Plot-scale modeling of soil water dynamics and impacts of drought conditions beneath rainfed maize in Eastern Nebraska

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ContentslistsavailableatSciVerseScienceDirect

Agricultural

Water

Management

jo u r n al hom ep ag e :w w w . e l s e v i e r . c o m / l o c a t e / a g w a t

Plot-scale

modeling

of

soil

water

dynamics

and

impacts

of

drought

conditions

beneath

rainfed

maize

in

Eastern

Nebraska

Paolo

Nasta

∗

,

John

B. Gates

DepartmentofEarthandAtmosphericSciences,UniversityofNebraska-Lincoln,Lincoln,NE,USA

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received21December2012 Accepted28June2013 Keywords: Rainfedmaize Rootwateruptake Soilproﬁle Waterstress Soilwaterbalance Climateforcing

a

b

s

t

r

a

c

t

Intermittentdroughtperiodsposemajorchallengestothemanagementofrainfedagriculturalsystems becausetheirproductivityissensitivetowaterstressduringcropdevelopment.Theobjectiveofthisstudy wastoassesssoilwaterdynamicsandcropstresspatternsduringthedroughtyearof2012,whichwas amongthemostsevereonrecordintheUSCornBelt.Thestudyutilizedacontinuousmatricpotential pro-filemonitoringrecordfromJune2008–December2012beneatharainfedcornplotinEasternNebraskato provideadirectcomparisonofthe2012growingseasonwithmoderatetorelativelywetperiodswithin 2008–2011.Theanalysiswasbasedonatransientunsaturatedzonemodelthatwascalibratedwith laboratory-measuredwaterretentionfunctionsandmatricpotentialmeasurementsfromheat dissipa-tionsensors.Ineachyearofthemodelsimulation,soilwaterstoragevolumessteadilydecreasedduring thegrowingseasonandincreasedepisodicallyfollowingprecipitationeventsoutsideofthegrowing sea-son.Precipitationduringthe2012growingseasonwas<50%ofthemeanforgrowingseasons2009–2012 consequently,soilwaterstoragelossduring2012was∼14%ofinitialstorageincomparisonto8–9%in 2009–2011.Modelresultssuggestthatthe2012soilwaterdeficitwaspartiallybufferedbyupwardflux ofdeepsoilmoisture,withapproximately17%ofrootwateruptakein2012derivingfrommoisture redis-tributedfrombelowtherootzone.Nevertheless,rootzonematricpotentialsexceededthecropwilting point( =−8000cm)in2012forthefirsttimewithinthemonitoringrecord.Theseresultshighlightthe needforheightenedattentiontodroughtresilienceofrainfedcroppingsystemsgivenfutureclimate predictionsthatinvolveincreaserainfallintermittency.

1. Introduction

Currentandfutureratesofglobalfoodproductionarehighly dependentupontheproductivityofrainfedagriculture.Asof2000, approximately75%ofglobalharvestedagriculturalareaand66%of totalcerealcropproductionwasassociatedwithrainfed agricul-ture(Portmannetal.,2010).Althoughtypicallylessproductivein termsofcropyieldperunitareathanirrigatedsystems(Bruinsma, 2003;Siebertand Döll,2010), itis likelythat rainfedcrop pro-ductionwillaccountfora signiﬁcantpercentage offuturegains inglobalfoodyields(Rosegrantetal.,2002).Onekeyfactorthat affects the continued importance of rainfed agriculture is that watersupplyforlarge-scaleirrigationislikelytobecome increas-inglyscarceinmanyregions.Long-termdeclinesofgroundwater storagevolumeshavebeenwidelydocumentedinmanyirrigated

Abbreviations:RWU,rootwateruptake;RMSE,rootmeansquarederror;DOY, dayofyear;GS,growingseason;WY,wholeyear.

∗ Correspondingauthor.Tel.:+14028906874. E-mailaddress:paolo.nasta@unina.it(P.Nasta).

basins(McGuire,2009;Scanlonetal.,2012;Aeschbach-Hertigand Gleeson,2012),andrecentestimateshavesuggestedthatglobal groundwaterextractionsexceedsustainablelevelsbyafactorof twoormoreonaverageglobally,withmuchhighervalues appar-entinseveralmajoragriculturalregions(Wadaetal.,2010;Gleeson etal.,2012).Thus,optimizingcropyieldsofrainfedsystemsis criti-calforbothmeetingfutureglobalfoodsecuritygoalsandsustaining freshwaterresources.

Rainfedproductionofcorn(ZeamaysL.)intheUnitedStates playsanimportantroleinglobalgrainsupplygiventhat>50%of globalcornexportsderive fromtheUSand thatapproximately 60%ofplantedcornareain theUSis currentlymanagedunder rainfedconditions(USDA/NASS;http://www.nass.usda.gov/; last accessed 12 December 2012). Mean annual rainfall generally decreasesfromeasttowestacrosstheUSCornBelt,andasaresult thespatialdistributionofrainfedcultivationis largelycentered uponcentralandeasternareaswhereseasonalwateravailability (fromresidualsoilmoistureandprecipitationduringthegrowing season) isgreatest. Althoughrainfed cropyieldsper hectarein these areas are often amongst the world’s highest (FAOSTAT 2010data,http://faostat.fao.org;lastaccessed12December2012; KucharikandRamankutty,2005),yieldscanbesharplyreduced 0378-3774/$–seefrontmatter © 2013 Elsevier B.V. All rights reserved.

