Linking sea level dynamic and exceptional events to large-scale atmospheric circulation variability: A case of the Seine Bay, France

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Linking sea level dynamic and exceptional events to

large-scale atmospheric circulation variability: A case of

the Seine Bay, France

Imen Turki, Nicolas Massei, Benoît Laignel

To cite this version:

Imen Turki, Nicolas Massei, Benoît Laignel. Linking sea level dynamic and exceptional events to

large-scale atmospheric circulation variability: A case of the Seine Bay, France. Oceanologia, Polish

Academy of Sciences, 2019, 61 (3), pp.321-333. �10.1016/j.oceano.2019.01.003�. �hal-02070404�

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ORIGINAL

RESEARCH

ARTICLE

Linking

sea

level

dynamic

and

exceptional

events

to

large-scale

atmospheric

circulation

variability:

A

case

of

the

Seine

Bay,

France

Imen

Turki

*

,

Nicolas

Massei,

Benoit

Laignel

ContinentalandCoastalMorphodynamicLaboratory,NormandyUniversity,Rouen,France Received16September2018;accepted15January2019

Availableonline1February2019

Oceanologia(2019)61,321_—330

KEYWORDS

Sealeveldynamic; Envelopeapproach; Demodulatedsurges; Stormevents; Climatepatterns

Summary Inthisstudy,themulti-time-scalevariabilityoftheSouthEnglishChannel(caseofthe SeineBay,NorthFrance)sealevelanditsexceptionaleventshavebeeninvestigatedinrelationwith theglobalclimatepatternsbytheuseofwaveletmulti-resolutiondecompositiontechniques.The analysishasbeenfocusedonsurgesdemodulatingbyanenvelope approach.The low-frequency componentsoftheinterannual(2.1-yr,4-yr,7.8-yr)andtheinterdecadal(15.6-yrand21.2-yr) time-scales,extractedfrom46-yearsdemodulatedsurges,havebeencorrelatedto36exceptionalstormy eventsaccordingtotheirintensity.Resultshaverevealedﬁvecategoriesofstormsfunctionontheir correlationwiththeinterannualandtheinterdecadaldemodulatedsurges:eventswithhighenergy aremanifestedatthefullscaleswhilemoderateeventsareonlyobservedattheinterannualscales. Thesuccessionofstormsismainlycarriedbythelastpositiveoscillationsoftheinterannualandthe interdecadal scales. A statistical downscaling approach integrating the discrete wavelet multi-resolutionanalysis foreachtime-scalehasbeenusedtoinvestigatetheconnectionbetweenthe localdynamicofsurgesandtheglobalatmosphericcirculationfromSLPcomposites.Thisrelation illustratesdipolarpatternsofhigh-lowpressuressuggestingpositiveanomaliesattheinterdecadal scalesof15.6-yrand21.3-yrandtheinterannualscalesof4-yrwhilenegativeanomaliesat7.8-yr should berelated to a series of physical mechanisms linked to the North-Atlantic and ocean/ atmospheric circulation oscillating at the same time-scales. The increasing storm frequency is probablyrelatedtotheGulfStreamvariationanditsweakeningtrendinthelastyears.

PeerreviewundertheresponsibilityofInstituteofOceanologyofthePolishAcademyofSciences.

* Correspondingauthorat:ContinentalandCoastalMorphodynamicLaboratory,NormandyUniversity,Rouen76821,France. Tel.+0033235146952;fax:+0033235140019.

E-mailaddresses:imen.turki@univ-rouen.fr(I.Turki),nicolas.massei@univ-rouen.fr(N.Massei),benoit.laignel@univ-rouen.fr(B.Laignel). Availableonlineatwww.sciencedirect.com

ScienceDirect

jo u rn al ho m e p age : w w w. jo ur na ls .e l se v i er.c o m / o ce an o lo g i a/

https://doi.org/10.1016/j.oceano.2019.01.003

0078-3234/©2019InstituteofOceanologyofthePolishAcademyofSciences.ProductionandhostingbyElsevierSp.zo.o.Thisisanopen accessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

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1. Introduction

During the last decades and in relation with the global evolution induced by climate change, the oceanographic scientificcommunityhavedevoted theireffortstoimprove ourunderstandingoftheimpactsofclimatefluctuationson coastalhydrodynamicvariability,inparticularduringstormy events.Severalapproacheshavebeenextensivelyemployed toinvestigatetheextremephysicaldynamicofthesealevel andsimulatetheimpactoftheglobalclimateoscillationsfor providing different coastal projections. For this reason, determininghowandtowhatextentthelarge-scaleclimate oscillations can be identified in the oceanographic para-metersandstormsurgesisrequired.

In thepresent contextof globalchanges,thecombined effectsofthesealevelriseandthelandlossarecommonly mentioned as a consequence of climate variability (e.g.,

Devoy, 2008; Nicholls et al., 2010). In the same context, thelandlossitselfisoftenaresultofanincreasingstorminess responsibleforcoastalerosion(Stiveetal.,2002)orﬂooding areaswhoserepeated restorationmight beinefﬁcient and thelandisabandoned.

