WATER RESOURCES RESEARCH, VOL. 36, NO. 4, PAGES 841-849, APRIL 2000 Funneled flow mechanismsin a sloping layered soil: Laboratory investigation M. T. Walter,• J.-S. Kim,2 T. S. Steenhuis, 3 J.-Y. Parlange,3 A. Heilig,3 R. D. Braddock,4 J. S. Selker,5 and J. Boll6 Abstract. Artificial capillarybarriersare beingusedto divert water awayfrom sensitive undergroundregions.Conversely,funneledflow over natural capillarybarriersmay increasethe dangerof groundwatercontaminationby decreasingthe travel time and contactarea. There havebeen relativelyfew experimentalstudiesof capillarybarrier flow patterns.In this study,waterwasapplieduniformlyacrossthe top surfaceof a backlit tilting chamber,1 cm thick, 110 cm high, and 180 cm long, in which a coarsesandlayer wasimbeddedin a fine sand.Beddingslopeand water applicationrateswere varied between 0ø and 12ø and 1 and $ cm h-,• respectively. After attainingsteadystate,matric potentialwasmeasuredalongthe texturalinterface,and photosof dye traceswere taken in order to visualizestreamlines.The funneledflow was characterizedby three discrete regions:an initial capillarydiversion,a breakthroughregion,and a toe diversion.The breakthroughregionconsistedof a significantzone of partial breakthroughwhere the vertical flux into the coarselayer was lessthan the water applicationrate. The lateral distanceof the capillarydiversionwas explainedwell by previouslypublishedrelationships when the water entryvalue at the texturalinterfacewasreplacedby lower, observed matric potentialat whichbreakthroughoccurredat the mostupslopepoint. The lengthof the capillarydiversionwasoverpredictedusingthe air entryvalue.Finally, the toe of the coarselayer had significant,observedeffectson funneledflow patterns,which have previouslyreceivedlittle, if any, attention.The resultsof this studyimply that the slopeof the coarselayer and infiltrationrate will largelygovernthe effectiveness of capillary barriersand that capillarybarriersare lesseffectivethan previouslyassumed. Glasset al., 1989]; and (3) lateral flow, in which the flow of water and solutesis concentratedand moveslaterallyalongan Preferentialflowhasbeenimplicatedin the increasedrate of inclined soil-layer interface. Theoretical understandingand contaminanttransport,particularlypesticides,to groundwater subsequent mathematicaldescriptions of the pertinenthydrau[Steenhuis andParlange,1991;Flury,1996].Preferentialflow is lic mechanismsare critical to anticipating and preventing definedas the unevenmovementof water and solutesthrough groundwaterpollution. This study investigatespreferential porousmedia, typicallysoil, characterizedby regionsof en- flow due to lateral flow. hancedflux suchthat a smallfractionof the mediaparticipates There are two primarymechanicalcategories of lateralflow. in most of the flow. There are a numberof preferentialflow The mostfamiliar categoryis typicallyreferredto as saturated mechanisms: (1) physicalconduitssuchas macropores,struc- interflow [Betsonet al., 1968], subsurfacestorm flow [Hursh, tural cracks, and biopores that provide preferential paths 1936],or throughflow[Kirbyand Chorley,1967]andmayoccur throughwhichwatermaybe rapidlytransmitted[Bouma,1981; where an upper soil region is underlain by a hydraulically Beven,1981;Bevenand Germann,1982]; (2) fingerphenomrestrictivelayer suchas bedrockor a fragipan [Hewlettand ena, in either layered[Hill and Parlange,1972]or nonlayered Hibbert, 1963; Whipkey,1965;Dunne and Black, 1970;Pilgram soils[Tarnaiet al., 1987;Selkeret al., 1992], that arisesfrom et al., 1978;Stagnittiet al., 1986]. Becauseof the low permewetting-frontinstability[Parlangeand Hill, 1976;Hillel, 1987; abilityof the underlyinglayer,water movingverticallythrough a soilprofileis partiallyimpededat the interfacecausingwater •Department of Environmental Science, Universityof Alaska,Ju- to accumulateabovethe restrictivelayer and to flow laterally Beau. The secondmajor category,first shown 2Department of Agricultural Engineering, Chungbuk NationalUni- acrossit (downslope). by Gardner[1960], is commonlynow referred to as funneled versity,Chongju,SouthKorea. 