Time Domain Reflectometry Probe for Simultaneous Measurementof Soil Matric Potential and Water Content

K. Noborio, R. Horton,* and C. S. Tan

ABSTRACTSimultaneous measurement of matric potential, »|», and water con-

tent, 6, is demanded in many disciplines. Time domain reflectoinelry(TDR) has been routinely used to measure water content and electri-cal conductivity of soil. Previous efforts to combine TDR probeswith porous materials functioning as tensiometers were successful,but these probes were still constrained by characteristics of tensiome-ters, such as the need to supply water and measuring ranges \\i >-85 kPa. A new i|/-6 TDR probe was developed to overcome short-comings of the previous work. A portion of the TDR rod was embed-ded in a dental plaster (gypsum), whose matric potential equilibratedwith surrounding soil. The rest of the TDR rod was inserted into thesoil. The TDR technique was used to determine dielectric constants,K, of both the gypsum and the soil. The new >|»-6 TDR probes weretested in clay loam soil using a pressure-plate apparatus to produceK-i|t relationships of the gypsum and the soil for -1000 < i|> <-10 kPa. Changes in K of the gypsum corresponded well to appliedpressures for —1000 < >J» < —30 kPa, but K values did not noticeablychange for i|» > — 30 kPa. Values of K of the soil corresponded wellto the whole »|» range tested. The new probes accurately measure 0and 41 of soil when soil water content gradually decreases or increases.The newly developed i|»-0 TDR probe requires no more maintenancethan ordinary TDR probes and requires no additional instrumen-tation.

ASOIL WATER characteristic curve—the relationshipbetween water content, 6 (m3 m~3), and matric

potential, \\i (kPa)—is one of the most important param-eters to study water flow in soil. A pressure-plate appa-ratus, combined with the oven-drying soil method, ispopularly used to establish water characteristic curvesin the laboratory. However, in situ determination ofwater characteristic curves is difficult. Measuring soilwater content may be relatively easy in both destructive(e.g., sampling soils) and nondestructive (e.g., TDR,neutron scattering method) manners. Matric potentialof soil is often measured with a tensiometer in situ;however, its measuring range is limited to i|/ > -85 kPa(Cassel and Klute, 1986). Thermocouple psychrometrycan be used for a wide range of \\i but is very sensitiveto temperature changes (Rawlins and Campbell, 1986);thus, it may not be suitable for routine field measure-ments. Measuring water, thermal, or electrical proper-ties of a constructed porous medium equilibrated withsurrounding soil is another attempt to indirectly mea-

K. Noborio and R. Horton, Department of Agronomy, Iowa StateUniversity, Ames, IA 50011-1010; and C.S. Tan, Greenhouse andProcessing Crops Research Centre, Agriculture and Agri-Food Can-ada, Harrow, ON Canada NOR 1GO. Journal Paper no. J-18077 of theIowa Agriculture and Home Economics Experiment Station, Ames,Iowa, Projects no. 3262 and 3287, and supported by Hatch Act andState of Iowa. Received 21 Sept. 1998. Corresponding author(rhorton@iastate.edu).

Published in Soil Sci. Soc. Am. J. 63:1500-1505 (1999).

sure the matric potential of soil. For specific ranges ofwater potential, the heat-dissipation method, the filter-paper method, or the gypsum block electrical-resistancemethod may be used in the laboratory and the field(Campbell and Gee, 1986).

Time domain reflectometry is routinely used to mea-sure water content and electrical conductivity both inthe laboratory and the field (Dalton et al., 1984; Nadleret al., 1991; Noborio et al., 1994; Heimovaara et al.,1995). For simultaneous measurement of 0 and t\i ofsoil with a TDR probe, Baumgartner et al. (1994) andWhalley et al. (1994) attached porous materials func-tioning as tensiometers to the end of hollow electrodesof the TDR probe. However, their probe configurationhas the same constraints as tensiometers, that is, theneed to supply water to tensiometers and the limitedmeasuring range for fy > -85 kPa.

To estimate fy values by measuring the dielectric con-stant, K, or water content of an equilibrated porousmaterial, TDR techniques have been applied to a com-mercial product (e.g., Equitensiometer, Delta-T De-vices, Cambridge, England) and to a TDR probe inceramic discs described by Or and Wraith (1999a).When both 0 and \\i need to be measured, an additionalprobe is required to measure 0. There is a need todevelop a probe that simultaneously measures wideranges of 0 and \\> in situ.