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Nomenclature

˛ waterretentionshapeparameter,cm−1 a empiricalcoefficientinEq.(5),cmd−1 b empiricalcoefficientinEq.(5),– ˇ transpirationefficiencyfunction,– D waterdrainage,cmd−1

ε soilporosity,cm3_cm−3

Ea actualevaporation,cmd−1

Ep potentialevaporation,cmd−1

ET0 referencepotentialevapotranspiration,cmd−1

ETc maizepotentialevapotranspiration,cmd−1

Hr relativehumidity,–

K hydraulicconductivity,cmd−1 extinctioncoefﬁcient,– Kc cropcoefﬁcient,–

Ks saturatedhydraulicconductivity,cmd−1

LAI leafareaindex,cm2_cm−2

m waterretentionshapeparameter,– n waterretentionshapeparameter,– P grossprecipitation,cmd−1

Q cumulativewaterﬂux,cm R netrainfall,cmd−1 b drybulkdensity,gcm−3

RI rainfallinterception,cmd−1 Rn netsolarradiation,MJm−2d−1

T airtemperature,◦C tortuosityparameter,– t time,d Ta actualtranspiration,cmd−1 Tp potentialtranspiration,cmd−1 WS waterstorage,cm Wsp windspeed,ms−1

soilmatricpotential,cm

max maximumallowedsoilmatricpotential,cm min minimumallowedsoilmatricpotential,cm obs observedsoilmatricpotential,cm

sim simulatedsoilmatricpotential,cm surf surfacesoilmatricpotential,cm

z soildepth,cm zr rootzonedepth,cm

soilwatercontent,cm3_cm−3

r residualwatercontent,cm3cm−3

s saturatedwatercontent,cm3cm−3

in situationswhere drought periodscoincidewiththe growing season(SchlenkerandRoberts,2006;Grassinietal.,2009).

In 2012, the Corn Belt region was affected by the most severe drought to affect US agriculture in at least 25 years (USDA/ERS,http://www.ers.usda.gov;NationalDroughtMitigation Center,http://droughtmonitor.unl.edu,lastaccessed12December 2012).Thetransitionfromapproximately50cmofprecipitation inthe2011growingseasonto24cmofprecipitationinthe2012 growingseasonatthestudysite(HighPlainsRegionalClimate Cen-ter; http://www.hprcc.unl.edu/maps/normals/; last accessed 10 December2012)offersanexcellentopportunitytogaugehowsoil waterdynamicsrespondtotemporalextremesinrainfall.Thistopic hashighrelevancefor theresilienceof rainfedagricultural sys-temswithrespecttoclimaticvariabilityanddrought(Rockström etal.,2004;Cooperetal.,2008;Rockströmetal.,2009).In par-ticular,recent modeling projections have suggested that future climaticconditionsmayincludeincreasedfrequencyandseverity ofextremeweatherevents(IPCC,2007).Therefore,ﬁeld investiga-tionsunderextremesofmoistureavailabilityaredesirableinorder

togainabetterunderstandingofhowsoilwaterandcropyields areaffectedbyrapidclimaticvariability.Also,incaseswherecrop yieldsmaystronglybeneﬁtfromrelativelysmallinvestmentsin supplementalirrigationduringdryspells,detailedassessmentof soilwaterdynamicscanhelptoreﬁneamountsandtimingofwater applications(Rockströmetal.,2004).

The primary aim of this study wasto assess plot-scale soil waterdynamicsandtemporalpatternsofcropwaterstressbeneath rainfedcornduringthe2012drought-affectedgrowingseasonin comparisontopreviousyears(2008–2011).Thestudyutilized near-continuousunsaturatedzoneprofilematricpotentialmonitoringin ordertosupporttransientmodelingofsoilwaterdynamicswithin andbelowtherootzone.Monitoringofsoilmoistureandmatric potentialshasbeenwidelyusedtocharacterizesoilwater avail-abilitybeneathrainfedcornonarangeofspatialscales(Assouline etal.,2012; Irmaketal.,2012;Lietal., 2012).Developmentof hydrologic fluxestimatesfrom matricpotentials (e.g. partition-ingthesoilwaterbudgetintoredistribution,drainage,evaporation and transpiration)furtherrequirescharacterizationofhydraulic propertiesofthevadosezoneandcropphysiologicalparameters that affectrootwater uptake(Feddesetal., 2004;Bastiaanssen etal.,2007).Althoughmanypreviousstudieshaveinvestigatedsoil waterdynamicsunderirrigatedcornusingtransientmodelingwith theRichardsequation(recentexamplesfromthisjournalinclude Pandaetal.,2004;Chenetal.,2010;Mastrociccoetal.,2010),to ourknowledge,this is thefirstreportedmodelingof rootzone soilwaterdynamicsunderrainfedcornproductiontoutilize con-tinuousprofilematricpotentialmonitoringwithheatdissipation sensors.Also, asa forwardunsaturated zone modeling applica-tion,thestudyincorporatesanuncommonlevelofdetailinfield measurementsavailableforcalibrationandvalidation,including multipleyearsof hourlymatric potentialmeasurementsat sev-eraldepthswithinandbelowtherootzone,localweather data, andlayeredunsaturatedhydraulicpropertiesdeterminedby lab-oratorymeasurement(ratherthanpedotransferfunctions,which haveahigherdegreeofuncertainty).

2. Materialsandmethods

2.1. Studylocation

Thestudysiteislocatedwithinarainfed(non-irrigated)ﬁeldin EasternNebraska(nearthetownofOakland,BurtCounty;96.53◦ E,41.83◦ N;415ma.s.l.)withinanareaofrollingterrain associ-atedwithglacialtillandstreamdissectionofoverlyingloessunits. Meanannualprecipitationisabout66cm/yearfrom1982to2012 (dataforDecember2012incompleteatthetimeofwriting),and localmonitoringrecordsshowsigniﬁcantinterannualvariabilityin annualprecipitation,rangingbetween23cmin1983and105cm in1982andavariationofapproximately4◦Cinaverageannual temperature,rangingbetween7.1◦Cin1996and11.5◦Cin2012 (Fig.1a).Annualprecipitationdisproportionatelyoccursinspring andearlysummer(thewettestmonthsaretypicallyApril,Mayand June;Fig.1b).

