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

Computers and Electronics in Agriculture 31 (2001) 213– 237 www.elsevier.com/locate/compag

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

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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mass. Widely accepted in situ methods to measure soil water content may be radioactive 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 require calibration for each soil and special caution to avoid possible health hazards. An alternative non-destructive method to measure soil water content was developed by Davis and Chudobiak, (1975) using time domain reflectometry (TDR). It was based on the procedure introduced by Fellner-Feldegg, (1969). TDR determines the dielectric constant of an object using simple electrodes inserted into the object. Topp et al., (1980) proposed an empirical relationship between dielectric constant and volumetric water content of soils with several textures. An advantage of TDR is simultaneous measurement of water content and bulk electrical conductivity of soil with a single probe (Dalton et al., 1984). In addition, water content measurement is only slightly susceptible to changes in soil bulk 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 bulk density for swelling clay soils, but not for non-swelling soils. Establishing an automated and multiplexed TDR system is relatively easy with minimal maintenance (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., Beaverton, OR)1, was originally developed for detecting locations of breaks or short-circuits in telephone and cable TV lines. Its popularity has also contributed to the use of TDR techniques for water and salinity measurement in soil. Likewise, other commercially available TDR systems have helped extend TDR techniques in many disciplines, e.g., TRASE Systems (Soilmoisture Equipment Corp., Santa Barbara, CA), TRIME (IMKO GmBH, Ettlingen, Germany), Moisture Point (ESI Environmental Sensors Inc., Victoria, BC, Canada), Theta Probe (Delta-T Devices Ltd., Burwell, Cambridge, England)1, and others, specifically designed for soil water and/or salinity measurement. In this review, theories behind measuring water content and salinity of soil using TDR are introduced. Geometry and characteristics of TDR probes are also addressed.

2. Theory

2.1. Dielectric constant TDR determines the dielectric constant s by measuring the propagation time of electromagnetic waves, sent from a pulse generator of a cable tester (Fig. 1), immersed in a medium. Electromagnetic waves propagate through a coaxial cable to 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, the State of Iowa, or Texas A&M University.

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

2Ls 0.5 , c

(1)

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

  ct 2L

2

.

(2)

In a commercial TDR cable tester such as the 1502/B/C (which is most commonly used in soil science and hydrology), the term (ct/2) in Eq. (2) is reduced to 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. Arrows indicate directions of electromagnetic waves. L and La represent the actual probe length and an apparent probe length displayed on the cable tester, respectively. Using Eq. (3) with L and La, the dielectric constant 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 a three-wire type probe (L=0.145 m). La indicates an apparent probe length from the beginning to the end of the probe. Vp was set to 0.66.

s=

  La L

2

,

(3)

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

  La/Vp L

2

.

(4)

For estimating water content, a Vp value is generally selected equal to 0.99 to achieve the maximum measuring resolution of the instrument (Cassel et al., 1994; Amato and Ritchie, 1995; Ranjan and Domytrak, 1997; Sta¨hli and Stadler, 1997). The apparent distance La between the initial and final reflections can be determined from waves reflected back from a probe. Examples of waveforms from a three-wire type probe embedded in a sandy soil and water are shown in Fig. 2. The waveforms were acquired using the 1502C and transported through RS-232C ports to a computer for storage and further analysis (Fig. 1). The reflection coefficient z in the Y-axis in Fig. 2 is defined as a ratio of the reflected amplitude of the signal from a cable to the signal amplitude applied to the cable (Tektronix, 1990). If there is an open circuit in the cable, nearly all the energy will be reflected back. The reflected amplitude will be equal to the incident amplitude and z= + 1. If there is