The acceleration ofthesealevel risealong thecoastal mid-Atlanticinrecentdecades,wheretheclimateisstrongly influencedbytheGulfStream(GS),ispossiblycausedbythe AtlanticMeridional OverturningCirculation (AMOC) andits upperbranch, the GS. Consequently, coastal communities haveobservedasignificantincreaseinfloodingfrequencyin thelastyears(Mitchelletal.,2013).

BythehypothesisthatthevariationintheGSlocationand strengthisresponsibleonchangesintheseasurfaceheight gradient across the GS and, consequently, the sea level variability on both sides of the stream, the elevation of theseasurfacegradientisproportionaltothesurface velo-cityoftheGS.Then,theweakeningoftheGSstrengthwill raisethesealevelnorthwestoftheGS;whichissuggestedby severalrecent studies (e.g., Ezer andCorlett, 2012; Ezer etal.,2013;Levermannetal.,2005;Sallengeretal.,2012). TheimpactoftheGSvariationoncoastalsealevelhasbeen demonstratedbymanyobservations(Sweetetal.,2009)and circulationsmodels(Ezer,2001)oftheAtlanticOceansand, also,byGlobalClimatemodels(Yinetal.,2009).

Theeffectsofcontinuouschangesinatmosphericpatterns onsealeveldynamicandstormyeventshavebeen investi-gatedthroughaseriesofprobabilisticapproachesbasedonof climate indices by the use of nonstationary analyses of extremes(e.g.Minguez etal.,2012).Marcosetal.(2012)

have related changes in the median and the higher-order percentilesof observedwaterlevels in theMediterranean Sea by the large-scale atmospheric circulation of winter North Atlantic Oscillation (NAO). Moreover, Menendez and Woodworth (2010) have demonstrated that changes in extremeeventsareduetochangesinmeansealevels;they havereportedtheimportantroleoftheNAOandtheArctic Oscillation(AO)indicesontheextremesealevelvariability alongtheEuropeancoasts.Then,Masinaetal.(2015)have showna similarbehavior betweenthe regional andglobal scales at Venice and Porto Corsini (Adriatic Sea) from a detailed analysis of the annual mean sealevel evolution. Theyhaveevidencedarelationbetweenincreasingextreme waterlevelssincethe1990sandchangesinwindregime,in

particular, the intensiﬁcation of Bora and Sirocco winds eventswhoseintensityandfrequencyhavebeen increased afterthesecondhalfofthe20thcentury.

One of the challenges in investigating the sea level dynamicwithglobalpatternsrelatedtoClimatecirculation ishowtoidentifythemulti-scalevariabilityassociatedwith thedifferentphysicalprocessesinvolved.

Intheframeworkofthefurtheraltimetrymissionof Sur-face Water and Ocean Topography (SWOT), planned for launch in 2021, Turki et al. (2015) have investigated the low-frequencies of the sea levelvariability in the eastern English Channel (NW France) at annual andinter-monthly scales. Such changes result from the combining effect of meteorologicalandoceanographyforceswithanimportant contributionofthehydrologicalsignalcomingfromtheSeine river; theclimate signature of the NAO circulation isalso observed at the annual scales. Massei et al. (2017) have focusedontherelationofthelocalSeinehydrological varia-bilitywith theglobalclimatepatterns,andthetime-scale dependenceofthisconnectionbydevelopingadownscaling modelingbasingonanempiricalstatisticalapproach.Their workshaveshownthatthemulti-scalelinksbetweenthesea levelpressure(SLP)andtheregionalhydrologicalvariations are statistically signiﬁcant for frequencies greater than 2years (3.2-yr,7.2-yrand19.3-yr); theyshould becaused bycouplingeffectsofNorth-Atlanticoceanicpathsand atmo-sphericcirculation.

Inthiscontext,thepresentresearchhasbeencarriedout toinvestigatethemulti-time-scalevariabilityofthesealevel intheSeineBay(SouthEnglishChannel)anditsexceptional eventsinrelationwiththeglobalclimatepatternsbytheuse of high-resolution spectral techniques. A special focus is devotedtotheconnectionofstormyeventsandtheir occur-rencewiththeatmosphericcirculation.Thepaper is orga-nizedas follow.Aftertheintroduction, thesecondsection presents the data andthe methodological approach used. Section3 providesall resultsanddiscussionsofthe multi-scale sea level variability in relation to the exceptional eventsandtheteleconnectionsoftheatmospheric circula-tion. Finally, some concluding remarks and further researchesarepresentedinSection4.

