Wave climatology in the Apostle Islands, Lake Superior

22 Pages·2015·7.13 MB·English

PUBLICATIONS
Journal of Geophysical Research: Oceans
RESEARCH ARTICLE Wave climatology in the Apostle Islands, Lake Superior
10.1002/2014JC010278
JoshuaD.Anderson1,ChinH.Wu1,andDavidJ.Schwab2
KeyPoints:
(cid:2)WaveclimateoftheApostleIslands 1DepartmentofCivilandEnvironmentalEngineering,UniversityofWisconsin-Madison,Madison,Wisconsin,USA,2U-M
inLakeSuperiorfor35yearwas WaterCenter,UniversityofMichigan,AnnArbor,Michigan,USA
hindcast
(cid:2)Statisticsofthewaveclimatereveal
thespatialvariabilityofwave Abstract ThewaveclimateoftheApostleIslandsinLakeSuperiorfor35year(1979–2013)washindcast
properties
andexaminedusingathird-generationspectralwavemodel.WavemeasurementswithintheApostle
(cid:2)AnincreasingtrendofSWHisfound
duetoclimatechange IslandsandoffshoreNOAAbuoyswereusedtovalidatethemodel.Statisticsofthesignificantwaveheight,
peakwaveperiod,andmeanwavedirectionwerecomputedtorevealthespatialvariabilityofwaveproper-
Correspondenceto: tieswithinthearchipelagoforaverageandextremeevents.Extremevalueanalysiswasperformedtoesti-
C.H.Wu, matethesignificantwaveheightatthe1,10,and100yearreturnperiods.Significantwaveheightsinthe
[email protected]
interiorareasoftheislandsvaryspatiallybutareapproximatelyhalfthoseimmediatelyoffshoreofthe
islands.Duetoreducedwintericecoverandaclockwiseshiftinwinddirectionoverthehindcastperiod,
Citation:
long-termtrendanalysisindicatesanincreasingtrendofsignificantwaveheightsstatisticsbyasmuchas
Anderson,J.D.,C.H.Wu,and
D.J.Schwab(2015),Waveclimatology 2%peryear,whichisapproximatelyanorderofmagnitudegreaterthansimilaranalysisperformedinthe
intheApostleIslands,LakeSuperior,J. globaloceanforareasunaffectedbyice.Twoscientificquestionsrelatedtowaveclimateareaddressed.
Geophys.Res.Oceans,120,4869–4890,
First,thewaveclimatechangeduetotherelativeroleofchangingwindfieldsoricecoversoverthepast35
doi:10.1002/2014JC010278.
yearswasrevealed.Second,potentialblufferosionaffectedbythechangeofwaveclimateandthetrendof
lowerwaterlevelsintheApostleIslands,LakeSuperiorwasexamined.
Received1JUL2014
Accepted10JUN2015
Acceptedarticleonline15JUN2015
Publishedonline14JUL2015
1.Introduction
Informationaboutthewaveclimateiscrucialtomanyenvironmentalandsocietalissues.Forexample,inthe
ApostleIsland,areaofLakeSuperiorrecreationalboatinginvolvestensofthousandsofsailboats,motorboats,
andkayaksperyear[Kraftetal.,2007].Extremewaveconditionscanposenavigationhazardsforrecreational
watercraftandresultintragicdrowningincidents(DuluthNewsTribune,12September2010and9September
2011). Safe design of coastal and offshore structures also requires accurate knowledge of wave climate
extremes[Panchangetal.,2013].Furthermore,waveclimatecanaffectmanygeomorphicandecologicproc-
esses.Particularly,coastalwaveenergyhasbeendirectlyrelatedtoshorelinedamage,propertyloss,andbluff
recession[Meadowsetal.,1997;Swensonetal.,2006;LinandWu,2014].Lakebedsedimentresuspensionhas
beenshowntobedominatedbywave-generatedshearstressduringlargestormevents[Schwabetal.,2006].
Approximately3%ofthecoastlineintheApostleIslandsNationalLakeshoreofLakeSuperiorisdesignatedas
wetland[Kraftetal.,2007],whichissignificantlyaffectedbywaveexposure[Thomasenetal.,2013].Lastbut
notleast,laketroutareeconomicallyimportantspeciesthatpreferentiallyspawninathresholdofelevated
wavedisturbanceorturbulence[FitzsimonsandMarsden,2014].Spatialinformationaboutthewaveclimate
canprovideinsightintothehistoricalandpresentsuccessofembryonicsurvivaloflaketroutintheApostle
Islands[CoberlyandHorrall,1980;Schrametal.,1995].Inviewoftheseimportantconsequences,itisimpera-
tivetocharacterizewaveclimatologyaroundtheApostleIslandsinLakeSuperior.
