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ContentslistsavailableatScienceDirectAtmosphericResearchjournalhomepage:www.
elsevier.
com/locate/atmosresImprovingWRFmodelturbine-heightwind-speedforecastingusingasurrogate-basedautomaticoptimizationmethodZhenhuaDia,JuanAob,QingyunDuana,,JinWangb,WeiGonga,ChenweiShena,YanjunGanc,ZhaoLiubaStateKeyLaboratoryofEarthSurfaceProcessesandResourceEcology,FacultyofGeographicalScience,BeijingNormalUniversity,Beijing100875,ChinabBeijingGoldwindScience&CreationWindpowerEquipmentCo.
,Ltd.
,Beijing100176,ChinacStateKeyLaboratoryofSevereWeather,ChineseAcademyofMeteorologicalSciences,Beijing100081,ChinaARTICLEINFOKeywords:WRFParameteroptimizationSurrogatemodeling-basedoptimizationTurbine-heightwind-speedforecastingABSTRACTImprovingturbine-heightwind-speedforecastingusingamesoscalenumericalweatherprediction(NWP)modelisimportantforwind-powerpredictionbecauseofthecubiccorrelationbetweenwindpowerandwindspeed.
Thisstudyinvestigateshowasurrogate-basedautomaticoptimizationmethodcanbeusedtoimprovewind-speedforecastingbyanNWPmodelbyoptimizingitsparameters.
AkeychallengeinoptimizingNWPmodelparametersisthetremendouscomputationalrequirementsofsuchanexercise.
AglobalsensitivitymethodknownastheMultivariateAdaptiveRegressionSpline(MARS)methodwasfirstusedtoidentifythemostsensitiveparametersamongalltunableparameterschosenfromsevenphysicalparameterizationschemesoftheWeatherResearchandForecast(WRF)model.
Then,ahighlyeffectiveandefficientoptimizationmethodknownasadaptivesurrogatemodeling-basedoptimization(ASMO)wasusedtotunethesensitiveparameters.
InacasestudycarriedoutoverEasternChina,thesevenparametersthatweremostsensitivetowind-speedsimulationwereidentifiedfromamong27tunableparameters.
ThosesevenparameterswereoptimizedusingtheASMOmethod.
Thepresentstudyindicatesthatthehourlywind-speedsimulationaccuracywasimprovedby8.
7%duringthecalibrationphaseandby7.
58%duringthevalidationphase.
Inaddition,clearphysicalinterpreta-tionswereprovidedtoexplainwhytheoptimalparametersleadtoimprovedwindspeedforecasts.
Overall,thisstudyhasdemonstratedthatautomaticoptimizationmethodisahighlyeffectiveandefficientwaytoimprovewind-speedforecastingbyanNWPmodel.
1.
IntroductionWiththerapidgrowthoftheglobaleconomy,consumptionoftra-ditionalfossilfuelssuchascoalandoilhassoared,leadingtoanenergysourcedepletioncrisis.
Theresultingenvironmentalproblemssuchasairandwaterpollutionarebecomingcritical(Boffey,1970).
Develop-mentofrenewableenergyresourcesisthoughttobethemostpromisingresponsebecausetheseresourcesarebasicallyinexhaustible,offerhugecapacity,andareclean,withverylittlepollution.
Duetoitswidedis-tribution,windenergy,asthemajorrenewableenergyresourceavail-able,hasbeenwidelyusedtogenerateelectricityaroundtheworld(GrubbandMeyer,1993;NationalRenewableEnergyLaboratory,2008;Luetal.
,2009;Moemkenetal.
,2018).
Windturbineshaveusuallybeenbuiltonmountaintopsorincoastalareaswithstrongwind.
Theturbinerotorisinstalledataheightabovethetowerbottom(usuallythegroundsurface)rangingfrom70to110m,whichiscalledtheturbineheightinthisstudy.
Theturbine-heightwindspeedisacriticalvariableaffectingtheamountofwind-generatedelectricitythatcanbeproduced.
Whentheturbine-heightwindspeedisbetween3and15ms1,windelectricitygenerationstarts,andthecorrespondingelectricpowerproductionisapproxi-matelyacubicfunctionofwindspeed(JaramilloandBorja,2004;Yangetal.
,2017).
Thisimpliesthatwind-power(i.
e.
,wind-generatedelec-tricpower)estimationaccuracyreliesmainlyontheaccuracyoftur-bine-heightwind-speedforecasting.
Additionally,whenthewindspeedis>15ms1,andespeciallyhigherthan20–25ms1,theturbinecomponentswillbedamagedduetoexcessivepowerinputs,whichdisturbthestableoperationofthewind-poweredelectricalgenerationsystemandcausehugeeconomiclosses.
Thebestsolutionistoshutdowntheturbinesbeforestrongwindsarrive.
Therefore,theforecastingaccuracyofturbine-heightwindspeedisbecomingveryimportantfortheaccurateevaluationofwindpowerandthesafeoperationofwind-https://doi.
org/10.
1016/j.
atmosres.
2019.
04.
011Received10December2018;Receivedinrevisedform8April2019;Accepted9April2019Correspondingauthorat:BeijingNormalUniversity,NO.
19,XinjiekouwaiStreet,HaidianDistrict,Beijing,China.
E-mailaddress:qyduan@bnu.
edu.
cn(Q.
Duan).
AtmosphericResearch226(2019)1–16Availableonline11April20190169-8095/2019PublishedbyElsevierB.
V.
Tpoweredelectricalgenerationsystemsinwindfarms.
Wind-speedforecastingmethodsincludestatisticalestimationmethodsandphysicalmodel-basedsimulationmethods.
Commonsta-tisticalestimationmethodsincludepredictivetime-seriesmodelsbuiltusingKalmanfilters(Bossanyi,1985)orautoregressivemovingaveragefunctions(Sfetsos,2002)andcorrelationmodelsbuiltusingartificialneuralnetworks(Mohandesetal.
,1998)orfuzzylogic(Pinsonetal.
,2003).
Thepredictiveaccuracyofthesestatisticalmodelsdependsstronglyonthereliabilityofpastdataobservationsandthenumberofobserveddatapoints.
Inaddition,statisticalmodelstendtohaveashortpredictionleadtime,usuallysixtoeighthours.
Unlikestatisticalmodels,physicalmodel-basedmesoscalenumericalweatherprediction(NWP)modelshavesignificantadvantagesforoperationalforecastingofturbine-heightwindspeed.
AnNWPmodelnotonlyislessdependentonobserveddataandthereforecancompensatefordatadeficiencies,especiallyincomplexterrain,butalsohasalongerforecastperiod,with72-hpredictionaccuracy>80%.
Inrecentdecades,mesoscaleNWPmodelshavebeenwidelyusedtoprovidehigh-resolutionwind-speedforecasts.
Forinstance,Lazietal.
(2010)assessedtheperformanceoftheEtamodelonthewindforecastsfortheNasuddenpowerplantsatGotlandIsland,Sweden.
Dvoraketal.
(2010)usedtheNationalCenterforAtmosphericResearchMesoscaleModelversion5(MM5)modeltosimulatemulti-yearhigh-resolutionwindspeedat80mtoassessthewindenergyresourceinoffshoreCalifornia.
TheWeatherResearchandForecasting(WRF)model(Skamarocketal.
,2008)isanew-generationmesoscaleNWPmodeldevelopedonthebasisoftheMM5model.
Ithasamodularstructurethatfacilitatesintegrationofvariousphysicalprocessmodules,andeachphysicalmodulehasbeendevelopedbyadifferentgroup(Dudhia,2014).
Re-cently,moreandmorestudieshaveevaluatedturbine-heightwindspeedusingtheWRFmodel.
Deppeetal.
(2013)evaluatedthesimu-lationabilityoftheWRFmodelon80mturbine-heightwindspeedatthePomeroy,IowawindfarmsiteinUnitedStates.
Hahmannetal.
(2015)foundthatthebiasesinmeanannualwindspeedbetweenWRFsimulationsandobservationsatheightsaround100mwerefarsmallerthanthoseobtainedbyusingwindsdirectlyfromthereanalysisatoffshoresitesovertheNorthandBalticSeas.
However,smallbiasesinsimulatedwindspeedhaveasignificanteffectonwind-powerpredic-tionaccuracybecauseofthecubicrelationshipbetweenwindpowerandturbine-heightwindspeed.
Moreover,theWRFsimulationhassignificanterrorsofitsownduetoitsimperfectdescriptionsofsub-gridphysicalprocessesandtopography.
Improvingthesimulationaccuracyofturbine-heightwindspeedintheWRFmodelisthereforeofcriticalimportance.
Asinothernumericalmodels,therearethreemainsourcesofun-certaintyintheWRFmodel:thespecificationofinitialandboundaryfields,therealismofthemodelphysicsrepresentation,andthespeci-ficationofmodelparameters(Dietal.
,2015).
Toreduceinitialandboundaryerrors,three-andfour-dimensionalvariationdataassimila-tion(3DVAR/4DVAR)methodsareusedtoimprovethespecificationofinitialandboundaryfieldsfortheWRFmodelbyingestingdiscreteobservationaldatafromdiversesources.
Wangetal.
(2013)improvedthesurface-layerwindforecastingaccuracyoftheWRFmodelinawind-powerfarmusingthe3DVARmethod.
Fanetal.
(2013)assimi-latedquickscatterometerocean-surfacewinddataintoaWRFmodelusingthe3DVARmethodtoobtainahigh-qualitysimulationofthesurfacewindfieldintheChukchi/BeaufortSearegion.
