DIVISION S-l-SOIL PHYSICS

Small Spatial Scale Soil Water Content Measurement with Time-Domain ReflectometryM. Amato and J. T. Ritchie*

ABSTRACTPlants growing on stored soil water often exhibit symptoms of water

deficit even though a relatively large quantity of soil water is availablefor uptake where roots are present in the subsoil. To explore thepossibility that this less effective absorption phenomenon was relatedto nonuniform root distribution or root clumping around soil peds,we examined the suitability of time-domain reflectometry for measuringsoil water content distribution on a small spatial scale. Measurementswere made on clay loam and sandy clay soils with 21-mm-long parallelbalanced transmission lines and compared with gravimetric watercontent measurement. Water content values ranged from oven dry tosaturation. To quantify the error in propagation time measurementusing short transmission lines, measurements were made in air usingrod lengths ranging from 10 to 150 mm. The coefficient of variationwas quite high (2.8-7.3%) for times shorter than 100 ps for air-drysoil. In this case, the technique proved less reliable. For longer times,corresponding to higher water contents, the coefficient of variationwas <3%. A few samples of clay loam soil with water contents >0.29m3 m~ 3 showed excessively high values of dielectric constant. Careshould be taken in data interpretation at high water content for thesemedia. Time-domain reflectometry proved effective in measuring watercontent with the tested transmission line for values >0.07 m3 m~3

Thus, a tool is provided for in situ measurement of spatial variabilityor at a spatial scale compatible with many problems ranging fromthe water uptake of clustered roots to seed germination in the field.

THE DESCRIPTION AND PREDICTION of Soil WatCt mOVC-ment for field conditions that are almost always

heterogeneous in space and time is important (Hamblin,1985). The characterization of the spatial distributionof roots and water movement can provide importantinformation to quantify plant water uptake and to explaindiscrepancies between plant-soil-water model predic-tions and field-scale water measurements (Tardieu andManichon, 1986; Passioura, 1988). However, the studyof small-scale soil water distribution has been limitedby lack of suitable techniques operational at a smallspatial scale. In one dimension, Dunham and Nye (1973),using a thin section (2 mm) technique, determined thegravimetric water content of soil layers as a function ofdistance from a plane of onion (Allium cepa L.) roots.Hsieh et al. (1972) studied the bidimensional water distri-bution around root hairs using a nondestructive gamma-ray technique. Hainsworth and Aylmore (1983) usedcomputer-assisted tomography with x-ray, and Phogatet al. (1991) used dual-source gamma rays for threedimensions. These techniques were developed for labora-tory measurements in containers. Small-scale techniques

M. Amato, Dipartimento di Produzione Vegetale, Universita'della Basili-cata, Potenza, Italy 85100; and J.T. Ritchie, Michigan State Univ., EastLansing, MI 48224. Received 25 Mar. 1993. "Corresponding author(rotman % staff% % cssdept@banyan. msu.edu).

Published in Soil Sci. Soc. Am. J. 59:325-329 (1995).

have not been developed for field monitoring and charac-terization of the soil water content.

Time-domain reflectometry (TDR) is a technique formeasuring the volumetric soil water content that can beused in container studies as well as in the field. It isbased on the determination of the apparent dielectricconstant (Kt) of soil. This quantity is calculated fromthe velocity of propagation of an electromagnetic signalin the frequency range of 1 MHz to 1 GHz along atransmission line in the soil, neglecting losses along theline as reviewed by Topp and Davis (1985). The signalis partially reflected by any discontinuity on the line andis displayed on an oscilloscope screen as a trace withtime units on the independent axis. In some newer instru-ments that use TDR for cable testing, the axis of theoscilloscope displays length instead of time, to help locatefaults along a cable. Lengths are obtained by multiplyingpropagation times by the signal velocity, cvp, where c isthe propagation velocity in vacuum, and vp is a fractionaryvalue mat can be set on the instrument.

Topp et al. (1980) suggested an empirical equation tocalculate the volumetric water content from K^ in mineralsoils. A number of researchers have pointed out limita-tions, advantages, and possible future developments ofthis technique. Among the limitations is the problem thatthe maximum length of the TDR transmission line isdependent on the soil type. In soils with high clay content,signal attenuation may limit the maximum length to <1m, while much longer lines may be used in sandy soils(Topp and Davis, 1985). The use of short transmissionlines for small-scale measurements is limited by theinstrument accuracy because the travel times for smalldistances are short and depend on the line geometry.Topp et al. (1984) reported consistently low values ofTDR-determined volumetric water contents 9T comparedwith gravimetrically measured volumetric 9g when mea-suring water content in the 0- to 50-mm soil layer, using150-mm parallel balanced metal rods partially insertedin the soil.

