Correlation between long-term marine temperature time series from the eastern and western English Channel: Scaling analysis using empirical mode decomposition

HAL Id: hal-01285576

https://hal.sorbonne-universite.fr/hal-01285576

Submitted on 9 Mar 2016

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

Distributed under a Creative Commons Attribution - NonCommercial - NoDerivatives| 4.0

International License

series from the eastern and western English Channel:

Scaling analysis using empirical mode decomposition

Jonathan Derot, François G Schmitt, Valérie Gentilhomme, Pascal Morin

To cite this version:

Jonathan Derot, François G Schmitt, Valérie Gentilhomme, Pascal Morin. Correlation between

long-term marine temperature time series from the eastern and western English Channel: Scaling analysis

using empirical mode decomposition. Comptes Rendus Géoscience, Elsevier Masson, 2016, 348 (5),

pp.343-349. �10.1016/j.crte.2015.12.001�. �hal-01285576�

External

Geophysics,

Climate

Correlation

between

long-term

marine

temperature

time

series

from

the

eastern

and

western

English

Channel:

Scaling

analysis

using

empirical

mode

decomposition

Jonathan

Derot

,

Franc¸ois

Guillaume

Schmitt

*

,

Vale´rie

Gentilhomme

,

Pascal

Morin

a

UMRLOG8187,laboratoired’oce´anologieetdege´osciences,universite´ duLittoralCoˆted’Opale,32,avenueFoch,62930Wimereux,France

b

UMRLOG8187,CNRS,laboratoired’oce´anologieetdege´osciences,28,avenueFoch,62930Wimereux,France

c

UMRLOG8187,laboratoired’oce´anologieetdege´osciences,universite´ deLille-1,28,avenueFoch,62930Wimereux,France

d_{UMRAD2M7144,e´quipechimiemarine,stationbiologiquedeRoscoff,placeGeorges-Teissier,29680Roscoff,France}

e_{Sorbonneuniversite´s,UPMC,universite´ Paris06,UMR7144,adaptationetdiversite´ enmilieumarin,stationbiologiquedeRoscoff,29680}

Roscoff,France

1. Introduction

In recent years, there has beenan increasing global concerninprotectingthebiodiversityandwaterqualityof marineandcoastalwaters.Suchaconcernispresentfor exampleintwokeyEuropeanparliamentdirectives:the WaterFrameworkDirective(WFD,Directive2000/60/ECof 23 October 2000) and the Marine Strategy Framework Directive(MFSD,Directive2008/56/ECof17 June2008). Thesehaveledtoagreaternumberofmarineprotected

areas,includingseas,oceans,andlakes,allwiththeaimof protectingnaturalorculturalresources.

IntheframeworkofsuchEuropeandirectives, moni-toringsystemsincoastalwatersisessentialincollecting information on physical, biogeochemical, and biological parameters.Manymonitoringprogramshavebeen instal-ledwithweeklyormonthlyon-sitesampling.Dueinpart to physical forcing, such as waves and turbulence, the marine environment is highly variable on smallertime scales.Consequently,severalautonomousandautomatic monitoringprogramshavebeeninstalledinrecentyears (Chang and Dickey, 2001; Chavez et al., 1997; Dickey, 1991; Dickeyet al., 1993; Dur et al., 2007; Nam et al., 2005). These operate typically at 10 to 30min time

ARTICLE INFO Articlehistory:

Received10December2015

Acceptedafterrevision11December2015 Availableonlinexxx

HandledbyDidierRoche

Keywords:

Temperaturedynamics Autonomousmonitoring EnglishChannel Cross-correlationanalysis

Timedependentintrinsiccorrelation method

Powerspectra

Empiricalmodedecomposition

ABSTRACT

High-frequencytemperaturefluctuationsrecordedintheEnglishChannelarecompared usingtwolong-termautonomousunderwatermonitoringstationsatlessthan20-min timeresolution.Measurementsweretakenfrom2005to2011fromtwosystems460km apartinthewesternandeasternpartsoftheEnglishChannel.Spectralanalysisreveals similarstatisticalbehaviors,withapproximate5/3spectraandseveralforcingfrequencies inrelationtotidalanddailycycles.Aco-spectrastudyrevealsatransitionscaleof11days. TheinfluenceofthisscaleisalsovisiblethoughTime-DependentIntrinsicCorrelation analysis(TDIC)–arecentlyintroducedcross-correlationanalysisbasedonEmpiricalmode decomposition. This helps to spatialize high-frequency temporal records at a fixed location.