ToreduceerrorsinWRFphysicalrepresentations,manystudieshaveanalyzedtherepresentativenessofvariousphysicalpara-meterizationschemesforthesimulationofthephysicalprocessesre-latedtowind.
Fernández-Gonzálezetal.
(2019)analyzedtheWRFuncertaintyassociatedwiththemultiphysicsandthemultipleinitialandboundaryconditionfortheshort-termwindspeedprediction,andfoundthatthephysicalparameterizationuncertaintywasgreaterforshort-termwindforecasts.
SomestudiesbuiltWRFensemblefore-castingsystemstoimprovethewindspeedanddirectionforecastsusingseveralsetsofparameterizationschemecombinations(Traiteuretal.
,2012;Fernández-Gonzálezetal.
,2018;Panetal.
,2018).
Notedthattheensembleforecastingaccuracywouldbefurtherimprovedusingamoreadvancedpost-processingtechnique(Holmanetal.
,2018);someotherstudiesfocusedonthesensitivityofthedifferentboundarylayerschemestowindforecaststoquantifytheirsuitableboundarylayerschemes(Hariprasadetal.
,2014;Avolioetal.
,2017;Tymviosetal.
,2018;Xiangetal.
,2019).
However,verylittleresearchhasbeendoneonparameteroptimi-zationtoimproveturbine-heightwind-speedforecastingintheWRFmodel.
Thekeychallengeincludestwoaspects:(1)theWRFmodelhasmanytunableparameters,whichmakesparameteroptimizationdiffi-cultifallparametersareadjusted;and(2)aWRFrunisveryexpensive,whichmakesitdifficulttofindtheoptimalparametervaluesfortra-ditionaloptimizationmethodsbecauseofrelativelylowsearcheffi-ciency.
Therefore,ahighlyefficientoptimizationmethodshouldbeusedtoconductparameteroptimizationofacomplexWRFmodel.
ToperformparameteroptimizationforthecomplexdynamicmodelssuchasWRF,twostepsarerecommended(Dietal.
,2015).
Thefirstistoconductparameterscreeningusingasensitivityanalysis(SA)methodtochoosethesensitiveparameterstobeoptimized.
NotallparametersaresensitivetotheWRFoutputs(e.
g.
,theturbine-heightwindspeed),andiftheinsensitiveparametersarecalibrated,notonlyistheWRFsimu-lationaccuracynotsignificantlyimproved,butalsothehugecompu-tationresourcesarewasted.
ManystudieshaveevaluatedparametersensitivityforcomplexweatherandclimatemodelsusingqualitativeandquantitativeSAmethods(Qianetal.
,2015;Dietal.
,2017).
TheseresultshavedemonstratedthattheMultivariateAdaptiveRegressionSpline(MARS)methodisaveryeffectiveandefficientqualitativeSAmethodtoidentifythesensitiveparameters.
Oncethesensitiveparametershavebeendetermined,thenextstepinvolvesconductinganoptimizationoftheseparameters.
However,theefficiencyoftraditionaloptimizationmethodsisstilllowevenforop-timizingthesensitiveparametersasasmallproportionofalltunableparameters.
Therefore,amorehighlyeffectiveandefficientoptimiza-tionmethodshouldbeused.
Wangetal.
(2014)proposedanadaptivesurrogatemodeling-basedoptimization(ASMO)methodbycombiningthemoresuitableGaussianProcessesregressionmethodandtheshuf-fledcomplexevolution(SCE-UA)globaloptimizationalgorithm.
Duanetal.
(2017)firstconductedhighlyefficientparameteroptimizationfortheWRFmodeltoimprovetheaccuracyofsummerprecipitationsi-mulationintheGreaterBeijingareausingtheASMOmethoddevelopedbyWangetal.
(2014).
Finally,theaccuracyofprecipitationsimulationwasimprovedbyapproximately18%usingonly127modelruns.
Morerecently,theASMOmethodhasbeenappliedtoparameteroptimizationofcomplexlandandweathermodels(Gongetal.
,2015;Dietal.
,2018).
However,theASMOmethodhasnotyetbeenappliedtoparameteroptimizationfortheWRFmodeltoimprovethesimulationaccuracyofturbine-heightwindspeed.
Thepresentworkintendstoimplementahighlyeffectiveandeffi-cientparameteroptimizationstrategyincludingMARS-basedparameterSAandASMO-basedsensitivityparameteroptimizationfortheWRFmodeltoimproveturbine-heightwind-speedsimulation.
Thereason-ablenessandapplicabilityoftheoptimalparametersobtainedbytheASMOmethodwillthenbeassessed.
Thispaperisorganizedasfollows.
Section2presentsthemetho-dology,includingtheMARSSAmethodandtheASMOoptimizationprocedure.
Section3describestheexperimentdesign,includingthesimulationdesign,thetunableparameters,andthestatisticalmetrics.
Section4firstpresentstheresultsofthesensitiveparametersinbriefandthenpresentsanalysesoftheoptimizationresults,includingtheoptimizationefficiencyandaccuracyimprovementforwind-speedandwind-powersimulations.
Comparisonsofvalidationeventsimulationsandphysicalinterpretationsofwhytheoptimalparametersleadtoimprovedwind-speedforecastsarealsodescribedinthissectiontoprovidefurtherproofofthereasonablenessandapplicabilityoftheZ.
Di,etal.
AtmosphericResearch226(2019)1–162optimalparametersobtained.
Conclusionsarepresentedinthelastsection.
2.
MaterialsandmethodsAnintegratedparameteroptimizationprocedureforcomplexdy-namicmodelssuchasWRFshouldconsistoftwosteps.
First,parameterSAshouldbeconductedforalltunableparametersusinganSAmethodtoscreenasmallnumberofsensitiveparameters.
Second,thescreenedsensitiveparametersshouldbeoptimizedusingahighlyeffectiveandefficientparameteroptimizationmethodinsteadofmoretraditionaloptimizationmethods.
2.
1.
Goodlatticepoint(GLP)samplingmethodUniformityisoneoftheimportantindicesforsamplingmethodsbecauseuniformsampleshelptoobtainmoreaccurateparametricSAandoptimizationresults.
Theuniformitiesofthreecategoriesofquasi-Monte-Carlomethods,includingtheGLPmethod,theHaltonsequence,andtheSobol'sequence,havebeencomparedbyGongetal.
(2016),whodemonstratedthattheGLPmethodhashigheruniformitythantheothertwomethodswiththesamesamplesize.
Therefore,GLPsamplingmethodsarerecommendedtogenerateuniformsamplesforfurtherSAandASMOmethods.
TheGLPmethodwasfirstproposedbyKorobov(1959a),anditsdesigncanbebrieflydescribedasfollows.
Let(n;h1,…,hs)beavectorofintegerssatisfying1≤hi1,whichleadstoaparametervaluewithnophysicalsignificance.
Therefore,therangeofradiation_2issetto0.
5–1.
0.
Theradiation_3parameterisascalingfactorrelatedtothediffusivityangleofcloudopticaldepth,anditsrangeissetto0.
9–1.
08basedonthelimitsontherangeofdiffusivityangleintheprogramcode.
TheparameterrangesaredeterminedbasedonacomprehensiveanalysisofparameterperturbationsandarethereforethoughttobesuitableforperformingSAunderallwindconditions.
Moreover,thesixteencalibrationeventsareselectedfromfourseasonsofoneyear,whichalsodemonstratesthattheparameterrangesaresuitabletodifferentseasons.
Fig.
2.
Theeightwindprocesses,includingvariationsinwindspeedanddirection.
Z.
Di,etal.
AtmosphericResearch226(2019)1–1653.
3.
StatisticalmetricsThestatisticalmetricsusedtoevaluatewind-speedsimulationsaretherootmeansquareerror(RMSE),thecorrelationcoefficient(R),andtheWeibullprobabilitydensityfunction.
Anotherstatisticalmetricusedtoevaluateaveragewindpoweriswindpowerdensity(WPD).
RMSEcanbeexpressedasfollows:(3)wheresimitandobsitrepresentthesimulatedandobservedturbine-heightwindspeedattheithobservationstationattimet,andMandTarethetotalnumbersofobservationstationsandtimesteps.
Toprovideabetteroptimizationresultformulti-eventcases,thenormalizedRMSE(NRMSE)isusuallyusedasthecostfunction;itsformulacanbeexpressedasfollows:(4)whereRMSEpirepresentstheRMSEvalueofthesimulationwiththeperturbedparametervaluefortheitheventandRMSEdefirepresentstheRMSEvalueofthesimulationwiththedefaultparametervalueforithevent.
Nisthenumberofsimulationevents.
WhenNRMSEis6.
5ms1,andthemaximumimprovementoccursinthesi-mulationofthestrongestwindspeed.
Forwindspeeds6.
5ms1.
Inaddition,ithasbeendemonstratedthatWRFmodelsimulationscanbettercapturethedailyvariationcharacteristicsofturbine-heightwindspeed.
ByconvertingUniversalTimeCoordinates(UTC)intolocaltime(i.
e.
,Beijingtime),itisfoundthatthewindspeedislowerinthedaytimeandhigheratnight.
Morespecifically,thelowestwindspeedoccursat~14:00localtime(correspondingto6:00,30:00,and54:00inUTC,asshowninFig.