3Department of Agricultural andBiological Engineering, Cornell flow [Kung,1990].Funneledflowis an uniquecategoryof flow University,Ithaca, New York. phenomenareferringto the situationin whicha capillarybar4Environmental Sciences, GriffithUniversity, Nathan,Queensland, rier developsabovea coarselayerwhichunderliesa relatively Australia. et al., 1990].At 5Department of Bioresource Engineering, OregonStateUniversity, fine soil[Miyazaki,1988;Kung,1990;Steenhuis Corvallis. low flows,whenthe matticpotentialat the texturalinterfaceis 6Department of Biological andAgricultural Engineering, University so low that water cannotenter into the coarse,underlyingsoil, of Idaho, Moscow. the capillarybarrier effectivelyrestrictsvertical water flux, Copyright2000 by the AmericanGeophysicalUnion. forcingthe water to movelaterallyalongthe beddinginterface. Capillarybarriershavereceivedincreasedattentionas an apPaper number 1999WR900328. 0043-1397/00/1999 WR900328509.00 plication for isolatingburied wastesfrom hydrologicfluxes 1. Introduction 841 842 WALTER ET AL.: FUNNELED FLOW MECHANISMS IN SLOPING LAYERED SOIL .• Oscillating Dripper 180 cm Unsaturated, ?e Drippers at20 em Intervals Fine Soil Fine Soil Layer HI Tensiometers (spaced at 19 cm intervals) • CapillaryFringe • 1cm Figure 2. Schematicof the experimentalsetup(not to scale). CoaU•sSea•j•lt•da'ye Figure 1. Schematicof the funneledflow systemdividedvertically into three regionsand a graphical representationof deflectionof streamlinesas they passthe boundariesbetween regions.Here tk• is the slopeof the coarselayer. [Morrisand Stormont,1997;Selker,1997].Zaslavskyand Sinai [1981],Mualem[1984],andYehet al. [1985]studiedlateralflow causedby severallayersof fine and coarsesoil. We will focus in this study on the flow over and through capillarybarriers.Three regionsare distinguished (Figure 1): an upper unsaturated,fine soil layer region;a lower unsaturated, coarsesoil region; and, between these two, a tensionsaturatedfine layer or capillaryfringe. The capillaryfringe is wettest near the coarse-fine interface and is drier near the upper edge of the fringe. Becauseof textural differencesbetween the layers,there can be a sharpboundarybetweensoil moisturecontents;that is, thoughthe matric potentialis continuousacrossthe soil layer interface,differencesin pore size distributionsbetweenthe layersresultin discretedifferencesin moisture content. It is commonlyassumedthat the "water entry"suctionvalue [Hillel and Gardner, 1970;Hillel and Baker, 1988] of the underlying coarse layer is a critical parameter for describing and/or predictingflow throughtextural interfaces.The water entryvalue, generallyconsidereda propertyof the underlying soil,wasmeasuredby bothHillel and Gardner[1970]andHillel and Baker [1988]for horizontallayeringas the potentialat the interface coarselayer. The vertical movementof water into the coarse layer is referred to asbreakthrough.Ross[1990] calculatedfor steadystate conditionsthe distanceto where there is no net downslopelateral flow beyondthe point of breakthrough;Pan et al. [1997]simulatedtransientflowthroughslopinglayersand foundthat the flowof wateris directedpartiallyupslopeduring heavyrains.Modeling studiesby Oldenbergand Pruess[1993] and Webb[1997]suggested a partialbreakthroughregionalong the fine-coarseinterface in which, at steadystate, the vertical flux is lessthan the water applicationrate. There is disagreement in thesemodelingstudiesabouthow the flow changesin the partial breakthroughregion. There have been few detailedlaboratorystudieswhere the flow throughand alongthe interfacehavebeenmeasured.The objectiveof thispaperis to givebetter informationon the flow throughand alongthe capillarybarriersunder well-controlled conditions.Specifically,this study(1) qualitativelycharacterizes the funnel flow regimesalong a fine over coarselayer interfaceof finite lengthunderconstantrainfall intensity;(2) describes,explains,and quantifiesthe effects of the rainfall rate and slope on these regimes;and (3) definesmeasured parametersfor quantifyingfunnel flow and breakthrough. after the water started to flow across the interface. It will be referred to as the effectiveinterfacewater entry matric potential. At the texturalinterfaceboth the quantityof flow and matric potentialincreasedownslope.Once the potential increasesto a high enoughvalue,water will startmovingdownwardinto the 2. Materials and Methods Figure 2 is a schematicof the experimentalsetup.Experimentswere performedin a glasschamber180 cm long,110 cm high, and 1 cm thick, backlitwith high-intensityfluorescent light to help visualizethe streamlinesand the distributionof moisturecontent [Glasset al., 1989]. The chamberwas filled with fine sandembeddedwith a 15 cm thick, 160 cm longlayer of coarsesand.Relevantpropertiesof the fine and coarsesand are shownin Table 1. Figure 3 showsthe characteristicmatric potential versussoil moisturerelationshipsfor the two sands. Spatiallyuniformrainfallwasappliedoverthe top of the chamber usinga single,chain-driven,oscillatingdropper.The slope Table 1. PhysicalPropertiesof the SoilsUsed in the Study Saturated Weight of Particle Size Classes,*% Type Fine Coarse *Particle 0.59-0.85 <0.25 0.25- 0.425 0.425- 0.59 7.0 0.6 32.7 20.5 35.8 3.2 6.8 23.6 diameters are in millimeters. 