Spatial variability analysis of reference evapotranspiration in Iran utilizing fine resolution gridded datasets

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

Spatial

variability

analysis

of

reference

evapotranspiration

in

Iran

utilizing

fine

resolution

gridded

datasets

Tayeb

Raziei

_,

_Luis

_S.

_Pereira

a_{CEER-BiosystemsEngineering,InstituteofAgronomy,TechnicalUniversityofLisbon,Portugal} b_{SoilConservationandWatershedManagementResearchInstitute(SCWMRI),Tehran,Iran}

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received15February2013 Accepted2May2013 Available online 1 June 2013 Keywords:

Referenceevapotranspiration Radiationadjustmentcoefficient Temperatureadjustment Griddeddatasets Kriging Spatialvariability

a

b

s

t

r

a

c

t

Monthlyaveragesofmaximumandminimumtemperature,meanrelativehumidity,sunshineduration andwindspeedat2mheight,relativeto148Iranianweatherstationsandperiod1991–2005wereutilized forinterpolationandgriddingthevariablesto1◦_{inlatitudeandlongitude.TheOrdinarykrigingmethod}

wasusedcoupledwithasphericalisotropicvariogram.MonthlyprecipitationoftheAPHRODITEdataset wasregriddedtothesamemeshgridforcomputingthearidityindexjointlywiththegriddedvariables. TherequiredelevationforestimationofEToateachgridnodewasextractedfromthedigitalelevationmap

ofIran.Theadequacyofgriddedvariableswasprovedthroughasetofstatisticalindicatorsappliedtothe cross-validatedinterpolationerrors.ThePenman–Monteith(PM-ETo)referenceevapotranspiration(ETo)

wasestimatedusingthegriddedvariablesandstatisticallycomparedwiththoseofobservationaldatasets relativetosomestationscoveringallclimaticregionsofIran.ResultsindicatedthatthePM-ETocomputed

usinggriddedvariableswellfittedthePM-ETocomputedusingobservedfullweathervariablesatthose

selectedstations.ETowasalsoestimatedbytheHargreaves–Samani(HS)andFAO-PMtemperature(PMT)

methodsusinggriddedvariablesofminimumandmaximumtemperature(TminandTmax).Toestimate

ETo withHSandPMTmethods,appropriatekRs,anempiricalradiationadjustmentcoefficient,were

consideredforeachstation,whereasTminwasadjustedforestimationofthedewpointtemperature

(Tdew)usedforPMTcomputation.ItwasfoundthattheappropriatekRsforbothHSandPMTmethodsare

identicalalloverthecountryandtheyaresmallerindry-sub-humidtohumidareasandhigherin semi-aridtohyper-aridclimates.TheresultsuggestedthattheHSandPMTmethodsappropriatelypredictETo

alloverIraniftheappropriatekRsareutilized.ThespatialpatternsofETocomputedwithHSandPMT

methodsfoundtobeidenticalandresembletothatofPM-ETo,allshowingagradualincreasingfrom

northtosouth,withthelowestETovaluesobservedovernorthernhumidandsub-humidclimatesofIran

andlargerEToforaridandhyper-aridclimatesinthesouthernandeasterncountry.Resultsindicated

thattheHSandPMTmethodsareappropriatealternativesforestimationofEToforallclimaticregions

ofIran,eitherwhenusingobservationorgriddeddata.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Anaccurateestimationofreferenceevapotranspiration(ETo)is

essentialforagriculturalandhydrologicalstudies,waterresources management,watershedmanagement and,morespecificaly,for estimation of crop water requirements, supporting irrigation scheduling,droughtmanagementandclimatechangestudies.The Penman–MonteithETo(PM-ETo)equationproposedbyFoodand

AgriculturalOrganizationofUnitedNations(FAO),usinggrassas referencecrop(Allenetal.,1998)hasbeensuccessfullyapplied atdifferenttimescalesin variousclimaticregionsoftheworld

∗ Correspondingauthor.Tel.:+351213653480.

E-mailaddresses:[email protected](T.Raziei),[email protected]

(L.S.Pereira).

(Pereiraetal.,1999;Smith,2000;Allenetal.,2006).ThePM-ETo

equationrequiressolarradiationdataorsunshinedurationfor esti-matingnetradiation(Rn),maximumandminimumtemperature

(TmaxandTmin,respectively),psychrometricorrelativehumidity

(RH)datafor estimatingthevapour pressuredeficit(VPD), and windspeed(U).TheparametersofPM-ETocanbecomputed

appro-priatelyfollowingtheproceduresproposedbyAllenetal.(1998) and revisited by Nandagiri and Kovoor (2005) and Gong et al. (2006).Usingappropriateapproachesitispossibletoaccurately computeETo withlimiteddatasuchaswithTmaxandTmin only

asdemonstrated inpreviouspapers appliedtoIran (Raziei and Pereira,2013),theMediterraneanregion(Todorovicetal.,2013) andotherregions(Popovaetal.,2006;Caietal.,2009). Neverthe-less,toadequatelyestimateETo foragivenareaadensestation

networkprovidingtherequiredweatherdatasetsisessential. How-ever,therequiredfullweatherdatasetsforestimationofPM-ETo

0378-3774/$–seefrontmatter © 2013 Elsevier B.V. All rights reserved.

arelackinginmanypartsoftheworld,particularlyinremoteareas, thatlimitstheapplicationofPM-ETo.

Due to the complex orography and wide latitudinal extent (Fig.1a),Irancomprisesdiverseclimatesrangingfromveryhumid intheCaspianSearegiontoaridand hyperaridinthecentral, southernandeasternIran.Therefore,tohaveaspatially compre-hensiveanalysisofEToforIran,adensenetworkofweatherstations

measuringtherequiredvariablesforETo estimationisessential.

Contrarily,the distribution of the available meteorological sta-tionsinmostpartsofIranisirregularandsporadic,particularly incentral-easterncountrywherethestationsarequitesparse.This irregularityaremorepronouncedfrom1981backward, particu-larlyrelative tosunshine duration, relative humidity and wind speedvariablesrequiredforcomputationofPM-ETo.Additionally,

theconsidered variables suffer fromsubstantial missing values thatmakesdifficultandlessreliabletheiruseforEToestimation,

althoughthecomputationofEToforIranusingadenseand

uni-formdistributedstationnetworkoragriddeddatasetisdesirable andofparamountimportanceforagriculturalandwaterresources managementpracticesintheregion.

Therearesomeglobal scalefineresolution gridded datasets developedwiththeaimofbeingusedininvestigationofclimate patternanalysis aswellasin studyingthespatialvariability of evapotranspirationanddrought.Themostwellknownmonthly gridded datasets at globalscale are theClimatic Research Unit (CRU) datasets (http://www.cru.uea.ac.uk/cru/data), the Global Precipitation Climatology Project (GPCP) (Adler et al., 2003, http://precip.gsfc.nasa.gov)and the worldclimdataset (Hijmans et al., 2005, http://www.worldclim.org). The inverse distance weighting(IDW,Jonesetal.,1986),theShepardmethod(Shepard, 1968)andtheKrigingandSplines(Hutchinson,1995)arethemost popularandwidelyusedtechniquesutilizedtoproducethemost well-known globalandcontinental scalesgridded datasets.The IDWisbasedontheassumptionthattheclimaticvalueat unsam-pledpointsisadistanceweightedaverageoftheclimaticvaluesat thenearbysamplingpoints.Similarly,themethodofSheparduses aninversedistanceweightedalgorithm,butdifferentlyitusesleast squaresmethodtoeliminateorreducethebull’seyeappearancein thegeneratedcontours.TheKrigingmethodisacollectionoflinear regressionmethodsthattakesintoaccountthestochasticnature ofthedatausingaparametricvariogramfunctiontomodelthe spatialcorrelation,thusinvolvingthedevelopmentofoneormore semivariogrammodelsthatbestfitthedatatoarriveatoptimum stationweightsforinterpolation(Dalyetal.,2002).Splineisalsoa statisticalinterpolatorcloselylinkedtoKrigingwithcomparative results(Laslett,1994).Itproducessmoothedsurfaces,and there-foreismostusefulforapplicationinglobalorcontinentalscales interpolation(e.g.,Newetal.,1999).However,theperformanceof thesemethodsvariesasafunctionofvariousfactors,includingthe temporalandspatialscaleandthedensityofstations(Hofstraetal., 2008)aswellastheclimaticdifferencesamonglocationsusedin interpolation.

Morerecently,dailygriddedprecipitationdatasetshavebeen developedforEurope(E-OBSdataset,Haylocketal.,2008),North America (Maurer et al., 2002), South America (Liebmann and Allured,2005),Asia(Yatagaietal.,2009),Spain(Herreraetal.2012) andPortugal(Belo-Pereira etal.,2011)usingdensenetworksof observatories.Though theCRUdatasetprovidesthe1961–1990 climatenormals for sunshine and wind speed at a very coarse spatialresolution of 10◦ latitude×10◦ longitudeat globalscale (Newetal.,2002),noneoftheavailablegriddeddatasetsprovides sunshineandwindspeedtimeseriesatfinespatialresolutionto beusedinETo estimation.Therefore,itisdesirabletodevelopa

fineresolutiongriddeddatasetsforIranusingasmuchas avail-able observatories across the country to provide the required variables for ETo estimation as well as for drought variability

analysisusingvariantsofthePalmerDroughtSeverityIndex includ-ingitsmodifiedversionforMediterraneanconditions(MedPDSI, Pereira etal., 2007)or theReconnaissanceDrought Index(RDI, Tsakirisetal.,2007).