2.2. Fieldandlaboratorymeasurementmethods

Heatdissipationmatricpotentialsensors(modelnumber229L, Campbell Scientific, Pullman, WA) were installed in a vertical profileintheunsaturatedzoneon5June2008(depths30,61,91, 152and244cm).Theheatdissipationsensormethodwaschosen overotherwidely-usedmethods,suchasfieldtensiometry,forthe combinedreasonsof(1)measurementrangeand(2)suitabilityfor long-termmonitoring.Incontrasttotensiometricmeasurements, heatdissipationsensorshavethedistinctadvantageofnotneeding

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Fig.1.(a)Annualcumulativeprecipitation,P(bluebars)andaveragetemperature,T(redline)atthestudysite(1982–2012)and(b)monthlyclimatenormals(1982–2012).

intermittent refilling or degassing. Moreover, the tensiometric measurement range is typically limited to above ∼1000cm, whichisaseriouslimitationforrainfedagriculturalapplications becausematricpotentials duringthegrowingseasoncanreach significantlylowervalues.Themeasurementprincipleofheat dis-sipationsensorshasbeendescribedindetailelsewhere(Flintetal., 2002;productmanualavailableathttp://www.campbellsci.com) and is brieflysummarized here.Each sensor includesa porous ceramicsheathsurroundingaheatingelement.Thesensor’srate oftemperatureincreaseafteranappliedheatingpulseissensitive totheporewatercontentoftheceramic,whichinturnisdriven byambientmatricpotentials.Heatpulsetimingand durationis controlledbyadatalogger,andtemperaturesaremeasuredwith internal thermistors,providing hourly matric potentialrecords. Priortoinstallation,sensor-specificcalibrationcurvesofheat dis-sipationrates(temperaturechangeovera20sintervalfollowing a heat pulse) versus matric potentials were determined using a multi-point laboratory calibration procedure using regulated pressureplatechambersfollowingthemethodofFlintetal.(2002). Field-deployedsensorsweresurroundedwithsilicaflourtoensure goodhydrauliccontactwithsurroundingsediments,andplacedat designateddepthswithinanunsaturatedzoneboreholethatwas subsequentlyback-filledwithcoresedimentsandthencappedto preventpreferentialflow.

Undisturbedsoilsampleswerecollectedatfourdepths(38cm, 114cm,187cm,and267cm)tomeasuresoilhydraulicand physi-calproperties.Particle-sizedistribution(PSD)analyses(GeeandOr, 2002)classiﬁedthesoilsfromsiltyclaytosiltyclayloam(Table1). SaturatedhydraulicconductivityvaluesKs(cmd−1)weremeasured

byeithertheconstantorthefallingheadmethodwithfour repeti-tionsforeachsoilsample(ReynoldsandElrick,2002).Thesaturated soilwatercontentvaluess(cm3cm−3)andthedryingsoilwater

retentiondatapointsweremeasuredusingapressureplate appara-tus(DaneandHopmans,2002).Oven-dried(105◦C)soilcoreswere usedtodeterminedrybulkdensityb(gcm−3),andtotalporosity

εwascalculatedfromdrybulkdensityassumingaparticledensity of2.65gcm−3(Table1).

Anautomatedweatherstationrecordeddailygross precipita-tionP(cmd−1), airtemperatureT (◦C),relativehumidityHr(%),

windspeedWsp(ms−1),andnetsolarradiationRn(MJm−2d−1)

(NOAA-NWS, 2007).The reference potential evapotranspiration ET0(cmd−1)wascomputedwiththePenman–Monteithequation

fromthemeteorologicaldata(Allenetal.,1998).Thecrop coefﬁ-cient(Kc;dimensionless),theleafareaindex(LAI;dimensionless)

androotgrowingfunctionformaizewerederivedfrompublished literatureoncorninNebraska(SharmaandIrmak,2012;Piccinni etal.,2009).Theseparametersarespeciﬁedasafunctionoftime

(dayofyearorDOY)accordingtogrowthstage:baresoilfor vege-tationdormancyfromJanuary1(DOY1)toMay9(DOY129);crop plantingandemergencefromMay10(DOY130)toJuly15(DOY 196);tassel,silkingandblister-kernelphasesfromJuly16(DOY 197)toAugust2(DOY214);maturegrowthphasefromAugust3 (DOY215)toOctober31(DOY305);baresoilforvegetation dor-mancyfromNovember 1toDecember 31(DOY 306-365).Leap years(2008and2012)haveanadditionalday.Thecodeto com-putetheDOYisreportedinTable2.5ofAllenetal.(1998).The correspondinglinearequationsareasfollows:

Kc=

⎧

⎪

⎨

⎪

⎩

0.1 1<DOY<129 0.0144DOY−1.77 130<DOY<196 1.05 197<DOY<214 −0.0118DOY+3.59 215<DOY<305 0.1 306<DOY<365 (1) LAI=

⎧

⎪

⎨

⎪

⎩

0 1<DOY<129 0.083DOY−10.83 130<DOY<196 5.5 197<DOY<214 −0.062DOY+18.79 215<DOY<305 0 306<DOY<365 (2)

Therootdepth(zr)isdescribedbyacontinuousgrowingfunction

fromDOY130(zr=0)toDOY305(maximumzr=135cm)withthe

followingequation: zr=

⎧

⎨

⎩

0 1<DOY<129 0.776DOY−100.86 130<DOY<305 0 306<DOY<365 (3)

Eqs. (1)–(3) do not take into account interannual physiologi-caladaptationofthecrop.PotentialcropevapotranspirationETc

(cmd−1)isestimatedasET0multipliedbyKc.ETcissubsequently

partitionedintopotentialevaporationEp(cmd−1)andpotential

transpiration Tp (cmd−1) according to the following empirical

equation:

Ep=ETce−LAI (4)

where(–)isthedimensionlessextinctioncoefﬁcientforglobal solarradiationinside thecanopyand isassumedtobeequalto 0.463(Ritchie,1972).Theresidualfractionofthepotential evapo-transpirationisassumedequaltothepotentialtranspiration,Tp.

