Reprinrcd from lhe S:úl Scicncc ,"'OCIC/y (?/ America .lournalVolume 66, 110. 6, Nov.-Dec. 2002

(,77 South Segoe Rei., Madison, WI 53711 USA

Soil Water Retention Measurements Using a Combined Tefisiõmeter-CoiledTimeDomain Reflectometry Probe

ABSTRACT

Carlos M, P, Vaz, Jan w. Hopmans." Alvaro Macedo, Luis H. Bassoi, and Oorthe Wildensehild

The ohjcctive 01' the presented study was to develop a single prnbethat ean he used to determine soil water retention curves in bothlaboratory and field conditions, by including a coiled time domainreflectometry (TOR) probe around the porous eup 01' a standardtensiometer. The combined tensiometer-eoiled TOR probe was eon-strucled by wrapping two copper wires (0.8 mm diam. and 35.5 em

long) along a 5-em long porom, cup of a standard tensiometer. Thedielectrie constam 01' live different soils (Osu Flaco Icoarse-loamy,mixed Typic Cryorthod-flne-Ioamy, mixed, mesie Ustollie Haplargid I.Ottawa sand IF-50-siliea sand I.Columbia ICoarse-loamy, mixed, su-peractivc, nonacid, thermic Oxyaquic Xerofluvents I, Lincoln sandyloam (sandy, mixed, thermic Typic Ustitluvents), and a washed sand -SRI30) was measured with the combined tensiometer-coiled TORprohe (coil) as a function of the soil water content (O) and soil watermatric potential (h). The measured dielectric constam (E,.,,;,) as a íunc-tion 01' water content was cmpirically titted with a third-order pol~-nnmial equation, allowing estimation 01'O(h)-cun'es from lhe comhinedtenskuneter-coiled TI>R probe measurcments, with R' values largcrthan 0.98. In additiun, lhe mixing mudei approach, adapted for lhe ten-siomerer-coiled TOR probe, was successful in explaining lhe fune-tional form ofthe coiled TOR data with about 30% ofthe eoiled-TORprobe measurement explained hy the bulk soil dielectric constam. Thisnew TOR development provides in situ soil water retention data fromsimultaneuus soil water matric potenlial and water contenl measure-ments wilhin approximately lhe sarne small soil volume around lhecombined probe, but requires soil specific calibration because of slighldesaturation 01' lhe porous cup 01' lhe tensiometer.

MEASUREMENT or soil water eontent e as a functionof soil water matrie potential h in unsaturated

soils yields the soil water retention curve. A prior iknowledge of this curve is essential in both fundamentaland applied soils rescarch. Severa] mcthods are uscd todetermine the soil watcr retention curve Irorn laboratorvmeasurcrncnts on undisturbed or disturhed soil sarnples(Dane and Hopmans. 2002: Klute. 1996). Favorablemcasurcrnent methods are the hanging water column.thc suction tablc method. and the multistep outflowmcihod using a glass porous pia te and funnel. tensiontable. or pressure cells, respectively.

In the field. a cornbination of severa I methods is gen-erally applied as well. In most experiments though. 11is mcasurcd with a tcnsiometer, connected to a mcr-cllry manomctcr, vacuurn gauge. or prcssure transduccr.whcrcas neutron modcration, garnrnu-ray attcnuation.

C. Vaz and i\. Maccdo, Emhrapu. Auricultur.il lnstrumcnuuion Ccn-ter. 1'.0. Box 741. I356() L)7(}Sao Carlox.Bravil: ,1.W. Hopmans, Dep.of Land, Air ano Watcr Rcsourccs. Hvdrolouv. Univ. o! California.Davis. C A L)5616: L.H. Bassoi. Embrapa. Setllr-Ario Conter. 1'.0. Box23. 563()()-()()(). Petrolina-PE. Brazil: D. Wildensehild. Tcchnical Univ.01' Dcnmark. Bldg. 115. DK-2t;()() Lynghy. Denmark. Rcccived 27Nov. 20()1. "Corrcsponding author (jwhoprnansô'ucdavis.edu).

Publishcd in Soil Sei. Soe. Arn. J. 66:1752-175L) (20()2).

TDR. or gravimetric methods are used to determine thevolumetric water content (Seholl and Hibbert. 1973:Watson et al., 1975; Cheng et al., 1975; Arya et al..1975; Royer and Vaehaud. 1975: Simmons et aI.. 1979:Gardner et al.. 2001). Oisadvantages of field estimationof soil water retention curves are related to the consider-able time effort involved and instrumentation required.and the relatively small range of soil water matric poten-tials that can be measured with a tcnsiorneter (Bruce andLuxmoore, 1986). In addition. h and 8 measurementsgenerally pertain to different soil volumes. making theirinterpretation difficult and uncertain.

