HandbookpartII:TheoryVersion7.2/March2017GlobalMeteorologicalDatabaseVersion7SoftwareandDataforEngineers,PlanersandEducationTheMeteorologicalReferenceforSolarEnergyApplications,BuildingDesign,Heating&CoolingSystems,EducationRenewableEnergySystemDesign,AgricultureandForestry,EnvironementalResearch.MeteonormContentsMeteonormContentsContentsPARTII:THEORYRADIATION 1ReferencetimeinMeteonorm 1Worldwideinterpolationofmeteorologicaldata 2Methods 2Qualityoftheinterpolationonmonthlymeans 4Conclusions 4Thesolartrajectory 5Extraterrestrialsolarradiation 8Clearskyradiation 9UnderlyingbasicconceptsintheSoDa/ESRAclearskymodel 9Theestimationofclearskyradiation 10UsingtheSoDaLinketurbidityfactormappedresource 11Generationofglobalradiation 13Stochasticgenerationofglobalradiation 13Generationofdailyvalues 13NewMarkovtransitionmatrices(MTM) 15Validation 17Generationofhourlyvaluesfromdailyvalues 19Radiationoninclinedsurfaces 24Calculationofradiationcomponentswithgivenglobalhorizontalradiation 24PerezModel 24Validation 25Calculationofglobalanddiffuseradiationoninclinedsurfaces:"Perez-model" 28Albedo 29Validationoftheslopeirradiancemodel 29Modificationofradiationduetohorizon 31Modificationofdirectradiationbyskylineprofile 31Modificationofdiffuseradiationbyskylineprofile 316.7.4Conclusions 32Minutetimeresolutionradiationdata 33Minutetominutegenerationmodel 33Timeseriesminutemodel 33Hofmannminutemodel 33SkartveitandOlsethminutemodel 34Validation 34Minutetominutediffuseradiation 36Minutetominuteglobalradiationoninclinedplanes 38TEMPERATUREANDADDITIONALPARAMETERS 39Temperaturegeneration 39Introduction 39Estimationofdailymeanairtemperatures 39Stochasticgeneration 40Dailyminimumandmaximumtemperatures 42Derivingthetemperatureprofilefromtheirradianceprofile 43Validation 44Generationofsupplementaryparameters 47Dewpointtemperatureandrelativehumidity 47Validation 49Wet-bulbtemperatureandmixingratio 53Cloudcover 55Longwaveradiation 57Longwaveradiationemittedfromlevelground 57Longwaveradiationemittedbytheatmosphere 58Radiationbalance 58Conclusionsonlongwaveradiationmodelling 58Illuminance 59Wind 59Windspeed 59Winddirection 62Atmosphericpressure 64Heatingdegreedays 64Precipitation 64Dailyprecipitationvalues 64Hourlyvalues 65Validation 6Drivingrain 68Spectralradiation 69Sunshineduration 70Photosyntheticactiveradiation(PAR) 70PrecipitableWater 70Uncertaintymodel 71Methods 71Results 72Summaryofresults 75LITERATURE 76PAGE79MeteonormTheoryPAGE79MeteonormTheory7 Radiation7 