DTIC ADA580642: Surface Circulation in the Iroise Sea (W. Brittany) from High Resolution HF Radar Mapping

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JournalofMarineSystems109-110(2013)S153–S168
ContentslistsavailableatSciVerseScienceDirect
Journal of Marine Systems
journal homepage: www.elsevier.com/locate/jmarsys
Surface circulation in the Iroise Sea (W. Brittany) from high resolution HF
radar mapping
Alexei Sentchev a,⁎, Philippe Forget b, Yves Barbin b, Max Yaremchuk c
aLaboratoired'OcéanologieetGéosciences(CNRS-UMR8187),UniversitéduLittoral-Côted'Opale,62930Wimereux,France
bLaboratoiredeSondagesElectromagnetiquesdel'EnvironnementTerrestre(CNRS-UMR6017),UniversitéduSudToulonVar,83130LaGarde,France
cNavalResearchLaboratory,Bldg.1009,StennisSpaceCenter,MS39529,USA
a r t i c l e i n f o a b s t r a c t
Articlehistory: Thedatafromtwohigh-frequencyradars(HFR)operatingintheIroiseSeaarere-processedbyapplyingan
Received10September2010 improvedversionofthedirectionfindingalgorithm,removingwave-inducedsurfacecurrentsandthevari-
Receivedinrevisedform9November2011 ationalinterpolationonaregulargrid.Combiningtheseprocessingtechniquesallowedreconstructionof
Accepted29November2011 thesurfacecurrentsatalevelofdetailsthatwasnotpreviouslyavailable.Refinedresolutionenabledtoiden-
Availableonline11December2011 tifyfine-scalestructuresofsurfacecirculation,toquantifythevariabilityoftidalcurrentsandtheresidual
(timeaveraged)velocityfield,andtoexplainspatialintermittenceinpolarizationofthetidalcurrentellipses.
Keywords:
Theanalyzeddataspantwomonth-longperiodsinspringandlatesummerof2007.Themajorfindingsin-
HFradar
Tidalcurrent clude(a)adipolestructureinthevorticityfieldcharacterizedbytwooppositelyrotatingeddies,generated
Residualflow ontheleewardsideoftheUshantIslandatflood(negativepolarity)andatebb(positivepolarity);(b)anex-
Eddyfield tremelystrongfortnightlyvariabilityoftidalcurrentsnorthwestoftheUshantIslandwiththehighestveloc-
IroiseSea ity magnitude of 3.9m/s caused by the interference of the major semi-diurnal tidal constituents; (c) a
significantcontributionofthehigherordernonlineartidalharmonicstothesurfacecurrentsintheFromveur
strait,whichmaintainsstrongtidalcurrentsandaffectstheshapeoftheirfortnightlymodulation.Theresid-
ualcirculationischaracterizedbytwodistinctzonesapproximatelyseparatedbythe100misobath:inthe
offshorezonetheresidualcurrentshaveasignificantcontributionofthewind-drivencomponent,whereas
thenearshorezoneischaracterizedbyextremelystrong(upto0.4m/s)time-independentresidualcircula-
tionfeaturingtwopermanentanticycloniceddies:northofthewesternextremityoftheSeinarchipelago,
and north the Ushant Island. The acquired data and the presented results could be useful for regional
modelvalidationandstudiesofthelocaleddydynamics,tidalfronts,andpassivetracertransportinthe
region.
©2011ElsevierB.V.Allrightsreserved.
1.Introduction westernBrittanycoasttomonitorsurfacecurrentsupto140kmoff-
shore. The Iroise Sea circulation is very difficult to study by in situ
Inrecentyears,high-frequency(HF)Dopplerradarsystemshave methods, as it is dominated by extremely strong tidal currents,
hadstunningsuccessinthemappingofsurfacecurrents.Theability oftenexceeding3m/s,andaffectedbystrongandoftenviolentwest-
tomapsurfacecirculationincoastaloceanareashasbroughtnewin- erly and southwesterly winds. Low pressure atmospheric systems
sightstothecomplexitiesofphysicalprocessesinnearshorewaters, (cyclones), generated in the Northwestern Atlantic, regularly cross
andallowedsignificantadvancesinourunderstandingofcirculation theIroiseSeaandmightcausesignificantsurgesontheWestBrittany
andoceanographicconditionsinmanycoastalregions(e.g.Bassinet coast with sea surface rise up to 0.50m (Bouligand and Pirazzoli,
al., 2005; Breivik and Sætra, 2001; Haus et al., 2000; Kaplan et al., 1999). Surface currents in the Iroise Sea are also affected by swell
2005;Kovacevicetal.,2004;Marmorinoetal.,1999;Sentchevetal., andwindwaves.Violentstorms,oftenoccurringinwinter,contribute
2009a,2009b;Yoshikawaetal.,2007). tothereputationoftheIroiseSeaasoneofthemostdangerousseas
IroiseSeaisoneoftheregions,continuouslymonitoredbyHFra- inEurope.