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Table1

Measuredphysicalpropertiesofthesoilproﬁleatthemonitoringsiteincludingtexturalpercentagesandclassiﬁcations,soilbulkdensity(b)andsoilporosity(ε).

Proﬁleinterval,cm Sampledepth,cm Sand,% Silt,% Clay,% Classiﬁcation b,gcm3 ε,cm3cm−3

0–42 38 3.4 55.1 41.5 Siltyclay 1.18 0.556

43–120 114 3.2 60.3 36.5 Siltyclayloam 1.21 0.543

121–228 187 3.1 68.7 28.2 Siltyclayloam 1.37 0.483

229–300 267 3.0 65.8 31.2 Siltyclayloam 1.29 0.514

TherainfallinterceptionRI(cmd−1)iscalculatedaccordingto Braden(1985): RI=aLAI

1− 1 1+bP/aLAI

(5) where a (cmd−1) is an empirical coefﬁcient, assumed as 0.025cmd−1 and b(–) denotesthesoilcoverfractiongivenby:

b=1−e−LAI ₍₆₎

Interceptionissubtractedfromthemeasuredrainfallinorderto obtainthenetrainfall(R). Fig.2 illustratestheaforementioned waterﬂuxes(P,EpandTp)forthesametimerecordassociatedto

thematricpotentialmonitoring. 2.3. Numericalmodelingmethods

ThenumericalHYDRUS-1Dmodel(ˇSim ˚uneketal.,2008)was usedtosimulateverticalmovementofwaterintheunsaturated zoneandrootwateruptake(RWU).HYDRUS-1Dnumerically inte-gratesthefollowingone-dimensionalRichardsequation:

∂

∂t

=C( )

∂

∂t

= 1

∂z

∂

K( )

∂

∂z

+1

−( ) (7)

where t (d) is time, z (cm) is soil depth (positive upward), (cm3_cm−3₎_is_the_soil_volumetric_water_content,_{C( )}_is_the

dif-ferentialwatercapacityfunction(cm−1),and( )istheRWUsink term(d−1).Osmoticpotentialsareassumedtobenegligiblebecause of thelow soil water salinityat thesite. The soil water reten-tionfunction( )isdescribedbyvanGenuchten’sequation(van Genuchten,1980): ( )=r+ s−r

1+(˛ )n

m (8a)

withMualem’scondition(Mualem,1976):

m=1−1_n (8b)

where ˛ (cm−1), m (–) and n (–) are shape parameters, r

(cm3_cm−3₎_and_s _(cm3_cm−3₎_are_residual_and _saturated_water

contents, respectively. Considering the degree of saturation, Se=(−r)/(s−r),whichvariesfrom0(=r)to1(=s),an

expression for the unsaturated hydraulic conductivity function K(Se)isobtainedbycombiningEq.(8a)withthepore-size

distribu-tionmodelofMualem(1976)toyield: K(Se)=KsSe

1−{1−Se1/m} m

2

(9) where(–)representsthetortuosityparameter.Tortuosityis com-monlyassumedtobeeither=0.5(Mualem,1976),=2(Burdine, 1953),=−1(SchaapandLeij,2000),oriscalculatedfrom simul-taneouswaterretentionandconductivitymeasurements.Inthis study,thewaterretentionparameters(˛,n,rands)retrieved

fromthedirectmeasurementsareinsertedinEq.(9)andis esti-matedasaﬁttingparameterinthehydraulicconductivityfunction. IncreasingvaluesofhavetheeffectofdecreasingthetermS

ein

Eq.(9)andthereforedecreasingthehydraulicconductivityfunction K(Se)suchthatitwillvaryfrom0(Se=0)toKs(Se=1).

Thesoilproﬁlelowerboundaryis300cmdepthandtheproﬁle is subdividedintofoursoillayers (assumedinternally homoge-neous)accordingtotexturalandhydraulicinformation(0–42cm, 43–120cm,121–228cm,229–300cm).Foreachsoillayer,sandKs

weremeasured(seedescriptionabove),whereastheremainingsoil hydraulicparameters(r,˛andn)wereobtainedbyﬁttingEq.(8)

tothemeasuredretentiondataandminimizingthesquared pre-dictionerrors(asshowninFig.3andsummarizedinTable2).The RWUsinkterm(Eq.(7))isdeﬁnedas:

( )=ˇ( )ϕ(zr)Tp (10)

Fig.2. Dailyvaluesofprecipitation(P),potentialevaporation(Ep),andpotentialtranspiration(Tp)forthetimerecordJune2008–December2012.Snowfallisnotreported.

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Fig.3. Measured(points)andoptimized(dashedlines)waterretentionfunctionsfor(a)0–42cmdepth;(b)43–120cmdepth;(c)121–228cmdepth;and(d)229–300cm depth.

where ϕ(zr) (cm−1) is the normalized water uptake

distri-butionand ˇ( ) is thedimensionless RWU efficiency function (0<ˇ<1),whichdependsonthesoilmatricpotentialand deter-mines water stress. The root density distribution of corn was assumedtolinearlydecreasewithincreasingsoildepth(Feddes etal.,1978).TheRWUstressparametersformaizewerespecified usingliterature-derivedvaluesthatareintegratedasdefaultvalues intotheHYDRUS-1Dsoftwarepackage(ˇSim ˚uneketal.,2008). Opti-malrootwaterextraction(ˇ=1)occurswithinthematricpotential range₋₃₀cm> >₋₆₀₀cm.Waterstress(0<ˇ<1)thendecreases linearlyuptotheestimatedwiltingpointforcorn( =−8000cm) forwhich there istotal reduction (ˇ=0) (Coelho and Or,1999; Metselaarandde JongvanLier, 2007).Theactualtranspiration flux,equivalenttorootwaterextractionrateTa(cmd−1)integrated

acrosstherootzone,wascomputedbynumericalintegrationofEq. (10).