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a short circuit, nearly all the energy will be delivered back to the cable tester through the ground. The polarity of the reflected pulse will be opposite of the incident pulse and z = −1. Therefore, the reflection coefficient for soil and weakly conducting solutions is usually between − 1 and + 1. The initial reflection point from the beginning of a probe is easily found by immersing 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 is independent of the medium between and surrounding the probe (Maheshwarla et al., 1995). Details for finding the initial and final reflection points using a computer are found in Baker and Allmaras, (1990). In their method, acquired TDR waveforms are first smoothed and differentiated with respect to t. Then a maximum value of the derivative of the data is found as the slope of a tangent line for the smoothed wave at the final reflection. The intersection of this tangent line with a horizontal line — representing the minimum value of a line between the initial and final reflections is identified as the final reflection point. Baker and Allmaras, (1990) determined the initial reflection point in a similar manner as the final reflection point. For a very dry soil (Fig. 2), the final reflection from a three-wire probe is found in a similar manner to wet soils, but instead of a horizontal line a tangent line, which represents a slope just before the final reflection, is used (Heimovaara and Bouten, 1990). Hook et al., (1992) developed a method to improve reflection location determination by remotely shorting various locations of a probe using diodes.

3. Soil water content Because the dielectric constant of water is much larger than other soil constituents (Table 1), determining water content by measuring an apparent dielectric constant 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 cable tester. Table 1 Dielectric constants of soil constituents and major textures of soils (Curtis and Defandorf, 1929) Material

Dielectric constant

Air Water Ice Basalt Granite Sandstone Dry loam Dry sand

1 80 at 20°C 3 at −5°C 12 7–9 9–11 3.5 2.5

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For homogeneous soil, volumetric water content q (m3 m − 3) is then calculated using a calibration curve empirically determined by Topp et al., (1980) as q = − 5.3× 10 − 2 +2.92 × 10 − 2s− 5.5× 10 − 4s 2 + 4.3× 10 − 6s 3

(5)

They found an apparent dielectric constant s of soil was not strongly sensitive to temperature (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 (moistened with salt-free water, 0.01 N CaSO4, or 2000 ppm NaCl solution). As the temperature of sandy and clay soils increased from 1 to 40°C, s increased by about 10% (Davis and Chudobiak, 1975). The temperature effect on TDR-measured s is large in a wetter and courser textural soil (Halbertsma et al., 1995), whereas that is large in a wetter and finer textural soil (Pepin et al., 1995). Pepin et al., (1995) speculated that a larger temperature effect for wetter and finer-textured soils dominated by free water might be attributed to bound water, which had a smaller temperature dependency for s than free water. The puzzling temperature effect on TDR-measured s for different textural soils was investigated experimentally by Wraith and Or, (1999) and theoretically by Or and Wraith, (1999). They concluded that the amount of bound water restricted, depending on clay minerals, on soil particles was attributed to the temperature effect. The effect of soil structure in Eq. (5) is negligible (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 in sandy soils, respectively. Volumetric water content in organic soil and vermiculite is, however, underestimated by Eq. (5). In glass beads, it is overestimated (Topp et al., 1980) as well as in swelling and non-swelling clay soils (Bridge et al., 1996). Herkelrath et al., (1991) also found Eq. (5) underestimated q for loam with well-developed organic horizons. Likewise, Pepin et al., (1992) found that Eq. (5) underestimated q for peat at s\17. Malicki et al., (1996), however, reported that these estimation errors were overcome 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) overestimated q in soils moistened with saline water. Based on experiments with clay loam to coarse sand moistened with saline water, Wyseure et al., (1997) proposed a new calibration to account for the effect of saline water on the apparent dielectric constant 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 or goethite has little effect on the measurement of La (Robinson et al., 1994). The calibration curve by Topp et al., (1980) has been confirmed by numerous authors, including, Patterson and Smith, (1981) for silt loam and clay, even with ice; Topp et al., (1982b) for silt loam; Smith and Patterson, (1984) for sand to clay loam, even with ice; Topp et al., (1984) for clay to very fine sandy loam; Topp and Davis, (1985a) for sandy loam over clay; Drungil et al., (1989) for sand and sandy loam 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 and with layered profiles; and Reeves and Elgezawi, (1992) for fine sandy loam mixed with 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 Patterson and Smith, (1981), Hayhoe et al., (1983), Stein and Kane, (1983), Smith and Patterson, (1984), Spaans and Baker, (1995), and Seyfried and Murdock, (1996). Although the calibration curve by Topp et al., (1980) has been successfully applied to many situations, other calibrations have also been proposed based on the linear relationship between q and s 0.5 (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 et al., (1980) and the q – s 0.5 relation can be made equivalent. For finer textural soils such as silt loam and sandy loam, Yu et al., (1997) proposed a more general relation as q –s k, where k represents a calibration exponent, to correct overestimation of q at s B5 when using the q–s 0.5 relation. The theoretical relationship between the dielectric constant of soil constituents and q 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). For peat to crushed limestone, the mixing model’s q agrees well with TDR-measured q. Jacobsen and Schjønning, (1995) summarized the accuracy of TDR-estimated q using various empirical equations and mixing models. They suggested that the calibration of Topp et al., (1980) might be the first choice if the accuracy of 9 0.02 − 0.03 m3 m − 3 was acceptable. Malicki et al., (1996) proposed a new general calibration equation that incorporated soil bulk density as q=