darssince2006(Fig.1).Asystem,composedoftwohigh-frequency CirculationintheIroiseSeahasbeenstudiedpreviouslybymany
Wellen Radars (WERA) operating at 12.4MHz, is deployed on the authors by means of field measurements (Le Boyer et al., 2009;
Mariette and Le Cann, 1985; Pingree et al., 1975) and numerical
modelling (Mariette et al., 1982; Muller et al., 2009, 2010). These
⁎ Correspondingauthor.
studiesinvestigatedthecharacteroflocalgeostrophicandtidalcircu-
E-mailaddresses:[email protected](A.Sentchev),
lations,eddyfrontaldynamicsandshedlightontheroleoftidalmix-
[email protected](P.Forget),[email protected](Y.Barbin),
[email protected](M.Yaremchuk). ing in controlling cross-frontal heat and mass exchange. They also
0924-7963/$–seefrontmatter©2011ElsevierB.V.Allrightsreserved.
doi:10.1016/j.jmarsys.2011.11.024
S154 A.Sentchevetal./JournalofMarineSystems109-110(2013)S153–S168
Distance (km)
0 25 50 75 100
145
48°40 English Channel 50oN
m
Met Buoy 150 Ushantur St. G Brittany 48oN
e
v Loire R.
de (deg N) 48°20 Fro Mm olène Le Conquet Distance GoBfiuslcfay G 46oN
Latitu Iroise Sea (km) aronne 44oN
R
.
6oW 4oW 2oW 0o
B
48°00 Sein Arch.
50 m
100 m
35
−6°00 −5°40 −5°20 −5°00 −4°40
Longitude (deg W)
Fig.1.LocationoftheIroiseSeaandHFRsurveyarea(greysquarecontourontherightpanel).ExperimentaldomainintheIroiseSea(greyshading)andradarcoveragezone(left
panel).Radarsitesareshownbygreycircles.Greybrokencontoursshowcoverageareaforindividualradars.Squaresdenotelocationsofthemetbuoyandtidalgaugestation.Open
circleindicatesthelocationofthegridpointwherewaveinducedcomponentofsurfacecurrentwasanalyzedindetail(cf.Fig.2dandFig.3b).Contourintervalofthebathymetryis
50m(greysolidlines).Greydashedlinesshowcoverageareasfortheindividualradars.Geographicnamesusedinthetextarealsoshown.
allowedbetterunderstandingoftherolethatdifferentphysicalforc- First,weperformhighresolutionsurfacecurrentmappinginboth
ing mechanisms play in the Lagrangian circulation of the basin. In temporal and spatial dimensions (20min and 1km) by applying a
particular,theinfluenceofthebottomthermalfrontonsurfacecircu- novelapproachtotherawHFRdataprocessinginconjunctionwith
lationandlarge-scaleeddymotionsassociatedwithfrontaldynamics high-performancevariationalinterpolationtechnique.Highazimuth-
wereevidencedin(LeBoyeretal.,2009;Mulleretal.,2009).Howev- alresolutionoftheradialvelocitiesisachievedbytheHFRsignalpro-
er, with the exception of the recent field study of Le Boyer et al. cessing using an improved version of the MUSIC direction finding
(2009),itisdifficulttofindadetailedobservation-baseddescription algorithm(Lipaetal.,2006).Theradialvelocitiesaretheninterpolat-
ofthecirculationinthisareainliterature.Quantitativeestimatesof edontheregulargridusingavariational2dVarmethod(Yaremchuk
thesmallscalecirculationfeatures,theirmagnitudeanddependence and Sentchev, 2009, referred hereafter as YS09). Furthermore, the
onvariousforcingfactorsremainrelativelyuncertain.Thisshortcom- contributionofsurfacewavestotheradarderivedvelocitiesisesti-
ingisprimarilyduetothedifficultiesinacquisitionofthelong-term mated with the method recently developed by Ardhuin et al.
high-resolutioninsitudatabecauseoftheextremelystrongcurrents (2009).Thesethreetechniqueshavebeenimplementedforproces-
and severe meteorological conditions in this part of the Atlantic singofHFRdatafortwoselectedperiods:inspringandlatesummer
Ocean. Complexity of the physical processes occurring in the Iroise 2007 representing in total 52days. The summer period is synchro-
Sea in conjunction with complex topography renders modelling of nizedwiththeextensivefieldexperimentintheIroiseSeaabroadof
thecirculationalsodifficult.Inthatrespect,remotesensingofsurface theR/V“CôtesdelaManche”(LeBoyeretal.,2009).