0.85-1.4 4.1 65.8 Bulk Density, Hydraulic Conductivity, g cm-3 cmd- • 1.56 5443.2 11318.4 1.60 WALTER ET AL.: FUNNELED FLOW MECHANISMS 3. -20 -15 -5 0 , •. -50 -45 , Fine Sa'nd - -40 -35 -30 '• },.•k,• Drying -25 -20 ..... -10 0 I 5 0 10 20 30 40 50 60 70 80 90 100 % Saturation Figure 3. 843 Results develop(Plate 1). In most of the experimentsa clear lateral flow regionwithoutwater flowingthroughthe coarselayer formednear the toe of the coarselayer;thiswill be referredto as the toe diversionin the subsequent discussion. Table2 showsthe lengthsof the threeobserved flowregimes for all the experiments, namely,the capillarydiversionlength occurringupslope on the fine-coarseinterface, the breakthrough region length, and the toe diversionwhich occurs downslope on the fine-coarse interface.The lengthof capillary diversionwas measuredfrom the inflectionpoint of the dye trace closestto the upslopeend of the chamberto the point wherethe dyefirstpenetratesinto the coarselayer.Thislength is approximatelythe sameas from the top of the layer to the beginningof the breakthroughregiontakinginto accountthe "rainshadow"at the uppermostend.The breakthrough region wasmeasuredas the total lengthalongthe interfacethrough which breakthroughwas observed.Toe diversionwas measuredasthe distancebetweenthe downslopeendof the breakthroughregionand the toe of the coarselayer. Becausethe locationof the inflectionpoint, near the fine-coarseinterface, of the most uphill dye trace was shiftedfrom experimentto experiment,the total lengthof the three zonesvaried.Espe- .......... AirEntry ----ar -5 SOIL witha flowrateof 120mmd-•, a breakthrough zonedidnot o.W_ett! ng ' " a _.. • -15 LAYERED Plate 1 showsphotographsof the dyed streamlinesfrom representativeexperimentalruns. The coarselayer appears whitein the photographs. Plate 1 showsthe coarselayersloping downhillfrom right to left, exceptof coursefor the three horizontalcases.For all the slopedexperimental runsthe dye traceswere obviouslydiverteddownslope(referredto as capillarydiversion)and,in mostcases,penetratedthe coarselayer at somepoint (breakthrough).Only for the run slopedat 7.1ø -10 -55 IN SLOPING Characteristiccurvesfor the fine soil. ({b•)waschangedbetweenexperiments by tiltingthe chamber on a centeredfulcrum(Figure 2). The matricpotentialalong the interfacewasmeasuredwith ninetensiometers placedat 19 cm increments(Figure 2); one tensiometeris located3 cm from beyondthe end of the toe of the coarselayer. Between experimentalrunsthe chamberwasdraineduntil there wasno waterflowingout of the bottomof the chamber.The drainage period lastedfrom 24 to 72 hours. Combinationsof four slopesand three rainfall rates providednineexperimentalruns(Table2). Eachexperimentalrun was initiated with uniform rainfall until steadystateflow was øand7.1øslopes, achievedand the flow lines did not changeanymore.This ciallyforthe280mmd-• flowrateforthe11.7 typically tookabout48hoursfor a 120mmd- • rainfallrate,24 the uphill dye trace was bent to the left and resultedin a hoursfor rainfallrate of 280 mm d-•, and about12 hoursfor shorterlength.Also, althoughthe flow domain describedin rainfall rate of 680 mm d -•. thisstudyis steadystate,theboundaries betweenbreakthrough Once steadystatewasachieved,the tensiometerswere read, and no breakthroughzoneswere somewhatdifficultto deterand a sequenceof three colors(red, yellow,and green)were minewith highprecisionbecauseof diffusionof the dyetracers simultaneously drippedat a slowrate at the surfaceat 20 cm and the coarsenetworkof dyedstreamlines. A streamlineanalysis wasalsoperformedto better quantify intervals;eachcolorwas appliedtwiceso a total of 120 cm of the soil surfacereceiveddye (Figure 2). With the aid of the the degreeof breakthroughalongthe interface.The distances backlightingand the dye tracesit was simpleto visualizethe between theverticalstreamlines in thefinesoilLI andbetween dyed streamlinesand measurethe different zones. the