Thepresentstudyaimstodevelopagriddeddatasetsat1◦ lati-tude×1◦longitudespatialresolutionusingdatarecordsrelativeto 148Iranianweatherstationsrelativelyregularlydistributedover thecountry,tobeusedforestimationofEToatafinespatial

resolu-tionoverIran,includingusingestimationmethodsrequiringTmax

andTmin only.Differentlyfromotherstudiesassessingthe

accu-racyofvariousequationsforEToestimationusinglimtedweather

data,thisstudyaimstoaccuratelyproducegriddedweatherdata setsforETocomputationandassessesthespatialvariabilityofETo

computedwithbothfullandlimitedweatherdataatcountryscale.

2. Materialandmethods

2.1. Data

TherequiredvariablesforcomputationofEToatmonthlytime

scale,i.e.,monthlyaveragesofTmaxandTmin,meanRH,sunshine

duration and wind speed at 2mheight relative to148 Iranian weatherstationsdistributedoverthecountry(Fig.1b)wereutilized forinterpolationandgriddingtheconsideredvariablesatafine spa-tialresolutionof1◦latitude_×1◦longitude.Therequiredvariables, particularlysunshinedurationandwindspeed,aremeasuredat irregularlyspacedlocationsoverthecountryfortheperiodbefore 1990,sufferingalsofromsubstantialmissingvalues. This situa-tionlimitscomputationofETooverthecountry,aimingtoanalyse

long-termtimevariabilityofETo,includingtoassesspossible

influ-encesofclimatechange.Differently,alltheIraniansynopticand climaticweatherstationshavecompletedatarecordsfrom1991 onward,beingquitesuitable andappropriate fora comprehen-siveanalysisofspatialvariabilityandregionalizationofEToacross

Iran.Thestationsconsideredforthepresentstudyarerelatively regularlydistributed throughthe country(Fig.1b), particularly in westernand northern areaswhere the stationnetworksare favourablydense.Theclimaticrecordspassedacarefulquality con-trolbytheIranianmeteorologicalorganizationandencompassed veryraremissingvaluesintheselectedtimeperiod(1991–2005). Theobservedmissingvaluesatafewstationsweremore concen-tratedin1991andmostlycorrespondtothesunshineandwind speedrecords.Table1showsthenumberofusedstationsavailable eachyearforgriddingthevariables;itisevidentthatthe num-berofstationsusedforgriddingsunshinedurationandwindspeed arerelativelysmallerandscatteredthanthoseforTmax,Tminand

RHvariables.Thetime seriesofthevariableswereinvestigated forpossiblenon-homogeneitiesbycomparingthetimeseriesofa

Table1

Numberofstationsusedforgriddingthevariables.

Year Tmax Tmin RH Sunshine Windspeed

1991 140 140 118 116 118 1992 146 146 121 128 125 1993 146 147 137 116 133 1994 145 143 137 128 140 1995 147 148 146 143 145 1996 148 148 147 147 147 1997 148 148 146 147 147 1998 148 148 147 147 147 1999 148 148 148 147 148 2000 148 148 148 145 148 2001 148 148 148 146 148 2002 148 148 145 143 148 2003 148 148 148 147 148 2004 144 144 141 141 142 2005 144 144 142 141 142

Fig.1. (a)TopographicmapofIran,(b)spatialdistributionoftheweatherstationsutilizedforgridding,(c)spatialdistributionofthegridpointsoverIran,and(d)spatial variabilityofthearidityindexoverIran.Thestationshighlightedwithred+inpart(b)arethoseselectedforcomparisonbetweenobservationalbasedETowiththeETo

computedusinggriddedvariables.

givenstationwiththoseofneighbouringstations;theresultproved thatallthevariableswerehomogeneousinthechosentimeperiod. Toestimatefewobservedmissingmonthlyclimaticdata,aspatial method(PerryandHollis,2005)wasusedbywhichthemissing valuesatasinglepointwereestimatedthroughthegridding pro-cedurebasedonalldataavailableforasinglemonth,takinginto accountboth therelativepositionsofsamplingpointsandtheir distances.

The Digital Elevation Model (DEM) map of Iran (Fig. 1a), extractedfromsatelliteimagesoftheAdvancedSpaceborne Ther-malEmissionand Reflection Radiometer (ASTER)developed by jointcooperationbetweenNASAandJapan’sMinistryofEconomy, TradeandIndustry(METI),andJapanSpaceSystemswasusedto extracttheelevationofthegridpointsinordertobeusedfor esti-mationofEToateachgridnode(Fig.1c).

2.2. Interpolationandgriddingprocedure

Todevelopthegriddeddatasetoftheclimatevariables con-sideredinthepresentstudy,wehaveusedtheOrdinaryKriging (OKrig)methodasappropriateinterpolatorsinceitissimpleand widelyusedforgriddingmanygeophysicalfields(Matheron,1971; Biauetal.,1999).OKrigwasusedbyBelo-Pereiraetal.(2011)and Herreraetal.(2012)forclimategriddingpurposes,assumingthat

themeanisunknown,thusfocusingonthespatialcomponentand usingonlythesamplesinthelocalneighbourhoodfortheestimate. SinceKrigingtakesintoaccountboththerelativepositionsof samp-lingpointsandtheirdistancesfromtheinterpolatedpoint(Dirks etal.,1998),itmaybethemostaccuratemethodforinterpolation inareaswithlowresolutionnetworks,asisthecaseforthestations networkinthepresentstudy(Fig.1b).Itisalsoaveryappropriate methodwhenthereisnotastrictconfidenceonthedata measure-ments.Moreover,thismethodproducesvisuallyappealingsurface plotsfrom irregularlyspaced datatoexpressexistenttrendsin thedataset,sothathighpointsmightbeconnectedalongaridge ratherthanisolatedbybull’s-eyetypecontours.TheOKrigmethod isthesimplestformofKrigingand isless sensitivetothe den-sityofobservationsnetwork(Belo-Pereiraetal.,2011);itassumes thatdataarestationary,i.e.theycontainnosignificanttrends(or drifts)overthespatialrange(JournelandHuijbregts,1978). How-ever,manyregionalizedvariablesshowlocaltrendsorevenbroader regionaltrendswhenspatiallyanalysed.Thesetrendsareusually notaproblembecausethestationarityassumptionappliesonlyto thesearchneighbourhoodusedintheinterpolation,whichmaybe reasonablyhomogeneous,andnottotheentiredataset(Holdaway, 1996).Moreover,theconsideredtimescale(monthly)andthe cli-maticvariablesusedinthisstudymakethevariablestobenearly stationaryintimeandinspacewhencomparedtodailyvariables

(Shenetal.,2001).However,problemsstilloccurforthewindspeed variable,particularlyinthesouthernregions,duetoitsextreme variability.Griddingwindspeeddataconsistsofthemain limita-tionofthisstudy.ItisworthnothingthattheutilizationoftheOKrig methodinthepresentstudyinexplicitlyincludestheroleof topog-raphysincethestationsnetworkarerepresentativeofawiderange ofelevationvariabilityandgeographicfeaturesofIran(Fig.1aand b).

The spatial variability of the data points as a function of distancewasevaluatedthroughinspectionoftheexperimental var-iogramsforallconsideredmonthsandvariablesusingGS+software (http://www.gammadesign.com).Inspectionoftheexperimental variogramsrelativetoallthevariablesandmonthssuggestedthat thesphericalisotropicmodelmostoftenbestfittedthe experimen-tal variograms. Therefore, to minimizecomputation procedure, aseparatevariogramwasfittedtothelong-termmeanof each variableandindividualmonth,i.e.,thefittedvariogramforeach variablehasthesameformforeachmonthregardlessoftheyear, assumingthatthespatialvariabilityofthevariablehasnotchanged overthe1991–2005timeperiod(Holdaway,1996).

2.3. Evaluationofgriddingprocedures

The accuracy and performance of the interpolation method wasfirst assessed bycarrying outa cross-validation.To do so, foreachmonth,theclimatevariablesforeachstationwere esti-matedafterexcludingthatstationfromtheinputdata.Thisprocess wasrepeatedforallthestations,witheachremovedstationbeing reinsertedbackintothenetwork afterit hasbeeninterpolated (WillmottandMastuura,1995;Holdaway,1996).Thedifferences betweentheestimated(crossvalidated)andobservedvalues,i.e., residualsorerrors, wereanalysed.bothspatially andtemporally toexaminetheaccuracyoftheinterpolationasafunctionoftime andspaceandtoexamineiftheerrorsshowanyspatialtrend.The empiricaldistributionofthecross-validatederrors associatedto theconsideredvariableswereevaluatedtoquantifythedegreeof imprecisionintheinterpolationresult,i.e.theuncertaintyofthe interpolationmethodwasassessedbyexaminingtheproportionof theerrorsthatfallwithinthe95%confidenceintervalofthefitted normaldistribution(PhilipsandMarks,1996).

The interpolation errors were further evaluated using the Willmott(1981)indexofagreement,dIA,toexaminethedegree

ofagreementbetweenobservationsandestimationsfor agiven map.Assuch,foreachmonthandvariable,thepredictionerror wasaggregatedoverallthestationstoexpresstheindexof agree-ment.ThedIAindexisanon-dimensionalmeasurethatrepresents

theratiobetweenthemeansquareerrorandthepotentialerror, definedasthesumofthesquaredabsolutevaluesofthedistances fromthepredictedvaluestothemeanobservedvalueanddistances fromtheobservedvaluestothemeanobservedvalue(Willmott, 1981;Moriasietal.,2007): dIA=1− n













wherePi andOi arerespectivelytheinterpolatedand observed

valuesforagivenstation,nisthenumberofstationsusedfor inter-polationforeachmap,andOistheassociatedmeanoftheobserved valuesattheconsideredstations.dIAvariesbetween0and1;avalue

of1indicatesaperfectagreementbetweentheobservedand inter-polatedvalues,while0indicatesnoagreementatall(Willmott, 1981;Moriasietal.,2007).Asanon-dimensionalmeasure,thedIA

indexisausefultooltoevaluatetheaccuracyoftheinterpolation

estimation.ThemonthlyvariationofthedIAcorrespondingtoall

consideredvariableswerecompactlyrepresentedbybox-Whisker plotstoinvestigatethestabilityoftheinterpolationperformance asafunctionoftime.