(s 0.5 −0.819 − 0.168zb − 0.159z 2b) (7.17 +1.18zb)

(6)

where q is volumetric soil water content (m3 m − 3), s the dielectric constant of soil, and zb the bulk density of soil (Mg m − 3). They tested Eq. (6) with wide ranges of soil textures (organic soil to sand), bulk densities (0.13 –2.67 mg m − 3) and organic carbon contents (0 – 487 g kg − 1). Their new calibration reduces the variance of their q estimates to approximately one fifth of the q estimates made with a calibration equation without accounting for bulk density. Schaap et al., (1996) confirmed the validity of Eq. (6) in the laboratory with non-shrinking forest litters at sE 4.0. For sB4.0, 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 free water, and bound water becomes dominant at sB 4.0. Jacobsen and Schjønning, (1993a,b), however, reported that inclusion of soil bulk density in their own calibration improved the accuracy of q estimated using TDR in the laboratory, but not in the field. For heterogeneous soil, measurement of water content using TDR was theoretically and experimentally investigated by Topp et al., (1982a,b). When the heterogeneous layers were oriented perpendicular to a TDR probe, they found that TDR-measured water content of the layered soil agreed well with a linearly weighted average water contents over profiles. Topp et al., (1982a) expressed the weighted average of water content q( (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 to attenuation of electromagnetic waves. There were no final reflections for concentrations \0.1 mol kg − 1 n of NaCl solution.

% ziqi

q( =

i=1 n

(7)

% zi

i=1

where n is the number of layers; zi the thickness of layer i, and qi the volumetric water content of layer i. Nadler et al., (1991) confirmed the relationship between TDR measurements and Eq. (7), although they had difficulties interpreting the TDR waveforms – as did Dasberg and Hopmans, (1992) — when a very wet soil layer was overlying a very dry soil layer. For heterogeneous layers oriented parallel to a TDR probe, q estimated using TDR, however, is heavily biased toward the water 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 an electrolyte solution could be determined as a function of the derivative of reflection coefficient with respect to time of the TDR waveform at t= 0. Later, several researchers 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 and concluded 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 for layered soils.