Determination of wave climate statistics often relies on analysis of historical wave records. Many of the
aforementionedwave-dependentissuesareassessedusingthestatisticaldistributionofthreewavecharac-
teristics:SignificantWaveHeight(SWH),MeanWaveDirection(MWD),andPeakWavePeriod(PWP),i.e.,the
periodatthepeakoftheenergyspectrum.Toaccountforinterannualvariability,theWorldMeteorological
Organization’s(WMO)standarddurationforanevaluationofclimateis30years[WorldMeteorologicalOrga-
nization,2007].HistoricalmeasurementsbytheNationalDataBuoyCenterofNOAAarethebestcandidate
to meet this criterion. In the Great Lakes, these buoys have been in operation since the early 1980s, i.e.,
approximately30years.However,thespatialcoverageofwavebuoysislimitedtoafewlocationsperlake.
Thebuoylocationsaretypicallyoffshore,farawayfromcoastalareaswherewavecharacteristicsaresignifi-
VC2015.AmericanGeophysicalUnion.
AllRightsReserved. cantly altered by nearshore transformation processes. Consequently, wave hindcast through modeling is
ANDERSONETAL. WAVECLIMATOLOGYINLAKESUPERIOR 4869
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10.1002/2014JC010278
usuallyemployedtofillinthepaucityofmeasuredwavedataandprovidethespatialvariabilityofwavecli-
mate[CairesandSterl,2005;Jensenetal.,2012].
Inthepast,modelsforhindcastingwavedatasetshavebeensuccessfullyappliedtoobtainwaveclimate
statistics such as annual means, seasonal variability, return level estimates, correlation with atmospheric
cycles,andlong-termtrendsonbothglobal[SterlandCaires,2005;Chawlaetal.,2013;Stopaetal.,2013a]
andregionalscales[Panchangetal.,2008;Watersetal.,2009;Dodetetal.,2010].IntheGreatLakes,hind-
castingofthewaveclimatehasbeenledbytheU.S.ArmyCorpsofEngineersundertheWaveInformation
Studies(WIS)project[ResioandVincent,1978;Hubertzetal.,1991;Jensenetal.,2012].Recently,theWISpro-
jecthascompletedawavemodelhindcastforLakeSuperiorfortheperiodfrom1979to2012.Datafrom
the WIS project include various products like historical time series of SWH, monthly means and maxima,
extreme value analysis of SWH, and wave percent occurrence tables (http://wis.usace.army.mil/hindcasts.
shtml).Nevertheless,dataarelimitedtotheselectedWISlocationsintheLakeSuperioranddonotinclude
wavesinsidemanyshelteredareas,e.g.,theApostleIslands.Whileotheroperationalwavemodels,including
the Donelan model developed by the Great Lakes Environmental Research Laboratory in the early 1980s
[Liu et al., 1984] and Wave Watch III model developed by National Centers for Environmental Prediction
withimprovedmodelphysics[Alvesetal.,2014],havebeenusedforLakeSuperior,theoverallgridresolu-
tions range from 3 to 10 km. With the dimensions of the Apostle Islands as small as 250 m and adjacent
islandsseparatedbyaslittleas1km,nowavehindcastdatainsidetheislandshavebeenreported.
Giventherecentfindingofclimatechange,assessingthefutureofthewaveclimateisincreasinglyimportant.
Intheocean,waveclimatetrendshavebeenquantifiedduetochangesinwindspeedanddirection[Caires
andSterl,2005;Dodetetal.,2010].InLakeSuperior,increasingsummerwindspeedsoverLakeSuperiorhave
been shown due to a decreased water-air temperature gradient [Desai et al., 2009], supporting the finding
that water temperatures are rising faster than the air [Austin and Colman, 2007]. Liu and Ross [1980]
showedthatunstableconditionscanenhancewavegrowthwhenwatertemperaturesarewarmerthanthe
air.GiventheobservedriseinwatersurfacetemperaturesofLakeSuperiorandalengtheningofthestratified
season[AustinandColman,2007],atmosphericunstabilitycanfurtherelevatethewaveclimate.Furthermore,
trendsofthewaveclimateintheGreatLakescanbeaffectedbytheobservedlossoficecover.Schwabetal.
[2006] showed that decreased ice cover in the southern basin of Lake Michigan allowed for greater occur-
rence of large sediment resuspension events forced by waves. In the Apostle Islands, Howk [2009] showed
thaticecoverhasbeendecreasingatahigherratethantheaveragerateofLakeSuperior,suggestingthat
thewaveclimateintheApostlesisparticularlysusceptibletoclimatechange.Whilemuchevidenceexiststo
indicatethewaveclimateintheApostleIslandsisincreasing,therehasbeennoquantificationofthesetrends
intheApostlesoranywhereontheGreatLakes.Additionally,therehasbeenlittleexaminationofhowwave
climatetrendsaffectedbyicelosscomparedtothosefoundinareasunaffectedbyice.Lastly,relativerolesof
windsandicecoversinmodifyingthewaveclimateintheApostleIslandsareunclear.