Inordertore-evaluatetheperformanceofgriddingdatasetsto appropriatelyestimatePM-ETo,thePM-ETocomputedusing

grid-deddatasetswascomparedwiththeestimatedPM-ETousingfull

observationaldatasetsforsomeselectedstationsdistributedover thecountry(Fig.1b).Thisstepofperformanceevaluationisvery crucialinexaminingthepropagationofestimationerrorsrelative tothefivegriddedvariablesinPM-ETo.Todoso,thetimeseriesof

theestimatedPM-ETofortheselectedstationswerestatistically

compared withthatof gridded datasetsaveraged overthegrid pointssurroundingagivenstation.Withthisobjective,theroot meansquareerror,RMSEandthemodellingefficiency,EF,were usedinadditiontothedIAindex(NashandSutcliffe,1970;Moriasi

etal.,2007).TheRMSEcharacterizesthevarianceoftheerrors;the smallerRMSEthebetteristhemodel’sperformance.EFdetermines therelativemagnitudeoftheresidualvariancecomparativelyto themeasureddatavariance;asinEq.(2),itisdefinedfromthe ratioofthemeansquareerrortothevarianceintheobserveddata. EFindicatesthatwhentheresidualvarianceequalstheobserved datavarianceitresultsEF=1.0;contrarily,whenEFequalszeroor isnegativethisindicatesthattheobservedmeanOisasgoodor betterpredictorthanthemodel.

EF=1− n









The PM-ETo equation is aimed to describe grass reference

evapotranspiration,i.e.,therateofevapotranspirationfroma hypo-theticalcropwithanassumedfixedheight(12cm),dailysurface resistance(70sm−1)andalbedo(0.23),approximatelyresembling theevapotranspirationfromanextensivesurfaceofadisease-free greengrasscoverofuniformheight,activelygrowing,completely shadingtheground,andwithadequatewaterandnutrientsupply (Allenetal.,1998).ThePM-EToequationforcalculationofdailyETo

takestheform: ETo= 0.408(R

n−G)+_T+273900 u2(es−ea)

+(1+0.34u2)

(3) whereEToisthegrassreferenceevapotranspiration[mmday−1],Rn

isthenetradiationatthecropsurface[MJm−2day−1],Gissoilheat fluxdensity[MJm−2day−1],Tismeandailyairtemperatureat2m height[◦C],u2iswindspeedat2mheight[ms−1],esissaturation

vapourpressure[kPa],eaisactualvapourpressure[kPa],es−eais

vapourpressuredeficit[kPa],istheslopeofthevapourpressure curve[kPa◦C−1],andisthepsychometricconstant[kPa◦C−1].This equationusesstandardmeteorologicalrecordsofsolarradiationor sunshineduration,minimumandmaximumairtemperature,air humidityandwindspeed.Toensuretheintegrityofcomputations, theweathermeasurementsshouldbemadeat2m(orconverted tothatheight)aboveanextensivesurfaceofgreengrass,shading thegroundandnotshortofwater.TheparametersofEq.(3)can beestimatedfromtheobservedclimaticvariables followingthe standardmethodsproposedbyAllenetal.(1998).

Netradiation(Rn)iscomputedasthealgebraicsumofthenet

shortwaveradiation(Rns)andthenetlongwaveradiation(Rnl):Rns,

resultsfromthebalancebetweenincomingandreflectedsolar radi-ation(Rs)adoptinganalbedoof0.23forthegrassreferencecrop.Rnl

resultsfromthebalancebetweenthedown-comingandthe out-goinglongwaveradiationemittedbythevegetationandthesoil. ComputationswereperformedasproposedbyAllenetal.(1998). WhenRsisnotmeasured,itcanbeestimatedfromtheobserved

sunshinedurationwiththeAngström(1924)equation: Rs=





whereRsissolarorshortwaveradiation[MJm−2day−1],nisactual

durationofsunshine[h],Nismaximumpossibledurationof sun-shineordaylighthours[h],n/Nisrelativesunshineduration[−], Raisextraterrestrialradiation[MJm−2day−1],asisthecoefficient

expressingthefractionofextraterrestrialradiationreachingthe earthonovercastdays(n=0),andas+bsisthefractionof

extrater-restrialradiationreachingtheearthonclearskydays(n=N).The valuesas=0.25andbs=0.50arerecommendedwhenthese

frac-tionsarenotcalibratedusingasetofgoodqualitydataonboth n/NandRs.ExtraterrestrialradiationRaanddaylighthoursNare

computedforanygivendayasafunctionofthelatitudeofthesite (Allenetal.,1998).

Rsmaybecomputedfromtemperaturedataonly(Allenetal.,

1998)as: Rs=kRs



(Tmax−Tmin)Ra (5)

wherekRsistheempiricalradiationadjustmentcoefficient[◦C−0.5]

whosevaluesforIranarespatiallydistributedasreportedbyRaziei andPereira(2013):kRsforthestationslocatedinsub-humidto

humidclimatesvariedbetween0.10and0.18,whiletheyranged from0.11to0.20forthestationssituatedinthesemi-aridto hyper-aridclimates.

VPDwasestimated asthedifferencebetweenthesaturation andtheactualvapourpressure (es and earespectively).

Satura-tionvapourpressureiscomputedastheaverageofeo_(Tmax)and

eo_(T

min).Whenusingmeanrelativehumidity(RHmean),theactual

dailyvapourpressureeaiscomputedas(Allenetal.,1998):

ea= RHmean

50/eo_(T

min)+50/eo(Tmax)

(6) Intheabsenceofhumiditydata,eamaybeobtainedbyassuming

thatthedewpointtemperature,Tdew,isclosetothedailyminimum

temperature,Tmin: ea=eo(Tmin)=0.611exp

discussedbyRazieiandPereira(2013).

Whenwindspeedisnotavailable,usinganaverageregional windspeedvalue,orjusttheworldaveragevalueof2ms−1,is gen-erallyappropriatebutmaybequestionableforaridandhyper-arid regionswhenhighwindspeedoccurs(RazieiandPereira,2013).

AcombinationofestimationsusingEqs.(5)and(7)withan esti-mateofwindspeedleadstothepossibleuseofEq.(3)usingonly temperaturedata,thesocalledPMtemperaturemethod(PMT). Eq.(3)mayalsobeusedadoptingestimationsbyEqs.(5)and/or (7)whenrespectivelyradiationand/orhumiditydataaremissing (Popovaetal.,2006).Inalternative,theHargreavesand Samani (1985)equation(HS)maybeusedbecauseitrequiresonlyobserved TminandTmaxfortheestimationofETo[mmday−1],whichisgiven

as:

ETo=0.0135kRsRa





(Tmax−Tmin)(T+17.8) (8)

whereRaistheextraterrestrialradiationasdefinedearlier,andis

thelatentheatofvaporization[MJkg−1]forthemeanair tempera-tureT[◦C],thatiscommonlyassumedequalto2.45MJkg−1.0.0135

Table2

CorrectionofTdewestimatesfromTminforestimationofactualvapourpressure.

Climatezones AnnualP/ETo CorrectedTdew(◦C)

Hyper-arid <0.08 Tdew=Tmin−4

Arid 0.08–0.20 Tdew=Tmin−2

Semi-arid 0.20–0.50 Tdew=Tmin−1

Drysub-humid 0.50–0.65 Tdew=Tmin−1

Moistsub-humid 0.65–1.0 Nocorrectionforaridity Humid >1.0 Nocorrectionforaridity

isafactorforconversionfromAmericantotheInternational sys-temofunitsandkRsistheradiationadjustmentcoefficientdefined

inEq.(5).IntheapplicationtoIran(RazieiandPereira,2013),kRs

wasfoundtovarysimilarlywiththevaluesestimatedforthePMT usingEq.(5),i.e.,between0.13and0.18,inthesub-humidtohumid climatesand0.14and0.20forthestationssituatedinthesemi-arid tohyper-aridclimates.

