Scaling Hydraulic Properties of a Macroporous Soil Binayak P

WATER RESOURCES RESEARCH, VOL. 35, NO. 6, PAGES 1927-1931, JUNE 1999

Scaling hydraulic properties of a macroporous soil Binayak P. Mohanty U.S. SalinityLaboratory, Riverside, California

Abstract. Macroporoussoils exhibit significant differences in their hydraulicproperties for differentpore domains.Multimodal hydraulicfunctions may be usedto describethe characteristicsof multiporositymedia. I investigatedthe usefulnessof scalingto describe the spatialvariability of hydraulicconductivity (K(-h)) functionsof a macroporoussoil in Las Nutrias, New Mexico. Piecewise-continuoushydraulic conductivity functions suitable for macroporoussoils in conjunctionwith a hybrid similarmedia-functional normalization scalingapproach were used.Results showed that gravity-dominatedflow and the related hydraulicconductivity (K(-h)) functionsof the macroporeregion are more readily scalablethan capillary-dominatedflow propertiesof the mesoporeand microporeregions. A possiblereason for this behavioris that gravity-dominatedflow in the larger poresis mostlyinfluenced by the pore diameterwhich remains more uniform as comparedto tortuousmesopores and microporeswith variableneck and body sizesalong the pore length.

1. Introduction set measuredusing disc infiltrometersin an agriculturalfield near Ames, Iowa. In that study the saturated hydraulic con- Near-saturatedhydraulic properties of soil are importantfor ductivity(Ksat) at eachmeasurement location (x) wasfound to predictingwater flow in macroporoussoil. Mohanty et al. be an ideal (physical)scale factor for K, while anotherempir- [1997] showedthe presenceof bimodalhydraulic conductivity ical scalefactor was estimated for h; all K(- h) data couldthen functionsusing disc infiltrometers and multistepoutflow meth- be coalescedto one unimodal Gardner-type function. In this ods with detached soil cores at a field site in Las Nutrias, New paper we will investigatethe suitabilityof scalingschemes for Mexico. New multimodal piecewise-continuousfunctions were bimodal-type piecewise-continuoushydraulic conductivity usedto describethe K(-h) relationshipfor the macroporous functionsof a macroporoussoil in Las Nutrias, New Mexico. soil: g(h)=•k•(h) = •k• (• -(%lhl)•-x[1 [1 + (,ph)np]mp/2+ 2. Experimental Methods p p The data usedin this paper were taken from Mohantyet al. (mp= 1 - 1/rtp) h <- h*•c (1) [1997]. The experimentalfield is a 6-ha commercialagricul- tural farm, situated on an alluvial flood plain of the Rio Knp(h)= K* + K*[e(h-h*)a- 1] h*•: < h -< 0 (2) Grande, near Las Nutrias, New Mexico. The climate is arid to semiarid and has a wide range of temperaturesand rainfall. Knp(h)= K* + K*[e(-h*)a- 1] h>0 (3) The field site consistsprimarily of silty clay loam sediments whereKp is the hydraulicconductivity of thepth capillary- with moderate to poor drainageprope, rties, underlainby fine dominatedflow domain [L T-i], Knpis the hydraulic conduc- sands and with no impeding strata to a depth of about 7 m tivityfor noncapillary-dominatedflow domain [L T-i], h isthe [Natural ResourceConservation Service, 1992]. Surface hori- equilibriumsoil water pressurehead of the bulk soil acrossall zons, however,contained visible root channels,worm holes, andcracks thereby composing a complex network of preferen- flowdomains [L], h*K • h *0 = h * is the criticalor breakpoint soil water pressurehead where flow changesfrom capillary- tial flow paths.Surface infiltration measurementsat 0-, 3-, 5-, 7-, 10-, 13-, 15-, 17-, 20-, 25-, 30-, 60-, and 150-mm soil water dominatedto noncapillary-dominatedflow or vice versa [L], K* isthe hydraulic conductivity corresponding to h * [L T-i], 8 tensionswere made at ninesites in thesummer of 1994,using is a fitting parameterrepresenting effective macroporosity or ponded and tension infiltrometer proceduresas describedby other structural features contributingto noncapillarydomi- Mohantyet al. [1994,1997]. To mi0imizeany site disturbance, natedflow [L-i], ap [L-1] andrip [dimensionless] arefitting the water-supplytower of the tensioninfiltrometer was refilled parameters[van Genuchten, 1980] for pth capillary-dominated duringthe experiment using the procedure of Ankeny [1992]. The siteswere selectedsuch that they representdifferent soil flowdomain, and kp is thesaturated hydraulic conductivity for capillary-dominatedflow domain p subjectedto Ekp = K*[:•L seriesand texturesacross the field.Ankeny [1992] cautioned T-q. that infiltration for tensions below 10 mm should be interpreted carefullybecause of possibleinaccuracies in the applied Shouseand Mohanty [1998] showed the successof a hybrid scalingapproach combining similar media scalingand func- tensiondue to bubbling.As such,we interpreted the infiltra- tional normalizationto coalescea near-saturatedK(-h) data tion rate in this narrow range of tensionsonly in a qualitative manner so as to reveal relative trends near saturation. The data This paperis not subjectto U.S. copyright.Published in 1999by the were used to developpiecewise-continuous hydraulic conduc- American GeophysicalUnion. tivity functionswhose fitting parameterscould be further ad- Paper number 1999WR900050. justed duringmodel calibration[Mohanty et al., 1997].For the