ß2016TheAuthors.PublishedbyElsevierMassonSASonbehalfofAcade´miedessciences. ThisisanopenaccessarticleundertheCCBY-NC-NDlicense( http://creativecommon-s.org/licenses/by-nc-nd/4.0/).

* Correspondingauthor.

E-mailaddress:[email protected](F.G.Schmitt).

ContentslistsavailableatScienceDirect

Comptes

Rendus

Geoscience

w ww . sc i e nce d i re ct . co m

http://dx.doi.org/10.1016/j.crte.2015.12.001

1631-0713/ß2016TheAuthors.PublishedbyElsevierMassonSASonbehalfofAcade´miedessciences.ThisisanopenaccessarticleundertheCCBY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

resolution at fixed position, corresponding to Eulerian sampling. There is a factor of about 1000 between samplingat 20-min resolution and samplingeverytwo weeks. In the following, 20-min sampling resolution is referredtoas‘‘highfrequency’’.Therearesensorsableto measure physical or biogeochemical quantities at even higherfrequencies(Seurontetal.,1999),butsuchsystems havenotbeenoperatingautonomouslyforseveralyears. Herewefocusonthetemporalvariabilityof tempera-tureusingtwodatasetsrecordedatfixedlocationsalong theFrenchcoastalareaoftheEnglishChannel.Thefirstone isamooring,locatedinthewesternEnglishChannelinthe bayofMorlaix.Thesecondisanautomaticsystemcalled MARELCarnot,locatedintheeasternEnglishChannelat theexitoftheharborofBoulogne-sur-Mer.Inbothcases, the data from these automatic systems were recorded long-term(suchdenominationisusuallyusedforrecord periodslargerthanaboutfiveyears)usinganautomatic systemathighfrequency,withmorethanone measure-mentperhour.

High-frequency measurements at a fixed location correspondtoanEulerian samplingofa highly variable time-scale system. Sometimes such measurements are consideredlimitedduetothefactthattheyprovidealocal viewintime,wherespatialinformationislacking.Here,in order to have a view on the temporal and spatial link between two high-frequency measurement time series (recordedattwolocationsseparatedbyseveralhundred kilometers), weshallstudy thecorrelationbetween the two series. The study of the multiscale correlations betweenthesetimeserieswillprovideuswiththefirst hintataspatializationofatimeseriesatfixedlocations.In thiscontext,wewillconsidersevenyearsofdata,between 2005and2011,fortwodifferenttemperaturerecords.The

following section presents the characteristics of these automaticsystems,theirdatasets,andtheirclimatology. We then proceed with showing some spectral and co-spectralanalyses.Thelastsectionconsiderstime depen-dent intrinsiccorrelationanalysis ofboth time series–a new correlation method based on the empirical mode decompostion.

2. Datapresentationandclimatology 2.1. EstacadeatRoscoff

Thefirstofthetwostationsisconsideredhere,where measurementsoftemperatureweretakenatthecoastal siteofEstacade(48843.56N,3858.58W)locatedinthebay ofMorlaixinthewesternEnglishChannel(Fig.1),from 2005to2011.Inthis area,characterizedby strongtidal currentsandtidalamplitudeover6m,thewatercolumn remainscompletelymixedthroughouttheyear. Tempera-turewasmeasuredwithasamplingfrequencyof10min usingaSeabirdSBE39recorderinstalledonamooringat theseabottom(meanwaterdepth:5.8m).Thepercentage of available datafor this period is close to 97%, which correspondsto329,294datapointsacquired(Fig.2).The analytical precision of temperaturemeasurementsfrom theSeabirdSBE39sensoris0.018C;therawdataatthe outputofthissystemarepresentedinFig.2withagreen pattern.

