ContentslistsavailableatSciVerseScienceDirect
Agricultural
Water
Management
jo u r n al h om ep a g 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
Estimation
of
ET
o
with
Hargreaves–Samani
and
FAO-PM
temperature
methods
for
a
wide
range
of
climates
in
Iran
Tayeb
Raziei
a,b,∗,
Luis
S.
Pereira
baSoilConservationandWatershedManagementResearchInstitute(SCWMRI),Tehran,Iran bCEER–BiosystemsEngineering,InstituteofAgronomy,TechnicalUniversityofLisbon,Portugal
a
r
t
i
c
l
e
i
n
f
o
Articlehistory:Received24September2012 Accepted21December2012 Available online 14 February 2013 Keywords:
Referenceevapotranspiration Dewpointtemperature Radiationadjustmentcoefficient Temperatureadjustment Humidvs.aridregions Windspeed Spatialvariability
a
b
s
t
r
a
c
t
Monthlydatarecordsof40Iranianstationsdistributedoverthecountry,fortheperiod1971–2005, wereutilizedforestimationofreferenceevapotranspiration(ETo)usingPenman–Monteith(PM-ETo),
Hargreaves–Samani(HS)andFAO-PMtemperature(PMT)methods.ToestimateETowithHSandPMT
methods,appropriatekRs,anempiricalradiationadjustmentcoefficient,wereconsideredforeachstation,
whereasTminwasadjustedforestimationofTdewandusedonlyforPMTcomputation.Itwasfoundthat
theappropriatekRsforbothHSandPMTmethodsareidenticalforagivenstationanditisgenerally
smallerinsub-humidandhumidthaninsemi-aridtohyper-aridclimates.TheperformanceofthePMT wasfurtherimprovedinbotharidandhumidclimateswhenTminwasadjusted.Theresultsuggested
thattheHSandPMTmethodsappropriatelypredictEToforallclimaticregionsofIraniftheappropriate
kRswasutilized.However,theconsideredmethodsshowedweakperformancesforsomestationsinarid
andhyper-aridclimatesofeasternandsouthernIranowingtotheeffectofextremeandvariablewind speedinherentinthePM-ETo.Thus,theroleplayedbywindspeedinEToestimationwasexamined;
theresultindicatedthattheexistenceofextremewinds,andalsothetimevariabilityofwindspeed, isresponsiblefortheobserveddiscrepanciesbetweenPMTandPM-EToestimates.Thespatialpatterns
ofETocomputedwithHSandPMTmethodsfoundtobeidenticalandresembletothatofPM-ETo,all
showingagradualincreasingfromnorthtosouth,withthelowestETovaluesobservedovernorthern
humidandsub-humidclimatesofIranandlargerEToforaridandhyper-aridclimatesinthesouthern
andeasterncountry.ResultsindicatedthattheHSandPMTmethodsareappropriatealternativesfor estimationofEToforallclimaticregionsofIran.
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
Adequateestimation ofreferenceevapotranspiration (ETo)is
ofparamountimportanceinagriculturaland hydrological
stud-ies,water resourcesmanagement and watershed management.
Inparticular,itisrequiredforestimationofcropwater
require-ments,supportingirrigationscheduling,droughtmanagementand
climatechangestudies.ThemethodologiesofEToestimation
rede-fined by Food and Agricultural Organization of United Nations
(FAO)weresuccessfully appliedatdifferenttime scalesin
vari-ousclimaticregionsoftheworld(Allenetal.,1998,2006;Smith,
2000).ThePenman–MonteithETo(PM-ETo)equationreferstograss
asreference cropandrequires solarradiation dataor sunshine
∗ Corresponding author at: Soil Conservation and Watershed Management ResearchInstitute(SCWMRI),Tehran,Iran,andCEER–BiosystemsEngineering, InstituteofAgronomy,TechnicalUniversityofLisbon,Portugal.
Tel.:+351213653480.
E-mailaddresses:tayebrazi@yahoo.com(T.Raziei),lspereira@isa.utl.pt (L.S.Pereira).
durationforestimatingnetradiation(Rn),maximumandminimum
temperature(Tmax andTmin,respectively),psycrometricor
rela-tivehumiditydataforestimatingthevapourpressuredeficit(VPD)
andwindspeed(U)WhenformulatingthePM-EToequation
advec-tioneffectswerenotconsidered(Allenetal.,1998;Pereiraetal.,
1999).Advectionimpactsoncropevapotranspirationmustbe
con-sideredthroughthecropcoefficientsandnotETo(Allenetal.,1998).
However,whensearchingfor ETo dataestimationunder
advec-tiveconditions,BerengenaandGavilán(2005)foundthatdailyETo
estimatesusingthePM-EToequationmatchedwellthelysimeter
observationsofgrassET.Goodresultsarereportedfordaily
compu-tationsusinghourlydatainlocationshavingadvectiveinfluences
(Allenetal.,2006).
ToappropriatelycomputetheparametersofPM-ETo the
pro-cedures proposed by Allen et al. (1998) should be followed.
AlternativeprocedureshavebeentestedbyNandagiriandKovoor
(2005), who have shown the need for strict adherence to the
recommendedparametercomputationprocedures,especiallyfor
estimatingvapourpressuredeficitandnetradiationparameters.
Gavilán et al. (2007) reported that the methods proposed by
Allen etal. (1998) for estimating Rn and G are appropriate for 0378-3774/$–seefrontmatter © 2013 Elsevier B.V. All rights reserved.
estimationofEToforbothdailyandhourlytimescales.Gongetal. (2006)performedasensitivityanalysisofPM-EToparametersand
pointedtotheveryhighinfluenceofsolarradiationandrelative
humidityinaccurateestimationofPM-ETo.However,lackoffull
weatherdatasetsinmanypartsoftheworld,particularlyinremote
areas,limitstheapplicationofPM-ETo.Thus,alternativeaccurate
approachesrequiringlimiteddataareneeded,whichhasledtoa
hugenumberofrelatedstudiesfocusingvariousclimates.
AccordingtoAllenetal.(1998),andbasinguponformer
stud-iestocomparetheperformanceofETtemperaturemethods,mainly
thestudybyJensenetal.(1990),whenfullweatherdataarelacking
ETocanbeestimatedeitherusingtheempiricalHargreaves–Samani
(HS)equation(HargreavesandSamani,1985),orempirically
esti-matingRn,VPDandUforusinginthePM-EToequation,including
throughusingdatafromneighbourweatherstations(Allen,1997).
VariousETtemperaturemethodswerethenexcluded– and
con-sequentlyarenotconsideredinthisstudy–,particularlytheET
climaticequationofThornthwaite(1948),thatlargely
underesti-matesgrassETo comparativelytoPM-ETo (Allenetal.,1994).In
bothaforementionedmethodstheminimumsetofdatarequired
consistsofTmaxandTmin.ThelatterapproachforusingthePM-ETo
withonlyTmaxandTminiscalledhereinasPMtemperature(PMT)
methodandisalsoreferredinliteratureasreducedsetPMmethod
(e.g.,MartinezandThepadia,2010).BoththeHSandPMTmethods
havereceivedacontinuousattentionfromresearchcontrarilyto
theuseofneighbourweatherdata;however,arecent
methodol-ogybasedonprincipalcomponentanalysistoestimateETowhen
nolocalclimaticinputsareavailable(MartíandZarzo,2012)may
providenewdevelopmentsinthisdomain.
TheEToestimatedbytheHSequationhavebeensuccessfully
comparedwiththeETocomputedwiththePM-EToequationusing
fulldatasets,orwithgrasslysimeterdata,indicatingthattheHS
methodperformswellinmostclimaticregions,withthe
excep-tionofhumidareawhereittendstooverestimateETo(Nandagiri
andKovoor,2006;TrajkovicandKolakovic,2009;Martinezand Thepadia,2010;Tabari,2010).SincetheHSmethodwasempirically
developedbasedondatafromaridtosub-humidenvironments,it
maynotfitwelltoconditionsfardifferentfromthoseconsidered
foritscalibrationasitisthecaseforhumidclimates.Temesgen
etal.(2005)alsostatedthattheHSmethodunderestimatesETo
fordryandwindylocationsduetonotconsideringawindfactor
andconcludedthatitismoreaccuratewhenappliedfor5or
7-dayaveragesthanfordailytimescales.However,despiteaquite
goodperformanceoftheHSequationinmostapplications,
par-ticularlywhenitisusedforirrigationschedulingpurposes,many
authorsattemptedtorecalibratetheHScoefficientsorparameters
inordertoimproveitsperformance(e.g.,DroogersandAllen,2002;
Trajkovic,2007;Fooladmandetal.,2008),ortomodifythe
equa-tionitself(DiodatoandBellocchi,2007).Thisresultedinalarge
numberofversionsoftheHSequation,thatrelateswiththe
pur-poseofmanyresearcherstofindlocallycalibratedversionsofthe
HSequation.
Basedonacarefulanalysisofthehistoryandapplicationsofthe
HSequation,Hargreavesand Allen(2003)concludedthat
recal-ibratingtheexponentsand coefficientsoftheHSequationonly
increasedthecomplexityoftheequation.TheHSmethodis
usu-allypreferredwithrespectivetoothermorecomplicatedequations
sinceitisreasonablyadequateandrequiresonlymaximumand
minimumairtemperatures(HargreavesandAllen,2003).Thisis
veryimportantinregionswheresolarradiation,airhumidity,and
windspeeddataarelackingorareofloworquestionablequality,
whilethemaximumandminimumairtemperaturesareavailable
inmostofagro-climaticandweatherstationssinceairtemperature
canbemeasuredwithlesserrorsandbylesstrainedindividuals
than theother required climate variables used in combination
equations.