TheariditymapofIrandevelopedbyRazieiandPereira(2013) wasupdatedhereinusingthegriddedvariables(Fig.1d)to char-acterizethegridpointswithrespecttotheglobalaridityindex (UNEP,1997)whichisrequiredforadjustingminimum temper-atureforestimationofPMTasdescribedinSection2.5,Table2 andEq.(9).TheUNEParidityindexconsistsoftheratioofmean annualprecipitation(P)tomeanannualpotential evapotranspi-rationcomputed withtheThornthwaite method(Thornthwaite, 1948).Tocomputethearidityindexfortheconsideredgridpoints (Fig.1c)monthlyprecipitationcorrespondingtothegroundbased Asian Precipitation-Highly-ResolvedObservationalData Integra-tion Towards the Evaluation of Water Resources (APHRODITE) projectfortheMiddleEast(Yatagaietal.,2008,2009)were regrid-dedtothesamemeshgridasinFig.1c.AsinRazieiandPereira (2013),theupdatedmapofaridityindexshowninFig.1dpoints tothehumidand sub-humidclimatesover coastalareasofthe CaspianSeainnorthernIran.Dry-sub-humidclimatefeaturesoccur inthehighestpartsoftheAlborzmountainchaininthenorth,thus actingasatransitionalband,isolatinghumidandsub-humid cli-matesofthecoastalareasoftheCaspianSeafromthesemi-arid areasofinteriorIran.Thedry-sub-humidclimatealso character-izesaremarkablepartofwesternIranoveranarrowbandofthe highestmountainsalongtheZagrosmountainchain,duetoits rela-tivelyhighannualprecipitationaccompaniedwithcoldwintersand moderatesummers.Semi-aridclimatesrefertothemountainous areasofwestern,northernandnorth-easternIran,whereasaridand hyper-aridclimatesdominatecentral,southernandeasternIran (Fig.1d).Incomparisontothepreviousstudy(RazieiandPereira, 2013),thedrysub-humidclimateappearsdominantoverthe high-estpartofZagrosmountainrangesinwesternIran,whereasthe hyper-aridclimatefeaturescentralandsouth-easterncountryas wellasasmallareainsouth-westernIran.

2.5. PerformanceevaluationofHSandPMTmethods

AsinRazieiandPereira(2013)atrialanderrorprocedurewas appliedtoalldatasetstofindthebestvaluesfor kRs sincethe

relations proposedby Samani(2000, 2004) didnotshowtobe appropriate.PMTcomputationswerealsoperformedwith tem-peraturecorrectionforaridityeffectsasinTable2orforhumidity impactsonTdewasproposedbyTodorovicetal.(2013)andRaziei

andPereira(2013):

Tdew=((Tmin+Tmax)/2)−ad (9)

withad=2◦Cforthemonthswhen0.8<P/ETo<1.0andad=1◦Cif

P/ETo>1.0.

Theresultsof ETo estimatedby PMTandHS methodsusing

limitedweatherdatawerecomparedwiththoseofreference PM-ETocomputedusingfulldatasets.ToassesstheperformanceofHS

andPMTmethodswithrespecttoPM-ETo,relativetoallpairsof

observedandpredictedvaluesforeachgridpoint,inadditiontothe coefficientofdetermination(R2_{)ofalinearregressionforcedtothe}

origin,themodellingefficiency(EF)andtheindexofagreement, (dIA)wereused.TheseindicatorsarebrieflyexplainedinSection

2.3andtheirequationsaregiveninliterature,e.g.,thecomparative studyofETomodelsbyTodorovicetal.(2013).

3. Results

3.1. Performanceoftheinterpolation

Fig.2illustratesthedistributionofthecross-validatederrorsof thevariableswiththefittednormaldistribution.Thefigure sug-geststhat theinterpolation errors associated totheconsidered variablesarecentredaroundzeroandareapproximatelynormally distributed,thusindicatingthattheinterpolatedresultspreserved relativelywelltheoriginaldistributionofthevariables.Forallthe variables,themajorityofinterpolationerrors(morethan80%)fall withinthe95%confidenceinterval,indicatingthattheestimations aregenerallyclosetotheobservations,whichisanindicationof reasonablyaccurateinterpolation.

ThemonthlyvariationofcomputeddIAindexforallthevariables

arerepresentedinFig.3throughbox-Whiskerplotstoillustrate theperformanceoftheinterpolationmethod.Fig.3aand3bshow monthlyvariationsofdIAforTmaxandTmin,respectively;theyshow

thatdIAmostlyliesabove0.95forbothvariables,whichindicatesa

verygoodagreementbetweenestimationsandobservations. How-ever, thedegree of agreement varies among months, withthe highestagreementinwinterandlowestinsummer.The notice-ableloweragreementinsummermonthsmaybeattributedtothe morelocalizedandindependenttemperaturecharacteristicsdue tosubstantialtopographiceffectsontemperatureanddeveloping microclimatesinthisseason,thusreducingthespatially consisten-ciesofthevariables.ThoughthemonthlyvariationofdIAindexfor

TmaxandTminareidentical,theestimationerrorisslightlyhigher

forthelatervariablebecauseitismoresensitivetolocalclimate andadvection.

Fig.3csuggeststhattheestimatedvaluesformeanRHarein goodagreementwiththeobservedones;alargerestimationerror fromDecembertoMarchindicatesthatRHismoreheterogeneous inspace duringwinterthanin summer.Thismaybeexplained by theintrusion ofvariable sources ofhumidair into different partsofIranbydifferentatmosphericcirculationtypesinwinter (Razieietal.,2012a,2012b).However,contrarilytotemperature variables,theestimationerrorforsunshine(Fig.3d)ishighly vari-able(widerspreadforthe25–75%percentiles)duringallmonths, thoughinmostcasesthelowerquartileoftheboxplotofdIAlies

above0.90,thuspointingtoasatisfactoryaccuracyofinterpolation. Thisvariabilitymayalsorelatetotheinfluenceofdifferent atmo-sphericcirculationtypesindifferentiatingthetargetarearegarding toclearness/cloudinessoftheskyacrossthecountry.Duststorms shouldalsobeconsideredasanotherresponsiblefactorin differ-entiatingtheclearnessoftheskyinaridandhyper-aridclimatesof central,easternandsouthernIran,eveninveryshortdistances.This phenomenonmaycauseanoticeableunderestimationofsunshine durationinsomestationsduetoobscuringthesunshinerecorder, resultinginanoticeablereductioninsunshinerecordsthatmay locallybefardifferentfromtheneighbouringsites.Asisillustrated inFig.3e,theestimationerrorisnoticeablyhighforinterpolation ofwindspeed,resultinginmuchlowerdIAvaluesincomparison

totheothervariablesshowninFig.3a–d.Thehigherestimation errorforwindspeedislikelytobeduetothefactthatwindspeed is highlyvariablein spaceas itis a locally dependentvariable, thuscausingittobehighlyspatiallynon-continuouseveninshort distances.Windspeedvariesmuch throughoutthecountryand therespectivespatialpatternshowsalargelocaldependencyas analysedinaformerstudyonETo(RazieiandPereira,2013).This

characteristiccanberelatedtothesubstantialeffectofthe topog-raphy,thatcaninducechangesinwindspeedanddirectioninshort

Fig.2.Distributionofthecross-validatedinterpolationerrorsfor(a)Tmax(◦C),(b)Tmin(◦C),(c)meanrelativehumidity(%),(d)sunshineduration(hour/month)and(e)wind

Fig.3.Box-WhiskerPlotsoftheindexofagreement(dIA)relatingtheobservedandinterpolatedmonthlyvaluesof:(a)Tmax,(b)Tmin,(c)relativehumidity,(d)sunshineand

(e)windspeed.Eachplotshowsthemedian,interquartilerange(box)andouterquartiles(whiskers)oftheagreementforallmonths.

distances,thusmakingthewindparametertobeknownastheless correlatedvariableinspace.Thisismuch pronouncedinrugged areaslikeIran(Fig.1a),whereplainareasareseparatedby moun-tainsandhighlands.Moreover,everyregionmayhavelocalwinds withlimitedareasofinfluence,whichinducessubstantial differ-encesamongwindmeasurementsofnearbystations.However,the

relatively higher agreement found for summer months can be relatedtothelessspatiallyvariablewindspeedthroughoutIran duetothedominationofstablesynopticpatternsoverwholethe countryinthisseason(Razieietal.,2012a,2012b;Zaitchiketal., 2007);theoccurrenceofextremesummerwindineasternIranis anexception.

Theaccuracyoftheinterpolationofthevariablesisreasonably highandacceptable,particularlyregardingtotheTmax,Tmin,RH

andsunshineduration.Therelativelyhigherestimationerrorsfor windspeedwereexpectedsinceitisalocallydependentvariable andissubstantiallyinfluencedbytopographyandregional advec-tionasanalysed in apreviousstudy(Raziei andPereira, 2013). Thestationnetworksofthepresentstudy(Fig.1b)isrelatively sparse,particularlyinthecentral-eastern andsouthern partsof Iran,andcontainssevereelevationgradients(Fig.1a)thatarelikely tocauselargeestimationerrors forsparseandisolatedstations throughcross-validationprocedure.InsuchanareaasIran,which isrelativelylargewithdiverseclimatesandtopographicfeatures, withholdingastationfromthenetworksthroughcross-validation procedureoftenforcestheinterpolatortohaveanestimationfor isolatedpointsbasedupon muchapart locations;consequently,

largeestimationerrorsyieldforsparseandisolatedstations.This isalsothecaseforthehighelevationstationsscatteredinwestern andnorthernmountainousareas.Withholdingsuchstationsfrom thenetworksmeansthattheestimatingvaluesforthosepoints, baseduponmuchlowerelevationpoints,resultinhigher estima-tionerrors.However,thecross-validationerrorsmayexceedactual interpolationerrorssincethenetworkisslightlydegraded(ton−1 stations),makingitmoresparselocally,specificallywhendealing withsparseandirregularlyspacednetworksofstations.Therefore, therealinterpolationresultwouldbemoreaccurateandcloserto theobservationsthanthatrelativetothecross-validationoutputs (WillmottandMastuura,1995).