6a),whereasthewindspeedatlocalnighttime(correspondingto12:00–24:00,36:00–48:00,and60:00–72:00inUTC,asshowninFig.
6a)isrelativelystrongandsteady.
Overall,therea-sonablesimulationresultsprovethesuitabilityoftheWRFmodeltosimulateturbine-heightwindspeed,andthesignificantimprovementofFig.
5.
Comparisonofwind-speedsimulationerrorsforsixteenevents(1)–(16)usingtheWRFmodelwithdefaultandoptimalparameters.
Fig.
6.
Comparisonsoftimevariationsinobservedandsimulatedturbine-heightwindspeedusingtheWRFmodelwithdefaultandoptimalparametersfor:(a)72-hleadtimes(b)fourseasons.
Z.
Di,etal.
AtmosphericResearch226(2019)1–168thehourlysimulationsdemonstratestheeffectivenessoftheASMOparameteroptimizationmethod.
Becausethe16optimizationevents[(1)–(16)]arechosenfromthefourseasonsofoneyear(i.
e.
,fromJune2014toMay2015),thecomparisonsofoptimizedanddefaultsimulationsareconductedforthefourseasons.
Specifically,events(1)–(4),(5)–(8),(9)–(12),and(13)–(16)belongedtosummer,fall,winter,andspringrespectively.
Fig.
6bshowsthecomparisonresultsforobservedandsimulatedtur-bine-heightwindspeedwithdefaultandoptimalparametersforthefourseasons.
Comparedtoobservations,thesimulationswithbothdefaultandoptimalparametershavetheconsistentvariancechar-acteristicthatturbine-heightwindspeedishighestinspringandlowestinsummer.
Itisalsoapparentthattheoptimalparametersgreatlyim-provetheturbine-heightwind-speedsimulationsforthefourseasonscomparedtothedefaultparameters.
Theimprovementratesinspringandfallwithstrongwindareobviouslyhigherthanthoseinsummerandwinterwithlightwind,whichconfirmsoncemorethattheASMOmethodachievessignificantimprovementforthesimulationofstrongwind(seeFig.
6a).
Fig.
7showstheWeibullPDFsofobservedandsimulatedturbine-heightwindspeed.
WhencomparingthemedianvaluesoftheWeibullPDFs,itisfoundthattheWRFsimulationswithdefaultparametersoverestimatewindspeedscomparedtotheobserveddataandthatthesimulatedvaluesofaveragewindspeedareclosertoobservationswhenASMOparameteroptimizationisused.
Similarly,thefrequencyofthesimulatedmedianwindspeedisalsobroughtclosertoobservationsbyparameteroptimization.
ComparingthewholesetofWeibullPDFsfortheobservationsandthesimulationwithdefaultparameters,itisde-monstratedthatthesimulationwithdefaultparametersstronglyover-estimatesthefrequencyofstrongwindswithspeeds>7ms1andunderestimatethefrequencyoflightwindswithspeeds500Wm2.
Forthenorthernprovinces,theaverageWPDrangesfrom200to300Wm2.
Forthesouthernpro-vinces,theaverageWPDrangesfrom100to200Wm2.
Fig.
11alsoshowsthepositionsoftheobservationstationsmarkedwithredaster-isks.
FromthepositionsoftheobservationstationsandtheWPDspatialdistribution,itisclearthatmostoftheobservationstationsarebuiltintheregionswithhighwindenergy,butafewarebuiltinregionswithlowwindenergy(seethebottomrightcornerinFig.
11).
Therefore,fromtheviewpointofwind-energysimulation,itcanbeconcludedthatthelocationsofsomealready-builtobservationstationsareinappropriate.
4.
5.
ValidationanalysisofWRFoptimalparametersComparedwiththedefaultparameters,thesuperiorityoftheop-timalparametersobtainedbytheASMOmethodforimprovingWRFturbine-heightwind-speedsimulationhasbeendemonstratedintheoptimizationperiod.
However,forthevalidationperiodwhennewFig.
10.
ComparisonofsimulatedandobservedWPDvaluesoverthefourseasons.
Fig.
11.
SpatialdistributionofsimulatedWPDwiththeoptimalwindspeed.
Theredasterisksrepresentthepositionsoftheobservationstations.
(Forin-terpretationofthereferencestocolourinthisfigurelegend,thereaderisre-ferredtothewebversionofthisarticle.
)Z.
Di,etal.
AtmosphericResearch226(2019)1–1611eventsmustbesimulated,thequestionwhethertheoptimalparametersarestilleffectivedeservestobeinvestigated.
SixnewvalidationeventsareselectedfromJune2014toMay2015,asshowninTable2.
Thedesignsofthedomainandsimulation,thevariationcharacteristicsofwindspeedanddirection,thesimulationduration,andtheforcingdatasourcearethesameasintheparameteroptimizationexperiment.
Fig.
12acomparestheRMSEofsimulatedhourlyturbine-heightwindspeedusingtheWRFmodelwithdefaultandoptimalparametersforthesixvalidationevents.
Overall,comparedwiththeWRFsimula-tionswithdefaultparameters,theaverageimprovementpercentageofRMSEintheWRFwind-speedsimulationsis7.
58%usingWRFsimu-lationswithoptimalparameters.
Moreover,allvalidationeventsimu-lationsareimprovedusingtheWRFsimulationswithoptimalpara-meters,andthewind-speedsimulationsareimprovedbypercentagesvaryingfrom2.
63%to12.
29%.
Fig.
12bshowsacomparisonofRforthesimulatedhourlyturbine-heightwindspeedusingtheWRFmodelwithdefaultandoptimalparameters.
Overall,theaverageimprovementpercentageofRintheWRFwind-speedsimulationswithoptimalparametersis6.
49%,demonstratingthattheoptimalparameterscanalsoimprovethecorrelationofWRFturbine-heightwind-speedsimu-lationsinthevalidationevents.
Notethatoneofthesixsingle-objectivesimulationsexperiencesnegativeimprovement,whichmayberelatedtotheparametervaluesobtainedbyoptimizingRMSE.
Notethattheobservedwindevolutionforthecalibrationandva-lidationperiodsfollowstwopatternvariations:oneisthatwhenthewindspeedincreases(lighttostrong),thewinddirectionexperiencesasouth-to-northvariation,andtheotheristhatwhenthewindspeeddecreases(strongtolight),thewinddirectionexperiencesanorth-to-southvariation.
However,itisunknownwhethertheoptimalpara-metersstillworkwhenotherwindpatternsaresimulated.
Inthissec-tion,twooppositewindpatternsareselectedforsimulationtovalidatefurtherthesuperiorityoftheoptimalparameters.
Eachpatternincludesthree3-daywindevents.
Fig.
13a–cshowsthefirstpattern,inwhichwhenwindspeeddecreases(strongtolight),thewinddirectionvar-iationisapproximatelysouth-to-north;Fig.
13d–fshowsthesecondpattern,inwhichwhenwindspeedincreases(lighttostrong),thewinddirectionvariationisapproximatelynorth-to-south.
Fig.
13a–fillus-tratesthenewevents(A)-(F),respectively.
Thetwocategoriesofsimulationsareseparatelycomparedtoex-aminewhethertheoptimalparametersworkforsimulationsofotherwindpatterns.
Fig.
14showsthecomparisonresults.
Itisapparentthattheoptimalparametersimprovethesimulationsofallsixwindeventscomparedwiththedefaultparameters.
Overall,usingWRFsimulationswithoptimalparameters,theaverageimprovementpercentagesinRMSEinhourlyturbine-heightwind-speedsimulationforthetwonewlysimulatedwindpatternsare6.
68%and4.
66%,respectively.
Thisdemonstratesthattheoptimalparametersarereasonableforsimulatingdifferentwindpatterns,andthemethodisthereforeeffectiveinim-provingWRFturbine-heightwind-speedsimulation.
Overall,theoptimalparametersobtainedbyoptimizingtheRMSEofturbine-heightwind-speedsimulationsusingtheASMOmethodnotonlyimprovetheRofwind-speedsimulationsintheoptimizationperiod,butalsoimprovetheRMSEandRofwind-speedsimulationsinthevalidationperiod.
Inaddition,theoptimalparameterscanbeusedtosimulateotherwindpatterns.
Theseanalysesdemonstratecompre-hensivelythattheoptimalparameterscanbeusedtoimproveturbine-heightwind-speedsimulationsinthestudyarea.
Therefore,theoptimalparametervaluesarethoughttobereasonableandeffective.
4.
6.
PhysicalinterpretationandverificationoftheoptimalparametervaluesThevaluesofthedefaultandoptimalparametersarenormalizedwithintheirrangestoprovideaclearerillustrateofthevariationsbe-tweenthem.
Fig.
15showsacomparisonofthenormalizedoptimalanddefaultparametervalues.
AlltheoptimalparametervaluesshowTable2ThesixvalidationeventsfromJune2014toMay2015.
EventsDurationI2014/09/26–2014/09/28II2014/09/29–2014/10/01III2014/12/28–2014/12/30IV2014/12/31–2015/01/02V2015/03/14–2015/03/16VI2015/03/17–2015/03/19Fig.
12.
Comparisonsofsimulationerrorsofhourlyturbine-heightwindspeedusingWRFmodelwithdefaultandoptimalparametersfor:(a)RMSE(b)R.
Z.
Di,etal.
AtmosphericResearch226(2019)1–1612Fig.
13.
Twodifferentwindpatterns.