RadiationInthischapter,thetheoreticalbasisofMeteonormispresented.Tokeepthelengthofthetextwithinreasonablelimits,someofthematerial(i.e.longerexplanations)hasbeenomitted.ReferencesaremadetothecontributioninSolarEnergyconcerninginterpolationandgenerationofradiationdata(Remundetal.,1998)andthetechnicalpublicationondatainterpolationpresentedatthe14thSolarEnergyPVConferenceinBarcelona(RemundandKunz,1997).ReferencetimeinMeteonormHourlyvaluesaredesignatedbytheendtimeoftheinterval.Thusthevaluefor14.00hoursreferstotheaveragevalueoftheintervalfrom13.00to14.00hours.Thecentralvalueofthisintervalis13.30hours.Thecomputerprogramcontainsaninternaltimereferenceinminutes,whichdefinesthepositionofthecenteroftheintervalinrelationtotheendtime.Intheexamplegivenhereitis-30minutes.Thereferencetimecanbechangedintheprogram.Alterationsare,however,onlynecessaryintwocases:Whenhourlyvalueswhosecentralvaluedoesnotcorrespondtothehalf-hourareimported.Whenhourlyvalueswhosecentralvaluedoesnotcorrespondtothehalf-houraretobegenerated.Exampleof1:Measuredvaluesareassumedtobeavailable.Themeasurementintervalextendedfromonehalf-hourtothenext(e.g.00:30to01:30).Thehourlyaveragewascalculatedbasedonthisintervalandstoredattheendtime(e.g.01:30).As,however,Meteonormonlyallowsintegerhourlyvalues(h)from1to24,itisonlypossibletousethefullhour(e.g.1)asendtimefortheinterval.Thecomputerprogrammustbeinapositiontodeterminebyhowmuchthegivenendtime(e.g.1)differsfromtheeffectivecentervalue(e.g.01:00).Asthemeasurementinterval(e.g.01:00)correspondsinthisexampletothegivenendtime(e.g.1),thereferencetimerequiredbyMeteonorm(IZRM=differencebetweentheeffectivecenteroftheintervalandthegivenendtimeinminutes)is0.Exampleof2:HourlyvaluesaretobegeneratedusingthereferencetimeformeasureddataoftheSwissMeteorologicalOffice(SMA).ThemeasurementintervaloftheSMAextendsfrom10minutesbeforethefullhourto20minutesbeforethenextfullhour(e.g.00:50to01:40),e.g.the10-minutevaluesareaveragedandstoredattheendtime(e.g.01:40).Thecenteroftheintervalis10minutesafterthefullhour(e.g.01:10).TheendtimeoutputintheMeteonormcomputerprogramcorrespondstothefullhour(e.g.1).Theeffectivecenteroftheinterval(e.g.01:10)differsinthiscaseby10minutesfromthegivenendtime(e.g.1).Meteonormthusrequires10asreferencetime.WorldwideinterpolationmeteorologicaldataForthesimulationofsolarenergysystems,meteorologicaldatafromallpartsoftheworldisneeded.Formanyregions,measureddatamayonlybeappliedwithinaradiusof50kmfromweatherstations.Thismakesitnecessarytointerpolateparametersbetweenstations.Themethodgivenbelowenablesthedatatobeinterpolatedandmonthlyvaluestobeobtainedforalmostallpointsoftheglobe.MethodsTocalculatemeteorologicaldataforanydesiredlocationintheworld,aninterpolationproceduremustbeapplied.Forglobalradiation,thisisdonewitha3-Dinversedistancemodel(Shepard’sgravityinterpolation),basedontheintroductionbyZelenkaetal.(1992)(IEATask9),withadditionalNorth-Southdistancepenalty(WaldandLefèvre,2001),where:GhxwiGhxizizxgvwi1ii2wkwithidiRfordiR

