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InitialDraft
InvestigationofWaveEnergyConverterEffectsonNear‐shoreWaveFields:
ModelGeneration,ValidationandEvaluation‐KaneoheBay,HI
JesseRoberts*,Grace,Chang**,andCraigJones**
*SandiaNationalLaboratories**SeaEngineeringInc.
March2012
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TableofContents
TableofContents......................................................................................................................................................ii Introduction................................................................................................................................................................1 Model.............................................................................................................................................................................2 SWANValidation......................................................................................................................................................4 Results...........................................................................................................................................................................5 Summary...................................................................................................................................................................14 References................................................................................................................................................................15
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IntroductionKaneoheBay,locatedonthewindward(northeastern)sideoftheislandofOahu,Hawaii,presentlyhasashallowwater(30m)waveenergytestberthandisunderconsiderationtodevelopuptotwoadditionalberthsindeeperwaters(60m‐70m)potentiallymakingitthelocationofthefirstfullscalewaveenergytestsite(WETS)intheUnitedStates(Figure1).OneobjectiveoftheWETSistoprovide a location that contains all necessary in‐water and land‐side infrastructure to supportsimpleconnectionofup to threewaveenergyconversion(WEC)devices for testingpurposes.Tosupport the site‐selection process, it is necessary to determine the anticipated incident waveclimateonthestudysite,aswellastheeffectsoftheWEConthepropagationofwavesintoshore.As such, a numerical model was developed in order to better comprehend both the existingcondition(i.e.noWECdevice)waveconditionsandthosethatmaybepresentwhenaWECdevice(orWECarray) is installed. Specific concerns include,butarenot limited to, impactsof theWECdevice(s)onthenear‐shorerecreationalsurfclimateaswellasresultantshorelineerosion.
Figure1.Left:MapofOahu,HIwithKaneoheBayoutlinedinred.Right:MapofKaneoheBay.
As deepwater waves approach the coast, they are transformed by certain processes includingrefraction (as they pass over changing bottom contours), diffraction (as they propagate aroundobjects such as headlands), shoaling (as the depthdecreases), andultimately, energydissipation(duetobottomfrictionandbybreaking).Thepropagationofdeepwaterwavesintothestudysitewasmodeledusingtheopen‐sourceprogram,SWAN(SimulatingWAvesNearshore),developedbyDelft Hydraulics Laboratory. SWAN has the capability of modeling all of the aforementionedprocessesinshallowcoastalwaters.TheSWANmodelisanon‐stationary(non‐steadystate)thirdgenerationwavemodelbasedonthediscrete spectral action balance equation. SWAN is fully spectral over the total range of wavefrequencies. Wave propagation is based on linear wave theory, including the effect of wavegenerated currents. The processes of wind generation, dissipation, and nonlinear wave‐waveinteractions are represented explicitly with state‐of‐the‐science, third‐generation formulations.SWAN provides many output quantities including, but not limited to, two dimensional spectra,significantwave height (Hs), wave period (mean and peak, Tp), wave direction (peak andmean,MWD),anddirectionalspreading.TheSWANmodelhasbeensuccessfullyvalidatedandverifiedin
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laboratory and complex field cases. Sandia National Labs and Sea Engineering, Inc. (SEI) havevalidatedthemodelatnearbyWaimanaloBayaswellasseverallocationsonthemainlandUnitedStates(e.g.SantaCruzBight,MontereyBay,andHumboldtBay,California).
ModelThe SWAN model requires minimum inputs typical of numerical wave propagation models:boundaryconditionssuchasoffshoredeepwaterwaveparameters(Hs,Tp,andMWD)andthesite’sbathymetry. The digital elevation model (DEM) used to generate the model topography andbathymetry was gathered from an SEI survey of the proposed WETS location and the MainHawaiian IslandsMultibeamSynthesisprojectwebsite,apartof theHawaiianMappingResearchGroup(HMRG)attheUniversityofHawaiiatManoa.1SeaEngineering,Inc.haspreviouslycollectedhigh‐resolutionmulti‐beamdatawithintheproposedWETS boundaries. In addition, adjacent, high‐resolution, near‐shore multi‐beam datasets and acoarseresolution(50mgridspacing)datasetwereobtainedfromtheHMRGwebsitetocomprisesufficientdatatofillthenumericalmodelingdomain.Figure2illustratestheSWANmodelgridbathymetryandmodeldomainextents.Thebathymetricgridcellsize is50metersonasideandtheoveralldomaindimensionsareroughly25kminthenorth‐south direction and 30 km in the east‐west direction. For model validation purposes, asimplistic,coarsegridmodelwasemployed.Thecoarsegridwavespectrumboundaryconditionswere parametrically specified along each of the offshore boundaries (northerly, easterly, andsoutherly) of themodel domain in entirety. A constant parameter significant wave height, peakwaveperiod, andmeanwavedirectionwas selected for each coarse gridmodeling scenario andcorresponding offshorewave spectra (frequency anddirection)were subsequently generatedbythemodel code. Inorder to investigate thepotential effectsofnear‐shoreWECdevices, anestedgridmodelwasoperatedsuchthatthecoarsegridmodel(describedabove)propagatedwavesfromdeepwater into a near‐shore, finer gridmodel.Modeledwave spectra from the coarse gridwerespecifiedforeachgridpointinthefinergridmodelandallowedtopropagateintoshore.The coarse grid offshore wave conditions for validation exercises were derived from NationalOceanic and Atmospheric Administration (NOAA) National Data Buoy Center (NDBC) Station51000.Westerlywavesareblockedby landatKaneoheBay soonlywaves fromanortherly andeasterlydirectionwereusedas input to themodel forvalidation. In this investigation, themodelwas run as a stationary (steady‐state)modelwithin SWAN.Model validationwas providedwithdatafromanear‐shoreCoastalDataInformationProgram(CDIP)buoy.Thecoarsemodelcomputationalgridcomprisedofthesameoveralldomaindimensionsasthegridbathymetry(25kmby30km).Thecomputationalgridspacingusedforthisinvestigationwas100metersonaside.Thecoarsergridspacingprovidedforcomputationallyefficientmodelgeneration,validation,andevaluation.Inordertoascertainthelocaleffectsofsmall‐scaleWECdevicesontheproximate wave conditions, a finer gridmodel computational grid was operated. The finer griddomaindimensionswereapproximately1kmby1kmwith20metergridspacingonaside(Figure2).