TheaccuracyofthePMTequationhasbeenassessedbyseveral
authorsthroughcomparingitsresultswiththoseofthePM-ETo
or otherETequations, HSincluded. Popovaet al.(2006) found
moreaccurateresultsforPMTthanforHS,whichtendedto
over-estimate ETo in the Trace plain areaof southern Bulgaria. For
Pyrenees,López-Morenoetal.(2009)obtainedbetterresultswith
PMTwhencomparedwithHSmethod.Similarly,JablounandSahli
(2008)foundbetterestimatesforPMTthanforHSinNorthernand
CentralTunisia.AnapplicationofPMTforNorthernChina,
char-acterizedwithmonsoonclimate,alsohaveshownthatthePMT
estimatesbetterfitted tothePM-ETo than HS(Liu and Pereira,
2001;Pereiraetal.,2003).ApplicationofPMTtodifferentclimates
ofSouthAfricashowedtobesuperiortoHSandthatbetterresults
wereobtainedwhenappliedto5-dayratherthandailytimescales
(Annandaleetal.,2002).TheestimatedETocomputedbyPMTand
HSmethodforSerbiasuggestedthatPMTfittedbetterPM-ETothan
HS(Trajkovic,2005).Differently,it wasfoundthattheHS
pro-ducedsmalleroverestimationerrorsthanPMTinahumidclimate
(MartinezandThepadia,2010).Kra(2010)appliedamodifiedPMT
methodinWestAfrica, while Caietal. (2007)useda modified
PMTapproachfor estimatingETo withdaily forecastmessages;
lately,thePMTwasadaptedfor usingdailyforecasted weather
dataforirrigationschedulingpurposes(Caietal.,2009).Paredes
andRodrigues(2010)foundsmallerrorswithPMTrelativetoHS,
thusadoptingittoestimateEToinPortugalforirrigation
sched-ulingpurposes;theyfoundthatestimationerrorswerelargerin
humidlocationscomparativetodryerones.Gocicand Trajkovic
(2010)proposedasoftwaretoestimateEToforminimizing
com-putationerrorsusingthePMToranadjustedHSequationwhen
weatherdataaremissing.However,currentliteratureshowthat
therearenoattemptstocalibratetheradiationadjustment
coef-ficientkRsusedtoestimatesolarradiationfromthetemperature
differenceinPMTand,non-explicitly,inHS(HargreavesandAllen,
2003;Samani,2000,2004).Thiscalibrationisthereforealineto
beexploredinthisstudy.Moreover,literaturelookstobe
contro-versialwhencomparingHSandPMTresultsaswasidentifiedby
Todorovicetal.(2013).
Duetothecomplexorographyandwidelatitudinalextent,Iran
containsdiverseclimatesrangingfromveryhumidintheCaspian
Searegion toarid and hyper aridin the central, southern and
easternIran.Inthisvastarea,thestationsrecordingtheclimate
variablesneededforestimationofPM-EToareverysparseandin
manycaseshaveincompleterecords,particularlyinthe
central-southerncountrywheretheIraniandesertsaresituated.Therefore,
tohave a reliableestimation of ETo at a finespatial resolution
overthecountry,itisimportanttouseaccuratemethods
requir-inglimitedweatherdatathatcanbeavailableinadensenetwork
throughthecountryasitisthecasefortemperature.Toourbest
knowledge,Dinpashoh(2006)istheonlyauthorthathasestimated
EToforthewholecountryusingPM-EToandHSmethods,butdid
nottestedthepossibleadvantagesinusingcalibratedvaluesfor
theradiationadjustmentcoefficientortemperatureadjustmentfor
dewpointtemperatureestimationforthePMTmethodasproposed
byAllen(1996).TheadequatenessofusingPM-EToinIranisalso
demonstratedbyDinpashohetal.(2011)throughatrendanalysis
ofPM-ETofor16Iranianweatherstations.
Several authors have also assessed the application of other
methodsrequiringminimumdataforestimationofETo insome
partsofIranratherthanforthewholecountry(Fooladmandand
Haghighat,2007;AhmadiandFooladmand,2008;Rahimikhoob, 2010;Tabari etal., 2011a;Tabariand Aghajanloo,2012).
How-ever,acalibrationoftheradiationadjustmentcoefficientwasnot
attemptedinanyofthelaterreferredstudiesandthePMTandHS
methodswerenotcompared.Therefore,theobjectiveofthepresent
studyistoevaluatethepotentialandaccuracyofthePMTandHS
Fig.1.Spatialdistributionof(a)theutilizedweatherstationsand(b)thearidityindexoverIran.
andtorefinethemethodologiesforbetteradaptingboththePMT
andHSmethodstotheexistingenvironmentalconditions.Thus,it
isaimedtocomparethePMTandHSmethods,tofindthebest
val-uesfortheradiationadjustmentcoefficienttobeusedwithboth
methods,toassesstheadvantageincorrectingtheminimum
tem-peraturewhenestimatingVPD,andtoassesstheimpactsofhigh
windspeedinaridzones.Theseobjectivesaresettosupportawide
rangeofirrigationmanagementandwaterresourcesapplications,
particularlyrelativetodroughts,foruseinregionswhereweather
dataaremissing,areincompleteorareofquestionablequality.
2. Materialsandmethods
2.1. Data
Thedatausedforthisstudyaremonthlyaveragesofmaximum
andminimumtemperature(◦C),relativehumidity(%),sunshine
duration(h)andwindspeed(ms−1)relativeto40Iranian
synop-ticstationsdistributedoverthecountryasdepictedinFig.1a;the
associatedcoordinatesareshowninTable1.Themajorityofthe
selectedstationshavethelongestandnearlycompletedatarecords
fortheperiod1971–2005,particularlyconsideringsunshine,
rela-tivehumidityandwindspeeddata.Theselectedstationsarefirst
ordersynopticstationsthatpassedcarefulqualitycontrolbythe
Iranianmeteorologicalorganizationand arequiteregularly
dis-tributedthroughthecountry(Fig.1a).However,thetimeseries
oftheconsideredvariableswerefurtherinvestigatedforpossible
non-homogeneitiesbycomparingthetimeseriesofagivenstation
withthoseofneighbouringstations.Theresultprovedthatallthe
variableswerehomogeneous,withtheexceptionofwindspeed
recordsatTabass,Bam,Semnan,Kashan,Khoramabad,Dezfuland
Chabaharstations,whichexhibitedextremestepchangesand
non-homogeneity.Therefore,thewinddatasetsatthese7stationswere
correctedthroughestablishinglinearregressionbetweenthe
con-sideredstationdataandthoseofneighbouringstationsasproposed
byAllenetal.(1998).
Theconsideredstationsforthepresentstudyencompassseveral
representativestationsforeachclimaticsub-regionofIran,defined
hereinonthebasisoftheglobalaridityindex(UNEP,1997)adopted
bytheUnited-NationsConventiontoCombatDesertification.The
Table1
Coordinatesandthearidityindex(AI)oftheutilizedweatherstations.
Stations Lat. Lon. Alt AIindex Stations Lat. Lonn. Alt AIindex
Astara 38.4 48.9 −18.0 1.67 Shiraz 29.5 52.6 1484.0 0.35 Anzali 37.5 49.5 −26.2 2.09 Tabriz 38.1 46.3 1361.0 0.35 Rasht 37.3 49.6 −6.9 1.64 Torbat 35.3 59.2 1450.8 0.35 Ramsar 36.9 50.7 −20.0 1.45 Zanjan 36.7 48.5 1663.0 0.44 Babolsar 36.7 52.7 −21.0 1.04 Abadan 30.4 48.3 6.6 0.07 Ilam 33.6 46.4 1337.0 0.68 Ahwaz 31.3 48.7 22.5 0.10 Gorgan 36.9 54.3 13.3 0.61 Bam 29.1 58.4 1066.9 0.04
Kermanshah 34.4 47.2 1318.6 0.56 BandarAbas 27.2 56.4 9.8 0.09
Khoramabad 33.4 48.3 1147.8 0.55 Birjand 32.9 59.2 1491.0 0.20 Sanandaj 35.3 47.0 1373.4 0.59 Bushehr 29.0 50.8 19.6 0.15 Arak 34.1 49.8 1708.0 0.41 Chabahar 25.3 60.6 8.0 0.07 Dezful 32.4 48.4 143.0 0.25 Isfahan 32.6 51.7 1550.4 0.14 Ghazvin 36.3 50.1 1279.2 0.41 Kashan 34.0 51.5 982.3 0.12 Hamedan 35.2 48.7 1679.7 0.48 Kerman 30.3 57.0 1753.8 0.17 Khoy 38.6 45.0 1103.0 0.41 Sabzevar 36.2 57.7 977.6 0.20 Mashhad 36.3 59.6 999.2 0.33 Semnan 35.6 53.6 1130.8 0.14 Mehrabad 35.7 51.3 1190.8 0.24 Tabass 33.6 56.9 711.0 0.06 Urmia 37.5 45.1 1315.9 0.48 Yazd 31.9 54.3 1237.2 0.05 Shahrekord 32.3 50.9 2048.9 0.48 Zabol 31.0 61.5 489.2 0.04 Shahroud 36.4 55.0 1345.3 0.20 Zahedan 29.5 60.9 1370.0 0.08
UNEParidityindex,whichisalsoadoptedbyFAOandused
world-wideconsistsoftheratioofmeanannualprecipitation(P)tomean
annualpotentialevapotranspirationcomputedwiththe
Thornth-waitemethod(Thornthwaite,1948).Thecomputedaridityindex
fortheconsideredstationsarealsopresentedinTable1to
climat-icallycharacterizetheusedstations,whilethespatialdistribution
oftheindexoverthecountryisdepictedinFig.1b.Themapof
arid-ityindexpointstothehumidandsub-humidclimatesovercoastal
areasoftheCaspianSeainnorthernIran.Dry-sub-humidclimate
featuresoccurinthehighestpartsoftheAlborzmountainchainin
thenorth,thusactingasatransitionalband,isolatinghumidand
sub-humidclimatesofthecoastalareasoftheCaspianSeafrom
thesemi-aridareasofinteriorIran(Fig.1b).Thedry-sub-humid
climatealsocharacterizesaremarkablepartofwesternIrandue
toitsrelativelyhighannualprecipitationaccompaniedwithcold
wintersandmoderate summers.Semi-aridclimatesrefer tothe
mountainousareasofwestern,northernandnorth-easternIran,
whereasaridandhyper-aridclimatesdominatecentral,southern
andeasternIran(Fig.1b).Theclimatesub-regionsofIranproduced
hereinbasedonthespatialvariabilityofthearidityindex,though
methodologicallyandconceptuallydifferent,areinrelativelygood
agreementwiththeresultsoftheprecipitationbased
regionaliza-tionstudiesforIraninillustratingthemainstructureoftheIranian
climate(e.g.,Dinpashohetal.,2004;Razieietal.,2008).