Thesystem-dependentupperboundaryconditionsaredailynet precipitation(R=P−RI)andpotentialevaporation(Ep).Freezing

andthawingofprecipitationisassumedtooccurinstantaneously accordingto mean daily temperature. The minimumallowable soilmatricpotentialvalueattheupperboundary( min;denoted

“hCritA”inHYDRUS-1D)wascalculatedthroughtheKelvin equa-tion:

min=−

GcT

Mg ln Hr (11)

whereMisthemolecularweightofwater(=0.018015kgmol−1), gisthegravitationalaccelerationconstant(=981cms−2)andGcis

thegasconstant(=8.314Jmol−1K−1).Whensurfacematric poten-tial surf is less than min, the prescribed ﬂux on the upper

boundaryofthesoilproﬁleswitchestoaconstantheadtype bound-arycondition(Dirichlet’scondition),resultinginreductionofthe potentialevaporation(Ep)intoactualevaporation(Ea).A

propor-tionofRisroutedintorunoffif surfexceedsthemaximumsoil

surfacematric potentialvalue max=0.5cm that representsthe

nominaldepthofsurfacewaterpondingallowablebeforerunoff generation.

Freedrainageisassumedatthebottomboundaryofthesoil pro-filedomain(300cm),enablingcontinuous(downward)drainageto occurunderaunittotalhydraulicgradient(drivenbyonlythe grav-itationalgradientcomponent).Initialconditionswerespecifiedby linearlyinterpolatingmeasuredmatricpotentialscorresponding totheinitialtime(firstDOY,5June2008).Thesimulationswere undertakenusingafiniteelementgridwithfinerspacingatthetop ofthesoilprofile(0.55cm)andcoarseningwithdepth(5.46cmgrid at300cmdepth).

2.4. Modelcalibrationmethods

Calibrationwasachievedbyadjustingthetortuosity parame-ter(j)foreachsoillayerjtooptimizemodelﬁttomeasuredsoil

matricpotentialsduring2008.Thej-valueswereassignedby

min-imizingthesquarederrorsbetweenobserved( _obs)andsimulated ( sim)soilmatricpotentialvalueswiththeLevenberg–Marquardt

nonlinear minimization method (Marquadt, 1963). The objec-tivefunctionOF()embedsthe vector thatincludesthefour Table2

Hydraulicparametersofthesoilproﬁle:residualwatercontent(r),saturatedwatercontent(s),shapeparameters(˛andn)andsaturatedhydraulicconductivity(Ks).

Proﬁleinterval,cm Sampledepth,cm r,cm3cm−3 s,cm3cm−3 ˛,cm−1 n,– Ks,cmd−1

0–42 38 0.095 0.521 0.0129 1.15 181.47

43–120 114 0.101 0.541 0.0031 1.19 9.53

121–228 187 0.081 0.467 0.0022 1.22 1.65

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Fig.4.(a)Measuredand(b)simulatedsoilmatricpotential( )valuesforthemonitoredsoildepthsduringthecalibration(2008)andvalidation(2009–2012)periods.Matric potentialrangesassociatedwithrootwateruptakestressarealsoshown.Horizontalarrowsdenotethegrowingseasons(130<DOY<305).

tortuosityparametersjforeachsoillayerj.TheOF()isdeﬁned

as: OF ()= N08

i=1

obs(ti)− sim(ti,)

2 (12)

whereticorrespondstothetime(DOY)associatedwithobserved

andsimulatedvariables,startingfromtheﬁrstdayofthe installa-tion(5June2008)andendingon31December2008(N=210).In ordertoensurephysicalconsistencyacrossjvalues(a

fundamen-talrequirementtoobtaina monotonicallydecreasinghydraulic conductivityfunction),theparametersjwereconstrainedusinga

minimumvalueof−2/mj<j(Petersetal.,2011).Thereisno

the-oreticalmaximumvalueforj;however,previousstudiessuggest

thatjusuallydoesnotexceedthevalueof15(SchuhandCline,

1990;Kosugietal.,2002).Becausetheobjectivefunctionmaybe stronglyaffectedbylocalminimaduringthesearch,theinversion procedurewasiterativelyexecutedusingvaryingcombinationsof initialestimates.

Quantitativemodelperformancewasassessedusingtheroot meansquarederrors(RMSE)betweendailymeasuredandmodeled matricpotentials,expressedinlog10-scale:

RMSE=

N i=1

log10 obs(ti)−log10 sim(ti)

2

N (13)

whereNisthenumberofdays.ThreeRMSEtypesarepresentedin Table4:(1)calibrationperiodrangingfrom5June2008upto31 December2008(RMSEcal;N=210),(2)theentire2009–2012

post-calibrationmonitoringrecord(RMSEval;N=1448),(3)2009–2012

measurementsthattookplaceduringthegrowingseasonsonly (RMSEgs;N=700).

3. Resultsanddiscussion

3.1. Measuredmatricpotentials

Themeasuredmatricpotentialrecordillustratesstrong season-alityinsoilwaterconditionsthroughouteachyearoftherecord (2008–2012;Fig.4a).Rapiddryingtrendsfortheshallowesttwo sensors(30cmand61cm)generallybeganinMaytoearlyJune, coincidingwithinitialcropgrowth.Increasingtimelagsrelative to the date of drying onset at 30cm occurred with increasing sensor depth, reﬂecting theprogressivedownward propagation ofdrying frontseach summer.Thedegreeof temporal variabil-ityalsodecreased withdepth,and thedeepestsensor(244cm) remainedrelativelyconstantthroughouttherecord( _∼50cm). The localwater tableis approximately ∼300cm belowsurface, and it is apparentthat the 244cm sensor remained near satu-rationbecauseitwaswithinthecapillaryfringethroughoutthe monitoringperiod.Thenumberofsensorsreportingmatric poten-tialsthatareindicativeofcropwaterstress( <−600cm)varied byyear.In2010and2011,onlythe30cmand61cmsensorsfell below <−600cmduringthegrowingseason.The91cmsensor fellbelow <−600cmin2008,2009and2012.The152cmsensor onlyfellbelow <−600cmduring2012.Yearlyminimummatric potentialsreportedbythe30cmsensor(shallowestsensor)ranged from =−3456cmin2009to =−9136cmin2012.Wintermatric potentialsreturnedto >−600cmforallsensorsinallyearsexcept for2012,reﬂectingweaksoilmoisturereplenishmentfollowingthe 2012growingseasonbecauseofprolongeddroughtconditions. 3.2. Modelcalibrationandperformance

The tortuosity values estimated by statistical ﬁt during the calibration procedure ranged from −1.56 to +5.01. The largest

Table3

Tortuosityparameters(1,2,3,4)optimizedthroughinversemodeling,including95%conﬁdencelimitsandcorrelationcoefﬁcients.