breakthroughstreamlines in the coarselayerL c weremea- Table 2. The ObservedCharacteristic Lengthsand the Characteristic Parametersof the Funnelandthe Breakthrough Flows Lengthsof the Flow Regimes,cm Run 1 2 3 4 5 6 7 8 9 Slope, Flow Rate, deg mmd- 1 11.7 11.7 7.1 7.1 7.1 3.5 0 0 0 280 680 120 280 680 120 120 280 680 Toe Diversion 16 0 NB 18 9 23 55 25 15 NB indicatesno breakthrough; NA indicatesnot applicable. Breakthrough Capillary Region Diversion 24 95 NB 59 105 70 89 120 130 90 43 NB 54 29 53 0 0 0 Observed •i, cm -9.9 -9.2 NB -9.4 -9.6 no data NA NA NA 844 WALTER ET AL.' FUNNELED -rio w Slope 120 mm day- FLOW MECHANISMS IN SLOPING 280 mm day- LAYERED SOIL 680 mm day- 11.7ø 7.1 ø 3.5 ¸ 0 Plate 1. Photographsof experimentalrunswith dye tracers. sured,asshownin Figure4. Usingcontinuityand basicflow net theory, the ratio of the average leakagepenetratinginto the coarselayerp to the rainfall or infiltrationrate i canbe implied by the ratio of lengthsbetweenverticalstreamlinesin the fine and coarselayers: lines in the fine layer, and L c is the distancebetweenstreamlinespenetratingthe coarselayer (Figure4). Whenp/i = 1.0, the average leakage, or breakthroughflow, is equal to the rainfall rate; this is referred to as complete breakthrough. Figure 5 showsthe p/i ratio along the slope for the three experimentsfor which enough streamline data could be obp/i = Lc/Ll• (1) tainedfor thisanalysis.Eachp/i ratio is plotted at the midpoint wherep is the averageflux penetratingthe coarselayer be- betweenthe two breakthroughstreamlines.As can be seen in tweenthedyedstreamlines, Lf isthedistance betweenstream- Figure5a, therewere insufficientdata to calculatep/i for some WALTER ET AL.: FUNNELED FLOW MECHANISMS IN SLOPING Dye Traces LAYERED SOIL 845 Dye Tracesx '. • Fine Soil .. .. .__C__o?_se_ '::. . " Figure 4. Schematicof dye tracersobservedin the experimentalchamberand lengthsL betweenvarious streamlines. runs;in one run, therewasno breakthroughflow, and in others throughregionsof the horizontalexperimentswas0.99,which there was only one or part of one streamlinein the break- is very closeto 1.00,indicatingfull breakthroughin the entire through. Accordingto these results,of the three analyzed breakthroughlayer. slopedexperiments onlythe 7.1ø, 680 mm d-• run reached The measuredmatric potential along the fine-coarseintercompletebreakthrough;the others apparentlyattained only face for the 11.7ø sloped,7.1ø sloped,and horizontal(0ø) expartial breakthrough;that is, the magnitudeto the break- perimentsas well as the breakthroughregionsin each run throughflow waslessthan the water applicationrate. For the (patternedareas)are shownin Figure 6. The right-handsides 0øslopethe ratio of flow throughthe layerwas approximately of the graphsin Figure 6 correspondto the upslopeend of the 1 (Figure 5b). The averageintegralof p/i acrossthe break- chamberwhichmatchesthe photographsin Plate 1. The position of the coarselayer toe is indicatedby the vertical,dashed lines in Figure 6. The patterned areas in Figure 6 showthe extentof the breakthroughfor eachinfiltrationrate; the light- est area corresponds to the 680 mm d-• experiments, the intermediate areacorresponds withthe280mmd-•, andthe mostdensepatterncorresponds withthe 120mm d-•. In all 1.2 1 0.8 0.6, 0.4 0.2 0 0 20 40 60 80 100 120 140 160 DownslopeDistance Along Interface (cm) . X,• _i=680 ..• 0.8 0.t5. 0.4 o(Horizontal) 0.2.- Slope=0 (b) cases,as expected,the highestcurve (least negativematric potential)corresponds to the highestflow rate, and the lowest curve corresponds to the lowestflow rate. Also, as expected, matric potential increasesin the downslopedirection as divertedwater inducesmoistureaccumulation(Figure6). In the experimentwith the 0ø slope,there are very small differencesin the matric potential alongthe fine-coarseinterfacein the breakthroughzone (Figure6), indicatingthat there is very little sidewaysflow, and thus full breakthroughis expected.This conclusion is corroboratedby the streamlineanalysis presentedbefore, adding credenceto our experimental and streamlineanalysismethods. The matricpotentialsin the breakthroughzone at whichfull breakthroughoccurs(i.e., breakthroughcapacityequals the infiltrationcapacityof the overlyingsand)are nearlyconstant foreachflowrate:½eequals--7.7cmfor680mmd-•; -8.7 cm for 280 mm d-•; -9.5 cm for 120mm d-•. We refer to these potentialsas "the effectiveinterfacewater entry values"be0 I I causethe flow conditionsat full