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Dalton et al., (1984) described the relationship of signal amplitudes along a probe in a conducting medium (Fig. 3) as (VR −VT) = VTexp( − 2hL)

(8)

where VT is the signal amplitude after partial reflection from the beginning of the probe, VR the signal amplitude after reflection from the end of the probe and h the attenuation coefficient expressed as h=

60p| s 0.5

(9)

Dalton et al., (1984) combined Eqs. (8) and (9) to describe EC (|D) of a medium as |D =

s 0.5 (120pL)ln[VT/(VR −VT)]

(10)

A reflection for VR needs to be adequately determined by distinguishing the breakpoints, levels and gradients from measured waveforms. The reflection is, however, sometimes indistinguishable because of waveform distortion due to loss of higher frequencies. This distortion results partly from impedance mismatches between a probe and a cable tester (Noborio et al., 1994) and signal attenuation caused by a long cable (Heimovaara, 1993). Although Eq. (10) can determine electrical conductivity using measured waveforms and a probe length (without any empirical values), obtaining a distinguishable VR reflection is critical for this method. Nadler et al., (1991) proposed an alternative procedure to determine electrical conductivity, not using the VR reflection. Later, Heimovaara, (1992) and Baker and Spaans, (1993) found that the procedure of Nadler et al., (1991) was equivalent to that of Giese – Tiemann (G – T method) presented by Topp et al., (1988). The G–T method determines EC (|G – T) as |G − T =

  K Zu



1 − z 1 + z

(11)

where K is the geometric constant of a probe (m − 1), Zu the characteristic impedance of a cable (V), and z the reflection coefficient at a distant point from the first reflection on the waveform. It is defined as, z = (V − V0)/V0, where V is the signal amplitude at the distant point (e.g., about 10 times larger than La as shown in Fig. 3) and V0 the signal amplitude from the TDR instrument. The magnitude of reflections at V decreases as concentration of a medium increases as shown in Fig. 3. The decrease in V due to an electrolyte solution depends on physical characteristics of the probe as well as solution concentration. The geometric constant K is experimentally determined by immersing the probe in solutions of known electrical conductivity |T at T°C (Dalton et al., 1990). Or, alternatively, a K value is determined (Baker and Spaans, 1993) by

 

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K=

m 0c Z0 L

(12)

where m0 is the permittivity of free space (8.9× 10 − 12 F m − 1), c the velocity of light in free space (3× 108 m s − 1), L the TDR probe length (m), and Z0 the characteristic impedance of the probe (V). A Z0 value for the probe is determined by immersing the probe into a non-conductive medium (e.g. deionized water) (Baker and Spaans, 1993) as Z0 =Zus 0.5 ref



1 + z0 1 − z0



(13)

where sref is the dielectric constant of the non-conductive medium as a reference. The dielectric constant of water swater for sref is a function of temperature (Hasted, 1973) expressed as swater =84.740 −0.40008T +9.398×10 − 4T 2 − 1.410×10 − 6T 3

(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, q, with Eq. (4) and Eq. (5) and the apparent or bulk electrical conductivity of soil, |a, which can be expressed by |D or |G – T with Eq. (4) and Eq. (10). For fine sandy loam moistened with saline water, Dasberg and Dalton, (1985) found that there was good agreements between |a measured by a four-electrode resistivity method (Rhoades and van Shilfgaarde, 1976) and TDR, and q measured by the neutron scattering method and TDR. Nadler et al., (1984) estimated the electrical conductivity of soil pore water with TDR-measured water content and bulk EC by |w25 =fT(|a −l|s)F(q)

(15)

where |w25 is the electrical conductivity of soil pore water at 25°C (electrical conductivity is usually reported at 25°C). A temperature-correction function fT is included ( fT =1.00 +(25 −T)/49.7 +(25− T)2/3728 for 200 T047°C, data obtained from U.S. Salinity Laboratory Staff, 1954), where T is the soil pore water temperature (°C), |a the apparent or bulk electrical conductivity of soil (S m − 1) described by Eq. (10) or Eq. (11), |s the electrical conductivity of solid materials (S m − 1), l an empirical parameter, and F(q) a formation factor accounting for the tortuosity of current flow. Heimovaara et al., (1995) found that the temperature dependency of |a was similar to that of a solution. To evaluate F(q), Noborio et al., (1994) and Risler et al., (1996) used a transmission coefficient proposed by Rhoades et al., (1976) in Eq. (16): F(q) =

