measurement of soil water content and electrical conductivity by time domain reflectometry: a review

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Computers and Electronics in Agriculture 31 (2001) 213–237 Measurement of soil water content and electrical conductivity by time domain reflectometry: a review K. Noborio * Department of Agronomy, Iowa State Uni6ersity, Ames, IA 50011 -1010, USA Abstract Non-destructive measurement of soil water content and electrical conductivity has been desired for many years. Recent development of time domain reflectometry (TDR) enables us to simultaneously obtain soil water content and electrical conductivity using a single probe with a minimal disturbance of soil. Research on water and solute transport in porous media using TDR has flourished in the last few years. In this review article, an overview of theoretical background for measuring water content and electrical conductivity is presented as well as characteristics of different types of probes. Limitations of applying TDR techniques to measuring soil water content and salinity are also addressed. The review is designed to equip other scientists and engineers with background information so that the development of TDR for studies on water and chemical movement can continue. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Measurement; Time domain reflectometry; Water content; Electrical conductivity; Soil www.elsevier.com/locate/compag 1. Introduction Measurement of water content in porous media is a major interest in many disciplines. This paper will focus on soil. Although gravimetric sampling for water content is the most accurate method, soil samples must be removed from a soil Journal paper no. J-18003 of the Iowa Agriculture and Home Economics Experiment Station, Ames, IA, Project no. 3287, and supported by Hatch Act and State of Iowa. * Present address: Faculty of Agriculture, Iwate University, Morioka, Iwate 020-8550 Japan. E-mail address: [email protected] (K. Noborio). 0168-1699/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S0168-1699(00)00184-8

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Page 1: Measurement of soil water content and electrical conductivity by time domain reflectometry: a review

Computers and Electronics in Agriculture

31 (2001) 213–237

Measurement of soil water content andelectrical conductivity by time domain

reflectometry: a review�

K. Noborio *Department of Agronomy, Iowa State Uni6ersity, Ames, IA 50011-1010, USA

Abstract

Non-destructive measurement of soil water content and electrical conductivity has beendesired for many years. Recent development of time domain reflectometry (TDR) enables usto simultaneously obtain soil water content and electrical conductivity using a single probewith a minimal disturbance of soil. Research on water and solute transport in porous mediausing TDR has flourished in the last few years. In this review article, an overview oftheoretical background for measuring water content and electrical conductivity is presentedas well as characteristics of different types of probes. Limitations of applying TDRtechniques to measuring soil water content and salinity are also addressed. The review isdesigned to equip other scientists and engineers with background information so that thedevelopment of TDR for studies on water and chemical movement can continue. © 2001Elsevier Science B.V. All rights reserved.

Keywords: Measurement; Time domain reflectometry; Water content; Electrical conductivity; Soil

www.elsevier.com/locate/compag

1. Introduction

Measurement of water content in porous media is a major interest in manydisciplines. This paper will focus on soil. Although gravimetric sampling for watercontent is the most accurate method, soil samples must be removed from a soil

� Journal paper no. J-18003 of the Iowa Agriculture and Home Economics Experiment Station, Ames,IA, Project no. 3287, and supported by Hatch Act and State of Iowa.

* Present address: Faculty of Agriculture, Iwate University, Morioka, Iwate 020-8550 Japan.E-mail address: [email protected] (K. Noborio).

0168-1699/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved.

PII: S0168-1699(00)00184-8

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K. Noborio / Computers and Electronics in Agriculture 31 (2001) 213–237214

mass. Widely accepted in situ methods to measure soil water content may beradioactive methods such as the neutron scattering method (Gardner and Kirkham,1951) and the gamma ray attenuation method (Reginato and van Bavel, 1964).These methods are quite accurate and non-destructive; however, they requirecalibration for each soil and special caution to avoid possible health hazards. Analternative non-destructive method to measure soil water content was developed byDavis and Chudobiak, (1975) using time domain reflectometry (TDR). It was basedon the procedure introduced by Fellner-Feldegg, (1969).

TDR determines the dielectric constant of an object using simple electrodesinserted into the object. Topp et al., (1980) proposed an empirical relationshipbetween dielectric constant and volumetric water content of soils with severaltextures. An advantage of TDR is simultaneous measurement of water content andbulk electrical conductivity of soil with a single probe (Dalton et al., 1984). Inaddition, water content measurement is only slightly susceptible to changes in soilbulk density (for non-swelling soils), temperature and salinity (Topp et al., 1980).Sabburg et al., (1997) found a dependency for volumetric water content on soil bulkdensity for swelling clay soils, but not for non-swelling soils. Establishing anautomated and multiplexed TDR system is relatively easy with minimal mainte-nance (Baker and Allmaras, 1990; Heimovaara and Bouten, 1990; Herkelrath et al.,1991). An off-the-shelf cable tester, such as the 1502/B/C (Tektronix, Inc., Beaver-ton, OR)1, was originally developed for detecting locations of breaks or short-cir-cuits in telephone and cable TV lines. Its popularity has also contributed to the useof TDR techniques for water and salinity measurement in soil. Likewise, othercommercially available TDR systems have helped extend TDR techniques in manydisciplines, e.g., TRASE Systems (Soilmoisture Equipment Corp., Santa Barbara,CA), TRIME (IMKO GmBH, Ettlingen, Germany), Moisture Point (ESI Environ-mental Sensors Inc., Victoria, BC, Canada), Theta Probe (Delta-T Devices Ltd.,Burwell, Cambridge, England)1, and others, specifically designed for soil waterand/or salinity measurement.

In this review, theories behind measuring water content and salinity of soil usingTDR are introduced. Geometry and characteristics of TDR probes are alsoaddressed.

2. Theory

2.1. Dielectric constant

TDR determines the dielectric constant k by measuring the propagation time ofelectromagnetic waves, sent from a pulse generator of a cable tester (Fig. 1),immersed in a medium. Electromagnetic waves propagate through a coaxial cableto a TDR probe, which is usually rod, made of stainless steel or brass. Part of an

1 References to specific products do not imply endorsement by the author, Iowa State University, theState of Iowa, or Texas A&M University.

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incident electromagnetic wave is reflected at the beginning of the probe because ofthe impedance difference between the cable and the probe. The remainder of thewave propagates through the probe until it reaches the end of the probe, where thewave is reflected. The round-trip time t of the wave, from the beginning to the endof the probe can be measured by a sampling oscilloscope on the cable tester, isdescribed (Fellner-Feldegg, 1969) as

t=2Lk0.5

c, (1)

where t is the round-trip time (s); L, TDR probe length (m); k, the dielectricconstant of the medium, and c, the velocity of electromagnetic waves in free space(m s−1) (3×108). Rearranging Eq. (1) with respect to k gives

k=� ct

2L�2

. (2)

In a commercial TDR cable tester such as the 1502/B/C (which is mostcommonly used in soil science and hydrology), the term (ct/2) in Eq. (2) is reducedto an apparent probe length La displayed on the cable tester (Baker and Allmaras,1990)

Fig. 1. Block diagram of TDR to measure water content and bulk electrical conductivity of soil. Arrowsindicate directions of electromagnetic waves. L and La represent the actual probe length and an apparentprobe length displayed on the cable tester, respectively. Using Eq. (3) with L and La, the dielectricconstant of soil is calculated.

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Fig. 2. Examples of TDR waveforms in air-dried sand, water-saturated sand and distilled water using athree-wire type probe (L=0.145 m). La indicates an apparent probe length from the beginning to theend of the probe. Vp was set to 0.66.

k=�La

L�2

, (3)

where La is determined as a distance between reflections at the beginning and theend of the probe (Fig. 2). When the 1502/B/C is used, a ratio of the velocity ofpropagation, Vp in a coaxial cable to that in free space should be selected formeasurement. For any selected Vp values, La should be corrected as in free spacebecause a probe in soil has the different Vp from the coaxial cable. Thus, Eq. (3) isrewritten (Amato et al., 1993) as,

k=�La/Vp

L�2

. (4)

For estimating water content, a Vp value is generally selected equal to 0.99 toachieve the maximum measuring resolution of the instrument (Cassel et al., 1994;Amato and Ritchie, 1995; Ranjan and Domytrak, 1997; Stahli and Stadler, 1997).

The apparent distance La between the initial and final reflections can be deter-mined from waves reflected back from a probe. Examples of waveforms from athree-wire type probe embedded in a sandy soil and water are shown in Fig. 2. Thewaveforms were acquired using the 1502C and transported through RS-232C portsto a computer for storage and further analysis (Fig. 1). The reflection coefficient r

in the Y-axis in Fig. 2 is defined as a ratio of the reflected amplitude of the signalfrom a cable to the signal amplitude applied to the cable (Tektronix, 1990). If thereis an open circuit in the cable, nearly all the energy will be reflected back. Thereflected amplitude will be equal to the incident amplitude and r= +1. If there is

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a short circuit, nearly all the energy will be delivered back to the cable testerthrough the ground. The polarity of the reflected pulse will be opposite of theincident pulse and r= −1. Therefore, the reflection coefficient for soil and weaklyconducting solutions is usually between −1 and +1.