(a)-(c)isthefirstcategory,inwhichthewindspeedgraduallydecreasesandthewinddirectionexperiencesanapproximatelysouth-to-northvariation;(d)-(f)isthesecondcategory,inwhichthewindspeedgraduallyincreasesandthewinddirectionexperiencesanapproximatelynorth-southvariation.
Fig.
14.
Comparisonsofsimulationerrorsinhourlyturbine-heightwindspeedusingtheWRFmodelwithdefaultandoptimalparametersfor:(a)thewindpatternwithwindspeeddecreasingandwinddirectionchangingsouth-to-north(b)thewindpatternwithwindspeedincreasingandwinddirectionchangingnorth-to-south.
Z.
Di,etal.
AtmosphericResearch226(2019)1–1613inconsistentvariations.
Forthekarman(thevonKármánconstant)andradiation_2(scalingrelatedtoaerosolsinglescattering)parameters,theirvaluesarebasicallyunchangedandremainedthesameasthedefaultparametervalues.
Forthesurface_1(scalingrelatedtosurfaceroughness)parameter,thevaluevariesfromtheminimumforthede-faultparametertothemaximumfortheoptimalparameterinitsrange.
Fortheotherfourparameters,theiroptimalvaluesarelowerthantheirdefaultvalues.
Ithasbeenfoundfrompreviousanalyses(e.
g.
,Fig.
6)thatthede-faultsimulationparametersgenerallyoverestimatewind-speedvaluescomparedwithobservationsandthattheoptimalsimulationpara-metersreducethisoverestimation.
Thespecificphysicalinterpretationoftheparametervariationisthefollowing.
Largervaluesofsurface_1meanagreaterroughnesslengthtobedefinedinthesurfacelayer,whichelevatesthezero-planedisplacementheightandthereforere-duceswindspeedatturbineheight.
Largervaluesofkarmanenhancethemagnitudeoftheturbulentlengthscaleintheplanetaryboundarylayer,leadingtostrongerverticalmixingduringdaytime.
However,largervaluesofkarmanalsoleadtoincreasesintheexchangecoeffi-cientformomentumnearsurface,causingareductionofwindspeed.
Smallervaluesofconvection_2(scalingrelatedtoentrainmentflow)leadtolowerratiosofentrainmenttoupdraftflux,whichenhancestheupdraft,leadingtodecreasesinhorizontalwindspeeds.
Themicro-phys_2parameter(scalingrelatedtoicefall)directlyaffectsthecon-versionratefromcloudicetorainwaterinthedescriptionofthemi-crophysicsparameterizationscheme.
Therefore,smallervaluesofmicrophys_2eventuallybringsaboutreductionsinprecipitation,leadingtodecreasesinevapotranspirationorturbulenceandreductionsinturbine-heightwindspeed.
Largervaluesofradiation_2leadtomorescatteringofsolarradiationreflectedtothesky,whichreducestheamountofshortwaveradiationreachingthesurface,furthersuppres-singevaporationandultimatelyleadingtodecreasesinwindspeeds.
Smallvaluesofland_2(scalingrelatedtosoilporosity)leadtolowersoilporosity,whichsuppressestheconveyanceofsoilwaterandheatup-wardfromgroundwatertothesurfaceandthusdecreasesthedifferencebetweensurfaceenergiesatdifferentlocations,blockingthedevelop-mentofwindspeed.
Theplanetary_3parameter(profileshapeexponentofthemomentumdiffusivity)hasapositiveeffectonthemomentumdiffusivitycoefficient.
Whenplanetary_3decreases,theeddyturbulencediffusivityintensityisweakened,inducinglowerwindspeedatturbineheight.
5.
ConclusionsThisstudyfirstusestheglobalSAmethodtoidentifythesevensensitiveparametersfrom27tunableparametersinsevenWRFphysicalparameterizationschemesandthenoptimizesthesevensensitivityparametersfromthesixWRFphysicalparameterizationschemesusingtheASMOmethodtoimproveturbine-heightwind-speedsimulationoverEasternChina.
TheWRFmodelsimulationswithdefaultandop-timalparametersarecomparedfromfiveaspects,includingthevaria-tionofturbine-heightwindspeedovera72-hleadtimeandthefourseasons,theWeibullfrequencydistributionofwindspeed,wind-speedandtemperatureprofilesfrom1000to100hPa,thecorrelationofsi-mulatedwindspeed,andthespatialandtemporaldistributionofWPDinthestudyarea.
Inaddition,theapplicabilityoftheoptimalpara-metersobtainedbytheASMOmethodisexaminedinnewsimulationsofthesixvalidationeventstoshowtheirsuperioritiestothedefaultparametersforimprovingturbine-heightwind-speedsimulation.
TheoptimizationresultsdemonstratethatparameteroptimizationforthecomplexWRFmodel,whichhasverytime-consumingcalcula-tionrequirements,canbeconductedusingtheASMOmethod.
Inpar-ticular,theoptimalvaluesofthesevenparametersinthisstudyareobtainedusing131samples,including100initialand31adaptivesamplesobtainedusingtheASMOmethod.
Thisapproachgreatlyre-ducesthenumberofWRFmodelrunsanddemonstratesthattheASMOmethodisahighlyeffectiveandefficientoptimizationmethodandiswellsuitedtooptimizetheparametersofothercomplexweatherandclimatemodels.
BycomparingtheWRFmodelsimulationswithdefaultandoptimalparameters,itisfoundthatthehourlyturbine-heightwind-speedsi-mulationisimprovedby8.
7%usingASMOoptimization.
Variationanalysesofwind-speedtimeseriesshowthattheWRFsimulationwithdefaultparametersoverestimateswindspeed,whereastheWRFsimu-lationwithoptimizedparametersgreatlyreducestheoverestimationtrend.
BycomparingthesimulatedWeibullfrequencydistributions,ithasbeenfoundthattheWRFmodelwithoptimalparametersreducesthefrequencyofsimulatedstrongwindsandincreasesthefrequencyofsimulatedlightwinds,bringingtheoptimizationresultsclosertoob-servations.
Besidesimprovingturbine-heightwind-speedsimulation,theWRFmodelwithoptimalparametersalsoimprovesthesimulationofwindandtemperatureprofilesfrom1000to100hPa.
Similarly,italsoimprovestheRofturbine-heightwind-speedsimulationbyap-proximately4%inadditiontoimprovingRMSEby8.
7%asthecostfunction.
BasedontheWPDformula,ithasbeendemonstratedthattheWRFmodelwithoptimalparametersimprovesWPDestimationby36%.
ByexaminingthespatialdistributionofWPDsimulationswithoptimalwindspeeds,ithasalsobeenfoundthatthelocationsofafewobservationstationsbuiltinregionswithlowwindenergyarein-appropriate,althoughmostofthestationsarebuiltinhigh-wind-energyFig.
15.
Comparisonofthenormalizedoptimalanddefaultparametervalues.
Z.
Di,etal.
AtmosphericResearch226(2019)1–1614regions.
Finally,theapplicabilityoftheoptimalparametersisalsodemonstratedbycomparingturbine-heightwind-speedsimulationsfortwocategoriesofnewvalidationevents:oneisthesamepatternasthecalibrationevents,whereastheotherrepresentsanoppositepattern.
TheresultsshowthattheWRFmodelwithoptimalparametersim-provestheRMSEandRofwindspeedsimulationsforthesamepatternofsixvalidationeventsby7.
58%and6.
49%respectively.
Forthetwodifferentpatterns,theaverageRMSEimprovementpercentagesofwind-speedsimulationsforthethreevaliationeventsare6.
68%and4.
66%,respectively.
Thisfullydemonstratesthereasonablenessoftheoptimalparameters.
However,itshouldbenotedthatgenerallythewind-speedsimula-tionsareimprovedbytheWRFmodelwithoptimalparameters,butthatseveralsinglesimulationsshownegativeimprovements.
Thesephenomenaarecausedbythedefinitionofthesingle-objectivecostfunction,whichallocatesequalweighttoeachsinglesimulationandthenaveragesallthesimulationerrors.
Ifthesuitableweightsareusedtoconstructthemulti-objectivecostfunction,itwillbepossibletoimproveallthesinglesimulationsusingmulti-objectiveoptimizationmethodssuchasNSGA-II(Debetal.
,2002)andASMO-PODE(GongandDuan,2017).
Inaddition,thesameapproachcanbemigratedtoothermulti-variablejointoptimizationproblemssuchaswindspeed,tem-perature,andpressure.
AcknowledgementsThisresearchwassupportedbytheMinistryofScienceandTechnologyofChina(No.
IUMKY201603),theStrategicPriorityResearchProgramoftheChineseAcademyofSciences(Nos.
XDA19070104,XDA20060401),theIntergovernmentalKeyInternationalS&TInnovationCooperationProgram(No.
2016YFE0102400),theSpecialFundforMeteorologicalScientificResearchinthePublicInterest(No.
GYHY201506002,CRA–40:40-yearCMAglobalatmosphericreanalysis),theNationalBasicResearchProgramofChina(No.
2015CB953703),andtheNaturalScienceFoundationofChina(41305052).
WeacknowledgeNationalCenterforEnvironmentalPredictionReanalysisdataset(http://rda.
ucar.
edu/datasets/ds083.
2/)andsoundingdataset(http://weather.
uwyo.
edu/upperair/sounding.
html).
Thehourlyturbine-heightwind-speedda-tasetareavailuponrequestfromtheauthorDr.
Ao.
AppendixA.