More recently. TOR has been used in combinationwith tensiometer and electrical resistance techniques todetermine in situ soil water retention curves. Baumgart-ner et aI. (1994) and Whalley et aI. (1994) cornbined shal-low stainless steel electrodes with a porous stainless steelmaterial in a standard two parallel probe configurationfor sirnultaneous in situ measurement of e and h. Prelim-inary results showed its functionality and effectiveness.but limitations were related to the difference in mea-sured soil volume between e and h measurements 01' thisprobe. Simultaneous measurement of e and h was alsosuggested by Noborio et al. (1999) using a TDR probepartially ernbedded in a porous gypsum block. Assum-ing hydraulic equilibrium between the porous block andthe surrounding soil. bulk soil dielectric-water contentrelationships could be determined after laboratory cali-bration of the porous blocks. Results were promising.but further research is needed to select the ideal porousmaterial with a watcr content sensitivitv over a widerange of h. whereas the response time. temperature. andhysicrcsis effects of the porous material rernain to bcíurthcr investigated. Moreover. lhe prcscnted devclop-ment required rneasurernents of fl and 11 in nearby butseparate soil volumes. ~

A new soil water matric potential sensor was pre-sented by Or and Wraith (1999) that combines porousceramic and plastic ring materiais stacked within a stain-less steel coaxial cage of 17.5 em long. The probe con-sisted of several porous disks with different pore-sizedistrihutions. allowing water eontent sensitivity over awidc range 01' 11. Similar to existing porous hcat dissi-pation and clectrical rcsistancc sensors. thc 11 01' thcsurrounding soil can be deterrnincd uíter laboratorv cali-hration 01' thc porous cornpositc sensor. Thc authorssuggcsicd that pairing 01' standard TOR probos with thisnew scnsor makes possiblc thc in situ dcrcrrnination 01'soil retention curves using conventional TOR instru-mentation.

The development 01' new probo designs (Selkcr ct al..

Abbreviations: h. soil water matric potcnt ial: PVC. poh vinvl chloridc:TDR. time dornain rcflcctomcuy.

1752

VAZ ET AL.: MEASUREMENTS WITH A COMBINED TENSIOMETER-COILED TDR PROBE 1753

1993; Nissen et aI., 1998; Nissen et aI., 1999a) has allowedexciting new applications of the TDR technique in soilstudies because of their miniaturization and combina-tion of TDR with other probes and equipment. Forinstance, Selker et aI. (1993) with their serpentine typeprobe were able to determine the e at the soil surfaceand Nissen et aI. (1999b) studied fingered flow and insta-ble flow phenomena using small coiled TDR probes(1.5 em in length and a 0.36-cm diam.). Vaz and Hop-mans (2001) and Vaz et aI. (2001) combined a coiled-TDR probe with a cone penetrometer to measure thesoil penetration resistance and water content simultane-ously in a soil profile.

The objective of the presented study was to developa single probe that can be used to determine soil waterretention curves in both laboratory and field conditions,by incIuding a coiled TDR probe around the porouscup of a standard tensiometer. The main advantage ofthe presented combined probe design is the sirnultane-ous measurement of e and h at the same spatiallocationwithin approximately the same bulk soil volume aroundthe porous cup. ln addition to a direct calibration ofthe combined probe, an additional objective of thisstudy was to test the mixing model approach of Rothet aI. (1990), using the dielectric data of the combinedtensimeter-coiled TDR probe data.

MATERIALS AND METHODSProbe Design

Details of the combined tensiorneter-coiled TDR probe areshown in Fig. 1. A 50 n coaxial cable was guided along and

Coaxialcable50n

Copper wire(conductor)

PYC pipe

Water

PositionA ~

Epoxy /.IT:. :--..;;.;.J,cover

EE

<'l

Copper wire(ground)

Ceramicporous cup

Position B

$23 mm .~.::::::::::::.Copper

wire$ 0.8 mrn

Porous cup wall(3 mm)

Fig.1. Detailed diagram of the tensiometer-coiled TDR probe.

partially embedded in the outside wall of the polyvinyl chlo-ride (PVC) pipe of the tensiometer, and was soldered at Loca-tion A to two copper wires (0.8 mm in diam. and 35.5 em long).A pair of parallel copper wires (ground and conductor) wascoiled using a 3-mm spacing along a standard 5-cm long porouscup (porosity about 34%, Soil Moisture Equipment, Santa Bar-bara, CA) of the tensiometer and was glued in the cup wallat Position B with epoxy. Copper wires were wrapped in smallgrooves machined into the porous cup to prevent their move-ment during tensiometer installation. Porous cup wall thick-ness was around 3 mm.