2.2. MethodstoestimateETo
ThePM-ETo equationis aimedto definethegrass reference
evapotranspiration, i.e., the rate of evapotranspiration from a
hypotheticalcropwithanassumedfixedheight(12cm),surface
resistance(70sm−1)andalbedo(0.23),approximatelyresembling
theevapotranspirationfromanextensivesurfaceofadisease-free
greengrasscoverofuniformheight,activelygrowing,completely
shadingtheground,andwithadequatewaterandnutrientsupply
(Allenetal.,1998).ThePM-EToequationforcalculationofdailyETo
takestheform:
ETo=0.408(Rn−G)+(900/(T+273))u2(es−ea
)
+(1+0.34u2)
(1)
whereEToisthegrassreferenceevapotranspiration(mmday−1),
Rnisthenetradiationatthecropsurface(MJm−2day−1),Gissoil
heatfluxdensity(MJm−2day−1),Tismeandailyairtemperatureat
2mheight(◦C),u2iswindspeedat2mheight(ms−1),esis
satura-tionvaporpressure(kPa),eaisactualvaporpressure(kPa),es−ea
isvaporpressuredeficit(kPa), isslopeofthevaporpressure
curve(kPa◦C−1),and ispsychometricconstant(kPa◦C−1).This
equationusesstandardmeteorologicalrecordsofsolarradiation
orsunshineduration,minimumandmaximumairtemperature,air
humidityandwindspeed.Toensuretheintegrityofcomputations,
theweathermeasurementsshouldbemadeat2m(orconverted
tothatheight)aboveanextensivesurfaceofgreengrass,shading
thegroundandnotshortofwater.TheparametersofEq.(1)can
beestimatedfromtheobservedclimaticvariablesfollowingthe
standardmethods proposedbyAllenetal. (1998),whereasthe
missingclimaticdatacanbeestimatedempiricallyasfollows.
Rniscomputedasthealgebraicsumofthenetshortandlong
waveradiation(RnsandRnl,respectively).Rns,resultsfromthe
bal-ancebetweenincomingandreflectedsolarradiation(Rs)adopting
analbedoof0.23,andRnlresultsfromthebalancebetweenthe
down-comingandtheoutgoinglongwaveradiationemittedbythe
vegetationandthesoil.Computationswereperformedasproposed
byAllenetal.(1998).WhenRsisnotmeasured,itcanbeestimated
fromtheobserveddurationofsunshinehourswiththeAngström
(1924)equation: Rs=
as+bsn N Ra (2)whereRsissolarorshortwaveradiation(MJm−2day−1),nisactual
sunshineduration(h),Nismaximumpossiblesunshineduration
(h),n/N isrelativesunshine duration,Ra isextraterrestrial
radi-ation(MJm−2day−1),asisthecoefficientexpressingthefraction
ofextraterrestrialradiationreachingtheearthonovercastdays
(n=0),andas+bsisthefractionofextraterrestrialradiation
reach-ingtheearthonclearskydays(n=N).RaandNarecomputedfor
anygivendayasafunctionofthelatitudeofthesite(Allenetal.,
1998).WhenusingmonthlytimestepsRaandNarecomputedfor
thecentraldayofthemonth.Thevaluesas=0.25andbs=0.50are
recommendedwhenthesefractionsarenotlocallycalibratedusing
asetofgoodqualitydataonbothn/NandRs.
Whenradiationandsunshinedurationmeasurementsarenot
available,thePMTmethodusestheHargreavesradiationequation
(HargreavesandSamani,1982)fortheestimationofsolarradiation
(Rs)inalternativetoEq.(2):
Rs=kRs
(Tmax−Tmin)Ra (3)
wherekRsistheempiricalradiationadjustmentcoefficient(◦C−0.5).
For‘interior’locations,wherelandmassdominatesandairmasses
arenotstrongly influencedbya largewater body,Allen(1997)
andAllenetal.(1998)proposedkRs∼= 0.16for‘interior’areasand
kRs∼= 0.19for‘coastal’locations.Thesevaluesarethesameasthose
proposedpreviouslybyHargreaves(1994).Inherenttoits
empir-icalnature,thereissomeuncertaintyrelativelytothiscoefficient
(Samani,2004).Popovaetal.(2006)reportedthatfortemperate
climatekRs valueschangelittle.Differently,fora wide rangeof
climatesasintheMediterraneancountriesalargevariationwas
observed(Todorovicetal.,2013).
Vapourpressure deficit(VPD) is computedasthe difference
betweenthesaturationvapourpressure(es)andtheactualvapour
pressure(ea).esiscomputedastheaverageofthesaturationvapour
pressureatTmaxandTmin.Variousapproximationsmaybeusedto
estimateeadependinguponavailabledata.Whenonlymeandaily
relativehumidity(RHmean)dataareavailable,asforthecomplete
datasetsusedinthisstudy,eaiscomputedas(Allenetal.,1998):
ea= RHmean
50/(eo(T
min))+50/(eo(Tmax))
(4)
Intheabsenceofhumiditydata,eamaybeobtainedbyassuming
thatthedewpointtemperature,Tdew,isclosetothedailyminimum
temperature,Tmin.Then,iftheweatherstationcanbeconsidereda
referencesitewhereTdew=Tmin,eaiscalculatedby
ea=eo(Tmin)=0.611exp
17.27T min Tmin+237.3 (5)TheHSmethod(HargreavesandSamani,1985)requiresonly
observedTminandTmaxfortheestimationofETo(mmday−1),which
isgivenas:
ETo=0.0135kRsRa
(Tmax−Tmin)(T+17.8) (6)
whereRaistheextraterrestrialradiationasdefinedearlier,andis
thelatentheatofvaporization(MJkg−1)forthemeanair
tempera-tureT(◦C),thatiscommonlyassumedequalto2.45MJkg−1.0.0135
isafactorforconversionfromAmericantotheInternationalsystem
ofunitsandkRsistheradiationadjustmentcoefficientdefinedin
Eq.(3).InthecommonversionofHSequationthevaluekRs∼= 0.17
2.3. TemperatureadjustmentforestimatingPMT-ETo
Dataqualityassessmentanddatacorrectionfornon-reference
weathersites,i.e.,wherearidityis dominant,wereproposedby
Allenetal.(1998)asapre-conditionforaccuracyofPM-ETo
calcula-tions.Infact,thePM-ETodefinitionimpliestheconsiderationofan
activelygrowinggrasscropcompletelyshadingthegroundandnot
shortofwater.However,many,ifnotthemajorityoftheweather
dataaroundtheglobearereportedfromnon-referencesites,and
theirusetoestimateETomaycauselessaccuracyofestimates.If
dataqualityisessentialforanykindofevapotranspiration
stud-ies(Allenetal.,2011),requirementsforariditycorrectionsrelate
specificallywiththePM-EToequationandcropreference
defini-tion.ThatcorrectionwasanalyzedbyAllen(1996),Jensenetal.
(1997)andTemesgenetal.(1999),andreferstocorrect
temper-atureby2or3degrees toapproach Tmin ofTdew whenthesite
temperatureishigherthanthatexpectedforareferencesitewhile
airhumidityislower.Temesgenetal.(1999)haveshownsmall
effectsofthiscorrectiononEToestimatedwiththeHSequation
becausethisequationdoesnotexplicitlyusedewpoint
temper-atureandwindspeed,bothofwhichareaffectedbysitearidity.
Theseauthorsalsoconsideredthatwherethearidityofthesite
increasesitmixesupthetopandbottomlayersoftheatmosphere.
Themixing of differentlayers in turnreducesthetemperature
range(TR=Tmax−Tmin)bydecreasingTmaxduringdaytimeandby
increasingTmin duringnight-time,therebykeeping theincrease
inestimatedETolowerthanthatforPM-EToasaridityincreases.
ThehumiditytermisonlyimplicitlycontainedintheTRtermof
theHargreaves equation.The analysisby Hargreaves andAllen
(2003)agreeswiththehypothesisofTemesgenetal.(1999),thus
notconsideringtheneedforsiteariditycorrectionwhentheHS
equationisused.
ThePMTmethodusesasinputonlymeasuredminimumand
maximumairtemperaturefortheestimationofETobythe
PM-ETo equation(Eq. (1)), whereas wind speed is fixedto 2ms−1
(the average value of 2000 weather stations over the globe)
andsolarradiationandactualvapourpressureareestimatedby
Eqs.(3) and (5), respectively (Allen et al.,1998; Popovaet al.,
2006).
Asdiscussedbefore,whenapplyingthePMTmethodthereis
a need for adjustmentof temperature used for the estimation
ofactualvapourpressure. Tmin mightbegreaterthan Tdew in a
non-referenceweather station, as for a stationlocatedinside a
townorhavingdryorbareground.Then,theestimatedvaluefor
Tdew fromTmin mayrequirecorrection(Allen,1996;Allenetal.,
1998; Temesgen et al., 1999), which is expected to be higher
inmorearidclimates.Considering theclimatezonesdefinedin
Table 2 and illustrated in Fig. 1b, the corrections of Tdew are
proposed for all months where P/ETo<0.65 (Todorovic et al.,
2013).