currentsbyHFradars(HFR)providesauniqueopportunitytoestab- Second,westudytheresultingsurfacecirculationpatternsfrom
lishamonitoringsysteminthebasinonaregularbasis. theperspectiveofdifferentmodesofvariability.Wefocusonphysical
Astheexperimentaldatarequiredformodelvalidationhavebeen processesgoverningthetidalcurrentsandresidualcirculationinthe
extremely scanty until recently, in 2005, the French Naval Oceano- area.TheHFRobservationsrevealedflowcomplexityandvariability
graphic Centre (SHOM) put forward an initiative to perform the atalevelofdetailsthatwerenotpreviouslyavailable.Refinedresolu-
HFRobservationsofsurfacecirculationintheIroiseSea.Theexperi- tionallowedustoidentifyfine-scalestructuresofsurfacecirculation,
ment was designed to get better knowledge on physical processes toquantifythevariabilityoftidalcurrentsandresidualvelocityfield,
governingthecirculationandtoperformthevalidationofnumerical andtoexplainpatchinessinpolarizationoftidalcurrentellipses.
models. Beam Forming (BF) algorithm actually used for processing The paper is organized as follows. In Section 2, we present the
theradardatainnearlyreal-time(Marietteetal.,2006)providesra- study site, the environmental data (recorded and derived from nu-
dial velocities of surface current along sixteen beams with 9° azi- mericalmodeling)duringselectedperiodsoftheradarexperiment,
muthal discretization. The angular resolution of the system is too the HFR network, and briefly describe the methods of analysis. In
coarseand,toouropinion,unabletocapturethefinescalestructure Section3,wedescribeandanalyzetheobservedfeaturesofsurface
ofthesurfaceflow,especiallyaroundtheislandsandintheFromveur circulation,flowvariability,andthefine-scalestructuresinvorticity
Straitwhichareofparticularinterest. andresidualvelocityfieldsintheIroiseSea.Discussionoftheresults
Inthepresentstudyweaddresstwochallenges. andsummaryarepresentedinSection4.
A.Sentchevetal./JournalofMarineSystems109-110(2013)S153–S168 S155
2.Dataandmethods southern part, there is a group of islets and rocks belonging to the
Seinarchipelago.Onlyapartofitisexposedatlowtide.
2.1.Studysiteandenvironmentalconditions In the Iroise Sea, tidal currents are generally characterized by
clockwiserotationinresponsetothejointeffectoftheCoriolisforce
Thestudysite,IroiseSea,islocatedintheextremenorth-eastern andseasurfacegradientsrelatedtotidalwavepropagation.Incident
partoftheGulfofBiscay(Fig.1).Thisisashallowwaterareawith tidalwavesarrivefromtheGulfofBiscay,travelaroundtheW.Brit-
depth gradually decreasing westward from 50 to 150m with more tanyPeninsulaandentertheEnglishChannel.Thetidalwaves’inter-
gentle bottom slope in the South. In the North, there is a group of actionsisthedominantfactorthatdeterminesvariabilityofthesea
small islands, islets and rocks that form Molène archipelago, and a surfaceheight(SSH)andcurrentsintheregion.TheSSHvariability
bigger, 8×4km, Ushant Island. It is separated from the Molène in the Le Conquet harbor exposes variations of 2 to 7m (Fig. 2a),
Islands by the 2km wide and 50m deep Fromveur strait. In the withthepredominantsemi-diurnal period,smalldiurnalinequality
8
(a)
m)
n ( 6
o
ati
v
e 4
El
e
c
a 2
urf
S
0
10/4 14/4 18/4 22/4 26/4 30/4 4/5
(b)
7 m/s
d
n
wi
d
e
v
er
s
b
O
10/4 14/4 18/4 22/4 26/4 30/4 4/5
(c)
7 m/s
d
n
wi
d
e
v
er
s
b
O
24/8 28/8 01/9 05/9 09/9 13/9 17/9
4 0.2
(d)
3
m) m/s)
Hs ( 2 0.1 ss (
U
1
0 0
24/8 28/8 01/9 05/9 09/9 13/9 17/9
Time (days)
Fig.2.Externalforcingdata.(a)TidalelevationobservedinLeConquetharbourinApril–May2007.WindmeasurementsmadeatMetBuoywithintheradarcoveragezoneduring
April–May(b)andAugust–September2007(c)(RegionalMet-officedata).Arrowsshowobservedwinddirection.Windspeedscaleisgivenintherightuppercorner.(d)3-hdata
ofsignificantwaveheight,Hs(solidline),andwave-inducedvelocity,Uss(dashedline),inAugust–September2007inthemiddleofthestudyarea.SeeFig.1forlocationofmea-
surementpoints.