The initial reflection point from the beginning of a probe is easily found byimmersing the probe in water or air or by shorting a probe near the beginning.Heimovaara, (1993) recommended that the initial reflection point be found in air.The initial reflection point from the beginning of a probe is a fixed value and isindependent of the medium between and surrounding the probe (Maheshwarla etal., 1995). Details for finding the initial and final reflection points using a computerare found in Baker and Allmaras, (1990). In their method, acquired TDR wave-forms are first smoothed and differentiated with respect to t. Then a maximumvalue of the derivative of the data is found as the slope of a tangent line for thesmoothed wave at the final reflection. The intersection of this tangent line with ahorizontal line — representing the minimum value of a line between the initial andfinal reflections is identified as the final reflection point. Baker and Allmaras, (1990)determined the initial reflection point in a similar manner as the final reflectionpoint. For a very dry soil (Fig. 2), the final reflection from a three-wire probe isfound in a similar manner to wet soils, but instead of a horizontal line a tangentline, which represents a slope just before the final reflection, is used (Heimovaaraand Bouten, 1990). Hook et al., (1992) developed a method to improve reflectionlocation determination by remotely shorting various locations of a probe usingdiodes.

3. Soil water content

Because the dielectric constant of water is much larger than other soil con-stituents (Table 1), determining water content by measuring an apparent dielectricconstant of moist soil is quite reasonable (Hoekstra and Delaney, 1974). Eq. (4)gives an apparent dielectric constant of soil using waves collected with a TDR cabletester.

Table 1Dielectric constants of soil constituents and major textures of soils (Curtis and Defandorf, 1929)

Material Dielectric constant

Air 1Water 80 at 20°CIce 3 at −5°CBasalt 12Granite 7–9

9–11SandstoneDry loam 3.5Dry sand 2.5

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For homogeneous soil, volumetric water content u (m3 m−3) is then calculatedusing a calibration curve empirically determined by Topp et al., (1980) as

u = −5.3×10−2+2.92×10−2k−5.5×10−4k2+4.3×10−6k3 (5)

They found an apparent dielectric constant k of soil was not strongly sensitive totemperature (10–36°C), soil texture (clay to sandy loam), bulk density of soil(1.14–1.44 mg m−3, for non-swelling soils) and soluble salt content (moistenedwith salt-free water, 0.01 N CaSO4, or 2000 ppm NaCl solution). As the tempera-ture of sandy and clay soils increased from 1 to 40°C, k increased by about 10%(Davis and Chudobiak, 1975). The temperature effect on TDR-measured k is largein a wetter and courser textural soil (Halbertsma et al., 1995), whereas that is largein a wetter and finer textural soil (Pepin et al., 1995). Pepin et al., (1995) speculatedthat a larger temperature effect for wetter and finer-textured soils dominated by freewater might be attributed to bound water, which had a smaller temperaturedependency for k than free water. The puzzling temperature effect on TDR-mea-sured k for different textural soils was investigated experimentally by Wraith andOr, (1999) and theoretically by Or and Wraith, (1999). They concluded that theamount of bound water restricted, depending on clay minerals, on soil particles wasattributed to the temperature effect. The effect of soil structure in Eq. (5) isnegligible (Keng and Topp, 1983). Topp et al., (1980) and Horino and Maruyama,(1993) reported that there was no hysteresis effect on Eq. (5) in glass beads and insandy soils, respectively.

Volumetric water content in organic soil and vermiculite is, however, underesti-mated by Eq. (5). In glass beads, it is overestimated (Topp et al., 1980) as well asin swelling and non-swelling clay soils (Bridge et al., 1996). Herkelrath et al., (1991)also found Eq. (5) underestimated u for loam with well-developed organic horizons.Likewise, Pepin et al., (1992) found that Eq. (5) underestimated u for peat atk\17. Malicki et al., (1996), however, reported that these estimation errors wereovercome by accounting for the effect of bulk density or porosity (Eq. (6)).

Dalton et al., (1990) and Noborio et al., (1994) found that Eq. (5) overestimatedu in soils moistened with saline water. Based on experiments with clay loam tocoarse sand moistened with saline water, Wyseure et al., (1997) proposed a newcalibration to account for the effect of saline water on the apparent dielectricconstant of soils. The presence of magnetite in soil (\15% in a dry soil and \5%in a wet soil) causes larger La in Eq. (4) whereas, the presence of hematite orgoethite has little effect on the measurement of La (Robinson et al., 1994).

The calibration curve by Topp et al., (1980) has been confirmed by numerousauthors, including, Patterson and Smith, (1981) for silt loam and clay, even withice; Topp et al., (1982b) for silt loam; Smith and Patterson, (1984) for sand to clayloam, even with ice; Topp et al., (1984) for clay to very fine sandy loam; Topp andDavis, (1985a) for sandy loam over clay; Drungil et al., (1989) for sand and sandyloam with varying gravel contents; Grantz et al., (1990) for Fe-rich volcanic soils,Nadler et al., (1991) for silt loam moistened with non-saline and saline water andwith layered profiles; and Reeves and Elgezawi, (1992) for fine sandy loam mixedwith oil shale solid waste. Because the dielectric constant of ice is similar to dry soil

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(Table 1), liquid water content in frozen soil has also been investigated by Pattersonand Smith, (1981), Hayhoe et al., (1983), Stein and Kane, (1983), Smith andPatterson, (1984), Spaans and Baker, (1995), and Seyfried and Murdock, (1996).

Although the calibration curve by Topp et al., (1980) has been successfullyapplied to many situations, other calibrations have also been proposed based on thelinear relationship between u and k0.5 (Ledieu et al., 1986; Alharthi and Lange,1987; Herkelrath et al., 1991; Ferre et al., 1996; Malicki et al., 1996; Topp et al.,1996). By using specific coefficients (Ferre et al., 1996), the calibration of Topp etal., (1980) and the u–k0.5 relation can be made equivalent. For finer textural soilssuch as silt loam and sandy loam, Yu et al., (1997) proposed a more generalrelation as u–kg, where g represents a calibration exponent, to correct overestima-tion of u at kB5 when using the u–k0.5 relation.

The theoretical relationship between the dielectric constant of soil constituentsand u based on a dielectric mixing model has been examined by Ansoult et al.,(1985), Alharthi and Lange, (1987), Roth et al., (1990), Dasberg and Hopmans,(1992), Dirksen and Dasberg, (1993), Friedman, (1997) and Weitz et al., (1997). Forpeat to crushed limestone, the mixing model’s u agrees well with TDR-measured u.Jacobsen and Schjønning, (1995) summarized the accuracy of TDR-estimated u

using various empirical equations and mixing models. They suggested that thecalibration of Topp et al., (1980) might be the first choice if the accuracy of90.02−0.03 m3 m−3 was acceptable.

Malicki et al., (1996) proposed a new general calibration equation that incorpo-rated soil bulk density as

u=(k0.5−0.819−0.168rb−0.159rb

2)(7.17+1.18rb)

(6)

where u is volumetric soil water content (m3 m−3), k the dielectric constant of soil,and rb the bulk density of soil (Mg m−3). They tested Eq. (6) with wide ranges ofsoil textures (organic soil to sand), bulk densities (0.13–2.67 mg m−3) and organiccarbon contents (0–487 g kg−1). Their new calibration reduces the variance of theiru estimates to approximately one fifth of the u estimates made with a calibrationequation without accounting for bulk density. Schaap et al., (1996) confirmed thevalidity of Eq. (6) in the laboratory with non-shrinking forest litters at kE4.0. ForkB4.0, water bound to the surface of soil particles causes deviations from Eq. (6)because the dielectric constant of bound water may be smaller than that of freewater, and bound water becomes dominant at kB4.0. Jacobsen and Schjønning,(1993a,b), however, reported that inclusion of soil bulk density in their owncalibration improved the accuracy of u estimated using TDR in the laboratory, butnot in the field.

For heterogeneous soil, measurement of water content using TDR was theoreti-cally and experimentally investigated by Topp et al., (1982a,b). When the heteroge-neous layers were oriented perpendicular to a TDR probe, they found thatTDR-measured water content of the layered soil agreed well with a linearlyweighted average water contents over profiles. Topp et al., (1982a) expressed theweighted average of water content u( (m3 m−3) with Eq. (7) as

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Fig. 3. TDR waveforms in NaCl solution and distilled water with a three-wire type probe (L=0.045 m).As concentration of the solution increased, the amplitude of reflected signals decreased due toattenuation of electromagnetic waves. There were no final reflections for concentrations \0.1 mol kg−1

of NaCl solution.

u( =%n

i=1

ziui

%n

i=1

zi

(7)

where n is the number of layers; zi the thickness of layer i, and ui the volumetricwater content of layer i. Nadler et al., (1991) confirmed the relationship betweenTDR measurements and Eq. (7), although they had difficulties interpreting theTDR waveforms – as did Dasberg and Hopmans, (1992) — when a very wet soillayer was overlying a very dry soil layer. For heterogeneous layers oriented parallelto a TDR probe, u estimated using TDR, however, is heavily biased toward thewater content of dry soil (Hokett et al., 1992a).