Differently,inhumidclimatewherecommonlyairhumidityis
highandtemperaturesarerelativelylow,verylikelyTdewishigher
ormuchhigherthanTmin.Therefore,forthehumidstationssituated
intheCaspianSearegion,consideringtherelationsforTdewinmoist
airproposedbyLawrence(2005),andfollowingthegoodresults
Table2
CorrectionofTdewestimatesfromTminforestimationofactualvaporpressure.
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
previouslyobtainedfortheMediterraneanarea(Todorovicetal.,
2013),Tdewwasestimatedasfollows:
Tdew=
T min+Tmax 2 −ad (7)withad=2◦Cforthemonthswhen0.8<P/ETo<1.0andad=1◦Cif
P/ETo>1.0.
2.4. Evaluationprocedure
Atrialanderrorprocedurewasappliedtoalldatasetstofindthe
bestvaluesforkRssincetherelationsproposedbySamani(2000,
2004)didnotshowtobeappropriate.PMTcomputationswere
per-formedwithtemperaturecorrectionforaridityeffects(Table2)or
forhumidityimpactsonTdewasdescribedinSection2.3.Theresults
ofETo estimatedbyPMTandHSmethodsusinglimitedweather
datawerecompared withthoseofreferencePM-ETo computed
usingfulldatasets.ToassesstheperformanceofHSandPMT
meth-odswithrespecttoPM-ETo,relativetoallpairsofobservedand
predictedvaluesforeachstation,inadditiontoalinearregression
forcedtotheorigin,severalstatisticalindicatorswerealsoused.
Theseindicatorsareexplainedbelowandtheirequationsaregiven
inliterature,e.g.,thecomparativestudyofETomodelsbyTodorovic
etal.(2013).
Ifthecoefficientofregressionbiscloseto1thenthepredicted
valuesarestatisticallyclosetotheobservedones;whenthe
coeffi-cientofdeterminationR2iscloseto1.0thenmostofthevariation
oftheobservedvalues canbeexplainedbythemodel.Theroot
meansquareerror,RMSEcharacterizesthevarianceoftheerrors;
thesmallerRMSEthebetteristhemodel’sperformance.
Themodellingefficiency,EF,wasusedtodeterminetherelative
magnitudeoftheresidualvariancecomparativelytothemeasured
datavariance;itisdefinedfromtheratioofthemeansquareerrorto
thevarianceintheobserveddata(NashandSutcliffe,1970;Moriasi
etal.,2007).EFindicatesthatwhentheresidualvarianceequalsthe
observeddatavarianceitresultsEF=1.0;contrarily,whenEFequals
zeroorisnegativethisindicatesthattheobservedmeanisasgood
orbetterpredictorthanthemodel.TheWillmott(1981)indexof
agreement,dIA,isalsoanon-dimensionalmeasurethatrepresents
theratiobetweenthemeansquareerrorandthe“potentialerror”,
definedasthesumofthesquaredabsolutevaluesofthedistances
fromthepredictedvaluestothemeanobservedvalueanddistances
fromtheobservedvaluestothemeanobservedvalue(Moriasietal.,
2007):dIAvariesbetween0and1;avalueof1indicatesaperfect
agreementbetweenthemeasuredandpredictedvalueswhile0
indicatesnoagreementatall(Moriasietal.,2007).
TheabovestatisticsmeasurethedegreeofaccuracyofETo
esti-mationusingPMTandHSmethodswithrespecttothePM-ETo,
however notgiving informationwhethertheaccuracy between
thetwo competing modelsissignificantly different.Toaddress
this issue, a test statistic proposed by Diebold and Mariano
(1995),whichiscommonlyusedinfinancialliterature,isadopted.
Althoughthis test isusually usedfor out-of-sampleforecasting
accuracyanalysis(MohammadiandSu,2010),hereitisusedtotest
theaccuracyofwithin-samplepredictionfollowingModarresand
Ouarda(2012),who recentlyapplieditinhydrologicalsciences.
Inthepresentstudy,thetestcanindicateifthereisasignificant
differencebetweenPMTandHS’sperformancesinestimatingETo.
Formally,lete1,t ande2,t,t=1,...,m,denotemodelerrors from
PMTanHSmodelsandg(e1,t)andg(e2,t)aretheirassociatedloss
functions,i.e.,thesquared-errorloss,anddt=g(e1,t)−g(e2,t)isthe
lossdifferential,thentheBstatistics(DieboldandMariano,1995)
isdefinedas:
B=
ds/m
Fig.2. (Continued).
wheredisthesamplemean,sisthevarianceoflossdifferential
andmisthenumberofobservations.Givencovariancestationarity
andshortmemorywithregardtodt,thetestimpliesan
asymp-toticdistributionwithzeromeanandunitvariance.Underanull
hypothesisofzeromean,thetwomodelshaveequalaccuracyif
thelossdifferentialhaszeroexpectationforalltobservations.The
nullhypothesisisrejectedinfavourofthealternativehypothesis
whenthestatisticB,inabsolutevalue,exceedsthecriticalvalueof
astandardunitGaussiandistribution(DieboldandMariano,1995).
3. Results
3.1. PerformanceofHSmethod
TheperformanceoftheHSmethodisevaluatedagainstthe
com-putedPM-EToinallconsideredstations(Fig.2andTable3).Fig.2
illustratestherelationshipbetweenPM-EToandHSestimateswhen
appropriatekRswereusedforallthestations.InTable3,in
addi-tiontothegoodnessoffitindicators,theappropriatekRsutilized
forcomputingHSforeachoftheconsideredstationsarealsogiven.
Fig.2 shows that the estimatedHS strongly correlateswith
PM-EToatmostofthestations,implyingthattheHSmethod
appro-priatelypredictsthePM-EToinallclimaticregionsofIranwhenthe
appropriatekRsisselected.AvisualinspectioninFig.2andTable3
suggeststhattheHSmethodperformswellforallclimaticzones
ofIranshowninFig.1b,particularlyforthestationscharacterized
withsemiaridtohumidclimatesinwesternandnorthernIran.The
HSestimatesforthestationslocatedinthecentral-southernand
easternaridtohyper-aridclimatesofIranshowalsoasatisfactory
agreementwithPM-ETo,thoughaverypooragreementwasfound
forZabolineasternIran.AslighterdeviationoftheHSestimation
fromthePM-EToforhigherETvalueswasalsoobservedforsome
otherstationscharacterizedwithsemi-aridtohyper-aridclimates
thougharereasonablyingoodagreement.Theobserveddeviation
insuchstations,particularlyforextremevalues,issupposedtobe
relatedtotheeffectofwindspeedonPM-ETocomputationthatis
addressedinSection3.4.
Goodresultsforhumidclimates(Fig.2andTable3)are
con-tradictingfindingsbymanyauthors(e.g.,TrajkovicandKolakovic,
Table3
StatisticallycomparingtheperformanceoftheHSwiththePM-ETo.
Climaticzone Stations kRs b R2 RMSE(mmd−1) EF dIA
Humid Astara 0.15 1.00 0.98 0.18 0.98 0.99
Anzali 0.18 1.03 0.92 0.37 0.96 0.98
Rasht 0.13 1.00 0.96 0.24 0.98 0.99
Ramsar 0.15 1.01 0.93 0.28 0.97 0.99
Babolsar 0.16 1.04 0.95 0.30 0.98 0.99
Moistsub-humid Ilam 0.20 1.02 0.95 0.52 0.99 0.99
Drysub-humid Gorgan 0.14 1.03 0.92 0.38 0.98 0.99
Kermanshah 0.16 1.00 0.97 0.40 0.99 0.99 Khoramabad 0.13 0.98 0.98 0.28 0.99 1.00 Sanandaj 0.16 1.04 0.95 0.54 0.98 0.99 Semi-arid Arak 0.16 1.00 0.97 0.33 0.99 0.99 Dezful 0.14 0.99 0.97 0.41 0.98 0.99 Ghazvin 0.15 0.98 0.98 0.31 0.98 0.99 Hamedan 0.17 1.01 0.96 0.45 0.98 0.99 Khoy 0.14 1.03 0.97 0.30 0.98 0.99 Mashhad 0.17 1.01 0.91 0.62 0.96 0.98 Mehrabad 0.21 1.02 0.98 0.37 0.98 0.99 Urmia 0.16 1.01 0.98 0.27 0.98 0.99 Shahrekord 0.14 1.00 0.96 0.37 0.98 0.99 Shahroud 0.18 0.99 0.94 0.49 0.98 0.99 Shiraz 0.17 1.00 0.97 0.37 0.99 1.00 Tabriz 0.21 1.02 0.95 0.56 0.99 1.00 Torbat 0.19 1.00 0.86 0.81 0.91 0.97 Zanjan 0.16 0.98 0.96 0.40 0.99 0.99 Arid Ahwaz 0.18 1.02 0.95 0.64 0.95 0.99 BandarAbas 0.19 1.02 0.82 0.63 0.94 0.97 Birjand 0.19 1.01 0.89 0.75 0.96 0.98 Bushehr 0.20 1.02 0.90 0.59 0.97 0.99 Isfahan 0.17 1.02 0.95 0.45 0.96 0.99 Kashan 0.15 1.03 0.99 0.27 0.99 1.00 Kerman 0.18 0.99 0.94 0.51 0.97 0.99 Sabzevar 0.20 1.00 0.94 0.62 0.98 0.99 Semnan 0.17 1.01 0.98 0.28 0.99 1.00 Hyper-arid Abadan 0.20 1.00 0.88 1.07 0.97 0.98 Bam 0.18 1.02 0.97 0.34 0.98 0.99 Chabahar 0.20 1.02 0.83 0.43 0.82 0.95 Tabass 0.17 1.03 0.95 0.55 0.95 0.99 Yazd 0.19 1.01 0.93 0.64 0.95 0.98 Zabol 0.22 0.74 0.64 2.86 0.68 0.86 Zahedan 0.19 1.01 0.93 0.60 0.92 0.98
thecalibrationofkRs,whichwasapparentlynotachievedbythe
referredauthors.