S156 A.Sentchevetal./JournalofMarineSystems109-110(2013)S153–S168
andpronouncedfortnightlymodulationduetotheinterferenceofthe beendocumentedbyMulleretal.(2007)whofoundaslightsystem-
semi-diurnal(M ,S ,N )andquarter-diurnal(M ,MS )constituents. aticvariationofthewinddirectionintheareabetweentheUshant
2 2 2 4 4
Both primary and secondary spring tides occur during the period IslandandtheBrittanycoast.
shown.Tidalvelocitiesandtransportsshowfortnightlyvariabilityin
responsetothespring-neapcycle.
Buoyancyforcinginthedomainisrelativelyweak.Themajorityof 2.2.HFRdataandmethodsofprocessing
freshwatercomesfromtheAulneandsmallerriverslocatedonthe
westernBrittanycoast.TheirdischargetotheIroiseSeaofapproxi- 2.2.1.HFRvelocitydata
mately 60m3/s observed in April 2007 (http://www.hydro. Asystemoftwohigh-frequencyWellenRadars(WERA)operating
eaufrance.fr)canbeconsideredasnegligible,comparedtodischarge at12.4MHzisdeployedonthewesternBrittanycoastfromJuly2006
of the Loire and Garonne rivers into the central part of the Gulf of todate.IndividualradarsitesarelocatedatCapeGarchine(siteG),a
Biscay (1200 and 900m3/s respectively) during the same period. seashoreflat-groundarea,andCapeBrezellec(siteB),50kmsouth-
Greatdistancebetweentheserivers'mouthsandtheIroiseSeafavors ward.Atbothsites,transmissionisdonebyanendfirearrayoffour
the fresh water dispersion and only a small quantity of freshwater antennasformingarectangle.Thereceivingarraycontains16equally
reachesthewesternBrittanycoast. spacedantennasparalleltotheshorelineandstretchedalong150m.
Fig.2bshowswindsmeasuredattheoffshoremetbuoy(seeFig.1 TheBeamforming(BF)method,actuallyusedforprocessingthe
forbuoylocation).Twodistinctwindregimeswereobservedduring radardatainnearreal-time,providesradialvelocitiesofsurfacecur-
thespringperiod.Betweenthe10thand22thofApril,(thefirst12- rentalongbeamswith3dBwidthof9°ontheaverage.Anautomatic
day period), winds were generally coming from the North and RFI(RadioFrequencyInterference)clearinghasbeenintegratedinto
North–East with moderate speeds ranging from 5 to 8m/s. From signal processing algorithm (Gurgel and Barbin, 2008), along with
April22untilMay5,variablewindregimewasobservedwithsmall thequalitycontrolforremovingoutliersandradialvelocitiesexceed-
dominationofnortheasterlywindswithspeedsupto10m/s.During ing4m/s.Theradial(alongbeam)resolutionis1.5kmandtherange
thelatesummerperiod,thewinds,generallystronger,wereblowing isoftheorderof140km.Inpractice,foroptimalimplementationof
mostlyfromthenorthernandnorth-easternsectors(Fig.2c). the RFI clearing method, the data were processed up to a range of
ThespectrumofthehourlywindsrecordedbytheoffshoreMet 120km.