In this paper, we present a design of a new TDRprobe that simultaneously measures 0 and ij*. A portionof the TDR probe is embedded in a porous material,and the rest is inserted into a surrounding soil. Thisunique configuration of the probe enables the simulta-neous measures of K for the porous material and K forthe soil, side by side, in almost the same sampling vol-ume. The new i|j-0 TDR probes are tested in clayloam soil.

MATERIALS AND METHODSProbe Design

The impedance of a transmission line (i.e., a probe) is afunction of the spacing and diameter of rods in addition tothe dielectric constant of the medium in which the probeis installed. If there are differences in impedance along thetransmission line length due to different diameters or spacingof rods being connected in series, one can detect differentreflections in TDR waveforms from the interfaces where thetwo different diameters or spacing of the rods are connected(Davis, 1975; Topp and Davis, 1985). The impedance, Z (fl),for a two-rod type transmission line can be approximated(Kraus, 1984) using Eq. [1]:

Z = (120/K05) \n(s/d) [1]

Abbreviation: TDR, time domain reflectometry.

1500

NOBORIO ET AL.: TDR PROBE FOR SIMULTANEOUS MEASUREMENT OF i\i AND I 1501

where K is the dielectric constant of a material surroundingthe transmission line, s is the spacing of the rods, and d is theradius of the rods.

To distinguish reflections from the interface between differ-ent diameters and spacings of rods, the impedance differencesshould be large enough in a full range of soil water contents,that is, dielectric constants. The two-rod transmission line orprobe consisted of two stainless-steel rods (1.6-mm diam. and25 mm apart) in which a portion was covered with coppertubes with larger outer diameters (3.2-mm diam., 50 mm long,and 5 mm apart) (Fig. 1). The copper tubes were soldered tothe stainless-steel rods at the both ends of the copper tubes.The copper tubes were then embedded in dental plaster (LabPlaster, Bayer Corp., South Bend, IN) following Phene et al.(1971). Lab Plaster's main constituent is gypsum. The powderplaster was mixed with deionized water in a ratio of 47 mLof water to 100 g of the Lab Plaster. The slurry of the plasterwas poured into a plastic cast in which the copper portion ofthe two rods was placed at the center of the cast.

To avoid concentrating the sensing volume around a rod,Knight (1992) and Petersen et al. (1995) suggested that a ratioof rod spacing to rod diameter (d/s) should be >0.02 to 0.1.Our probe design satisfied this criterion inasmuch as the ratioswere 0.064 and 0.64 for the stainless-steel portion and thecopper portion, respectively. Moreover, to avoid influencesof incidents occurring on or near the soil surface on TDRmeasurement, Petersen et al. (1995) found the distance be-tween TDR rods and the surface should be larger than 10,15, and 20 mm for probes with a rod-rod spacing of 10, 20,and 50 mm, respectively. Using Eq. [4] and [5] of Petersen etal. (1995), 8.6-mm-thick gypsum was sufficient to involve98.8% of the total electromagnetic energy. The distance be-tween the copper tubes and the nearest gypsum surface ofour probes was =10 mm. Thus, K measurement of the gypsumwith the configuration shown in Fig. 1 should be accurate, andthe probe should not require a wire screen as did Wraith andBaker (1991) to confine the electromagnetic energy.

According to Eq. [1], the stainless-steel portion of the trans-mission line in dry and wet soil yield Z = 238 ft and 75 ft,respectively, whereas the copper portion in dry and wet gyp-sum results in Z = 58 ft and 25 ft, respectively. The dielectricconstant of dry and wet soil was assumed to be 3 and 30 (Toppet al., 1980), respectively, and that of dry gypsum was assumedto be 5.6 (Curtis and Defandorf, 1929). The dielectric constantof wet gypsum was assumed to be the same as that of wetsoil. The diameters and spacings of rods were selected toprovide distinguishable diffraction of TDR waves at the inter-face between gypsum and soil for all combinations of watercontents of gypsum and soil. A 75-ft coaxial cable (RG-187/A, Alpha Wire, Elizabeth, NJ) was connected to the end ofthe copper tubes. The 75-ft coaxial cable provided a distin-guishable reflection from the beginning of the probe in thefull range of water contents of gypsum, especially when thegypsum was dry. Two i|)-6 TDR probes were constructedand tested.

CalibrationThe \\i-6 TDR probes were embedded in Harps clay loam

(fine-loamy, mixed, superactive, mesic Typic Caliaquoll; 37%sand, 35% silt, and 28% clay) in a pressure-plate apparatus.A layer =1.3 cm thick of air-dried Harps clay loam was placedin a PVC cylinder (15.2-cm diam. and 5.0 cm high) on a pres-sure plate, then two probes were horizontally placed on thesoil. Additional air-dried soil filled gaps between the probesand the cylinder. The extra 1.3-cm thickness of soil coveredthe probes on top. Using Eq. [4] and [5] of Petersen et al.