Fig.3aillustratesthespatialpatternofkRsappropriatefor
esti-mationofETo usingtheHSmethod.TheappropriatekRsforthe
stationslocatedinthedry-sub-humidtohumidclimatesof
west-ernandnorthernIranfoundtobebetween0.13and0.18,while
itrangesfrom0.14to0.20forthestationssituatedinthe
semi-aridtohyper-aridclimatesofcentral,southernandeasternIran.
ThefiguredepictsagradualincreasinginkRsmovingfromnorth
tosouthandfromwesttoeast,beingrelativelyinconcordanceof
theclimaticzonesofIrandepictedinFig.1.However,thespatial
configurationofthekRsisinterruptedbysomeeyeballs,
particu-larlyinnorthernhalfofthecountry,whereverthekRsvaluesare
fardifferentfromthesurroundingvalues.Inotherwords,thereare
afewcaseswheretheappropriatekRsforasinglestationdiffers
fromthegeneralpatternoftheregion.Forexamplethebestfitted
kRsforTabriz,innorth-westernIran,is0.21,whichismuchhigher
thanthenormoftheregion,whichcouldbeattributedtothelocal
highsummerwindspeed.Contrasting,kRs is0.15forKashan,in
centralIran,whichislowerthanthegeneralkRspatternforarid
andhyper-aridclimates.
TheperformanceoftheHSmethodinrelationtothePM-ETowas
assessedthroughasetofgoodnessoffitindicators(Table3).These
statisticsindicatethattheHSmethodsatisfactorilypredictsEToin
mostofthestations,whichissupportedbyR2higherthan0.90and
theregressioncoefficientbbetween0.98and1.02inapproximately
85%ofthestations.TheRMSEislowerthan0.70and0.50mmd−1
in90%and63%ofthestations,respectively.Theseresultsare
sup-portedwiththemodellingefficiency(EF),largerthan0.95andthe
indexofagreement(dIA)higherthan0.99inapproximately90%of
stations.Differently,largererrorsofestimateandlowergoodness
offitindicatorswereobtainedforZabol,Abadan,Torbat,Birjand,
Bandarabas,SabzevarandMashad,wherethevarianceofthe
resid-ualsoftheestimationishighanddoesnotrespondtotherequired
homoscedasticity,probablyduetolackofconsideringwindspeed
withintheHSmethod.
3.2. PerformanceofthePMTmethod
TheperformanceofthePMTmethodagainstthePM-EToinall
consideredstationswerealsoevaluatedgraphically(Fig.4)and
statistically(Table4).Tmin wascorrectedfor allconsidered
sta-tionsinsemi-aridtohyper-aridclimates(Table2)inordertobetter
estimateTdewforPMTcomputation.Forhumidclimates,Tdewwas
differentlyestimatedwithEq.(7).Atrialanderrorprocedurewas
adoptedtosearchfortheappropriatekRsusedforcomputationof
PMT,theirvaluesareindicatedinFig.4andTable4.Forsome
sta-tions,asanalyzedinSection3.4,windspeedcorrectionswerealso
Fig.3. SpatialpatternsoftheselectedkRsoverIranfor:(a)HSand(b)PMTmethods.
AsillustratedinFig.4,theestimatedPMTstronglycorrelate
lin-earlywithPM-EToinmostofthestations,implyingthatthePMT
appropriatelypredictsthePM-EToinallclimaticzonesofIran.Fig.4
suggeststhatthePMTparticularlyperformswellforthestations
characterizedwithsemiaridtohumidclimatesofwesternand
northernIran.ThePMTalsoperformsreasonablywellinhumid
climateoftheCaspianSearegioninthenorth,whereTdewwas
com-putedwithEq.(7),whichallowedtoconsidertheeffectofhighair
Table4
StatisticallycomparingtheperformanceofthePMTwithPM-ETo.
Climaticzone Stations kRs b R2 RMSE(mmd−1) EF dIA
Humid Astara 0.16 0.99 0.98 0.19 0.98 0.99
Anzali 0.20 1.00 0.94 0.32 0.94 0.99
Rasht 0.13 1.01 0.94 0.28 0.95 0.99
Ramsar 0.16 1.03 0.94 0.29 0.93 0.98
Babolsar 0.16 1.01 0.95 0.29 0.95 0.99
Moistsub-humid Ilam 0.19 0.99 0.96 0.44 0.96 0.99
Drysub-humid Gorgan 0.12 1.01 0.93 0.36 0.93 0.98
Kermanshah 0.14 1.03 0.97 0.41 0.97 0.99 Khoramabad 0.10 1.00 0.94 0.41 0.95 0.99 Sanandaj 0.12 1.00 0.94 0.50 0.95 0.98 Semi-arid Arak 0.14 1.01 0.96 0.39 0.96 0.99 Dezful 0.10 0.99 0.93 0.55 0.94 0.98 Ghazvin 0.13 1.02 0.97 0.34 0.97 0.99 Hamedan 0.15 1.01 0.96 0.46 0.96 0.99 Khoy 0.11 1.03 0.94 0.39 0.94 0.98 Mashhad 0.15 1.01 0.90 0.62 0.93 0.98 Mehrabad 0.21 1.01 0.98 0.40 0.97 0.99 Urmia 0.14 1.00 0.97 0.30 0.97 0.99 Shahrekord 0.11 1.03 0.93 0.44 0.93 0.98 Shahroud 0.17 1.00 0.94 0.49 0.95 0.99 Shiraz 0.16 1.01 0.96 0.44 0.96 0.99 Tabriz 0.20 0.99 0.96 0.45 0.97 0.99 Torbat 0.18 1.02 0.87 0.79 0.90 0.97 Zanjan 0.14 0.99 0.96 0.39 0.96 0.99 Arid Ahwaz 0.18 1.02 0.92 0.81 0.93 0.98 BandarAbas 0.17 1.00 0.90 0.46 0.92 0.98 Birjand 0.17 1.01 0.91 0.63 0.92 0.98 Bushehr 0.19 1.00 0.92 0.53 0.93 0.98 Isfahan 0.15 1.02 0.94 0.49 0.94 0.98 Kashan 0.11 1.00 0.96 0.36 0.97 0.99 Kerman 0.17 1.01 0.90 0.66 0.92 0.98 Sabzevar 0.20 1.01 0.95 0.55 0.96 0.99 Semnan 0.16 1.03 0.98 0.28 0.98 0.99 Hyper-arid Abadan 0.21 1.01 0.89 1.06 0.90 0.95 Bam 0.16 1.01 0.97 0.33 0.97 0.99 Chabahar 0.18 1.01 0.88 0.36 0.87 0.97 Tabass 0.15 1.01 0.92 0.61 0.94 0.98 Yazd 0.18 1.00 0.92 0.63 0.93 0.98 Zabol 0.20 0.67 0.67 3.29 0.53 0.81 Zahedan 0.18 0.99 0.92 0.58 0.93 0.98
humidity.TheestimatedPMTformostofthestationslocatedinthe
central-southernandeasternaridandhyper-aridclimatesofIran
showalsosatisfactoryagreementwithPM-ETo,thoughrelatively
weakassociationwerefoundforAbadan,Torbat,Birjand,Chabahar
and,mainly,forZabolstation(Fig.4andTable4).Allthesestations
alsoperformedpoorlyfortheHSmethod.
Thestationslocatedinwesternandnortherndry-sub-humidto
humidclimatesofIranhavekRsbetween0.10and0.18,whilekRs
Fig.4. (Continued).
variesfrom0.11to0.20forthestationssituatedinthesemi-arid
tohyper-aridregionsofcentral-easternIran(Table4andFig.3b).
AswasthecasefortheHSmethod,therearesomecaseswherethe
selectedkRsforastationdiffersfromtheregionalpattern,e.g.,the
selectedkRsforTabrizstationinnorth-westernIranismuchhigher
thanthekRsvaluesofthesurroundingstations.Fig.3bshowsthe
spatialpatternofkRsusedforestimationofPMToverIran,depicting
apatternverysimilarofthatfortheHSmethodinFig.3a.
Appar-ently,thekRsisinfluencedbyelevation,topographyandthearidity
indexthoughinthepresentstudyweakcorrelations(notshown)
werefoundbetweentheaforementionedfactorsandthekRsvalues
relativetoboththePMTandHSmethods.
ThestatisticsshowninTable4indicatethatthePMTmethod
sat-isfactorilypredictsEToinmostofthestations,whichissupported
byR2higherthan0.90andbcoefficientbetween0.98and1.02in
90and85%ofthestations,respectively.TheRMSEislowerthan
0.70and0.50mmd−1in90%and68%ofthecases,EFanddIAwere
≥0.90and≥0.98formorethan90%ofthestations.Theseresults
areonlyslightlybetterthanthecorrespondingresultsfortheHS
methodinTable3.ResultssuggestagoodestimationofETowith
PMT,particularlyforpracticalirrigationschedulingandforusing
indroughtindicescomputationsuchasthePDSI(e.g.,Pauloetal.,
2012).ResultsindicatethattheuseofPMTmethodforETo
esti-mationinthestudyareaisworthwhilewhenonlylimiteddataare
available.However,coefficientsofdetermination<0.90forZabol,
Chabahar,AbadanandTorbatsuggestthattheestimatedPMTin
thesestationssubstantiallydeviatesfromthePM-ETo.Theachieved
resultsforPMTareconsistentwiththoseobtainedforHS,which
showstheweakestagreementswithPM-EToforthesamestations
asPMT.
3.3. RoleoftemperatureadjustmentforTdewestimation
Theeffectivenessoftemperatureadjustmentinimprovingthe
PMTestimationwasstatisticallyevaluatedforallconsidered
sta-tions, by comparingthe regression coefficient b,R2 and RMSE
statisticsrelatingPMTandPM-ETodata,beforeandafter
tempera-tureadjustment(Table5).