1927 1928 MOHANTY: TECHNICAL NOTE

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Figure 1. Raw hydraulicconductivity K(h) of the Las Nutrias field site measuredusing a discinfiltrometer and the multistepoutflow method; (a) semilogscale and (b) log-logscale. above intensive infiltrometer measurements we used thin tively. Similar to our approachin the field, we were mostly layers(1-2 mm) of 40 to 60-meshcontact sand (minimum K - interested in relative trends rather than absolute values of the 48.81m d-•) to minimizeany interfacial effect of the sandon retention data near saturation.While the actual numbersmay the infiltration rate close to saturationas reported by Evens be imprecise,they couldbe adjustedby subsequentcalibration and Kanwar [1993]. The actual tensionsat the soil surfaceas of selectedparameters in the piecewise-continuousretention reportedhere were estimatedby assumingunit-gradient water functionso as to better representthe flow scenarioat the field flow through the sandlayer and by reducingthe tensionat the site [Mohantyet al., 1997]. For this purpose the in situ and baseof the infiltrometerwith the averagesand depth. laboratoryexperiments were carried out as carefullyas possi- Following the surface infiltration measurements,50-mm- ble usingvery small incrementsin the tensionnear saturation. diameterand 50-mm-longundisturbed s0il coreswere col- The K(h) data from all the three methodswere subsequently lected directlybelow the discfrom the same nine sitesrepre- superimposedfor the scalinganalysis. sentingdifferent soil seriesand texturesacross the field. The soil coreswere subsequentlyused for measuringwater retention and hydraulicconductivity data over a wider range (0 to 3. Scaling Analysis 1700-mm at 100-mm increments)of soil water tensions.The Scalingmethods in soil scienceinclude dimensional analysis, laboratorymethod of Richards[1965] and the multistepout- inspectionalanalysis, and functionalnormalization [Tillorson flow approachof Gardner[1956] were usedfor measuringsoil and Nielsen, 1984]. Miller and Miller [19•6] introduced the water retention and hydrauliccoqductivity functions, respec- concept of geo.metricsimilitude and similar media scaling MOHANTY: TECHNICAL NOTE 1929

100 >, 10'4 Gravity-dominatedFlow:• e• Flow '• 10• •-•,•,•.. Capillsry-dominated

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10~2 104 10ø 10• 102 103 104 Soil Water PressureHead (-mm) Figure 2. ScaledK(h) after usingK scalefactors (Ksat.•).