A-A' section

1.6mmo.d.stainless steel rods

gypsum block24x24x55 mm\

3.2 mm o.d.copper tubes

75 CJ coaxial cableRG-187/A

Fig. 1. Schematic of the i|»-8 TDR probe.

(1995), who modified Knight's work (1992), the 1.3-cm-thicksoil was sufficient to involve 95% of the total electromagneticenergy provided by a TDR cable tester. The soil and theprobes were saturated with deionized water for 1 d and placedin a pressure chamber. Nine different pressures were appliedto the system in a constant temperature room (20°C). Afterthe soil and gypsum were assumed to be equilibrated witheach applied pressure (equilibration times ranged from 2 to16 d), the pressure chamber was opened, and TDR waveformswere collected using a 1502 TDR cable tester (Tektronix Inc.,Beaverton, OR) connected to a 21X datalogger (CampbellScientific, Logan, UT) for control and data storage. AcquiredTDR waveforms were transferred to a computer and analyzedusing a procedure similar to that of Baker and Allmaras (1990).Waveform acquisition from the cable tester was duplicatedfor each pressure applied. Additional soil columns (4.75-cmi.d. and 5 cm high) were placed on the same pressure platefor determining equilibrated soil water content for each ap-plied pressure.

Dielectric constants of gypsum and soil were determined(Baker and Allmaras, 1990) in Eq. [2] as

K = (LJL)2 [2]where K is the dielectric constant of gypsum or soil, La is anapparent probe length on a cable tester (m), and L is a probelength (m). Apparent probe lengths for gypsum and soil wererepresented by Lag and La s, respectively, as in Fig. 2. The TDR-measured dielectric constant, K, of the gypsum was related tomatric potential, <\i (kPa), with an equation (Eq. [3]) similarto that of van Genuchten (1980):

K = Kr + (KS - Kr) [1/(1 + |a i|*|)f [3]where KS and Kr are dielectric constants at saturation and resid-ual water contents, respectively, and a, n, and m are calibration

1502 SOIL SCI. SOC. AM. J., VOL. 63, NOVEMBER-DECEMBER 1999

aH

U

0.8

0.6-

0.4-

0.2-

0.0-

Woo§H .o.2-|Wf-1 -0.4 -

-0.6

vi^-lOOOkPa^.

0.0 0.2 0.4 0.6 0.8 1.0

APPARENT DISTANCE (m)Fig. 2. Examples of TDK waveforms from Probe 1 in a clay loam

soil with different matric potentials. Apparent probe lengths forthe gypsum and the soil are represented by L,,g and /,„, respectively.

constants. The relationship between the TDR-measured di-electric constant, K, and the volumetric water content of soil,9 (m3 m-3), was established (Eq. [4]) (Yu et al., 1997) with:

= a + b K.C [4]where a, b, and c are calibration constants.

In addition, response time of the i|»-6 TDR probe duringdesorption was evaluated in a pressure chamber. The soil andthe probe were saturated with deionized water for 1 d on apressure plate, then placed in a pressure chamber. A 100-kPaexternal pressure was applied, and temporal changes in TDRwaveforms were measured at 1-h to 1-wk intervals. Followingdesorption, deionized water was sprinkled to near saturationon the surface of the same soil and probe. Temporal changesin TDR waveforms were again collected to evaluate responsetime during sorption without applying external pressures.

RESULTS AND DISCUSSIONExamples of waveforms from Probe 1 are shown for

i|j = -10, -100, and -1000 kPa in Fig. 2. Reflectionsfrom the beginning and end of the probe, in additionto the reflection from the interface between gypsumand soil, were consistently distinguishable in the wholepressure range we tested. Waveforms from Probe 2 werevery similar to Probe 1 (data not shown).