SupplementarydataSupplementarydatatothisarticlecanbefoundonlineathttps://doi.
org/10.
1016/j.
atmosres.
2019.
04.
011.
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com/locate/atmosresImprovingWRFmodelturbine-heightwind-speedforecastingusingasurrogate-basedautomaticoptimizationmethodZhenhuaDia,JuanAob,QingyunDuana,,JinWangb,WeiGonga,ChenweiShena,YanjunGanc,ZhaoLiubaStateKeyLaboratoryofEarthSurfaceProcessesandResourceEcology,FacultyofGeographicalScience,BeijingNormalUniversity,Beijing100875,ChinabBeijingGoldwindScience&CreationWindpowerEquipmentCo.
,Ltd.
,Beijing100176,ChinacStateKeyLaboratoryofSevereWeather,ChineseAcademyofMeteorologicalSciences,Beijing100081,ChinaARTICLEINFOKeywords:WRFParameteroptimizationSurrogatemodeling-basedoptimizationTurbine-heightwind-speedforecastingABSTRACTImprovingturbine-heightwind-speedforecastingusingamesoscalenumericalweatherprediction(NWP)modelisimportantforwind-powerpredictionbecauseofthecubiccorrelationbetweenwindpowerandwindspeed.
Thisstudyinvestigateshowasurrogate-basedautomaticoptimizationmethodcanbeusedtoimprovewind-speedforecastingbyanNWPmodelbyoptimizingitsparameters.
AkeychallengeinoptimizingNWPmodelparametersisthetremendouscomputationalrequirementsofsuchanexercise.
AglobalsensitivitymethodknownastheMultivariateAdaptiveRegressionSpline(MARS)methodwasfirstusedtoidentifythemostsensitiveparametersamongalltunableparameterschosenfromsevenphysicalparameterizationschemesoftheWeatherResearchandForecast(WRF)model.
Then,ahighlyeffectiveandefficientoptimizationmethodknownasadaptivesurrogatemodeling-basedoptimization(ASMO)wasusedtotunethesensitiveparameters.
InacasestudycarriedoutoverEasternChina,thesevenparametersthatweremostsensitivetowind-speedsimulationwereidentifiedfromamong27tunableparameters.
ThosesevenparameterswereoptimizedusingtheASMOmethod.
Thepresentstudyindicatesthatthehourlywind-speedsimulationaccuracywasimprovedby8.
7%duringthecalibrationphaseandby7.
58%duringthevalidationphase.
Inaddition,clearphysicalinterpreta-tionswereprovidedtoexplainwhytheoptimalparametersleadtoimprovedwindspeedforecasts.
Overall,thisstudyhasdemonstratedthatautomaticoptimizationmethodisahighlyeffectiveandefficientwaytoimprovewind-speedforecastingbyanNWPmodel.
1.
IntroductionWiththerapidgrowthoftheglobaleconomy,consumptionoftra-ditionalfossilfuelssuchascoalandoilhassoared,leadingtoanenergysourcedepletioncrisis.
Theresultingenvironmentalproblemssuchasairandwaterpollutionarebecomingcritical(Boffey,1970).
Develop-mentofrenewableenergyresourcesisthoughttobethemostpromisingresponsebecausetheseresourcesarebasicallyinexhaustible,offerhugecapacity,andareclean,withverylittlepollution.
Duetoitswidedis-tribution,windenergy,asthemajorrenewableenergyresourceavail-able,hasbeenwidelyusedtogenerateelectricityaroundtheworld(GrubbandMeyer,1993;NationalRenewableEnergyLaboratory,2008;Luetal.
,2009;Moemkenetal.
,2018).
Windturbineshaveusuallybeenbuiltonmountaintopsorincoastalareaswithstrongwind.
Theturbinerotorisinstalledataheightabovethetowerbottom(usuallythegroundsurface)rangingfrom70to110m,whichiscalledtheturbineheightinthisstudy.
Theturbine-heightwindspeedisacriticalvariableaffectingtheamountofwind-generatedelectricitythatcanbeproduced.
Whentheturbine-heightwindspeedisbetween3and15ms1,windelectricitygenerationstarts,andthecorrespondingelectricpowerproductionisapproxi-matelyacubicfunctionofwindspeed(JaramilloandBorja,2004;Yangetal.
,2017).
Thisimpliesthatwind-power(i.
e.
,wind-generatedelec-tricpower)estimationaccuracyreliesmainlyontheaccuracyoftur-bine-heightwind-speedforecasting.
Additionally,whenthewindspeedis>15ms1,andespeciallyhigherthan20–25ms1,theturbinecomponentswillbedamagedduetoexcessivepowerinputs,whichdisturbthestableoperationofthewind-poweredelectricalgenerationsystemandcausehugeeconomiclosses.
Thebestsolutionistoshutdowntheturbinesbeforestrongwindsarrive.
Therefore,theforecastingaccuracyofturbine-heightwindspeedisbecomingveryimportantfortheaccurateevaluationofwindpowerandthesafeoperationofwind-https://doi.
org/10.
1016/j.
atmosres.
2019.
04.
011Received10December2018;Receivedinrevisedform8April2019;Accepted9April2019Correspondingauthorat:BeijingNormalUniversity,NO.
19,XinjiekouwaiStreet,HaidianDistrict,Beijing,China.
E-mailaddress:qyduan@bnu.
edu.
cn(Q.
Duan).
AtmosphericResearch226(2019)1–16Availableonline11April20190169-8095/2019PublishedbyElsevierB.
V.
Tpoweredelectricalgenerationsystemsinwindfarms.
Wind-speedforecastingmethodsincludestatisticalestimationmethodsandphysicalmodel-basedsimulationmethods.
Commonsta-tisticalestimationmethodsincludepredictivetime-seriesmodelsbuiltusingKalmanfilters(Bossanyi,1985)orautoregressivemovingaveragefunctions(Sfetsos,2002)andcorrelationmodelsbuiltusingartificialneuralnetworks(Mohandesetal.
,1998)orfuzzylogic(Pinsonetal.
,2003).
Thepredictiveaccuracyofthesestatisticalmodelsdependsstronglyonthereliabilityofpastdataobservationsandthenumberofobserveddatapoints.
Inaddition,statisticalmodelstendtohaveashortpredictionleadtime,usuallysixtoeighthours.
Unlikestatisticalmodels,physicalmodel-basedmesoscalenumericalweatherprediction(NWP)modelshavesignificantadvantagesforoperationalforecastingofturbine-heightwindspeed.
AnNWPmodelnotonlyislessdependentonobserveddataandthereforecancompensatefordatadeficiencies,especiallyincomplexterrain,butalsohasalongerforecastperiod,with72-hpredictionaccuracy>80%.
Inrecentdecades,mesoscaleNWPmodelshavebeenwidelyusedtoprovidehigh-resolutionwind-speedforecasts.
Forinstance,Lazietal.
(2010)assessedtheperformanceoftheEtamodelonthewindforecastsfortheNasuddenpowerplantsatGotlandIsland,Sweden.
Dvoraketal.
(2010)usedtheNationalCenterforAtmosphericResearchMesoscaleModelversion5(MM5)modeltosimulatemulti-yearhigh-resolutionwindspeedat80mtoassessthewindenergyresourceinoffshoreCalifornia.
TheWeatherResearchandForecasting(WRF)model(Skamarocketal.
,2008)isanew-generationmesoscaleNWPmodeldevelopedonthebasisoftheMM5model.
Ithasamodularstructurethatfacilitatesintegrationofvariousphysicalprocessmodules,andeachphysicalmodulehasbeendevelopedbyadifferentgroup(Dudhia,2014).
Re-cently,moreandmorestudieshaveevaluatedturbine-heightwindspeedusingtheWRFmodel.
Deppeetal.
(2013)evaluatedthesimu-lationabilityoftheWRFmodelon80mturbine-heightwindspeedatthePomeroy,IowawindfarmsiteinUnitedStates.
Hahmannetal.
(2015)foundthatthebiasesinmeanannualwindspeedbetweenWRFsimulationsandobservationsatheightsaround100mwerefarsmallerthanthoseobtainedbyusingwindsdirectlyfromthereanalysisatoffshoresitesovertheNorthandBalticSeas.
However,smallbiasesinsimulatedwindspeedhaveasignificanteffectonwind-powerpredic-tionaccuracybecauseofthecubicrelationshipbetweenwindpowerandturbine-heightwindspeed.
Moreover,theWRFsimulationhassignificanterrorsofitsownduetoitsimperfectdescriptionsofsub-gridphysicalprocessesandtopography.
Improvingthesimulationaccuracyofturbine-heightwindspeedintheWRFmodelisthereforeofcriticalimportance.
Asinothernumericalmodels,therearethreemainsourcesofun-certaintyintheWRFmodel:thespecificationofinitialandboundaryfields,therealismofthemodelphysicsrepresentation,andthespeci-ficationofmodelparameters(Dietal.
,2015).
Toreduceinitialandboundaryerrors,three-andfour-dimensionalvariationdataassimila-tion(3DVAR/4DVAR)methodsareusedtoimprovethespecificationofinitialandboundaryfieldsfortheWRFmodelbyingestingdiscreteobservationaldatafromdiversesources.
Wangetal.
(2013)improvedthesurface-layerwindforecastingaccuracyoftheWRFmodelinawind-powerfarmusingthe3DVARmethod.
Fanetal.