3.1. Electrical conducti6ity of bulk soil or electrolyte solution

Fellner-Feldegg, (1969) proposed that electrical conductivity (EC) (S m−1) of anelectrolyte solution could be determined as a function of the derivative of reflectioncoefficient with respect to time of the TDR waveform at t=0. Later, severalresearchers have proposed alternatives to determine EC from TDR waveforms(Dalton et al., 1984; Topp et al., 1988; Zegelin et al., 1989; van Loon et al., 1990;Nadler et al., 1991). Nadler et al., (1991) investigated most of these methods andconcluded that their own reference method and the procedure of Dalton et al.,(1984) were the most suitable for calculating EC using TDR, including the case forlayered soils.

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Dalton et al., (1984) described the relationship of signal amplitudes along a probein a conducting medium (Fig. 3) as

(VR−VT)=VTexp(−2aL) (8)

where VT is the signal amplitude after partial reflection from the beginning of theprobe, VR the signal amplitude after reflection from the end of the probe and a theattenuation coefficient expressed as

a=60ps

k0.5 (9)

Dalton et al., (1984) combined Eqs. (8) and (9) to describe EC (sD) of a mediumas

sD=k0.5

(120pL)ln[VT/(VR−VT)](10)

A reflection for VR needs to be adequately determined by distinguishing thebreakpoints, levels and gradients from measured waveforms. The reflection is,however, sometimes indistinguishable because of waveform distortion due to loss ofhigher frequencies. This distortion results partly from impedance mismatchesbetween a probe and a cable tester (Noborio et al., 1994) and signal attenuationcaused by a long cable (Heimovaara, 1993). Although Eq. (10) can determineelectrical conductivity using measured waveforms and a probe length (without anyempirical values), obtaining a distinguishable VR reflection is critical for thismethod.

Nadler et al., (1991) proposed an alternative procedure to determine electricalconductivity, not using the VR reflection. Later, Heimovaara, (1992) and Baker andSpaans, (1993) found that the procedure of Nadler et al., (1991) was equivalent tothat of Giese–Tiemann (G–T method) presented by Topp et al., (1988). The G–Tmethod determines EC (sG–T) as

sG−T=�K

Zu

��1−r�

1+r�

�(11)

where K is the geometric constant of a probe (m−1), Zu the characteristicimpedance of a cable (V), and r� the reflection coefficient at a distant point fromthe first reflection on the waveform. It is defined as, r�= (V�−V0)/V0, where V�is the signal amplitude at the distant point (e.g., about 10 times larger than La asshown in Fig. 3) and V0 the signal amplitude from the TDR instrument. Themagnitude of reflections at V� decreases as concentration of a medium increases asshown in Fig. 3. The decrease in V� due to an electrolyte solution depends onphysical characteristics of the probe as well as solution concentration. The geomet-ric constant K is experimentally determined by immersing the probe in solutions ofknown electrical conductivity sT at T°C (Dalton et al., 1990). Or, alternatively, a Kvalue is determined (Baker and Spaans, 1993) by

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K=�o0c

L�

Z0 (12)

where o0 is the permittivity of free space (8.9×10−12 F m−1), c the velocity of lightin free space (3×108 m s−1), L the TDR probe length (m), and Z0 the character-istic impedance of the probe (V). A Z0 value for the probe is determined byimmersing the probe into a non-conductive medium (e.g. deionized water) (Bakerand Spaans, 1993) as

Z0=Zuk ref0.5 �1+r0

1−r0

�(13)

where kref is the dielectric constant of the non-conductive medium as a reference.The dielectric constant of water kwater for kref is a function of temperature (Hasted,1973) expressed as

kwater=84.740−0.40008T+9.398×10−4T2−1.410×10−6T3 (14)

where T is the water temperature between 0 and 100°C.

3.2. Electrical conducti6ity of soil pore water

Using a single probe, TDR simultaneously measures volumetric water content, u,with Eq. (4) and Eq. (5) and the apparent or bulk electrical conductivity of soil, sa,which can be expressed by sD or sG–T with Eq. (4) and Eq. (10). For fine sandyloam moistened with saline water, Dasberg and Dalton, (1985) found that there wasgood agreements between sa measured by a four-electrode resistivity method(Rhoades and van Shilfgaarde, 1976) and TDR, and u measured by the neutronscattering method and TDR. Nadler et al., (1984) estimated the electrical conduc-tivity of soil pore water with TDR-measured water content and bulk EC by

sw25= fT(sa−dss)F(u) (15)

where sw25 is the electrical conductivity of soil pore water at 25°C (electricalconductivity is usually reported at 25°C). A temperature-correction function fT isincluded ( fT=1.00+ (25−T)/49.7+ (25−T)2/3728 for 200T047°C, data ob-tained from U.S. Salinity Laboratory Staff, 1954), where T is the soil pore watertemperature (°C), sa the apparent or bulk electrical conductivity of soil (S m−1)described by Eq. (10) or Eq. (11), ss the electrical conductivity of solid materials (Sm−1), d an empirical parameter, and F(u) a formation factor accounting for thetortuosity of current flow. Heimovaara et al., (1995) found that the temperaturedependency of sa was similar to that of a solution. To evaluate F(u), Noborio etal., (1994) and Risler et al., (1996) used a transmission coefficient proposed byRhoades et al., (1976) in Eq. (16):

F(u)=1

uj(u)(16)

where j(u) is the transmission coefficient expressed as j(u)=au+b (with empiri-cally determined constants a and b depending on soil). Rhoades et al., (1976)

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originally proposed d=1 in Eq. (15), but later Rhoades et al., (1989) expressed d

and F(u) for sws\0.2–0.4 and ssB0.15 S m−1 as,

d=(fs+uws)2

fs

(17)

F(u)=1

(u−uws)(18)

where fs is the volumetric content of the solid materials in the soil (m3 m−3), sws

electrical conductivity of immobile water (S m−1), uws immobile water content (m3

m−3) and u the total water content (m3 m−3) (including both mobile and immobileregions). Using d=1 in Eq. (15), Noborio et al., (1994) found a fair agreementwithin 90.1 S m−1 between TDR-estimated sw25 and that from soil cores in thefield. In the laboratory, Risler et al., (1996) reported that Eq. (17) and Eq. (18) gavegood estimates of sw, as did Eq. (15) with d=1. Recently, Nissen et al., (1998b)estimated the laboratory values of sw (within 90.1 S m−1) from TDR-measuredu and sa using the relation u–sa–sw. This relationship was originally proposed byVogeler et al., (1996), and is similar to the original equation of Rhoades et al.,(1976). For swsB0.2 S m−1, Rhoades et al., (1989) proposed a more complexmodel, but the model has not been tested using TDR. Mallants et al., (1996)observed increases in d values due to increases in uws, when the total water contentincreased.

Instead of using the transmission coefficient, Heimovaara et al., (1995) used thetortuosity factor proposed by Mualem and Friedman, (1991) based on a waterretention function as

F(u)=ueffb

�&U

0

[1/h(x)]dx�2

&U

0

[1/h(x)2]dx(19)

where ueff is effective volumetric water content through which the current can flow,b is a calibration exponent, h(x) a water retention function and U the relativesaturation. Heimovaara et al., (1995) used van Genuchten’s equation (vanGenuchten, 1980) for h(x) and ignored the effect of ss so that d=0 in Eq. (15).Although estimates of sw using Eq. (15)-based equations agreed well with thosefrom soil-extract, solution samplers or effluent in coarse textured soils (Noborio etal., 1994; Heimovaara et al., 1995; Risler et al., 1996; Nadler, 1997; Persson, 1997),Nadler, (1997) found an extreme disagreement in clay soils. Vogeler et al., (1997)reported that strongly structured silt loams had a good agreement between TDR-es-timated and extracted sw, but less-structured silt loams and weakly structuredsandy loams had a poor agreement. In contrast, Nadler, (1991) found that soilstructure had little effect on measurement of sa using TDR. However, the transmis-sion coefficient or the tortuosity factor in the model is sensitive to changes in soilstructure (Mallants et al., 1996; Persson, 1997). Therefore, Mallants et al., (1996)and Persson, (1997) suggested that site-specific calibration between sa and sw might

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be needed, especially in heterogeneous soils. The effect of hysteresis is negligible forsw estimated by TDR (Nadler, 1997) and for sa measured by a four-electroderesistivity method (Bottraud and Rhoades, 1985).