2. Data

and

methodological

approach

2.1. Sealevelandclimatologicaldata set

Hourlysealevelmeasurements,extractedfromLeHavretide gaugebetween1964and2010,havebeen providedbythe NationalNavyHydrographicService(http://refmar.shom.fr/ en/home); see Fig. 1. Climatological data in the North AtlanticzonehavebeenextractedfromtheNationalCenter forEnvironmentalPredictionandNationalCenterfor Atmo-sphericResearch-1(NCEP/NCAR-1)reanalysis(Kalnayetal., 1996)withatimeresolutionofamonth.Thisdataset repre-sents the North Atlantic atmospheric dynamics over the North Atlantic region (758W—358E and 158E—758N) with a horizontal spatial resolution of 2.5*2.5 (i.e., 1125 grid-points). As suggested by previous researches, SLP ﬁeld is consideredasagood indicatorfor thelocalhydro-climatic conditions (e.g., Massei et al., 2017; Ruigar and Golian, 2015);ithasbeenusedinthepresentanalysis andwillbe

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referred to “large scale” in the subsequent parts of the analysiswhilelocalscale”referstothesealevel.

2.2. Tidalmodulationandresidual sealevel

Thetotalsealevelheight,resultingfromtheastronomical andthemeteorologicalprocesses,exhibitsatemporal non-stationarityexplainedbythecombiningeffectsofthe long-term trend in the meansea level, the modulation by the deterministic tidal component andthestochasticsignal of surges,andtheinteractionsbetweentidesandsurges.The occurrenceofextremesealevelsiscontrolledbyperiodsof highastronomically generatedtides, inparticularat inter-annual scales when two phenomena of precession cause systematicvariationofhightides.Themodulationof tides contributestotheenhancedriskofcoastalﬂooding.

Theseparationbetweentidalandnon-tidalsignals isan important taskin anyanalysisof sealevel timeseries.The stochasticcomponentassociatedwiththenon-tidalvariation in the Seine Bay, extracted from Le Havre tide gauge, is mainlyexplainedbythemeteorologicalandthehydrological effects of the Seine river reaching the bay during ﬂood events. By the hypothesis of independence between the astronomicalandthestochasticeffects,thenon-linear rela-tionship between both components is not considered to separatethetidalmodulationfromthetotalsealevel.

Usingtheclassicalharmonicanalysis,thetidalcomponent hasbeenmodeledasthesumofaﬁnitesetofsinusoidsat

specific frequencies to determine the determinist phase/ amplitude of each sinusoid and predict the astronomical componentoftides.Inordertoobtainaquantitative assess-ment of thenon-tidal contribution in storminess changes, technical methods basing on MATLAB t-tide package have beenusedto estimateyear-by-teartidal constituents.The sea level measurements present strong tidal modulations whichhavelongbeenrecognizedbytheirsignificanteffects onlong-termchanges (e.g.,Gratiotetal.,2008);in parti-cular,thoseproducedatinter-annualscales.Theseprocesses resultfrom18.61-yearlunarnodalcycleandthe8.85-year cycleoflunarperigeeandinfluencethesealevelasaquasi 4.4-year cycle (Menendez and Woodworth, 2010; Wood, 2001;WoodworthandBlackman,2004).

Ayear-by-yeartidalsimulation(ShawandTsimplis,2010) hasbeenappliedtothesealeveltimeseriestodeterminethe amplitudeandthephaseoftidalmodulationsusingharmonic analysisﬁttedto18.61,9.305,8.85,and4.425-year sinusoi-dalsignals(Pugh,1987).

2.3. Demodulatedsurgesbytheuseofenvelope technique

Oncetheannualsealeveltrend andthetidalcomponents have been removed, the residual signal has been used as 'surges' to be demodulated by an envelope approach, a preliminary step before the frequency decomposition by themulti-resolutionwavelet.

Figure1 Studyarea:theSeineBaylocatedinthesouth-easternEnglishChannel(NWFrance).

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Determiningenvelopesofastatisticalsignalisgenerally usedfordetectingtheamplitudemodulation.Inthepresent research,theobjectiveistodetectifany(andwhat) under-lyinglow-frequencycomponentcontrolsthevariationsofthe sealevelsignalamplitude.Themostknownenvelopeisthe analyticonebasedontheHilberttransform.Howeverandin practice, calculating envelopes of real signals in environ-mental contexts is different from analytic ones, although these uniquely define envelopes (Yang, 2017). The most methods for envelope identification depend on extrema detection followed by a low-pass filter. The envelopes of real signals are obtainedusing a splineinterpolation from extrema sequences, as used for instance in the empirical modedecomposition(EMD)(MasseiandFournier,2012; Mas-seietal.,2017).Here,thepresentworkismoreparticularly interestedinhighsurgeswithextremevaluesfrom consider-ingonlytheupperenvelopeofareal-valuedsurgesignalby identifyingallthelocalmaximaandinterpolatingbetween themusingacubicspline.

2.4. Atmospheric compositemaps

Therelationshipbetweenthelocalsealevelvariabilityand the global atmospheric patterns has been investigated to identifythephysicallinksatdifferenttime-scalesbytheuse of the Sea Level Pressure (SLP) ﬁeld. The procedure for investigating thisglobal/local scale connection consists in decomposingboththeSLPﬁeldandthesurgesignalacross thedifferenttime-scalesintoaseriesofwaveletdetails(WD) usingamultiresolutionanalysis.