Fig.4showsthespatialvariability ofthemeaninterpolation errorsrelativetoeachconsideredvariableobtainedfromcross vali-dation.Ingeneral,theseerrormapsdo notillustrateconsistent

Fig.4.Spatialvariabilityofmeancross-validatedinterpolationerrorsoverIran:(a)Tmax(◦C),(b)Tmin(◦C),(c)meanRH(%),(d)sunshineduration(hour/month)and(e)wind

spatialpatterns of errors but, contrarily,they indicatethat the interpolation errors are randomly distributed over the coun-try. Thelargestobserved errorsin themaps appearas isolated anomaliesinterspersedoverthearea. Mostofthespotareasof higherrors refertoisolatedstations,particularlyhighelevation siteswheresomevariables wereoverestimated/underestimated throughcross-validationduetousingdatafromsurrounding sta-tionswithlower elevations. Thisisthecase of overestimations of Tmin and Tmax in mountainous areas, since temperatureis a

topographydependentvariable.Differently,thenoticeable under-estimationsof Tmin and Tmax variables in Fig.4a and b mostly

correspondto isolated stations in areas of central-eastern Iran wherethestationsnetworkisquitesparseandwhereadvection mayaffecttemperature.Theobservedspatialdistributionoferrors,

particularlyforthecasesof sunshineduration, windspeed and RH(Figs. 4c–e)is likelytobeinfluenced bytheabruptchanges inclimatefeatures in shortdistances ortotheartefacts-like of uniquemicroclimatesaffectingspecificstations,aswellasto non-meteorologicalpeculiaritiesinthestationobservationsasnotedby DegaetanoandBelcher(2007).NoticeableunderestimationofRH (Fig.4c)inthecoastalareasofnorthernandsouthernIranisdueto theinfluenceofneighbouringdrierstationslocatedafew kilome-tresawayfromthecoastalstations.Thenoticeableoverestimation ofsunshinedurationintheCaspianSearegionislikelyrelatedto thefactthattheregionisextremelynarrow,thereforenotexisting enoughstationsinthisarea,thusinvolvingstationsofinteriorIran intheinterpolationprocedure,thatdeviatetheestimationresults relativetoobservationsinthisarea(Fig.4d).Theerrormapofwind

Fig.5.Spatialvariabilityoflong-termmeanofgriddeddatasetsoverIran:(a)Tmax(◦C),(b)Tmin(◦C),(c)meanRH(%),(d)sunshineduration(hour/month)and(e)windspeed

speed(Fig.4e)showssimilarcharacteristicswhichisexpectedas thewindspeedisalocallydependentvariableandsubstantially variesinspace(Newetal.,2002).

Fig.5showsspatialpatternsofthelong-termannualaverage ofthegriddedvariablesoverIran.Thespacevariationofannual averageofthegriddedvariablescoincidewellwiththereal spa-tialpatternsofeachvariableinIran(Alijani,1997;Masoudianand Kaviani,2007),i.e.,reflectingtheroleplayedbytopographyand seaneighbourhoodinspatialdistributionofthevariables.InFig.5a andbtheroleofnorthwest-southeastorientedZagrosmountains (Fig.1a)iswellrepresented.Inthesefigures,southernand cen-traleastern Iranarewellidentifiedas regionswiththehighest temperatureduetothelowerlatitudeand/oraltitude,aswellas duetothestablesubsidence ofthedynamichighpressure sys-temover thesouthern halfofIraninwarmseason,resultingin

veryhotanddryweatherfromApriltoSeptember.Theroleofsea neighbourhoodisalsowellillustratedinFig.5c,inidentifyingthe highestmeanrelativehumidityintheCaspianSearegion,inthe north,andthecoastalareasofOmanseaandPersianGulfinthe south.InFig.5c,themountainousareasofwesternandnorthern Iranshowannualmeanrelativehumidityequalto40–50%,while central-easternIranwherethedesertareasofDashteKavirand DashteLutarelocatedisidentifiedasthedriestareadueto posi-tioningintheleesideoftheZagrosandAlborzmountains(Fig.1a). Fig.5dshowsthatthesunshinedurationismostlycontrolledby lat-itudeandseaneighbourhood,butisalsoinfluencedbyorography. Therefore,mostpartsofIraninsouthernandcentral-eastern coun-tryaredepictedasareashavingannualmeanmonthlysunshine durationof270–300h,decreasinggraduallytothenorthduetothe additionaleffectoforographyandvicinityoftheseathatrepresent

anincreaseofrelativehumidityandcloudiness,thereforereducing sunshineduration.ThespatialvariabilityofwindspeedinIranis illustratedinFig.5e,showingthehighestandthelowestvaluesfor easternandcentral-northernIran,respectively.Thespatialpatterns ofthegriddedresultsoftheconsideredvariableslookmuch real-isticandinagreementswithliterature(Alijani,1997;Masoudian andKaviani,2007).

3.2. SpatialpatternofETo

Fig.6aillustratesthespatialpatternoflong-termmeanannual PM-ETo overIrancomputedbaseduponthegriddedinput

vari-ables.The figuresuggestsa gradualincrease of ETo fromnorth

toSouth, withthelowest values over thenorthernhumid and sub-humidclimatesofIranandlargerEToestimatesforaridand

hyper-arid climates in the southern and eastern country. The range of annual ETo varies from800mm in the humidcoastal

areasofsouthernCaspianSeaupto2400mminhyper-ariddesert areasofeasternIran.TheCaspianSeaareaischaracterizedwith 800–1000mmETo,whereasthemountainousareasofnorthernand

north-westernIrandepictETovaluesbetween1000and1400mm,

increasingsouthwardand eastwardduetothedecreasein lati-tudeand/oraltitude.Themountainousareasofsouthernpartof Zagrosanditswesternandeasternflanks,aswellasthefoothills of Alborz in mid-central Iran, exhibit ETo between 1400 and

1800mm,whiletheETo valuesforavastareaincentral,

south-ernandeastern Iranrangefrom1800to2400mm.Thehighest ETo,with2200to2400mm,occursinsouth-westernandeastern

Iran.ThehighETo insouth-westernIran isrelated to

tempera-ture,thehighestobservedinthecountry,andrelativelydominant heatadvectionandextremewindspeedinsummer.Differently, in eastern Iran, it likely relates to the very high wind speed (Fig.5e),drynessandheatadvection;averylowannualmean rel-ativehumidityoccursthere(<40%,Fig.5c), whichevenreduces to<25%insummer,whentheregionisexposedtoextremewind speed.

TrendsinETo havebeenreportedbyDinpashohetal.(2011)

fordifferentgeographicregionsofIran.Suchtrendsareexpected whensignificantchangesinanyvariableinvolvedinETo

estima-tionwouldoccur;usingthegriddeddatadeveloped maybetter supportingtounderstandtherespectivevariationpatterns.

ThespatialpatternofPM-ETooverIranproducedhereinusing

the gridded datasets as input variables is comparable to that presented by Raziei and Pereira (2013) and Dinpashoh (2006), thoughthe number of used stations in those works is far less thanfor thepresent studyand theconsidereddataperiodsare different.However,thespatialpatternofPM-ETo inthepresent

studyis much smoother and consistent thanthose of the pre-viousworks(RazieiandPereira,2013;Dinpashoh,2006)dueto usingmuch denserstations for gridding the variables, particu-larlythose relative tosunshine duration,relative humidity and windspeed,thatcommonlysufferfromsubstantialmissing val-ues.

Fig.6b–eshowsthespatialpatternsofseasonalPM-ETo over

Iran,depictingrelativelythesameconfigurationasforthemean annualpatternshowninFig.6a.Fig.6bsuggeststhatthespatial pattern of winter PM-ETo, with a southward increasing

gradi-ent,islargely controlledbylatitude, that canberelated tothe dominanceof large-scaleatmospheric synopticpatterns in this season(Raziei et al.,2012a, 2012b; Zaitchik et al., 2007). Con-trarily, Fig. 6c and 6e better reflect the role of topography in delineatingthespatialvariabilityofspringand autumnPM-ETo,

i.e., showingrelatively lower ETo over the mountain ranges of

Zagros and Alborz in western and northern Iran, respectively. As in Fig. 6b the role of topography in western Iran is rela-tively less evident in Fig.6d;this likely refers tothe fact that

Table3

StatisticallycomparingtheperformanceofPM-ETocomputedusingfull

observa-tionaldatasetsinsomeselectedstationsdistributedthroughIran(Fig.1b)andthose ofusinggriddedvariablesaveragedoverthefourgridssurroundingagivenstation.

Stations R RMSE(mmd−1_{) EF dIA} Tabriz 0.99 0.54 0.95 0.99 Zanjan 0.99 0.28 0.98 1.00 Hamedan 0.99 0.47 0.96 0.99 Kermanshah 0.99 0.27 0.99 1.00 Ahwaz 0.99 0.40 0.98 1.00 Shiraz 0.99 0.41 0.96 0.99 Tehran 1.00 0.45 0.96 0.99 Yazd 0.99 0.48 0.96 0.99 Kerman 0.99 0.27 0.99 1.00 Isfahan 0.99 0.24 0.99 1.00 Mashhad 0.99 0.40 0.97 0.99 Shahroud 0.99 0.56 0.93 0.98 Babolsar 1.00 0.13 0.99 1.00 Rasht 1.00 0.22 0.97 0.99 Iranshahr 0.98 0.63 0.94 0.98 Zahedan 0.99 0.47 0.95 0.99 Tabas 0.99 0.44 0.97 0.99 BandarAbas 0.99 0.30 0.97 0.99 Birjand 0.99 0.94 0.85 0.97 Zabol 0.98 2.15 0.80 0.95

thedynamichighpressuresystemthatrelativelydominatesthe wholecountryinsummeractsasalargescaledriverin control-ling the spatial variability of PM-ETo in this season. In all the

seasonsthelowestETo is observedintheCaspianseaareaand

thehighestvaluescorrespondtosouth-easternandsouth-western Iran.