2.2. MARELCarnotatBoulogne-sur-Mer

Thesecondtemperaturedatasetswererecordedbyan automaticsystemcalledMARELCarnot,whichissituated in the eastern EnglishChannelin the coastalwaters of

Fig.1.AmapshowingthemeasurementlocationinBoulogne-sur-Mer’scoastalwaters(France)atposition50844.42N,1834.06W,intheeasternEnglish Channel,andRoscoff(France)attheposition48843.56N,3858.58W,inthewesternEnglishChannel.

J.Derotetal./C.R.Geosciencexxx(2016)xxx–xxx 2

Boulogne-sur-Mer (France) at position 50844.42N, 1834.06W(Fig.1),withaperiodicityof20min(seeZongo et al. (2011) for a presentation of this data set).Water depth at this position varies between 5 and 11m; the measurementsaretakenusingafloatingsysteminserted inatube,1.5mbelowthesurface.Duetomaintenanceand failureoftheautomaticdevices,thereareseveralmissing data. We consider here data from 2005 to 2011. The percentageofavailabledataforthisperiodiscloseto88%, whichcorrespondsto138,574datapointsacquired(Fig.2). The MAREL Carnot station is included in the MAREL network (Automatic monitoring network for littoral environment, IFREMER, France), which is based on the deployment of moored buoys equipped with physico-chemical measuringdevices, workingin continuousand autonomous conditions (Berthome, 1994; Blain et al., 2004; Dur et al., 2007; Schmitt et al., 2008; Woerther, 1998;ZongoandSchmitt,2011).

2.3. Climatology

Weconsiderheretheclimatology,i.e.theaverage inter-annualvariations,estimatedbyaveragingthedataforeach calendarday.ThisisshowninFig.3forbothtemperature datasets,wherethedottedlinesrepresentupperandlower curvesbuiltusingthestandarddeviationestimatedover sixdifferentvalues(foragivencalendarday) correspond-ing tothesevenyears of thestudy. The climatologyof Roscoffshowsaclimatemoremaritimethanin Boulogne-sur-Mer,whichismorecontinentalwithwarmersummers andcolderwinters.Thereisaminimumofaround98Cand amaximumofaround168C,correspondingtoanannual meandeltaof78CforRoscoff,whileforBoulogne-sur-Mer itiscloseto128C,withamaximumofaround188Canda minimumofaround68C.Thetwocurvesarequitesmooth, showingaratherlimitedvariabilityaroundthisseasonal evolution. Thestandard deviationoftheclimatology, as

Fig.2. TemperatureMARELCarnot(Boulogne-sur-Mer)andRoscoffdataseriesbetween2005and2011.Verticallinesseparateeachyear.

Fig.3.TheclimatologyofbothMARELCarnotandRoscofftemperaturedata:inter-annualdailyaveragescomputedusingthedatafrom2005to2011.The dottedlinesrepresenttheupperandlowerlimitsestimatedusingtheirstandarddeviations;thelatterbeingestimatedoversevendifferentvalues, estimatedyearlyfrom2005to2011.Roscoffwatersaremoreinfluencedbyamaritimeclimate:wintersarewarmerandsummerscooler.

presentedinFig.3,ismoreimportantinthe Boulogne-sur-Merarea. Therefore,theinter-annualtemperature varia-tionsarelessmarkedintheRoscoffarea.

3. Spectralanalysesandco-spectra

We perform here spectral and co-spectral analyses. Fourierpowerspectrahavebeenusedinmanyprevious studies in aquatic sciences over several decades to characterize scaling regimes (Legendre and Legendre, 2012; PlattandDenman, 1975; Seurontet al., 1996a,b; Seuront et al., 1999; Seuront et al., 2002; Winder and Cloern,2010).Toperformco-spectralanalysis,asametime stepisneeded.Hence,forthisanalysis,alinear interpola-tionhasbeenperformedtodegradethetimestepto20min fortheRoscoffdataset.TwospectraareshowninFig.4,in log–logplot.Thespectraareclearly scaling,withslopes close to–5/3–as expected for passive scalar turbulence (Corrsin, 1951; Obukhov, 1949; Tennekes and Lumley, 1972).Therearetwopeakscloseto12hand1day,which areprobablyrelatedtotheimpactofdailyandtidalcycles. Thereareseveralslightpeaksathighfrequencies,anda largerpeakaround90 daysthatcouldberelatedtothe seasonalcycle.