Then, for each wavelet time-scale, an associated SLP composite map is constructed by: (1) calculating the

point-wise(i.e.ateachgrid-point)positivetemporalmean of the SLP field WD at this scale for high values of the correspondingsurgeWD, (2)similarly,calculate the point-wisenegativetemporalmeanofSLPfieldWDforlowvaluesof surgeWD,(3)computingthedifferencepositive mean-nega-tivemeanSLPvalueateachgridpoint(Masseietal.,2017). Here, “high”and “low”values ofsea levelWD have been chosensuchastheyexceed+0.5orfallbelow 0.5standard deviation (SD). Statistically significant regions have been estimated for each wavelet scale from the highest to the lowest frequencies; the degrees of freedom has been adjustedaccordingtothewaveletscaleandthe“effective” sample size N from the actual sample size N has been calculatedaccordingtothefirstorderautocorrelation coef-ficientAR[1]ofeachofthetwopositiveandnegativemean SLPWD(Mitchelletal.,1966).

3. Results

and

discussions

3.1. Sealeveldynamicandexceptionaleventsin theSeineBay

ThesealevelvariabilityintheSeineBay hasbeen investi-gatedfromthe46-yearrecord.Oncethetidalcomponents andtheregressivetrendofthesealevelrisewereremoved, thesignalofsurgeshasbeen demodulatedbyan envelope approach;then,theupperenvelopehasbeencalculatedby joininglocalextremaandusingasplinefunction(Fig.2a).

Taking the Fourier transform of the original and the demodulated surges, the spectrumsSS andSSM have been simulatedinFig.2bwiththeaimtoillustratethedifferent frequencycomponentscharacterizingeachsignal.

Compar-Figure2 (a)Themaximaenvelope(thickline)ofthemeanmonthlysurges(thinline)between1961and2010;(b)spectrumofthe originalSS,demodulatedSSMsurges,andthedifferenceSS SSM.

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ing both spectrums showsthat the interpolative envelope containsthemessagesignaloftheoriginalsurges:similarities ofthemaincomponentswiththemostvibrationofthe high-frequencycomponentsintheoriginalsignalvsaclear illus-tration of low-frequency components in the demodulated signal.Hence,thesimulatedupperenvelopecanbeusedto modulatethemaininformationofnonstationarysurges.

Theinterpolativeenvelope,usedfor demodulating non-stationarysurges,containsthelowerchirpsignalcomponent with the fault characteristic frequency and its harmonic interferences. The demodulated surges cover a series of frequencieswithdifferenttime-periodsabletoreconstruct themostvariabilityoftheoriginalsignal.Thisresultconﬁrms thelast investigationsreported byYang (2017); theyhave concludedthattheenvelopes ofreal-valuedstationaryand nonstationary signals contain some low-frequency compo-nentsoftheoriginalsignalandsomenewcomponents gen-eratedbythenew-Nyquistextremasampling.

Fig. 3 displaysthe continuous wavelet spectrum of the totalsealevel(a),surges(b)andthedemodulatedsurges(c). Theﬁrstspectrum(Fig.3a)showsthatmostoftheenergyis homogenouslylocatedaround1-yrwithmorethan90%ofthe totalvariance.Byremoving theastronomicalcomponents, the signal of surges reveals the existence of frequencies lower than 1-yr, differently distributed at 2-yr and 4-yr scales; it illustrates a non-homogenous repartition during the period 1964—2010 (Fig. 3b) with two peaksof energy inbothperiods1970—1980and2000—2001.The2-yrand4-yr frequenciesare evenmorepronounced inthespectrum of the demodulated surges where the interannual and the interdecadal frequencies of 8-yr and 15-yr, respectively, are clearly structuredwith ahighconcentration ofenergy (Fig.3c).

Amultiresolutionanalysishasbeenappliedtothe demo-dulatedsurgeswiththeaimtoextractthedifferent compo-nents explainingthe totalvariabilityof theenvelope.The processhasresultedintheseparationof9components,the so-calledwaveletdetailsnumberedfromD1toD9.

Thedifferentwaveletdetailshavebeenassociatedtothe followingtime-scales:intermonthly(D1,D2andD3),annual (D4),interannual(D5,D6andD7)andinterdecadal(D8and D9) scales. The most part of these frequencies has been illustrated as peaks of energy in the continuous wavelet spectrum(Fig.3c).

Thefocusofthepresentresearchistoinvestigatethekey roleofthelow-frequencycomponents(higherthan2-yr)with ameanexplainingvarianceof82.7%from thetotal demo-dulatedsignal(Table1):2.1-yr,4-yr, 7.8-yr,15.6-yr and21.3-yr.Thisdistributionofvariancebetween2-yrand 21-yrimpliestheimportanceofthelarge-scalevariabilityin surgesoftheSeineBay.