Resultssuggestedthattemperatureadjustmentsforhumidand
Table5
StatisticallyassessmentoftheeffectsoftemperatureadjustmentinPMTestimation.
Climaticzone Stations kRs Beforecorrection Aftercorrection
b R2 RMSE(mmd−1) b R2 RMSE(mmd−1) Humid Astara 0.16 1.00 0.96 0.24 0.99 0.98 0.19 Anzali 0.20 0.97 0.91 0.37 1.00 0.94 0.32 Rasht 0.13 1.05 0.88 0.39 1.01 0.94 0.28 Ramsar 0.16 1.01 0.88 0.33 1.03 0.94 0.29 Babolsar 0.16 0.97 0.88 0.38 1.01 0.95 0.29
Moistsub-humid Ilam 0.19 0.89 0.95 0.65 0.99 0.96 0.44
Drysub-humid Gorgan 0.12 0.97 0.80 0.47 1.01 0.93 0.36
Kermanshah 0.14 0.96 0.96 0.44 1.03 0.97 0.41 Khoramabad 0.10 0.97 0.94 0.43 1.00 0.94 0.41 Sanandaj 0.12 0.93 0.92 0.59 1.00 0.94 0.50 Semi-arid Arak 0.14 0.94 0.95 0.44 1.01 0.96 0.39 Dezful 0.10 0.91 0.89 0.75 0.99 0.93 0.55 Ghazvin 0.13 0.95 0.96 0.38 1.02 0.97 0.34 Hamedan 0.15 0.95 0.95 0.51 1.01 0.96 0.46 Khoy 0.11 0.98 0.92 0.41 1.03 0.94 0.39 Mashhad 0.15 0.93 0.87 0.73 1.01 0.90 0.62 Mehrabad 0.21 0.90 0.98 0.57 1.01 0.98 0.40 Urmia 0.14 0.95 0.95 0.38 1.00 0.97 0.30 Shahrekord 0.11 0.99 0.91 0.45 1.03 0.93 0.44 Shahroud 0.17 0.91 0.93 0.77 1.00 0.94 0.49 Shiraz 0.16 0.95 0.95 0.51 1.01 0.96 0.44 Tabriz 0.20 0.88 0.95 0.70 0.99 0.96 0.45 Torbat 0.18 0.90 0.83 0.88 1.01 0.88 0.77 Zanjan 0.14 0.93 0.95 0.46 0.99 0.96 0.39 Arid Ahwaz 0.18 0.95 0.92 0.80 1.02 0.92 0.81 BandarAbas 0.17 0.87 0.79 0.84 1.00 0.88 0.51 Birjand 0.17 0.93 0.89 0.68 1.01 0.91 0.63 Bushehr 0.19 0.89 0.88 0.78 1.00 0.92 0.52 Isfahan 0.15 0.93 0.93 0.56 1.02 0.94 0.49 Kashan 0.11 0.91 0.96 0.50 1.00 0.96 0.36 Kerman 0.17 0.94 0.90 0.68 1.01 0.90 0.66 Sabzevar 0.20 0.91 0.94 0.71 1.01 0.95 0.55 Semnan 0.16 0.94 0.98 0.36 1.03 0.98 0.28 Hyper-arid Abadan 0.21 0.95 0.89 1.05 1.01 0.89 1.06 Bam 0.16 0.90 0.96 0.56 1.01 0.97 0.33 Chabahar 0.18 0.84 0.73 0.80 1.01 0.88 0.36 Tabass 0.15 0.93 0.91 0.69 1.01 0.92 0.61 Yazd 0.18 0.92 0.92 0.73 1.00 0.92 0.63 Zabol 0.20 0.61 0.66 3.67 0.67 0.67 3.29 Zahedan 0.18 0.92 0.92 0.71 0.99 0.92 0.58
simplyusingTmin,considerablyimprovesPMTestimation,whereb
andR2 increasedandRMSEdecreased aftertemperature
adjust-ment for allstations characterizedwith humidand sub-humid
climatesofIran.Asanexample,thecoefficientofdetermination
forRashtandRamsarstationsincreasedfrom0.88 to0.94after
temperaturecorrection;for Ilam, RMSEdecreased from0.65 to
0.44mmd−1.Theseresultsindicatethatthegoodperformanceof
PMTestimationanalyzedintheprevioussectionislargelydueto
temperatureadjustmentforhumidity.
Temperatureadjustmentforstationssituatedinsemi-arid,arid
and hyper-aridclimates of Iranalso showedto haveimproved
EToestimation.Differentlyfromhumidclimateswhere
tempera-tureadjustmentnoticeablyimprovedtheR2statistic,theinfluence
of temperatureadjustment in semi aridto hyper-arid climates
largelyconsistedinsubstantially increasingtheregression
coef-ficient, withb approaching the 1:1 line. These results indicate
thatthetemperatureadjustmentforaridity,withloweringTdew
relativetorawTmin,leadstoovercomethecommonunder
esti-mationofPMTinaridconditions.Meanwhile,despitenegligible
improvements of R2, noticeable improvements in RMSE
statis-ticwereobservedformostofthestationssituatedinsemi-arid,
aridandhyper-aridclimates.Thisfactsuggeststhattemperature
adjustmentisofparamountimportanceforPMTestimationinsuch
climates.
3.4. RoleofwindspeedinPMTestimation
AswereshowninFigs.2and4,theestimatedETo bytheHS
andPMTmethodsshowpooragreementwiththePM-EToatsome
stationssituatedintheverydryclimateofeasternandsouthern
Iran,whereHSandPMTmethodslargelyunderestimateEToforthe
warmseason.Inexploringthepossiblefactorresponsibleforthe
observeddisagreement,wenoticedthattheconsideredstationsare
locatedintheareawhereextremewindspeedoccurs,particularly
inthesummer.
Thespatialpatternofthemeanseasonalwindspeedoverthe
countryisdepictedinFig.5tosupportananalysisaboutthe
pos-sibleroleplayedbythewindfactorinETo estimation.InFig.5a
andditisevidentthatthemeanautumnandwinterwindspeed
donotexceed2ms−1 inmostpartsofthecountryexceptfora
narrowbandinsouthernandeasternIran,wherewindspeedis
between3and4ms−1.Fig.5bshowsanincreaseofwindspeed
insouthernandeasternpartsofIranduringspring,contrarilyto
northernhalfofthecountry.Differently,windspeedinsummer
increasesdrasticallyineasternIran(Fig.5c),whereitmayexceed
8ms−1.Thesedataindicatethat themeanseasonalwindspeed
insouthernandeasternIran,particularlyforthewarmspringand
summerseasons,isoftenmuchhigherthanthecommondefault
Fig.5.Spatialpatternsofmeanseasonalwindspeed(ms−1)overIranfor:(a)autumn,(b)spring,(c)summerand(d)winter.
deviationofPMTestimatesrelativetoPM-ETodata,duringthose
seasons.Theroleof extremewindspeedonPM-ETo estimation
maybeveryimportant,mainlywhen itis associatedwithvery
hotweatherinsummer,whichcallsforusinganestimateofwind
speeddifferentthanthatofthedefaultvalueof2ms−1.SincetheHS
equationdoesnotincludeanywindspeedparameter,itsresultsare
likelyunderestimatingEToinwindyandhotconditionslikeZabol
andvariousotherstationslocatedinaridandhyper-aridclimates
ofsouthernandeasternIran(Fig.2).
Asdepictedin Fig.5,thehighest windspeed,particularlyin
summer,is observedinZabol,eastern Iran,where thePMTand
HSestimationshaveshowntheworstagreementwiththePM-ETo
(Figs.2and4).Thisresultsfromthefactthattheobservedwind
speedinthisstationisseveraltimeshigherthanthedefaultvalue
of2ms−1,particularlyduringtheveryhotsummerandlatespring.
Thesummerwindspeedisalsoconsiderablyhigherthan2ms−1in
Abadan,Sabzevar,Birjand,Torbat,ShahroudandMashadstations
insouthernandeasternIran,wheretheEToestimatedbyPMTand
HShaveshownaweakagreementwiththePM-EToforextremeETo
values.Thesummerwindspeedisalsohigherthanthefixedvalue
of2ms−1inTabriz,north-westernIran,givingrisetoawide
dis-persionofthehighestETovaluesinthescatterplotsofthisstation
(Figs.2and4).Inmostofthesestations,thehigherdeviationof
thePMT(andHS)estimationsfromthePM-ETocorrespondtothe
extremeETovaluesthatoccurredinthewarmseasonoftheyear.
Therefore,theobserveddisagreementbetweenthePMT(andHS)
estimationsandPM-ETointhesestationscanbepartiallyduetonot
consideringthewindspeedinfluenceinHSmethodandadefault
valueofonly2ms−1inPMT,whichismuchsmallerthantheactual
windspeedthatisusedforthePM-ETocomputation.
ToexaminetheroleplayedbywindspeedinPM-EToestimation,
Fig.6illustratestherelationshipbetweenestimatedETobyPMTand
PM-EToatsomeselectedstations,consideringdifferentscenarios:
(1)usingthedefaultwindspeedvalueof2ms−1inPMT
computa-tions,
(2)consideringonlythePM-ETodatacorrespondingtowindspeed
notexceeding2ms−1,
(3)usingobservedlocalwindspeedinPMTreplacingthedefault
windspeedvalue,and
(4)usingaverageseasonalwindspeedtoreplacethedefaultvalue
of2ms−1inPMTcomputation.