The aim of this study was to test the performance ofshort transmission lines for TDR measurement of soilwater content. The TDR determinations are based onpropagation time. The error in time measurement wasdetermined for short travel times ranging from 34 to504 ps corresponding to transmission lines between 10to 150 mm in length. Values of 0T were measured intwo soils with 21-mm-long transmission lines and com-pared with 0g.

MATERIALS AND METHODSA Tektronix 1502B cable tester (Tektronix, Beaverton, OR)

was used. Two types of transmission lines were chosen. Oneline was used to study the error in time determination and the

325

326 SOIL SCI. SOC. AM. J., VOL. 59, MARCH-APRIL 1995

other was for soil water content measurements. Both wereparallel balanced lines, consisting of two stainless steel rods,and had the same ratio of rod diameter and distance betweenrods. A balun (impedance transformer Anzac TP 103, Anzac,Burlington, MA) was used to minimize the signal reflectionat the transition point between the coaxial cable connected tothe instrument and the parallel transmission lines.

To evaluate the error in time measurement using shorttransmission lines, propagation times along a transmission lineset in air were measured with the TDR. The transmission lineconsisted of two 5-mm-diameter stainless steel rods partiallyinserted in a styrofoam support with a distance of 50 mmbetween rods. The refraction of the electromagnetic signalvelocity in vacuum (Yp) was set on the instrument at 0.99. Acorrespondence between points on the transmission line andon the oscilloscope trace was established by short-circuiting therods at selected positions. A short-circuit causes a downwarddeviation of the trace (Fig. 1) because it corresponds to areflection with sign change of the propagating signal. Thismakes it possible to easily read its position on the horizontalaxis of the oscilloscope. The transmission line rods weremarked at 10-mm increments up to 150 mm, and at each mark,the guides were short-circuited to determine the correspondingpoint on the oscilloscope trace (Fig. Ib and Ic). Travel timesof the signal between short-circuited points and a zero referencewere determined by dividing the corresponding distance onthe screen by the signal velocity used. The procedure wasreplicated five times per mark.

Two soils were used for water content determination: a clayloam (sand 36.5%, silt 24.1%, and clay 39.4%) and a sandyclay (sand 52.3%, silt 10.6%, and clay 37.1%). Volumetricwater content was determined with the TDR and gravimetricallyon samples prepared as follows for each soil: a 100 by 100mm wooden frame, 21 mm high, was attached to a plasticizedcardboard bottom. The box was filled with sieved soil, carefully

Distance

30

Fig. 1. Time-domain reflectometry (TDR) wavetraces correspondingto: (a) transmission line in air, (b) transmission line in air, short-circuited at Point 0, (c) transmission line in air, short-circuited at30-mm distance from Point 0. AB = TDR coaxial cable; BC =connections to parallel line; CD = parallel transmission line in air;X\ = short-circuited points; dx = corresponding distance on thetrace.

leveled to 21 mm, and covered with plastic wrap to preventevaporation during the measurements. The transmission linesconsisted of two stainless steel syringe needles to 21-mm lengthand inserted 14 mm in a rubber support (Fig. 2). The needleplastic sockets were used for connection with the balun-boardbanana plugs.

The area of soil explored by a transmission line with thegeometry described is a cylinder measuring 21 mm in lengthand 20 mm in diameter (Topp and Davis, 1985). To providea comparison for 9T, the soil around each transmission linewas sampled after each measurement with a plastic sampler(cylinder + piston, Fig. 2) with an inner diameter of 20 mm.After inserting the sampler, the area around it was clearedfrom the soil and the cardboard bottom was cut so that thesoil cylinder sampled could be ejected by pressing the piston.The value for 0g was then determined by weight difference onthe sampled volume after oven drying at 105 °C until constantweight was reached. For each soil box, two measurementswere considered as independent samples. They were takenfrom different locations in the box where TDR probes wereinserted, and subsequently, samples for 0g were taken. Mea-surements were made at soil water contents ranging from ovendry to saturation. The soil bulk density increased when soilswere dry, indicating some shrinkage. Bulk densities rangedfrom 1.15 to 1.45 g cm"3 for the clay loam soil and from1.29 to 1.42 for the sandy clay soil. Samples were discardedif the gravimetric procedure visibly caused problems in volumesampling (loss of soil or excessive compaction). A total of101 measurements for each soil were obtained.