Similarscales,reportedbyMasseietal.(2017)fromSeine watershed precipitations, have only presented a mean explained variance of 30% showing a low contribution of thelarge-scalesinthetotalenergyofthesignaland high-lightingthe eventualweak dependencebetween high and lowfrequencies.Inthecaseofhighdiscrepanciesbetween thedifferentfrequenciescomposingsomestatisticalsignals andwiththeaimtoextracttheirlow-frequencycomponents, demodulating their evolution by the use of the envelope techniqueshouldbeausefulwaytoinvestigatemoredeeply theirlarge-scalebehavior.

Atotalof36exceptionalstormyevents(fromE1to E36) producedintheSeinebayduringtheperiod1964—2010and with surges higherthan 2-yr return period level has been extractedfrom REFMARdatabase(Table2).The different stormshavebeenreportedtothelow-frequencycomponents ofthedemodulatedsurgesbyverticalcolorbars(Fig.4).

Fivecategorieshavebeendeﬁnedandattributedtothe differentstormsaccordingtotheirsurgereturnperiod(Re): “A” with Re=2-yr, “B” 2-yr <Re<5-yr, “C” with 5-yr <Re<10-yr, “D” with 10-yr <Re<20-yr and “E” with Re>20-y using gray, yellow, red, purple and dark purple colors,respectively.The closingeventssucceeding intime withina givenperiod (days to months)are represented in

Fig.4byonlyoneverticalbarwhosecolorisattributedtothe highercategoryofstormsproducedduringthisperiod.

Theﬁrsttwocategoriesofstormswithamoderatesurge returnperiodarerelatedto higherfrequenciesandcanbe observedatscalessmallerthan4-yr.Forexample,stormy eventsE8,E16 andE17-19 ofthe category “A”(gray box in

Fig.4)aremainlymanifestedat2.1-yrandseemtobenot expressed at higher scales. E3-7, E9-10 and E32-34 of the category “B” (yellow box in Fig. 4) are well observed at theinterannualscales2.1-yrand4-yr.The eventsE1, E11, E20-21,E35andE36ofthecategory“C”(redboxinFig.4)are manifestedat thethree scales2.1-yr,4-yrand7.8-yr.The category“E”,E13,E28-29andE30-31(darkpurpleboxinFig.4),

Figure3 Continuouswaveletdiagramofthemonthlymeansealevel:(a)thetotalsealevel,(b)thesurgesand(c)thedemodulated surges(maximaenvelope)between1964and2010.

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is fully manifested at the different time-scales while E2, E14-15andE23-27ofthecategory“D”(purple boxin Fig.4) passawaythelowestfrequencyof21.1-yr.

Accordingtothisanalysis,36highstormyevents(Re> 2-yr)havebeenidentiﬁedduringaperiodof46years;theyare ofdifferentcategoriesdependingonthesurgereturnperiod and the time-scale associated with the spectral period: 19eventsofcategory“A”with2.1-yr,6eventsofcategory “B”with4-yr,5eventsofcategory“C”with7.8-yr,3events

of each category “D” and “E” with 15.6-yr and 21.3-yr, respectively.

Thedistributionofstormsisnothomogeneousintimeand theiroccurrenceaccordingtothedifferentcategoriestakes a nonstationary behaviorsince thenumber of events in a windowofone-yearchangesintime.Resultshaveshownthat 24 among 46 years do not display any signiﬁcant event (Re>2-yr) emphasizing alternating phases of moderate energyandstorminess.Moderatephaseswithnon-signiﬁcant

Table1 EquivalentFourierperiod,standarddeviationandenergy,expressedasthepercentageoftotalstandarddeviationofthe maximaenvelope,associatedwitheachcomponent(i.e.waveletdetailsandsmooth)ofSeinesurgesbetween1964and2010.

Surges D1—D4 D5 D6 D7 D8 D9 Total

Fourierperiod(yr) 1 2.1 4 7.8 15.6 21.3 — Standarddeviation(m) 0.01 0.009 0.005 0.0035 0.003 0.005 _—

Energy(%) 17.3 32 26 11 8 5.7 100

Table2 Listofstormyeventsproducedbetween1964and2010;onlystormswithsurgereturnperiod(Re)higherthan2years. Numberofevent Dateofevent Returnperiodofsurges(Re) Tidalcycle

E1 20January1965 5—10years Springtide(coefﬁcient102)

E2 27November1965 10—20years Neaptide(coefﬁcient68)

E3 11March1967 2years Neaptide(coefﬁcient86)

E4 04October1967 2—5years Springtide(coefﬁcient113)

E5 13November1967 2years Neaptide(coefﬁcient63)

E6 02November1967 2—5years Springtide(coefﬁcient111)

E7 07January1968 2years Neaptide(coefﬁcient50)

E8 06July1969 2years Neaptide(coefﬁcient67)

E9 06February1974 2years Springtide(coefﬁcient)

E10 09February1974 2—5years Springtide(coefﬁcient112)

E11 25December1976 2—5years Neaptide(coefﬁcient70)

E12 15December1979 2years Neaptide(coefﬁcient66)

E13 13December1981 >20years Springtide(coefﬁcient104)

E14 25October1984 2years Springtide(coefﬁcient100)

E15 22November1984 10—20years Springtide(coefﬁcient102)

