Rhythmic morphology in a microtidal low-energy beach

1.1Introduction The morphology of sandy coasts, including the shoreline position and the bathymetry of the surf and shoaling zones, quite often displays complex and intriguing patterns. These patterns are sometimes nearly periodic alongshoreoratleastshowingsomesortofregularitywithanalongshorerecurrencelength,L,andarethenknownas rhythmiccoastalmorphologies .Sometypeshavebeendefinedintheliterature(Short,1999;Ribasetal.,2015)but theextremecomplexityofbeachdynamicsandtheincreasingcapacityandfrequencyofbeachmonitoringandfieldobservationsoftenchallengetheirtraditionalclassification(Guillénetal.,2017). Transversesandbarsystemsisonetypeofthosepatterns.Theterm transversebar (TB)isgenericallyappliedtosandbarsextendingperpendicularlytothecoastorwithanobliqueorientation(Shepard,1952).Theyusually occurinpatchesofafewofthemuptotens,theyareseparatedbytroughsandtheyaretypicallyattachedtotheshore.Thealongshorespacing,L,isdefinedasthedistancebetweensuccessivebarcrests.Withadominantlongshore currenttheytendtomigratedowndriftwithmigrationratesupto40 m/d(RibasandKroon,2007;Pellónetal.,2014).Theysometimesshowanasymmetryoftheircross-section(thedown-currentflankbeingsteeperthantheupcurrentflank,Pellónetal.,2014). Severaltypesoftransversebarshavebeenreportedintheliterature(see,e.g.,Pellónetal.,2014;Ribasetal.,2015).Thefirstonesare TBRbars ,whichareassociatedtotheTransverseBarandRip(TBR)stateinthestandard beachstateclassification(WrightandShort,1984).Theyaretypicallywideandshort-crestedandtheiroriginisthemergingofthehornsofacrescenticbarintothebeach.Thesecondtypeare mediumenergyfingerbars ,MEFB, whicharesometimesobservedinopenmicrotidalbeachesundermedium-energyconditions(KonickiandHolman,2000;Khabidov,2001;RibasandKroon,2007)andtheyalwayscoexistwithshore-parallel(orcrescentic)bars.They arethinandelongatedincontrastwiththewiderandshorterTBRbars.MEFBareephemeral(residencetimefrom1 dayto1 month),attachedtothelow-tideshorelineor,occasionally,totheshore-parallelbar.Theyarelinkedtothe Rhythmicmorphologyinamicrotidallow-energybeach AnnaMujal-Colilles1a,⁎ [email protected] ManelGrifoll1a AlbertFalqués2b 1aLaboratorid’'EnginyeriaMarítima,DepartmentofCivilandEnvironmentalEngineering,UPC-BarcelonaTech,C/JordiGirona,1-3,08034Barcelona,Spain 2bDepartmentofPhysics,UPC-BarcelonaTech,C/JordiGirona,1-3,08034Barcelona ⁎Correspondingauthor. Abstract ObservationsofrythmicfeaturesalongtheinnersideoftheTrabucadorbarrierbeacharecoupledtotwonumericalmodelstounravelthemechanismsofitsformation.TheTrabucadorisalong(6Km)narrow(125 m) barrierandmicrotidalbeachattheSWsideoftheEbrodelta(Catalonia).Itsinnersideisalowenergybeachwithasandyshallowterracefeaturinganintricatealongshorerhythmicmorphology.Sixteenaerialorthophotos from1946to2014havebeenanalyzedandcomplementedwithfieldobservationsfrom1986topresent.Thismorphologyisdynamicbutitisusuallycharacterizedby:a)longfingertransversebars(LFTB)andb)largescale shorelineundulations(LSSU).TheLFTBarethinandelongatedwithalengthoftheorderoftheirspacing.Theyareintertidalandtypicallyattachtotheshorelinebyamegacusp,commonlyopeningananti-clockwiseangleof 10°–40°withtheshorenormal.Therecanbemany,upto90,withboththemeanandthemostfrequentalongshorespacingintherange15‐–25 m.Spectralanalysisalwaysshowspeaksinthisrangeandsometimesadditional peaksintherange30‐–65 mthatcorrespondtothespacingbetweenthelargestbarswithsmallerbarsinbetween.TheLSSUtypicallyhavewavelengthsintherange150‐–250 m.Theirapexessometimescoincidewiththe shoreattachmentofthelargestbarsbutnotalways.NumericalmodellingshowsthatbothfeaturescouldemergeoutoffeedbacksbetweenhydrodynamicsandmorphologyduringtheSWwindeventsinvolvinga)deflectionof thelongshorecurrentbythebarscombinedwiththerefractivewavefocusingandb)gradientsintotalalongshoresedimenttransportratetriggeringthehigh-anglewaveinstability. Keywords:Longfingertransversebars;sShorelineundulations;sSpectralanalysis;AlfacsBay;lLowenergybeach;hHigh-anglewaveinstability;sSurfzonemorphodynamicinstabilities presence of alongshore wavedriven current and theyare up-current oriented, i.e., their distal tip is shifted up-current withrespect tothe shore-attachment. Theirspacing is in therange L ≈ 15 − 200 m. Finally, the long finger transversebars type,LFTB,whichgroupsthe'‘large-scalefingerbars'’andthe'‘low-energyfingerbars'’oftheclassificationofPellónetal.