buoyisgiveninFig.3a.Spectralanalysisofbothzonalandmeridional Radialvelocitiesfromtworadarsarecombinedtoprovidesurface
windcomponentsandthetotalkineticenergyofthewindshowsthe currentmapsat20-minacquisitionrate(http://www.previmer.org/
rednatureofthespectrumwhichfollowsapowerlowwithspectral observations/courants/radar_hf_iroise). The accuracy of the radar-
slope close to −5/3, mainly in higher frequency band (>1 cyc/d). derivedvelocitieshasbeenestimatedbySHOM(OceanographicDivi-
Thespectrumrevealsavarietyofatmosphericmotionswithsignifi- sionoftheFrenchNavy)throughacomparisonwithsurfacedrifters
cant peaks at diurnal and sub-diurnal frequencies (0.55, 0.35, and andADCPcurrentmeasurementsforaperiodof7months.Inthema-
0.2cyc/d).Diurnalpeakevidencestheeffectofseabreeze,whereas jorityofsituations,thediscrepancyinvelocitymeasuredbydifferent
othersignificantpeaksarewithintherangeofcyclonic-anticyclonic instruments did not exceed0.15m/s (Le Boyer et al., 2009). It was
frequencies. They are certainly related with cyclonic activity over also noticed that a large fraction of this discrepancy might not be
the North Atlantic. Small scale variability of the local winds has due to instrumental errors, but to the definition of the “surface
(a) (b)100
1/2
101
y) y)
da da 10−1
s/ s/
e e
cl cl
y y
22/s)/(cm 100 −5/3 22/s)/(cm 10−2 1
y ( y ( 1/4
sit sit
en 10−1 en 1/6
al D al D 10−3
ctr ctr
e e
p p
S S
wer 10−2 wer 10−4
o o
P P
10−3
10−1 100 101 10−1 100 101
Frequency (cycles/day) Frequency (cycles/day)
Fig.3.PowerspectraofthewindandHFradardata.(a)WindspectrumrecordedattheMetbuoyinApril–May2007.(b)Kineticenergyspectraatthesameperiodfortwoselected
gridpointsoftheradarcoveragezone:apointclosesttotheMetbouy(blackline)andapointinthecentralpartofthezone(greyline).SeeFig.1forpointlocation.Numbersstand
fordominanttidalperiod(indays).Errorbarindicates95%confidenceiterval.
A.Sentchevetal./JournalofMarineSystems109-110(2013)S153–S168 S157
velocity”,asothermeasurementtechniquesaresensitivetotheshear TheDFtechniquewasappliedtotheHFRdatatoretrieveradial
oftheEuleriancurrent,toStokesdrift,totheseastate,etc. velocitiesfortwoselectedperiods,namely,from10Aprilto5May,
Despiteagoodqualityoftheradialvelocitiesrecordedbythera- andfrom24Augustto19September2007.Thesecondperiodwas
dars, angular resolution of the system is relatively coarse and does ofparticular interestbecauseitcoincidedwith extensivefieldex-
not capture the fine scale structure of the surface flow, especially periment(LeBoyeretal.,2009).Duringtheseperiods,bothradars
aroundUshant-MolèneIslandsandintheFromveurstraitwhichare worked continuously with low data loss. Fractional availability of
ofparticularinterest. radial velocity data for both radars during the two periods is
shown in Fig. 5. The data were available in at least 50% of time
2.2.2. Application of the direction finding method for processing the within a cone with a radius of approximately 100km. Despite of
radardata itslowaltitude(20m),theUshantIslandstronglyaffectsavailabil-
Toobtainhigherresolutionradialvelocitymaps,theHFRsignals ityofradardataprovidingdropsinthedatareturnto25%(forsite
were reprocessed by using the Multiple Signal Classification B) and to 50% (for site G) behind the island. The fractions of the
(MUSIC)directionfinding(DF)algorithmofSchmidt(1986)driven datareturnbytheindividualradarsareshowninFig.5bythincon-
by the parameterization of Lipa et al. (2006). In contrast to BF, the tours.Theinterpolationgridgivenbytheboldcontourhasapprox-
DFmethodseeksforthebearingsfromwhichtheenergeticDoppler imately4000points,equallyspacedby1.1km,andcoversanearly
lines originate. If no solution is delivered in a given direction slot, circular area with the seaward limit of 90km from the coast. The
thenthe DF methodleaves a gap in the velocity record. If multiple condition of 50% availability of the radial velocity data is met in
Dopplershiftsolutionsaredeliveredinthesamebin,apoweraver- the majority of the interpolation area with the exception of the
agedDopplershiftvalueiscalculated.Themaximumvalueofradial northernpartforsiteB.Theanglebetweenradarbeamsatpoints
velocity measured by a radar operating at a wavelength λ ofbeamintersectionwasgreaterthan30°allovertheinterpolation
(12.4MHz)islimitedbyf ⋅λ/2(4.3m/s),wheref istheBraggfre- area.
B B
quency(0.359Hz)correspondingtotheradarfrequency.