Time Domain Retlectometry TheoryTime domain reflectometry is a soil moisture measurement

technique (Topp et aI. 1980) that is based on lhe velocity mea-surement or travei time of electromagnetic (EM) waves alonga wave guide of known length inserted into the soil. The traveitime of TDR (7) is proportional to the square root of the ap-parent bulk dielectric constant of the transmitted medi um (1:),as determined by the following expression:

T= 2L~c

[1]

where L (cm) is the length of the coiled wave guide betweenPositions A and B, and c (3 x 10" m çl) is the speed of lightin vacuum. Since the dielectric constant is highly dependent onmoisture content, travei time measurements can be directlyrelated to bulk soil volumetric water content. Using a coiledwave guide design has a distinct advantage as compared withthe traditional straight wave guide of the TDR. When usinga narrow spacing between the coiled parallel wires, the lengthof the wave guide per unit soil depth is increased therebyimproving the relative precision of the water content measure-ment, whereas the increased length of the transmission linesimproves the accuracy of the travei time measurement fromthe wave forms. Typical waveforms of the tensiorneter-coiledTDR in water, and dry and saturated glass beads (Potters In-dustrial Ltda, Rio de Janeiro, Brazil) are presented in Fig. 2.These were obtained with the tensiometer-TDR probe posi-tioned in the center of a 500-mL beaker filled with distilledwater or glass beads of particle size between 150 and 300 umand a bulk density of 1.55 g cm ". The dielectric constants cal-culated from the travei time measurernents, were 46.6 for wa-

1.0

0.9.•....\:::: 0.8Q)

'13~ 0.7q....;

Q)

o 0.6U\:::: 0.5.9.•....u 0.4Q)

r;:::

~ 0.3

0.2

o 5 10 15 20 25

Time, nsFig.2. Waveforms of the tensiometer-coiled TDR probe in water,

saturated and dry glass beads (particle size = 150-300 j.lm, bulkdensity [p] = 1.55 g cm"),

1754 50lL ser. soe. AM. J .. VOL. 66. NOVEMBER-DECEMBER 20m

ter. Y.3 for dry bcads, and 22.4 for the saturated glass bcads,As is evident Irorn the cxarnplc traces. the wave Iorrns 01'the coiled-TDR probc are clear, allowing precise estimationsof travcl times (T). Thc increascd travel distance using the35.5-cllltranslllission lines is achieved while maintaining exccl-lent depth rcsoluiion 01' lhe TDR mcasurcrncnt bccausc ofthe 3-1ll1ll spacing bctwccn the eoiled transmission wires. Thehigh precision and depth resolution 01' the coiled-TDR designohowever. comes aI lhe expense of a decreased sensitivity of thebulk soil dieleetric constant. as caused by contribution of lheporous cup to the cornposite dielectric constant. decreasinglhe range 01' bulk dielcctric values from soil dryness 10 satura-tion. Moreover. the longer transmission lines may attenuatelhe signal in saline soil environrnents, necessitating shorterlengths under sueh conditions.

Direct Calibration

Direet calibration 01' the tensiorneter-coiled TDR probe(C,ool versus soil water eontent) was carried out in a funnel ap-paratus (Fig. 3) eontaining a glass porous plate (pyrex. 10- 10

15-l1-mpore size. Corning. NY). whieh was in hydraulic contactwit h a hanging water column. While inereasing this watercolumn lcngth. watcr from the soil sarnple drained freely intoa burcttc. with lhe distance between the ccruer of the ceramie01' the tcnsiomerer and lhe drain outlet equal to lhe imposedh. After saturation of the porous plate by adjusting the drainend of the tuhing just above lhe plate. lhe soil was earefullypacked in the Iunnel with lhe cornbined tensiorneter-coiled

Coaxialcables500

ESoN...-,

connectorsto cable

teste r

TD R probe positioned in thc center of the soil sarnplc. Subsc-quent soil saturation was achieved by further elevation of thewater-Iillcd tubing to slightly above the surfaee of thc soil sarn-plc. Using the cornbined tensiometer-TDR probe. the soil waterretention data of five soils were detcrrnined. Thcsc investi-gated soils were a Oso-Flaco fine sand. reported by Hccr amanel aI. (1997) and Eehing and Hopmans (1993). a Ottawa sand(natural quartz sand, 0.1- to O.4-mm partic\e diam .. F-50 silieasand, U.S. Siliea CO.. Berkeley Springs. WY). a Columbia finesandy loam (Coarse-Ioamy. mixed, superactive. nonaeid. ther-mie Oxyaquie Xerofluvents). a Lincoln sandy loam (obtainedfrom the EPA R.S. Kerr Environmental Research Laboratory.Ada. OK), both reported by Liu et aI. (199S). and a washedsand (SRJ30 supreme sand-30. Silica Resources Ine .. Marys-ville, CAl.