breakthroughare similar to 0 20 40 60 SO 100 120 140 160 thoseoccurringin columnstudiesbyHillel and Gardner[1970]. DownslopeDistanceAlong Interface (cm) The matricpotentialdata in the breakthroughregionfor the Figure 5. Leakageto infiltration ratios,p/i, for six experi- slopedexperimentssuggestthe presenceof a partial break- ments(i is in mmd-•). (a) Slopedcoarselayerexperiments.through. In the sloped experiments,breakthroughoccursat (b) Horizontalcoarselayer. matricpotentialslessthan ½e(Figure 6); for example,for the 846 WALTER ET AL.: FUNNELED FLOW MECHANISMS IN SLOPING LAYERED SOIL Toe ofCoarse Layer Distance Along Interface (cm) _•Downhill -20 20 40 60 80 100 120 140 160 -6.0 -10.0 -12.0 -14.0 -16.0 -18.0 Shaded Areas Show Extent & -20 0 20 40 60 80 100 120 140 160 Location of Breakthrough -6.0 Zones -8.o -lO.O Ii•.•___680 mm day 4 -12.o -14.o 280 mm day 4 -16.o -18.0 ?[•120 mm day 4 -20 0 20 40 60 80 100 120 140 1 i0 -6.0 -lO.O -12.0 -14.0 -16.0 -18.0 Figure 6. Steadystatematricpotentialsalongthe fine-coarse interfaceandlocationof breakthrough regions for eight experimentalruns. 680mmd-•, horizontal experiment, ½eis about-7.7 cm,yet breakthroughregion, which suggeststhat there is a partial in the slopedexperiments with the samewaterapplicationrate, breakthroughoccursat a lowermatricpotential,approximately -9.5 cm. This valuevaried slightlyfrom experimentto experiment (Table 2) but was generallyabout -9.5 cm (standard deviationof 0.3 cm) and is shownby the horizontaldashed lines in Figure 6. This value will be referred to as the initial interfacewater entrymatricpotential½i, at whichthe narrowest pores at the interfaceform a continuousnetwork.Under low flow conditions the effective and initial interface breakthroughregion on both sidesof the complete breakthroughregion.Thoughtherewerenot enoughmeasurements to preciselydefinethe pressuredistributionnearthe toe of the coarselayer, in most experimentsa linear interpolationbetweentensiometers spanningthe downslope edgeof the breakthroughlayer suggests that ½i may be the point for which breakthroughceases(Figure6). water entrymatricpotentialare equal,and the originaldefinitionof Hillel and Gardner[1970]is valid for ½i. Thoughthe matricpotentialdatafor the slopedexperiments suggest completebreakthrough for severalof the runs(Figure 6), regionsof constantmatric potential are only observed amongtwo or three tensiometers.A longer chamberwould haveallowedbetterverificationif the matricpotentialcontours are parallel within the completebreakthroughregions.The observation of breakthroughat matricpotentialslowerthan ½e corroborates the existence of a partialbreakthrough zoneidentifiedin the streamlineanalysis(Figure5). Figure6 showsthat the matric potential dropsnear the downslopeedge of the 4. Discussion The experimentsshowthreefunneledflowregimes:capillary diversion,breakthrough,and toe diversion.Figure 7 is a schematic,basedon the resultsof this study,whichsummarizesthe theoreticalpartition of flow alongan inclinedcoarselayer of finite lengthembeddedin a fine soil.Table 3 summarizesthe importantcharacteristics for each of thesefunneledflow regimes.Dependingupon the conditions,this three-regimedescriptioncan developfully or partially.Kung's[1990]original "funnelflow" wasactuallythe casewherea breakthroughzone doesnot develop.Each of the three flow regimeswill now be discussed separately,startingat the upslopeend. WALTER ET AL.: FUNNELED FLOW MECHANISMS IN SLOPING LAYERED SOIL 847 nfiltratingWater Lateral Capillary Fringe-.x, Lateral --CoarseSoilLayer D wnslopePartial' reaKtnrougn , ' , ' , Ddkwns [ø.,Pe' Pa,rtial .... •reaKtnrougn -• , / ] •._ _ 1oe. I • :•: • :•.• • ,-'• , ' , Upslope Partial ' /$-'B•a•ough Complete Breakthrough _iversionii Breakthrough i -Diversiøn I ! I I I I I I I I ! I I ! XoXa Xe I Xi 0 Figure 7. Schematicof the funneledflow systemdividedlaterally into zonesof flow alongthe coarse-fine interface. Capillary Diversion dry and that water would enter at the water entry value obThe results in Table 2 show that the length of capillary tained from the wetting branch of the water characteristic diversionis inverselyproportionalto the rainfall rate and di- curveof the coarsesoil.In our experimentthe water enteredat rectly proportionalto the inclinationof the coarselayer; that an initial interfacewater entry matric potential ½i - -9.5 cm 4.1. is, a high infiltration rate resultsin a relativelyrapid accumulation of water alongthe