Changes in the dielectric constant of the gypsum andthe soil corresponding to external pressures applied areshown in Fig. 3. Dielectric constants of the gypsum andthe soil were determined using Eq. [2] with apparentprobe lengths La,g for the gypsum and Las for the soilas shown in Fig. 2. The observed \\I-K relationship forthe gypsum was almost identical for the two 4<-0 TDRprobes. The \\>-K relationship for the gypsum was estab-lished using Eq. [3] with data from these two probes.Fitted parameters were Kr = 3.158, KS = 21.452, a =0.0207, n = 3.150, and m = 0.228. The correlation coeffi-cient was r2 = 0.998. If the I|J-K relationship for thegypsum differed from soil to soil, it would be necessaryto confine the electromagnetic energy by enclosing thegypsum with a wire screen (e.g., Wraith and Baker,1991). The observed I|/-K for the soil was similar for thetwo probes, but differed by as much as K = 0.85, whichis equivalent to 0 = 0.016 m3 m~3. This difference may

H

<

18U

3[H3

o probe #1probe #2

« - - probe #1X--.. probe #2

10

MATRIC POTENTIAL y (-kPa)Fig. 3. Calibration of the TDR-measured dielectric constant of the

gypsum and the soil against matric potential for the i|i-0 TDRprobes. Bars indicate ± one standard deviation of measurement.For the gypsum, a calibration curve was established with r2 = 0.998using fitted parameters, K, = 3.158, K, = 21.452, a = 0.0207, n =3.150, and m = 0.228.

be within the acceptable error range. Changes in K forthe gypsum were sensitive enough to detect a changefor -1000 < \\> < -30 kPa, but almost insensitive for\\i > -30 kPa. These characteristics of the gypsum usedwere similar to those of the gypsum reported by Bourgetet al. (1958) and those of the ceramic discs used by Orand Wraith (1999a). In contrast, a nylon block (Bourgetet al., 1958) and a porous material used for a heat-dissipation sensor (Reece, 1996) are sensitive at -1 £4* < -100 kPa, but lose sensitivity at i|> > -100 kPa. Aporous material having a semi-log linear relationshipbetween K and \\> in a wide range of matric potential,perhaps 0 to —1500 kPa, may be ideal.

When the 4<-0 TDR probes were embedded in quartzsand for calibration, the gypsum did not respond wellto desorption of the sand (data not shown). Or andWraith (1999a) reported a similar limitation of theirTDR-based matric potential sensor in coarse-texturedsoils. This phenomenon might result from restricted wa-ter flow at the interface between the smooth surface ofa porous sensor material and coarse soils (Gardner,1986). Gardner (1986) suggested coating the porous sen-sor material with diatomaceous earth to reduce this phe-nomenon.

Advantages of 0 measurement using TDR may beextended to the 4>-K calibration of the gypsum becausethere is little effect of temperature and salinity on Kor 0 determination (Topp et al., 1980). Unlike othermethods for measuring fy, such as thermocouple psy-chrometry and the gypsum block-resistance method(Campbell and Gee, 1986), we can expect temperatureindependence in the VJJ-K relationship because Hal-bertsma et al. (1995) reported that a fine-textured soilshowed little effect of temperature on TDR-measured0. Others, however, reported temperature dependencyof K in fine-textured soils (Pepin et al., 1995; Wraithand Or, 1999b). Or and Wraith (1999b) proposed amechanistic model for the temperature dependency ofsoil K. Thus, we may need temperature compensationfor the gypsum, which has tight pore-size distribution,

NOBORIO ET AL.: TDK PROBE FOR SIMULTANEOUS MEASUREMENT OF i|i AND I 1503

grt

a.CD

§

0.6-r

0.5-

0.4-

0.3-

0.2-

0.1 -

0.0

• probe #1o probe #2+ Ren et a). (1999)

- - - - Topp et al. (1980)

6 =-0.0340+0.0458 K0718

r2=0.987

(A)

19

0 5 10 15 20 25 30 35 40DIELECTRIC CONSTANT K

0.3

IOu

0.2-

0.1-

0.0

probe #1probe #2

- conventional

101 102

MATRIC POTENTIAL v (-kPa)Fig. 4. (A) Relationship between TDR-determined dielectric con-

stant and gravimetrically-determined water content. The calibra-tion curve was determined using only the data obtained by Probes1 and 2. (B) Comparison of water characteristic curves for the clayloam determined by the \\i-0 TDR probes with that determinedby the conventional-pressure apparatus.

when the probe is exposed to large temperature differ-ences such as occur in surface soil. Although salinityeffects on TDR-measured K are not completely under-stood (Ren et al., 1999), the \\I-K relationship should beconsistent when the calibration is made under fixedconditions, that is, the gypsum block is always moistenedwith a saturated solution of dissolved gypsum (Gard-ner, 1986).

Hysteresis in the gypsum, however, may influence thecalibration. Tanner and Hanks (1952) and Bourget et al.(1958) found hysteresis when they measured electricalresistance between electrodes in a gypsum block as afunction of matric potential. Although hysteresis be-tween TDR-measured K and 9 was negligible (Topp etal., 1980; Horino and Maruyama, 1993), there may behysteresis between \\> and K in the gypsum because thehysteresis between \\i and 9 in other porous media (e.g.,soil) has been evident (Royer and Vachaud, 1975; Wat-son et al., 1975).