Eq. (15) can be reduced to a simpler expression (Kachanoski et al., 1992; Wardet al., 1994; Vogeler et al., 1997) as

sw= f0(u)+ f1(u)sa (20)

where f1(u) and f0(u) are empirical constants. Persson, (1997) extended Eq. (20) toa fourth-order polynomial equation. Instead of using absolute values of bulk soilEC (sa) to investigate solute transport in soil, Kachanoski et al., (1992) directlyused impedance readings appearing on a TDR cable tester. The 1502/B/C cabletester automatically calculates impedance with the equation expressed (Nadler etal., 1991; Wraith et al., 1993) by

ZL=Zu

(1+r)(1−r)

(21)

where ZL is the impedance load (V) and r the reflection coefficient at a point, wherethe reading is made such as r� in Fig. 3. Substituting sa in Eq. (20) with ZL

−1 inEq. (21), Hamlen, (1997) estimated resident concentration, C (kg m−3), at u usingEq. (22). This is based on the work of Kachanoski et al., (1992) and Ward et al.,(1994, 1995) as

C=o(u)+g(u)ZL

−1 (22)

where o(u) and g(u) are empirical parameters as functions of u. Moreover, relativesolute mass, rather than absolute solute concentration, may be estimated, so thatempirical parameters such as K in Eq. (11), f0(u) and f1(u) in Eq. (20), and o(u) andg(u) in Eq. (22) need not to be determined (Kachanoski et al., 1992). Heimovaaraet al., (1995) proposed to account for the resistance of a cable in ZL to extend therange of linearity between C and ZL

−1. Eq. (22) is then modified to

C=o(u)+g(u)(Ztot−Zcable)−1 (23)

where Ztot is the total impedance (V) of the cable tester, coaxial cable, and TDRprobe inserted in a sample, and Zcable the combined series impedance (V) in thecoaxial cable, connectors, and cable tester.

4. Configuration and installation of probes

4.1. Probe type: two-, three-wire, or others

A two-wire type probe with an impedance-matching transformer (necessary intheory) has been popular since it was introduced by Davis, (1980) (Fig. 4A). A fewresearchers have used two-wire type probes without transformers and have hadconsistent results for water content measurement (Stein and Kane, 1983; Ledieu etal., 1986; Malicki and Skierucha, 1989; Malicki et al., 1992; Rajkai and Ryden,

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1992; Kelly et al., 1995). Patterson and Smith, (1985), however, warned that theremight be a risk of encountering stray voltages and currents that could increasemeasurement uncertainties when a matching transformer was not used. In addition,a two-wire type probe with an ordinal impedance-matching transformer (e.g.,ANZAC model TP-103) is considered not suitable for measuring electrical conduc-tivity because the signal’s amplitude after the final reflection decreases due to lowfrequency attenuation (Spaans and Baker, 1993). Thus, they developed a newimpedance-matching transformer with which the signal’s amplitude did not de-crease. However, Kachanoski et al., (1992) used a two-wire type probe attached toa 200 V shielded TV antenna cable with an ordinal impedance-matching trans-former and obtained consistent values. They used only a portion of the wave aftermultiple reflections ceased, but before wave amplitude decreased (Kachanoski et al.,1993). Ferre et al., (1998) confirmed that use of an ordinal matching transformerwith a 200 V shielded TV antenna cable did not affect EC measurement.

Zegelin et al., (1989) introduced multi-wire type probes simulating a coaxial cell,as used by Fellner-Feldegg, (1969) and Topp et al., (1980). Thus, a multi-wire type

Fig. 4. Structural diagram of typical probes, (A) three-wire, and (B) two-wire type probes. Dimensionsindicated were taken from the references. Note that a three-wire type probe simulates a coaxial cell anddoes not need an impedance-matching transformer.

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probe doesn’t need an impedance-matching transformer. The three-wire type probe,shown in Fig. 4B is practical for common use. A three-wire type probe generally givessimpler waveforms than does a two-wire type probe. Simpler waveforms enable betterdefinition of signal’s travel time along a probe length, especially suitable for salinesoils and for soil layers having extreme differences in u (Zegelin et al., 1989; Nadleret al., 1991). A three or more-wire type probe provides a more distinct reflection(containing more straight lines in the waveforms from the end of the probe) thandoes a two-wire type probe (q.v., Fig. 4 of Zegelin et al., 1989). One inconvenienceof using a three-wire probe may be that the reflection from the beginning of the probein dry soil significantly differs from the reflection in very wet soil or water as shownin Fig. 2. This is inconvenient for the automated interpretation of waveforms.

Another type of probe is introduced to specifically measure volumetric watercontent at the soil surface (Selker et al., 1993). The probe is flat and rectangular (Fig.5A). It requires its own calibration between dielectric constant and water content,which provides a similar standard deviation (S.D.) of 90.02 m3 m−3 from thegravimetrically measured water content to that found using two-wire type probes(L\0.1 m) by Topp et al., (1984). Maheshwarla et al., (1995) investigated therelationship between dielectric constant and water content for TDR probes (withnon-conventional geometries) from both theoretical and experimental points of view.Multi-purpose TDR probes have also been developed (besides measuring watercontent and electrical conductivity). Baumgartner et al., (1994) and Whalley et al.,(1994) added porous materials to the end of hollow stainless steel rods and let themwork as tensiometers and solution samplers. Baumgartner et al., (1994) found thatmeasured water content using solid rods and hollow stainless steel rods with porousmaterials were almost identical in the entire ranges of water contents (0.11BuB0.37m3 m−3) they tested. Noborio et al., (1996) combined the functions of TDR and adual-probe heat-pulse device to simultaneously measure water content, heat capacityand thermal conductivity of soil. They reported that although insertion of a heaterand a thermocouple wire inside the hollow center rod of their TDR probe distortedwaveforms, the deformation did not affect water content determination. ModifiedTDR probe geometries do not seem to affect estimation of dielectric constant andwater content, but do affect waveforms. Baker and Goodrich, (1987) and Lauren,(1997) also combined the functions of TDR and a single thermal probe for measuringsoil water content and thermal conductivity. Recently, Ren et al., (1999) redesignedthe probe of Noborio et al., (1996) and simultaneously measured water content,electrical conductivity, heat capacity and thermal conductivity of soil.

4.2. Material and length of probes

Stainless steel rods have been the dominant material for probes in recent years,whereas brass rods were popular in early days. Davis, (1980) used PVC pipes coveredwith longitudinal, variable-width aluminum strips as electrodes (Fig. 5B). Noborioet al., (1994) made temperature measurements using hollow stainless steel rodsenclosing thermocouple wires in an outer electrode. They found that there was nosignificant effect on TDR waveforms by the enclosed thermocouple wires.

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Fig. 5. Structural diagram of several alternative probes designed by; (A) Selker et al., (1993), (B) Davis,(1980), and (C) Davis, (1975).

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In theory, probe length does not affect the accuracy of water content measure-ment in non-conducting media. In practice, however, determination of reflectionpoints on TDR waveforms and calculations of dielectric constant are very sensitiveto small errors in an apparent probe length La (Eq. (4)). More errors may beintroduced by using short probes (LB0.1 m) (Stein and Kane, 1985; Reeves andElgezawi, 1992). Shorter probes create shorter La, and small errors in determiningLa (especially for dry soils having small dielectric constant of 2–5) induce largeruncertainties in dielectric constant. Topp et al., (1984) reported errors in determin-ing water content using a 0.05 m long probe were significant (S.D.=90.037 m3

m−3) and suggested using a probe with LE0.1 m to achieve an accuracy ofS.D.=0.02 m3 m−3 in the field. Topp and Davis (1985b) suggested using a 0.1–1.0m long probe in the field — where TDR-measured water content agreed to within2% of gravimetrically determined water content. Using a Tektronix 1502B cabletester (whose effective bandwidth is 1 GHz by Heimovaara et al., 1996), with a0.021 m long two-wire type probe, Amato and Ritchie, (1995) reported an errormeasurement of S.D.=90.023 m3 m−3. This deviation is equivalent to S.D.=90.022 m3 m−3 obtained using L\0.1 m long probes by Topp et al., (1984) in thefield. The latter is obtained, when dielectric constant is greater than 2, which isequivalent to water content greater than 0.07 m3 m−3. Using a high bandwidth (20GHz) TDR instrument (which provides clearer waveforms especially in dry soilsthan the 1502/B/C does) with a 0.025 m long two-wire type probe, Kelly et al.,(1995) measured water content of sand ranged 0–0.3 m3 m−3 with S.E.=90.021m3 m−3. For conducting media, attenuation of TDR signals depends on theconfiguration of a probe, including length and spacing. Thus, Dalton and vanGenuchten, (1986) suggested that a practical lower limit for the probe length (forsimultaneous measurement of water content and EC) is about 0.1 m. Nissen et al.,(1998a) introduced a new design of a probe by coiling a 0.295 m long thin copperwire on a PVC rod to make a 0.015 m long probe. The accuracy of the coil proberelative to gravitationally determined soil water content is S.D.=90.017 m3 m−3

in the range of water content between 0.01 and 0.135 m3 m−3 (Nissen et al., 1999).Using three-wire type probes attached to 50 V coaxial cables and the 1502/B/C,

Heimovaara, (1993) found that a 0.1 m long probe could be used with a cablelength up to about 15 m without losing distinct reflections from the beginning andend of the probe. Similar results are obtained using probes longer than 0.2 m withup to 24 m long cables. Short probes (L=0.05 m) cannot be used with long cables(L\3.2 m) when measuring dry soils because of indistinguishable reflections(Heimovaara, 1993). This occurs due to increased rise time of the voltage pulsefrom cable filtering of the high frequency components. If a TDR instrument with ahigher bandwidth is used, shorter probes with longer cables than those describedabove can be used.