1 qx(q)

(16)

where x(q) is the transmission coefficient expressed as x(q)= aq + b (with empirically determined constants a and b depending on soil). Rhoades et al., (1976)

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originally proposed l=1 in Eq. (15), but later Rhoades et al., (1989) expressed l and F(q) for |ws \0.2 – 0.4 and |s B 0.15 S m − 1 as, l=

(ƒs +qws)2 ƒs

F(q) =

(17)

1 (q − qws)

(18)

where ƒs is the volumetric content of the solid materials in the soil (m3 m − 3), |ws electrical conductivity of immobile water (S m − 1), qws immobile water content (m3 m − 3) and q the total water content (m3 m − 3) (including both mobile and immobile regions). Using l =1 in Eq. (15), Noborio et al., (1994) found a fair agreement within 90.1 S m − 1 between TDR-estimated |w25 and that from soil cores in the field. In the laboratory, Risler et al., (1996) reported that Eq. (17) and Eq. (18) gave good estimates of |w, as did Eq. (15) with l= 1. Recently, Nissen et al., (1998b) estimated the laboratory values of |w (within 9 0.1 S m − 1) from TDR-measured q and |a using the relation q – |a –|w. This relationship was originally proposed by Vogeler et al., (1996), and is similar to the original equation of Rhoades et al., (1976). For |ws B0.2 S m − 1, Rhoades et al., (1989) proposed a more complex model, but the model has not been tested using TDR. Mallants et al., (1996) observed increases in l values due to increases in qws, when the total water content increased. Instead of using the transmission coefficient, Heimovaara et al., (1995) used the tortuosity factor proposed by Mualem and Friedman, (1991) based on a water retention function as

F(q) = qeffi

& &

[



2

[1/h(x)]dx

0 [

(19) 2

[1/h(x) ]dx

0

where qeff is effective volumetric water content through which the current can flow, i is a calibration exponent, h(x) a water retention function and [ the relative saturation. Heimovaara et al., (1995) used van Genuchten’s equation (van Genuchten, 1980) for h(x) and ignored the effect of |s so that l=0 in Eq. (15). Although estimates of |w using Eq. (15)-based equations agreed well with those from soil-extract, solution samplers or effluent in coarse textured soils (Noborio et al., 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-estimated and extracted |w, but less-structured silt loams and weakly structured sandy loams had a poor agreement. In contrast, Nadler, (1991) found that soil structure had little effect on measurement of |a using TDR. However, the transmission coefficient or the tortuosity factor in the model is sensitive to changes in soil structure (Mallants et al., 1996; Persson, 1997). Therefore, Mallants et al., (1996) and Persson, (1997) suggested that site-specific calibration between |a and |w might

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be needed, especially in heterogeneous soils. The effect of hysteresis is negligible for |w estimated by TDR (Nadler, 1997) and for |a measured by a four-electrode resistivity method (Bottraud and Rhoades, 1985). Eq. (15) can be reduced to a simpler expression (Kachanoski et al., 1992; Ward et al., 1994; Vogeler et al., 1997) as |w =f0(q) + f1(q)|a

(20)

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

(1 + z) (1 −z)

(21)

where ZL is the impedance load (V) and z the reflection coefficient at a point, where 1 the reading is made such as z in Fig. 3. Substituting |a in Eq. (20) with Z − in L −3 Eq. (21), Hamlen, (1997) estimated resident concentration, C (kg m ), at q using Eq. (22). This is based on the work of Kachanoski et al., (1992) and Ward et al., (1994, 1995) as 1 C = m(q) + k(q)Z − L

(22)

where m(q) and k(q) are empirical parameters as functions of q. Moreover, relative solute mass, rather than absolute solute concentration, may be estimated, so that empirical parameters such as K in Eq. (11), f0(q) and f1(q) in Eq. (20), and m(q) and k(q) in Eq. (22) need not to be determined (Kachanoski et al., 1992). Heimovaara et al., (1995) proposed to account for the resistance of a cable in ZL to extend the 1 range of linearity between C and Z − L . Eq. (22) is then modified to C = m(q)+ k(q)(Ztot −Zcable) − 1