Asshown in Fig.6a–f, thePMTmethodextremely
underes-timatesETo valuescorrespondingtothesummers inShahroud,
Mashad,Torbat,Abadan,BirjandandZabolstations,thusleadingto
verylowcoefficientsofdetermination,eventhoughtheoptimum
bslopecouldbeachievedforsome.Byexcludingtheobservations
withwindspeed>2ms−1fromtheanalysis(scenario2),the
Fig.6.RelationshipsbetweenestimatedETobyPMTmethodandPM-EToatsomeselectedstationswhen:thewindspeedisfixedat2ms−1forPMTcomputation(a–f);data
withlocalwindspeed>2ms−1wasnotconsidered(g-i);localactualwindspeedwastakenforPMTcomputations(m–r),andregionalaveragesofseasonalwindspeedwere
usedforPMTcomputations(s–x).
increasedcoefficientsofdeterminationandreducedresidualsofthe
variancerepresentedbyanarrowerdispersionbandofthescatter
plotsshowninFig.6g–l.Tofurtherjustifytheroleofwindspeed
intheassociationbetweenthePMTandPM-ETo,Fig.6m–r
illus-tratesthattheassociationbetweenthetwomodelssubstantially
improvedwhenlocalwindspeedwasusedforPMTcomputation
ratherthan thedefaultvalue(scenario 3).Differentlyfrom
dis-cussionsintheliteraturesuggestingthatwindspeedhasverylow
impactonEToestimation,theresultsobtainedwithscenario3
illus-tratedthatitisanimportantfactorinaridandsemi-aridclimates
whenthestationsareexposedtoextremewindspeed,particularly
inhotseasons.Asanexample,Fig.6fshowsthescatterplotfor
theextremelywindystationofZabol,ineasternIran,whichiswell
knownforitsextremesummerwindspeedthatusuallydominates
theregionforthewholesummertime(Fig.5c).Asisdepictedin
Fig.6fbothR2andbareverylowforscenario1,thusindicating
averypoorestimationofETo byPMT.Substantialimprovement
wasobservedfor scenario2,whenthedatawithextremewind
speed(windspeed>4m−1)wereexcluded,whichledtoa
Table6
TheDieboldandMariano(1995)BtestforequalaccuracyofPMTandHSmethods(statisticallysignificantBstatisticsareinbold).
Climaticzone Stations BStatistic RMSE(PMT) RMSE(HS)
Humid Astara 0.75 0.19 0.18
Anzali −5.82 0.32 0.37
Rasht 4.10 0.28 0.24
Ramsar 0.15 0.29 0.28
Babolsar −1.38 0.29 0.30
Moistsub-humid Ilam −4.57 0.44 0.52
Drysub-humid Gorgan −1.65 0.36 0.38
Kermanshah 0.90 0.41 0.40 Khoramabad −2.24 0.41 0.28 Sanandaj −1.31 0.49 0.54 Semi-arid Arak 3.97 0.39 0.33 Dezful 6.71 0.55 0.41 Ghazvin 1.53 0.34 0.31 Hamedan 1.13 0.46 0.45 Khoy 5.16 0.39 0.30 Mashhad 0.18 0.62 0.62 Mehrabad 2.58 0.40 0.37 Urmia 4.98 0.30 0.27 Shahrekord 5.60 0.44 0.37 Shahroud 0.07 0.49 0.49 Shiraz 5.69 0.44 0.37 Tabriz −7.88 0.45 0.56 Torbat −1.69 0.77 0.81 Zanjan −1.25 0.39 0.40 Arid Ahwaz 5.87 0.81 0.64 BandarAbas −9.72 0.51 0.63 Birjand 2.03 0.63 0.75 Bushehr −5.09 0.52 0.59 Isfahan 7.72 0.49 0.45 Kashan 1.08 0.36 0.27 Kerman 7.94 0.66 0.51 Sabzevar −5.19 0.55 0.62 Semnan −0.55 0.28 0.28 Hyper-arid Abadan 0.67 1.06 1.07 Bam −2.25 0.33 0.34 Chabahar −3.23 0.36 0.43 Tabass 1.95 0.61 0.55 Yazd −0.51 0.63 0.64 Zabol 12.02 3.29 2.86 Zahedan −0.49 0.58 0.60
theselectedthresholdforZabolwassettowindspeed>4m−1since
veryfewcaseshavewindspeed<2m−1.Fig.6ralsodemonstrates
amuchimprovedgoodnessoffitwhenlocalwindspeedwasused
forPMTcomputationratherthanthedefaultvalueof2ms−1
(sce-nario3),thoughtheregressionstillremainsnonlinear,whichcan
berelatedtothequalityofthewinddata;howeveritcouldnotbe
appropriatelyanalyzedasthewindisalocaldependentvariable,
sohavingextremespatialvariabilityinthisregion.
InordertofindapracticalsolutionforimprovingthePMT
esti-mates,itwassupposedthatusinganappropriateregionalwind
speed instead of using a default value couldimprove the PMT
estimationin windyareas(scenario 4);relatedresultsusingan
averagedseasonalwindspeedareshowninFig.6s–x.Inthis
sce-nario,twofixedwindspeedvalueswereused,respectivelyforcold
andhotseasons.AsshowninFig.6s–x,thisapproachwasableto
improveR2butdidnotprovideimprovedregressioncoefficients
sincebvaluesindicateaquitelargeoverestimationofETo.Since
alltheobservationdatasetshavedifferentwindspeeds,usingthe
seasonalmeanvalueimprovedsomepartsofthescatterplotbut
adverselyimpactedsomeother parts.Therefore, it canbe
con-cludedthatsincethewindspeedishighlyvariableintime,itislikely
thatitstimevariationmayhavemoreinfluencethanitsmagnitude
inestimatingPMT.Inmostofthestationsthewindspeedoften
isaround 2ms−1 throughouttheyear,whereas extremewinds
maydominateastationonlyforspecificperiodsoftheyearasis
illustratedinFig.5;henceadoptinganyfixedvaluemayleadto
under-orover-estimationbythePMTmethod.Asillustratedin
Fig.6s–x,usingseasonalwindspeedinsteadofthedefaultvalueof
2ms−1islesssuccessfulinimprovingPMTresultsinwindystations
andisthereforenotadvisable.
3.5. ComparingPMTandHSmethods
As discussed earlier,the performances of both PMTand HS
methodsaregenerallyadequateforestimatingEToforallclimatic
regionsofIranusinglimitedavailabledatasets.Table6presents
theresultoftheDieboldandMariano(1995)Bstatistictestthat
wasusedforcross-comparisonoftheadequacyoftheestimations
bythetwomethodsrelativetothePM-ETo.Thetestvalueisout
oftheinterval[−1.96,1.96]whenthereisasignificantdifference
at95%level.ResultsinTable6showthatHSequationperformed
significantlybetterthanPMTfor14stationswhilePMTperformed
significantlybetterfor9stations.Itisworthnotingthatthestatistic
Bispositive(negative)andsignificantwhenHS(PMT)performed
better.BetterresultsforHSlargelyovercomethoseofPMTforthe
semi-aridregionwhilePMThasshowntobesuperiorforthehumid
andsub-humidareas.However,differenceswerenotsignificant
for43%ofstationsconsideredinthisstudy.Despitethese
statis-tic,theusersshouldanalyzethesizeoferrors,particularlyRMSE,
Fig.7. SpatialpatternofannualETooverIranestimatedby(a)PM-ETo,(b)HS,and(c)PMTmethods.
theregressioncoefficientb,aswellastheefficiencyindicatorsEF
anddIA.
3.6. SpatialpatternofETo
The spatial pattern of annual ETo over Iran estimated with
thePM-ETo methodusingfulldatasets(Fig.7a)showsagradual
increaseofETofromnorthtoSouth,withthelowestvaluesover
thenorthernhumidandsub-humidclimatesofIranandlargerETo
estimatesforaridandhyper-aridclimatesinthesouthernand
east-erncountry.TherangeofannualETo variesfrom700mminthe
humidcoastalareasofsouth-westernCaspianSeaupto2800mm
inhyper-ariddeserticareasofeasternIran.Mostpartsofthecoastal
areasoftheCaspianSeaandthemountainousareasofnorthernand
north-westernIrandepictETovaluesbetween700and1200mm,
increasingsouthwardand eastwardduetothedecreasein
lati-tudeand/oraltitude.Themountainousareasofmid-westernand
north-easternIran,aswellasthemid-centralregionofthecountry,
exhibitETobetween1200and1600mm,whiletheETovaluesfor
avastareaincentral,southernandeasternIranrangefrom1600
to2000mm.ThehighestETowith2000–2800mmisobservedin
south-westernandeasternIran.ThehighEToinsouth-westernIran
isrelatedtotemperature,thehighestobservedinthecountry.
Dif-ferently,ineasternIran,itrelatestotheveryhighwindspeedand
dryness,withoccurrenceofverylowannualmeanrelative
humid-ity(<40%)thatevenreducedto<25%insummerwhentheregion
isexposedtoextremewindspeed.ThespatialpatternofPM-ETo
overIranrepresentedhereiniscomparabletothatofforDinpashoh
(2006),thoughthenumber ofusedstationsand theconsidered
dataperiodsaredifferent.Theobtainedresultisalsoconsistent
withtheresultsachievedbyTabarietal.(2011a,b)andTabariand
Aghajanloo(2012)foreastern,westernandnorthernIran,
respec-tively,consideringboththemagnitudeandspatialvariabilityof
ETo.
Fig.7bandcshowsthespatialpatternsofETooverIran
com-putedwiththeHSandPMTmethods,respectively.Thesespatial
patternsareidenticalandalsoresembletothatofPM-EToshown
inFig.7a.However,Fig.7bshowslowerestimatesofETofor
east-ernIranrelativetoFig.7aandcsinceitwasnotpossibletouse
localwindspeedforHSestimationcontrarilytothecaseforPM
andPMTmethods.TheobservedconcordanceofHSandPMTmaps
(Fig.7bandc)withthemapofPM-ETo(Fig.7a),consideringboth
thespatialpatternandthemagnitudeoftheestimations,in
addi-tiontoresultsinTables3and4,indicatesthattheHSandPMT
methodsareappropriatealternativesforestimationofEToinall
cli-maticregionsofIran,particularlyfortheveryremoteareas,when
onlyminimum and maximumtemperature areavailable. Using
PMTmaybepreferablewhenthedatasetispartlycomprisingfull
dataorpartiallyfull databecausethenit ispossibletousethe
PMTfortheperiodswhenradiationorhumiditydataarerequired.
