River flow prediction using artificial neural netw

River¯owpredictionusingarti®cialneuralnetworks:generalisationbeyondthecalibrationrangeC.E.Imrie*,S.Durucan,A.KorreT.H.HuxleySchoolofEnvironment,EarthScienceandEngineering,ImperialCollegeofScience,TechnologyandMedicine,RoyalSchoolofMines,PrinceConsortRoad,LondonSW72BP,UKReceived4May1999;receivedinrevisedform28February2000;accepted2March2000AbstractArti®cialneuralnetworks(ANNs)provideaquickand¯exiblemeansofcreatingmodelsforriver¯owprediction,andhavebeenshowntoperformwellincomparisonwithconventionalmethods.However,ifthemodelsaretrainedusingadatasetthatcontainsalimitedrangeofvalues,theymayperformpoorlywhenencounteringeventscontainingpreviouslyunobservedvalues.Thisfailuretogeneraliselimitstheiruseasatoolinapplicationswherethedataavailableforcalibrationisunlikelytocoverallpossiblescenarios.Thispaperpresentsamethodforimprovedgeneralisationduringtrainingbyaddingaguidancesystemtothecascade-correlationlearningarchitecture.TwocasestudiesfromcatchmentsintheUKarepreparedsothatthevalidationdatacontainsvaluesthataregreaterorlessthananyincludedinthecalibrationdata.Theabilityofthedevelopedalgorithmtogeneraliseonnewdataiscomparedwiththatofthestandarderrorbackpropagationalgorithm.TheabilityofANNstrainedwithdifferentoutputactivationfunctionstoextrapolatebeyondthecalibrationdataisassessed.q2000ElsevierScienceB.V.Allrightsreserved.Keywords:Arti®cialneuralnetworks;Rivermodelling;RiverTrent;RiverDove;Cascade-correlation;Backpropagation1.IntroductionThispaper,reportsontheinitial®ndingsofaEuropeanCommissionfundedinternationalresearchprojectaimedatusingarti®cialneuralnetworks(ANNs)topredictriver¯owandqualitydownstreamofindustrialef¯uentdischarges.Assuch,theresearchdescribedinthispaperfocusesondevelopingameth-odologyforANNmodellingwhichensuresmodelgeneralityintermsofoverallperformanceandtheabilitytoestimateextremevalues.Theapplicationofarti®cialneuralnetworks(ANNs)tovariousaspectsofhydrologicalmodellinghasundergonemuchinvestigationinrecentyears.ThisinteresthasbeenmotivatedbythecomplexnatureofhydrologicalsystemsandtheabilityofANNstomodelnon-linearrelationships.Althoughdeterministicmodelsstrivetoaccountforallphysicalandchemicalprocesses,theirsuccessfulemploymentmayberestrictedbyaneedforcatchment-speci®cdataandthesimpli®cationsinvolvedinsolvingthegoverningequations.Theuseoftime-seriesmethodsmaybecomplicatedbynon-stationarityandnon-line-arityinthedata,requiringexperienceandexpertisefromthemodeller.ANNsofferarelativelyquickand¯exiblemeansofmodelling,andassuchapplicationsJournalofHydrology233(2000)138±153:S0022-1694(00)00228-6*Correspondingauthor.Fax:[phone].E-mailaddresses:[e-mail](C.E.Imrie),[e-mail](S.Durucan),[e-mail](A.Korre).ofANNmodellingarewidelyreportedinhydrologi-calliterature(RamanandSunilkumar,1995;MaierandDandy,1996;Lokeetal.,1997;Shamseldinetal.,1997;ZhangandStanley,1997;BrionandLingir-eddy,1999).AlthoughANNshavealreadybeenshowntoproduceriver¯owpredictionmodelsthatperformwellwithrespecttoconventionalmodels(CrespoandMora,1993;Karunanithietal.,1994;Hsuetal.,1995;AbrahartandKneale,1997;DawsonandWilby,1998),theirapplicationisasyetrestrictedtotheresearchenvironment.Oneofthemainconcernsasso-ciatedwiththeirusein,forexample,¯oodpredictionorreal-timewastewatertreatmentcontrol,iswhetherornotatrainednetworkwillgeneralisewhenpresentedwithnewdata.Thisissuewas®rsthigh-lightedbyMinnsandHall(1996),whofoundthattheirANNrainfall-runoffmodelswereunabletoesti-matesyntheticallygenerated¯oodpeaksinexcessofthosecontainedwithinthecalibrationdata.Theclimaticvariationsobservedoverthepastfewyearshavegivenrisetorecord-breaking¯oodanddroughtconditions,whichstressestheneedfora¯ex-iblemodelwhichisabletocapturesuchextremevalues.DawsonandWilby(1998)usedANNstopredictrainfall-runoff6hinadvance,andfoundthatamaximum¯owwhichexceededthelocalhistoricpeakwasunderestimatedinatestofthemodel'sperformance.Campoloetal.(1999)appliedANNsto¯oodforecastinginanuplandcatchment,andobservedthatalmostall¯oodpeakswereunderesti-mated.Karunanithietal.(1994)usedANNstopredictthe¯owoftheHuronRiverinMichigan,andfoundthatpeakrunoffswereconsiderablyunderestimated.Seeetal.(1997)foundthatanANNriver-levelfore-castingmodelfortheRiverOuseintheUKperformedpoorlyathighlevels.Ontheotherhand,Hsuetal.(1995)observedthatwhileneuralnetworkmodellingofrainfall-runoffwassuccessfulincapturinghigh¯ows,thelower¯owswereconsistentlyoveresti-mated.TheremaybeanumberofreasonswhyANNmodelsareunabletopredictextremevalues,andavarietyofremedieshavebeenproposed.Forexample,DawsonandWilby(1998)andCampoloetal.(1999)suggestthattheunderestimationofpeak¯owscouldbeduetoalackofinformationprovidedtothenetwork,suchastheantecedentrainfall.Karunanithietal.(1994)suggestthattheproblemcouldbealle-viatedbyincludingmorehigh-¯owpatternsinthetrainingdataset,whileHsuetal.(1995)proposemodellinglogtransformationsof¯owvaluestoreducethegapbetweenthehighandlow¯owcondi-tions.Seeetal.(1997)alteredtheirapproac