Processeddirectionsspannedtheaperturefrom−70°to70°with
respecttothenormallineofthereceivingantennaarray,thusprovid- 2.2.3.Variationalinterpolation
ing the azimuthal resolution of 2°. The azimuthal resolution varies Velocity vector maps were generated from radial velocity data
along a given beam from 0.35km (1.6km for BF) to 2.8km using the variational interpolation technique, 2dVar (YS09). This is
(12.6kmforBF)at10and80kmrange,respectively. non-local,kinematicallyconstrainedalgorithm.Itusesacombination
Fig.4showsradialvelocitiesprovidedbyBFandDFmethodsfor ofradialvelocitiesatallmeasurementpointstoreconstructtheveloc-
the same acquisition time. In general, similar spatial patterns on ityvectorinonelocation.Thisfeatureoftheinterpolatingtechnique
both velocity maps are found. However the pattern on the BF map canhelptoovercomesomelimitationsrelatedtoalackofdata.The
issmearedinazimuthanditcanbedifficulttodeterminethespatial smoothnessoftheinterpolatedvectorfieldisenforcedbypenalizing
extension or the limits for different structures in the velocity field. thesquaredLaplacianofvelocityandalsoofitscurlanddivergence,
Detailedanalysisofvelocitymapsfordifferentperiodsoftidalcycle thusprovidingthealgorithmwithflexibilityandefficientcontrolof
revealed that the magnitude and spatial variation of the velocity smoothness.Kinematicconstraints(zerofluxonrigidboundary),in-
field were poorly represented by BF algorithm. However, the en- corporatedinto2dVar,appearparticularlyusefulgivenalargenum-
hancedresolutionprovidedbytheDFmethodinherentlyintroduces ber of islands in the study area. The 2dVar interpolation was
gaps (see above) and noise in the radial velocity field (Fig. 4b). developed and employed to reconstruct vector current fields using
Noise comes from the fact that the velocity estimated at a given syntheticdatawithdifferent(upto50%)signal/noiseratiosandalso
range for a particular bearing can originate from another bearing arealdatasetfromtheradarexperimentinBodegaBay,northernCal-
dependingonthecomplexityoftheoceanwaveandcurrentcondi- ifornia,in theGulfofLion,westernMediterranean (Sentchevetal.,
tions (Barrick and Lipa, 1996, 1997). The variational method used 2009a,2009b),anddemonstratedcertainadvantagescomparedtoal-
forradialvelocityinterpolationfrombothradarunits(Section2.2.3) ternative interpolation techniques (e.g., local interpolation, OMA
performsgapfillingandoffersanefficientcontrolofthenoiselevel. (Mulleretal.,2009)).
Fig.4.RadialvelocitymapsonApril17,2007(4:10am)derivedfromradardataprocessingby(a)beamformingand(b)directionfindingmethods.
S158 A.Sentchevetal./JournalofMarineSystems109-110(2013)S153–S168
Fig.5.Cumulativeavailabilityoftheradialvelocitydata(inpercent)forradarstationB(a)andG(b)duringthetwoperiodsofanalysis(thincontourlines).Boldcontourenvelops
theareawheresurfacevelocityvectorsweregeneratedateachtimeintervalbythevariationalalgorithm.
2.2.4.Velocityerrorsestimation onApril10,2007).Themapcombinesinformationabouttheavail-
Thevariationalapproachusedforvelocityinterpolationallowses- abilityofthedata,accuracyofradialvelocitymeasurements,andgeo-
timatingerrorsofthevelocityfield(YS09).Theinverseerrorcovari- metricdilutionofprecision(GDOP).Theresultantvelocityerrorsare
ance matrix C−1 for gridded velocity is the matrix H of second lessthan15cm/sinthemajorityofthedomain,andrapidlyincrease
derivativesofthecostfunctionwithrespecttouandv(theHessian (upto40cm/s)inareaspoorlycoveredbyobservations.Thecondi-
matrixofthevariationalproblem).AsthematrixHmaynotnecessar- tiononangleintersection(b30°),adoptedforconfigurationofthein-
ilyhavethefullrank,weseekforitsgeneralizedinversebydiscarding terpolationdomain,preventserrorgrowthatfarranges.Itshouldbe
eigenvectorscorrespondingtosmalleigenvalues.Typically,0.02%of emphasizedthattheerrordistributioncorrespondingtovelocitiesof
theeigenvectorsarerejectedduringtheinversionofH. theobservedcirculationpatterndoesnotgivetheobservationalsig-
Fig.6shows,asanexample,themapoferrorsofinterpolatedve- naltonoiseratio.Thisratiocanbederivedbycomparingtheradial
locity(currentvectormagnitude)forthefirstHFRsnapshot(00:10 velocitymapswithspatialdistributionoftheaccuracyoftheradial
velocitymeasurements.Thelatterdependsuponthesystemconfigu-
Vel. Err. (cm/s) ration,levelofbackscatteredenergy,seasurfacestate,variabilityof
km currents within the radar measurement cell, …, and might attain
25 403530 8–10cm/s.