3.3. Re-evaluationofgridbasedPM-ETo

TheadequacyofthegriddedvariableswhenusedforPM-ETo

estimationacrossIranwasassessedthroughasetofgoodnessof fitindicators(Table3)appliedtosomeselectedstations represen-tativeofallclimaticandgeographicfeaturesofIran(Fig.1b).The statisticsindicatethatthePM-ETo computedusinggridded

vari-ableswellfittedthePM-ETocomputedusingobservedfullweather

variablesatselectedstations,whichissupportedbyacorrelation coefficient(R)higherthan0.98andtheEFanddIAstatisticshigher

than0.94.ExceptforZabolandBirjandinthearidandwindy east-ernIran,theRMSEislowerthan0.65mmd−1inallstations,giving agoodindicationoftheaccuracyofthegriddingprocessin esti-matingvaluesofeachvariableatalllocationswhichappearedin theresultantPM-ETo.TherelativelyloweragreementinZaboland

Birjandstations,asindicatedbyhigherRMSEandlowerEF indi-cators,canbepartiallyrelatedtothesparserstationnetworkin easternIranusedforgriddingthevariablesandtotheinfluence ofthesmoothedgriddedwindvariableforthearea,whichis rela-tivelylowerthantheactualobservedwindspeedatthesestations, particularlyforZabol,whereitswindspeedisfarhigherthanthose ofthesurroundingbutdistantstations(RazieiandPereira,2013).

ThehighagreementbetweenPM-ETocomputedusinggridded

and observationvariables (Table3)is anindicationof the ade-quacyofthegriddingprocesses,whichcanserveasausefultool toprovidefinespatialresolutiondatasetsoftherequiredvariables foradequatelyestimationofPM-ETo alloverthecountryto

sup-portawiderangeofagriculturaland irrigationmanagement,as wellaswaterresourcesapplicationsatcatchmentandwatershed scale.Thisisparticularlyimportantforareaswherethestations havingfulldatasetsrequiredforestimationofPM-ETo areeither

verysparseorsufferfromsubstantialmissingvalues,particularly consideringsunshineduration andwind speedvariables, which mostoftenfacedatagaps.

Fig.7. SpatialdistributionofmeanannualETocomputedby(a)HSmethod,(b)PMTmethod,(c)spatialpatternofkRsforHS-ETo,(d)spatialpatternofkRsforPMT-ETo,(e)

spatialpatternofHS/PM-EToratioand(f)spatialpatternofPMT/PM-EToratiooverIran.

3.4. EstimationofETowithtemperaturemethods

The satisfactory result achieved using the gridded variables inestimatingPM-ETopresentedin theprevioussection

encour-aged usto estimateETo withtemperaturemethods using only

thegriddedvariablesofTmin andTmax.Fig.7aand bshow

spa-tialpatternsoflong-termmeanannualHS-EToandPMT-EToover

Iran,respectively,computedusingthegriddedvariables ofTmin

and Tmax. Spatial variability of HS-ETo and PMT-ETo are

iden-tical and resembleto that of PM-ETo depictedin Fig. 6a, with

thesamemagnitudeofETo alloverthecountry,suggestingthat

the HS and PMT methods can be used as alternatives to full dataPMmethod(Eq.(3))toappropriatelyestimateETo allover

the country using only Tmax and Tmin. Spatial patterns of the

appropriatekRsusedforestimationofHS-EToandPMT-ETothrough

thecountry,showninFig.7canddrespectively,areverysimilar andconsistent,indicatingthattheappropriatekRsusedfor

estima-tionofETobybothmethodsstronglyco-varyacrossthecountry.

Forbothmethods,thelowestkRsisobservedintheCaspianSea

regionandinthemountainousareasofwesternIran,whilethe highestkRsis observedinthehyper-arid regionofeastern Iran.

ThebestfittedkRsforestimationofHS-EToinmountainousareasof

westernandnorthernIrancharacterizedwithsemi-aridtohumid climates (see Fig.1d)ranges from0.14 to0.18, while it varies between0.19and0.25 inaridtohyper-aridclimatesof central-eastern and south-western Iran(Fig.7c). Spatial pattern of the appropriatekRsusedforestimationPMT-ETo isidenticaltothat

Table4

StatisticalindicatorscomparingtheperformanceofHSandPMTmethodswithPM-EToestimatesfortheclimaticzonesdepictedinFig.1d.

Climaticzone HSvs.PM-ETo PMTvs.PM-ETo

RMSE(mmd−1_{) R}2 _d IA EF RMSE(mmd−1) R2 dIA EF Hyper-arid 0.66 0.94 0.98 0.93 0.62 0.94 0.98 0.94 Arid 0.59 0.95 0.98 0.94 0.58 0.95 0.98 0.94 Semi-arid 0.41 0.97 0.99 0.97 0.45 0.97 0.99 0.96 Dry-subhumid 0.35 0.98 0.99 0.97 0.40 0.97 0.99 0.96 Moist-sub-humid 0.26 0.98 0.99 0.98 0.32 0.96 0.99 0.96 Humid 0.29 0.98 0.99 0.95 0.25 0.97 0.99 0.97

thanthatofHS-EToinwesternIran,whereitrangesbetween0.11

and0.17,andisreasonablyhigherinaridandhyper-aridareasof easternIran,wherethebestfittedkRsvariesbetween0.25and0.29

(Fig.7d).Theresultsuggeststhatthedifferencebetweenthebest fittedkRsforHSandPMTmethodsisnegligibleinmostpartsofIran,

withtheexceptionofcoldandhumidareasofwesternIranandthe verydryandwindyareasofeasterncountrywherethedifference isreasonablyhigher.Thepresentresultsareinagreementwiththe previousstudyforIranbyRazieiandPereira(2013)usingsparse andirregularlyspacednetworkofstations.

TheannualEToestimatesbyHSandPMTmethodswere

com-paredtothePM-EToestimatesforalltheconsideredgridpoints

shownin Fig.1bby meansof theratioofHS(PMT)toPM-ETo

(Fig.7eandf).SpatialpatternoftheratioHS/PM-ETodepictsthat

theHSestimationiswithin10%differencetoPM-ETo estimates,

i.e.,HS/PM-ETorangedfrom0.98to1.09throughthecountry,thus

indicatingthattheHSestimateswellagreedwithPM-ETo.TheHS

estimatesformajorityportionofthecountryinwestern,central andsouthernIrancoincidewithPM-EToestimates(ratiobetween

0.98and1.04),whereasineasternandnorth-easternIrantheHS slightlyover-estimatedETo(ratiobetween1.04and1.09;Fig.7e).

Fig.7fdepictsspatialdistributionoftheratioofPMTestimatesto PM-ETowhichisrelativelysimilartothatofHSmethodillustrated

inFig.7e.Excepteastern,north-easternandasmallareain north-westernIranwhichshowsaslightoverestimation(ratiobetween 1.04and1.08),thePMTestimationcoincides wellwithPM-ETo,

particularlyforsouth-easternandcentral-westernIran.

Table4illustratesstatisticalindicators,averagedforeach cli-matic zoneidentified in Fig.1d, usedtostatisticallyassess the performancesofHSand PMTmethodswithrespecttoPM-ETo.

Thequitehighvalues oftheaverageofEFanddIA indicatorsas

wellasthelowvaluesofRMSEsuggestthatboththeHSandPMT methodsareaccurateandworthwhileapproachesforETo

estima-tioninallclimaticregionsof Iran.The tablesuggeststhat both

methodshaverelativelysimilarperformanceinallclimatezones. ThestatisticsaresimilartothosecomputedbyRazieiandPereira (2013)usingobservationaldatasets.However,theRMSEvaluesof thepresentstudyaregenerallysmallerthanfortheformeronethus indicatingthatusinggriddeddatasetstoestimatemonthlyETowith

temperaturemethodsprovidesaccurateestimationsalloverthe country.

TheHSmethodperformsslightlybetterthanPMTinsemi-arid, dry-sub-humidandmoist-sub-humidclimatesasindicatedby rea-sonablylowerRMSEand higherEFand dIA statisticsfor theHS

method.However,thePMTshowsslightlybetterperformancein arid,hyper-aridandhumidclimatesconsideringitslowerRMSE valuesandhigherEFanddIAwithrespecttoHSmethod.Verylikely,

betterperformanceofPMTintheseregionsisrelatedtothe adjust-mentofminimumtemperaturewhichhasbeenalreadyprovedby RazieiandPereira(2013)forthesameregions.

Fig.8 illustratesthe spatialdistribution ofthe coefficientof determination(R2_{)relatingHS-ET}

oandPMT-ETowithPM-ETo

esti-matesthroughIran.Resultssuggest thatbothmethodsperform quitewellalloverthecountrywithrelativelyidenticalspatial vari-abilityandR2_values.TheR2_{valueforbothmethodsishigherthan}

0.95alloverthecountryexceptforsouth-easternIran,with rela-tivelylowerR2_{values,rangingfrom0.90to0.95.Resultsindicate}

thattheHSandPMTmethodsexplainmorethan95%ofthe vari-ationofPM-ETo inmostpartsofIranwhich isindicativetothe

accurateestimationbybothmethods.BetterperformanceofPMT methodinhyper-aridregionofsouth-easternIranis evidentin Fig.8b,wherethePMTmethodshows slightlyhigherR2 _values

withrespecttoHSmethod(Fig.8a)thatcanberelatedtothe cor-rectioninminimumtemperatureforariditywhenusingPMT.The RMSE,EFanddIAstatisticsshowsimilarspatialdistributionover

thecountry(notshown).