Siarting frorn saturation. the h was deereased in steps byincreasing the length of the hanging water eolumn. After hy-draulic equilibrium was established for each step. as indicatedby zero drainage rate, the required TDR. tensiometer. andwater volume measurements were eompleted. Initial suctionincrements were 5 em, but after the soil-air entry value wasexeeeded. suetion steps were inereased to 10 em. The maxi-mum applied suctions were about 80 em for the Oso Fiaeo.Ottawa. and washed SRI. 170 em for the Lincoln soil. and325 em for the Columbia fine sandy loam. The funnel waseovered with perforated PYC film to prevent evaporation.

Dieleetrie measurements were eonducted with a I502C Tek-tronix eable teste r (Tektronix. Inc .. Irvine. CAl connected to

Rubber septum

Water leveI

PVC tube

Sintered glassporous plate

Needle

h

~ =950 mm

BuretteFig.3. Experimental design for determining soil water retention curves with the combined tensiometer-coiled TDR probe.

VAZ ET AL.: MEASUREMENTS WITH A COMBINED TENSIOMETER-COILED TDR PROBE 1755

the serial port of a laptop computer. The winTDR98 software(http://psb.usu.edu/wintdr98 [verified 29 May 2002]) was usedto identify the first and second reflection points of the wave-form and to calculate the dielectric constant (Vaz and Hop-rnans, 2001a). Water content at each step was determinedfrom measured drain water volumes in the burette. The h wasdetermined by adding the height of the water column of thetensiometer (320 mm) to the tensimeter pressure transducer(Soil Measurement Systems lnc., Tucson, AZ) readings, imme-diately below the rubber septum of the tensiometer (Fig. 3).At selected times, the bulk soil dielectric coefficient (Eso;]) wasmeasured with a two-rod 5-cm long conventional-TDR probeas tested in Vaz and Hopmans (2001a), simultaneously withthe combined tensiometer-coiled TDR, h and drainage out-flow readings (Fig. 3). At the end of each experiment, the soilmaterial was oven-dried to determine the saturated watercontent and bulk density (Table 1). Calibration curves wereobtained by fitting the experimental Eco;] data versus watercontent with a third-order polynomial equation.

Testing of Mixing ModelIn addition to the direct calibration, the mixing model ap-

proach (Birchak et al., 1974: Dobson et al., 1985; Roth et al.,1990), adapted to the tensiometer-coiled TDR probe, wastested. However, rather than application of the mixing modelto include ali three soil phases directly, the dielectric constantmeasured with the tensiometer-coiled TDR probe (Eco;]) wasrelated to the soil dielectric constant of the surrounding soil,determined by the conventional probe (Eso;]) and to the dielec-tric constant of the water-filled ceramic cup of the tensiometer(Ecup), according to:

Ego;] (e[h]) = WE~up (h) + (1 - w) E~oi] (e[h]) [2]where w is a weighting factor (O :s w :s 1) that partitions themeasured dielectric constant as determined by the coiled-TDRprobe between contributions from the water-filled porous cup(Ecup) and the bulk soil (Esc,]). Hence, the dielectric constant mea-sured by the tensiometer-coiled TDR probe is a weighted aver-age dielectric constant of the soil (solid particles, water, andair) and the water-filled ceramic porous cup. Since the mixingmodel includes the unknown B-dependency of E,o;], it cannotgenerally used as a substitute for the empirical calibrationcurve, unless the relationship between water content and thesoil's dielectric such as Topp et al.'s (1980) equation is known.