Depth,cm opt,– Pmin,5% Pmax,95% 1,– 2,– 3,– 4,–

1 38 −1.56 −1.81 −1.31 1

2 114 −0.0137 −0.26 0.23 0.056 1

3 187 3.91 2.68 5.14 0.53 0.17 1

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Table4

Rootmeansquareerrorsfor thecalibration (RMSEcal)andvalidation periods (RMSEvalandRMSEgs)foreachmatricpotentialsensorlocatedintherootzone(zr)or belowtherootzone(z−zr).ValidationperiodRMSE-values,RMSEvalandRMSEgsare reportedbothforthewholeyear(WY)andforthegrowingseason(GS),respectively.

Sensordepth,cm RMSEcal RMSEval(WY) RMSEgs(GS)

zr 30 0.42 0.49 0.41

61 0.57 0.52 0.47

91 0.40 0.82 0.69

z−zr 152 0.84 0.92 0.94

244 0.40 0.33 0.39

tortuosityvalues wereestimated for the deepestproﬁle layers (Table 3).Thispattern is notcorrelated withsediment texture, andmaybepartiallyattributabletosoilcompactionwithdepth. However,thelargerangeinthe95%conﬁdenceintervalforthetwo deepestlayers(2.68<3<5.14and−0.03<4<10.03)indicatesa

relativelyhighdegreeofuncertainty. Especiallyforthedeepest sensor,thelowsensitivityisduetothesmalltemporalvariations ofthematricpotentialvaluesthatarenearsaturation.Thisimplies strongequiﬁnalityofthetortuosityestimateforthe244cmsensor becausetheS

etermisclosetounity.Ontheotherhand,thevery

lowvaluesofthecorrelationmatrixindicatelowinter-dependence ofthefourtortuosityparameters.

Thetemporaltrendsinsimulatedmatricpotentialsgenerally agreedwellwiththeobservedmatricpotentialsthroughoutthe 2008–2012monitoringperiod (Fig.4a and b).Simulated matric potentialstendedtocaptureboththetimingandmagnitudeof dry-ingpatternsinmostcases,includingtheseveredryingin2012. Onenotableexceptionwasthebehaviorofthe30cmand61cm sensorsduringthe2011growingseason;themodelpredicteda stabilizationofmatricpotentialsatapproximatelyDOY1220while measuredmatricpotentialscontinuedtosharplydecline.

The RMSEcal values for sensors within the root zone range

from 0.40cm to 0.57cm. RMSEval values were generally

com-parable to RMSEcal values, suggesting that model performance

didnot diminishsigniﬁcantly outside of thecalibrationperiod. The highestRMSEcal valuewas for thesensor at 152cm depth

(RMSEcal=0.84cm), which remained relatively wet throughout

themonitoringperiodand wasslightly butconsistently under-predictedbythemodel.TheRMSEcalvalueforthe152cmsensor

wasgreaterthantheRMSEcalvalueforthe244cmsensorbecause

theformerwassubjecttogreatertemporalvariability.

Cross-comparisonsbetweenmeasuredandmodeleddata pri-marilyclusteralongthe1:1linefor <−100cm(Fig.5aandc), illustratingthestrongmodelperformanceunderrelativelydry con-ditions(whichoccurredprimarilyduringthegrowingseason).In contrast,divergencefromthe1:1lineabove =−100cmsuggests asystematicmodelunderestimationofsimulatedmatricpotential valuesathigher(wetter)ranges.Thisbiaswithinthewetrange ofsensormeasurementsmaybeprimarilyattributabletosensor error,consideringthatheatdissipationsensorshaveshowntohave reducedperformanceabove =−100cm(Flintetal.,2002).Model structureduringcropdormancyperiodsmayalsoplaya rolein thewetrange bias becauseKc during dormancyis poorly

con-strained(assumedequalto0.1inthiscase,seeEq.(1))andthis periodcoincided withthewettest near-surfacemoisture condi-tions.Thedistributionoftheerrors(indecimallogarithmicscale) showssigniﬁcantnegativebiasforthefullyeardataset(Fig.5b), reﬂectingmodelunderestimationofmeasuredmatricpotentialin thewetrange.However,withinthegrowingseason,error distribu-tionsareapproximatelyGaussian(accordingtothe2_-test;_Fig.₅_d)

without signiﬁcantover or underestimation. Hence, the model performance is strongest for evaluation of soilwater dynamics withinthegrowingseasons underprimarilylow moisture con-ditions, which is the focus on this investigation.The fact that RMSEgsvalueswithintherootwereuniformlylowerthanRMSEval

Fig.5.Erroranalysesofsimulatedversusmeasuredmatricpotentials(indecimallogarithmicscale):(a)scatterplotconsideringwholeyeardata(WY),(b)frequency distributionoferrorsconsideringwholeyeardata(WY),(c)scatterplotconsideringgrowingseasondataonly(GS),(d)frequencydistributionoferrorsconsideringgrowing seasondataonly(GS).Dashedlineinparts(a)and(c)denotestheline1:1correlation.