(23)

where Ztot is the total impedance (V) of the cable tester, coaxial cable, and TDR probe inserted in a sample, and Zcable the combined series impedance (V) in the coaxial 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 in theory) has been popular since it was introduced by Davis, (1980) (Fig. 4A). A few researchers have used two-wire type probes without transformers and have had consistent results for water content measurement (Stein and Kane, 1983; Ledieu et al., 1986; Malicki and Skierucha, 1989; Malicki et al., 1992; Rajkai and Ryde´n,

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1992; Kelly et al., 1995). Patterson and Smith, (1985), however, warned that there might be a risk of encountering stray voltages and currents that could increase measurement 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 conductivity because the signal’s amplitude after the final reflection decreases due to low frequency attenuation (Spaans and Baker, 1993). Thus, they developed a new impedance-matching transformer with which the signal’s amplitude did not decrease. However, Kachanoski et al., (1992) used a two-wire type probe attached to a 200 V shielded TV antenna cable with an ordinal impedance-matching transformer and obtained consistent values. They used only a portion of the wave after multiple reflections ceased, but before wave amplitude decreased (Kachanoski et al., 1993). Ferre´ et al., (1998) confirmed that use of an ordinal matching transformer with 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. Dimensions indicated were taken from the references. Note that a three-wire type probe simulates a coaxial cell and does 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 gives simpler waveforms than does a two-wire type probe. Simpler waveforms enable better definition of signal’s travel time along a probe length, especially suitable for saline soils and for soil layers having extreme differences in q (Zegelin et al., 1989; Nadler et 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) than does a two-wire type probe (q.v., Fig. 4 of Zegelin et al., 1989). One inconvenience of using a three-wire probe may be that the reflection from the beginning of the probe in dry soil significantly differs from the reflection in very wet soil or water as shown in Fig. 2. This is inconvenient for the automated interpretation of waveforms. Another type of probe is introduced to specifically measure volumetric water content 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 the gravimetrically 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 the relationship between dielectric constant and water content for TDR probes (with non-conventional geometries) from both theoretical and experimental points of view. Multi-purpose TDR probes have also been developed (besides measuring water content 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 them work as tensiometers and solution samplers. Baumgartner et al., (1994) found that measured water content using solid rods and hollow stainless steel rods with porous materials were almost identical in the entire ranges of water contents (0.11BqB 0.37 m3 m − 3) they tested. Noborio et al., (1996) combined the functions of TDR and a dual-probe heat-pulse device to simultaneously measure water content, heat capacity and thermal conductivity of soil. They reported that although insertion of a heater and a thermocouple wire inside the hollow center rod of their TDR probe distorted waveforms, the deformation did not affect water content determination. Modified TDR probe geometries do not seem to affect estimation of dielectric constant and water content, but do affect waveforms. Baker and Goodrich, (1987) and Laure´n, (1997) also combined the functions of TDR and a single thermal probe for measuring soil water content and thermal conductivity. Recently, Ren et al., (1999) redesigned the 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 covered with longitudinal, variable-width aluminum strips as electrodes (Fig. 5B). Noborio et al., (1994) made temperature measurements using hollow stainless steel rods enclosing thermocouple wires in an outer electrode. They found that there was no significant 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 measurement in non-conducting media. In practice, however, determination of reflection points on TDR waveforms and calculations of dielectric constant are very sensitive to small errors in an apparent probe length La (Eq. (4)). More errors may be introduced by using short probes (LB 0.1 m) (Stein and Kane, 1985; Reeves and Elgezawi, 1992). Shorter probes create shorter La, and small errors in determining La (especially for dry soils having small dielectric constant of 2–5) induce larger uncertainties in dielectric constant. Topp et al., (1984) reported errors in determining water content using a 0.05 m long probe were significant (S.D.= 9 0.037 m3 m − 3) and suggested using a probe with LE 0.1 m to achieve an accuracy of S.D. =0.02 m3 m − 3 in the field. Topp and Davis (1985b) suggested using a 0.1 –1.0 m long probe in the field — where TDR-measured water content agreed to within 2% of gravimetrically determined water content. Using a Tektronix 1502B cable tester (whose effective bandwidth is 1 GHz by Heimovaara et al., 1996), with a 0.021 m long two-wire type probe, Amato and Ritchie, (1995) reported an error measurement of S.D.= 90.023 m3 m − 3. This deviation is equivalent to S.D.= 9 0.022 m3 m − 3 obtained using L \ 0.1 m long probes by Topp et al., (1984) in the field. The latter is obtained, when dielectric constant is greater than 2, which is equivalent to water content greater than 0.07 m3 m − 3. Using a high bandwidth (20 GHz) TDR instrument (which provides clearer waveforms especially in dry soils than 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. = 9 0.021 m3 m − 3. For conducting media, attenuation of TDR signals depends on the configuration of a probe, including length and spacing. Thus, Dalton and van Genuchten, (1986) suggested that a practical lower limit for the probe length (for simultaneous 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 copper wire on a PVC rod to make a 0.015 m long probe. The accuracy of the coil probe relative to gravitationally determined soil water content is S.D.= 9 0.017 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 cable length up to about 15 m without losing distinct reflections from the beginning and end of the probe. Similar results are obtained using probes longer than 0.2 m with up 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 pulse from cable filtering of the high frequency components. If a TDR instrument with a higher bandwidth is used, shorter probes with longer cables than those described above can be used. System costs can be reduced without compromising the accuracy of La determination in Eq. (3), i.e. volumetric water content, by using 75 V coaxial cables. These are less expensive than 50 V coaxial or 200 V TV antenna cables (Hook and Livingston, 1995). In fact, a 75 V coaxial cable connected to a three-wire type probe generally 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 require impedance-matching transformers, which are needed for use of 200 V TV antenna cables. However, caution must be paid, when electrical conductivity is determined. Using different impedance between the cable tester output and a coaxial cable produces 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 salt solutions 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 120 2s ln Z= (24) d