System costs can be reduced without compromising the accuracy of La determi-nation in Eq. (3), i.e. volumetric water content, by using 75 V coaxial cables. Theseare less expensive than 50 V coaxial or 200 V TV antenna cables (Hook andLivingston, 1995). In fact, a 75 V coaxial cable connected to a three-wire type probegenerally creates a more distinct reflection at the beginning of a probe than a 50 V

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coaxial cable. Use of 50 or 75 V coaxial cables, of course, does not requireimpedance-matching transformers, which are needed for use of 200 V TV antennacables. However, caution must be paid, when electrical conductivity is determined.Using different impedance between the cable tester output and a coaxial cableproduces wrong answers using Eq. (11). In such a case, the K/Zu term in Eq. (11)should be experimentally determined by immersing a probe into a series of saltsolutions with known electrical conductivities as did by Nadler et al., (1991).

4.3. Spacing and diameter of rods

The wire spacing and diameter of rods strongly affect the impedance of a probe.The characteristic impedance Z (V) of a two-wire type probe can be approximated(Kraus, 1984) by

Z=120

kln�2s

d�

(24)

where k is the dielectric constant of a material surrounding the probe, s the spacingof rods, and d the diameter of the rods. With various rod diameters connected inseries (Fig. 5C), abrupt reflections of TDR signals occur due to impedancedifferences corresponding to the locations, where diameters are different. Using thistype of probe, water content at multiple locations can be determined with a singleprobe (Davis, 1975; Davis and Chudobiak, 1975; Davis, 1980; Topp and Davis,1981; Topp et al., 1982b; Topp and Davis, 1985a). Topp and Davis, (1985a),however, reported that for non-homogeneous soils a probe with discontinuities didnot always give detectable reflections from discontinuities located near the end ofthe probe. Moreover, the construction of such probes is labor intensive andtime-consuming.

Zegelin et al., (1989) demonstrated that variously spaced three-wire probes(2s=3–20 cm in Fig. 4) provided the identical k values for water. Increased wirespacing means greater attenuation of the high-frequency component of the TDRsignal (Topp and Davis, 1985b). Deviations from the desired parallel spacing donot significantly affect k measurement; therefore, it is not critical that the probes beexactly parallel (Stein and Kane, 1983). High-energy density around electrodes cangenerate a ‘skin effect’. This causes errors in u measurement due to local non-uni-formities such as air gaps around the electrodes. To minimize this effect, wirediameter should be appropriate for the spacing between the electrodes (Knight,1992). For example, for a two-wire type probe with d=2 and s=20 cm (d/s=0.1),about 23% of the energy (and the measurement sensitivity) is contained within twocylinders of diameter 4 cm around the wires. While, for a probe with d=1 ands=20 cm (d/s=0.05), about 38% of the energy is contained within the samecylinders around the wires (Knight, 1992). Therefore, Knight suggested that a rulefor the probe design of two- and three-wire type probes, such that d/s\0.1, toreduce energy concentration around the wires. Petersen et al., (1995) experimentallyfound that good determination of u could be obtained with a configuration as smallas d/s=0.02. However, the effects of diameter and spacing of rods on the signalattenuation in conducting media have not been fully investigated.

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4.4. Installation and spatial sensiti6ity

Annan, (1977) theoretically concluded that air gaps around electrodes in soilcould cause serious error in determination of k. Ferre et al., (1996) also reportedtheoretical considerations regarding the effects of air gaps and coated rods on traveltime of electromagnetic waves. Coated rods are used to measure u in highlyconductive media shown in Fig. 2. Topp et al., (1982b) reported that there was nosignificant difference in u determined with probes installed with or without pilotholes (where the latter might create air gaps between rods and surrounding soil). Onthe other hand, Rothe et al., (1997) found that probes installed with pilot holesalways showed higher u than probes installed by being pushed. With the aid ofX-ray computed tomography, they observed 5–20% larger soil bulk density inregions surrounding the probes installed by being pushed. This ‘‘packing’’ con-tributes to lower water content readings with TDR than the probes installed withpilot holes. Hokett et al., (1992a) found experimentally that when soil was dry theair-filled crack between the electrodes had only a small effect on measured watercontent; however, in wetter soils measured water content was reduced as much as46%. In contrast, the effect of water-filled cracks is small in both dry and wet soils.Using a numerical model, Knight et al., (1997) reported that the effect of gaps andcoatings on k determination with a three-wire type probe was larger than with atwo-wire type probe. Partial air gaps surrounding less than 1/12 of the rodcircumference does not significantly affect dielectric constant determination. Thebulk EC (sa) of soil determined by TDR is also insensitive to quality of contactbetween rods and soil, which is a major advantage over a four-electrode resistivitymethod (Nadler et al., 1991).

In terms of the spatial sensitivity of a two-wire type probe with d=3.175 mmand s=5 cm, Baker and Lascano, (1989) experimentally found that the sensitivityof TDR with water was largely confined to a quasi-rectangular area of about20×65 cm2 surrounding the rods, with no significant variation in sensitivity alongthe rod length. With air, however, TDR is sensitive only in the vicinity of rods withareas of 20 cm in diameter. They also found that sensitivity along the electrodesends abruptly at the end of the electrodes. Thus, they suggested that water contentnear the soil surface was measurable using TDR. Nielsen et al., (1995) reported thatu near the soil surface (:2.5 cm below the surface) was measured within S.D.=90.022 m3 m−3 using a two-wire type probe with rods spaced 5 cm. Petersen et al.,(1995) studied details of spatial sensitivity in terms of the probe design. They foundthat a two-wire type probe directly connected to a 50 V coaxial cable with rodspacing of 1, 2 and 5 cm could accurately measure u as close to the soil surface as1, 1.5 and 2 cm, respectively. Whalley, (1993) found that a three-wire type probewas more sensitive to u than a two-wire probe; however, the magnitude of decreasesin sensitivity due to air gaps around the electrodes were similar in both types ofprobes. A three-wire type probe is sensitive between the outer electrodes andespecially around the center electrode.

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5. Conclusions

Applications of TDR techniques to measurement of water content and electricalconductivity in soil have progressed in the last two decades. Several kinds ofinstruments, e.g. 1502/B/C (Tektronix, Inc.), TRASE Systems (Soilmoisture Equip-ment Corp.), TRIME (IMKO GmBH), Moisture Point (ESI Environmental Sen-sors Inc.), Theta Probe (Delta-T Devices Ltd.)1 and others, based on time domainreflectometry have been developed so that we can now have some freedom to selecta proper instrument. Selection could be based on physical dimensions of probes andinstruments and on built-in software for interpreting waveforms. However, currentpopular TDR systems need to be located close to probes, probably as far as 20 mor so, because of a limited bandwidth of B2.5 GHz. If a TDR system can belocated far from the probes, such as using a high-bandwidth TDR instrument ormultiplexed telemetric probes, precise spatial distribution of soil water and chemi-cals contents may be more readily investigated in a watershed scale (e.g. up toseveral km2). Moreover, because reflected waves from a probe contain moreinformation such as demonstrated by Heimovaara, (1994) than that just formeasuring water content and electrical conductivity, further research may beneeded to extract other useful information. Effects on waveforms produced byheterogeneous distribution of water, solute and/or solid particles in soil have notbeen fully investigated. Such studies would be valuable in clarifying behaviors ofelectromagnetic waves in heterogeneous materials. Using more advanced TDRtechniques in the future, soil water and solute regimes may be explored morethoroughly from theoretical and experimental points of view.

Acknowledgements

This article is based on work carried out at the Department of Soil and CropSciences, Texas A&M University and has been continued in the Department ofAgronomy, Iowa State University. The author appreciates Dr. Robert Horton ofIowa State University for reviewing a manuscript draft.

References

Alharthi, A., Lange, J., 1987. Soil water saturation: dielectric determination. Water Resour. Res. 23,591–595.

