship between actual water content (qm) and square root ofpermittivity at different levels of solution electrical conductivity (0, 0.5, 1,1.5, 2, 2.5, and 5 dS/m) in the sand. Values are the mean of three replications.

338 Soil Research G. Kargas et al.

linear, especially >5 dS/m. In that case, the water content of0.3 cm3/cm3 was equivalent to a permittivity value of 50.5(Fig. 7). From the above results, it is evident that theTDR300 is particularly sensitive to soil bulk EC. Also, thereis a limit above which the relationship ceases to be linear(0.6 dS/m). It might be possible that, due to this limit, the r2

value of the clay soil calibration curve was lower than those ofthe remaining soil types, since clay had a maximum value forbulk EC of 0.59 dS/m (Table 1). Therefore, even small increasesin soil bulk EC values render the empirical calibration morecomplicated. Especially in cases when sudden changes occurin soil solution EC, such as after a fertiliser application orexcessive leaching events, the calibration of the TDR300might be impossible.

Conclusions

The results of the study showed that calculated apparentpermittivity values for sand compared reasonably well withTopp’s calibration equation. However, for the other fourinorganic soils, the determined apparent permittivity waslarger than that predicted by Topp’s calibration equation for agiven water content. Deviations from Topp’s equation increasedwith increasing bulk soil EC and clay content. Moreover, thecalibration equation supplied by the manufacturer did noteffectively describe the water content.

The experimental results suggested that the relationshipqm–Her was strongly linear. However, there was distinctinstrument sensitivity to soil texture, indicating the need forindividual soil calibration. For the TDR300 sensor, the mostaccurate results were provided by the proposed soil-specificcalibration equations obtained using multi-point calibrationequations. Two-point calibration equations representedsufficiently accurately the actual water content (�0.03 cm3/cm3) in all tested porous media, except for clay soil.Furthermore, the results indicated that the slope of the linearrelationship was significantly influenced by soil bulk EC.

The response of the sensor to bi-layered systems followed thearithmetic averaging scheme for water and loam soil, whereasfor butanol and sand it ranged between the two schemes, incontrast to TDR that utilises very high frequencies. The observedaveraging schemes of permittivity measurements support theconviction that the TDR300 has a relatively low operatingfrequency.

The effect of soil solution EC on permittivity calculationbecomes significant at values that are much lower than therecommended limit (EC <2 dS/m) set by the manufacturer.Even at EC 0.5 dS/m, an effect on permittivity wasdetermined. The relationship qm–Her was linear within therange 0–0.6 dS/m of bulk EC. Finally, TDR300 calibrationbecomes a particularly complicated procedure whenever anabrupt change in soil bulk EC occurs, such as afterfertilisation or excessive leaching events or an abrupt changein soil temperature resulting from irrigation, since such changescan alter the relationship qm and Her.

Acknowledgements

The authors wish to thank the two anonymous reviewers for theirconstructive and insightful comments.

References

Anisko T, NeSmith DS, Lindstrom OM (1994) Time domain reflectometryfor measuring water content of organic growing media in containers.HortScience 29, 1511–1513.

Campbell Scientific Inc. (1996) ‘CS615 water content reflectometerinstruction manual.’ Campbell Scientific Inc.: Logan, UT)

Chan CY, Knight RJ (1999) Determining water content and saturation fromdielectric measurements in layered materials.Water Resources Research35, 85–93. doi:10.1029/1998WR900039

Chan CY, Knight RJ (2001) Laboratory measurements of electromagneticwave velocity in layered sands. Water Resources Research 37,1099–1105. doi:10.1029/2000WR900356

Da Silva FF, Wallach R, Polak A, Chen Y (1998) Measuring water contentof soil substitutes with time domain reflectometry (TDR). Journal ofthe American Society for Horticultural Science 123, 734–737.

Delta-T Devices Ltd (1999) ‘ThetaProbe ML2x User manual.’. (Delta-TDevices Ltd: Cambridge, UK)

Delta-T Devices Ltd (2005) ‘User manual for the WET sensor (type WET-2).’ (Delta-T Devices Ltd: Cambridge, UK) Available at: www.delta-t.co.uk

Evett SR, Parkin GW (2005) Advances in soil water sensing: The continuingmaturation of technology and theory. Vadose Zone Journal 4, 986–991.doi:10.2136/vzj2005.0099

Evett SR, Tolk JA, Howell TA (2005) Time domain reflectometry laboratorycalibration in travel time, bulk electrical conductivity, and effectivefrequency. Vadose Zone Journal 4, 1020–1029. doi:10.2136/vzj2005.0046

Evett SR, Tolk JA, Howell TA (2006) Soil profile water contentdetermination: Sensor accuracy, axial response, calibration,temperature dependence, and precision. Vadose Zone Journal 5,894–907. doi:10.2136/vzj2005.0149

Ferre A, Topp GC (2002) ‘Methods of soil analysis. Part 4. Physicalmethods.’ Soil Science Society of America Book Series, Vol. 5.pp. 434–446. (Soil Science Society of America Inc.: Madison, WI)

Heimovaara TJ (1994) Frequency domain analysis of ttime domainreflectometry waveforms: 1. Measurement of the complex dielectricpermittivity of soils. Water Resources Research 30, 189–199.doi:10.1029/93WR02948

IMKO (2000) ‘Operating manual TRIME-FM.’ (IMKOMicromodultechnikGmbH: Ettlingen, Germany)

Jones SB, Blonquist JM, Robinson DA, Rasmussen VP, Or D (2005)Standardizing characterization of electromagnetic water contentsensors: Part 1. Methodology. Vadose Zone Journal 4, 1048–1058.doi:10.2136/vzj2004.0140