basedon a characteristiclength scale that is relatedto particle h _< -30 mm size and pore dimensionin a particular geometricarrange- ment. Hopmarts[1987] and Vogelet al. [1991] compareddif- K(h) = K* + K*[e (h+3ø)•- 1] -30 mm < h -< 0 ferent methodsto scale soil hydraulicproperties. Jarvis and Messing[1995] used a two-lineexponential model to describe K(h) = K* + K*[e (3ø)a- 1] h > 0 (6) and scalethe K(-h) relationshipof a macropore-mesopore system.More recently,Shouse and Mohanty [1998] scaled the whereK* = 0.00555 mm s-•, • = 0.0015mm-•; n = 1.80; near-saturatedK(h) using a hybrid schemeof similar media m = 0.444; and & - 0.098mm •-•. As givenby Shouseand scalingand functionalnormalization. Ksa t was usedas a (phys- Mohanty[1998], Ksawc at anypositionx in the fieldwas used to ical) scalefactor for K, while an empiricalscale factor (a) was scaleK x for the entire tensionrange (0-1700 mm). This was used for h. The saturatedhydraulic conductivity was used to repeatedfor ail measurement locations. Before conducting any reduce gravity-dominated macropore flow variability, if scalingfor h, we examined the scaledK for inherent charac- present,near saturationbecause of soil structuralfeatures that teristicsassociated with the bimodal-typehydraulic conductiv- have little or no influence on water flow under unsaturated ity functions.The translationof the raw K data (Figure 1) to conditions[Mohanty et al., 1996,1997]. For the near-saturated relative or scaledK data (Figure 2) showedtwo important K the similarmedia concept is not necessarilylimited to geo- features:(1) K between0 and -30-mm soilwater pressure metricalsimilarity as givenby Miller and Miller [1956]but may head(gravity-dominated flow region) showed better coalescing be more of a combinationof dynamic,kinematic, and geomet- behavioras compared to K below -30-mm soilwater pressure ric similarityrepresented by Ksa t [Shouseand Mohanty, 1998]. head (capillary-dominatedflow region),and (2) Ksat•c wasa Dynamicsimilarity refers to the force (e.g.,gravitational, cap- suitableand effectivephysical scale factor for K near satura- illary, adsorptive,and viscous)relationships between different tion, consistentwith observationsby Shouseand Mohanty soilpore systems.Kinematic similarity represents relationships [1998].In the individualflow regions(gravity-dominated flow betweenmotions (e.g., progress of a wettingfront with time or (h > -30 mm) and Capillary-dominatedflow (h < -30 mm)), depth) in different soil systems.Geometrical similarity ac- paired[Krel(h), h ]i= •,... ,N,x=•,-.. ,X datapoints were sub- countsfor size(e.g., particle dimensions, pore dimensions,and sequentlyscaled to the reference curve using functional nor- tortuosity)relationships between the soil systems. malizationof h [Tillotsonand Nielsen, 1984]. Following Shouse At the field site, soil hydraulicconductivities measured with and Mohanty[1998], the (empirical)scale factor/3 x for a cer- a discinfiltrometer between 0 and -30-mm soilwater pressure tain infiltrationsequence at sitex consistingof N data points head were found to be, at all measurement locatiohs, several (i.e., tensionsteps) was then found by minimizingthe sum-of- ordersof magnitudehigher than the hydraulicconductivity at squareddifferences (SS) between the referencerelative hy- -30-mm soilwater pressurehead thus indicating an approxi- draulicconductivity curves and the scaleddata pointsfor each mate matching point between the gravity-dominatedmacro- flow region (p): pore flow region and the capillarity-dominatedmatrix flow i=N region(Figures la and lb). An arbitrarilyselected (K, h) data set was used to define the reference model for the bimodal SS= • [j•xhi-h•ef] 2 (7) i=1 piecewise-continuousformulation, that is, .ref (1 - (-Ihl)"-'[1 + (alhl)"]-m)2 J,x i = 1,- -., N Vx (8) K(h): K* [1+ (clhl)"]m/2 (4) h i,x 1930 MOHANTY: TECHNICAL NOTE

10o

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] i=N K(-h) curvesfor the biporoussoil system;the hybridscaling 13x= • • 13,,x Vx (9) approachappears quite adequatein representingthe hydraulic i=1 conductivityvariability of the gravity-dominatedflow region Once13x,(p ) for a spatiallocation (x) wasknown, scaled (h > -30 mm) acrossthe studyarea. However, as given by Jury h ,*',x( = 13x,(p)h i,x) values were calculated for all tension steps et al. [1987],in the capillary-dominatedflow region(h < -30 (i = 1,---, N) in the flow region(p). Figure 3 showsthe scaled mm), furtherscaling of K is necessary(results not shownhere).

Arrangementsof Particies and Pores in a BiporousSoil System

Micropores

...... -......

......

Water MoleculesMoving in Macroporesand Micropores Figure 4. Typicalsoil particle and pore arrangementsand flow pathstaken by water moleculesin a biporous media. Open and solid circlesindicate water particlesat time to and t•, respectively. MOHANTY: TECHNICAL NOTE 1931