Bluffrecession,stronglycorrelatedwithwaveclimate[Swensonetal.,2006],isasignificantissueaffecting
theeconomicdevelopmentandpropertysafelyinthecoastalcommunityintheGreatLakes[Angel,1995;
Meadowsetal.,1997].ConservationoftheshorelineiscruciallyimportantintheApostleIslands,possessing
thelargestcollectionoflighthousesintheNationalParkSystem[Kraftetal.,2007].Inthepast,characteriza-
tion of coastal bluff stability and recession within the Apostles has had to be performed with the limited
informationofthewaveclimate[Swensonetal.,2006;Pendletonetal.,2007].Asaresult,difficultiesinpro-
jecting bluff recession in Lake Superior have been recognized and acknowledged. To remedy this issue,
obtaining reliable wave climate are desperately needed since waves typically play a dominant role in the
recessionratesofcoastalbluffs.Forexample,wavescanelevatebluffrecessionbyerodingnearbylakebed
sediments,aprocessknownasdowncutting[LinandWu,2014].Additionally,wavescanerodesedimentsat
thetoeof a bluff,resultingin asteeperslopethat becomesunstableandis morepronetofailure[Brown
etal.,2005].Meanwhile,waterlevelscanalsoaffectblufferosionbyraisingorloweringtheimpactheightof
wavesonablufftoe[Meadowsetal.,1997;Castedoetal.,2013].Brownetal.[2005]andSwensonetal.[2006]
showed that bluff recession is correlated well with the magnitude-based wave impact height, defined as
theelevationofwaverunupminustheelevationofablufftoe.WhilethemeanwaterlevelsonLakeSupe-
rior have been steadily decreasing over the past 30 years [Assel et al., 2004; Gronewold et al., 2013], it is
unclearifthelowerlakelevelsreducetheelevatedwaveclimateonoverallimpactofcoastalbluffsinApos-
tleIslands.
ANDERSONETAL. WAVECLIMATOLOGYINLAKESUPERIOR 4870
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The objective of this paper is to analyze the wave climate of the Apostle Islands in Lake Superior to the
addressthetwosciencequestions.First,howwouldthewaveclimatechangeduetochangingwindfields
or ice covers over the past 35 years? Second, how would the combined changing wave climate and the
trend of lower water levels affect the coastal bluff erosion? To answer these questions, a wave model of
LakeSuperiorwithjustifiablespatialresolutionintheApostleIslandsregionisdevelopedandappliedina
35yearhindcast(1979–2013).WavemeasurementscollectedwithintheApostleIslandsandfromoffshore
NOAAbuoysareusedtovalidatethemodel.Statisticsofthewaveclimateincludingsignificantwaveheight,
peakwaveperiod,andmeanwavedirectionareobtainedforaverageandextremeevents.Extremevalue
analysisisperformedtoestimatethesignificantwaveheightforarangeofreturnperiods.Long-termtrends
ofwaveheightarequantifiedtoevaluatetheeffectsofclimatechangeonwaveclimatestatistics.Finally,
theeffectsofwaveclimateandlowwaterleveltrendonblufferosionareexamined.
The paper is organized as follows. Description of the bathymetry and atmospheric climate in the Apostle
Islandsisprovidedinsection2.Section3describesthedatasourcesformodelinputsofwindandice,wave
modelperformance,thestatisticalmethodsappliedintheanalysisofthehindcastwaves,andthemethod
forbluffrecessionanalysis.Section4presentstheresultsofthehindcastincluding:statisticsofthreewave
climate parameters (SWH, MWD, and PWP), return value estimates of SWH, long-term trends in SWH, and
trendsinwaveimpactsoncoastalbluffs.Section5discussestheperformanceandlimitationofwavemod-
eling, effects of ice-time on wave statistics, the role of ice and wind on long-term wave climate statistics,
and the role of water level and wave climate on bluff recession. Finally, a summary of the major findings
fromthisstudyisgiveninsection6.
2.StudySite
TheApostleIslandsarelocatedofftheBayfieldPeninsula(BP)inthewesternarmofLakeSuperior.Including
all21islandsandtheadjacentmainland,thesitecontainsover300kmofGreatLakescoastline[Kraftetal.,
2007]. Water depths within the archipelago are typically less than 60 m except for a deep channel in the
east,whichrangesfrom100to140m(seeFigure1).Alongthenorthwesternboundary,watersareshallow
withdepthsrangingfrom40mtolessthan20m.Multipleshoalsandheadlandsexistpredominantlyatthe
outeredgesoftheislandnetworkwithnortheastalignment,mostnotablytheGullShoal(GS)attheeastern
exterior.ANOAAmeterologicalstation(DISW3),locatedonthenorthernboundaryofthearchipelago,has
collectedhourlywindmeasurementssince1983.ThehistoricalrecordofDISW3indicatesthattheaverage
windspeedis5.03m/swithameandirectiondirectlyfromthewest.Thestrongeststormwindsblowfrom
thenortheastbutlargewesterlywindeventsareequallycommon.Icecoverhasahighinterannualvariabili-
tyandmaybepresentfromDecembertoMay[Assel,2003;Kraftetal.,2007].IcecoverattheCityofBay-
field,locatedontheeasterncoastoftheBP,hasbeendecreasingatarateofapproximately14.7daysper
decadesince1975[Howk,2009].