Amato, M., Ritchie, J.T., 1995. Small spatial scale soil water content measurement with time-domainreflectometry. Soil Sci. Soc. Am. J. 59, 325–329.

Amato, M., De Lorenzi, F., Olivieri, B., 1993. Riflettometria nel dominio del tempo (TDR) per lamisura dell’umidita volumetrica del terreno. I: Principi generali ed applicazioni. Riv. di Agronomia27, 1–8.

Annan, A.P., 1977. Time-domain reflectometry — air-gap problem for parallel wire transmission lines.Geol. Surv. Can. Paper 77-1B, 59–62.

Page 20: Measurement of soil water content and electrical conductivity by time domain reflectometry: a review

K. Noborio / Computers and Electronics in Agriculture 31 (2001) 213–237232

Ansoult, M., De Backer, L.W., Declercq, M., 1985. Statistical relationship between apparent dielectricconstant and water content in porous media. Soil Sci. Soc. Am. J. 49, 47–50.

Baker, T.H.W., Goodrich, L.E., 1987. Measurement of soil water content using the combined time-do-main reflectometry — thermal conductivity probe. Can. Geotech. J. 24, 160–163.

Baker, J.M., Lascano, R.J., 1989. The spatial sensitivity of time-domain reflectometry. Soil Sci. 147,378–384.

Baker, J.M., Allmaras, R.R., 1990. System for automating and multiplexing soil moisture measurementby time-domain reflectometry. Soil Sci. Soc. Am. J. 54, 1–6.

Baker, J.M., Spaans, E.J.A., 1993. Comments on ‘‘Time domain reflectometry measurements of watercontent and electrical conductivity of layered soil columns.’’. Soil Sci. Soc. Am. J. 57, 1395–1396.

Baumgartner, N., Parkin, G.W., Elrick, D.E., 1994. Soil water content and potential measured byhollow time domain reflectometry probe. Soil Sci. Soc. Am. J. 58, 315–318.

Bottraud, J.C., Rhoades, J.D., 1985. Referencing water content effects on soil electrical conductivity-salinity calibration. Soil Sci. Soc. Am. J. 49, 1579–1581.

Bridge, B.J., Sabburg, J., Habash, K.O., Ball, J.A.R., Hancock, N.H., 1996. The dielectric behaviour ofclay soils and its application to time domain reflectometry. Aust. J. Soil Res. 34, 825–835.

Cassel, D.K., Kachanoski, R.G., Topp, G.C., 1994. Practical considerations for using a TDR cabletester. Soil Tech. 7, 113–126.

Curtis, H.L., Defandorf, F.M., 1929. Dielectric constant and dielectric strength of elementary sub-stances, pure inorganic compounds, and air. In: Washburn, E.D. (Ed.), International Critical Tablesof Numerical Data, Physics, Chemistry, and Technology, vol. 6. McGraw-Hill, New York, pp.73–107.

Dalton, F.N., Herkelrath, W.N., Rawlins, D.S., Rhoades, J.D., 1984. Time-domain reflectometry:simultaneous measurement of soil water content and electrical conductivity with a single probe.Science 224, 898–990.

Dalton, F.N.Th., van Genuchten, M., 1986. The time-domain reflectometry method for measuring soilwater content and salinity. Geoderma 38, 237–250.

Dalton, F.N., Dasberg, S., Rhoades, J.D., Nadler, A., 1990. Time domain reflectometry: simultaneousin-situ measurement of soil water content and salinity BARD final report. Project no. US-868084.Bet Dagan, Israel.

Dasberg, S., Dalton, F.N., 1985. Time domain reflectometry field measurements of soil water contentand electrical conductivity. Soil Sci. Soc. Am. J. 49, 293–297.

Dasberg, S, Hopmans, J.W., 1992. Time domain reflectometry calibration for uniformly and nonuni-formly wetted sandy and clayey loam soils. Soil Sci. Soc. Am. J. 56, 1341–1345.

Davis, J.L., 1975. Relative permittivity measurements of a sand and clay soil in situ. Geol. Surv. Can.Paper 75-1C, 361–365.

Davis, J.L., 1980. Electrical property measurements of sea ice in situ using a wide-band borehole radarand a time-domain reflectometer. Proc. Int. Workshop Remote Estimation Sea Ice Thickness, St.John’s, Newfoundland 80-5, 155–187.

Davis, J.L., Chudobiak, W.J., 1975. In situ meter for measuring relative permittivity of soils. Geol. Surv.Can., Part A Paper 75-1, 75–79.

Dirksen, C., Dasberg, S., 1993. Improved calibration of time domain reflectometry soil water contentmeasurements. Soil Sci. Soc. Am. J. 57, 660–667.

Drungil, C.E.C., Abt, K., Gish, T.J., 1989. Soil moisture determination in gravely soils with time domainreflectometry. Trans. ASAE 32, 177–180.

Fellner-Feldegg, H., 1969. The measurement of dielectrics in the time domain. J. Phys. Chem. 73,616–623.

Ferre, P.A., Rudolph, D.L., Kachanoski, R.G., 1996. Spatial averaging of water content by time domainreflectometry: implications for twin rod probes with and without dielectric coating. Water Resour.Res. 32, 271–279.

Ferre, P.A., Redman, J.D., Rudolph, D.L., Kachanoski, R.G., 1998. The dependence of the electricalconductivity measured by time domain reflectometry on the water content of sand. Water Resour.Res. 34, 1207–1213.

Page 21: Measurement of soil water content and electrical conductivity by time domain reflectometry: a review

K. Noborio / Computers and Electronics in Agriculture 31 (2001) 213–237 233

Friedman, S.P., 1997. Statistical mixing model for the apparent dielectric constant of unsaturated porousmedia. Soil Sci. Soc. Am. J. 61, 742–745.

Gardner, W., Kirkham, D., 1951. Determination of soil moisture by neutron scattering. Soil Sci. 73,391–401.

Grantz, D.A., Perry, M.H., Meinzer, F.C., 1990. Using time-domain reflectometry to measure soil waterin Hawaiian sugarcane. Agron. J. 82, 144–146.

J. Halbertsma, E. van den Elsen, H. Bohl, W. Skierucha, in: L.W. Petersen, O.H. Jacobsen,(Eds.),Temperature effects on TDR determined soil water content, 1995. Proceedings of theSymposium: Time-domain Reflectometry Applications in Soil Science, Research Centre Foulum,September 16, 1994. SP report no. 11., vol. 3. Danish Institute of Plant and Soil Science, Lyngby,Denmark.

C.J. Hamlen, The effect of initial and boundary conditions on solute transport through undisturbed soilcolumns, Ph.D. Dissertation, The University of Guelph, Guelph, Ont., Canada, 1997.

Hasted, J.B., 1973. Aqueous dielectrics. Chapman and Hall, London.Hayhoe, H.N., Topp, G.C., Bailey, W.G., 1983. Measurement of soil water contents and frozen soil

depth during a thaw using time-domain reflectometry. Atmosphere-Ocean 21, 299–311.Heimovaara, T.J., 1992. Comments on ‘‘Time domain reflectometry measurements of water content and

electrical conductivity of layered soil columns’’. Soil Sci. Soc. Am. J. 56, 1657–1658.Heimovaara, T.J., 1993. Design of triple-wire time domain reflectometry probes in practice and theory.

Soil Sci. Soc. Am. J. 57, 1410–1417.Heimovaara, T.J., Bouten, W., 1990. A computer-controlled 36-channel time domain reflectometry

system for monitoring soil water contents. Water Resour. Res. 26, 2311–2316.Heimovaara, T.J., 1994. Frequency domain analysis of time domain reflectometry waveforms. 1.

Measurement of the complex dielectric permittivity of soils. Water Resour. Res. 30, 189–199.Heimovaara, T.J., Focke, A.G., Bouten, W., Verstraten, J.M., 1995. Assessing temporal variations in

soil water composition with time domain reflectometry. Soil Sci. Soc. Am. J. 59, 689–698.Heimovaara, T.J., de Winter, E.J.G., van Loon, W.K.P., Esveld, D.C., 1996. Frequency-dependent

dielectric permittivity from 0 to 1 GHz: time domain reflectometry measurements compared withfrequency domain network analyzer measurements. Water Resour. Res. 32, 3603–3610.

Herkelrath, W.N., Hamburg, S.P., Murphy, F., 1991. Automatic, real-time monitoring of soil moisturein a remote field area with time domain reflectometry. Water Resour. Res. 27, 857–864.

Hoekstra, P., Delaney, A., 1974. Dielectric properties of soils at UHF and microwave frequencies. J.Geophys. Res. 79, 1699–1708.

Hokett, S.L., Chapman, J.B., Cloud, S.D., 1992a. Time domain reflectometry response to lateral soilwater content heterogeneities. Soil Sci. Soc. Am. J. 56, 313–316.