fine-coarseinterfaceand thereforea relatively steep increasein matric pressure [Warrick et al., 1997]. A rapid increasein matric pressuretranslatesinto a short distancealong the interfacebefore the matric potential reachesthe initial water entry suction.Steenhuiset al. [1991] extendedwork by Ross[1990]whichmathematicallydescribes the maximumlength of the capillarydiversionLcd, basedon the aboveprinciplesand an exponentialconductivityfunction: (_+0.3cm),whichis obviously differentthanthevaluederived from the wetting curve of the coarsesoil. It is likely that these laboratoryexperimentsrepresentfield conditionsmore realisticallythanthe "verydry" scenarioassumed for (2). Evenwhen the coarselayeris verydry,vapordiffusionwill eventually"wet up" the coarse layer when the fine layer is wet as shown. DiCarlo et al. [1999] found for a similar sharp boundaryin fingeredflow that vaporwould move acrossthe boundarywetting up the dry soil. Thus the assumptionthat the coarsesoil staysdry might not be reasonable.Using the initial interface water entrymatricpotential½i - -9.5 cm, insteadof ½*w, capillarylengthspredictedwith (2) fit the observedlengths with R2 = 0.98 anda standard errorof 10%(Figure8). The whereha is the effectiveair entryvaluefor the finesoil;½*wis mcd• tan(qb•)a-• + -•- (2) the water entryvalue for the soilwater characteristicfunction pointslyingbelowthe 1:1line are verycloseto the line and can of the coarselayer, and a is the coefficientin the conductivity be reasonablyexplainedby experimentalerror. The experifunctionof theformK = Kfsexp(-a½) for ½ < ½*•andK = mental run with a slopeof 7.1ø and water applicationrate of meaning Kfsfor ½ >- ½*w.As shownin Figure3, ha is between-9 and 120mm d-1 (Table2) did not havebreakthrough, - 10cmand½*w = - 5 cm.Thevaluefor a is0.58cm-1.Using that the capillarydiversionwasgreaterthan 140 cm.Equation the capillarydiversion(125 cm), becausethe thesevalues,(2) predictscapillarydiversionlengthswhichare (1) underpredicts 3 to 4 timesgreaterthan thoseobservedin theseexperiments. toe of the coarselayer began to affect the flow before breakIn the derivationof (2) it was assumedthat the soilwasvery throughcommenced. Table 3. Characterizationof the Funnel Flow Zones Along the Inclined Fine-CoarseInterface Location* Flow Regime 0 < x < x, X, • X < Xe xe -< x < x, x, -< x < Xo Xo < x < L capillarydiversion breakthroughregion(partial, upslope) breakthroughregion breakthroughregion(partial, downslope) toe diversion *See Figure 7 for graphicaldetails. Matric Potential ½ 0 < 0, • 0 = 0i • 0 < 0i 0 < ½e ½e 0 < ½e 0, Downslope Lateral Flow Leakage increasing decreasing no flow increasing increasing no breakthrough increasingdownslope constant,completebreakthrough decreasingdownslope no breakthrough 848 WALTER ET AL.: FUNNELED FLOW MECHANISMS IN SLOPING LAYERED SOIL slopeandverylowrainrate(120mm d-j) in whichthe toe o 120 diversionwasenhanced(55 cm) and(2) steepslope(11.7ø)and highrainfallrate(680mmd-j) in whichtherewasnoclearly lOO • 80 20 o data 0 20 40 60 80 100 120 Observed definedtoe diversion.The relative similarityof toe diversion length suggeststhat matric potential gradientsimmediately below the toe may be more significantto the toe diversion mechanismthan slopeor water applicationrate. In Figure 6 the drop in potentialnear the toe is relativelyconstant,corroboratingthe similarityin toe lengths.The relativelylongtoe diversion in the horizontal,120mm d-• run maybe better describedby studyingthe temporal developmentof funneled flow; this type of investigationwas outsidethe focusof this study. Figure 8. Observedcapillary diversionlengthsversuspredictedmaximumlengthsusingthe relationshipfrom Steenhuis 5. et al. [1991]. Conclusions This studydemonstratedfunneledflow and breakthrough flow underlaboratoryconditions.The resultsagreedwell with For the two soilsusedin this experiment,the air entryvalue the theory and providedsomenew insightsinto the mechaof the fine sandha is almostequalto the initial interfacewater nismsinvolved.Three zoneswere experimentallyobservedand entrymatricpotential.The lastterm in (1) is theninsignificant theoreticallyidentified:capillarydiversion,breakthrough,and comparedwith the first term, and (1) resemblesthe relation- toe diversion. ship presentedby Ross[1990]. The equationof Ross[1990] Of particularinterestis the experimentalobservationof an thenalsofitsthedataverywell(R2 -- 0.97, standard errorof initial interfacewater entry matric