E16 15October1987 2years Neaptide(coefﬁcient28)

E18 03January1990 2years Springtide(coefﬁcient103)

E19 26February1990 2years Springtide(coefﬁcient106)

E20 20January1994 2—5years Neaptide(coefﬁcient50)

E21 15April1994 5—10years Springtide(coefﬁcient100)

E23 25December1999 10—20years Springtide(coefﬁcient104)

E24 22January2000 5—10years Springtide(coefﬁcient106)

E25 08February2000 2years Neaptide(coefﬁcient88)

E26 04April2000 2years Springtide(coefﬁcient98)

E27 02September2000 2years Springtide(coefﬁcient94)

E28 10October2000 >20years Springtide(coefﬁcient101)

E29 29October2000 2years Springtide(coefﬁcient95)

E30 17September2001 >20years Springtide(coefﬁcient115)

E34 08April2005 2—5years Springtide(coefﬁcient104)

E35 11March2008 5—10years Springtide(coefﬁcient106)

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stormsarelongerwith3—4successiveyearsduringtheﬁrst 35years(1964—2000)anddecreaseto2yearsinthe begin-ningofthelastdecadewhenthesuccessionofeventsseems tobemoreimportant.Stormyphasesdisplaydifferent cate-goriesofeventsmainlydistributedbetweenNovemberand Februarywithonly11%ofstormsobservedinOctober.Some eventsforeachofSeptember(2000,2001),April(1994and 2000) and March (1967 and 2008), July (1967) have been associatedwiththecategory“A”.

Thisconnectionbetweenthelow-frequencycomponents andthehistoricalrecordoftheexceptionaleventssuggests thatstormswouldoccurdifferentlyaccordingtoaseriesof physical processes oscillating at multi-time-scales; these processescontroltheirfrequencyandtheirintensity.

Theseasonaldependencebetweenstormyeventsandthe extremesealevels,alreadyobservedinpreviousworks(e.g.,

TsimplisandWoodworth,1994),is mainlycausedby astro-nomicalforcesofspringtidesandmeteorologicalconditions ofseasonalstorms.Thisdependenceexplainsthedistribution ofstorms andtheirorganization intime; whichisstrongly relatedtothelarge-scalevariabilityofsurges.Forexample, thefourstormsof1967(E3toE6)andtheﬁvestormsof2000 (E25toE29)showaseasonaldependenceintheirsuccession, tidalphaseandintensity(returnperiod).

Thecombiningeffectoflocaldrivenforceswith meteor-ological,oceanographicandhydrologicaloriginsexplainsthe mostsignificantofthestochasticsignalofsurgesintheSeine Bay where the fluvial activity plays an important role in changesofwaterelevations.Thisactivityislargelyobserved duringfloodingperiods;anexampleisproducedinDecember 2001 (e.g., Massei and Fournier, 2012) when E31 of the categoryAhasoccurred.

The origin of physical processes responsible for storm surgesexhibitsatemporal nonstationarybehaviordueto a

combinationbetweentheseasonal,theinterannualandthe interdecadal variability, and a non-linear interaction betweenthe different time-scales.The assessment ofthe nonstationary effect on the estimation of extreme surges should be largely considered in the methods of extreme analysisbytheuseofthenonstationarymodels.Forexample, atime-dependent GeneralizedExtremeValue(GEV) distri-butionhasbeenusedbyMasinaandLamberti(2013)tomodel thenonstationaryfeaturescontained inthesealeveltime series by introducing the seasonality effect of GEV para-meters(location,scaleandshape) inorder toimprovethe ﬁttingofextremevaluesandreducetheuncertaintyonthe estimationofthereturnlevels.

3.2. Relationshipbetweenstormsurgedynamics andtheatmosphericpatterns

Thissectionisfocusedontheconnectionbetweenthelocal large-scale variability of surges and the global climate changesinducedbytheatmosphericcirculation.

Theclimate patterns, extensively studiedover the last two decades, have been mainly described by the NAO mechanisms(e.g.Hurrelletal.,2003).TheSLPﬁelds cover-ingtheEnglishChannel,between1964and2010,havebeen used with their different structures to characterize the climatepatterns fromthe waveletmultiresolution decom-positionintodifferenttime-scales.

FivecompositemapshavebeencalculatedfromtheSLP ﬁeldandthelarge-scalecomponentsofdemodulatedsurges (Fig.5).Providedmapsarefocusedonlyonlowfrequencies rangingbetween2.1-yr(D5)and21.3-yr(D9)whose ﬂuctua-tions correspond to oscillations periods less than half the lengthofthetimeseries,andwiththehigh-energy contribu-tiononthevarianceofthetotalsignal.Assuggestedbythese

Figure4 Multiresolutiondecompositionofthemonthlysurges,usingtheso-called,redundant,maximum-overlapdiscretewavelet transform.Waveletdetailatscaleshigherthan1year:2.1-yr,4-yr,7.8-yr,15.6-yrand21.3-yr.The36exceptionalstormyeventswith differentcategoriesfunctionoftheirreturnperiod(Re),occurredduringtheperiod1964—2010,areillustratedbycoloredboxes:“A” (grayline)Re=2-yr,_“B”(yellowline)2-yr_<Re_<5-yr,_“C”(redline)5-yr_<Re_<10-yr,_“D”(purpleline)10-yr_<Re_<20-yrand_“E” (darkpurpleline)>20-yr.