3.Methods
3.1.Data
3.1.1.WindField
In this study, gridded 10 m winds (U ) from the Climate Forecast System Reanalysis (CFSR) were usedto
10
drivethewavemodel.TheCFSRproductsareproducedbytheNationalCenterforEnvironmentalPrediction
(NCEP)usingacoupledglobalatmospheric-oceanic-ice-landmodelwithadvanceddataassimilationtechni-
quesandanextensivedatabaseofmeteorologicalobservations[Sahaetal.,2010].TheoriginalCFSRdata
setspansfrom1979to2010andcontinuestooperateasthesecondversionoftheClimateForecastSystem
(CFSv2)withmultipleimprovementsoverCFSR,includingahigherspatialresolution[Sahaetal.,2014].Spa-
tialresolutionoftheCFSRisapproximately38km((cid:3)20kmforCFSv2)andtemporalresolutionis1h,asig-
nificant upgrade from previous global reanalysis products. The spatial resolution rivals focused regional
products like the North American Regional Reanalysis. Data can be accessed through the National Center
forAtmosphericResearch(http://rda.ucar.edu/pub/cfsr.html).
ComparisonofCFSRwindswithmeasurementsfrommeteorologicalstationsatthestudysitesandoffshore
buoyswasmadehere.Atmosphericstability,whichcanaffectwavegrowth,wasaccountedforbyadjusting
CFSR gridded winds to an equivalent neutrally stable wind speed [Liu and Schwab, 1987]. Specifically, all
ANDERSONETAL. WAVECLIMATOLOGYINLAKESUPERIOR 4871
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Figure1.ApostleIslandsbathymetrymapandlocationonLakeSuperior.Sitesidentifiedwithacircle(•)aremeteorologicalorwaveobser-
vationstations.Sitesidentifiedwithatriangle(~)areUSACEWISstations.Sitesidentifiedwithasquare((cid:2))arelocationsanalyzedfor
waveimpactsonbluffs.TheunstructuredSWANmeshappliedinthehindcastisoverlaidonthemap.Thenonhydrostaticphase-resolving
modeldomainisidentifiedasaboxfilledwithdiagonallinesatapproximately478Nand290.98E.
measured data wereconvertedto 10 m height using the Monin-Obukhov similarity theory.Figure 2 shows
statisticalcomparisonsofCFSRandmeasuredwindsattwocoastalstations(DISW3andSXHW3)andtwooff-
shorebuoylocations(St.45006andSt.45001).Ingeneral,CFSRwindsmatchwellwiththeobservations,espe-
ciallyatlarge windspeeds,but CFSRwinds slightly overpredictmeasuredvalues(positivebias) with higher
biasesattheoffshorebuoys.Ofthefourstationsshown,onlySXHW3waslocatedinalandcellintheCFSR
model.Consequently,CFSRunderpredictsobservedwindspeedspresumablyduetoahigherdragcoefficient
implementedforland,whichisconsistentwithfindingsoftheCFSRwindsneartheland-seainterfaceinthe
ocean[Chawlaetal.,2013].Toaccountforthisunderprediction,weextrapolatedCFSRwindmagnitudesfrom
sea/watergridstolandgridsandretainedtheoriginaldirectionofthelandgrid.Abetteragreementbetween
theextrapolatedandmeasuredwindsatthehigherquantilesisshowninFigure2c(plusmarkers).
Water temperatures were obtained from the ‘‘Great Lakes Surface Environmental Analysis’’ product of the
NOAACoastWatchnodeatGLERL.Dailyaveragedlakewidesurfacetemperaturesfrom1995to2013were
availableandthelong-termaveragedtemperatures(1992–2013)wereusedforyearspriorto1995.Gridded
air temperatures were from the CFSR data archive. An extrapolation technique similar to the technique
usedforgriddedwinddatawasemployedforairtemperaturesattheland-seainterface.
3.1.2.IceField
Icethatcanimpedewaveformationandtransmissionwasconsideredinthewavemodelhindcast.Theinter-
actionbetweenwavesandiceisacomplexprocessthatshouldbeaddressedinwavehindcast.Inthisstudy,
weemployeda commontechniquebymaskingmodelgridswithlandwheniceconcentrationexceededa
particularthreshold.Iceconcentrationistheareaoficecoverdividedbythetotalareaofwater.Previousstud-
ieshaveimplementedarangeoficeconcentrationthresholdsrangingfrom30to50%[Hubertzetal.,1991;
Bennington et al., 2010; Tuomi et al., 2011]. Furthermore we implemented a land mask by lowering water
depthstozerowheniceconcentrationsexceededathresholdof30%undertheassumptionthatwavescan
be consideredunaffected by icefor ice concentrations 30% andbelow[Tuomi etal.,2011]. Great Lakes ice
data prior to 2003 have been digitized to gridded fields, which are available at http://www.glerl.noaa.gov/
ANDERSONETAL. WAVECLIMATOLOGYINLAKESUPERIOR 4872
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Figure2.ScatterdensityplotsofCFSRandobservedU10(m/s)atselectlocations.Colorscalingislogarithmicandrepresentsthepercentageofhourlyrecordsoccurringwithina0.53
0.5m/ssquare.AlsoshownareQ-QplotsforrawCFSRandobservedU10(solidcircle).Atstation(c)SXHW3,aQ-QplotfortheextrapolatedoverseaCFSRwindsandobservedwindsis
shown(plus).Theverticalandhorizontaldashedlinesrepresent99.9%quantileforeachsource.Thethickgreylineisthelineofequivalence.Collectionperiodsfortheavailableobserva-
tionsareshownaboveeachplot.
data/ice/atlas[Assel,2003].After2003,griddedfieldsoficeconcentrationhavebeenproducedbytheNOAA/
National Ice Center and can be obtained online (http://www.natice.noaa.gov/products/great_lakes.html).