(7.2.1)wi0otherwiseiNSixd2f22iNSix

z2fNS10.3ixisinx2wi:weightiwk:sumofoverallweightsR:searchradius(max.2000km)v:verticalscalefactors:horizontal(geodetic)distance[m]zx,zi:altitudesofthesites[m]i:gv:Numberofsites(maximum6)verticalgradienti,x:latitudesofthepointsTheverticalscalefactorvandtheverticalgradientgvaredependingontheparameter(Tab.7.2.1).Tab.7.2.1:MonthlyverticalscalefactorsvandgradientsgvforinterpolationParametervgvGh1500.0Ta4000.001Td4000.002FF3000.0RR2000.0Rd3000.0Sd4000.002Theotherparameters(temperature,wind,humidityandrain)canbeinterpolatedusingsimilarprocedures.TheverticalfactorvinEqn.7.2.1isadjustedtogetthesmallestdeviations.Forinterpolatingtemperatureandwinddata,furtherinformationonlocaleffectsisneeded.Theinfluenceoftheseashoreisconsideredinthefollowingway:increasedwindspeed(1m/s)forallmonths,increasedtemperatureinwinter,andlowertemperatureinsummer(notappliedtotropicalregions)(Tab7.2.2).Tab.7.2.2:Monthlycorrectionfactorsfortemperatureforlocalfeaturesin°C(slightlymodifiedsiamodel)FeatureZoneJanFebMarAprilMayJuneJulyAugSepOctNovDecopenA0.00.00.00.00.00.00.00.00.00.00.00.0depressionA-1.6-0.7-0.5-0.4-0.4-0.3-0.3-0.2-0.2-0.4-0.7-1.2coldhollowA-3.9-2.8-1.7-0.4-0.4-0.3-0.3-0.2-0.2-1.0-2.2-3.8sea/lakeA-0.5-0.7-0.7-0.4-0.71.1cityA1.11.01.2S-facinginclineS-facinginclineNS2.91.03.7W/E-facinginclineW/E-facinginclineNSvalleyvalleyNS0.21.00.21.00.11.0*S-facingincline.Forsouthernhemisphere:N-facingincline!Zone: N:Regionsnorthof45°Norsouthof45°S A:General S:Regionssouthof45°Nandnorthof45°SFeature: Depression:Smallandmediumdepressionswithformationofcoldhollows,particularlyinwinter,orstronglyshaded.Mainlyconfinedtomountainousregions.Coldhollow:IncludestheextensivecoldhollowsofcentralAlpinevalleyssuchasinupperEngadineinSwitzerland.Lake:Vicinityofseaorlargerlakes(>100km2).Sitenotmorethan1kmfromtheshore.City:Applicabletocentersoflargercitieswithover100,000inhabitants.(SeealsoFig.2.2.1andTab.2.2.1)Tab.7.2.3:Monthlycorrectionfactorsforwindspeedinm/sdependingonterrain.SimplifiedWASPmodel(RisoeNationalLaboratory,1990).Terrain Correctionfactor(applicabletoallmonthsofyear)shelteredterrain(cities) -1.0open 0.0sea/lake 1.0Summits(hillsandridges) 3.0QualityoftheinterpolationonyearlymeansFollowinginterpolation,theaccuracyoftheresultswasfoundbycrosscorrelationmethodtobeasfollows:Interpolationofglobalradiation:meanbiasederror(mbe):0W/m2(0%);rootmeansquareerror(rmse):12W/m2(6.9%)(Tab.7.2.4).Fortemperatureinterpolation,thembewas0.0°Candthermse1.2°C.Usingthenearestneighborinterpolationmethodasabenchmark,thermseforglobalradiationwouldbe14%andthatfortemperature3.4°C.Tab.7.2.4:Qualityofthegroundbasesinterpolationofyearlyvalues.Gh[%]Ta[°C]Td[°C]FF[m/s]RR[%]Rd[d]Sd[%]TimeperiodAll2000-092000-092000-091961-901961-901961-90Europe6.31.00.71.223259.6WesternEurope5.91.00.71.2242510.5Switzerland6.71.00.51.2252710.3Germany4.11.00.41.118226.6France1.217307.4Asia1.031217.6Japan0.914147.6Africa1.028517.8NorthAmerica4.91.00.60.818268.4SouthAmerica1.0294216.0Australia/Ocean.6.0253616.0World1.025289.1ConclusionsWiththeMeteonormVersion7database,itispossibletosimulatesolarenergysystemsinallpartsoftheworldonaconsistentbasis.Theinterpolationerrorsaremostlywithinthevariationsofclimatefromoneyeartothenext.Thequalityoftheinterpolationofallparameterswasimprovedwiththeadditionalstationsandqualitychecksofversion7.2.Forradiationfurtherimprovementsweremadeusinggroundandsatellitedata(Chapter3.1.2),whicharenotincludedinthetestabove(butinchapter8.3).SolartrajectoryInsolarenergyapplications,theknowledgeofthegeometricalparametersofthesolartrajectoryisnecessary.Sinceversion5.0(2003)asetofalgorithmsbasedontheEuropeanSolarRadiationAtlasESRA(2000)isused.Inthefollowingformulae,anglesaregiveninradians[rad]whennototherwisestated.Viewedfromafixedpointontheearth'ssurface,thesolarpositionisdefinedbytwoangles(Figs.7.3.1and7.3.2):Solaraltitudehs:Anglebetweenhorizontalplaneandlinejoiningthecentersoftheearthandthesun(solarelevation).Solarazimuths:Anglebetweentheprojectionofthestraightlinejoiningthecentersoftheearthandthesunonthehorizontalplaneandduesouth.s>0inpositivesolardirection,s<0innegativesolardirection.sunsunzenithNWhssPSEFig.7.3.1: SolarpositionviewedfromapointPontheearth'ssurfaceZ:Z:axisofrotationzenithearthPzP:pointonearth‘ssurface:Latitudezzenithangle-hsdeclinations:hourlyangleYssunXFig.7.3.2: Solarposition(declination,zenithangleandhourlyangle)Thetwoanglesmaybeexpressedasafunctionoflatitude(),solardeclination()andhourlyangle(s)(7.3.1to7.3.4).scnnnssss