According to Raziei and Pereira (2013) the occurrence of extremesummerwindsineastern aridandhyper-arid areasof

Fig.8. Spatialdistributionofcoefficientofdetermination(R2_{)relatingPM-ET}

IranresultedinextremePM-ETothatareunderestimatedbyboth

HSandPMTmethods.Thus,toeliminateunderestimations,large kRsvalueswereidentified,whichisinagreementwiththeresults

obtainedwithobservationdata(RazieiandPereira,2013). Inaridandhyper-aridclimates,advectionoftenimpactslocal equilibriumsaturationdeficitbytransportingexcessheatduring windydays, resulting inenhanced ET rate(Brakke et al.,1978, Malek,1987).Surface heatingis adominant climaticfeaturein Iranduringwarmseason(April–October)duetotheexistenceofa strongairsubsidence,providingexcessheatenergyforadvectionof sensibleheatflux(Zaitchiketal.,2007)mainlyinsouthern(Malek, 1987)and easternIran (DaneshkarArastehand Tajrishy,2008). However,asdefinedbyAllenetal.(1998),ETocomprisesonly

ver-ticalfluxes,notincludingadvectioneffects;thuscropcoefficients used tocompute cropevapotranspiration fromETo need tobe

adjustedtoconsideradvection(Allenetal.,1998).However,the FAO-PMequationissupposedtoperformwellevenwhenadvection occurs(BerengenaandGavilán,2005;Allenetal.,2006). Never-theless,theadvectiveenergycarriedbyextremesummerwinds passingoverdryandhotdesertsmayalsobeconsideredasan addi-tionalfactorresponsiblefordeviatingtheestimatebyHSandPMT fromPM-EToandconsequentlyleadingtofithigherkRsvaluesfor

regionswhereadvectionoccurs.

4. Discussionandconclusions

Aiming at providing high resolution spatial surfaces of ETo

estimatesforIran,monthlyaveragesofmaximumandminimum temperature,meanrelativehumidity,sunshinedurationandwind speed at 2m height, relative to 148 Iranian weather stations distributedover thecountrywereutilizedfor interpolationand griddingthevariables.Theresultssuggestedthattheaccuracyof theinterpolationoutputsisreasonablyhigh,particularlyregarding totheTmax,Tmin, RHand sunshine duration.Higher estimation

errorswerefoundforwindspeedbecauseitisalocallydependent variableandsubstantiallyinfluencedbytopography.Results indi-catethatthePM-ETocomputedusingthegriddedvariableswellfit

thePM-ETocomputedusingobservedfullweathervariables

rela-tivetotheselectedstationsrepresentativeofallIranianclimates. Thishighagreementisanindicationtotheadequacyofthe grid-dingprocesses,which canserveasausefultool toprovidefine spatialresolutiondatasetsoftherequiredvariablesforadequately estimatingPM-EToalloverthecountrytosupportawiderangeof

applications.Thisisparticularlyimportantforareaswhereweather stationsareeitherverysparseorsufferfromsubstantialmissing values,particularlyrelativetosunshinedurationandwindspeed variables.

Thespatialpatternoflong-termmeanannualPM-ETooverIran

computedwiththegriddedvariablessuggestsagradualincrease ofETo fromnorth tosouth, withthelowestvalues over

north-ernhumidandsub-humidclimatesofIranandlargerestimatesin aridandhyper-aridclimatesofsouth-easterncountry.Thespatial patternsofspringandautumnPM-EToreflecttheroleof

topogra-phywhilethepatternsofwinterandsummerPM-ETodepictthe

dominanceoflarge-scaleatmosphericsynopticpatterns.

TheestimatedETowithtemperaturemethodsusingonly

grid-dedvariablesofTminandTmaxwellagreedwithPM-EToallover

thecountry. Spatialpatternsof long-termmean annualHS-ETo

andPMT-ETocomputedwiththegriddedvariables areidentical

and resembletothatof PM-ETo.Thissuggeststhat theHSand

PMTmethodscanbeusedwhenonlylimitedvariablesare avail-able.SpatialpatternsoftheappropriateradiationcoefficientkRs

usedwiththeHSandPMTmethodsarealsoverysimilarand con-sistentthroughoutIran,indicatingthattheappropriatekRsshow

strongco-variabilityacrossthecountry.Forbothmethods,lower

kRsareobservedintheCaspianSearegionandmountainousareasof

westernIran,whilehigherkRsareobservedinhyper-aridregions

ofeasternIran.ItcouldbeconcludedthatthekRsincreaseswith

skyclearnessasgovernedbylatitudeandaltitudeanddecreases forcloudylocationswithlowertemperature.kRsalsoincreasesfor

windylocationsasisthecaseineasternIran.

SpatialpatternsoftheratioofannualEToestimatedbyHSand

PMTmethodstothePM-ETo estimatesdepictedthattheHSand

PMTestimationiswithin10%differencetoPM-EToestimates,

indi-cating thatboth methods wellagreedwithPM-ETo throughout

Iran.StatisticssuggestthattheHSmethodperformsslightly bet-ter insemi-arid,dry-sub-humid and moist-sub-humidclimates, whereas PMT slightly betterperformed in arid,hyper-arid and humidclimates.Verylikely,thegoodperformanceofPMTisrelated totheadjustmentofminimumtemperaturewhenestimatingthe dewpointtemperature.Furtherstudiessuggestedbytheachieved resultsincludeassessingtheimpactofheatadvectiononET esti-mationwithtemperaturedataonly,aswellasfurtheranalysingthe timeandspacevariabilityofwindspeedthroughIran.An evalua-tionoftheadoptedETomethodologieswhenusingdailydatasets

isalsorequired.AfurtheranalysisofETotrendsinrelationtothe

computationalmethodsusedisalsodesirable.

Thestudy wassuccessfulin providingmeansfor reasonably accurateEToestimatesforIranatafinespatialresolutionthatcan

beusedforvariousagriculturalandwaterresourcesmanagement purposesatregionaltowatershedlevels.Therefore,itcanalsobe concludedthatthesemethodologiesmaybeusedinotherareasin ordertodevelophighresolutiongriddedEToestimatesforarange

ofspatialscales.

References

Adler,R.F.,Susskind,J.,Huffman,G.J.,Bolvin,D.,Nelkin,E.,Chang,A.,Ferraro,R., Gru-ber,A.,Xie,P.P.,Janowiak,J.,Rudolf,B.,Schneider,U.,Curtis,S.,Arkin,P.,2003.

Theversion2globalprecipitationclimatologyproject(GPCP)monthly precipi-tationanalysis(1979-present).JournalofHydrometeorology4,1147–1167.

Alijani,B.,1997.TheClimateofIran.PayameNourPublicationSeries,Teheran,Iran, pp.221(inPersian).

Allen,R.G.,Pereira,L.S.,Raes,D.,Smith,M.,1998. CropEvapotranspiration. Guide-linesforComputingCropWaterRequirements.FAOIrrig.Drain.Pap.56.FAO, Rome,pp.300.

Allen,R.G.,Pruitt,W.O., Wright,J.L.,Howell,T.A.,Ventura,F.,Snyder,R., Iten-fisu,D.,Steduto,P.,Berengena,J.,Baselga,J.,Smith, M.,Pereira,L.S.,Raes, D.,Perrier,A.,Alves,I.,Walter,I.,Elliott,R.,2006. Arecommendationon standardized surfaceresistance forhourly calculationofreference ETo by theFAO56Penman–Monteithmethod.AgriculturalWaterManagement81, 1–22.

Angström,A.,1924.Solarandterrestrialradiation.QuaterlyJournalofRoyal Mete-orologicalSociety50,121–125.

Belo-Pereira,M.,Dutra,E.,Viterbo,P.,2011.Evaluationofglobalprecipitationdata setsovertheIberianPeninsula.JournalofGeophysicalResearch116,D20101,

http://dx.doi.org/10.1029/2010JD015481.

Berengena,J.,Gavilán,P.,2005.Referenceevapotranspirationestimationinahighly advectivesemiaridenvironment.JournalofIrrigationandDrainageEngineering 131(2),147–163.

Biau,G.,Zorita,E.,vonStorch,H.,Wackernagel,H.,1999.Estimationofprecipitation bykrigingintheEOFspaceofthesealevelpressurefield.JournalofClimate12, 1070–1085.

Brakke,T.W.,Verma,S.B.,Rosenberg,N.J.,1978. Localandregionalcomponentsof sensibleheatadvection.JournalofAppliedMeteorology17,935–963.

Cai,J.,Liu,Y.,Xu,D.,Paredes,P.,Pereira,L.S.,2009.Simulationofthesoilwater bal-anceofwheatusingdailyweatherforecastmessagestoestimatethereference evapotranspiration.HydrologyandEarthSystemSciences13,1045–1059.

Daly,C.,Gibson,W.P.,Taylor,G.H.,Johnson,G.L.,Pasteris,P.,2002. A knowledge-basedapproachtothestatisticalmappingofclimate.ClimateResearch22, 99–113.

DaneshkarArasteh,P.,Tajrishy,M.,2008.CalibrationPristley–Taylormodelto esti-mateopenwaterevaporatonunderregionaladvectionusingvolumebalance method–casestudy:Chahnimehreservoir,Iran.JournalofAppliedSciences8 (22),4097–4104.

Degaetano,A.T.,Belcher,B.N.,2007. Spatialinterpolationofdailymaximumand minimumairtemperaturebasedonmeteorologicalmodelanalysesand inde-pendentobservations.JournalofAppliedMeteorologyandClimatology46, 1981–1992.

Dinpashoh,Y.,2006. StudyofreferencecropevapotranspirationinI.R.ofIran. AgriculturalWaterManagement84,123–129.

Dinpashoh,Y.,Jhajharia,D.,Fakheri-Fard,A.,Singh,V.P.,Kahya,E.,2011. Trendsin referenceevapotranspirationoverIran.JournalofHydrology399,422–433.