Griddediceconcentrationsrangedfrom0to99%andthespatialresolutionrangedfrom1.25to2.5km.Ice
concentrationdatawerelinearlyinterpolatedintimeto adailyresolution [Assel,2005].Spatialinterpolation
fromgriddedicedatatomodelgridswasaccomplishedbythenearestneighbortechnique.
3.1.3.WaveMeasurements
Offshorewavedataatthethreebuoys, Stations(St.) 45001, 45004, and45006 (see Figure1), weredown-
loadedfromtheNOAANationalDataBuoyCenter.Datesofthemeasurementsvariedslightlyforeachbuoy
but nearly covered the full duration of the model hindcast (Table1). Each buoy measured SWH and PWP
duringtheircollectionperiods,butonlySt.45001beganmeasuringMWDin2004.Furtherwavemeasure-
mentswithintheApostleIslandswerecollectedatthreesites(Figure1)atvarioustimesbetween2011and
2013(Table1).AttheGSandOakShoal(OS)sites,a1MHzNortekAcousticWaveandCurrent(AWAC),man-
ufacturedbyNortekAS,wasdeployedatapproximately12mwaterdepth.TheAWACusesacombination
ofacousticsurfacetrack,pressuresensor,andacousticvelocimetrytomeasureSWH,PWP,andMWD[Nortek
AS, 2005]. At the sea cave (SC) site, wave measurements were obtained using a single Acculevel pressure
sensor, manufactured by Keller America, at 1.8 m above the bed in a water depth of 4 m. Pressure data
wereconvertedtobulkwavestatisticswithapplicationofthelineartransferfunctionandspectralanalysis
ANDERSONETAL. WAVECLIMATOLOGYINLAKESUPERIOR 4873
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Table1.SWANModelHindcastValidationStatisticsatAvailableLocations
SWH PWP Direction
Site RecordDuration Bias(m) RMSE(m) SI R Bias(s) RMSE(s) SI R Bias(8) RMSE(8)
SC 5Jun2011to11Oct2013 20.02 0.12 0.47 0.85 20.27 1.20 0.35 0.63
OS 2Jul2013to1Oct2013 20.03 0.10 0.44 0.77 20.12 0.90 0.34 0.60 9.6 41.2
GS 11Oct2011to14Jan2012 0.06 0.18 0.26 0.92 0.04 1.00 0.25 0.76 3.2 34.8
St.45006 22Jun1981to30Nov2013 20.02 0.27 0.42 0.88 20.25 0.99 0.25 0.76
St.45001 3May1979to31Dec2013 20.02 0.30 0.37 0.90 20.19 0.80 0.18 0.82 7.7a 32.0a
St.45004 26Apr1980to23Apr2013 0.04 0.29 0.37 0.91 20.08 0.79 0.18 0.81
ST95231 1Jan1979to31Dec2012 0.04 0.15 0.38 0.94 0.22 0.83 0.25 0.85 2.5 35.7
ST95216 1Jan1979to31Dec2012 0.02 0.15 0.29 0.96 0.20 0.75 0.21 0.89 21.5 28.7
ST95205 1Jan1979to31Dec2012 0.01 0.14 0.53 0.88 0.11 1.19 0.38 0.77 0.1 43.3
aDirectionaldatalimitedto21April2004to31December2013.
[Sorensen, 2006; Jones and Monismith, 2007], which has been shown to produce wave height estimates
accuratetowithin5%[BishopandDonelan,1987].MWDestimatescouldnotbedeterminedfromthepres-
suresensor,butMWDismostlikelyperpendiculartotheshoreduetorefractiveeffects.Timeseriesplotsof
themeasured SWHs and PWPsduring the most energetic conditions foreach site will be shownand dis-
cussedinsection3.2.2.
3.2.Modeling
3.2.1.WaveModel
The third-generation spectral wave model, Simulating WAves Nearshore (SWAN), was used to estimate
waveparametersinthisstudy.AfullyimplicitnumericalschemewasimplementedtotheSWANmodelto
remove the Courant stability criterion in explicit time stepping schemes [Booij et al., 1999]. To further
improvetheefficiency,recentmodificationsincludethedevelopmentofaparallelizedcodestructureand
unstructuredgrids[Zijlema,2010].SWANhasbeensuccessfullyappliedtomanycoastallocationstoexam-
inewaveclimate[Gormanetal.,2003;Panchangetal.,2008;Watersetal.,2009;Stopaetal.,2013b].