(7.3.1)cncsns

(7.3.2)s coshs Thedeclination()istheanglebetweentheequatorialplaneandthestraightlinejoiningthecentersoftheearthandthesun.Itisdeterminedbythelawsgoverningthesolartrajectory,andcanbeexpressedasgiveninEqn.7.3.3aandb(Bourges,1985).0.00649790.405906sint0.0020054sin2t0.002988sin3tt2twith

(7.3.3a)t0dyt1t10.52n002365.2422n0yINTy4

(7.3.3b): declination[rad] dy: dayofyeary: year λ: longitudeINT standsforintegerpartoftheargumentandyforyearanddyfordaynumberoftheyear.Fortheequinox,thedeclinationiszero,forthesummersolstice+23.4°andforthewintersolstice-23.4°.Itisthisvariationwhichisresponsiblefortheseasonsoftheyear.Thehourlyangle(s)isalsoknownassolartime(ST)inradians(7.3.4).????

=(?????12)??

(7.3.4)Theastronomicaldaybeginsandendswhenthecenterofthesun'sdiskispreciselyonthe(flat)horizon.Thecalculationoftheanglesofsunriseandsunset(ss)ismadeusingEqn.7.3.5,obtainedbysolvingEqn.7.3.1withhs=0.=????????????[?tan???tan??] (7.3.5)AsanaddedfeatureinMeteonormVersion6.0theradiationisalsomodeledforthosehours,whentheelevationispositiveatthebeginningortheendofthehourlytimeperiod,butnotatthecentre.Eitherthebeginortheend(theonewithpositiveelevation)istakenassolarelevationforthosehours.Forthosehoursthepartofthetime,whenthesunisabovetheastronomichorizoniscalculated.Thegeneratedradiationvaluesaremultipliedwiththispart.Generallytheradiationparametersareverysmallforthosehours.DimensionlessquantitiesFormanychainlinkstheclearnessindexisused.ThisindexisdefinedbyMonthlyKTm

GhmGh0mKTd

GhdG

(7.3.6)0dhourlyKTh

GhG0OpticalairmassIncalculatingtheradiationontheearth'ssurface,theopticalmassmisrequired.Thisisdefinedastherelativethicknessoftheairpathtraversedbyasun'sraywhenitreachestheearth'ssurface.Forverticalimpingementofthesunraysatsealevel,massumesthevalue1.Thevalueoftheopticalairmassdeclineswithincreasingaltitude,andincreaseswithdecliningsolaraltitude(Eqn.7.3.7)Thesolaraltitudeangleisfirstcorrectedforrefraction.mpp0