(2014).Theyarecharacterizedbylongcrests,whicharetypicallylargerthanthealongshore spacingwhichmayvaryintherange L ≈ 10 − 500m.Theyaregenerallyobservedtobepersistentfeaturesinlowtomediumwaveenergysystemwhoseforeshoreisaveryflatterrace(Evans,1938;NiederodaandTanner,1970; BrunerandSmosna,1989;Falqués,1989;GelfenbaumandBrooks,2003;).Thewavefocusingcausedbytopographicrefractionbythebarsseemstobeanessentialprocesstothem.Althoughtheyaremostoftenobservedonmicrotidal beaches,theymayalsoexiston meso andmacrotidalcoasts(Levoyetal.,2013;Pellónetal.,2014).Theytendtobeorientedalmostperpendiculartotheshoreorwithasmallangle. Inadditiontosurf/shoalingzonebathymetry,theshorelineitselfcanalsodisplayanalongshorerhythmicityintheformofundulationsorcuspateshapes.Someofthemarelinkedtotransversebarsystems,sothattheirapexes developattheshoreattachmentsofthebarsandtheembaymentsinbetweencorrespondtothetroughsinbetweenbars.Theyareknownas megacusps .Shorelinesmayalsodisplayundulationsatascalewhichislargerthansurfzone rhythmicbars,i.e., L ≫ Xb ,where Xb isthewidthofthesurfzone.Theselargescaleundulationshavetypicalalongshorewavelengths>1Km(onopenoceanbeaches)andarelinkedtosimilarundulationsinthedepthcontourswell offshorethesurfzone.Theyhavebeencalled Km-scaleshorelinesandwaves (IdierandFalqués,2014). Theoriginanddrivingmechanismsofnearshorealongshorerhythmicpatternshavebeenpuzzlingscientistsforlong.Theirstrikingandrelativelyregularmorphologyalongwithitsclearcharacteristicalongshorespacingin spite of the multi-scale high complexity of coastal dynamics suggests that something important occurs in the physics at that particular length scale. A common assumption in the past was that a pre-existing template in the hydrodynamics(currentsand/orwaves)imprintsitsparticularpatternonthemorphology(HolmanandBowen,1982).Sincethefeedbackfromthedevelopingmorphologyintothehydrodynamicsisignoredinthisapproachthesetype ofexplanationshavebeenincreasinglydiscarded(CocoandMurray,2007).Alternatively,ithasbeenfoundthatrhythmicmorphologiescanemergefrominternalinstabilitiesofthecouplingbetweenmorphologyandhydrodynamics throughthesedimenttransport(CocoandMurray,2007;Ribasetal.,2015).Thishasbeenshownforcrescenticbars(Deigaardetal.,1999;Falquésetal.,2000;Calveteetal.,2005;Garnieretal.,2008),transversebars(Garnieretal., 2006;Ribasetal.,2003,2012),beachcusps(Cocoetal.,2000;Doddetal.,2008)andKm-scaleshorelineundulations(Ashtonetal.,2001;FalquésandCalvete,2005;vandenBergetal.,2012;KaergaardandFredsoe,2013),andis knownasthe self-organizationtheory . Checkingtheself-organizationexplanationforalongshorerhythmicfeaturesneedsfrequentanddetailedbathymetricsurveysalongwithmeasurementsofcurrentsandwavesduringthetimewherethefeaturesareincipient. Sincethistypeofinformationisveryscarce,providingdetailedandhighqualitydataonrhythmicmorphologydevelopmentanddynamicsisstronglyvaluable.ThesouthwesternflankoftheEbrodelta(Catalonia)featuresalongspitor barrierbeachcalledTrabucadorbeach,whichseparatestheAlfacsBayfromtheopenMediterraneanSea.TheinnersideoftheTrabucadorbeachcommonlydisplaystransversebarsandmegacuspswithatypicalalongshorespacingof tensofm.Atthesametime,aerialphotos(availablesince1946)alsoshowthepresenceoflargerscaleshorelineundulations,upto~250 m.TheTrabucadorbeachcanbeconsideredas"“low-energy"”sinceitisshelteredfromthe openseawaves.ApreliminarydescriptionofthissystemwasdonebyFalqués(1989). There are in the literature manytheoretical studies onrhythmic surfzone bars andonlarge scaleshorelineundulations. However,theapplication of such studiestospecific features observed in natureismuch scarcer. Moreover,therearenostudiesofrhythmicsurfzonebarscoexistingwithlargescaleundulations.Therefore,theTrabucadorbeachcasehasprovidedauniqueopportunityofstudying,forthefirsttime,bothtypesoffeaturesin coexistenceandfrombothviews:observationsandmodelling. Theprimaryobjectiveofthepresentpaperisamorethoroughdescriptionandcharacterizationoftherhythmicmorphologyinthisbeach.Wemainlyusespectralanalysisoftheshorelinesfromaerialorthophotosduringthe period1946‐–2014 alongwith occasional field observationsbyone ofthe authorsduring the period1986‐–2014. Wehypothesize that their morphology and thelength scales are largely self-organized and thesecond objective is investigatingthephysicalmechanismsdrivingitsformationanddynamicsbymeansofnumericalmodelling. 2.2StudyAreaandmorphology 2.1.2.1Geographicalsettingandmeteo-oceanographicconditions TheEbrodeltaislocatedinthewesternMediterraneansea,NEoftheIberianpeninsula,inCatalonia(seeFigure.1).Asaresultoftheinteractionoftheriverandmarinedynamics(Jiménezetal.,1997),thepresentdaydelta extendsaround25 kmoffshoreandhasanareaofabout325Km2.Onthelateralmarginsitfeaturestwospits,onetrendingtotheNW(ElFangar),anothertrendingtotheSWandconsistingoftheTrabucadorbarrierbeachandLa Banyapeninsula.Betweenthesouthwesternspit(TrabucadorandLaBanya)andthemainland,thereisasemi-enclosedbaycalledAlfacsbay.Itisnearlyrectangularabout16 kmlongand4 kmwide,withanaveragedepthofabout4 m (6.5inthecenterofthebay).TheAlfacsbaycanbegeomorphologicallyclassifiedasabar-builtsemi-enclosedlagoonformedastheresultofthereworkingofanabandonedlobeofthefirstEbroRivermouth,directedtothesouthby