(2013)assimi-latedquickscatterometerocean-surfacewinddataintoaWRFmodelusingthe3DVARmethodtoobtainahigh-qualitysimulationofthesurfacewindfieldintheChukchi/BeaufortSearegion.
ToreduceerrorsinWRFphysicalrepresentations,manystudieshaveanalyzedtherepresentativenessofvariousphysicalpara-meterizationschemesforthesimulationofthephysicalprocessesre-latedtowind.
Fernández-Gonzálezetal.
(2019)analyzedtheWRFuncertaintyassociatedwiththemultiphysicsandthemultipleinitialandboundaryconditionfortheshort-termwindspeedprediction,andfoundthatthephysicalparameterizationuncertaintywasgreaterforshort-termwindforecasts.
SomestudiesbuiltWRFensemblefore-castingsystemstoimprovethewindspeedanddirectionforecastsusingseveralsetsofparameterizationschemecombinations(Traiteuretal.
,2012;Fernández-Gonzálezetal.
,2018;Panetal.
,2018).
Notedthattheensembleforecastingaccuracywouldbefurtherimprovedusingamoreadvancedpost-processingtechnique(Holmanetal.
,2018);someotherstudiesfocusedonthesensitivityofthedifferentboundarylayerschemestowindforecaststoquantifytheirsuitableboundarylayerschemes(Hariprasadetal.
,2014;Avolioetal.
,2017;Tymviosetal.
,2018;Xiangetal.
,2019).
However,verylittleresearchhasbeendoneonparameteroptimi-zationtoimproveturbine-heightwind-speedforecastingintheWRFmodel.
Thekeychallengeincludestwoaspects:(1)theWRFmodelhasmanytunableparameters,whichmakesparameteroptimizationdiffi-cultifallparametersareadjusted;and(2)aWRFrunisveryexpensive,whichmakesitdifficulttofindtheoptimalparametervaluesfortra-ditionaloptimizationmethodsbecauseofrelativelylowsearcheffi-ciency.
Therefore,ahighlyefficientoptimizationmethodshouldbeusedtoconductparameteroptimizationofacomplexWRFmodel.
ToperformparameteroptimizationforthecomplexdynamicmodelssuchasWRF,twostepsarerecommended(Dietal.
,2015).
Thefirstistoconductparameterscreeningusingasensitivityanalysis(SA)methodtochoosethesensitiveparameterstobeoptimized.
NotallparametersaresensitivetotheWRFoutputs(e.
g.
,theturbine-heightwindspeed),andiftheinsensitiveparametersarecalibrated,notonlyistheWRFsimu-lationaccuracynotsignificantlyimproved,butalsothehugecompu-tationresourcesarewasted.
ManystudieshaveevaluatedparametersensitivityforcomplexweatherandclimatemodelsusingqualitativeandquantitativeSAmethods(Qianetal.
,2015;Dietal.
,2017).
TheseresultshavedemonstratedthattheMultivariateAdaptiveRegressionSpline(MARS)methodisaveryeffectiveandefficientqualitativeSAmethodtoidentifythesensitiveparameters.
Oncethesensitiveparametershavebeendetermined,thenextstepinvolvesconductinganoptimizationoftheseparameters.
However,theefficiencyoftraditionaloptimizationmethodsisstilllowevenforop-timizingthesensitiveparametersasasmallproportionofalltunableparameters.
Therefore,amorehighlyeffectiveandefficientoptimiza-tionmethodshouldbeused.
Wangetal.
(2014)proposedanadaptivesurrogatemodeling-basedoptimization(ASMO)methodbycombiningthemoresuitableGaussianProcessesregressionmethodandtheshuf-fledcomplexevolution(SCE-UA)globaloptimizationalgorithm.
Duanetal.
(2017)firstconductedhighlyefficientparameteroptimizationfortheWRFmodeltoimprovetheaccuracyofsummerprecipitationsi-mulationintheGreaterBeijingareausingtheASMOmethoddevelopedbyWangetal.
(2014).
Finally,theaccuracyofprecipitationsimulationwasimprovedbyapproximately18%usingonly127modelruns.
Morerecently,theASMOmethodhasbeenappliedtoparameteroptimizationofcomplexlandandweathermodels(Gongetal.
,2015;Dietal.
,2018).
However,theASMOmethodhasnotyetbeenappliedtoparameteroptimizationfortheWRFmodeltoimprovethesimulationaccuracyofturbine-heightwindspeed.
Thepresentworkintendstoimplementahighlyeffectiveandeffi-cientparameteroptimizationstrategyincludingMARS-basedparameterSAandASMO-basedsensitivityparameteroptimizationfortheWRFmodeltoimproveturbine-heightwind-speedsimulation.
Thereason-ablenessandapplicabilityoftheoptimalparametersobtainedbytheASMOmethodwillthenbeassessed.
Thispaperisorganizedasfollows.
Section2presentsthemetho-dology,includingtheMARSSAmethodandtheASMOoptimizationprocedure.
Section3describestheexperimentdesign,includingthesimulationdesign,thetunableparameters,andthestatisticalmetrics.
Section4firstpresentstheresultsofthesensitiveparametersinbriefandthenpresentsanalysesoftheoptimizationresults,includingtheoptimizationefficiencyandaccuracyimprovementforwind-speedandwind-powersimulations.
Comparisonsofvalidationeventsimulationsandphysicalinterpretationsofwhytheoptimalparametersleadtoimprovedwind-speedforecastsarealsodescribedinthissectiontoprovidefurtherproofofthereasonablenessandapplicabilityoftheZ.
Di,etal.
AtmosphericResearch226(2019)1–162optimalparametersobtained.
Conclusionsarepresentedinthelastsection.
2.
MaterialsandmethodsAnintegratedparameteroptimizationprocedureforcomplexdy-namicmodelssuchasWRFshouldconsistoftwosteps.
First,parameterSAshouldbeconductedforalltunableparametersusinganSAmethodtoscreenasmallnumberofsensitiveparameters.
Second,thescreenedsensitiveparametersshouldbeoptimizedusingahighlyeffectiveandefficientparameteroptimizationmethodinsteadofmoretraditionaloptimizationmethods.
2.
1.
Goodlatticepoint(GLP)samplingmethodUniformityisoneoftheimportantindicesforsamplingmethodsbecauseuniformsampleshelptoobtainmoreaccurateparametricSAandoptimizationresults.
Theuniformitiesofthreecategoriesofquasi-Monte-Carlomethods,includingtheGLPmethod,theHaltonsequence,andtheSobol'sequence,havebeencomparedbyGongetal.
(2016),whodemonstratedthattheGLPmethodhashigheruniformitythantheothertwomethodswiththesamesamplesize.
Therefore,GLPsamplingmethodsarerecommendedtogenerateuniformsamplesforfurtherSAandASMOmethods.
TheGLPmethodwasfirstproposedbyKorobov(1959a),anditsdesigncanbebrieflydescribedasfollows.
Let(n;h1,…,hs)beavectorofintegerssatisfying1≤hi1,whichleadstoaparametervaluewithnophysicalsignificance.
Therefore,therangeofradiation_2issetto0.
5–1.
0.
Theradiation_3parameterisascalingfactorrelatedtothediffusivityangleofcloudopticaldepth,anditsrangeissetto0.
9–1.
08basedonthelimitsontherangeofdiffusivityangleintheprogramcode.
TheparameterrangesaredeterminedbasedonacomprehensiveanalysisofparameterperturbationsandarethereforethoughttobesuitableforperformingSAunderallwindconditions.
Moreover,thesixteencalibrationeventsareselectedfromfourseasonsofoneyear,whichalsodemonstratesthattheparameterrangesaresuitabletodifferentseasons.
Fig.
2.
Theeightwindprocesses,includingvariationsinwindspeedanddirection.
Z.
Di,etal.
AtmosphericResearch226(2019)1–1653.
3.
StatisticalmetricsThestatisticalmetricsusedtoevaluatewind-speedsimulationsaretherootmeansquareerror(RMSE),thecorrelationcoefficient(R),andtheWeibullprobabilitydensityfunction.
Anotherstatisticalmetricusedtoevaluateaveragewindpoweriswindpowerdensity(WPD).
RMSEcanbeexpressedasfollows:(3)wheresimitandobsitrepresentthesimulatedandobservedturbine-heightwindspeedattheithobservationstationattimet,andMandTarethetotalnumbersofobservationstationsandtimesteps.
Toprovideabetteroptimizationresultformulti-eventcases,thenormalizedRMSE(NRMSE)isusuallyusedasthecostfunction;itsformulacanbeexpressedasfollows:(4)whereRMSEpirepresentstheRMSEvalueofthesimulationwiththeperturbedparametervaluefortheitheventandRMSEdefirepresentstheRMSEvalueofthesimulationwiththedefaultparametervalueforithevent.
Nisthenumberofsimulationevents.
WhenNRMSEis6.
5ms1,andthemaximumimprovementoccursinthesi-mulationofthestrongestwindspeed.
Forwindspeeds6.
5ms1.
Inaddition,ithasbeendemonstratedthatWRFmodelsimulationscanbettercapturethedailyvariationcharacteristicsofturbine-heightwindspeed.
ByconvertingUniversalTimeCoordinates(UTC)intolocaltime(i.
e.
,Beijingtime),itisfoundthatthewindspeedislowerinthedaytimeandhigheratnight.
Morespecifically,thelowestwindspeedoccursat~14:00localtime(correspondingto6:00,30:00,and54:00inUTC,asshowninFig.