An optimal design of the coiled probe would minimize thecontribution of the cup to the dielectric measurement (orminimize the value of w), thereby maximizing the sensitivityof the coiled probe measurement to bulk e. The exponent nis a shape factor whose value depends on the soi1 particle'sorientation with respect to the applied electric field and mustbe -1 :s n :s + 1 (Roth et al., 1990). However, its physicalsignificance was criticized by Hilhorst et al. (2000). Dielectricconstants Eco;]and Esc;]vary with e and corresponding h, whereasthe value of Ecup depends on the water content of the porous

Table 1. Soil bulk density (p), saturated water content (6",), andporosity (<I» and fitted parameters a and E, (Fig. 6).

p 6~lt <l>t

Soil g em":' em] cm" Ot E,

Oso Flaco 1.53 0.400 0.423 0.46 4.99Ottawa 1.65 0.348 0.377 0.49 5.00SRI 1.60 0.373 0.396 0.49 5.00Colurnbia 1.35 0.485 0.491 0.76 3.63Lincoln 1.72 0.292 0.351 0.76 4.72

t Estirnated frorn outf1ow data.:~Estirnated frorn soil bulk density: <I> = 1 - p/p" where p, = 2.65 g cm",

cup that is controlled by the soil h. The standard porous cupsare manufactured such that the air-entry value (or bubblingpressure) of the porous ceramic cup is larger than 700 em, toprevent entry of air into the tensiometer for h larger (lessnegative) than -700 cm. Hence, in principie, the pores of theporous cup should remain completely water-filled during thedrainage experiment. However, some pores of the ceramiccup may partially drain as suction is applied to the soil (Orand Wraith, 1999), without exceeding its air-entry value. Inaddition, some drainage of the porous cup is facilitated iftrapped air is present in the porous cup. This may occur eventhough no appreciable amounts of air can enter into the tensi-ometer. Consequently, the ceramic cup is characterized by aretention curve. In the conducted drainage experiments, Cem]

was measured with the combined tensiometer-coiled TDRprobe, whereas E,,,,] was determined from dielectric measure-ments with the conventional-TDR probe (two-rod, 5-cm long).

To test the validity of Eq. [2] for the coiled-TDR probe,we must first determine values for Eso;] and Ecup' The dielectricconstant of the bulk soil (Esc;]), as measured with the conven-tional straight TDR probe, can be written in terms of thefractional bulk volume of each three soil phases (solid, gas,and water), according to Dobson et aI. (1985):

Eso;] = [(1 - ~) Es" + (~ - e) E~ + eE~l]/" [3]

where <I> (em' cm ") and e (em:' cm ":') denote the soil porosityand volumetric water content, respectively, and E,,, e, are thedielectric constant of the air and water, respectively, withassumed values of E, = 1.0 and e, = 80. The dielectric constantof the soil solid material Es varies from 3 to 5. depending onits texture, mineralogy, and organic matter content and willbe fitted accordingly. As in the mixing model of Eq. [2], theexponent a depends on the geometry of the soil solid phaseand the soil's orientation with respect to the applied electricfield between the two straight wave guides of the conventionalTDR probe (Roth et al., 1990).

To account for the influence of water potential on the di-electric of the porous cup (Ecup), its relation must be determinedseparately. An additional experiment was conducted to deter-mine Ecup of the water-filled tensiometer-coiled TDR probe,with the porous cup exposed to the dry air of the laboratory.As a result of the evaporation of water on the ceramic porouscup surface, water in the tensiometer will experience suction,which will increase as the cup is continuously exposed to evapo-ration. From simultaneous dielectric measurement of thecoiled cup in air (Eco;].,,,) and tensiometer readings, the follow-ing two-phase mixing model can be formulated:

E~~il.ai, (h) = WE~~p (h) + (1 - w) E~' [4]

where E, is the dielectric constant of air (equal 1), w is theweighting factor, and m is the shape factor with a value likelyto be different than in Eq. [2], but equally constrained toranges of - 1 :s m :s + 1. The weighting factor (w) was assumedequal to the value used in Eq. [2], since the electrical fieldconfiguration can be considered approximately independentof the type of dielectric material surrounding the probe (water,air, or wet soil), and is a property of the prohe design (Knight,1992, Ferre et al, 1998) only.

Dependence of Eco;].,,;, with h was fitted with an equationsimilar to that of van Genuchten (1980):

1'-1

Ecoil·,,;, = E,cs + (Es", - E,cs) C + ~'Yh)p)~ [5]

where E,e, and E<a' are the dielectric constants of the tensiome-ter-coiled TDR probe measured at residual and saturationconditions and 'Y and pare empirical parameters. Hence, after

1756 SOIL SCI. soe. AM. l ..VOL. 66, NOVEMBER-DECEMBER 2002

fitting of C,e" C,at, -y, and p ta the experimental cup-in-air dataand subsequent substitution of Eq. [5) into Eq. [4), ceor can bewritten in terms of the h, and weighting and shape factor para-meters w and m, assuming that s, = 1.0 (Eq. [A 1)). Subse-quently, after fitting Eq. [3) to each soil type, yie!ding soil-specific values of c, and o , Eq, [2) was fitted to ali soilscombined, yielding parameter values for w, n, and m. Thefinal form of the resulting mixing model is Eq. [A2) in the Ap-pendix.

