IN SITU MEASUREMENT OF THEEFFECTIVE TRANSPORT VOLUME FOR

SOLUTE MOVING THROUGH SOIL

B. E. CLOTHIER,* M. B. KIRKHAM, AND J. E. MCLEAN

AbstractA simple field method for measuring the soil's effectively mobile

water fraction during near-saturated flow is presented. Initial charg-ing of the immobile fraction 0im is achieved by first wetting the soilwith a disk permeameter until steady conditions prevail. The disk isthen removed and rapidly replaced, but now filled with a tracer so-lution. Subsequently after a period of infiltration with tracer (0.1 MKBr), the soil underneath is sampled. The ratio of the measured toapplied concentration, c*/cm, in the samples will be the fraction of thesoil's water that is effectively mobile. We assume that the antecedenttracer concentration is zero, and that the mobile fraction, 6m, is atconcentration cm. Disk permeameters, set at the slightly unsaturatedpotential head >K = ~20 mm, wetted Manawatu fine sandy loam toa water content of 80 = 0.414 m3 at-3. From analysis of the tracerconcentrations measured under the disk, we deduced 6m to be just0.203. This semimobility was in accord with the observed depthwisepenetration of tracer, as well as other measures of mobility previouslyfound by others from longer term leaching studies carried out nearby.

DEEPER THAN expected penetration of surface-ap-plied chemicals in the field, coupled with labo-

ratory observations of tailing in solute breakthroughs,have lead to a reassessment of the description andmodeling of solute transport. To account for thesephenomena, the soil's water has often been thoughtof as comprising two phases, one mobile and the othereffectively immobile. This has led to a rewriting ofthe chemical-transport equation based on the work ofCoats and Smith (1964) where, during steady unsat-urated flow, q (m S"1).

fl 3cm dcin

°m dt + 6imlT -^-«^. Mwhere z is the depth in the soil (m) and t is time (s).

B.E. Clothier, Environmental Physics Section, Dep. of Scientificand Industrial Research (DSIR), Private Bag, Palmerston North,New Zealand; M.B. Kirkham, Evapotranspiration Lab., Dep. ofAgronomy, Kansas State Univ., Manhattan, KS 66506-3801; andJ.E. McLean, Utah Water Research Lab., Utah State Univ., Lo-gan, UT 84322-8200. Contribution from DSIR, Kansas State Univ.,and Utah State Univ. Received 8 July 1991. * Corresponding au-thor.

Published in Soil Sci. Soc. Am. J. 56:733-736 (1992).

Both convection and the dispersion characterized byD (m2 s-1) are considered limited to the mobile frac-tion, 6m (m3 m~3). The concentration of tracer cim (M)in the immobile fraction, 6im (m3 m~3) can be relatedto that in the mobile fraction, cm (A/), by

9 «>£in

dtitn = a(cm - cim) , [2]

where a is a rate constant (s-1). This formulation thenallows more rapid and deeper transmission of non-absorbed solute, as a result of the effective transportvolume, 9m, being less than the water-filled porosity,8.

Laboratory studies with saturated flow through shortcolumns of artifically aggregated soils have revealeda dependence of 6m on various factors such as q andaggregate size (Nkedi-Kizza, et al, 1983). At the fieldscale, however, a significant improvement in the de-scription of solute transport has already been achievedsimply by dividing the soil's 0 into two constant do-mains. One is considered effectively mobile, the otheressentially immobile. Roth et al. (1990) realized goodqualitative agreement between their field data and arandom-walk model of tracer movement through twocomplementary domains. For the more permeable sur-face 0.8 m of their soil, they assumed that only 20%of the transport volume was effectively mobile. Ad-discott's (1977) functional model simply divided thesoil into a mobile depth equivalent of water and aretained fraction. The effective separation between thetwo was simply inferred from the soil's static water-retentivity curve, ty(Q). Despite such modeling efforts,there are few, if any, field techniques for directly andindependently measuring the effective 0m.

Here we describe a simple and rapid means for mea-suring in the field the effective 0m during near-satu-rated flow at i|>0. This can be done simply as part ofa routine procedure that also provides both the soil'snear-saturated hydraulic conductivity, K0, and itssorptivity, 50. If so wished, these measurements couldbe carried out across a range of i|>0 in order to assessthe impact on 0m of certain fractions of the soil's ma-croporosity.