waves(Pritchard,1952,Nienhuisetal.,2017). The bay receivesconsiderableamount of freshwater from rice crops(oftheorder of10m3·s‐−1during openedchannels)leading an almost stablestratificationthroughouttheyear.So, accordingtoconductivity,temperatureanddensityprofilersduringdifferentperiods,thesemi-enclosedlagoonisclassifiedhydrodynamicallyasasalt-wedgeestuary(Llebotetal.,2014;Cerralboetal.,2015a).Thebedismadeofsiltand clay(largestpercentagesinthemiddleofthebay)(Palacinetal.,1991).However,nexttotheinnersideoftheTrabucadorbarrierbeachthereisasandyandshallowshelf,seeFigure.2,thatiscomposedoffinesandwith D 50 ≈ 0.15 − 0.3 mm(Falqués,1989).Thisshelfdeepensfrom0toroughly0.7 mwithinabout125 mwidthand,presumably,ithasbeenbuiltoutofsedimentsfromtheoutersideofthebeachduringoverwashevents. ThewindregimeintheEbroDeltaischaracterizedbytheprevalenceofNorth-Westerlywindsduringautumnandwinterandonshore/offshorewinds(dailysea-breeze)duringsummer(Cerralboetal.,2015b;Grifolletal.,2016). Usingone-yearobservedwinddata,Grifolletal.(2015)estimatethemonthlypercentageoftimeofNWwinds:duringwinterthispercentagewasabout80%decreasingduringsummerto20%.Seebreezeoccursdailyduringsummer andinalesserextendduringspring.North-Westerlywindsarise15 m·s‐−1andtypicalvaluesofsea-breezeareoftheorderof8 m·s‐−1.Accordingtothewindclimate,andbecausethisbeachissheltered,wavesareexpectedtobevery smallincomparisontotheopen-seasideoftheTrabucador. Thisbeachismicrotidal,withtidalrange~0.25 m,butsea-leveloscillationduetoseichesactivityisrelevant(Cerralboetal.,2014)withamplitudesofmorethan>0.5 mmeasuredwithinthebaywithcharacteristicperiodsof1 h and3 h(0thand1stseichemodes).ThewatercirculationinAlfacsbayatshorttemporalscales(ordersofhours)isdominatedbythelocalwindandtheoccasionalseicheactivity(Cerralboetal.,2015a).Atlargetemporalscalesthe Figure1Fig.1Left:theEbrodeltawiththeTrabucadorbeach(inyellow).Othergeographicallocationsmentionedinthetextarealsoshown.Right:TheTrabucadorbarrierbeachin2012.Theshallowshelfwiththetransversebarscanbeseenattheinnerside.Source:ICGC.(For interpretationofthereferencestocolourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.) alt-text:Fig.1 Figure2Fig.2a)Detailedviewofthetransversebarsystemin2012.b)ViewoftheinnerTrabucadorbeachin2013wherethelargescaleundulationsarevisible.Source:ICGC.WhitearrowrepresentstheNorth. alt-text:Fig.2 waterresponseconsistsofacombinedeffectofagravitationalcirculationduetofreshwaterinputsandtheresidualeffectofwinds.Duringseicheactivitymaximumvelocitiesinthenodelocationreach0.5 m/s.Numericalmodelling excercises presented by Cerralbo et al. (2014) identify the antinode location near Trabucador beach shore, so that the expected velocities due to seiche activity are negligible. No measurements of currents are available at the TrabucadorinnerbeachwherebarsarelocatedbutthecurrentswereestimatedwithpassivetracersduringthefieldcampaignofSeptember1988(Falqués,1989).WithNorthwindof7.3 m/samaximumcurrentof0.30‐–0.35 m/stothe SWwasobservedoverthecrestofabarwithwaterdepthof0.05‐–0.1 m.Thecurrentwasclearlyfavoredbythebreakingofthesmallwavesoverthebar.Atthesametime,atthedeepsbetweenthebarswith0.3‐–0.5 mdepthcurrents of0.15‐–0.20 m/swereobserved.Themaximumcurrentintheoppositedirectionwasabout0.2 m/swith6.1 m/swindfromtheS-SE. 2.2.2.2Thealongshorerhythmicmorphologicalsystem ThissystemwasfirstdescribedbyFalqués(1989) on thebasis offieldobservations andtheanalysis ofaerial photos and maps.Periodicvisual inspectionssuggestthat the rhythmicsystem isverypersistent,althoughits prominencevariesfromveryobvioustonearlynonexistent.ThecharacteristicmorphologicalunitsareshowninFigure.2:barsandassociatedmegacuspsinFigure.2aandlargescaleshorelineundulationsinFigure.2b. 2.2.1.2.2.1Barsandmegacusps TheinnerTrabucadorbeachusuallyfeaturesmanylongfingertransversebars(LFTB).Theyareelongatedwithdifferentorientationsbutmostofthemtrendnearlyperpendiculartothecoastline(seeFigure.3)andtheyaretypicallyrotatedtothe leftwithrespecttoshorenormalviewingfromthebeach(anangle ϕ ≈ 10 − 40°),i.e.,theytrendapproximatelytotheW.Manyofthemreachthecoastlineandamegacuspdevelopsattheattachmentpoint(seeFigure.3c).Similarmegacuspshavebeen describedbyEvans(1939,1938). ThelengthandalongshorespacingoftheLFTBareofthesameorderofmagnitude,theformertendingtobelargerthanthelatter.Thespacingroughlyrangesbetween5 mand100 mbutistypicallyabout20 m.Theirverticalreliefcanreach about0.4 m.Typically,theyareinter-tidal,becomingmostlyemergedatlowtide.Ascanbeseenintheaerialphotos,thewholebarsystemusuallyextendsoffshoreintotheAlfacsBayacrossasignificantportionoftheshallowshelf.Accordingtolocal fishermen,thebarshavebeentherefor,atleast,thelast70 years.Indeed,theyarealreadyvisibleinanaerialphotoof1946. Figure.3cshowsabathymetricsurveytakeninAugust1986(Falqués,1989)anddisplaying4mainbars.Theangleofthemainbarswiththeshorenormalis14°,24°,19°totheleftviewingfromthebeach.Thesebarshaveanasymmetriccross-bar profilesteeperattheNEsideandmilderattheSWside.Theiralongshorespacingisabout60‐–70 m.Atthetroughbetweentwomainbarsthereisaminorbarnotconnectedtotheshorelineandshowingaweakoppositeasymmetry.Thesesmallerbarsin betweenthelargerones(inlengthandinalongshorewavelength)arerelativelycommonallalongthebeach.Thebarsystemisdynamicandactive.AclearindicationwasobtainedinSeptember1988whenitwasobservedhowtheshapeofabarchanged andhowthecrestmigratedabout0. 