RESULTS AND DISCUSSIONDirect Calibration

Dielectric constant values as measured with the tensi-ometer-coiled TDR (Ccoil) for ali five tested soil materiaisare presented in Fig. 4. Notably at high water contentvalues, Ccoil is smaller than the bulk soil dielectric con-stant at equal water content values, because of the con-tribution of the lower dielectric of the saturated porouscup to the composite or bulk dielectric measurement ofthe coiled TDR probe. However, the opposite is trueat low e values when Ccoil is larger than Csoil. Unexpectedly,the results in Fig. 4 show that the Ccoil is variable for thesame water content among five different soils. As is dem-onstrated later, this soil dependency was caused by theslight desaturation of the porous cup by increasing soilwater suction of the surrounding soil, thereby affectingthe composite dielectric of the coiled TDR probe mea-surement volume that includes the porous cup. Sinceincreasingly finer-textured soils will required increasingsuction to achieve identical e values, the finer-texturedColumbia soil (solid triangles in Fig. 4) had the lowestCcoil value for a given e among ali five soils. This largestsuction causes maximum desaturation of the porous cup.thereby decreasing ccup and Ccoil as compared with theother soils with the same volumetric water content value.

Variation of Ccoil with e for ali soils analyzed suggeststhat the combined tensiometer-coiled TDR probe can

------- -,24 I

o Oso Flaco

• Ottawa r22 * SRl

_0.•. Columbia *20 o Lincoln

~18

ó' • ° .•.•

16 o • e .•.'s 01 ...Jow o. B

14 $~ li-•...12 õP~~;/10 t..~• lJ8 #0.0 0.1 0.2 0.3 0.4 0.5

Soil Water Content , em' cm'Fig. 4. Dieleetric constant measured with the tensiometer-coiled TO R

probe (E'''iI) as a function of the soil water contento

be used to determine e of the soil after soil-specific cali-bration. This was done by fitting the Ccoil and e data witha third-order polynamial equation, using the indepen-dently measured water content data frorn outflow mea-surements. Fitted parameters and correlation coefficientsfor ali soils are presented in Table 2. We conclude thatthe third-order polynomial equation provides excellentfitting af the experimental data with correlation coeffi-cients (R2) between 0.986 and 0.995.

Using the polynomial calibration curves for each soil,water content was estimated frorn the measured Ccoil data,thereby providing soil water retention information whencombined with the independently measured h data.Agreeably, ali predicted retention data were determinedby polynomial fitting to the measured data, and were notindependently obtained. Figure 5 shows the resultinge(h) relationships comparing data with water contentdetermined by the tensiometer-coiled TDR probe (solidsymbols) and by drainage outflow measurements (opensymbols). Measured and estimated retention values aredose, but some deviations are apparent for the OsoFlaco sand in the low water content range, and for theColumbia sail near saturation. Measured saturated wa-ter content values (either by outflow (Table 1) or frorncoiled TDR measurements) in Fig. 4 were lower thanpredicted from porasity calculations (<1> = 1 - pJp"where p, denotes the dry soil bulk density and Ps =2.65 g cm"), likely because of air entrapment.

Mixing Model ValidationDielectric constant data measured with the canven-

tianal-TDR probe as a function of the water contentmeasured by outflow are presented in Fig. 6. The dielec-tric behavior of most soils was similar to the Topp equa-tion (Topp et al., 1980), as indicated by the dashed !ine,indicating that the 5-cm long transmission !ines were suf-ficiently long to yield re!iable e data. However, the di-electric values for the Columbia and Lincoln soils werehigher than for the other soils and the Topp equationfor reasons that are not clear. Fitting Eq. [3] to thesedata provides sail dependent e, and a values, which arepresented in Table 1. Fitted values of c" which dependon soil texture, mineralogy, and organic matter, are in therange found for most mineral soils (3-5). The o-valuesfor Oso Flaco, Ottawa, and SRI (sandy soils) are doseto reported values (approximately 0.5) for various soils(Dobson et al., 1985; Dasberg and Hopmans, 1992; Rothet al., 1992; Panizovsky et aI., 1999; Vaz and Hopmans,2001a.b), but a values for the Columbia and Lincolnloamy soils were much higher than values normally found(a = 0.76). Hilhorst et aI. (2000) attributed these largedeviations in a values to assumptions of Birchak's mix-

Table 2. Third-order polynomial equation coefficients obtainedwith the coiled TDR-probe dielectric data (C,,,;I) for each soi!.