ThenthesameFAO-PMequationisusedwitheitherobservation
orestimateddata. Differently,theHSmethodis preferableifit
is not desirable to correct Tmin data tocompensate for station
4. Discussionandconclusions
Monthlyaveragesofmaximumandminimumtemperature,
rel-ativehumidity,sunshinedurationandwindspeed,corresponding
totheperiod1971–2005at40Iraniansynopticstationsdistributed
over the countrywereutilized for estimation of ETo usingthe
PM-ETo,thetemperaturePMTandHSmethods.Aimingata
com-parativeanalysisofthebehaviourofthesemethods,theclimatic
zonesofIranwereidentifiedutilizingtheUNEParidityindex,which
isbasedontheratioofmeanannualprecipitationtomeanannual
potentialevapotranspiration.ToestimateETo usingboththeHS
andPMTmethods,appropriatevaluesforkRs,anempirical
radi-ationadjustmentcoefficient,weresearchedforeachstation.For
estimationofTdewfromTmintobeusedwiththePMT,thelatterwas
correctedforaridity.Forhumidclimatesanempiricalapproachto
estimateTdew fromthemeantemperaturewasusedandapplied
forPMTestimation.TheperformanceoftheHSandPMTmethods
againstPM-ETowereevaluatedthroughasetofcommonlyused
statistics.
ResultsshowthatsearchingappropriatekRsforestimationof
solarradiationforbothHSandPMTmethodsresultsinsignificant
accuracyimprovementintheestimationofETo.Itwasobserved
thatkRsvaluesforthestationslocatedinthesub-humidandhumid
climatesofwesternandnorthernIranaresmallerthanthosefor
thesemi-aridtohyper-aridclimatesofcentral,southernand
east-ernIran,suggestinganorth-southandwest-eastincreasingspatial
trend. It was also found that the kRs values selected for both
methodsinagivenstationareeitheridenticalorshownegligible
difference.Despiteresultshereinconcernawiderangeofclimates,
itisdesirabletohavetheseresultsconfirmedthroughstudies
rel-ativetootherareasandusingdifferenttimestepcomputations.
Theadjustmentof Tmin for estimatingTdew tobeused with
thePMTmethodhasshowntohighlyimprovetheperformance
ofthemethodforsemi-aridtohyper-aridclimates.Moreover,the
adoptionofanempiricalapproachtoestimateTdewfromthe
mini-mumtemperaturealsosignificantlyincreasedtheaccuracyofPMT
estimationforhumidclimates.Overall,estimatesbyHSandPMT
stronglycorrelatewithestimatesbyPM-ETo,implyingthatthe
con-sideredmethodsappropriatelypredictEToforallclimaticregions
ofIraniftheappropriatekRswasconsidered.Resultsdescribedalso
indicatethatwhendatasetsareincomplete,particularlyrelativeto
radiationandairhumiditydata,ETocalculationsmaybeperformed
fortheperiodswhendataarelackingwiththeFAO-PMequation
usingradiationand/orVPDparametersestimatedfromTmaxand
TminasforthePMTmethod.
ThestatisticaltestondifferencesbetweenHSandPMTmethods
hasshownthatHSismoreoftensignificantlysuperiortoPMTin
thesemi-aridregionwhilethePMTperformedsignificantlybetter
thanHSinhumidandsub-humidareas.However,nosignificant
differenceswerefoundfor43%ofcases.
Aweak/pooragreementwashoweverfoundforsomestations
situatedintheverydryclimateofeasternandsouthernIranowing
to therole played there by extreme and variable wind speed.
TheobserveddiscrepanciesbetweenHS(andPMT)andPM-ETo
inthestationssituatedineasternIranisattributedtotheextreme
windspeed,particularlyduringsummerwhenEToishigher.The
observeddisagreementbetweentheestimationsbyPMT(andHS)
andPM-ETomaybepartiallyduetonotconsideringwindspeedin
HSmethodandtothelesseffectivedefaultwindspeedvalue
usu-allyconsideredforPMTestimation,whichismuchlowerthanthe
actualvalueusedthereforPM-ETocomputation.However,using
seasonalregionalvaluesasdefaultwindspeedvaluesdecreased
the variance of residuals and the heteroscedasticity of
regres-sionsbutincreasedtheregressioncoefficientsandthereforeETo
becameover-estimatedinthesehotandwindylocations.Itislikely
thatthetimevariabilityofwindspeedplaysamajorroleinthe
discrepanciesbetweenPMTandPM-EToestimatesandthereforeit
ishardlypossibletofindadefaultvalueorempiricalfunctionthat
takesthatvariabilityintoaccountinPMTwhenwindspeeddataare
notavailable.Giventhesecircumstances,itislikelynotappropriate
totryfindingamodificationofHSforconsideringwindspeed.
How-ever,consideringtheneedtominimizeerrors inestimatingETo
whenonlytemperaturedataareavailableinareaswherewindmay
playamajorrole,thisproblemremainsopentofurtherresearch
developments.
ThespatialdistributionofannualEToshowedagradual
increas-ing from north to south, with thelowest ETo values observed
overnorthernhumidandsub-humidclimatesofIranandlarger
ETo estimates for aridand hyper-arid climates in thesouthern
andeasterncountry.ThespatialpatternsofETocomputedusing
limitedweatherdatawithHSandPMTmethodsareidenticaland
resembletothat ofPM-ETo,thusconfirmingtheabovereferred
conclusionsindicatingthattheHSandPMTmethodsare
appropri-atealternativesforestimationofEToinallclimaticregionsofIran,
particularlyfortheveryremotestationshavingonlyminimumand
maximumtemperaturerecords.
References
Ahmadi, S.A.,Fooladmand,H.R.,2008. Spatiallydistributedmonthlyreference evapotranspirationderivedfromthecalibrationofThornthwaiteequation:a casestudy,SouthofIran.IrrigationScience26,303–312.
Allen,R.G.,1996.Assessingintegrityofweatherdataforreference evapotranspira-tionestimation.JournalofIrrigationandDrainageEngineering122(2),97–106. Allen,R.G.,1997.Self-calibratingmethodforestimatingsolarradiationfromair
temperature.JournalofHydrologicEngineering2(2),56–67.
Allen,R.G.,Smith,M.,Perrier,A.,Pereira,L.S.,1994.Anupdateforthedefinitionof referenceevapotranspiration.ICIDBulletin43(2),1–34.
Allen,R.G.,Pereira,L.S.,Raes,D.,Smith,M.,1998.CropEvapotranspiration. Guide-linesforComputingCropWaterRequirements.FAOIrrig.Drain.Pap.56.FAO, Rome,300p.
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 standard-izedsurfaceresistanceforhourlycalculationofreferenceETobytheFAO56
Penman–Monteithmethod.AgriculturalWaterManagement81,1–22. Allen,R.G.,Pereira,L.S.,Howell,T.A.,Jensen,M.E.,2011.Evapotranspiration
informa-tionreporting:I.Factorsgoverningmeasurementaccuracy.AgriculturalWater Management98(6),899–920.
Angström,A.,1924.Solarandterrestrialradiation.QuarterlyJournaloftheRoyal MeteorologicalSociety50,121–125.
Annandale,J.G.,Jovanovic,N.Z.,Benadé,N.,Allen,R.G.,2002.Softwarefor miss-ing dataerror analysisofPenman–Monteithreference evapotranspiration. IrrigationScience21,57–67.
Berengena,J.,Gavilán,P.,2005.Referenceevapotranspirationestimationinahighly advectivesemiaridenvironment.JournalofIrrigationandDrainageEngineering 131(2),147–163.
Cai,J.B.,Liu,Y.,Lei,T.W.,Pereira,L.S.,2007.Estimatingreference evapotranspira-tionwiththeFAOPenman–Monteithequationusingdailyweatherforecast messages.AgriculturalandForestMeteorology145,22–35.
Cai,J.,Liu,Y.,Xu,D.,Paredes,P.,Pereira,L.S.,2009.Simulationofthesoilwater bal-anceofwheatusingdailyweatherforecastmessagestoestimatethereference evapotranspiration.HydrologyandEarthSystemSciences13,1045–1059. Diebold,F.X.,Mariano,R.S.,1995.Comparingpredictiveaccuracy.JournalofBusiness
andEconomicStatistics13,253–263.
Dinpashoh,Y.,2006.StudyofreferencecropevapotranspirationinI.R.ofIran. Agri-culturalWaterManagement84,123–129.
Dinpashoh,Y.,Fakheri-Fard,A.,Mogaddam,M.,Jahanbakhsh,S.,Mirnia,M.,2004. SelectionofvariablesforthepurposeofregionalizationofIran’sprecipitation climateusingmultivariatemethods.JournalofHydrology297,109–123. Dinpashoh,Y.,Jhajharia,D.,Fakheri-Fard,A.,Singh,V.P.,Kahya,E.,2011.Trendsin
referenceevapotranspirationoverIran.JournalofHydrology399,422–433. Diodato,N.,Bellocchi,G.,2007.Modelingreferenceevapotranspirationover
com-plexterrainsfromminimumclimatologicaldata.WaterResourcesResearch43, W05444,http://dx.doi.org/10.1029/2006WR005405.
Droogers,P.,Allen,R.G.,2002.Estimatingreferenceevapotranspirationunder inac-curatedataconditions.IrrigationandDrainageSystems16,33–45.
Fooladmand,H.R.,Haghighat,M.,2007.Spatialandtemporalcalibrationof Har-greavesequationforcalculating monthlyETo basedonPenman–Monteith
method.IrrigationandDrainage56,439–449.
Fooladmand,H.R.,Zandilak,H.,Ravanan,M.H.,2008.Comparisonofdifferenttypes ofHargreavesequationforestimatingmonthlyevapotranspirationinthesouth ofIran.ArchivesofAgronomyandSoilScience54(3),321–330.