snhstrue278hstrue5.6364pp0

.2

(7.3.7)refrhstruehshsrefrhsrefr0.061359

hshs2128.9344hs277.3971hs2z:Heightabovesealevel[m] hs:Solaraltitudeangle[rad]ExtraterrestrialsolarradiationOutsidetheearth'satmosphere,thesolarradiationintensityis1'366W/m2(I0)(7.4.1).Asurfaceexposedtothesuncanonlyreceivethisvalueifitisplacednormaltothedirectionofradiation.Anydeviationfromthisdirectionleadstoareductionofincidentradiation.Inthecaseofasurfacelyingoutsidetheearth'satmospherethatisparalleltothehorizontalplane,theradiationisdescribedasextraterrestrialhorizontalsolarradiation(G0).Thisradiationcorrespondstothemaximumpossibleradiationwhichwouldoccurattheearth'ssurfaceifitwereunhinderedbytheatmosphereandthehorizon.GoGoatmosphereI0hsGhmaxsun earthequatorFig.7.4.1: Extraterrestrialsolarradiation(G0)andmaximumradiationforclearsky(Ghmax).Usingtheequationforradiationoutsidetheearth'satmosphereandforthesolarangle(hs)(7.3.1),theextraterrestrialhorizontalsolarradiationcanbecalculated(7.4.1)(SfeirandGuarracino,1981).G0I0sinsI01366W/m210.0334

0.048869

(7.4.1)cos

365.25 whereisthecorrectiontoactualsolardistanceatanyspecifictimeintheyear.dy:dayofyear :SolaraltitudeangleClearskyradiationThemaximumradiationisdefinedastheradiationoccurringondayswithaclear,cloudlesssky.Notonlytheglobalbutalsothedirectanddiffuseradiationsareofinterest.Foracloudlesssky,theglobalradiationtakesmaximumvalues.Themaximumglobalradiationcalculatedherecorrespondstothegreatestpossiblevalueofglobalradiationperhouratthespecifiedaltitude.Forarestrictedperiod,theglobalradiationcanattainveryhighvaluesevenwithacloudysky.Thisoccurswhensunlight,havingpenetratedthroughintensivelyreflectingclouds,impingesdirectlyontheearth'ssurface.Themaximumglobalradiationisstronglyaltitudedependent,andincreaseswithincreasingheightabovesealevel.Attheupperedgeoftheatmosphere,ittakesthevalueoftheextraterrestrialglobalradiation.Sinceversion5.0ofMeteonorm,anewsetforclearskyradiationisused.TheEuropeanUnionFP5frameworkprojectSoDastudies(RemundandPage,2002)showedthattheuseofaslightlyenhancedESRAclearskyirradiancemodel(Rigollieretal.,2000)deliversbestresults.Thefollowingchaptersareadirectresultofthesestudies.UnderlyingbasicconceptsintheSoDa/ESRAclearskymodelTheclarityoftheskyaboveanysitehasanimportantimpactontheintensityofboththebeamirradi-anceandtheamountofscattereddiffuseradiationundercloudlessskyconditions.Acapacitytoaddresstheseissuesiscriticalinachievingsoundirradiationestimates.Energyislostfromthesolarbeambythreeroutes:molecularscatteringbythegasesintheatmosphere.spectralabsorption,forexamplebygaseouswatervapour,primarilylocatedintheloweratmosphere,andbyozone,whichislocatedprimarilyinthestratosphere,andalsobythepermanentatmosphericgaseslikecarbondioxide.scatteringandabsorptionduetonaturalaerosolsandmanmadeaerosolsintheatmosphere.Theelevationofthesiteabovesealevelreducestheeffectiveatmosphericpathlengthandhastobetakenintoaccount.Theamountofaerosolpresentintheatmosphereandtheamountofwatervapourpresenttypicallydecreaseexponentiallywithincreasesinsolaraltitude.Themodelingprocesshastoallowforthis.Thedetailedassessmentoftheseimpactsiscomplex.Thereareadvantagesforpracticaluserstobeabletoexpresstheimpactsofvariousfactors,likevariationsatmosphericwatervapourcontentsandaerosols,inasingleeasilycomprehensibleindex.TheESRA/SoDaclearskyresourceisbasedontheuseoftheconceptoftheLinketurbidityfactortoachievethissimplicity.TheguidanceofKasten(1996)wassoughtintheevolutionofthepreciseformulationadopted.TheLinketurbidityfactoratheightzmetresabovesealevel,TL(z),wasobjectivelydefinedbyKasten(1983)as:RTLz1DzzR