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Table5

Simulatedcumulativewaterﬂuxesforthegrowingseasonsof2009–2012:grossprecipitation(P),rainfallinterception(RI),referencepotentialevapotranspiration(ET0),

potentialcropevapotranspiration(ETc),potentialtranspiration(Tp),potentialevaporation(Ep),waterstorage(WS),waterdrainage(D),actualevaporation(Ea),actual

transpiration(Ta)andwaterstress(Tp−Ta).

2009 2010 2011 2012 Input,cm P 43.15 62.24 53.71 29.11 RI 4.64 4.42 3.97 2.22 ET0 90.62 100.59 96.53 120.83 ETc 60.23 64.42 62.01 79.02 Tp 48.57 51.57 49.87 63.58 Ep 11.66 12.85 12.14 15.44 Output,cm WS130 140.12 141.33 140.55 132.60 WS304 127.77 130.29 127.29 114.34 D −0.71 −5.22 −5.38 −0.48 Ea 11.60 12.80 12.03 15.14 Ta 38.91 45.91 45.07 29.55 Stress(Tp−Ta) 9.66 5.66 4.80 34.03

conﬁrmsthatmodelperformanceismostpreciseduringthe grow-ingseason.

3.3. Waterbudget

Precipitationamountsduringthegrowingseasons2009–2012 rangedfromamaximumof62cmin2010toaminimumof29cm in2012(Table5).Although2012hadthelowestannualamount ofgrowingseasonprecipitationwithinthe2008–2012period,a similarlylowrainfalltotaloccurredinthe1983growingseason accordingtolocalmeteorologicalrecords(seeFig.1a).Simulated rainfallinterception(RI)rates wereapproximately10%ofgross precipitation(P)foreachgrowingseason2008–2012.Simulated growingseasonETcvaluesweresimilarfor2009,2010and2011

(rangeofapproximately60–64cm);2012hada highervalueof 79cm(thereductionofET0intoETcassociatedwithKcwas

approx-imately35%forallfouryears).Eprepresentedapproximately20%

ofETcbasedonEq.(4).Typicaloflocalclimaticconditions,Epand

Tpportrayedrelativelyregularperiodicpatterns,whereas

precipi-tationhadgreatertemporalvariabilityandepisodicity.Simulated runoffwasnegligiblebecausewaterpotentialsatthesoilsurface rarelyexceeded max.Also,reductionsofEarelativetoEptended

tobesmall(i.e.Ea≈Ep)becausewaterpotentialsatthesoilsurface

wererarelylowerthan min.

Modeledsoilwaterﬂuxesandstoragetrendsaresynthesized inTable5andFig.6.Soilwaterstoragevolumesdecreasedeach yearduringthegrowingseason.Theamountofsoilwaterstorage lossduringthegrowingseasonwasrelativelyconstantat approxi-mately12cmperseasonin2009–2011(Table5;WS130andWS305

indicatesoilwaterstorageattheinitialandfinaldaysofgrowing season,respectively).Asapercentageoftotalrootzonewater stor-ageatthebeginningofthegrowingseason,waterstoragelosses were8.8%,7.8%and9.4%forthegrowingseasonsof2009,2010, and2011,respectively.Incontrast,soilwaterstoragelossduring the2012growingseasonwasapproximately18cm, or13.8%of initialstorage,reflecting thesignificantly lowergrowingseason precipitationtotal(29cmcomparedto62cmin2010,for exam-ple).Waterlossattributablesolelytoevapotranspirationcanbe assessedbysubtractingwater lossfromdeepdrainage(D)from thestorage changes over the growingseason.Considering that thedeepdrainageinthegrowingseasonsof2010and2011was approximately5–6cmperseason,itmaybeinferredthatwaterloss attributabletoevapotranspirationin2009wasabouttwicethatof 2010and2011.Thesoilwaterlossattributableto evapotranspira-tioninthedroughteventof2012wasgreaterthanthoseobserved intherelativelywetyearsoftherecord(2010and2011)byafactor ofapproximatelyfour.Aftereachgrowingseason,soilwater stor-ageincreasedintermittentlyfollowingprecipitationeventsinfall

Fig.6.Simulatedcumulativewaterbudgettermsfor2009–2012:(a)waterstorage(WS;cm)and(b)waterﬂuxes(Q)at30cmdepth(solidline)andat150cmdepth(dashed line).Horizontalarrowsdelimitthegrowingseason(130<DOY<305).

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andsnowmeltandstormeventsinspring(Fig.6a).Boththetiming andthepeaksoilwaterstorageamountswererelatively consis-tentacrosseachyearofthemonitoringrecord,occurringduring thespringandreachingmaximumstoragevaluesof141–153cm.

In2009–2011,waterredistributionwithintherootzonewas predominantlydownward(negative)outsideofthegrowing sea-sonbasedonsimulatedwaterﬂuxesat30cm(Q30)and150cmsoil

depth(Q150)(Fig.6b).Flowdirectionstendedtobereversedineach

growingseason,duringwhichupwardmoistureﬂowwasdriven bynear-surfaceevapotranspiration.The2012growingseason fea-turedanotabledecreaseofmatricpotentialvaluesforallsensors exceptthe244cm,whichwasaffectedbythecapillaryfringe. Simu-latedﬂuxesacrosstherootzoneboundary(approximatedbyQ150)

suggestthatdeep(sub-rootzone)soilmoisturetendedto func-tionasawatersourcetotherootzoneduringthegrowingseasons, whereasnegativevaluesindicatethatdeepdrainageoccursinthe wetseasons(Fig.6b).ComparisonofannualQ150 valueswithTa

valuessuggestthatdeepsoilmoisturecontributionsaccountedfor 0–17%ofannualrootwateruptake(17%in2009and2012; negligi-blecontributionsin2010and2011).Simulatedcumulativelower boundarydrainagerates(acrossthe300cmdepthplane)wereless than1cminthegrowingseasonsof2009and2012,and approx-imately5–6cmfor2010and2011(Table5),withmostdrainage eventsin2010and2011occurringduringlatespringwhenthe soilwaterstorageisnearitsmaximum.However,theassumedfree drainagelowerboundaryconditiondoesnotpermitpositivevalues fordeepdrainage.Therefore,possibledischargesfromthewater tablecouldnotbeassessed.