Hook, W.R., Livingston, N.J., 1995. Propagation velocity errors in time domain reflectometry measure-ments of soil water. Soil Sci. Soc. Am. J. 59, 92–96.

Hook, W.R., Livingston, N.J., Sun, Z.J., Hook, P.B., 1992. Remote diode shorting improves measure-ment of soil water by time domain reflectometry. Soil Sci. Soc. Am. J. 56, 1384–1391.

Horino, H., Maruyama, T., 1993. Measurement of soil water content using time domain reflectometrywith a three-rod probe. Trans. Jpn. Soc. Irrig. Drain. Reclam. Engng. 168, 119–120 in Japanese.

Jacobsen, O.H., Schjønning, P., 1993a. A laboratory calibration of time domain reflectometry for soilwater measurement including effects of bulk density and texture. J. Hydrol. 151, 147–157.

Jacobsen, O.H., Schjønning, P., 1993b. Field evaluation of time domain reflectometry for soil watermeasurement. J. Hydrol. 151, 159–172.

Jacobsen, O.H., Schjønning, P., 1995. Comparison of TDR calibration functions for soil waterdetermination. In: L.W. Petersen, O.H. Jacobsen (Eds.), Proceedings of the Symposium: Time-Do-main Reflectometry Applications in Soil Science, Research Centre Foulum, September 16, 1994. SPreport no. 11, vol. 3, Danish Institute of Plant and Soil Science, Lyngby, Denmark, pp. 25–33.

Kachanoski, R.G., Pringle, E., Ward, A., 1992. Field measurement of solute travel times using timedomain reflectometry. Soil Sci. Soc. Am. J. 56, 47–52.

Kachanoski, R.G., Pringle, E., Ward, A., 1993. Reply to ‘‘Comments on ‘Field measurement of solutetravel times using time domain reflectometry’’. Soil Sci. Soc. Am. J. 57, 879.

Page 22: Measurement of soil water content and electrical conductivity by time domain reflectometry: a review

K. Noborio / Computers and Electronics in Agriculture 31 (2001) 213–237234

Kelly, S.F., Selker, J.S., Green, J.L., 1995. Using short soil moisture probes with high-bandwidth timedomain reflectometry measurements. Soil Sci. Soc. Am. J. 59, 97–102.

Keng, J.C., Topp, G.C., 1983. Measuring water content of soil columns in the laboratory: a comparisonof gamma ray attenuation and TDR techniques. Can. J. Soil Sci. 63, 3–43.

Knight, J.H., 1992. Sensitivity of time domain reflectometry measurements to lateral variations in soilwater content. Water Resour. Res. 28, 2345–2352.

Knight, J.H., Ferre, P.A., Rudolph, D.L., Kachanoski, R.G., 1997. A numerical analysis of the effectsof coatings and gaps upon relative dielectric permittivity measurement with time domain reflectome-try. Water Resour. Res. 33, 1455–1460.

Kraus, J.D., 1984. Electromagnetics, third ed. McGraw-Hill, New York.Lauren, A., 1997. Physical properties of the mor layer in a Scots pine stand. III. Thermal conductivity.

Can. J. Soil Sci. 77, 643–648.Ledieu, J., De Ridder, P., De Clerck, P., Dautrebande, S., 1986. A method measuring soil water

moisture by time-domain reflectometry. J. Hydrol. 88, 319–328.Maheshwarla, S.V., Venkatasubramanian, R., Boehm, R.F., 1995. Comparison of time domain reflec-

tometry performance factors for several dielectric geometries: theory and experiments. Water Resour.Res. 31, 1927–1933.

Malicki, M.A., Skierucha, W.M., 1989. A manually controlled TDR soil moisture meter operating with300 ps rise-time needle pulse. Irrig. Sci. 10, 153–163.

Malicki, M.A., Plagge, R., Renger, M., Walczak, R.T., 1992. Application of time-domain reflectometry(TDR) soil moisture miniprobe for the determination of unsaturated soil water characteristics fromundisturbed soil cores. Irrig. Sci. 13, 65–72.

Malicki, M.A., Plagge, R., Roth, C.H., 1996. Improving the calibration of dielectric TDR soil moisturedetermination taking into account the solid soil. Eur. J. Soil Sci. 47, 357–366.

Mallants, D., Vanclooster, M., Toride, N., Vanderborght, J., van Genuchten, M.Th., Feyen, J., 1996.Comparison of three methods of calibrate TDR for monitoring solute movement in unsaturated soil.Soil Sci. Soc. Am. J. 60, 747–754.

Mualem, Y., Friedman, S.P., 1991. Theoretical predication of electrical conductivity in saturated andunsaturated soil. Water Resour. Res. 27, 2771–2777.

Nadler, A., Frenkel, H., Mantell, A., 1984. Applicability of the four-probe technique under extremelyvariable water contents and salinity distribution. Soil Sci. Soc. Am. J. 48, 1258–1261.

Nadler, A., 1991. Effect of soil structure on bulk electrical conductivity (ECa) using the TDR and 4Ptechniques. Soil Sci. 152, 199–203.

Nadler, A., Dasberg, S., Lapid, I., 1991. Time domain reflectometry measurements of water content andelectrical conductivity of layered soil columns. Soil Sci. Soc. Am. J. 55, 938–943.

Nadler, A., 1997. Discrepancies between soil solute concentration estimates obtained by TDR andaqueous extracts. Aust. J. Soil Res. 35, 527–537.

Nielsen, D.C., Lagae, H.J., Anderson, R.L., 1995. Time-domain reflectometry measurements of surfacesoil water content. Soil Sci. Soc. Am. J. 59, 103–105.

Nissen, H.H., Moldrup, P., Henriksen, K., 1998a. High-resolution time domain reflectometry coil probefor measuring soil water content. Soil Sci. Soc. Am. J. 62, 1203–1211.

Nissen, H.H., Moldrup, P., Henriksen, K., 1998b. Time domain reflectometry measurements of nitratetransport in manure-amended soil. Soil Sci. Soc. Am. J. 62, 99–109.

Nissen, H.H., Moldrup, P., de Jonge, L.W., Jacobsen, O.H., 1999. Time domain reflectometry coil probemeasurements of water content during fingered flow. Soil Sci. Soc. Am. J. 63, 493–500.

Noborio, K., McInnes, K.J., Heilman, J.L., 1994. Field measurements of soil electrical conductivity andwater content by time-domain reflectometry. Comput. Electron. Agri. 11, 131–142.

Noborio, K., McInnes, K.J., Heilman, J.L., 1996. Measurements of soil water content, heat capacity,and thermal conductivity with a single TDR probe. Soil Sci. 161, 22–28.

Or, D., Wraith, J.M., 1999. Temperature effects on soil bulk dielectric permittivity measured by timedomain reflectometry: a physical model. Water Resour. Res. 35, 371–383.

Patterson, D.E., Smith, M.W., 1981. The measurement of frozen water content by time domainreflectometry: results from laboratory tests. Can. Geotech. J. 18, 131–144.

Page 23: Measurement of soil water content and electrical conductivity by time domain reflectometry: a review

K. Noborio / Computers and Electronics in Agriculture 31 (2001) 213–237 235

Patterson, D.E., Smith, M.W., 1985. Comment on ‘‘Monitoring the unfrozen water content of soil andsnow using time domain reflectometry’’ by Jean Stein, Douglas L. Kane. Water Resour. Res. 21,1055–1056.

Pepin, S., Plamondon, A.P., Stein, J., 1992. Peat water content measurement using time domainreflectometry. Can. J. For. Res. 22, 534–540.

Pepin, S., Livingston, N.J., Hook, W.R., 1995. Temperature-dependent measurement errors in timedomain reflectometry determinations of soil water. Soil Sci. Soc. Am. J. 59, 38–43.

Persson, M., 1997. Soil solution electrical conductivity measurements under transient conditions usingtime domain reflectometry. Soil Sci. Soc. Am. J. 61, 997–1003.

Petersen, L.W., Thomsen, A., Moldrup, P., Jacobsen, O.H., Rolston, D.E., 1995. High-resolution timedomain reflectometry: sensitivity dependency on probe-design. Soil Sci. 159, 149–154.

Rajkai, K., Ryden, B.E., 1992. Measuring aerial soil moisture distribution with the TDR method.Geoderma 52, 73–85.

Ranjan, R.S., Domytrak, C.J., 1997. Effective volume measured by TDR miniprobes. Trans. ASAE 40,1059–1066.

Reeves, T.L., Elgezawi, S.M., 1992. Time domain reflectometry for measuring volumetric water contentin processed oil shale waste. Water Resour. Res. 28, 769–776.

Reginato, R.J., van Bavel, C.H.M., 1964. Soil water measurement with gamma attenuation. Soil Sci.Soc. Am. Proc. 28, 721–724.