(7.5.1)whereR(z)istherelativeopticalthicknessrelatingtoRayleighscatteringbythegaseousmoleculesintheatmosphereandozoneabsorptionandD(z)istherelativeopticalthicknessassociatedwithaerosolextinctionandgaseousabsorptionotherthanozoneinthestratosphere.FurtherelaborationmaybefoundinTerzenbach(1995).Note:insomerecentscientificstudiesthegaseousabsorptionbythepermanentgasesintheatmospherehasbeenincorporatedwithinR(z).ThisproducesadifferentdefinitionoftheLinketurbidityfactor.Theactualpathlengththroughtheatmosphereisdescribedquantitativelyusingtheconceptoftherelativeopticalairmass.TherelativeopticalairmassatsealevelcanbecalculatedwithEqn.7.3.7,bysettingp=p0.R(z)andD(z)arebothfunctionsofairmassbecausewearedealingwithbroadbandradiation(asopposedtomonochromaticradiation).Thebeamirradiancenormaltothebeamisgivenby:BnI0

expmTz

[W/m2] (7.5.2)LRInrecentyearsseveralscientistshavewidenedtheconceptofRayleighopticalthicknesstoincludeabsorptionbyarangeofabsorbinggasesthatoccurnaturallyinthecleandryatmospherelikecarbondioxide,oxygen,andcertainoxidesofnitrogen.ThisprocessincreasesthevalueofR(z),thedenomi-natorinEqn.7.5.1,andsoyieldslowervaluesofthecalculatedturbidityfactorfromirradianceobservations.LRTheSoDa/ESRApolicyinthefaceoftheserecentchangeshasbeentoretainaconstantquantitativedefinitionoverhistorictimeoftheLinketurbidityfactor.ThecompromiseadoptedtakesadvantageofrecentimprovedknowledgeabouttheeffectofairmassontheRayleighopticalthickness.TheoldRayleighopticalthicknessvaluesarealignedwiththenewclearskyopticalthicknessvaluesatairmass2.Thisalignmentisdonebymakingadefinedmatchatairmass2betweenthenewalgorithmsandtheold,whichhavebeenmaintainedasthereferenceforLinketurbidityfactorinputs.Thisalignmentyieldsanadjustmentfactorof0.8662neededtoachievethismatchwhichisincludedinEquation7.5.3.ThebeamirradiancenormaltothebeamiscalculatedusingthestandardizedoriginalKastenairmass2Linketurbidityfactor,as:BnI0

mT

R

[W/m2] (7.5.3)LwhereTListheairmass2LinketurbidityfactorasdefinedbyKasten'sformulationandmistherelativeopticalairmasscorrectedforstationpressure.LKastenhasprovidedthefollowingguidelinefortypicalvaluesofTLinEurope(Tab.7.5.1).Tab.7.5.1: TypicalvaluesofTLinEurope.Verycleancoldair TLK=2Moistwarmorstagnatingair TLK=4to6 Cleanwarmair TLK=3Pollutedair TLK>6TheestimationofclearskyradiationForequationsofglobalclearskyradiationwerefertothepublicationofRigollieretal.(2000),chapteraboutirradiancemodel.Fordiffuseclearskyradiationthefollowingcorrectionsareused:TheformulationofthehorizontalsurfacediffuseradiationirradiancealgorithminESRA(2000)andRigollieretal.(2000)didnotmakeanyallowanceforvariationsinthesiteatmosphericpressurethoughsuchacorrectionwasmadeintheassociatedbeamestimates.FurtherinvestigationhasshownthedesirabilityofincludingthepressurecorrectionintheESRAdiffusealgorithm.L 0Setting(T*L 0DcI0

s

Trd

*

[W/m2] (7.5.4)LTrd(TL*)isthediffusetransmittancefunctionwhichrepresentsthetransmittancewiththesunatthezenith,ItiscalculatedusingEqn.7.5.5.LTT*302302T*704T*2rdL L L

