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