Inthisstudy,weconstructedanunstructuredmeshforthewholeofLakeSuperiorwithhigherresolutionin
theApostleIslands.Themeshconsistedofapproximately27,000triangularelementsrangingfromacharac-
teristiclengthof5kmthroughoutthemajorityofthelakeareato100–500mintheApostleIslandsregion
(Figure1).Discretizationinspectralspacewassetupwith50logarithmicallyspacedfrequencybandsrang-
ing from 0.05 to 5 Hz and 36 evenly spaced directional bands of 108. The model time step was set to 10
min.Allavailablesourcetermformulationsandtunableparametersweresettotheirdefaultvalues[SWAN
Team, 2013] except for wind growth and whitecap dissipation, which were set to the formulations com-
monly referred to as WAM cycle 4 [Booij et al., 1999]. Currents and fluctuating water levels were omitted
duetotheuncertaintyinthewindforcing,whichismostcommonlythedominantsourceoferrorinwave
modeling [Jensen et al., 2012]. To implement a land mask for ice cover, water surface elevations were set
belowbedelevationswhereicewaspresent.Modelgridswithzerowaterdepthwereeffectivelyremoved
fromthecomputationaldomainofthewavemodelandbehavedsimilarlytolandboundaries.
3.2.2.CalibrationandValidation
TheSWANmodelwascalibratedbyvaryingtwoparametersinthewhitecapdissipationformulation[SWAN
Team,2013].Theoverallrateofwhitecappingdissipation,C ,wasvariedwithincrementsof0.5from1.0to
ds
6.0,andtheparameterwhichdeterminesthedependencyofwhitecappingbasedonwavenumber,d,was
varied by increments of 0.2 from 0.0 to 1.0. Evaluation of the results was based on minimizing the root-
mean-squareerror(RMSE)betweenthemodelandmeasuredSWHattheSCandGSsitesfortheperiod10–
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
31October2011.TheRMSEisdefinedbyRMSE5 1 PN ðM2OÞ2,whereNisthenumberofsamples,M
N i51 i i
is model data, and O is observation data. Numerical tests revealed that both sites exhibited a similar
response in RMSE to variations in the calibration parameters and that RMSE quantities were minimized
whenC 53.5andd51.0.DefaultvaluesfortheSWANmodelareC 54.5,d50.5;however,itisrecom-
ds ds
mendedtoused51.0forbetteragreementofPWPsduringlowenergyeventswhileretuningC [SWAN
ds
Team,2013].AnapplicationofSWANintheGulfofMexicofoundC 52.0andd50.7providedthebestfit
ds
[Siadatmousavietal.,2011].
ANDERSONETAL. WAVECLIMATOLOGYINLAKESUPERIOR 4874
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Figure3.ScatterdensityplotsoftheSWANandWISmodeledSWHs(m)atthreelocations(seeFigure1).Colorscalingislogarithmicandrepresentsthepercentageofhourlyrecords
occurringwithina0.130.1m2.AlsoshownareQ-QplotsforSWANandWISSWHs(solidcircle).Theverticalandhorizontaldashedlinesrepresentthe99.9%quantileforeachsource.
Thethickgreylineisthelineofequivalence
Validation of model performance was based on statistical quantities commonly applied in wave modeling
studies[Gormanetal.,2003;Stopaetal.,2013b].Specifically,thebias51 PN ðM2OÞ,RMSE,scatterindex
N i51 i i
(SI)5 RMSE ,andcorrelationcoefficients(R)forSWH,PWP,andMWDwereevaluated.ForMWD,alimitof
N1 PNi51Oi
1808wasappliedtoerrorestimates(M-O)duetothecircularnatureoftheproperty.Validationstatisticswere
computedwithtwosourcesofdata.First,wecomparedtheSWANmodelresultstotheUSACEWIShindcast
results, which were computed with the WAM Cycle 4.5 wave model [Jensen et al., 2012]. In this case, WIS
modelresultsreplacedobservedvalues(O)inthecomputationofthestatistics.Table1showsthevalidation
statisticsatthreeWISstations(ST95231,ST95216,andST95205),locatedaroundtheperimeteroftheApostle
Islands(seeFigure1).Inaddition,weexaminedthescatterdensityandQ-QplotsofSWHtocomparemodel
resultsforextremeevents(Figure3).Whiledifferencesexistbetweenthetwohindcastresults,thetwodata
setscorrelatewell.Second,wecomparedtheSWANmodelhindcastresultstoavailableinsitumeasurements.