6a),whereasthewindspeedatlocalnighttime(correspondingto12:00–24:00,36:00–48:00,and60:00–72:00inUTC,asshowninFig.
6a)isrelativelystrongandsteady.
Overall,therea-sonablesimulationresultsprovethesuitabilityoftheWRFmodeltosimulateturbine-heightwindspeed,andthesignificantimprovementofFig.
5.
Comparisonofwind-speedsimulationerrorsforsixteenevents(1)–(16)usingtheWRFmodelwithdefaultandoptimalparameters.
Fig.
6.
Comparisonsoftimevariationsinobservedandsimulatedturbine-heightwindspeedusingtheWRFmodelwithdefaultandoptimalparametersfor:(a)72-hleadtimes(b)fourseasons.
Z.
Di,etal.
AtmosphericResearch226(2019)1–168thehourlysimulationsdemonstratestheeffectivenessoftheASMOparameteroptimizationmethod.
Becausethe16optimizationevents[(1)–(16)]arechosenfromthefourseasonsofoneyear(i.
e.
,fromJune2014toMay2015),thecomparisonsofoptimizedanddefaultsimulationsareconductedforthefourseasons.
Specifically,events(1)–(4),(5)–(8),(9)–(12),and(13)–(16)belongedtosummer,fall,winter,andspringrespectively.
Fig.
6bshowsthecomparisonresultsforobservedandsimulatedtur-bine-heightwindspeedwithdefaultandoptimalparametersforthefourseasons.
Comparedtoobservations,thesimulationswithbothdefaultandoptimalparametershavetheconsistentvariancechar-acteristicthatturbine-heightwindspeedishighestinspringandlowestinsummer.
Itisalsoapparentthattheoptimalparametersgreatlyim-provetheturbine-heightwind-speedsimulationsforthefourseasonscomparedtothedefaultparameters.
Theimprovementratesinspringandfallwithstrongwindareobviouslyhigherthanthoseinsummerandwinterwithlightwind,whichconfirmsoncemorethattheASMOmethodachievessignificantimprovementforthesimulationofstrongwind(seeFig.
6a).
Fig.
7showstheWeibullPDFsofobservedandsimulatedturbine-heightwindspeed.
WhencomparingthemedianvaluesoftheWeibullPDFs,itisfoundthattheWRFsimulationswithdefaultparametersoverestimatewindspeedscomparedtotheobserveddataandthatthesimulatedvaluesofaveragewindspeedareclosertoobservationswhenASMOparameteroptimizationisused.
Similarly,thefrequencyofthesimulatedmedianwindspeedisalsobroughtclosertoobservationsbyparameteroptimization.
ComparingthewholesetofWeibullPDFsfortheobservationsandthesimulationwithdefaultparameters,itisde-monstratedthatthesimulationwithdefaultparametersstronglyover-estimatesthefrequencyofstrongwindswithspeeds>7ms1andunderestimatethefrequencyoflightwindswithspeeds500Wm2.
Forthenorthernprovinces,theaverageWPDrangesfrom200to300Wm2.
Forthesouthernpro-vinces,theaverageWPDrangesfrom100to200Wm2.
Fig.
11alsoshowsthepositionsoftheobservationstationsmarkedwithredaster-isks.
FromthepositionsoftheobservationstationsandtheWPDspatialdistribution,itisclearthatmostoftheobservationstationsarebuiltintheregionswithhighwindenergy,butafewarebuiltinregionswithlowwindenergy(seethebottomrightcornerinFig.
11).
Therefore,fromtheviewpointofwind-energysimulation,itcanbeconcludedthatthelocationsofsomealready-builtobservationstationsareinappropriate.
4.
5.
ValidationanalysisofWRFoptimalparametersComparedwiththedefaultparameters,thesuperiorityoftheop-timalparametersobtainedbytheASMOmethodforimprovingWRFturbine-heightwind-speedsimulationhasbeendemonstratedintheoptimizationperiod.
However,forthevalidationperiodwhennewFig.
10.
ComparisonofsimulatedandobservedWPDvaluesoverthefourseasons.
Fig.
11.
SpatialdistributionofsimulatedWPDwiththeoptimalwindspeed.
Theredasterisksrepresentthepositionsoftheobservationstations.
(Forin-terpretationofthereferencestocolourinthisfigurelegend,thereaderisre-ferredtothewebversionofthisarticle.
)Z.
Di,etal.
AtmosphericResearch226(2019)1–1611eventsmustbesimulated,thequestionwhethertheoptimalparametersarestilleffectivedeservestobeinvestigated.
SixnewvalidationeventsareselectedfromJune2014toMay2015,asshowninTable2.
Thedesignsofthedomainandsimulation,thevariationcharacteristicsofwindspeedanddirection,thesimulationduration,andtheforcingdatasourcearethesameasintheparameteroptimizationexperiment.
Fig.
12acomparestheRMSEofsimulatedhourlyturbine-heightwindspeedusingtheWRFmodelwithdefaultandoptimalparametersforthesixvalidationevents.
Overall,comparedwiththeWRFsimula-tionswithdefaultparameters,theaverageimprovementpercentageofRMSEintheWRFwind-speedsimulationsis7.
58%usingWRFsimu-lationswithoptimalparameters.
Moreover,allvalidationeventsimu-lationsareimprovedusingtheWRFsimulationswithoptimalpara-meters,andthewind-speedsimulationsareimprovedbypercentagesvaryingfrom2.
63%to12.
29%.
Fig.
12bshowsacomparisonofRforthesimulatedhourlyturbine-heightwindspeedusingtheWRFmodelwithdefaultandoptimalparameters.
Overall,theaverageimprovementpercentageofRintheWRFwind-speedsimulationswithoptimalparametersis6.
49%,demonstratingthattheoptimalparameterscanalsoimprovethecorrelationofWRFturbine-heightwind-speedsimu-lationsinthevalidationevents.
Notethatoneofthesixsingle-objectivesimulationsexperiencesnegativeimprovement,whichmayberelatedtotheparametervaluesobtainedbyoptimizingRMSE.
Notethattheobservedwindevolutionforthecalibrationandva-lidationperiodsfollowstwopatternvariations:oneisthatwhenthewindspeedincreases(lighttostrong),thewinddirectionexperiencesasouth-to-northvariation,andtheotheristhatwhenthewindspeeddecreases(strongtolight),thewinddirectionexperiencesanorth-to-southvariation.
However,itisunknownwhethertheoptimalpara-metersstillworkwhenotherwindpatternsaresimulated.
Inthissec-tion,twooppositewindpatternsareselectedforsimulationtovalidatefurtherthesuperiorityoftheoptimalparameters.
Eachpatternincludesthree3-daywindevents.
Fig.
13a–cshowsthefirstpattern,inwhichwhenwindspeeddecreases(strongtolight),thewinddirectionvar-iationisapproximatelysouth-to-north;Fig.
13d–fshowsthesecondpattern,inwhichwhenwindspeedincreases(lighttostrong),thewinddirectionvariationisapproximatelynorth-to-south.
Fig.
13a–fillus-tratesthenewevents(A)-(F),respectively.
Thetwocategoriesofsimulationsareseparatelycomparedtoex-aminewhethertheoptimalparametersworkforsimulationsofotherwindpatterns.
Fig.
14showsthecomparisonresults.
Itisapparentthattheoptimalparametersimprovethesimulationsofallsixwindeventscomparedwiththedefaultparameters.
Overall,usingWRFsimulationswithoptimalparameters,theaverageimprovementpercentagesinRMSEinhourlyturbine-heightwind-speedsimulationforthetwonewlysimulatedwindpatternsare6.
68%and4.
66%,respectively.
Thisdemonstratesthattheoptimalparametersarereasonableforsimulatingdifferentwindpatterns,andthemethodisthereforeeffectiveinim-provingWRFturbine-heightwind-speedsimulation.
Overall,theoptimalparametersobtainedbyoptimizingtheRMSEofturbine-heightwind-speedsimulationsusingtheASMOmethodnotonlyimprovetheRofwind-speedsimulationsintheoptimizationperiod,butalsoimprovetheRMSEandRofwind-speedsimulationsinthevalidationperiod.
Inaddition,theoptimalparameterscanbeusedtosimulateotherwindpatterns.
Theseanalysesdemonstratecompre-hensivelythattheoptimalparameterscanbeusedtoimproveturbine-heightwind-speedsimulationsinthestudyarea.
Therefore,theoptimalparametervaluesarethoughttobereasonableandeffective.
4.
6.
PhysicalinterpretationandverificationoftheoptimalparametervaluesThevaluesofthedefaultandoptimalparametersarenormalizedwithintheirrangestoprovideaclearerillustrateofthevariationsbe-tweenthem.
Fig.
15showsacomparisonofthenormalizedoptimalanddefaultparametervalues.
AlltheoptimalparametervaluesshowTable2ThesixvalidationeventsfromJune2014toMay2015.
EventsDurationI2014/09/26–2014/09/28II2014/09/29–2014/10/01III2014/12/28–2014/12/30IV2014/12/31–2015/01/02V2015/03/14–2015/03/16VI2015/03/17–2015/03/19Fig.
12.
Comparisonsofsimulationerrorsofhourlyturbine-heightwindspeedusingWRFmodelwithdefaultandoptimalparametersfor:(a)RMSE(b)R.
Z.
Di,etal.
AtmosphericResearch226(2019)1–1612Fig.
13.
Twodifferentwindpatterns.