A calibration curve for the clay loam was made byfitting the volumetric water content and the TDR-mea-sured dielectric constant to Eq. [4]. Calibration con-stants were then determined as a = -0.0340, b = 0.0458,and c = 0.718, with r2 = 0.987 (Fig. 4A). The calibrationcurve was determined using data collected by Probes 1

os

i8u

w

50 100 150 200 250 300 350

ELAPSED TIME (h)

35

On<OH

IUU

gw§2nno

§25

ELAPSED TIME (h)Fig. 5. Response time of the dielectric constant of the gypsum and

the soil during (A) desorption from saturation to i|< = -100 kPafollowed by (B) water absorption.

and 2. Water content measured using TDK with Eq. [2]and [4] agreed well with gravimetrically determined 9,for 9 > 0.12 m3 m~3. For 0.05 < 9 < 0.12 m3 irT3,however, TDR overestimated 0. This overestimationmay not be attributed to the special configuration ofour probe design because Ren et al. (1999) reportedthe same trend using a 4-cm long three-rod probe inthe same soil. When the general calibration curve (Toppet al., 1980) was used instead of Eq. [4], the middlerange of water contents was well estimated, but perfor-mance was poor near saturation and in dryer regions(Fig. 4A). Using calibration curves for matric potential(Eq. [3], Fig. 3) and for water content (Eq. [4], Fig. 4A)estimated using the 4»-9 TDR probes, water characteris-tic curves for the clay loam were comparable to thosedetermined by the conventional pressure-plate appara-tus (Fig. 4B). Deviation from the data collected by theconventional method was found at 41 > —20 kPa and-500 < »|i < -200 kPa, due to calibration errors for the\\I-K. relationship of the gypsum and the 9-K relationshipof the clay loam, respectively.

Temporal changes in K for the gypsum and the soilduring desorption and absorption are shown in Fig. 5Aand B, respectively. During desorption at i|> = -100

1504 SOIL SCI. SOC. AM. J., VOL. 63, NOVEMBER-DECEMBER 1999

kPa (Fig. 5A), the soil K started decreasing just afterpressure was applied and reached the first plateau in40 h, then decreased again to the equilibrium value. Thegypsum K increased slightly in the first few hours, thenstarted decreasing as with the soil (similar to Or andWraith, 1999a). The response time of the gypsum duringdesorption corresponded well to that of the soil.

During absorption (Fig. 5B), the soil responded im-mediately, but took about 15 h to equilibrate. The gyp-sum also responded almost immediately and reachedthe first plateau in an hour. The slow response to reachthe true equilibrium following the fast response to reachthe first plateau might result from entrapped air insidethe gypsum block. The trapped air might be released,allowing the gypsum to gradually reach equilibrium.The gypsum also took about 15 h to equilibrate. Theseresponse times for both desorption and absorptionmight be acceptable in the field where i|; gradually de-creases by evapotranspiration and increases by slow wa-ter infiltration. However, ij; measurement under condi-tions of quick changes in water status near the soilsurface due to rain or irrigation may be less reliable.

CONCLUSIONSA new v|j-0 TDR probe that simultaneously measures

matric potential and water content of soil was developedand tested in the laboratory. Like previously reporteddevices using gypsum as a porous medium, our newprobes showed the similar response of \\i changes withan effective range of fy < -30 kPa. Water content mea-sured by these probes agreed with gravimetrically deter-mined 0 using a soil-specific calibration. The responsetime was similar to other devices using gypsum as aporous medium. This new TDR probe can be used tosimultaneously monitor 0 and v|; in the field. More re-search is needed to find (i) ideal porous materials witha wide range of water retention and a fast response to thewater status of the surrounding soil, and (ii) temperatureand hysteresis effects on the K-I|J relationship of theporous materials.

ACKNOWLEDGMENTSThe authors thank Dr. Massimo Sementilli, Windsor, On-

tario, Canada, for providing the sample of dental plaster; Mr.Don Pahlman, Greenhouse and Processing Crops ResearchCentre, Agriculture and Agri-Food Canada, for technical as-sistance; and the Raymond and Mary Baker Trust for finan-cial support.

GARRIDO ET AL.: FIBER OPTIC SENSOR FOR SMALL-SCALE MEASUREMENT OF SOIL WATER CONTENT 1505