3.1. Co-spectralanalyses

In order to compare the two dynamics at different scales, we have estimated the co-spectrum, defined as (BendatandPiersol,2000):

RT1;T2ðfÞ¼ ET1;T2ðfÞ     ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ET1ðfÞET2ðfÞ p (1)

whereEXY(f)istheco-spectrumofXandY.Whenthereisa

linearrelationbetweenXandY,RXYisequalto1,andfor

uncorrelatedprocessesRXY=0(BendatandPiersol,2000; Lumley,2007).Wefindthatthereisagoodcorrelationfor scaleslargerthan172days;thereisatransitionbetween 11 days and 172 days, and a decorrelation for smaller

scales(Fig.5).Theaverageresidualvelocityofthesurface currents(aftersubtractionoftidalcurrents)intheEnglish Channelwasmeasuredusingveryhighfrequencyradarsas beingbetween0.4and0.45m/s(SentchevandYaremchuk, 2007),andthedistancebetweenthetwostationsisaround 460km.Therefore,wecanassumeadecorrelationtimeof 460103_{/0.42512.5days.Thisisclosetothetransition}

scaleofabout11days,whichisfoundinFig.5.Hence,we maysay thathigh-frequency(scale<11 days) tempera-turefluctuationsareindependent,whereaslower frequen-ciesareconnected.

4. Time-dependentintrinsiccorrelationanalysis(TDIC) 4.1. TDICandEMD

We perform here a time–frequency analysis using Empirical Mode Decomposition (EMD),which was first introducedattheendofthe1990sinthefieldofphysical oceanography(Huangetal.,1998,1999).Ithassincebeen verysuccessfulwithapplicationsinmanyfieldsofscience, andhasreceivedseveralthousandcitations.Theaimofthis methodistodecomposeatime seriesina sumof time series called ‘‘modes’’, each having a characteristic frequency.Attheendofthedecomposition,themethod expressestheanalyzedsignalX(t)asasumofmodetime seriesCi(t)andaresidualr(t):

XðtÞ¼X

n

i¼1

CiðtÞþrðtÞ (2)

Themodeselectionisadaptive:thismeansthatthemode shapeCi(t)isnotdecidedapriori,butestimatedfromthe

datausinganalgorithmbasedonsuccessiveinterpolation passingthroughlocalmaxima.Theprecisealgorithmisnot repeatedhere.WerefertoHuangetal.(1998)orHuang etal.(2008,2009)fordetails.Anewcorrelationmethod, basedonEMD,hasrecentlybeenintroduced(Chenetal., 2010). The method uses EMD to decompose two time seriesintomodesC1,iandC2,i(i=1,...,n)andconsiderthe

Fig.4.FourierpowerspectraofBoulogne-sur-Mer(MARELCarnot)andRoscofftemperaturetimeseries,anda5/3slopestraightlineforcomparison, correspondingtopassivescalarturbulence.Somepeaksarevisible,correspondingmainlytoseasonal,daily,andtidalcycles.

J.Derotetal./C.R.Geosciencexxx(2016)xxx–xxx 4

correlationbetween them.The mainidea istoconsider thattheclassicalcorrelationimplicitlyassumes stationa-rityandlinearityofbothtimeseries.Theproposedmethod is thus a generalization. A local correlation is then estimatedbetweentwomodeshavingasimilar character-isticscale.Sincethemethodisdesignedtoworkalsofor non-stationary series, its estimation is made locally, as wellasglobally,forthewholeseries.TheEMDmethod, together with the Hilbert spectral analysis, is able to

extract,foreachmode,alocalfrequency.Eachmodehasa characteristic frequency, corresponding toa given time scaleTi.TherearethusthetimescalesT1,iandT2,iforthe

mode i of series No. 1 and No. 2. The correlation is estimatedoveralocalintervalcenteredaroundt:

ItwðtÞ ¼ t tw 2;tþ tw 2   (3)

Fig.5.Co-spectrainsemi-log(xaxis)plot,ofthetemperatureseriesinRoscoffandBoulogne-sur-Mer.Thereisagoodcorrelationforscaleslargerthan 172days,atransitionbetween172and11days,andarelativedecorrelationforscalessmallerthan11days.