potential •i, whichdiffers •%). conceptuallyfrom other studies.This value appearsto influence location of the upslopeboundary of the breakthrough 4.2. Breakthrough region as well as, thoughnot as confidently,the downslope As mentionedin section1, once the pressureincreasesto boundary.This is particularlyimportant if previouslyderived initial water entryvalue(•i), waterwill movedownwardinto relationships[e.g.,Ross,1990;Steenhuis et al., 1991]are to be the coarselayerinitiatingbreakthrough.As longasthe leakage usedto predictthe magnitudeof a capillarydiversion.Paraminto the coarselayer is lessthan the vertical flux from above, eterizingsuchrelationshipswith water entry valuesobtained water will accumulatealongthe interface.Once the pressure from soil characteristiccurvesmay lead to grossoverpredicreachesthe effectivewater entryvalue •e, the flowthroughthe tionsin the lengthof capillarydiversion.Unlike the effective coarselayer is equal to the infiltration rate, and there is no interfacewater entrysuction•e, the initial water entrysuction "net" downslopelateral flow eventhoughthe streamlinescon- ½t i appearsto be independentof the flow regime and is likely tinue to be refractedin this region. equalto the matricpotentialat whichthe smallestporesin the The graphof the slopedexperimentsshownin Figure5 is two media form a continuouspath. instructivewhen comparedto p/i ratiosfrom earlier research. Inasmuchas the typestratadescribedin thisstudyoccursin Ross [1990] did not addressthe valuesof p/i in the partial nature,understanding the mechanisms controllingflowaround breakthroughzone alongthe interface.He derivedthe break- it will be invaluableto practicalapplicationsinvolvingpollutant throughlengthfor p/i = 1. By neglectingthe partial break- transport, groundwater recharge, and perhaps subsurface throughzone,he thusoverpredictedthe lengthof the capillary storm flow. It may also help in the designof waste disposal diversion.Webb[1997]showednumericalsimulationresultsin facilities. whichthe capillarydiversion(p/i = 0) transitioninto complete breakthroughwas smoothedinto an "S" curve. The Acknowledgment.Thanksgo to Ole Wendrothand StephenWebb curvesin Figure5 are distinctlydifferentthoughexactlywhy is for their helpful review. currentlyunclearand requiresfurther investigation. 4.3. Toe Diversion References The toe diversionis interestingandwouldnot be expectedin the "infiniteslopinglayer"scenariowhichhasreceivedconsid- Betson,R. P., J.P. Marius, and R. T. Joyce,Detection of saturated interflow in soilswith piezometers,Soil Sci. Soc.Am. Proc., 32, erabletheoreticalattention[Oldenburg andPruess,1993;Webb, 602-604, 1968. 1997].The partialbreakthroughzoneof the toe arisesfrom the Beven, K. J., Kinematic subsurfacestormflow, Water Resour.Res., 17, 1419-1424, 1981. rapid decreasein mattic potential.The mattic potentialalong the interface becomes so low that water cannot enter into the coarselayer. Thoughboth the capillarydiversionand toe diversionare regionsof lateral flow only (and no flow through the coarselayer), the mechanisms governingthe flow are different. As shown in Table 2, there was relatively minimal correlationbetweenrainfall rate or interfaceslope.The toe diversion,the regionbetweenthe toe of the coarselayer and the toe end of the breakthroughregion,wasgenerallyaround 20 cm. The oply exceptions were the extremecasesof (1) no Beven, K. J., and P. Germann, Macroporesand water flow in soils, Water Resour.Res., 18, 1311-1325, 1982. Bouma,J., Commenton: Micro-, meso-,and macroporosityof soils, Soil Sci. Soc.Am. J., 45, 1244-1245, 1981. DiCarlo, D. A., T. W. J. Bauters, C. J. G. Darnault, T. S. Steenhuis, and J.-Y. Parlange,Lateral expansionof preferentialflow pathsin sands,Water Resour.Res., 35, 427-434, 1999. Dunne, T., and R. D. Black,An experimentalinvestigationof runoff predictionin permeablesoils,WaterResour.Res.,6, 478-490, 1970. Flury, M., Experimentalevidenceof transportof pesticidesthrough field soils-A review,J. Environ. Qual., 25, 25-45, 1996. WALTER ET AL.: FUNNELED FLOW MECHANISMS Gardner, W. R., Water movement in soil, film, Wash. State Univ., Pullman, 1960. IN SLOPING LAYERED SOIL 849 Drainagefrom a uniformsoillayeron a hillslope,WaterResour.Res., 22, 631-634, 1986. Steenhuis, T. S.,andJ.-Y. Parlange,Preferentialflowin structuredand sandysoils,in Preferential Flow, editedby T. J. Gish and A. Shirmoverification, Soil Sci., 148, 60-70, 1989. hammadi,pp. 12-21, Am. Soc.Agric. Eng., St. Joseph,Mich., 1991. Hewlett, J. D., and A. R. Hibbert, Moisture and energyconditions Steenhuis,T. S., K.