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compositemaps,therelationshipbetweenthedemodulated surgesandtheSLPfieldsisstatisticallysignificantandvaries spatiallyinmagnitudeandphase.Thespatialextentandthe locationofhigh-lowpressureregionsdisplayedbythe atmo-sphericpatternsare organizeddifferentlyaccordingtothe time-scalesofvariability.Both2.1-yrand7.8-yrtime-scales haveshowndipolarstructureswithhigh-pressureanomalies locatedoverthenorthernNorthAtlantic/sub-Arcticregions andlow-pressureanomaliesacrosstheAtlantic(2.1-yr time-scale)anddeveloping towardthe English Channelandthe NorthSea(7.8-yrtime-scale).Suchdipolarstructurescanbe associatedwiththetypicalwesterncirculation,reminiscent ofthenegativeNAOregime,moreparticularlyforthe7.8-yr time-scale. This distribution should be attributed to the cyclonic circulation over northwesternEurope (508N) with analternatingincreaseanddecreaseofWestmoisturefluxes fromtheAtlanticOceantothesouthernsideoftheEnglish ChannelandtheSeineBay.

Onthecontrary,4-yr(D6),15.6-yr(D8)and21.3-yr(D9) time-scaleshavepointedNorth-Southstructuresthatcould not be related to western circulation. Trough-shaped SLP anomaliesin thecenter ofthe North-Atlantic basin would suggestweakenedwesterncirculationdynamicsthatwould notbepreeminentatthesetime-scales.Intheiranalysisof multi-time-scalehydroclimatedynamicsovertheSeineriver watersheds in Northern France, Massei et al. (2017) have foundsimilar patternshapesof SLPcomposites calculated fromtheSeinerainfallatthesametime-scales.

Similarlow-frequencyoscillationshavealsobeenoutlined byFeliksetal.,2011inrelation withNAO patternsofthe simulatedmarineatmosphericboundarylayer(MABL)forced withSSTfromasimpleOceanDataAnalysis.Suchrelationsto

NAOindexhavebeenalsoobservedbyTurkietal.(2015)from thesealevelﬂuctuationsforscalesbetween1-yrand3-yr, whiletheoriginofhigherfrequencies,smallerthan1-yr,is relatedtotheseasonalcycleofalternatinghigh-lowenergy andchangesinriverdischargesandtemperature.

Thedifferenttime-scalesofthelocalvariabilityofsurges is not linearly related to the atmospheric circulation pro-cessessincetheirspatialextent,highlightedbythe wavelet-based composite analysis, seems to be not fully similar accordingtothedifferentscalesofthehydro-climatic varia-bility;eachtime-scaleisassociatedwithadetermined phy-sicalmechanismexplainingtheoscillationperiodofchanges. The “switch on” and “off” of the inﬂuence of climate patterns on the variability of surges have an important application for many predictability issues. In this way, if SLPstructuresandsurgesanomaliesareofsimilarpatterns, theuseofsurgesforpredictingitsvariabilityfromtheSLP patternsatdifferenttime-scalescouldincreasetheaccuracy ofstatisticalpredictions. At these scales,theatmospheric teleconnectionsexplainedbyaseriesofphysicalmechanisms showanonstationarybehaviorwithafocusinthestochastic variabilityofsurges.

This behavior is still under debate (Martin-Rey et al., 2012;Poloetal.,2008;Rodriguez-Fonsecaetal.,2009).

Accordingtotheirworksrelatedtothenonstationarities oftheAtlanticinﬂuenceonthePaciﬁcinthe20thcentury,

Lopez-paragesetal.(2013)haveshownthatthestatistical predictabilityoftherainfallvariabilitycanbeimprovedby selecting the most suitable predictors depending on the period onwhichthe predictionis carried out. They have alsosuggestedthatthenonstationarylinkbetweenrainfall andSSTtakesplacewhenthedipolarpatternsofrainfallis

Figure5 Composite mapsof SLP generated for eachscalebasedonsurge variability.Black dashed linesindicatestatistically signiﬁcantregions(Studentt-testwitha95%conﬁdencelimit).

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reinforcedandcoincideswithnegativephasesoftheAMO (Atlantic Multidecadal Oscillation) index along the 20th century.

Hence,theresultsobtainedherepointoutanonstationary behavioroftheteleconnectionsbetweenthelocalsurgesand theglobalSLPﬁeld,inparticularfortheinterannual oscilla-tions modulated by the interdecadal scales. The physical coherent modulation at a multi-scale variability is mainly relatedto theatmospheric circulationinﬂuencedgenerally byoceancurrentsandtheGulfStream(GS).Severalquestions behind the reasons for this nonstationary teleconnections remainopen,astheoriginofthemodulatingfactors.