(a)-(c)isthefirstcategory,inwhichthewindspeedgraduallydecreasesandthewinddirectionexperiencesanapproximatelysouth-to-northvariation;(d)-(f)isthesecondcategory,inwhichthewindspeedgraduallyincreasesandthewinddirectionexperiencesanapproximatelynorth-southvariation.
Fig.
14.
Comparisonsofsimulationerrorsinhourlyturbine-heightwindspeedusingtheWRFmodelwithdefaultandoptimalparametersfor:(a)thewindpatternwithwindspeeddecreasingandwinddirectionchangingsouth-to-north(b)thewindpatternwithwindspeedincreasingandwinddirectionchangingnorth-to-south.
Z.
Di,etal.
AtmosphericResearch226(2019)1–1613inconsistentvariations.
Forthekarman(thevonKármánconstant)andradiation_2(scalingrelatedtoaerosolsinglescattering)parameters,theirvaluesarebasicallyunchangedandremainedthesameasthedefaultparametervalues.
Forthesurface_1(scalingrelatedtosurfaceroughness)parameter,thevaluevariesfromtheminimumforthede-faultparametertothemaximumfortheoptimalparameterinitsrange.
Fortheotherfourparameters,theiroptimalvaluesarelowerthantheirdefaultvalues.
Ithasbeenfoundfrompreviousanalyses(e.
g.
,Fig.
6)thatthede-faultsimulationparametersgenerallyoverestimatewind-speedvaluescomparedwithobservationsandthattheoptimalsimulationpara-metersreducethisoverestimation.
Thespecificphysicalinterpretationoftheparametervariationisthefollowing.
Largervaluesofsurface_1meanagreaterroughnesslengthtobedefinedinthesurfacelayer,whichelevatesthezero-planedisplacementheightandthereforere-duceswindspeedatturbineheight.
Largervaluesofkarmanenhancethemagnitudeoftheturbulentlengthscaleintheplanetaryboundarylayer,leadingtostrongerverticalmixingduringdaytime.
However,largervaluesofkarmanalsoleadtoincreasesintheexchangecoeffi-cientformomentumnearsurface,causingareductionofwindspeed.
Smallervaluesofconvection_2(scalingrelatedtoentrainmentflow)leadtolowerratiosofentrainmenttoupdraftflux,whichenhancestheupdraft,leadingtodecreasesinhorizontalwindspeeds.
Themicro-phys_2parameter(scalingrelatedtoicefall)directlyaffectsthecon-versionratefromcloudicetorainwaterinthedescriptionofthemi-crophysicsparameterizationscheme.
Therefore,smallervaluesofmicrophys_2eventuallybringsaboutreductionsinprecipitation,leadingtodecreasesinevapotranspirationorturbulenceandreductionsinturbine-heightwindspeed.
Largervaluesofradiation_2leadtomorescatteringofsolarradiationreflectedtothesky,whichreducestheamountofshortwaveradiationreachingthesurface,furthersuppres-singevaporationandultimatelyleadingtodecreasesinwindspeeds.
Smallvaluesofland_2(scalingrelatedtosoilporosity)leadtolowersoilporosity,whichsuppressestheconveyanceofsoilwaterandheatup-wardfromgroundwatertothesurfaceandthusdecreasesthedifferencebetweensurfaceenergiesatdifferentlocations,blockingthedevelop-mentofwindspeed.
Theplanetary_3parameter(profileshapeexponentofthemomentumdiffusivity)hasapositiveeffectonthemomentumdiffusivitycoefficient.
Whenplanetary_3decreases,theeddyturbulencediffusivityintensityisweakened,inducinglowerwindspeedatturbineheight.
5.
ConclusionsThisstudyfirstusestheglobalSAmethodtoidentifythesevensensitiveparametersfrom27tunableparametersinsevenWRFphysicalparameterizationschemesandthenoptimizesthesevensensitivityparametersfromthesixWRFphysicalparameterizationschemesusingtheASMOmethodtoimproveturbine-heightwind-speedsimulationoverEasternChina.
TheWRFmodelsimulationswithdefaultandop-timalparametersarecomparedfromfiveaspects,includingthevaria-tionofturbine-heightwindspeedovera72-hleadtimeandthefourseasons,theWeibullfrequencydistributionofwindspeed,wind-speedandtemperatureprofilesfrom1000to100hPa,thecorrelationofsi-mulatedwindspeed,andthespatialandtemporaldistributionofWPDinthestudyarea.
Inaddition,theapplicabilityoftheoptimalpara-metersobtainedbytheASMOmethodisexaminedinnewsimulationsofthesixvalidationeventstoshowtheirsuperioritiestothedefaultparametersforimprovingturbine-heightwind-speedsimulation.
TheoptimizationresultsdemonstratethatparameteroptimizationforthecomplexWRFmodel,whichhasverytime-consumingcalcula-tionrequirements,canbeconductedusingtheASMOmethod.
Inpar-ticular,theoptimalvaluesofthesevenparametersinthisstudyareobtainedusing131samples,including100initialand31adaptivesamplesobtainedusingtheASMOmethod.
Thisapproachgreatlyre-ducesthenumberofWRFmodelrunsanddemonstratesthattheASMOmethodisahighlyeffectiveandefficientoptimizationmethodandiswellsuitedtooptimizetheparametersofothercomplexweatherandclimatemodels.
BycomparingtheWRFmodelsimulationswithdefaultandoptimalparameters,itisfoundthatthehourlyturbine-heightwind-speedsi-mulationisimprovedby8.
7%usingASMOoptimization.
Variationanalysesofwind-speedtimeseriesshowthattheWRFsimulationwithdefaultparametersoverestimateswindspeed,whereastheWRFsimu-lationwithoptimizedparametersgreatlyreducestheoverestimationtrend.
BycomparingthesimulatedWeibullfrequencydistributions,ithasbeenfoundthattheWRFmodelwithoptimalparametersreducesthefrequencyofsimulatedstrongwindsandincreasesthefrequencyofsimulatedlightwinds,bringingtheoptimizationresultsclosertoob-servations.
Besidesimprovingturbine-heightwind-speedsimulation,theWRFmodelwithoptimalparametersalsoimprovesthesimulationofwindandtemperatureprofilesfrom1000to100hPa.
Similarly,italsoimprovestheRofturbine-heightwind-speedsimulationbyap-proximately4%inadditiontoimprovingRMSEby8.
7%asthecostfunction.
BasedontheWPDformula,ithasbeendemonstratedthattheWRFmodelwithoptimalparametersimprovesWPDestimationby36%.
ByexaminingthespatialdistributionofWPDsimulationswithoptimalwindspeeds,ithasalsobeenfoundthatthelocationsofafewobservationstationsbuiltinregionswithlowwindenergyarein-appropriate,althoughmostofthestationsarebuiltinhigh-wind-energyFig.
15.
Comparisonofthenormalizedoptimalanddefaultparametervalues.
Z.
Di,etal.
AtmosphericResearch226(2019)1–1614regions.
Finally,theapplicabilityoftheoptimalparametersisalsodemonstratedbycomparingturbine-heightwind-speedsimulationsfortwocategoriesofnewvalidationevents:oneisthesamepatternasthecalibrationevents,whereastheotherrepresentsanoppositepattern.
TheresultsshowthattheWRFmodelwithoptimalparametersim-provestheRMSEandRofwindspeedsimulationsforthesamepatternofsixvalidationeventsby7.
58%and6.
49%respectively.
Forthetwodifferentpatterns,theaverageRMSEimprovementpercentagesofwind-speedsimulationsforthethreevaliationeventsare6.
68%and4.
66%,respectively.
Thisfullydemonstratesthereasonablenessoftheoptimalparameters.
However,itshouldbenotedthatgenerallythewind-speedsimula-tionsareimprovedbytheWRFmodelwithoptimalparameters,butthatseveralsinglesimulationsshownegativeimprovements.
Thesephenomenaarecausedbythedefinitionofthesingle-objectivecostfunction,whichallocatesequalweighttoeachsinglesimulationandthenaveragesallthesimulationerrors.
Ifthesuitableweightsareusedtoconstructthemulti-objectivecostfunction,itwillbepossibletoimproveallthesinglesimulationsusingmulti-objectiveoptimizationmethodssuchasNSGA-II(Debetal.
,2002)andASMO-PODE(GongandDuan,2017).
Inaddition,thesameapproachcanbemigratedtoothermulti-variablejointoptimizationproblemssuchaswindspeed,tem-perature,andpressure.
AcknowledgementsThisresearchwassupportedbytheMinistryofScienceandTechnologyofChina(No.
IUMKY201603),theStrategicPriorityResearchProgramoftheChineseAcademyofSciences(Nos.
XDA19070104,XDA20060401),theIntergovernmentalKeyInternationalS&TInnovationCooperationProgram(No.
2016YFE0102400),theSpecialFundforMeteorologicalScientificResearchinthePublicInterest(No.
GYHY201506002,CRA–40:40-yearCMAglobalatmosphericreanalysis),theNationalBasicResearchProgramofChina(No.
2015CB953703),andtheNaturalScienceFoundationofChina(41305052).
WeacknowledgeNationalCenterforEnvironmentalPredictionReanalysisdataset(http://rda.
ucar.
edu/datasets/ds083.
2/)andsoundingdataset(http://weather.
uwyo.
edu/upperair/sounding.
html).
Thehourlyturbine-heightwind-speedda-tasetareavailuponrequestfromtheauthorDr.
Ao.
AppendixA.
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atmosres.
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04.
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