s where s is the dielectric constant of a material surrounding the probe, s the spacing of rods, and d the diameter of the rods. With various rod diameters connected in series (Fig. 5C), abrupt reflections of TDR signals occur due to impedance differences corresponding to the locations, where diameters are different. Using this type of probe, water content at multiple locations can be determined with a single probe (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 did not always give detectable reflections from discontinuities located near the end of the probe. Moreover, the construction of such probes is labor intensive and time-consuming. Zegelin et al., (1989) demonstrated that variously spaced three-wire probes (2s = 3 – 20 cm in Fig. 4) provided the identical s values for water. Increased wire spacing means greater attenuation of the high-frequency component of the TDR signal (Topp and Davis, 1985b). Deviations from the desired parallel spacing do not significantly affect s measurement; therefore, it is not critical that the probes be exactly parallel (Stein and Kane, 1983). High-energy density around electrodes can generate a ‘skin effect’. This causes errors in q measurement due to local non-uniformities such as air gaps around the electrodes. To minimize this effect, wire diameter 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 two cylinders of diameter 4 cm around the wires. While, for a probe with d= 1 and s =20 cm (d/s = 0.05), about 38% of the energy is contained within the same cylinders around the wires (Knight, 1992). Therefore, Knight suggested that a rule for the probe design of two- and three-wire type probes, such that d/s\0.1, to reduce energy concentration around the wires. Petersen et al., (1995) experimentally found that good determination of q could be obtained with a configuration as small as d/s = 0.02. However, the effects of diameter and spacing of rods on the signal attenuation 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 soil could cause serious error in determination of s. Ferre´ et al., (1996) also reported theoretical considerations regarding the effects of air gaps and coated rods on travel time of electromagnetic waves. Coated rods are used to measure q in highly conductive media shown in Fig. 2. Topp et al., (1982b) reported that there was no significant difference in q determined with probes installed with or without pilot holes (where the latter might create air gaps between rods and surrounding soil). On the other hand, Rothe et al., (1997) found that probes installed with pilot holes always showed higher q than probes installed by being pushed. With the aid of X-ray computed tomography, they observed 5–20% larger soil bulk density in regions surrounding the probes installed by being pushed. This ‘‘packing’’ contributes to lower water content readings with TDR than the probes installed with pilot holes. Hokett et al., (1992a) found experimentally that when soil was dry the air-filled crack between the electrodes had only a small effect on measured water content; however, in wetter soils measured water content was reduced as much as 46%. 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 and coatings on s determination with a three-wire type probe was larger than with a two-wire type probe. Partial air gaps surrounding less than 1/12 of the rod circumference does not significantly affect dielectric constant determination. The bulk EC (|a) of soil determined by TDR is also insensitive to quality of contact between rods and soil, which is a major advantage over a four-electrode resistivity method (Nadler et al., 1991). In terms of the spatial sensitivity of a two-wire type probe with d =3.175 mm and s = 5 cm, Baker and Lascano, (1989) experimentally found that the sensitivity of TDR with water was largely confined to a quasi-rectangular area of about 20×65 cm2 surrounding the rods, with no significant variation in sensitivity along the rod length. With air, however, TDR is sensitive only in the vicinity of rods with areas of 20 cm in diameter. They also found that sensitivity along the electrodes ends abruptly at the end of the electrodes. Thus, they suggested that water content near the soil surface was measurable using TDR. Nielsen et al., (1995) reported that q near the soil surface (: 2.5 cm below the surface) was measured within S.D.= 9 0.022 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 found that a two-wire type probe directly connected to a 50 V coaxial cable with rod spacing of 1, 2 and 5 cm could accurately measure q as close to the soil surface as 1, 1.5 and 2 cm, respectively. Whalley, (1993) found that a three-wire type probe was more sensitive to q than a two-wire probe; however, the magnitude of decreases in sensitivity due to air gaps around the electrodes were similar in both types of probes. A three-wire type probe is sensitive between the outer electrodes and especially around the center electrode.