4. Discussion edited by G. C. Topp, W. D. Reynold, and R. E. Green, SSSASpec. Publ., 30, 123-141, 1992. Water flows through different pore groups (e.g., macro- Everts, C. J., and R. S. Kanwar, Interpreting tension-infiltrometerdata pores,mesopores, and micropores)in soil. Different physical for quantifying soil macropores: Some practical considerations, forces(e.g., gravity,capillarity, and absorption)dominate the Trans. ASAE, 36, 423-428, 1993. Gardner, W. R., Calculation of capillary conductivitiyfrom pressure flow processfor different pore groups.For example, gravity plate outflow data, Soil Sci. Soc.Am. Proc., 20, 317-320, 1956. may dominatethe flow processin the larger pores(or macro- Hopmans,J. W., A comparisonof variousmethods to scalesoil hy- pores),whereas capillary forces dominate the flow processin draulic properties,J. Hydrol., 93, 241-256, 1987. mesoporesand micropores.In this paper, pore region includ- Jarvis,N.J., and I. Messing,Near saturatedhydraulic conductivity in ing mesoporesand microporesis loosely defined as micro- soilsof contrastingtexture measuredby tensioninfiltrometers, Soil Sci. Soc. Am. J., 59, 27-34, 1995. pores.Because of differencesin the governingforces, hydraulic Jury, W. A., D. Russo,and G. Sposito,The spatialvariability of water conductivityincreases/decreases several orders of magnitude and solutetransport properties in unsaturatedsoil, II, Scalingmod- acrossone or more thresholdsoil water pressurehead(s) sep- els of water transport,Hilgardia, 55, 33-56, 1987. arating different flow regions.At the Las Nutrias field site the Loague, K, and R. E. Green, Statisticaland graphical methodsfor evaulatingsolute transport models: Overview and application,J. thresholdsoil water pressurehead between the two different Contam. Hydrol., 7, 51-73, 1991. flow regionswas approximately-30 min. K in the fast flow Miller, E. E., and R. D. Miller, Physical theory for capillary flow region(0 mm > h > -30 ram) showeda consistentpattern at phenomena,J. Appl. Phys.,27, 324-332, 1956. all measurementlocations with a proportionaleffect across the Mohanty,B. P., M.D. Ankeny, R. Horton, and R. S. Kanwar, Spatial field. The proportional effect could be scaledto a reference analysisof hydraulicconductivity measured using disc infiltrometers, Water Resour. Res., 30, 2489-2498, 1994. K(-h) curveby usingKsa t as the scalefactor for K and an Mohanty, B. P., R. Horton, and M.D. Ankeny, Infiltration and macro- empiricalh-scale factor (/3). In additionto Ksat and/3, K(h) in porosityunder a row crop agriculturalfield in a glacialtill soil, Soil the capillaryflow region(h < -30 mm) requiresfurther scal- Sci., 161,205-213, 1996. ing of K to coalesceall data to the referenceK(-h) curve. Mohanty, B. P., R. S. Bowman, J. M. H. Hendrickx, and M. T. van Genuchten,New piecewise-continuoushydraulic functions for mod- Scalingreduced the root mean square error (as defined by eling preferentialflow in an intermittent-flood-irrigatedfield, Water Loagueand Green [1991]) betweenthe data (raw or scaled) Resour. Res., 33, 2049-2063, 1997. and the referencemodel by more than 95% in the fast flow Natural ResourceConservation Service, Soil surveymap of Las Nu- region (0 mm > h > -30 mm) as comparedto 36% in the trias, New Mexico, report, Lincoln, Nebr., 1992. capillaryflow region(h -< -30 ram). This resultindicates that Richards,L. A., Physicalcondition of water in soil, in Methodsof Soil Analysis,Part 1, Agron.Monogr., vol. 9, edited by C. A. Black et al., gravity-dominatedflow and related hydraulicfunctions for the pp. 128-152, Am. Soc. of Agron., Madison, Wis., 1965. macroporeregion are more readilyscalable (i.e., no extra em- Shouse,P. J., and B. P. Mohanty, Scalingof near-saturatedhydraulic piricalK-scale factor of Juryet al. [1987] is needed) than cap- conductivitymeasured using disc infiltrometers, Water Resour. Res., illary-dominatedflow properties associatedwith the micro- 34, 1195-1205, 1998. Tillotson, P.M., and D. R. Nielsen, Scale Factors in soil science,Soil pores.We speculatethat one possiblereason for this behavior Sci. Soc. Am. J., 48, 953-959, 1984. is the fact that gravity-dominatedflow in larger poresis mostly van Genuchten,M. T., A closed-formequation for predictingthe influencedby the pore diameterwhich remainsmore uniform hydraulicconductivity of unsaturatedsoils, Soil Sci. Soc.Am. J., 44, comparedto more tortuousmicropores (Figure 4). The micro- 892-898, 1980. poreshave variable neck and body sizesthat are influencedby Vogel, T., M. Cislerova, and J. W. Hopmans, Porous media with linearly variable hydraulicproperties, Water Resour. Res., 27, 2735- the soil particle size and their arrangementalong the pore 2741, 1991. length thus causingdifferent water particlesto move signifi- cantlydifferent distancesin time (Figure 4). B. P. Mohanty, U.S. Salinity Laboratory, 450 West Big Springs Road, Riverside,CA 92507-4617. (bmøhanty@ussl'ars'usda'gøv)

References Ankeny, M.D., Methodsand theoryfor unconfinedinfiltrometer mea- (ReceivedJune 8, 1998;revised February 12, 1999; surements,in Advancesin Measurementof Soil PhysicalProperties, acceptedFebruary 12, 1999.)