20
120 15 2.2.5.Removingtheseastateinfluence
Surfacevelocityderivedfromradardataisestimatedfromthedif-
15 0
1 ferencebetweenthepositionoftheobservedandtheoreticalBragg
linesontheDopplerspectrumoftheseasurfaceecho(Stewartand
Joy, 1974). It is generally assumed that Bragg waves, i.e. waves
100 3
5 whosewavelength(atgrazingangle)isequaltothehalfoftheelec-
tromagneticwavelength,satisfythelineardispersionrelationshipof
15 oceanwaves.Consideringnonlinearitiesoftheoceansurface,Weber
20 10 andBarrick(1977)slightlymodifiedthisrelationshipaccountingfor
80 3025 1 0 aallthtyeopreestiocfatlheexpsurersfasicoengwrahviictyhwquaavnetsi.fiBersotchheeeeftfeaclt.(a1n9d8c3a)npbroevuidseedd
toextractthewaveinducedcurrentcomponentfromcurrentradio
40 10 measurements. The method of velocity correction was recently ap-
pliedtoradarmeasurementsintheIroiseSea,withaparticularinter-
3 estofstudyingthewind-currentrelationship(Ardhuinetal.,2009)
60 5
locally.Inthepresentpaperweapplythemethodtothewholearea
4035
ofradarcoverage.Informationonsurfacewaveswasprovidedevery
3hbythenumericalwavemodelWAVEWATCHIIIat1/30°resolution
20 40 60 80 km (2.5km) using the implementation described in Ardhuin et al.
(2009).AppendixAcontainsthedescriptionofthemethodapplied
Fig.6.Velocityerrors(cm/s)forasurfacecurrentvectormaponApril10,2007,00:10. for estimation of the wave induced surface current velocity vector,
A.Sentchevetal./JournalofMarineSystems109-110(2013)S153–S168 S159
U ,atthegridpointsofthewavemodel.ResultingvaluesofU were frequencyrange,thereisamoderateriseofenergywhichrevealsmo-
SS ss
spatiallyinterpolatedontheregularradargrid,theninterpolatedin tionswith3.3-dayperiod(Fig.3b).Analysisofsimilardistributionfor
time,andfinallysubtractedfromtheradarderivedcurrentvelocities. thewind(Fig.3a)doesnotshowanysignificantatmosphericforcing
Forconvenience,U willbereferredhereafterasStokesvelocityal- intidalband,suggestingtheabsenceofmodulationoftidalcurrents
SS
though in practice it represents approximately 85% of the model- bywind.
estimatedStokesdriftvelocity(cf.Appendix). Furthermore, we applied the principal componentanalysis (PCA)
Fig. 2d provides estimated Stokes velocity and significant wave technique to this data set in order to quantify tidal flow dynamics.
height during the second (late summer) period of analysis in a Ourapproachhasacertainadvantageoverafrequentlyusedharmonic
pointlocatedinthemiddleofthestudyarea(Fig.1).Strongcorrela- analysisbecauseitallowsquantifyingthetotalcontributionofalltidal
tion is observed between the wind speed and Uss. Northern winds constituentstoobservedcurrentsandassessingtime-spacevariability
with high speed, observed on August 29, September 3 and 18 of the currents.As tidal currents in the Iroise Sea are rotational, the
(Fig. 2c), produce surface currents with magnitudes greater than currentvelocityvectorevolvingoveratidalcycledrawsanellipse.Pa-
0.10m/s. Winds from North–East sector tend to weaken surface rametersofsynthesizedellipses,retrievedfromthePCA,provideori-
waves (H b1m) and the associated wave induced currents to less entation and magnitude of the dominant current. The anisotropy of
s
than0.10m/s(Fig.2d). oscillatorytidalflow(ellipseeccentricity)isquantifiedbyestimating
Fig.7summarizesthecontributionofStokesvelocitytothesur- theeigenvalueratioofthevelocitycorrelationtensor.ThePCAtech-
face currents in terms of the occurrence probability of a measured niquedoesnotgive,however,informationonthesignofrotationof
current magnitude U and the wave induced current velocity U . velocityvectors.Tofillthisgap,weperformedrotaryspectralanalysis
ss
Thesestatisticalestimatescoverbothstudiedperiods.Themodulus (EmeryandThompson,1997)ofvelocitytimeseries,referredhereaf-
of U isa small quantitycomparedto Uwith a peak ofoccurrence terasRSA.Thetechniqueinvolvesthedecompositionofthevelocity
ss
at0.05m/swhereastheoccurrencepeakforUis0.40m/s.Thehigh- vectorintotheclockwise(cw)andcounter-clockwise(ccw)rotating
estmagnitudeofStokescurrentdidnotexceed0.18m/sduringthe circular complex-valued components. First, the RSA was performed
period of interest. Moreover, U values are rather small compared toidentifythedominantfrequencyincurrentvelocityvariation.Both
ss
totheprecisionofradarsurfacecurrents.Forapointlocatedinthe cwS−(negative)andccwS+(positive)powerspectrarevealedpro-
middle of the study area (Fig. 1), the absolute values of the west– nouncedpeaksatthesemi-diurnalfrequency.Afterthat,therotaryco-
east (south–north) components of Uss exceed the intrinsic error of efficient,r=(S+−S−)/(S++S−),wasestimatedateverygridpointat
the corresponding current components, estimated as 4cm/s (7cm/ thesepeakvalues.rrangesfrom−1forclockwisemotionto+1for
s)in53%(7%)ofcases.Howeverthewest–eastcomponentofU is counter-clockwisemotion(r=0isoscillatingnon-rotationalflow).