In fact, the sea levelpressure (SLP) and the baroclinic instabilityofwindstressarerelatedtotheGSpathasgivenby NCEPreanalysis.Infact,thedominantsignalisanorthward (southward)displacementofthe GSafter theNAOreaches positive(negative)extrema(Frankignouletal.,2001).

Inthepresentcontextofglobalchanges,theunderlying issueofrisingsealevelsiscombinedtomorestormyevents andextremes.Theincreasingtrendofstormyeventsinthe SeineBay,probablyinducedbythesealevelrisescenariosof theEnglishChannel,shouldbehighlycorrelatedwithlarge variationsintheGStransport(Ezeretal.,2013).The hypoth-esisoftheGStransportreductionresultinginslowersurface geostrophic currents,smallergradients acrosstheGS, and highervariationsinthecoastalsealevelinthenorthGShas beensupportedbyglobalclimatemodelsandsatellite obser-vations.Ezeretal.(2013)havedemonstratedastrong rela-tion between the coastal sea level changes and the GS variationsontime-scalesrangingfromafewmonthstomany decadeswithanincreasingexplainedvariance.Theshiftof the GS from 6—8 year oscillation cycle to a continuous weakeningtrendsincethebeginningthelastcentury;which correspondstotheperiodofchangesinstormorganization andanincreaseintheirfrequencyintime.

4. Conclusions

Thisresearch isfocusedon investigatingthenonstationary dynamic of surges in the Seine Bay (southern side of the English Channel,NWFrance)andits nonlinearrelationship withtheglobalatmosphericcirculationbasingonaspectral approachofwaveletmulti-resolutiondecomposition.Bythe useanew techniqueofenvelope fordemodulatingsurges, thelarge-scalevariabilityhasbeenquantiﬁedduring46years (1964—2010).A total of36 exceptional stormyevents has beenreportedtotheinterannual(2.1-yr,4-yrand7.8-yr)and interdecadal (15.6-yr and 21.3-yr) time-scales of surges. Results have suggested a strong connection between the categories of storms, their intensity (return period 'Re') andtheirorganizationintimewiththelarge-scalevariability ofsurges.Infact,theinterannualscalesof15.6-yrand 21.3-yrhave been linked to stormyevents with Rehigherthan 10years;stormswithReof2yearsareonlymanifestedat 2.1-yrscales,whileeventswithRebetween2and10yearshave beenreportedto4-yrand7.8-yrscales.Dipolarpatternsof high-lowpressureshavebeendetectedat2.1-yrand7.8-yr scales and should be related to the western circulation havinganimpactontheseasurgemaxima,whilethe varia-bilityof4-yr, 15.6-yrand21.3-yrshouldobeytodifferent mechanismsrelatedtothepronouncedNorth-South

circula-tionprocessesandNAO,asinterpretedfromthedistribution ofSLPanomalies.

Thepresentinvestigationbringssomeinterestingresults about the nonstationary behavior the teleconnections betweenthelocalsurgesandtheglobalclimatecirculation atlarge-timescales.Bysimulating thelow-frequency com-ponentsofdemodulatedsurgesandSLPﬁelds,resultshave highlightedtheimportantroleoftheinterdecadal frequen-cies in the modulation of interannual variability. Deeper investigationsrelatedtothephysicalmechanisms responsi-bleforthisnonstationarydynamicarerequiredinorderto improve our understanding of the system climate-ocean changes.

Theconclusionofthisresearchsuggeststhatwind—stress variationsdrivenbyenergeticcurrentssuchas theGS may playakeyroleincoastal sealevelchanges. Establishinga strong connection between large-scale sea level changes withﬂooding risksandtheGSgradients couldimprove our understandingof the relation between the global climate patternsandthelocalsealevelchanges;alsoallowustoinfer the future projections of sea level change and extreme events.

Thisﬁnding canrepresentastep forwardin the under-standingof theroleof thesealevel surgesand shouldbe useful to improve the downscaling models of sea surges, thereforeallowingabetterassessmentofﬂoodrisks.Further workswillbefocusedon developingthe large-scale/local-scalenonstationarymodelsbytheuseofdifferentlarge-scale variables related tothe atmospheric circulation.This may allowproposingtheimprovedstatisticaldownscalingmodels and exploring the capabilities of such models to produce forecastsoftheprobabilityofextremesealeveltrendsby consideringtheinterannualandtheinterdecadalvariability ofglobalclimatepatterns.

Acknowledgments

TheauthorsaregratefultoANRfundedproject“RICCOCHET” of French national program as well as the international projectCOTESTfundedbyCNES-TOSCA andrelated tothe future mission of Surface Water and Ocean Topography (SWOT). Authors thank also National Navy Hydrographic Service and National Center for Environmental Prediction for providing sea level and atmospheric data. Also, the authorsgreatlythankthereviewersandtheeditorsofthe journalOceanologiafortheirusefulsuggestions toimprove themanuscript.

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