MethodIf we set a disk permeameter (Perroux and White, 1988)

of radius r0 to supply pure water to the soil at potential i|;0,then the soil, initially at 6n, wets to 60 right at the surface,at least for r < r0. Quite rapidly, the flux density out ofthe disk will become steady at q*. Soon thereafter, thespatial fields of both the water content and the pore water

734 SOIL SCI. SOC. AM. J., VOL. 56, MAY-JUNE 1992

velocity immediately under the disk will also become un-changing (Philip, 1986). Thus with this geometry, the rel-atively short period of wetting will be followed by a regimein which the near-disk water contents become steady atQ(r,z). Characteristically there will be little spatial variationin q(r,z), at least in the zone underneath the disk, withinwhich samples will be extracted for determination of 8m.

The method of detecting 9m that we propose here takesadvantage of the simplicity afforded by this spatial andtemporal constancy. Once q* has been realized, the diskcan be removed and the pure water quickly replaced witha solution containing a tracer at concentration cm. The diskcan then be immediately replaced. Subsequently, the tracerwill infiltrate into the soil until the solute has penetratedsome depth below the disk. Finally, when the disk is re-moved, a vertical face can be quickly excavated across adiameter, and a set of soil samples rapidly taken from un-derneath the disk (Fig. 1).

The measured water contents (6) and solute concentra-tions (c*) of the samples will allow partitioning of the solutebetween the mobile and immobile phases:

Disk permeameter

eimcim. [3]

Here we assume that, in the equilibrated region immediatelyunder the disk, the tracer concentration in the mobile phasewill be that supplied by the disk, namely cm. Furthermore,if the tracer is chosen so that none is present in the soilbeforehand, and if a is sufficiently small so that the im-mobile water remains essentially free of tracer at the timeof sampling, then Eq. [3] will reduce to

[4]

This will allow easy determination of the mobile phase frommeasurements of 6 and c*, along with the known cm.

Since we are only interested here in the 6m/0im partition-ing that occurs during near-saturated flow, we use an initialphase of transient wetting with a tracer-free solution to en-sure that, should 6n < 6im, the immobile phase will becomefully charged with tracer-free water as a result of the cap-illary forces that dominate the early-time flow from thedisk. Subsequently then, the tracer solution will only invade6m. The temporary removal of the disk from the soil surfaceto allow rapid refilling with tracer has little impact. Detailedlaboratory experiments and field observations have revealedthat q(t) and fy(r,z) quickly return to the steady values theyhad attained beforehand.

This technique not only provides the effective mobile/immobile ratio prevailing during flow at this »J»0, for appli-cation of standard disk permeameter procedures will alsoyield the soil's S0 and K0. From these properties we caninfer the macroscopic capillary length and time scales offlow (White and Sully, 1987). With further experimentationwe may be able to relate these characteristics to observedvalues of 6m, and so in a macroscopic sense deduce for thefield the kind of relationships Nkedi-Kizza et al. (1983)obtained for artificial media within short columns in thelaboratory.

Field ExperimentsThe three field experiments conducted on Manawatu fine

sandy loam were on bare soil within the 2-m-wide herbicidestrip underneath kiwifruit vines in the Massey UniversityOrchard, near Palmerston North. To deduce 50 and K0, weused the procedure of Smetten and Clothier (1989), whichrelies on measuring the q* emanating from disks of differentradii. We used disks with r0 of 20 and 97.5 mm, althoughwe only sampled under the larger disk. Prior to each ex-periment, we measured the soil's 6n, and then the equilib-

FaceexcavaQ end ofinfiltration

Array ofsamples

Fig. 1. A schematic of the location of the array of samplestaken from underneath the disk permeameter at the end ofinfiltration with a tracer.

rium 90. In all cases, the permeameters were set at thepotential head i[»0 = —20 mm, with the tracer solutionbeing 0.1 M KBr. Across all experiments, from the 24samples taken immediately under the disk, 60 = 0.414 ±0.017. Two initial experiments were conducted at sites within3 m of each other, the first being on drier soil (6n = 0.304± 0.023) than the second (6n = 0.402 ± 0.026). The soilprior to that second experiment had been thoroughly wettedby the 60 mm of rain that fell the preceding night; conse-quently, no small-disk observations were made, since S0would effectively be zero. Here the large-disk q* of 5.4 x10-4 mm s-1 approximately equalled the K0 of 4.9 x 10~4

mm s~ ] measured in Exp. no. 1, as expected. The finalexperiment was carried out about 30 m away, on the some-what dry soil (6n = 0.299 ± 0.024) surrounding a kiwifruitvine that had been covered at ground level to exclude rain-fall. Overall, K0 = 4.4 (± 0.8) x 1Q-4 mm s-1; for thetwo dry cases at 6n = 0.3, S0 = 0.7 (±0.2) x 10-J mmS1/2.