Ren, T., Noborio, K., Horton, R., 1999. Measuring soil water content, electrical conductivity, andthermal properties with a thermo-time domain reflectometry probe. Soil Sci. Soc. Am. J. 63,450–457.

Rhoades, J.D., van Shilfgaarde, J., 1976. An electrical conductivity probe for determining soil salinity.Soil Sci. Soc. Am. J. 40, 647–651.

Rhoades, J.D., Raats, P.A., Prather, R.J., 1976. Effects of liquid phase electrical conductivity, watercontent, and surface conductivity on bulk soil electrical conductivity. Soil Sci. Soc. Am. J. 40,651–655.

Rhoades, J.D., Manteghi, N.A., Shouse, P.J., Alves, W.J., 1989. Soil electrical conductivity and salinity:new formulations and calibrations. Soil Sci. Soc. Am. J. 53, 433–439.

Risler, P.D., Wraith, J.M., Gaber, H.M., 1996. Solute transport under transient flow conditionsestimated using time domain reflectometry. Soil Sci. Soc. Am. J. 60, 1297–1305.

Robinson, D.A., Bell, J.P., Bahelor, C.H., 1994. Influence of iron minerals on the determination of soilwater content using dielectric techniques. J. Hydrol. 161, 169–180.

Roth, K., Shulin, R., Fluhler, H., Attinger, W., 1990. Calibration of time domain reflectometry for watercontent measurement using a composite dielectric approach. Water Resour. Res. 26, 2267–2273.

Rothe, A., Weis, W., Kreutzer, K., Matthies, D., Hess, U., Ansorge, B., 1997. Changes in soil structurecaused by the installation of time domain reflectometry probes and their influence on the measure-ment of soil moisture. Water Resour. Res. 33, 1585–1593.

Sabburg, J., Ball, J.A.R., Hancock, N.H., 1997. Dielectric behavior of moist swelling clay soils atmicrowave frequencies. IEEE Trans. Geosci. Remote Sensing 35, 784–787.

Schaap, M.G., de Lange, L., Heimovaara, T.J., 1996. TDR calibration of organic forest floor media.Soil Tech. 11, 205–217.

Selker, J.S., Graff, L., Steenhuis, T., 1993. Noninvasive time domain reflectometry moisture measure-ment probe. Soil Sci. Soc. Am. J. 57, 934–936.

Seyfried, M.S., Murdock, M.D., 1996. Calibration of time domain reflectometry for measurement ofliquid water in frozen soils. Soil Sci. 161, 87–98.

Smith, M.W., Patterson, D.E., 1984. Determining the unfrozen water content in soils by time-domainreflectometry. Atmosphere-Ocean 22, 261–263.

Spaans, E.J.A., Baker, J.M., 1993. Simple baluns in parallel probes for time domain reflectometry. SoilSci. Soc. Am. J. 57, 668–673.

Spaans, E.J.A., Baker, J.M., 1995. Examining the use of time domain reflectometry for measuring liquidwater content in frozen soil. Water Resour. Res. 31, 2917–2925.

Stahli, M., Stadler, D., 1997. Measurement of water and solute dynamics in freezing soil columns withtime domain reflectometry. J. Hydrol. 195, 352–369.

Page 24: Measurement of soil water content and electrical conductivity by time domain reflectometry: a review

K. Noborio / Computers and Electronics in Agriculture 31 (2001) 213–237236

Stein, J., Kane, D.L., 1983. Monitoring the unfrozen water content of soil and snow using time domainreflectometry. Water Resour. Res. 19, 1573–1584.

Stein, J., Kane, D.L., 1985. Reply. Water Resour. Res. 21, 1057–1058.Tektronix, 1990. 1502C metallic time domain reflectometer. Operator manual. Tektronix, Inc., OR,

USA.Topp, G.C., Davis, J.L., Annan, A.P., 1980. Electromagnetic determination of soil water content:

measurements in coaxial transmission lines. Water Resour. Res. 16, 574–582.Topp, G.C., Davis, J.L., 1981. Detecting infiltration of water through soil cracks by time-domain

reflectometry. Geoderma 26, 13–23.Topp, G.C., Davis, J.L., Annan, A.P., 1982a. Electromagnetic determination of soil water content using

TDR: I. Applications to wetting fronts and steep gradients. Soil Sci. Soc. Am. J. 46, 672–678.Topp, G.C., Davis, J.L., Annan, A.P., 1982b. Electromagnetic determination of soil water content using

TDR: II. Evaluation of installation and configuration of parallel transmission lines. Soil Sci. Soc.Am. J. 46, 678–684.

Topp, G.C., Davis, J.L., Bailey, W.G., Zebchuk, W.D., 1984. The measurement of soil water contentusing a portable TDR hand probe. Can. J. Soil Sci. 64, 313–321.

Topp, G.C., Davis, J.L., 1985a. Measurement of soil water content using time-domain reflectometry(TDR): a field evaluation. Soil Sci. Soc. Am. J. 49, 19–24.

Topp, G.C., Davis, J.L., 1985b. Time-domain reflectometry (TDR) and its application to irrigationscheduling. In: Hillel, D. (Ed.), Advances in Irrigation, vol. 3. Academic Press, New York, pp.107–127.

Topp, G.C., Yanuka, M., Zebchuk, W.D., Zegelin, S., 1988. Determination of electrical conductivityusing time domain reflectometry: soil and water experiments in coaxial lines. Water Resour. Res. 24,945–952.

Topp, G.C., Watt, M., Hayhoe, H.N., 1996. Point specific measurement and monitoring of soil watercontent with an emphasis on TDR. Can. J. Soil Sci. 76, 307–316.

U.S. Salinity Laboratory Staff, 1954. Diagnosis and improvement of saline and alkali soils. AgricultureHandbook no. 60. U.S.D.A., U.S. Government Printing Office, Washington, DC.

van Genuchten, M.Th., 1980. A closed-form equation for predicting the hydraulic conductivity ofunsaturated soils. Soil Sci. Soc. Am. 44, 892–898.

van Loon, W.K.P., Perfect, E., Groenevelt, P.H., Kay, B.D., 1990. A new method to measure bulkelectrical conductivity in soils with time domain reflectometry. Can. J. Soil Sci. 70, 403–410.

Vogeler, I., Clothier, B.E., Green, S.R., Scotter, D.R., Tillman, R.W., 1996. Characterizing water andsolute movement by time domain reflectometry and disk permeametry. Soil Sci. Soc. Am J. 60, 5–12.

Vogeler, I., Clothier, B.E., Green, S.R., 1997. TDR estimation of the resident concentration ofelectrolyte in the soil solution. Aust. J. Soil Res. 35, 515–526.

Ward, A.L., Kachanoski, R.G., Elrick, D.E., 1994. Laboratory measurements of solute transport usingtime domain reflectometry. Soil Sci. Soc. Am. J. 58, 1031–1039.

Ward, A.L., Kachanoski, R.G., Elrick, D.E., 1995. Analysis of water and solute transport away from asurface point source. Soil Sci. Soc. Am. J. 59, 699–706.

Weitz, A.M., Grauel, W.T., Keller, M., Veldkamp, E., 1997. Calibration of time domain reflectometrytechnique using undisturbed soil samples from humid tropical soils of volcanic origin. Water Resour.Res. 33, 1241–1249.

Whalley, W.R., 1993. Considerations on the use of time-domain reflectometry (TDR) for measuring soilwater content. J. Soil Sci. 44, 1–9.

Whalley, W.R., Leeds-Harrison, P.B., Joy, P., Hoefsloot, P., 1994. Time domain reflectometry andtensiometry combined in an integrated soil water monitoring system. J. Agric. Engng. Res. 59,141–144.

Wraith, J.M., Or, D., 1999. Temperature effects on soil bulk dielectric permittivity measured by timedomain reflectometry: experimental evidence and hypothesis development. Water Resour. Res. 35,361–369.

Wraith, J.M., Comfort, S.D., Woodbury, B.L., Inskeep, W.P., 1993. A simplified waveform analysisapproach for monitoring solute transport using time-domain reflectometry. Soil Sci. Soc. Am. J. 57,637–642.

Page 25: Measurement of soil water content and electrical conductivity by time domain reflectometry: a review

K. Noborio / Computers and Electronics in Agriculture 31 (2001) 213–237 237

Wyseure, G.C.L., Mojid, M.A., Malik, M.A., 1997. Measurement of volumetric water content by TDRin saline soils. Eur. J. Soil Sci. 48, 347–354.

Yu, C., Warrick, A.W., Conklin, M.H., Young, M.H., Zreda, M., 1997. Two- and three-parametercalibrations of time domain reflectometry for soil moisture measurement. Water Resour. Res. 33,2417–2421.

Zegelin, S.J., White, I., Kenkins, D.J., 1989. Improved field probes for soil water content and electricalconductivity measurement using time domain reflectometry. Water Resour. Res. 25, 2367–2376.

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