4 mwithin20 hourshduringadailyfairweatherconditions.Themigrationwasconsistentwiththeasymmetryincross-barshape,i.e.,towardsthesteepestside.Itwasalsoobservedhowtheripplesatthebarcrestwere formed,changedtheshapeandsizeanddisappeared. Althoughtherearesomedifferences(e.g.,barorientationorlengthvsspacing)wethinkthesebarsshareimportantcharacteristicswiththosedescribedbyEvans(1938)astype2.Theyweredescribedas'‘largecuspswhichhavetheirapexes Figure3Fig.3a)Transversebarsatlowtideduringtheperiod1986‐–1988.b)Transversebarandtherefractivewavefocusingbyit.c)BathymetricmapofastretchoftheTrabucadorinnerbeachfromAugust1986showingaseriesof5barsand3megacusps.Thedepthsareincm. alt-text:Fig.3 continuingoutintothelakeasaridgeofsandonthelakebottom'’.Itwasclaimedtheyformonlowenergybeacheshavingaplentifulsupplyofsandandwithacross-shorebathymetricprofilewhichisabovetheequilibriumprofile,featuringashallow terrace. 2.2.2.2.2.2Largescaleshorelineundulations Accordingtovisual inspectionsoftheaerialphotos,inadditiontothesmall amplitude shoreline undulationsdeterminedbythemegacusps,therearelarger shoreline undulations(seeFigure.2b). The apexes of these undulations sometimes coincidewiththeattachmentofoneofthelargestbars.However,thereisnotaone-to-onerelationbetweenbarsandlargescaleundulationssince:i)therearealsosmallerbarswithmegacuspsattheembaymentsandii)sometimestheapexesofsome undulationsareapparentlynotassociatedtoanybar.Thewavelengthsoftheseundulationsareintherange100‐–250 m,i.e.,significantlylargerthanthetypicalalongshorespacingofthebars.Therefore,theycanbeidentifiedasKm-scaleshorelinesand wavesalthoughtheirwavelengthissmallerthanthatofthesimilarfeaturesdevelopingonopenoceanbeaches. 3.3Methods 3.1.3.1Imageprocessing ThissectiondescribesthemethodologyweusetoextracttheinformationofthebarpositionsfromtheimagesalongwiththealongshorewavelengthsusingaFourieranalysis.Aerialorthophotosfromthe InstitutCartogràfici GeològicdeCatalunya (ICGC)duringtheperiod1946‐–2014areanalyzedtoassessthetimeevolutionofthemorphologyandtoobtainitsalongshorewavelengths. TheavailableimagesarelistedinTable1.TheshorelineisclearlyvisibleinallofthembutidentifyingtheLFTBisnotsostraightforward.WehaveselectedthecentralstretchoftheTrabucadorBeach(2Km)wherethebarsare morevisible.Usually,thebarscanbedetectedfromelongatedpatcheswithacolourthatisinbetweenthecolourofthedrybeachandthecolourofthedeeperwater.Incaseofoldblackandwhiteimages,thedrybeachappearsin verylightgrey,thebarsabitdarkerandthetroughsdarkgrey.Incaseofcolourimages,thedrybeachappearsinlightyellow/brown,thebarsinthesamecolourscolorsbutdarker,andthedeeperwatersinblue.AscanbeseeninTable 1theimageshavedifferentresolution.Nevertheless,mostofthemareusefultolocateboththebarsandtheshorelineundulationsregardlessoftheirresolution,asshowninFigure.4a–b.However,theimagesfrom1983(Figure.4c), 1996,2000(Figure.4d)and2004arenotgoodenoughtocapturethelengthofthebarsduetothepoorqualityoftheorthophoto,butcanstillbeusedtoassessevaluatetheshorelineundulationsandthepositionofthebars. Table1OrthophotosavailableintheICGCwiththecorrespondingresolution.TheyearsthatarenotpresentinthetableareyearswheretheICGCdidnotperformaflightintheTrabucadorzone. alt-text:Table1 Year Resolution(cm/px) LFTBbars AlongshoreUnd. 1946 100 YES YES 1956 50 YES YES 1983 50 YES YES 1993 2500 NO YES 1994 50 YES YES 1996 2500 NO YES 2000 50 NO YES 2004 50 NO YES 2007 50 YES YES 2008 50 YES YES 2009 25 YES YES 2010 25 YES YES 2011 25 YES YES 2012 25 YES YES 2013 25 YES YES 2014 25 YES YES Themethodisbasedontrackingthesharpchangesincolourassociatedtothebarsandtotheshorelineinbetweenbarsbyamanualdigitalization.Inthisway,an ApparentShoreline/Bar signal(ASB)alongtheshoreisobtained. Thissignalis,therefore,influencedmainlybythesealevelandthelightduringtheflightoftheorthophoto.Thus,wedonotattempttoextracttheexactshorelinefromtheorthophotos,butasignalthatisrepresentativeenoughto capturethepositionofthemainbarsandtheundulationspresentintheshoreline.Inordertominimizetheinherenterrorsofamanualdigitalization,thesameprocedurewasrepeatedseveraltimes,obtainingdifferentsignalsfrom thesameorthophoto.Thesesensitivityanalysisonthemanualprofilingparametersshowednosignificantinfluencesonthefinalresults,sincethedifferencesbetweenwavelengthswerelowerthan5 