CoelTicients:6 = A + BE",t + CE".,' + DE",;,"'

Soil A B C D R'

Oso Flaco -1.4162 0.4282 -0.0333 0.1)00852 0.988Ottawa -0.7182 0.2285 -0.0151 0.000274 0.995SRI -0.8827 0.2868 -0.0226 0.000605 0.998Columbia -1.3665 0.3992 -0.0257 0.000450 0.986Lincoln -0.1484 0.0044 0.0150 -0.001120 0.993

VAZ ET AL.: MEASUREMENTS WITH A COMBINED TENSIOMETER-COILED TDR PROBE 1757

ing model, neglecting dielectric depolarization as causedby electric field refractions at phase interfaces.

The variation of Ecoil-.", measured by the tensiometer-coiled TDR probe in air, as a function of the h (Fig. 7)

80Oso Flacol

Ottawa ii

I

o

6o 60

70 o

50

40

30

20•......•....•o

r/) 10(J

o .0

0.0 0.1 0.2 0.3 0.4

Soil Water Content ,em3em-3

300 6 Columbia.li.6

~ o Lincoln

a 250 i! 'V SRl~o- 200 L::,ro.- l>..•...

C {1<l) ~.•...o 150 ~~ o ,I-; s<l)

~ 100 o l:t.

~6~ ~ ,- <>~....•

50 T'V ".li.o~~~~~o: l:t.

~ 6

o eo T'V .Ii.t::.

0.0 0.1 0.2 0.3 0.4 0.5

Soil Water Content ,em3em-3

Fig. 5. Comparison of soil water retention curves for Oso Flaco andOttawa (a) and SR', Columbia and Lincoln (b) with water contentmeasured by drainage outflow (open symbols) and after calibrationof the combined tensiometer-coiled TDR probe (solid symbols).

resulted in fitted values for the parameters c,e" Es"" -y.and p (Eq. [5]) equal to 5.716, 8.911, 0.045, and 2.092 re-spectively. As hypothesized earlier, the decrease of themeasured dielectric of the porous cup (Ecoil-"i') was causedby draining pores in the ceramic. Hence, the resultingdrainage curve in Fig. 7 may be characteristic for the pore-size distribution and entrapped air volume of the cup.

Tensiorneter-coiled TDR data (Ecoil) were fitted to Eq.[A2], yielding parameter values of w = 0.687, n = -0.48,and m = 0.34. The weighting factor w indicates the largeinfluence of the probe material (water-saturated ce-ramic porous cup) on the dielectric measurement of thetensiometer-coiled TDR probe. Possibly, the influenceof the geometry of the coiled probe (wire thickness andspacing) may be further investigated to reduce this wvalue, thereby increasing the sensitivity of the tensiorne-ter-coiled TDR probe. Different values for the shapefactor, n (wet soil) and m (air) are expected because itsvalue describes the position of the applied electricalfield relative to the geometry of the surrounding me-dium (Roth et al., 1990). Hilhorst et a!. (2000) proposedthat the shape factor is merely an empirical constant,to account for electric field refractions in the bulk soilthat are not considered in Birchak's mixing model. Vali-dation of the mixing model theory applied to the tensi-ometer-coiled TDR probe was conducted by comparingEcoil predicted with measured Ecoil data (Fig. 8). The linearfit of these data, when combining ali soils, resulted in acorrelation coefficient R2 = 0.83 and a root mean squarederro r RMSE = 0.4. Although the mixing model resultswere relatively poor for the Columbia soil near soil satu-ration, the general results of Fig. 8 validate the appliedmixing model concept for the coiled-TDR probe. Possi-ble errors may be caused by model complexity resultingin a large number of fitted parameters and inadequatesoil-probe contact. Further investigations are proposed

35.--------------------o Oso Flaco

30 • Ottawa I ••

* SRl _..J.li. Columbia • /

25 o Lincoln - //_~ /-Topp J «"20 ó1P -ft /ti ,

.~15 J

co ° ,,-° -6P jl,~0/:_-10 cP ; "

r7'p5

~/

o+-~-.--~~~--~~-.~--~~0.0 0.1 0.2 0.3 0.4 0.5

Soil Water Content, em' em-3

Fig.6. Bulk soil dielectric constant (1'.,;,,;,) as measured with a conven-tional TRD probe (two-rod 5-cm long) as a function of water con-tent as measured by drainage outflow measurements.