Fig.6.Cross-correlationplotbetweenRoscoffandBoulogne-sur-Mertemperatureseries,usingtheTDICmethod,basedonempiricalmodedecomposition. Thecorrelationisdonehereformodeshavingsimilarscales.Thecross-correlationistimedependent(horizontalaxis),andestimatedoverintervalof increasingwidths(verticalaxis).Colorscalesemphasizestrongeventsofcorrelationoranti-correlation.

where tw is the width of the interval:

twtd¼maxT1;i;T2;i.Thelocalcorrelationwrites(Chen

etal.,2010): RtwðtÞ¼corr Iftwg  C1;iðtÞC2;iðtÞ   (4) wherecorristheusualcorrelationcoefficient,tistime,and corr{It} symbolizes a correlation estimated over the

intervalt2I.Thisisperformedforeachmodei:RtwðtÞis

estimatedforeachtvalue(horizontalaxis),forintervalsof widthRtwðtÞ (verticalaxis). Acolorcodeis usedfor the

valueofthecorrelation.Theusualcorrelationcoefficientis thevalue obtained at thetop of thetriangle, when all valueshave beenused toestimatethelocalcorrelation. Thispowerfulmethodwasintroducedin2010(Chenetal., 2010)andhassincemetgrowing interest,andhasbeen used in several recent studies (Hong and Wang, 2014; HuangandSchmitt,2014;Yinetal.,2014).

HeretoperformtheTDICmethod(Fig.6),weuseda Matlab code written by Yongxiang Huang (Huang and Schmitt,2014);thiscodeisitselfbasedonthecodewritten byChenandHuang(Chenetal.,2010).TheTDICmethod has the advantage of giving a correlation for each characteristicscale, but for ourtime serieswitha time stepof20min,itwasnotpossibletoenterdirectlytheraw data, because of memory limitation to perform this computation.Inthiscontext,wehavedegradedourtime seriestoperformtheexperimentreportedinFig.6,where the newtime step used is 1 day. This is not affecting informationontimescaleslargerthanoneday,whichare theconcernhere.

4.2. ApplicationoftheTDICmethod

Fig.6representssixTDICgraphs,withacharacteristic timebetween3.65and388.00days.Apatternisvisibleon thefirstfourTDICgraphs(until40days).Foreachyear,on thebaselinethereis a bluepatchinsummerand a red patchinwinter,whichmeansthatthereisacorrelationin winter and an anti-correlation in summer. Considering largertimelags,atthescaleof3days(firstgraph)there seemstobenocorrelation.Onthecontrary,forscalesof8, 18,and40days(graphs2,3,and4),thecolorscaleimages showglobalcorrelationsbetweenthetwoseries.Foryears 2006–2008, the correlation is stronger at the scale of 40days,whereasforscales2009–2011thecorrelationis strongeratthescaleof18days.Onthelastgraphwitha scaleof388days,thereisalargeredcorrelationpatchon theleftsideandablueno-correlationpatchontheright side.Thispatterncouldbebecausetheamplitudesofthe temperaturesignalareverycloseforyears2007and2008. 5. Discussionandconclusion

We have performed a comparison between two automated fixed-point systems located in the English Channel.Firstly,wehaveconsideredtheclimatologyfor bothareas,andwehaveseenthatBoulogne-sur-Merwas situatedinamoretemperateclimatezonethanRoscoff. Secondly, we have observed that both temperature spectral slopeswereclose to5/3, which is thespectral

slope of a passive scalar in fully developed turbulence. Finally,bothcorrelationmethodshaveconvergedtowarda transitionscaleof11daysforbothseries:scalessmaller than11daysarenotcorrelatedandlargerscalespossess somecorrelation.