The sampling block used to extract all the samples in-stantaneously comprised thin-walled corers of 6-mm i.d.embedded in an acrylic block and located at 15-mm centers.These were arranged along three concentric rays. The hor-izontal row of seven corers sampled the soil some 10 mmbelow the surface, extending out to the permeameter's rim.A diagonal ray of seven corers and a vertical line of eightsamplers completed the array. Just prior to the final liftingof the disk, five additional samples were removed from thesoil surface along a transect radiating out from the rim.Finally, an additional surface sample was taken from near

NOTES 735

the location of the center of the disk. All soil samples wereplaced in sealed containers and, on immediate return to thelaboratory, their gravimetric water content was determined.Two additional 90-mL samples were drawn from soil closeby. These provided the bulk density, thereby allowing cal-culation of volumetric water contents from the gravimetricdata. To the oven-dried soil samples was added 25 mL ofdistilled water, along with 0.5 mL of ionic-strength bufferof 5 M NaNO3. The samples were then shaken periodicallyand finally allowed to settle overnight. The Br concentra-tion was measured using an Orion 94-35A specific-ion elec-trode and an Orion 94-35A specific-ion electrode and anOrion 701 pH meter (Orion Research, Boston, MA). Theconcentration of the Br in the soil is given in terms of themolarity of the liquid phase.

Results and DiscussionAs already noted, for our determination of 9m dur-

ing near-saturated flow at ty0, the soil was initially wetwith tracer-free water. Once a steady state prevailed,the disk was quickly removed, refilled, and then re-placed. Philip's (1986) linearized analysis of unsteadymultidimensional infiltration can be used to estimatethe arrival of near-steady conditions, and so indicatewhen tracer may be first introduced. Two character-istics times are relevant. The first, tgeom = [r0(90 —9n)/S0]2, represents the impact of the geometry of thewater source of radius r0 relative to the initially one-demensional character of the capillary-dominated flowinto the soil. The other characteristic time, t&av = (SJAT0)2, weights the longer term effect of gravity, relativeto the initial dominance of capillarity. For the firstfield experiment r^eom = 91 400 s, with rgrav muchless at 10 400 s, indicating here the dominance ofgravity over both capillarity and geometry that appearstypical of field soils (White and Sully, 1987). Philip(1986) related the onset time of the steady flux, tq*,to a ratio of these times. His analysis for a surfacehemisphere (Philip, 1986, Fig. 2) suggests here thattq* is of the order of ^rav. The data from Exp. no. 1reveal t* ~ fgrav/2. This moderate accord is not un-reasonable, given experimental errors and the approx-imate analysis of Philip (1986). His analysis nonethelesseasily provides a reckoner of the time after whichtracer may be added during a determination of the 6mpertaining to near-saturated flow.

The periods of prewetting in the three experimentswere 82, 23, and 48 min, respectively. The gxs were1.07 x 10-3, 5.40 x 10-4, and 5.23 x 10~4 mms-1, and the respective depths of KBr infiltration (/*)were 5.7, 15.7, and 10.7 mm.

We restrict our attention to the Br concentration ofthose samples within the disk's radius that we expectto be at equilibrium with the invading solution (Fig.2). Vertically, even in the worst case of the shortestexperiment (no. 1), the front of the invading solutionshould have been past the sampling depth of 10 mm.Here, /* = 5.7 mm, and even if all the water weremobile, 6m = 60 = 0.46 m3 m~3, the invasion frontwould be at 12.5 mm. Furthermore we assume cim =0. For this soil in the field, Tillman et al. (1991)considered a to be 0.005 h.-1. Their model, appliedhere to the worst case of the longest experiment (no.2), suggests that cim under the disk would have risento just 10% of cm.

0.08 -«'

0.06 -

0.04 -

0.02 -

0.00

Manawatu fine sandy loam: FieldDisk permeameters

•"'\ \

' CT

<»-<*

Rim of disk

Expt 1 - •Expt Z - aExpt 3 - a

~-3-50 100 150

Distance from origin, r (mm)200

Fig. 2. Three separate radial transects of the Br concentrationsampled at depth 10 mm following various periods ofinfiltration with 0.1 M KBr at potential head -20 mm. Theorigin was taken as the location of the surface sample, 7mm from the center of the disk permeameter.