metersm. Morespecifically,theASBsignalisobtainedfromtheimagesdetailedinTable1asfollows: 1. Manualprofiling:imagesareloadedtoaGISspecificsoftwareandaseriesofdotsismanuallyassignedtotheedgesofthebarcreststhatareattachedtotheshoreline(identifiedasasharpchangeincolour)andtotheshorelinestretchinbetweenbars(Figure.5a). Whilethereistypicallyasharpchangeincolouracrossthebarsthatallowsidentifyingrelativelywellbothedgesofabarcrest,thechangesalongthebarcrestsarequitegradual.Thus,thelengthofthebarsisnotwelldefinedfromtheimagesandisnotdiscussed here.Accordingtothehistoricalorthophotos,twoconcreteplatformswereconstructedalongtheinnerbeachandwerepresentintheshorelineprofilefrom1994to2000.InordertominimizethenoiseofthefinalFourieranalysis,theseplatformshavebeenremoved fromtheoriginalsignal. 2. Rotation:sincetheTrabucadorbarrierbeachisNorth-Eastoriented(55°)andtheFouriertransformneedsasingle-valuedsignal,theshoreline/barlineisrotatedtoapproximatethemeanshorelinealongthex-axis,usingaroadthatgoesalongthebarrierbeach(see Figure.5b).However,thebarsarestilltiltedtowardstheSouth-Westandasingle-valuedsignalisnotobtainedforallthebars.Thiscreatessomeproblemsinthenextstep. 3. Interpolation:theFourieranalysisrequiresanequispaceddigitalsignal.Thus,anewsignalisobtainedfromthepreviousstepbyinterpolatingtoanequispacedmesh.Alinearinterpolationwithaspacing ∆x = 0.5mturnedouttobesatisfactory,althoughweshould bearinmindthatitintroducesspuriouspeaksduetotheslightinclinationwithrespecttothenormaldirectionoftheTrabucadorbar,seeFigure.5c–d.ThesensitivitytodifferentinterpolationmethodsandgridspacinghasalsobeenexaminedinFigure.5dandthebest Figure4Fig.4Zoominoffourorthophotosduringdifferentyears.a)b)highqualityimages;c)d)lowqualityimages.Source:ICGC. alt-text:Fig.4 resultsareprovidedbythelinearinterpolation. Itisimportanttopointoutthatthepresentmethodologyincorporatessignificantnoisebelow10‐–15 mwavelengthduetothespuriouspeaksoftheASBsignaladdedduringtheinterpolationstep.Therefore,someexisting peaksaround10 mwillnotbecapturedaccuratelyusingourmethodology,asshowninFigure.5d.TheresultingASBsignalscanbeseeninFigure.6. Figure5Fig.5BrownpatchrepresentsthebeachcontourgivenbytheASBsignal.a)RawASBsignalfromthemanualprofiling.Theyellowlineindicatesthedirectionofthexaxisafterrotation;b)RotatedASBsignal;c)SensitivityanalysisoftheinterpolatedASBsignalasa functionoftheinterpolationspacing, ∆x .Thedifferentinterpolatedsignalsareshownindifferentcolours.;d)SensitivityanalysisoftheASBsignalinfunctionoftheinterpolationmethod.(Forinterpretationofthereferencestocolourinthisfigurelegend,thereaderisreferredtothe webversionofthisarticle.) alt-text:Fig.5 TheDiscreteFouriertransformofacontinuoussignal, f ( ξ ),inthespatialdomainisdefinedby: wherethecoefficientsare: andtheenergyofeachwavenumberis where λ 1 is the fundamental wavelength and ξ  is the spatial coordinate. The interpolation of the original ASB signal of the images provides a discrete signal and must be analyzed through a Discrete Fourier Transform (DFT) algorithm.SeveralalgorithmscanbefoundintheliteraturetocomputetheDFTandmostofthemareclearlyaffectedbythesamplingfrequencyandotherinherentalgorithmparameters.Thepresentresearchusesthe FastFourier Transform (FFT)assumingthatvalidwavenumberswillbebelow1 m‐−1.TheresultsobtainedaftertheFFTcomputationareveryclearforhighwavelengths(Figure.7a)butdonotshowrobustpeaksinthelowwavelengthrange,see Figure.7b. Therefore, low wavelength scales are analyzed using Bartlett’'s Method. Bartlett (1948) estimates the power spectra by averaging the DFT results of N segments of the original signal. This is useful if the wavelength distributionisuniformalongthesignalbutmaysmoothdownsomepeaksthatarepresentataparticularlocationofthesignal.Therefore,Bartlett'sresultswillenhancetheexistenceofmainwavelengths,presentrepetitivelyatthe Figure6Fig.6Manualprofilingresultsoftheorthophotoimages. alt-text:Fig.6 (1) (2) (3) Thedepthofclosure,Dc,isanimportantparameterforshorelinesandwaveformationoverwhichthereissomeuncertainty(Falquésetal.,2017).FromthemorphologyoftheinnerTrabucadorbeachencompassingfirstashallowterraceupto 0. 7 mdepthandthenasteepbreaktowardstheAlfacsbay(Figure.1),avalueDc ~ 0. 7 mseemsreasonable.Moreimportantly,theaerialphotosrevealthatthealongshorerhythmicbathymetryextendsuptowaterdepthofthisorderandthendisappears (Figure.1).Thus,wehereexploretwovalues,Dc = 0.6 mandDc = 0.75 m.Regardingtheshapeofthebathymetricperturbationalineardecayinbedlevelfrom1attheshorelineto0at Dc isconsidered.Theeffectofdifferentshapefunctionsonmodel shorelinesandwaveformationisdiscussedinIdieretal.