Table1summarizestheresultsforthethreesitesintheApostleIslandregionandthethreeNOAAbuoys.In
general,thewavemodelperformedreasonablywellinpredictingSWHwithlowbiasesandRMSEs.SIvalues
for the SWHs are slightly higher than those reported in other studies [Stopa et al., 2013; Rusu and Guedes
Soares, 2012],but this maybe explained bythecomparatively smallmean observed SWHsfrom this study,
whichisknowntoinflateSIvalues[Risetal.,1999].ValidationstatisticsforSWHswerecomparablebetween
measurementsitesintheApostleIslandsandatopenlakebuoyswiththeexceptionofslightlybettercorrela-
tioncoefficientsatthebuoys.Duetoambiguityinthespectralpeakandwavedirectionduringlowenergy
conditions,estimatesforPWPandMWDwerelimitedtotimeswhenSWH>0.15m.ModeledPWPswerebet-
teratoffshorelocationswithlowerSIvaluesbyasmuchasafactorof2.Validationstatisticsfortheoffshore
buoyswerealsocomputedoverthesametimeperiodasthenearshoreApostleIslanddataandasimilartrend
wasfound.ThenegativebiasinPWPisduetoawell-knownlimitationofSWANduringlowenergyconditions
[SWANTeam,2013].Anindicationofbettermodelperformanceduringmoreenergeticconditionsisseenfor
theGSsite,whichwasdeployedduringthefallandrarelyexperiencedcalmconditions.Astatisticaltrendsim-
ilartoPWPisseenforMWD.Overall,themodelperformanceisconsistentwiththeothermodelingstudiesin
thatthevalidationstatisticsofwavemodelingexhibitslowerqualityinshelteredandnearshorelocationsdue
to the more complex wave processes [Rusu et al., 2008]. In addition, the accuracy at offshore locations
increasessincewavecharacteristicslikePWPandMWDarebetterdefinedatlargervalues.Forinstance,when
SWH>0.5m,wavedirectionRMSEvaluesdecreaseto16.88and23.28fortheOSandGSsites,respectively.
Figure 4 shows time series plots for SWH at the three measurement sites inside theApostle Islands. Each
timeseriesspans60daysofmeasurementsandcontainsstormswithdominantwindsfromtheNEandNW
(windsnotshownhere).Modelwaveheightsmatchwellwithobservationsforboththepeakandduration
ofstormevents.Figure5showstimeseriesplotsofmodelandmeasuredPWPforthesamedatesshownin
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Figure4.SWHcomparisonsofmodel(solidline)andmeasurements(solidcircle)collectedwithintheApostleIslands.Duetothedeploy-
mentschedule,collectionyearsvarybetweensites:2011forSC,2013forOS,and2011–2012forGS.
Figure 4. ObservedPWP measurements were excluded if SWH<0.15 m. Overall, the SWAN model does a
reasonablejobcapturingPWPmagnitudes,especiallyduringenergeticconditions.However,afewinstan-
cesofrelativelylargeerrorsdoexist(Figure5aon5October,Figure5con9November),whichmaypartially
explainthelargererrorstatisticsatsiteswithintheislands(Table1).Shortinstancesofswellarewellpre-
dictedatthetailendofstormevents,whichcanbeseenmostvisiblyinFigure5aon1October.Themodel
performsconsistentlyinpredictingstormeventswithvariouswinddirections,demonstratingthereliability
andaccuracyofthemodelinsimulatingwindwavesthroughouttheApostleIslands.
3.3.Analysis
3.3.1.WaveStatistics
Statistics for the wave climate were based on the hourly model output over the duration of the hindcast
withtheomissionofperiodsofice.Effectsofomittingicecoveredperiodsinthecalculationofwaveclimate
statistics[Tuomietal.,2011]willbeaddressedinthediscussionsection.Inthisstudy,wavestatisticsinclud-
ingmean,0.90and0.99quantiles,andmaximumvaluesofSWH,PWP,andMWDwerecalculated.Thedeci-
mal of the quantile specifies the fraction of the data that do not exceed the quantile value. Unlike
calculatingstatisticsofSWHfromtheentirehindcastrecord,statisticsofPWPandMWDwerebasedoncon-
ditionspresentduringequivalentstatisticsofSWH.ThisdefinitionwaschosenbecausethemaximumPWPs
inthehindcastoccurredasintermittentswellduringsmallSWHs,e.g.,seeFigures4and5fortheGSsiteon
31 December. So, the maximum PWP and MWD correspond to the values present during the maximum
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Figure5.PWPcomparisonsofmodel(solidline)andmeasurements(solidcircle)collectedwithintheApostleIslands.EstimatesofPWP
duringlowwaves(H <0.15m)wereexcludedfromanalysis.YearsoftheplotsvarybetweensitesandarethesameasFigure4.
S
SWH.SincearangeofPWPsandMWDsoccurredforagivenquantileofSWH,arepresentativevaluewas
calculated by averaging PWPs or MWDs when the SWH was within 61 cm of the quantile value. This
methodeffectivelydeterminesthePWPsandMWDsthataremostprobableforagivenquantileofSWH.
3.3.2.ExtremeValue
EstimatesofSWHatvariousreturnperiods(i.e.,1,10,and100years)werecalculatedateachelement(loca-
tion)inthemodel.Thepeaks-over-threshold(POT)methodwasappliedtoselectindependenteventsfrom
thecontinuoustimeseriesofSWHs.Consecutiveexceedancesofthethreshold(i.e.,clusters)wereconsid-
eredasasingleindependenteventfromwhichonlythemaximumvaluewasretained.Duetothevariability
ofwindsinasinglestorm,werequiredthetemporalboundariesofconsecutiveclusterstobeseparatedby
at least 48 h [Caires and Sterl, 2005; Aarnes et al., 2012] to further ensure only independent events were
selected.DatasetsselectedbythePOTmethodwereassumedtobeindependentlydistributedwithagen-
eralizedParetodistribution(GPD)withacumulativedistributionfunctiongivenby
8
>>><12(cid:3)11nrx(cid:4)21=n if n6¼0
FðxÞ5 (1)
>>>:12exp(cid:5)2x(cid:6) if n50;
r
wherexvaluesarethePOTselecteddatasetminusthethresholdandtherangeofxisð0;1Þifn(cid:4)0and
ð0;r=nÞifn>0[Coles,2001].Theparametersnandrarereferredtoastheshapeandscale,respectively.