3.4. Cropwaterstress

Seasonal evolution of plant water stress is evaluated using simulatedTp−Taasanindicatorofrootwateruptakereduction

(shown in Fig. 7). Results suggest that RWU stress was inter-mittentwithineachgrowingseasonthroughout themonitoring period,andinsomecasesshiftedrapidlyafterweatherevents.For example,waterstresssharplydeclinedin15August2009(from 0.311to0.018cmd−1 onconsecutivedays) followinga 2.16cm rainfallevent.AsimilarscenariooccurredbetweenAugust21and August22in2011.Maximumwaterstressoccurredwithsimilar timing (early to mid-August) in each of the monitoring years. Thesimulatedsoilmatric potentialcorrespondingtoshallowest depthfellbelowthewiltingpoint( =−8000cm)in2012forthe ﬁrsttimewithinthemonitoringperiod.Signiﬁcantinter-annual variabilityincumulativewaterstresswasalsoevident(Table5). Cumulativegrowingseasonwaterstressrangedfromaminimum of5cmtoamaximumof9cmperseasonin2009–2011,compared to34cmin2012(Table5;Fig.7).Onapercentagebasis,reductions

Fig.7.SimulatedcropwaterstressdeﬁnedbyTp−Ta(2009–2012).Horizontal

arrowsdelimitthegrowingseason(130<DOY<305).

Fig.8.Cropwaterstress(shownwithdegreeofshading)asafunctionofdaily climaticboundaryconditions(ETc−P)andsoilwaterstorage(WS)2009–2012.

intranspirationduetowaterstressequatedtoameanof14%ofTp

for2009–2011and53%ofTpin2012.Thisrangestronglycontrasts

with typical irrigated conditions. For example, Li et al. (2012) observedthatreductionsintranspirationduetowaterstresswere neverless than20%for maizeunderirrigated conditionsinthe HeiheBasininwesternChina.

Fig.8 shows thedistribution of simulatedwater stress as a functionofclimatic(ETc−P)andsoilwaterstoragecontrols.Most

daily climaticvalues fell within therelatively narrow range of 0–1cmd−1.ThesmallpercentageofpointswithETc−P<0are

asso-ciatedwithmajorrainfalleventsthatledtodailyPexceedingETc.

Themostseveredailywaterstressoccurrencesweretightly clus-terednearETc−P=1cmd−1andintermediatewaterstoragevalues

of120–130cm.Theseoccurrencesofmaximumdailywaterstress mainlycoincidedwithearlytomiddlegrowingseasonperiodsthat experiencedlowrainfall;thesewereperiodswhendailyETc−P

valuesweregreatestbutsoilmoisturestorageamountshadnot yetreachedtheirminimumvalues(seeforexample28July2012; Fig. 8). Many of the days with lowest water storage amounts (110–120cm)didnotcoincidewithhighwaterstressbecausethey occurredsoonafterthegrowingseasonwhen ETc waslow but

waterstoragehadnotyetrecovered(seeforexample16October 2012;Fig.8).Theseresultsshowthatcropwaterstressismore closelyrelatedtodailyclimaticconditionsthantotalwaterstorage incurrentstudyareaintheEasternGreatPlains.Becausefew stud-ieshaveexaminedtherelationshipsbetweencropwaterstressand unsaturatedzonedynamicsbeneathdrylandcorn,itisunclearhow thesepatternsmayvaryindifferenttextural,climaticand vegeta-tionconditions.Forexample,itseemslikelythatacoarse-textured soilprofilewithadeeperwatertableundersimilarclimaticand vegetationconditionswouldcertainlyexhibitacloserrelationship betweencropwaterstressandprofilewater storage.Additional researchacrossdiverseenvironmentalsettingsare necessaryin ordertorefine current understandingofhow terrestrialfactors affectdroughtimpactsonrainfedcropstress.

4. Conclusions

The2012droughtintheUSCornBeltstronglyaffectedwater dynamicsinthesiltyclaytosiltyclayloamsoilprofileatthestudy sitein EasternNebraskainseveralrespectsrelative toprevious years.Notableeffectsofthe2012droughtincluded(1)increasing theseasonalsoilwaterstoragedepletionrate,(2)lowering near-surfacematricpotentialstoaminimumvaluethatwasbelowthe wiltingpointforcornforthefirsttimeinthefiveyear monitor-ingrecord(2008–2012),(3)increasingthemagnitudeofupward waterpotentialgradients,and(4)increasingthecontributionof

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sub-rootzonesoilmoisturestoragetoRWU(althoughona percent-agebasisitwascomparableto2009).Resultingwaterstress-related reductionsintranspirationwere55%ofpotentialtranspirationin 2012comparedtoameanof15%for2009–2011.Resultssuggest thatresidualsoilwater withinandbelow therootzonehelped tomitigateharmfulcropstresssomewhatbutwasnotsufficient topreventit,andthatthemostsignificantperiodsofcropwater stressweremostcloselyassociatedwithdryatmospheric condi-tionsratherthanadrysoilprofile.

Performancetestingofthecalibratedone-dimensional numeri-calﬂowmodelsuggestedthatthemodel’sreproductionofobserved matricpotentialswasacceptableandwasmostpreciseforthedry rangeoftherecord( <−102_cm)._Improvements_to_the_current

model’sperformancecouldbeenhancedwithincreasedrealismin crop-relatedboundaryconditionsparameters.

Acknowledgments

The authors acknowledgethe ﬁnancial support of the East-ernNebraskaWaterResourcesAssessmentProject(ENWRA)and its sponsor organizations. Field and laboratory data were pro-videdbytheUSGeol.Surv.NebraskaWaterScienceCenter.Dana DivineandGregorySteeleprovidedvaluablesuggestionsforthe manuscript.

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