Within the rim, the mean values of c*/cm are similarfor each experiment, being 0.45 ± 0.07, 0.48 ±0.09, and 0.52 ± 0.05 (Fig. 2). The grand mean of0.49 (±0.12) suggests that, for this soil at 00 = 0.414m3 m-3, solute is transported through just 9m = 0.203(Eq. [4]). Fractile analysis of all 27 observations re-vealed c*/cm to be normally distributed, the skewnessbeing just -0.29 and the kurtosis 2.12. The fre-quency distribution of the near-saturated 90 was alsofound to be Gaussian, with skewness 0.53 and kur-tosis 2.83. The coefficient of variation in 00 was justone-third that of c*, reflecting the uniformity of un-saturated wetting by the disk. Of note is the lack ofcorrelation between c* and 90, for 24 sample pairs, r2

was just 0.039. In the absence of significant correla-tion, it is thus reasonable to take the average value of6m from £[60 c*/cm] as E[Q0]E[c*]/cm, where E is theexpected value.

Interestingly, there appears a spatial coherency inthe pattern of c*, and so of 9m (Eq. [4]). A charac-teristic length scale of about 25 mm is evident in Fig.2. Fingering can be discounted, for this would be un-likely during the unsaturated flow imposed by this i|>0.Indeed, a degree of spatial uniformity was observedin the beneath-disk values of 00. That pockets of ap-parently immobile water exist on this spatial scale hasramifications for the efficacy of exchange between thetwo domains, which is here represented by a (Eq.[3]). The coarse spatial scale observed here lends sup-port to our assumption of a small a.

Little vertical penetration of tracer was detected,except in the longer term experiment (no. 2) on wetsoil. Here, /* = 15.7 mm of KBr during the 8.1 hthe disk was on the soil. Bromide was seen deeper inthe soil (Fig. 3). Under these wet conditions, little Brmoved beyond the rim of the disk (Fig. 2), confirmingthat flow from the disk was essentially one dimen-sional. If we simply take the overall mean 6m = 0.203,

736 SOIL SCI. SOC. AM. J., VOL. 56, MAY-JUNE 1992

then we would expect, from one-dimensional invasionwith no solute dispersion, to find the Br front at 77.3mm. Indeed, this is close to the independent data shownfor the vertical and diagonal transects in Fig. 3.

From detailed field experimentation with KBr in-filtration into dry Manawatu fine sandy loam, Tillmanet al. (1991) inferred that 0im = 0.18, whereas wefind it to be a similar value, 6im = 0.211. In an evenlonger term experiment during 2 yr with this soil,Snow et al. (1991) studied the movement of KC1 inthe field. Their lysimeter data indicated that, between250 and 550 mm, a 8m of 0.20 would account for thepeak-to-peak passage of the Cl~. Their noisier fielddata from suction cups suggested 0m = 0.1, albeitwith a coefficient of variation >1. Nonetheless, thereis reasonable accord between these values and the valueof 9m that we obtained nearby.

CONCLUSIONSWhereas the current tendency is to use inverse pro-

cedures to deduce the effective 6m (Snow et al., 1991),we have proposed a technique to measure it directlyusing a disk permeameter. We have found that, duringunsaturated flow at <|i0 = -20 mm, Manawatu finesandy loam in the field has an effective 6m = 0.203.Meanwhile the disk permeameter wet the soil to 60 =0.414. That only one-half of the soil's water was ef-fectively mobile is in general agreement with otherlonger term studies that have been carried out on thissoil. This simple technique will hopefully provide ameans of exploring, in the field, the dependence of6m on the characteristics of the flow regime, the prop-erties of the soil, and the invading chemical.

ACKNOWLEDGMENTS

Characteristically, Dr. Dave Scotter of Massey Univer-sity offered both critical comment and enthusiastic support.

:

0.08 J

<S^ ;' 't0 0.06 -

aO

e-S 0.04 -U0C0O

't. 0.02 -en ;

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Manawatu fine sandy loam: FieldDisk permeameter

{''?"V . A¥\ \ * / '\V. 9

> Y, / ',* ' ',\\,#V' / !\ ^̂ \i ' / I Expt 2:

r̂ K ' \ i ' T,LT "1 , i Horiz - eW, 9 ! Diag - D\f, / 1 Vert - ,. )

\ \ / *i v i \^k-e

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fcV-? .̂**- e) 50 100 150 2C

Distance from origin, r (mm)Fig. 3. Three transects of the Br concentration along the

horizontal (Fig. 2), as well as the diagonal and vertical,following 8.1 h of infiltration with 0.1 A/ KBr in Exp. no.2 at potential head — 20 mm.