(2017).RegardingthewaveconditionsweusetheSWANoutputsincaseofSWbreezeasareference.ThewaveheightisarobustoutputoftheSWANmodelsothatwefixHs = 0.25 mandwe exploreTpfrom2.5 sdownto1.25 s.Regardingthewaveangle,itisadvisabletoexploreawiderangeincludingtheoutputofSWAN(inordertoobtainathresholdanglefortheinstability)sothatweconsiderwaveanglesfromθ = 20°uptoθ = 70°(at D = 1.6 m).Finally,concerningthewavelengthoftheundulationsweexaminetherange100 m ≤ λ ≤ 500 m.Forthatrangeofwavelengths,theinstabilitycurves(growthrateσrasafunctionofλ)lookliketheonerepresentedinFigure.11bforHs = 0.25 m, Tp = 1.25 s,θ = 50°andDc = 0.6 m.Inthiscase,themaximumgrowthrateisσr=0.032d‐−1whichdefinesthedominantwavelength,λM = 180 m.Thismeansthatthecharacteristictimeformationofthoseundulationsisaboutσr‐−1 ≈ 31dassumingconstant waveconditions.AsshowninFigure.11c,thedominantwavelengthhasbeenexploredasafunctionofθforvariousDcandTp.Firstitisseenthattheformationofshorelineundulationsneedsaminimumwaveangleinaccordancewithhigh-anglewave instabilitytheory(Ashtonetal.,2001;FalquésandCalvete,2005).ForTp = 1.25 s,thisthresholdangleisabout40°forDc = 0.75 mand45°forDc = 0.6 m.ForTp = 2.5 sandDc = 0.6 mitis50°.Itisfoundthatthedominantwavelengthsrangebetween180 and500 mandtheyincreasewithDc.ForDc = 0.6 mandexcludingthosecorrespondingtotheanglesnearthethreshold,theyareintherange180‐–280 m.ForDc = 0.75 mtheyareintherange290‐–500 m.Therefore,therangeofvariabilityofthese wavelengthsasafunctionofthewaveparametersmatchesquitewelltherangeoflargealongshorelengthscalesrevealedbytheimageprocessingpresentedinSection4.1.Inparticular,therange150‐–250 mseemsquitewellcapturedbytheDc = 0.6 m modelresults.Thewavelengthsabout400 mcouldberoughlyassociatedtoDc = 0.75 m.Importantly,theexistenceofathresholdangleforshorelineinstabilityrulesoutthepossibilitythatNWwindeventscouldgeneratesuchlargescaleundulations. 5.5Discussionandpossibledrivingmechanisms 5.1.5.1Morphodynamiccharacteristicsoftheobservations. Previously,itisimportanttoidentifysomeofthecharacteristicsofthemorphologicalsystemthatcanprovidecluesintothedrivingprocesses: •Thesystemisnowadaysactive,itisnotrelict.ThisisveryobviousfromFigure.6.However,thefieldobservationsduringtheperiod1986topresentareveryscarceandtheaerialorthophotosareavailableonceayearatmost.Also,itissometimesdifficulttoascertain whetherthebarsarenotthereortheyaresimplynotvisible.Thus,withtheavailableinformationitisimpossibletoaccuratelyassessthetimevariabilityofthesystemandtrytolinkittoparticularmeteorologicalevents. Figure11Fig.11Modellinglargescaleshorelineundulationswith1D-morfoforstrongbreezefromtheSW.(a)cross-shoremeanbathymetricprofile,observed(diamonds)andanalyticalapproximationusedby1Dmorfo(thickline).(b)typicalinstabilitycurve,growthrateasafunction ofwavelength,showingadominantwavelengthabout180 m.TheparametersareHs = 0.25 m,Tp = 1.25 s,θ = 50°withDc = 0.6 m.(c)dominantwavelengthasafunctionofwaveangle,θ,forvariousDcandTpandforHs = 0.25 m.Belowθ = 40°thereisnoundulationgrowth. alt-text:Fig.11 •Therangeofwavelengths(Section4.1).Forthetransversebars/megacuspsitis15‐–65 mandtheoverallmostcommonisabout20 m.Forthelarge-scaleundulationsitisabout150‐–400 mbutthemosttypicalwavelengthsareabout150‐–250 m. •Refractivewavefocusingbythebars.AsshowninFigure.3b,thesmallwavesapproachingthebarsstronglyrefract,thewavecreststurntowardsthebarcrestandcrossthewavecrestscomingfromtheotherbarflank.Thiscreatesazonewithsmallbreakersoverthe barcrestandaquitestrongonshorecurrentoverthebar.Currentsofabout0.35 m/sandsedimentmobility(mainlybed-load)associatedtoithavebeenobservedbyFalqués(1989).Thisisaverystrikingandpersistentprocessonthisbeach.Thisprocesswasclearly describedbyNiederodaandTanner(1970)andwassuggestedtobeoneofthedrivingmechanismsofsometransversebars. •Obliquityandorientation.Accordingtotheaerialphotosthebarsarenotshorenormalbutoblique,i.e.,theyaretypicallyrotatedtotheleftviewingfromtheshoreananglerangingfrom10°to40°. •Alongshoreasymmetryofthecross-barbedprofile.Abathymetricmaptakenin1986(Figure.3c)showsanasymmetricprofileofallthebars,steeperattheNEflankofthebarsandmilderattheSWflank(exceptaminorone).Additionalbathymetricobservationsare notavailablesothatwedonotknowwhetherthisisalwaysthecaseornot.Fromthedistributionofdarkandlightcolorsintheaerialphotossomesymmetry/asymmetrycanbesometimesguessedanditseemsthattheasymmetryobservedinFigure.3cdoesnot alwaysoccur. 