Dirks,K.N.,Hay,J.E.,Stow,C.D.,Harris,D.,1998.High-resolutionstudiesofrainfall onNorfolkIsland,PartII:Interpolationofrainfalldata.JournalofHydrology208 (3–4),187–193.

Gong, L.,Xu, C.Y., Chen,D., Halldin,S., Chen,Y.D., 2006. Sensitivity of the Penman–Monteithreferenceevapotranspirationtokeyclimaticvariablesinthe Changjiang(YangtzeRiver)basin.JournalofHydrology329,620–629.

Haylock,M.R., Hofstra, N.,Klein-Tank, A.M.G., Klok,E.J., Jones,P.D.,New, M., 2008.AEuropeandailyhigh-resolutiongriddeddatasetofsurface temper-atureandprecipitationfor1950–2006.JournalofGeophysicalResearch113,

http://dx.doi.org/10.1029/2008JD010201,D20,119.

Herrera,S.,Gutiérrez,J.M.,Ancell,R.,Pons,M.R.,Frías,M.D.,Fernández,J.,2012.

Developmentandanalysisofa50-yearhigh-resolutiondailygridded precip-itationdatasetoverSpain(Spain02).InternationalJournalofClimatology32, 74–85.

Hijmans,R.,Cameron,S.,Parra,J.,Jones,P.,Jarvis,A.,2005. Veryhighresolution interpolatedclimatesurfacesforgloballandareas.InternationalJournalof Cli-matology25,1965–1978.

Hofstra,N.,Haylock,M.,New,M.,Jones,P.,Frei,C.,2008.Thecomparisonofsix meth-odsfortheinterpolationofdailyEuropeanclimatedata.JournalofGeophysical Research113,http://dx.doi.org/10.1029/2008JD010100,D21110.

Holdaway,M.R.,1996.Spatialmodellingandinterpolationofmonthlytemperature usingKriging.ClimateResearch6,215–225.

Hutchinson,M.F., 1995. Interpolatingmeanrainfallusingthinplate smooth-ingsplines.InternationalJournalofGeographicalInformationSystems9(4), 385–403.

Jones,P.D.,Raper,S.C.B.,Bradley,R.S.,Diaz,H.F.P.,Kelly,M.,Wigley,T.M.L.,1986.

NorthernHemispheresurfaceairtemperaturevariations:1851–1984.Journal ofClimateandAppliedMeteorology25,161–179.

Journel,A.G.,Huijbregts,C.J.,1978. MiningGeostatistics.AcademicPress,London, pp.600.

Laslett,G.M.,1994.Krigingandsplines:anempiricalcomparisonoftheirpredictive performanceinsomeapplications.JournalofAmericanStatisticalAssociation 89(426),391–400.

Liebmann,B.,Allured,D.,2005.DailyprecipitationgridsforSouthAmerica.Bulletin oftheAmericanMeteorologicalSociety86,1567–1570.

Malek,E.,1987. ComparisonofalternativemethodsforestimatingETpand evalu-ationofadvectionintheBajgaharea,Iran.AgriculturalandForestMeteorology 39,185–192.

Masoudian,S.A.,Kaviani,M.R.,2007. TheClimateofIran.IsfahanUniversityPress, Isfahan,Iran,pp.179(inPersian).

Matheron,G.,1971. Thetheoryofregionalizedvariablesanditsapplications.Les CahiersduCentredeMorphologieMathématique,No5.Fontainebleau,Ecole NationaleSupérieuredesMinesdeParis.

Maurer,E.P.,Wood,A.W.,Adam,J.C.,Lettenmaier,D.P.,Nijssen,B.,2002.Along-term hydrologicallybaseddatasetoflandsurfacefluxesandstatesforthe contermi-nousUnitedStates.JournalofClimate15(22),3237–3251.

Moriasi,D.N.,Arnold,J.G.,VanLiew,M.W.,Bingner,R.L.,Harmel,R.D.,Veith,T.L., 2007.Modelevaluationguidelinesforsystematicquantificationofaccuracyin watershedsimulations.TransactiononASABE50(3),885–900.

Nandagiri,L.,Kovoor,G.M.,2005.SensitivityoftheFoodandAgriculture Organiza-tionPenman–Monteithevapotranspirationestimatestoalternativeprocedures forestimationofparameters.JournalofIrrigationandDrainageEngineering131 (3),238–248.

Nash,J.E.,Sutcliffe,J.V.,1970. Riverflowforecastingthroughconceptualmodels: Part1.Adiscussionofprinciples.JournalofHydrology10(3),282–290.

New,M.,Hulme,M.,Jones,P.,1999. Representingtwentieth-centuryspace-time climatevaribility.PartI:developmentofa1961–90meanmonthlyterrestial climatology.JournalofClimate12,829–856.

New,M.,Lister,D.,Hulme,M.,Makin,I.,2002.Ahigh-resolutiondatasetofsurface climateovergloballandareas.ClimateResearch21,1–25.

Pereira,L.S.,Perrier,A.,Allen,R.G.,Alves,I.,1999. Evapotranspiration:reviewof conceptsandfuturetrends.JournalofIrrigationandDrainageEngineering125 (2),45–51.

Pereira,L.S.,Rosa,R.D.,Paulo,A.A.,2007. TestingamodificationofthePalmer droughtseverityindexforMediterraneanenvironments.In:Rossi,G.,Vega,T., Bonaccorso,B.(Eds.),MethodsandToolsforDroughtAnalysisandManagement. Springer,Dordrecht,pp.149–167.

Perry,M.,Hollis,D.,2005. Thegenerationofmonthlygriddeddatasetsforarange ofclimaticvariablesovertheUK.InternationalJournalofClimatology25(8), 1041–1054.

Philips,D.L.,Marks,D.G.,1996. Spatialuncertainityanalysis:propagationof inter-polationerrorsinspatiallydistributedmodels.JournalofEcologicalModeling 91,213–219.

Popova,Z.,Kercheva,M.,Pereira,L.S.,2006.ValidationoftheFAOmethodologyfor computingETowithmissingclimaticdata.ApplicationtoSouthBulgaria.Journal ofIrrigationandDrainage55(2),201–215.

Raziei,T.,Pereira,L.S.,2013. EstimationofETowithHargreaves–Samaniand FAO-PMtemperaturemethodsforawiderangeofclimatesinIran.AgriculturalWater Management121,1–18.

Raziei,T.,Bordi,I.,Santos,J.A.,Mofidi,A.,2012a.Atmosphericcirculationtypes andwinterdailyprecipitationinIran.InternationalJournalofClimatology,

http://dx.doi.org/10.1002/joc.3596.

Raziei,T.,Mofidi,A.,Santos,J.A.,Bordi,I.,2012b. Spatialpatternsandregimesof dailyprecipitationinIraninrelationtolarge-scaleatmosphericcirculation. InternationalJournalofClimatology32,1226–1237.

Samani,Z.,2000. Estimatingsolarradiationandevapotranspirationusing mini-mumclimatologicaldata.JournalofIrrigationandDrainageEngineering126, 265–267.

Samani,Z.,2004.Discussionof“HistoryandevaluationofHargreaves evapotrans-pirationequation”byGeorgeH.HargreavesandRichardG.Allen.Journalof IrrigationandDrainageEngineering,ASCE130(5),447–448.

Shen,S.S.P.,Dzikowski,P.,Li,G.,Griffith,D.,2001. Interpolationof1961–97daily temperatureandprecipitationdataontoAlbertapolygonsofEcodistrictandSoil LandscapesofCanada.JournalofAppliedMeteorology40,2162–2176.

Shepard,D.,1968.Atwo-dimensionalinterpolationfunctionforirregularly-spaced data.In:Proceedings of1968 ACMNationalConference.ACM, NewYork, pp.517–524.

Smith,M.,2000. Theapplicationofclimaticdataforplanningandmanagement ofsustainablerainfedandirrigatedcropproduction.AgriculturalandForest Meteorology103,99–108.

Thornthwaite,C.W.,1948.Anapproachtowardarationalclassificationofclimate. GeographicalReview38(1),55–94.

Todorovic,M.,Karic,B.,Pereira,L.S.,2013. Referenceevapotranspirationestimate withlimitedweatherdataacrossarangeofMediterraneanclimates.Journalof Hydrology481,166–176.

Tsakiris,G.,Pangalou,D.,Vangelis,H.,2007. Regionaldroughtassessmentbased onthereconnaissancedroughtindex(RDI).WaterResourcesManagement21, 821–833.

UNEP,1997. WorldAtlasofDesertification,2nded.UnitedNationsEnvironment Programme,Arnold,London,pp.182.

Willmott,C.J., Mastuura, K., 1995. Smart interpolation ofannually averaged air temperaturein theunited states. Journalof AppliedMeteorology 34, 2577–2586.

Willmott,C.J.,1981. Onthevalidationofmodels.PhysicalGeography2,184– 194.

Yatagai,A.,Arakaw,O.,Kamiguch,K.,Kawamoto,H.,Nodzu,M.I.,Hamada,A.,2009.

A44-yeardailygriddedprecipitationdatasetforAsiabasedonadensenetwork ofraingauges.SOLA5,137–140.

Yatagai,A.,Xie,P.,Alpert,P.,2008. Developmentofadailygriddedprecipitation datasetfortheMiddleEast.AdvancesinGeosciences12,165–170.

Zaitchik,B.F.,Evans,J.P.,Smith,R.B.,2007. Regionalimpactofanelevatedheat source:theZagrosplateauofIran.JournalofClimate20,4133–4146.