TheRoscoffsystemis installedonabottommooring, contrarytoMARELCarnot, whichrecords datafromthe surface. Bothsites areincoastalareas withstrong tidal currentsandconsequentlythewatermassisthoroughly mixed.Thespectralanalysisinsection3revealsthatmean forcings,whichseemtohaveaninfluenceontemperature, are cycles linked to day/night, tidal, seasons, and high tides.Theseforcingsaremainlycontrolledbyastronomical mechanisms.Overall,thesurfacecurrentsintheEnglish Channelgoeasttowardthestrait,fromtheAtlantictothe North Sea.Thesurface temperaturesfromRoscoff could influence thesurface temperaturein Boulogne-sur-Mer, withacharacteristictimeof11dayscorrespondingtoan average transport time. From the resultsof co-spectral analysis,alinkbetweenbothserieswasfoundforscales largerthan11days,whichisalsothetimescalefoundby consideringameanvelocityof0.5m/sandadistanceof 460km.TheTDICanalysisprovidedresultsconsistentwith thistimescale.Thisnewmethodisalsousefultolocally expresscorrelationevents.Here,wefoundthatforscales from8to40days,thereisacorrelationinwintersandan anti-correlationissummers.

Fixed-pointsystemsprovidetemporalinformation.We candrawaparallelwiththehypothesisproposedbyTaylor in turbulence(Taylor,1935), whichallows the transfor-mationoftemporalinformationintheturbulencefieldon spatialinformation,whenweknowthemeanvelocity.In this context, we couldcomparethe events recordedby automaticsystemstotheoutputsofanumericalmodel. Thiscouldgiveusinformationtorefinethemodeloutput. Withanaveragecurrentspeedof0.5m/sinourstudyarea anda samplingfrequencyof20min,wehaveadistance below 1 km: this scale is consistent with the spatial resolutionofcurrentlyusedmodels(Beamanetal.,2011; Limetal.,2013;WolanskiandKingsford,2014).Another perspective is toconsidera possiblelink withtheNAO (NorthAtlanticOscillation)variability,asperformedina recent study, where the authors considered the link between sea surfacetemperatureandtheNAO(Tre´guer etal.,2014).

Acknowledgements

The region ‘‘Nord–Pas-de-Calais’’ (France) and the ‘‘Agence de l’eau Artois Picardie’’ are thanked for the financialsupportgrantedtoJonathanDerot’sPhDthesis. IFREMERisacknowledgedforaccesstoMARELdataand ThierryCariouforaccesstoEstacadedata;wethankAlain Lefebvre and Michel Repecaud from IFREMER for dis-cussions.YongxiangHuangisthankedfordiscussionson the TDIC method. We thank Denis Marin (LOG) for realizing Fig. 1. The TDIC codeis free toaccess on the following website: http://www.fg-schmitt.fr/EMD_and_ multifractals.html. www.englisheditor.webs.com is also thankedforitsEnglishproofing.

J.Derotetal./C.R.Geosciencexxx(2016)xxx–xxx 6

References

Beaman,R.J.,O’Brien,P.E.,Post,A.L.,DeSantis,L.,2011.Anew high-resolutionbathymetrymodelfor theTerreAde´lieand GeorgeV continentalmargin.EastAntarctica.Antarct.Sci.23(01),95–103.

Bendat,J.S.,Piersol,A.G.,2000.Randomdata:analysisandmeasurement procedures.JohnWiley&Sons.

Berthome,J.,1994.MAREL:unre´seauautomatise´ deveillepour l’envi-ronnementlittoral.Equinoxe34–35.

Blain,S.,Guillou,J.,Tre´guer,P.,Woerther,P.,Delauney,L.,Follenfant,E., Gontier,O.,Hamon,M.,Leilde,B.,Masson,A.,2004.Highfrequency monitoringofthecoastalmarineenvironmentusingtheMARELbuoy. J.Environ.Monit.6,569–575.