-J. S. Kung, J.-Y. Parlange,J. S. Selker,and X.-X. Chen,Flow regimesin sandysoilswith inclinedlayers,in Proceedings within a slopingsoil massduring drainage,J. Geophys.Res., 68, 1081-1087, 1963. of TenthAnnual HydrologyDays, edited by H. Morel-Seytoux,pp. 78-94, HydrologyDays,Atherton, Calif., 1990. Hill, D. E., andJ.-Y. Parlange,Wettingfront instabilityin layeredsoils, Soil Sci. Soc. Am. J., 36, 697-702, 1972. Steenhuis,T. S., J.-Y. Parlange,and K.-J. S. Kung, Commenton "The Hillel, D., Unstableflowin layeredsoils:A review,Hydrol.Processes, 1, diversioncapacityof capillarybarriers"by BenjaminRoss,Water Glass,R. J., J.-Y. Parlange,andT. S. Steenhuis,Mechanismsfor finger persistence in homogenous, unsaturated,porousmedia:Theoryand 143-147, 1987. Hillel, D., and R. S. Baker, A descriptivetheory of fingeringduring infiltrationin layeredsoils,Soil Sci., 146, 51-56, 1988. Hillel, D., and W. R. Gardner, Measurementsof unsaturatedconduc- tivity and diffusivityby infiltrationthroughan impedinglayer,Soil Sci., 109, 149-153, 1970. Hursh, C. R., Stormwater and absorption,Eos Trans.AGU, 17, 301302, 1936. Resour.Res., 27, 2155-2156, 1991. Tamai, N., A. Aseda, and C. G. Jeevaraj, Fingering in twodimensional,homogeneous,unsaturatedporous media, Soil Sci., 144, 107-112, 1987. Warrick, A. W., P. J. Wierenga, and L. Pan, Downward water flow throughlayersin the vadosezone: Analytical solutionsfor diversions,J. Hydrol.,192, 321-337, 1997. Webb, S. W., Generalizationof Ross'tilted capillarybarrier diversion formulafor differenttwo-phasecharacteristic curves,WaterResour. Kirby, M. J., and R. J. Chorley,Throughflow,overlandflow and eroRes., 33, 1855-1859, 1997. sion,Bull. Int. Assoc.Sci.Hydrol.,12, 5-21, 1967. stormflowfrom forestedwatersheds, Bull. Kung,K.-J.S.,Preferentialflowin a sandyvadosezone,2, Mechanisms Whipkey,R. Z., Subsurface Int. Assoc.Sci.Hydrol.,10, 74-85, 1965. and implications,Geoderma,46, 59-71, 1990. Miyazaki,T., Water flow in unsaturatedsoillayeredslopes,J. Hydrol., Yeh, T.-C., L. W. Gelhar, and A. L. Gurjahr, Stochasticanalysisof 102, 201-214, 1988. unsaturatedflow in heterogeneous soils,2, Observationand applications, Water Resour.Res., 21, 465-471, 1985. Morris, C. E., and J. C. Stormont, Capillary barriers and subtle D Zaslavsky,D., and G. Sinai, Surfacehydrology,3, Causesof lateral covers:Estimatingequivalency, J. Environ.Eng., 123, 3-10, 1997. flow,J. Hydraul.Div. Am. Soc.Civ. Eng., 107, 37-52, 1981. Mualem, Y., Anisotropyof unsaturatedsoils,Soil Sci.Soc.Am. J., 48, 505-509, 1984. Oldenburg,C. M., and K. Pruess,On numericalmodelingof capillary J. Boll, Department of Biologicaland AgriculturalEngineering, Universityof Idaho,Moscow,ID 83844.(jboll@uidaho.edu) R. D. Braddock, Environmental Sciences, Griffith University, Pan,L. H., A. W. Warrick,and P. J. Wierenga,Downwardwater flow throughslopinglayersin the vadosezone: Time-dependence and Nathan, Queensland4111,Australia.(R.Braddock@ens.gu.edu.au) A. Heilig, J.-Y. Parlange,and T. S. Steenhuis,Department of Ageffectof slopelength,J. Hydrol.,199, 36-52, 1997. Parlange,J.-Y., and D. E. Hill, Theoreticalanalysisof wettingfront riculturaland BiologicalEngineering,Cornell University,Ithaca,NY instabilityin soils,Soil Sci., 122, 236-239, •976. 14853.(ah63@cornell.edu; jp58@cornell.edu; tssl@cornell.edu) J.-S.Kim, Departmentof AgriculturalEngineering,ChungbukNaPilgram,D. H., D. D. Huff, and T. D. Steele,A field evaluationof surfacesubsurfacerunoff, 2, Runoff processes, J. Hydrol.,38, 319tional University,Chongju 361-763, South Korea. (jskim@cbucc. 341, 1978. chungbuk.ac.kr) J. S. Selker,Departmentof BioresourceEngineering,OregonState Ross,B., The diversioncapacityof capillarybarriers,WaterResour. Res., 26, 2625-2629, 1990. University,Corvallis,OR 97331.(selkerj@engr.orst.edu) Selker,J. S., Designof interfaceshapefor protectivecapillarybarriers, M. T. Walter, Departmentof EnvironmentalScience,Universityof Water Resour. Res., 33, 259-260, 1997. Alaska,Juneau,AK 99801.(mtw5@cornell.edu) Selker,J. S., J.-Y. Parlange,and T. S. Steenhuis,Wetting front instability in homogenous sandysoilsunder continuousinfiltration,Soil Sci. Soc.Am. J., 56, 1346-1350, 1992. (ReceivedMay 14, 1999;revisedNovember1, 1999; Stagnitti,F., M. B. Parlange,T. S. Steenhuis,and J.-Y. Parlange, acceptedNovember2, 1999.) barriers, Water Resour.Res., 29, 1045-1056, 1993.