Modelling of a medium-term dynamics in a shallow tidal sea, based on combined physical and neural
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Modellingofamedium-termdynamicsinashallowtidalsea,
basedoncombinedphysicalandneuralnetworkmethods
AgnieszkaHerman*,RalfKaiser,HanzD.Niemeyer
CoastalResearchStation,LowerSaxonyWaterManagement,CoastalDefenceandNatureConservationAgency,AnderMu¨hle5,26548Norderney,Germany
Received2August2006;receivedinrevisedform23February2007;accepted26February2007Availableonline12March2007
Abstract
Thepaperpresentsanapproachtowardsamedium-term($decades)modellingofwaterlevelsandcurrentsinashallowtidalseabymeansofcombinedhydrodynamicandneuralnetworkmodels.Thetwo-dimensionalversionofthehydrody-namicmodelDelft3D,forcedwithrealisticwaterlevelandwindfields,isusedtoproduceatwo-year-databaseofwaterlevelsandcurrentsinthestudyarea.Thelinearprincipalcomponentanalysis(PCA)oftheresultsisperformedtorevealdominatingspatialpatternsintheanalyzeddatasetandtosignificantlyreducethedimensionalityofthedata.Itisshownthatonlyafewprincipalcomponents(PCs)arenecessarytoreconstructthedatawithhighaccuracy(over95%oftheoriginalvariance).Feed-forwardneuralnetworksaresetupandtrainedtoeffectivelysimulatetheleadingPCsbasedonwaterlevelandwindspeedanddirectiontimeseriesinasingle,arbitrarilychosenpointinthestudyarea.AssumingthatthespatialmodesresultingfromthePCAare‘universally’applicabletothedatafromtimeperiodsnotmodelledwithDelft3D,thetrainedneuralnetworkscanbeusedtoveryeffectivelyandreliablysimulatetemporalandspatialvariabilityofwaterlevelsandcurrentsinthestudyarea.Theapproachisshowntobeabletoaccuratelyreproducestatisticaldistri-butionofwaterlevelsandcurrentsinvariouslocationsinsidethestudyareaandthuscanbeviewedasareliablecomple-mentarytoole.g.,forcomputationallyexpensivehydrodynamicmodelling.Finally,adetailedanalysisoftheleadingPCsisperformedtoestimatetheroleoftidalforcingandwind(includingitsseasonalandannualvariability)inshapingthewaterlevelandcurrentclimateinthestudyarea.Ó2007PublishedbyElsevierLtd.
Keywords:Tidalinlets;Hydrodynamicmodelling;Principalcomponentanalysis;Neuralnetworks;NorthSea;WaddenSea;EastFrisianIslands
1.Introduction
Theinvestigationofmanyimportantaspectsofthecoastalzoneprocesses–e.g.,theanalysisofsediment
transportorstudiesconcerningthesafetyofvariouscoastalprotectionstructuresandthecoastitself–is
1463-5003/$-seefrontmatterÓ2007PublishedbyElsevierLtd.
doi:10.1016/j.ocemod.2007.02.004*Correspondingauthor.Presentaddress:InstituteofOceanography,UniversityofGdan´sk,Pilsudskiego46,81-378Gdynia,Poland.Tel.:+48585236879.E-mailaddress:herman@ocean.univ.gda.pl(A.
Herman).OceanModelling17(2007)
277–299www.elsevier.com/locate/ocemodpossibleonlyifdataconcerningmedium-term($decades)variabilityofwavesandcurrentsinthestudyarea
areavailable.Becauseofenormouscostsandtechnicaldifficultiesoflong-termmeasuringcampaignsonthe
onehand,andtypicalshortageofinputdatarequiredby(usuallyextremelycomputationallyexpensive)
numericalmodelsontheotherhand,theknowledgeoftemporalandspatialvariabilityofwavesandcurrents
inthecoastalzoneisusuallyverylimited.
TheworkpresentedinthisstudyispartofaresearchprojectMOSES(‘‘Modellingofthemedium-term
waveclimatologyattheGermanNorthSeacoast”),oneofthepurposesofwhichistoproduceamedium-
termdatabaseofwaterlevels,currentsandmeanwaveparametersforacoastalareaintheGermanWadden
Sea.Althoughthestate-of-the-arthydrodynamicandwavemodelsareabletoreproducethewaveandcurrent
processesinshallowtidalseaswithhighaccuracy,theirapplicationtomedium-termmodellingislimited
becauseofenormouscomputerresourcesthatarerequiredtoreachspatialandtemporalresolutionsufficient
toresolvealldetailsofthecomplicatedgeometryofthecoastalzone.Themethodstypicallyusedtoaddress
theseproblems,e.g.,nestingorgridswithvaryingspatialresolution,onlyinsomecasesprovideasatisfactory
solution.Moreover,theamountofdataproducedbythemodelsmakestheirdirectusageinfurtherapplica-
tions(e.g.,asinputformorphodynamicmodelling)practicallyimpossible.Therefore,evenifoneisableto
conductsufficientlylongsimulations,additionaldataanalysistoolsarenecessary,enablingthereductionof
theamountofdatawithoutlossofinformationcrucialfortheunderstandingoftheprocessesanalyzed
andforfurtherapplicationofthemodellingresults.
Inthepresentstudytheresultsofhigh-resolutionhydrodynamicsimulationsofwaterlevelsandcurrents
(wavemodellinginthestudyareawillbetreatedindetailelsewhere)areusedasastartingpointforthedevel-
opmentofaneuralnetwork-basedmodellingsystem,whichenablesfastandsufficientlyaccuratehindcasting
oftemporalandspatialpatternsofwaterlevelsandcurrentsinthestudyarea.Themainideabehindthe
approachdevelopedistodecomposethedatasetintoa(small)numberoffixedmodes,assumed‘universal’
overthefourdecadesstudied,andtomodelthetimevariationsofthosemodesonly,thusreducingthedimen-
sionalityoftheproblembymorethanthreeordersofmagnitude.Theresultspresentedinthispapershowthat