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5. Conclusions Applications of TDR techniques to measurement of water content and electrical conductivity in soil have progressed in the last two decades. Several kinds of instruments, e.g. 1502/B/C (Tektronix, Inc.), TRASE Systems (Soilmoisture Equipment Corp.), TRIME (IMKO GmBH), Moisture Point (ESI Environmental Sensors Inc.), Theta Probe (Delta-T Devices Ltd.)1 and others, based on time domain reflectometry have been developed so that we can now have some freedom to select a proper instrument. Selection could be based on physical dimensions of probes and instruments and on built-in software for interpreting waveforms. However, current popular TDR systems need to be located close to probes, probably as far as 20 m or so, because of a limited bandwidth of B2.5 GHz. If a TDR system can be located far from the probes, such as using a high-bandwidth TDR instrument or multiplexed telemetric probes, precise spatial distribution of soil water and chemicals contents may be more readily investigated in a watershed scale (e.g. up to several km2). Moreover, because reflected waves from a probe contain more information such as demonstrated by Heimovaara, (1994) than that just for measuring water content and electrical conductivity, further research may be needed to extract other useful information. Effects on waveforms produced by heterogeneous distribution of water, solute and/or solid particles in soil have not been fully investigated. Such studies would be valuable in clarifying behaviors of electromagnetic waves in heterogeneous materials. Using more advanced TDR techniques in the future, soil water and solute regimes may be explored more thoroughly from theoretical and experimental points of view.

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

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