Chang,G.,Dickey,T.,2001.Opticalandphysicalvariabilityontimescales fromminutestotheseasonalcycleontheNewEnglandshelf:July 1996toJune1997.J.Geophys.Res.:Oceans106,9435–9453.

Chavez,F.P.,Pennington,J.T.,Herlien,R.,Jannasch,H.,Thurmond,G., Friederich,G.E.,1997.Mooringsanddriftersforreal-time interdisci-plinaryoceanography.J.Atmos.Ocean.Tech.14,1199–1211.

Chen,X.,Wu,Z.,Huang,N.E.,2010.Thetime-dependentintrinsic corre-lationbasedontheempiricalmodedecomposition.AADA2,233–265.

Corrsin,S.,1951.Onthespectrumofisotropictemperaturefluctuationsin anisotropicturbulence.J.Appl.Phys.22,469–473.

Dickey,T.D.,1991.Theemergenceofconcurrenthigh-resolutionphysical andbio-opticalmeasurementsintheupperoceanandtheir applica-tions.Rev.Geophys.29,383–413.

Dickey,T.D.,Douglass,R.,Manov,D.,Bogucki,D.,Walker,P.,Petrelis,P., 1993.Anexperimentintwo-waycommunicationwitha multivari-ablemooredsystemincoastalwaters.J.Atmos.Ocean.Tech.10, 637–644.

Dur,G.,Schmitt,F.,Souissi,S.,2007.Analysisofhighfrequency tempera-turetimeseriesintheSeineestuaryfromtheMarelautonomous monitoringbuoy.Hydrobiologia588,59–68.

Hong, W., Wang, J., 2014. Multiscale behavior of financial time seriesmodelfromPottsdynamicsystem.NonlinearDynam.78(2), 1065–1077.

Huang,Y.,Schmitt,F.G.,Lu,Z.,Liu,Y.,2008.Anamplitude-frequencystudy ofturbulentscalingintermittencyusingHilbertspectralanalysis.EPL 84,40010.

Huang,N.E.,Shen,Z.,Long,S.R.,1999.Anewviewofnonlinearwater waves:TheHilbertSpectrum1.Annu.Rev.Fluid.Mech.31,417–457.

Huang,N.E.,Shen,Z.,Long,S.R.,Wu,M.C.,Shih,H.H.,Zheng,Q.,Yen,N.-C., Tung,C.C.,Liu,H.H.,1998.Theempiricalmodedecompositionand theHilbertspectrumfornonlinearandnon-stationarytimeseries analysis.Proc.Roy.Soc.London.Ser.A:Math.Phys.Eng.Sci.454, 903–995.

Huang, Y., Schmitt,F.G., 2014. Timedependent intrinsic correlation analysis oftemperature and dissolved oxygentime series using empiricalmodedecomposition.J.Mar.Syst.130,90–100.

Huang,Y.,Schmitt,F.G.,Lu,Z.,Liu,Y.,2009.Analysisofdailyriverflow fluctuationsusingempiricalmodedecompositionandarbitraryorder Hilbertspectralanalysis.J.Hydrol.373,103–111.

Legendre,P.,Legendre,L.F.,2012.Numericalecology,Elsevier,853p.

Lim,H.S.,Chun,I.,Kim,C.S.,Park,K.S.,Shim,J.S.,Yoon,J.J.,2013. High-resolutionoperationalcoastalmodelingsystemforthepredictionof hydrodynamicsinKoreausingawavecurrentcoupledmodel.J.Coast. Res.314–319.

Lumley,J.L.,2007.Stochastictoolsinturbulence.CourierDover Publica-tions.

Nam,S.H.,Kim,G.,Kim,K.R.,Kim,K.,Oh,L.,Kim,K.W.,Ossi,H.,Kim,Y.G., 2005.Applicationofreal-timemonitoringbuoysystemsforphysical andbiogeochemicalparameters inthecoastal oceanaroundthe Koreanpeninsula.J.Mar.Sci.Technol.39,54–64.