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Shape and scale parameter estimates were fitted using the maximum likelihood approach. Evaluation of
the fits was accomplished based upon the Anderson-Darling goodness-of-fit-test at the 5% significance
level[ChoulakianandStephens,2001].ThetestallowedustodeterminethevalidityofthefittedGPDand
appropriatethresholdvalues.
Inthisstudy,weusedthe95%quantileofthecompleteSWHtimeseriesforthethreshold,whichyieldeda
valid fit of the GPD at 85% of model grids. For locations with invalid fits using the 95% quantile as the
threshold,thequantilepercentagewasincrementallyincreasedupto99.5%untilavalidfitwasachieved.
Thequantilepercentagesappliedinsettingthethresholdsherearewithintherangeusedinotherstudies:
93–97%[Caires andSterl,2005] and99.7%[Aarneset al.,2012]. Afterdetermining thethreshold value, we
estimatedthereturnvalueas
8 rh i
<l1 ðkNÞn21 if n6¼0
x 5 n (2)
N
:l1rlogðkNÞ if n50;
wherelisthethreshold,kistheaveragenumberofexceedanceeventsperyear,andNisthereturnperiod
inyears.
3.3.3.Long-TermTrends
Tocalculatelong-termtrendsoverthe35yearhindcast,theleastsquareslinearregressionfitwasapplied
toannualstatistics.Duetothewintericeseason,weappliedthecommonpracticetocalculateannualsta-
tisticsbasedupontheclimateyear,definedasbeginningandendingonJunefirst[Schwabetal.,2006].The
Mann-Kendalltest[McLeodetal.,1990;WangandSwail,2002]wasusedtoassessthesignificanceofatrend
andtrendswereconsideredstatisticallysignificantwithapvaluelessthan0.05,i.e.,95%confidence.Long-
termtrendsofmultiplevariableswereexaminedinthisstudy:meanSWH,0.90and0.99quantilesofSWH,
icecoverduration,meanwindspeed,andmeanwinddirection.
3.3.4.NormalizedCumulativeWaveImpactHeight
Coastalbluffrecessionoccurswhenwaveactionerodestheblufftoe.Acommonindexforbluffrecessionin
the Great Lakes is thewave impact height (WIH), definedas the difference between wave runup and the
blufftoeelevation:
WIH5MWL1R1S2TOE (3)
whereMWListhemeanwaterlevelelevation,Risthewaverunupheight,Sisthewindsetup,andTOEis
theelevationoftheblufftoe[Brownetal.,2005].Swensonetal.[2006]proposedcumulativewaveimpact
height(CWIH),whichisthepositiveWIHsintegratedoveratimeperiod,toaccountforthefrequency,dura-
tion,andmagnitudeofallwaveeventsthatacttoerodeablufftoe.
Inthisstudy,weexaminethetrendsinCWIHatsixsites,asseenassolidsquaresinFigure1.Thethreesites
onthemainland(B1–B3)arecolocatedwithonesanalyzedinSwensonetal.[2006],andthethreesitesare
locatedontheislands(B4–B6)identifiedashavinghighcoastalchangepotentialbyPendletonetal.[2007].
SitesB5andB6havehistoricallighthousesatopthebluff.ToestimatetheWIHateachlocation,equation(3)
was applied. Mean water levels of Lake Superior were obtained at a monthly interval from the USACE-
Detroit District over the hindcast period. Wave runup was calculated using the modified Mase method
[Melby,2012]withdeepwaterwaveheightsandpeakperiodstakenfrommodelgrids(cid:3)1kmoffshoreofa
site.BeachslopesandtoeelevationsusedinrunupcalculationswereacquiredfromSwensonetal.[2006]
forsitesB1–B3andestimatedfromphotographsoftheshoresduringvisitstositesB4–B6.Windsetupand
setdownwereestimatedwithalinearforcebalanceapproach[Sorensen,2006].TheWIHwasestimatedat
each1houtputfromthehindcast.TheCWIHwastherebycalculatedbyintegratingovereachclimateyear
andnormalizingbythenumberofdaysinthatyear.Asimilarlong-termtrendanalysiswasperformedon
theCWIHsoverthehindcastperiodasdescribedinsection3.3.3.
4.Results
Inthissection,theresultsfromthe35yearhindcastarepresented.Contourplotsweregeneratedtoillus-
trate the spatial variability of the results within the Apostle Islands. To improve readability, contour plots
weresmoothedusingamedianfilterovera1km2area.
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