(7.5.5)Fd(s)isthediffusesolarelevationfunctionwhichadjuststhediffusezenithtransmittanceTrd(TL*)totheactualsolarelevationangles.ItiscalculatedusingEqn.7.5.6,wheresisinradians.FyAAsinAsin2

(7.5.6)d s 0 1 s 2 sThecoefficientsA0,A1andA2arecalculatedusingEquations7.5.7:0LLA31T*8T*20LL1LLA05T*1T*21LL

(7.5.7)2LLA51T*9T*22LLForregionsbelowapproximately500m,thechangesduetothenewformulationaresmall.InSwitzerlandtheclearskydiffuseradiationat1'000ma.s.l.isloweredby10%andtheglobalclearskyisloweredbyabout2.5%bythischange.At2'500mtheclearskydiffuseisloweredby30%andtheglobalisloweredbyabout3%(thediffusepartformsasmallerproportionoftheclearskyglobalirradiationathighersiteelevations).TheoutcomeofthevalidationinRigollieretal.(2000)isthereforenottouchedbythechange,asonlystationsbelow500mwereusedinthevalidation.LinketurbidityLinketurbidity(TL)isusedforinputoftheESRAclearskymodel.Forversion7.2anewturbidityclimatologyhasbeenincluded.It’sbasedonthedatabaseofSolarConsultingServices(Gueymard,2012)andincludesgroundandsatellitemeasurements(MODISandMISR)oftheperiod2000-2015.Inoppositiontothedatausedbetweenversion6and7.1noneedforfurtherreductionofTLdataisneeded.Highturbidityvaluesarereducedmorethanlowervalues.FormeanconditionsatmidlatitudesandindustrializedregionslikeEuropewithLinketurbidityofabout5,thevalueisloweredby20%toavalueof4.Additionallyitwasdetected,thatwithvariedturbidityvaluestheobserveddistributionofclearskyconditionscouldbematchedbetter.Alsomodelsproducingbeamradiationgavebetterresults,whenusingvariedturbidities.BydefaultthedailyLinketurbidity(TLd)valuesarevariedstochastically(optionallyitcansetconstant)(Eqn.7.5.8).TLdd1TLdd1r10.7TL0.5TL1120.51

(7.5.8)rN0,TL

TLd

L

1.21: FirstorderautocorrelationLm:tandrddeiationofyprturbatiosdeendngonmothlymensofTL: Standarddeviationofthenormallydistributedrandomfunction;theconstanthasbeenenhancedfrom0.1to0.25forversion7.2.r: Normallydistributedrandomvariablewithexpectedvalue0andstandarddeviation.WorlddigitalmapsoftheLinketurbidityfactorhavebeenpreparedona0.5”gridasabasicresource(Fig.7.5.1).Fig.7.5.1: YearlylongtermmeanofLinketurbidityfactor(period2000–2015).ThegivenTLvaluesarecoupledtothemeanaltitudeofthepixels.Inthesoftware,theTLvaluesareadoptedtotherealaltitudeofthesiteswiththefollowingequation:L1Lz2z21

0

(7.5.9)GenerationofglobalradiationTomeettodayneeds,monthlyaveragedataisnolongersufficient,andmanydesigncodescallforhourlyorminutedata.However,sincetheinterpolationofhourlyvaluesatarbitrarylocationsisextremelytimeconsuming(onlyfeasibleusingsatellitedata),andnecessitatesextensivestoragecapacity,onlyinterpolatedmonthlyvaluesatnodalpointsarestored.Inordertogeneratehourlyvaluesatanydesiredlocation,stochasticmodelsareused.Thestochasticmodelsgenerateintermediatedatahavingthesamestatisticalpropertiesasthemeasureddata,i.e.averagevalue,variance,andcharacteristicsequence(autocorrelation).Thegenerateddataapproximatesthenaturalcharacteristicsasfaraspossible.Recentresearchshowsthatdatageneratedinthiswaycanbeusedsatisfactorilyinplaceoflong-termmeasureddata(Gansleretal.,1994)