5.2.5.2Transversebars InSection4.2.2wehaveseenhowthemorfo55modeldescribestheself-organizedformationoftransversebarsoutofinitialbathymetricnoiseduringsome35 hourshofstrongSWbreeze(9 m/s).Ofcourse,35 hourshofsuch constantwindisunrealistic,butatleast6 hourshadayisquitecommonduringmanysummerdays.ThismeansthatthebarscouldformduringafewweeksofcommonsummerbreezeregimeatElTrabucador.Theobservedrangeof wavelengths,theobliqueorientation,thealongshoretranslationandeventhepresenceofdifferentbarsizesarecapturedbythemodel.Aquantitativecomparisononthealongshorecelerityisimpossiblewithoutknowingthewave conditionsfortheobservedtranslation.Accordingtothemorfo55equations,thephysicalprocessesthatareessentialfortheformationofthebarswouldbeasfollows.TheSWwinddriveswavesincomingobliquelytotheTrabucador beachfromtheW.ThebreakingofthesewavesdrivesalongshorecurrenttotheNE.Theincipientbarsactonthecurrentintwoways:a)theycauseameanderingofthecurrent,seawardatthecrestsandshorewardatthetroughs (bedfloweffect)andb)duetotherefractivefocusing,thereismorewaveenergyhencemorebreakingoverthecrestsandlesswaveenergyhencelessbreakingatthetroughs(bedsurfeffect).Thiscausesgradientsinwaveradiation stressesandinwave-setupthatalsoaltersthelongshorecurrent.Morfo55,then,computestheperturbedsedimentfluxanditturnsoutthatthegradientsinsedimentfluxcreatesedimentdepositionatthecrestsandsedimenterosion atthetroughstherebyapositivefeedbackoccurs.Thedetailsofthephysicalmechanismthatcandriveup-currentorientedtransversebarshadbeengenericallystudiedbyRibasetal.(2003),Garnieretal.(2006)andRibasetal.(2015). Regardingitsspecificapplicationtonature,Ribasetal.(2012)foundthatthemediumenergytransversefingerbarsobservedatNoordwijkbeach,theNetherlands,couldbeexplainedbythismechanism.However,thepresentresearch isthefirsttimethisfeedbackmechanismisfoundtodrivelongfingertransversebars(LFTB).AlthoughthephysicalmechanismissimilartoRibasetal.(2012)thereareanumberofdifferenceswiththepresentstudy(seeSection1).The mostessentialarei)thelevelofwaveenergy,ii)whethertheyareephemeralorpersistentandiii)whetherthereisashore-parallelbarornot.Moreover,thepresentstudyusesnonlinearmorphodynamictimeevolutionwhileRibasetal. (2012)uselinearstabilityanalysis.LFTBbarshavealsobeenobservedatElPuntalbeach,Santander(Cantabria,Spain)byPellónetal.(2014).However,therearetwoimportantdifferenceswiththeTrabucadorsystem:thosebarsare down-currentorientedandthetidalrangeissignificant,upto5 m.Moreover,amorphodynamicmodellingoftheirformationisnotavailablesothattheirformationmechanismisstillunknown. Thedrivingforceforthecurrentinthepresentsetupforthemorfo55modelisjustwavebreaking.OtherprocessescouldhelpindrivingacurrenttotheNEatElTrabucadorbeach.Firstofall,theSWwinditselfcoulddothis job.Pellónetal.(2014)comparedthewindandthewaveforcesonthewaterforatransversebarsysteminatidallow-energybeachandconcludedthattheywereofthesameorderofmagnitude.Cerralboetal.(2016)investigatethe watercirculationpatterninAlfacsBayusingafully3Doceannumericalmodel.TheirnumericalexperimentsshowedacurrentjetintheinnershoreoftheTrabucadorbeachassociatedtoNWwind.Also,lessfrequentNEwindsmaybe theoriginofasouthwestwardcurrentasalocalresponsetothewind.Asfarasweknow,thereisonlyonepublishedstudyonmorphodynamicinstabilitiesinducedbycurrentspartiallydrivenbywindinthesurfzone(Ribasetal.,2012). AlthoughtheenvironmentisquitedifferentfromElTrabucador(openoceanbarredbeach,mediumwaveenergyconditions)thatstudysuggeststhatwindeffectscouldreinforcetheself-organizationprocesspresentedinSection4.2.2. Certainly,moredetailedobservationsareneededalongwithspecificmodellingstudiesonmorphodynamicinstabilitiesgeneratedbypartiallywind-drivencurrent. TherefractivewavefocusingandbreakingbythebarswaspointedoutasthemainformationmechanismforLFTBbarsbyNiederodaandTanner(1970).Thiseffectisincludedinourmorfo55simulation(bedsurfeffect)butin combinationwiththelongshorecurrentdeflection(bedfloweffect)whichessentiallyoccursincaseofobliquewaveincidence.SincetheTrabucadorbarsareobliqueandfrequentlyasymmetrictheyverylikelyhaveformedunderthe actionofacurrent.IncontrastandaccordingtoNiederodaandTanner(1970),thebarswhichareprimarilyformedbytherefractivewavefocusingcanemergeevenincaseofnormalwaveincidencebeingshore-normalandcross-bar symmetric.Thus,weconcludethatthepresentbarsarenotformedonlybytherefractivewavefocusingbutbythecombinationofboththisprocessandthelongshorecurrentinteractionwiththebars. Atthispoint,wewonderwhichcouldbethepossibleroleofNWwindeventsonthebars.AmodelstudysimilartothatcarriedoutforSWwindisbeyondthescopeofthepresentworkandisleftforfutureresearch.Inthat case,thewaveincidenceisnearlyshore-normalandtherefractivewavefocusingcouldplayaroleininitiatingbarformationwithoutcross-barasymmetryandwithanearlyshore-normalorientation,accordingtoNiederodaandTanner (1970).Also,theNWwindcouldcontributetoreshapethebarsonceformedduringSWwindevents.Thus,wefinallyconcludethattheSWbreezewouldbetheprimarycauseofthetransversebarsalthoughtherecouldbesome influenceofNWwindeventsthatstillremainsunknown. WeshouldfinallymentionanimportantoccasionalprocessthattakesplaceattheTrabucadorbarrierbeach.DuringseverestormsfromtheEorNEtheTrabucadorbarrierbeachissometimesfloodedandbreached(Graciaet al.,2013).Overwashfanscanthenappearandtheyperhapsmightactasaninitialperturbationthatwouldinitiatethefeedbackmechanismsbetweenmorphologyandhydrodynamics.Theself-organizedprocesseswouldlateroncreate thelongfingertransversebarsandinducethealongshoreperiodicity.Sincethebarsaremuchthinnerthantheoverwashfansitisunlikelythatthesefansweretheseedforthebars. 