Kargas G, Kerkides P (2008) Water content determination in mineral andorganic porous media by ML2 theta probe. Irrigation and Drainage 57,435–449. doi:10.1002/ird.364

Kargas G, Kerkides P (2009) Performance of the THETA PROBE ML2 inthe presence of nonuniform soil water profiles. Soil & Tillage Research103, 425–432. doi:10.1016/j.still.2008.12.007

Kargas G, Soulis K (2012) Performance analysis and calibration of a newlow-cost capacitance soil moisture sensor. Journal of Irrigation andDrainage Engineering 138, 632–641. doi:10.1061/(ASCE)IR.1943-4774.0000449

Kargas G, Kerkides P, Seyfried M, Sgoumbopoulou A (2011) WET sensorperformance in organic and inorganic media with heterogeneousmoisture distribution. Soil Science Society of America Journal 75,1244–1252. doi:10.2136/sssaj2010.0238

Kelleners T, SeyfriedM, Blonquist J, Bilskie J, Chandler D (2005) Improvedinterpretation of water content reflectometer measurements in soils. SoilScience Society of America Journal 69, 1684–1690. doi:10.2136/sssaj2005.0023

Kelleners T, Paige GB, Gray ST (2009) Measurement of the dielectricproperties of Wyoming soils using electromagnetic sensors. Soil

Calibration of TDR300 dielectric moisture sensor Soil Research 339

Science Society of America Journal 73, 1626–1637. doi:10.2136/sssaj2008.0361

Kizito F, Campbell CS, Campbell GS, Cobos DR, Teare BL, Carter B,Hopmans JW (2008) Frequency, electrical conductivity and temperatureanalysis of a low-cost capactitance soil moisture sensor. Journal ofHydrology 352, 367–378. doi:10.1016/j.jhydrol.2008.01.021

Ledieu J, de Ridder P, de Clerck P, Dautrebande S (1986) A method ofmeasuring soil moisture by time-domain reflectometry. Journal ofHydrology 88, 319–328. doi:10.1016/0022-1694(86)90097-1

Logsdon SD (2009) CS616 calibration: field versus laboratory. Soil ScienceSociety of America Journal 73, 1–6. doi:10.2136/sssaj2008.0146

Regalado C, Ritter A, Rodriguez-Gonzalez RM (2007) Performance of thecommercial WET capacitance sensor as compared with time domainreflectometry in volcanic soils. Vadose Zone Journal 6, 244–254.doi:10.2136/vzj2006.0138

Robinson DA (2001) Comments on “Field calibration of a capacitance watercontent probe in fine sand soils”. Soil Science Society of America Journal65, 1570. doi:10.2136/sssaj2001.6551570x

Robinson DA, Jones SB, Blonquist JM, Friedman SP (2005) A physicalderived water content/permittivity calibration model for coarse—textured layered soils. Soil Science Society of America Journal 69,1372–1378. doi:10.2136/sssaj2004.0366

Roth C, Malicki M, Plagge R (1992) Empirical evaluation of the relationshipbetween soil dielectric constant and volumetric water content as the basisfor calibrating soil moisture measurements by TDR. European Journalof Soil Science 43, 1–13. doi:10.1111/j.1365-2389.1992.tb00115.x

Saarenketo T (1998) Electrical properties of water in clay and silty soils.Journal of Applied Geophysics 40, 73–88. doi:10.1016/S0926-9851(98)00017-2

Schaap MG, Robinson DA, Friedman SP, Lazar A (2003) Measurement andmodeling of the TDR signal propagation through layered dielectricmedia. Soil Science Society of America Journal 67, 1113–1121.doi:10.2136/sssaj2003.1113

Seyfried MS, Murdock MD (2001) Response of a new soil water sensor tovariable soil, water content and temperature. Soil Science Society ofAmerica Journal 65, 28–34. doi:10.2136/sssaj2001.65128x

SeyfriedMS, MurdockMD (2004) Measurement of soil water content with a50-MHz soil dielectric sensor. Soil Science Society of America Journal68, 394–403. doi:10.2136/sssaj2004.0394

Seyfried MS, Grant LE, Du E, Humes K (2005) Dielectric loss andcalibration of the hydra probe soil water sensor. Vadose Zone Journal4, 1070–1079. doi:10.2136/vzj2004.0148

Spectrum Technologies, Inc. (2009) ‘Field Scout TDR300, Product manual.’(Spectrum Technologies Inc.: Plainfield, IL)

Topp GC, Reynolds WD (1998) Time domain reflectometry: a seminaltechnique for measuringmass and energy in soil. Soil & Tillage Research47, 125–132. doi:10.1016/S0167-1987(98)00083-X

Topp GC, Davis JL, Annan AP (1980) Electromagnetic determination of soilwater content: Measurements in coaxial transmission lines. WaterResources Research 16, 574–582. doi:10.1029/WR016i003p00574

Topp GC, Davis JL, Annan AP (1982) Electromagnetic determination of soilwater content using TDR: I. Applications of wetting fronts andsteep gradients. Soil Science Society of America Journal 46, 672–678.doi:10.2136/sssaj1982.03615995004600040002x

YoungMH, Fleming JB,Wierenga PJ,Warrick AW (1997) Rabid laboratorycalibration of time domain reflectometry using upward infiltration. SoilScience Society of America Journal 61, 707–712. doi:10.2136/sssaj1997.03615995006100030001x

340 Soil Research G. Kargas et al.

www.publish.csiro.au/journals/sr