ss
generally higher than this error and can exceed it 4 times. In that WehavealsoestimatedtheEulerianresidualcurrentsandinvesti-
case,removingtheseastateinfluenceisusefultoimprovethequality gatedtheirrelationshipwithwindforcing.
ofcurrentvelocityestimates.
2.2.6.Principalcomponentandrotaryspectralanalysis 3.Results
Inordertoidentifyprocessesgoverningsurfacecirculationinthe
IroiseSea,spectralanalysisofvelocityrecordsindifferentlocations 3.1.Tidalcurrents:spatialpatternsandvariability
hasbeenperformed.Fig.3bshowsspectraldistributionofthetotalki-
neticenergyfortwoselectedgridpoints:apointclosesttotheMet Spatial and temporal variability of tidal currents is quantified
bouyandapointinthecentralpartoftheradarcoveragezone(see using the parameters of synthesized tidal current ellipses derived
Fig.1forlocations).Thedistributionclearlyshowsthatsurfacedy- fromthePCAandRSA.TheresultsaresummarizedinFig.8forthe
namicsintheIroiseSeaisdominatedbytides.ThespectrainFig.3b primaryspringtideperiod.Tidalcurrentellipses(Fig.8a)represent
indicate that most of the kinetic energy is distributed between the the 7-day averaged circulation pattern associated with the tidal
dominant tidal frequencies: semi-diurnal, quarter-diurnal, sixth- wavearrivingfromtheGulfofBiscayandtravelingnortheastwardto-
diurnal and diurnal, with prevailing semi-diurnal tide. In sub-tidal wardtheEnglishChannel.Thedetailedanalysisofellipseorientation
shows that tidal currents are controlled by the bottom topography
and peculiarities of the coastline. These factors tend to align the
0.12
radar measurement majoraxesalongthedepthcontours.
wave−induced current Onecandistinguishanisotropyofthecurrentfieldwithrelatively
0.1 highellipseeccentricityinthewesternpartoftheregionandintwo
locationsintheeasternpart:southoftheUshantIs.andinashallow
y
bilit 0.08 waterregionbetweentheMolèneIslandsandBrittanycoast.Thefor-
a mermightberelatedtothecurrentsquashagainsttheislandproduc-
ob ing more circular shape of ellipses. The latter reflects the effect of
r
ce p 0.06 bottTohme sfrpiacttiiaolndoinstrtiibdualticounrroefntthse(Dreoftaanryt,c1o9e6f1fi)c.ient (Fig. 8b) shows
n
e thatcurrentsarerotatingclockwise(cw)inthemajorityofthedo-
ur 0.04 main.Thisfeatureisrelatedtothespatialpatternoftheseasurface
c
oc gradients which tend to follow the propagation of the tidal wave
fromtheGulfofBiscayinabroadcwturnaroundtheBrittanyPenin-
0.02
sula(e.g.Luxetal.,2010).TheCoriolisforceactingonthecurrentsre-
inforcestheircwrotation(Defant,1961).
0 Themaximumnegativevaluesofr(upto−0.9)arefoundinthe
0.01 0.10 1.0 4.0
northeastern part of the region (Fig. 8b). Large positive values (up
velocity m/s
to0.7)areobservedinthreelocationsaroundtheUshantandMolène
Islands (Fig. 8b), and in the vicinity of the Sein archipelago (not
Fig.7.Probabilityofoccurrenceofthevelocitymagnitudeofsurfacecurrentsderived
shown). In the shallow water areas, east of Molène and north of
from radar measurements and the velocity magnitude of wave induced currents
(Stokescurrent). Sein islands, the bottom friction comes into play, alternating the