5.3.5.3Large-scaleshorelineundulations InSection4.2.3wehaveseenthatifweignorethetransversebarsandthedetailsofthesurfzonemorphologyapositivefeedbackbetweenhydrodynamicsandthesmoothedmorphologycanstilloccuratwavelengthsoneorder ofmagnitudelargerthantransversebarsiftheSWwaveincidenceangleislargeenough.Thisfeedbackisbasedonthealongshoregradientsinthecross-shoreaveragedbedelevationwhenthealongshoregradientsoftotallongshore transportcausedepositionattheshoalsoftheaveragedbathymetryanderosionatthedepressions.Thesegradientsoccurbecauseofthealongshorevariationsinwaverefractionandshoalingintheshoalingzone,whichmustbe coupledtothesurfzone.Dependingonsomeparameters,the1D-morfocomputationsgivearangeofwavelengthsλ ~ 180‐–500 mwhichmatchesquitewelltherangeoftheobservedlargescaleshorelineundulations.Wethusconclude thathigh-anglewaveinstabilityforSWbreezescouldprovideaplausibleexplanationforthelargescaleshorelineundulations. 6.6Concludingremarks TheanalysisoftheaerialorthophotosanddirectobservationsoftheTrabucadorbeachhaveshownthattheinnersidecommonlyfeaturesanintricateandcomplexmorphologythatisalongshorerhythmicatanumberof differentlengthscales.Themostapparentmorphologicalunitisthelongfingertransversebars(LFTB).Thesebarstypicallyattachtotheshorelinebyamegacuspandboththemeanandthemostfrequentalongshorespacingsare about L = 20m.Thespectralanalysisofthedigitalizedsignalsshowsmanypeakswithinter-annualvariability.However,thereisalwaysasignificantconcentrationofpeaksatthe15‐–25 mband.Thispreferentlenghscaleisalso confirmedbytheinsituobservations.Therefore,weconcludethatthedominantalongshorespacingoftheLFTBistypicallyabout20 m.Thespectralanalysisalsoshows(lessfrequent)peaksintheband L = 30 − 65m.Boththe orthophotosandthedirectobservationsshowthattheycorrespondtothespacingbetweenthelargestbarshavingminorbarsinbetween. Anothermorphologicalunitisthelargescaleshorelineundulations.TheirsystematicorrhythmicbehaviorisrevealedbythespectralanalysisoftheASBsignalsandbecomesveryclearinsomeoftheorthophotos.These undulationsseemtobeadifferentelementnotdirectlyrelatedtotheLFTB.Thecorrespondingalongshorewavelengthsofthoseundulationsrangebetweenabout150 mupto700 mbutthehighestconcentrationofspectralpeaks associatedtothemisaround200 m. Althoughthemorphologyishighlydynamic,itsmaincharacteristicsarepersistentintimeatleastforthelast70 years.Itisimportanttobearinmindthatthelackofsystematicexperimentalinformationhasnotyetalloweda detailedquantitativemodellingofthedevelopmentofthemorphologyduringthepertinentobservedmeteorologicalandhydrodynamicconditions.Despiteofit,wehaveusedthe2DHmorfo55andtheone-linelinearstability1D-morfo modelstoshowthatboththetransversebars/megacuspsandthelargescaleshorelineundulationscouldbeoriginatedbythewave-drivenalongshorecurrentduringthestrongSWbreezes.Thus,ourmodelresultssuggestthatthe primarycauseoftheobservedmorphologicalsystemisthefeedbacksbetweeni)wavesandcurrentsandii)morphology,throughsedimenttransportduringSWwindevents.Althoughtheinfluenceofotherweatherconditions,in particularNWorNEwind,couldbeimportantwethinkitisnotessentialforthegenesisofthemorphologyandisleftforfutureresearch.NotwithstandingthatourhypothesisthatthemaindriverisSWwindeventsseemshighly plausible,manyaspectsdeservefurtherattention.Fromthemodellingside,theroleofNWwindeventsandthewindforcingonthecurrentshouldbeinvestigated.Fromtheobservationalside,thestateofthebarsystemshouldbe monitoredatleastduringoneyeartoseewhetherbarsaremoreprominentinsummerorinwinter,andtoseekforpossiblecorrelationwithmeteorologicalevents,inparticularwithprevailingSWwinds.Also,directmeasurementof wavesandcurrentsatthesitewouldbehighlydesirableasapreviousstepofamorespecificmorphodynamicmodelling.Otherfutureworkswillbeaddressedtoevaluatethesignificanceoftheresultsatmethodologicalstepssuchas thecoastlineprofilingortheFourieranalysis. Uncitedreferences Calveteetal.,2001 Hallermeier,1978 Acknowledgements ThisresearchispartoftheSpanishGovernmentprojectCTM2015-63166225-C2-1-P(MINECO/FEDER).TheauthorswanttogratefullyacknowledgeDr.J.Guillénforprovidingbathymetricdataonthecrossshore beach profile at El Trabucador, Dr. R. Garnier for his support for the morfo55 runs and Dr. Cerralbo for providing numerical mesh information. The first author’'s funding comes from the research group LIM/UPC. References AshtonA.,MurrayA.B.andArnaultO.,Formationofcoastlinefeaturesbylarge-scaleinstabilitiesinducedbyhigh-anglewaves, Nature 414,2001,296–300. BartlettM.S.,Smoothingperiodogramsfromtimeserieswithcontinuousspectra, Nature 161,1948,686–687. 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