Obukhov,A.M.,1949.Thestructureofthetemperaturefieldinaturbulent flow.Izv.Akad.Nauk.SSSR,Ser.Geogr.andGeophys.13,58–69.

Platt,T.,Denman,K.L.,1975.Spectralanalysisinecology.Annu.Rev.Ecol. Syst.6,189–210.

Schmitt,F.G., Dur, G., Souissi,S., BrizardZongo, S., 2008. Statistical propertiesofturbidity,oxygenandpHfluctuationsintheSeineriver estuary(France).PhysicaA387,6613–6623.

Sentchev,A.,Yaremchuk,M.,2007.VHFradarobservationsofsurface currentsoffthenorthernOpalcoastintheeasternEnglishChannel. Cont.ShelfRes.27,2449–2464.

Seuront,L., Gentilhomme,V.,Lagadeuc,Y.,2002.Small-scale nutrient patchesintidallymixedcoastalwaters.Mar.Ecol.Prog.Ser.232, 29–44.

Seuront,L.,Schmitt,F.,Lagadeuc,Y.,Schertzer, D.,Lovejoy,S.,1999.

Universalmultifractalanalysisasatooltocharacterizemultiscale intermittentpatterns:exampleofphytoplanktondistributionin tur-bulentcoastalwaters.J.Plankton.Res.21,877–922.

Seuront,L.,Schmitt,F.,Lagadeuc,Y.,Schertzer,D.,Lovejoy,S.,Frontier,S., 1996a.Multifractalanalysisofphytoplanktonbiomassand tempera-tureintheocean.Geophys.Res.Lett.23,3591–3594.

Seuront,L.,Schmitt,F.,Schertzer,D.,Lagadeuc,Y.,Lovejoy,S.,1996b.

MultifractalintermittencyofEulerianandLagrangianturbulenceof oceantemperatureandplanktonfields.Nonlin.ProcessesGeophys.3, 236–246.

Taylor,G.I.,1935.Statisticaltheoryofturbulence.Proc.Roy.Soc.Lond.Ser. A151,421–444.

Tennekes,H.,Lumley,J.L.,1972.Afirstcourseinturbulence.MITpress.

Tre´guer,P.,Goberville,E.,Barrier,N.,L’Helguen,S.,Morin,P.,Bozec,Y., Rimmelin-Maury,P.,Czamanski,M.,Grossteffan,E.,Cariou,T.,2014.

Largeandlocal-scaleinfluencesonphysicalandchemical characte-risticsofcoastalwatersofwesternEuropeduringwinter.J.Mar.Syst. 139,79–90.

Winder,M.,Cloern,J.E.,2010.Theannualcyclesofphytoplankton bio-mass.Phil.Trans.R.Soc.B.365,3215–3226.

Woerther,P.,1998.Marel:Mesuresautomatise´esenre´seaupour l’envi-ronnementlittoral.L’Eau,l’industrie,lesnuisances67–72.

Wolanski, E., Kingsford, M.J., 2014. Oceanographic and behavioural assumptionsinmodelsofthefateofcoralandcoralreeffishlarvae. J.R.Soc.Interface11(98),20140209.

Yin,L.,Qiao,F.,Zheng,Q.,2014.Coastal-TrappedWavesintheEastChina SeaObservedbyaMooringArrayinWinter2006.J.Phys.Oceanogr. 44(2),576–590.

Zongo,S.,Schmitt,F.G.,2011.ScalingpropertiesofpHfluctuationsin coastalwatersoftheEnglishChannel:pHasaturbulentactivescalar. Nonlin.ProcessesGeophys.18,829–839.

Zongo,S.,Schmitt,F.G.,Lefebvre,A.,Re´pe´caud,M.,2011.Observations bioge´ochimiquesdeseauxcoˆtie`resa` Boulogne-sur-Mer a` haute fre´quence: lesmeasures automatiquesde la boue´eMAREL. In: Schmitt,F.G.(Ed.), Observationdese´cosyste`mesmarinset terres-tresdelaCoˆted’Opale:dunaturalismea` l’e´cologie.Pressesdel’UOF, Paris, pp.253–266.