The TDR oscilloscope trace length was determined by settingthe end of trace at the beginning of the rising portion of thecurve. Tangents to the curve were used as shown in Fig. 3,because the reflection at the end of the transmission line wasnot sharp. This was due at least in part to the signal rise timeand could create relatively high inaccuracies in determiningshort trace lengths. The trace length was converted into propa-gation times by dividing it by cvp.

The apparent K^ value of the samples was calculated frompropagation time:

K, = (ct/L,)2 [1]where c = propagation velocity of an electromagnetic signalin vacuum = 3 x 10s m s~', t = propagation time of theelectromagnetic signal in the transmission line (s), and L, =transmission line length (m).

The volumetric water fraction of the soil was calculatedwith the following equation (Topp et al., 1980):

d PLASTIC SOCKETSRUBBER SUPPORT

T21mm ( Lr)

PISTON

CYLINDER

20 mm 'B

Fig. 2. (a) Transmission line for small-scale time-domain reflectometrywater content measurements in soil; (b) soil sampler for gravimetricdeterminations (L, = transmission line length).

AMATO & RITCHIE: MEASURING SOIL WATER CONTENT WITH REFLECTOMETRY 327

Ii

Distance (m)

b) *

o

3.

c)

Distance (m)

Distance Cm)

dJ

e

Distance (m)

Fig. 3. Time-domain reflectometry wavetraces obtained with 21-mm-long transmission lines: (a) in air; (b) in clay-loam soil at Og = 4%;(c) in sandy-clay soil at 8g = 14%; (d) in sandy-clay soil at 8g =21%. The horizontal scale is set at 0.025 m per division. The verticalscale (the reflectance coefficient of the cable delivery system) is setat 92.5 millirho. The cursor (solid vertical line) is positioned at thebeginning of the trace. The end of trace is determined with tangentsto the curve.

0T= -5.3xlO-2 + 2.-5.5xlO-X2+4.3 [2]

This equation satisfactorily expresses the relationship betweenGT and K, for a range of mineral soils (Topp et al., 1980) andwas tested for the same clay loam soil used in this experimentby Amato et al. (1993b) with 150-mm transmission lines.

RESULTS AND DISCUSSIONThe results for propagation time determinations in air

are summarized in Fig. 4. The standard deviation oftime measurements ranged from 3 to 10.2 ps and in-creased with the mean. The coefficient of variation de-creased with increase in length. In the propagation timerange of 100 to 300 ps, corresponding to air dry andsaturation, the coefficient of variation was <3 %. Figure 4also shows the calculated error on the time determination,calculated by Amato et al. (1993a). The accuracy re-ported on the specification information (Tektronix, 1987)

toQ_

600-

500-

400-

300-

200-

100-

0

o Travel TimeA SD * 10a CV * 10

— Absolute Error* 10-- Percent Error*10

-B- -a-B -a- B -Q- n -o- -n-n

0 30 60 90 120 150

Distance on Rods (mm)Fig. 4. Time-domain reflectometry travel time as a function of distance

of marks on transmission line. CV = coefficient of variation (%):SD = standard deviation (ps). Absolute and percentage error arecalculated from data sheet specifications of the Tektronix 1502 Bcable-tester.

corresponds to +2% of the reading for the time baseaccuracy, +1.7 ps for the cursor positioning with vp =0.99 and 0.025 m per screen division, as used in thisexperiment. The absolute error therefore increases withtime, 2.3 to 11.8 ps for travel times of 34 to 505 ps,while the percentage of error decreases (to an asymptoticvalue of 2%). Thus, the overall correspondence betweenthe standard deviation values from actual measurementsand the calculated absolute error is quite good.

Comparison between measured values of OT and 0g areshown in Fig. 5 and 6 for the two soils. The differences 0g- 6T were analyzed with a paired Mest. Good agreementbetween the two methods was found in the clay loamsoil. The overall standard deviation was «0.023 m3

m"3, but in some cases, the deviation between methodsreached values up to «0.05 m3 m~3. The differenceswere not significant using a Mest for P = 0.05. Forsamples at 6g < 0.07 m3 m"3, the standard deviationwas higher than the overall standard deviation, probably

0.7-,

0.6-

0.5-

0.4-

0.3-

0.2-

0.1 -

0.00.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

,-3g m

Fig. 5. Comparison between time-domain reflectometry-determined(61) and gravimetrically determined (6g) volumetric water contentin the clay loam soil.