1758

9.08.58.07.57.0

1 6.5'õoco

6.05.55.04.54.0

SOIL seI. soe AM. J. VOL. IJÓ.NOVEMBER-DECEMBER 21J1J2

• • • •

• Measured-- Fitted by Eq. [5)

E =5.716res

E =8.911sat

a=0.045y=2.092

10 100- Water Potential, em

Fig.7. Oielectric constant of the tensiometer-coiled TOR probe in air,as a function of the porous cup water potential (or drainage curve).

to improve on the physically based mixing model resultsfor the combined tensiometer-coiled TDR probe.

We agree that soil-specific calibration of the combinedtensiometer-coiled TDR probe as caused by desatura-tion of the tensiometer cup restricts its wide application.Therefore, we are recommending to include a low-con-ductive, water-impermeable epoxy resin in the groovebetween the transmission lines and the porous cup or tolacquer-coat the wires, thereby largely eliminating localdesaturation and reducing the contribution of the por-

25.----------------------------~o Oso

• Ottawa

* SRI.•. Columbia20Q Lincoln

-o~<.) 15:a~c,

'õoco

10

1;1

.•.•. .•.Q. li(• !li

I .•.

. ,~Ecotiprcd. = 3.28 + 0.75E<oilmcas .

r2= 0.83;RMSE = OA

5+---~_,--~---.--~--._~--~5 10 15 20 25

0coil measuredFig. 8. Comparison of measured soil dielectric constant measured us-

ing the combined tensiometer-coiled TOR probe with estimatedvalues using the mixing model approach of Eq, 121.

ous CUpto the composite dielectric constant of the coiledTDR. One may also question the appropriateness of place-ment of the TDR wires in the porous cup. For example,it means that TDR readings are most sensitive to soildisturbance in the bottom of the excavation hole, whereadequate soil-TDR probe contact may be questionable.However, it was our goal to develop a combined sensorthat provides for the coupled measurement of both 8and h within approximately identical soil volumes. More-over, soil contact and soil disturbance problems canmake ali invasive soil measurements questionable. Im-proved alternative designs may provide for fitting thecoaxial cable inside the PVC pipe of the tensiometer.

Although we have shown that the mixing model isvalid, we do not propose adapting the mixing model asa procedure to estimate the coiled probe dielectric con-stant and consequently the water content. Instead, wesuggest using the empirical polynomial fitting approachto estimate water content and soil retention curves be-cause of its direct application, simplicity and accuracy.Application of the mixing model theory to the tensi-ometer-coiled TDR, however, allows a better under-standing of the influence of each specific dielectric (ce-ramic porous cup, water. air, soil) to the bulk dielectricconstant measured with the tensiometer-coiled TDRprobe, thereby providing information on ways to im-prove probe sensitivity.

CONCLUSIONSA combined tensiometer-coiled TDR probe was de-

veloped by wrapping two parallel wires around the po-rous cup of an existing tensiometer. By simply measur-ing the dielectric constant of the soil surrounding theporous cup with a cable teste r simultaneously with thetensiometer readings, both h and 8 are measured forthe same soil volume around the porous cup at the sametime. Directly fitting the coiled-TDR data (Ceoil) to inde-pendently measured water content measurements usinga third-order polynomial equation provided accuratewater content measurements that allowed in situ deter-mination of soil water retention data for ali tested soilsafter calibration, when combined with tensiometer mea-surements. Moreover, the mixing theory was tested forthe combined probe. Although the presented conceptand development was tested for laboratory conditionsonly, we believe that a similar combined probe designcan be equally applicable for estimation of field soilwater retention.

APPENDIX A

Substi (~~O":'( :~.~'~:~)[~:y~,'::hl'o f 'o ,)"

cu,!' (h) 1------------------w

+(w-I)-'-11I

[AI]Subsequent substitution of IA II into Eq. [2]. while using Eq.[3] gives the general form of the mixing model:

VAZ ET AL. MEASUREMENTS WITH A COMBINED TENSIOMETER-COILED TDR PRCl\3E 1759

E",i! (8. h)

+(11' - 1 )]'-'-'"

"+ (1 - IV) [( I - <1» E~' + (<1> - (1) E:: + (11'::l

[A2]Equation IA2) was fitted to the E,,,,]«(1.h) data, after a priorifitting of parameters E,e,' E"". '/, p . E, and a. to yield optimizedparameter values for IV (weighting factor), m and 11 (shapefactor parameters),

ACKNOWLEDGMENTS

We thank Jim Maclntyre and Atac Tuli for technical sup-port in the hanging column experiment. We thank reviewers fortheir excellent comments of an earlier version of the manuscript.This study was funded by FAPESP (98/04740-7), EMBRAPAand the University of Caliíornia. Davis.

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