328 SOIL SCI. SOC. AM. J., VOL. 59, MARCH-APRIL 1995

0.7-n

0.6-

fO 0.5-I£

ro0.4-

t 0.3-

qT 0.2-

0.1 -

0.0

1:1,

O.t) ' 0.1 ' 0.2 0.3 0.4 0.5 0.6 0.7

m^ m~^

Fig. 6. Comparison between time-domain reflectometry-determined(61) and gravimetrically determined (6g) volumetric water contentin the sandy clay soil.

due to the higher percentage of error in time determina-tion, especially for the oven-dry samples. For these lattersamples, the propagation time was between 67 and 84ps, which corresponds to an error of 3.0 to 4.6% (Fig.4). For dry samples, the errors in 0g determination hada higher relative importance than at high water content.The dry soil was quite loose. This may have causedsmall soil losses that were relatively important since thetotal volume sampled was small. The latter source oferror would explain the underestimation of 6g observedfor many samples at the dry end of the curve. In moistsamples (0g > 0.29 m3 m"3), about 30% of the 0T valueswere excessively high (0.14-0.40 m3 m~3 higher than6g). Such discrepancies can only partly be explained bysampling problems that occur in swelling soils at highwater content levels, where small volume sampling maycause considerable compaction. For the rest of the sam-ples at 0g > 0.29 m3 m~3, the standard deviation of thedifference 0g — 0T was comparable with the overallstandard deviation. No excessively high values werereported by Amato et al. (1993b) for the same soil with150-mm transmission lines.

For the sandy clay soil, the overall standard deviationof the difference 0g - 0T was 0.024 m3 m~3, and it washigher for both the dry and the wet end of the range.The excessively high values of 0T recorded for the clayloam soil at high water content were not found. Thus,errors for this soil are attributed to problems in samplingand tune determination. Volume sampling for the gravi-metric determination was made by assuming that TDRexplores a soil cylinder with diameter 1.4 times thedistance between transmission lines. This was based onempirical reports by Topp and Davis (1985). Actualdistribution of the electromagnetic field around the trans-mission line is certainly more complex. Baker and Las-cano (1989) reported that the total region explored islarger than that described above, although the contribu-tion of remote areas is small. This would be a sourceof discrepancies between 0j and 0g in heterogenous waterdistribution, because the two measures would refer todifferent soil volumes. Another source of error, in a

stratified medium, is the nonlinear relation between prop-agation velocity and the dielectric constant (Topp et al.,1982). In most cases, this error is small because it isalmost compensated by the relation between the dielectricconstant and soil water content (Topp et al., 1982).Although the samples for this experiment were preparedto have uniform water content, some spatial variationmay have been caused by slight soil compaction.

There is a lack of information in the literature oncentimeter-scale water content determination with TDR.Topp et al. (1984) obtained consistently low readingsusing TDR with probes inserted 50 mm in the soil. Theirerror was discussed in relation to travel time accuracywith short trace length. However, the consistent biasthey reported suggests a problem of calibration at smallspatial scale. The TDR probes used for the small-scalemeasurements were long, only partly inserted in soil,and tapered. This can cause a higher error in end-of-tracedetermination because of a smoother shape of the signaltrace. The probes used hi our experiment were parallel,of constant diameter, and spaced closer together, allcontributing to higher resolution in the measurementresolution and accuracy (Topp and Davis, 1985). Withthis scale, it is possible to measure in situ the soil watercontent spatial variations caused by such phenomena asnonuniform root distribution in subsoil.

CONCLUSIONSTime-domain reflectometry can be used to nondestruc-

tively determine soil water content on a small spatialscale with the probes described here. With this scale, itis possible to determine in situ the soil water contentspatial variations caused by such phenomena as nonuni-form root distribution in subsoil. The measurements inair and in dry soil showed that transmission times shorterthan 100 ps resulted in high error (4.7% and up). Thisresulted in the technique being less reliable for dry soilthan when the water content is in the intermediate ranges.For water content higher than 0.07 m3 m~3 (wave traveltunes longer than 100 ps) the percentage of error was<3%. In the clay loam soil at 0g > 0.29 m3 m~3, someof the 0T values were excessively higher than expected.This was probably due to errors in determination oflength or in sampling problems.

ACKNOWLEDGMENTSThe authors thank the Inst. for the Study of Agronomical

Problems in the South-National Research Council of Italy(ISPAIM-CNR) for use of the Tektronix cable tester; Dr. S.Pagano from Istituto di Cibernetica CNR Italy and Dr. BrunoOlivieri from the Inst. for the Physics of the Atmosphere (IFA)CNR Italy for useful discussion and suggestions on TDRproblems; and Dr. F. Pierce, Michigan State Univ., for criticalreading of the manuscript.

EVETT ET AL.: MICROLYSIMETER TEMPERATURES AND EVAPORATION 329