1http:// www.soest.hawaiian.edu/HMRG/Multibeamn/index.php
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WECdeviceswere represented in themodel as “obstacles” towave propagation. An obstacle, inmodelsense,hindersorcompletelyblockswavepropagation.ThoughthereareseveraloptionsforspecifyinghowobstaclesareutilizedinSWAN,themostbasicisaspecificationoftransmissionandreflection coefficients, which basically specify the fraction of wave energy that is allowed totransmitpastandtheamountofwaveenergythatisreflectedby,theobstacle.Forsimplicityandextremeconservatism,thetransmissionandreflectioncoefficients inthis investigationwerebothsetequalto0(i.e.noreflectionortransmission,energyis100%absorbedbytheobstacle).Thesecoefficient values will produce the largest changes in wave propagation parameters (e.g. waveheightsandperiods)andareconsideredenvironmentallyconservative.Morespecificinformationonenergyabsorptionwillbeincorporatedinfuturework,whenmoreinformationisknownaboutthetypesofWECdevicesthatwillbedeployedattheWETS.Furthermore, when obstacles are specified in SWAN, they need to intersect with a connectionbetween two grid points to have any effect on model predictions. The implications of this aretwofold: 1)Obstacle(s)maynothave any effect onmodelpredictions if theydonot cross a gridpointconnectionand2)theeffectofobstaclesonwavepropagationisdirectlydependentuponthecomputational grid spacing.Obstaclesof varyingdimensionsmayhave the sameeffectonmodelpredictions if they each cross the same connection(s) between grid points. In thismodel study,since the computational grid spacing is approximately 20 meters on a side, obstacles (i.e. WECdevices)smallerthanthiscannotberepresented.
Figure2.Modeldomainbathymetrywith30,60,and90mcontoursdrawnforreference.White
coloringindicatesland(elevationabove0ftMSL).Thedashedboxdenotestheboundariesofthefinergrid,nestedmodel.TheblackstarindicatesthelocationoftheMokapuPointCDIPbuoyusedfor
modelvalidation.ThewhitesquaresdenotethelocationsofmodelobstaclestosimulateWECdevices.
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SWANValidationThe SWANmodelwas validated by initiating coarse gridmodel scenarioswith deepwaterwaveparameters obtained from the NOAA NDBC Station 510002. The buoy is located at 23°32’47”N,154°3’20”W in approximately 4000 meter water depth. Model results were extracted atcoordinates 21°24.9’N, 157°40.70’W, which is the location of CDIP buoy Station 098, MokapuPoint3.TheMokapuPointCDIPbuoyislocatedinapproximately100mwaterdepth.Tovalidatethemodel,significantwaveheights,peakwaveperiods,andmeanwavedirectionswereextractedandcomparedtothemeasureddatafromCDIPStation098.Inthisinvestigation,SWANmodelvalidationwasconductedfordailynoon(1200hours)andmidnight(0000hours),between19and29February2012.Theabilityofawind‐wavemodeltopredictwavecharacteristicscanbeevaluatedinmanyways.Here,modelperformanceanalysis(modelvs.measured)wasassessedthroughthecomputationofrootmeansquareerror(RMSE),scatter index(SI),andbias(ormeanerror;ME).Scatter indexisdefined as the root mean square error normalized by the average observed (measured) value(Komen et al. 1994). Mean error allows for the detection and evaluation of bias in the wavecharacteristic data forecasts. When examining results of ME analysis, a positive value wouldindicatetheaverageover‐predictionofanobservedvaluewhileanegativevalueindicatesaverageunder‐prediction of the observed value. The model performance metrics are defined by theequationsbelow.
Wherex1,i ismodeldata,x2,i ismeasureddata,Nisthenumberofdatapoints,andtheover‐barintheequationforSIdenotesthemean(arithmeticaverage)value.TheSWANmodelperformancestatisticscomputedfortheMokapuPointlocationarepresentedinTable 1. Model data showed good agreement to observed data (Figure 3). The wave heightsexhibited amean error of 0.26m (i.e. slight over‐prediction). The peak periods showed a slightunder‐prediction of 0.21 s. Themeanwave directionswere over‐predicted by approximately 15degrees (clockwise) from the measured data. All values are considered within good agreementbasedonthislimitedvalidationperiod.
Table1.SWANmodelperformancestatisticscomputedforresultsatMokapuPoint.Variable RMSE SI BiasorMEHs(m) 0.40 0.14 0.26Tp(s) 0.65 0.07 ‐0.21
2 http://www.ndbc.noaa.gov 3 http://cdip.ucsd.edu
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MWD(°) 18.26 0.24 15.16
Figure3.SWANmodelvalidationresultsforMokapuPoint.Modeldataareshowninredand
measuredCDIPStation098dataareshowninblue.Uncertainty in these predictions may have arisen from multiple sources. The SWAN model issensitivetobathymetry;therefore,themodelisgenerallylimitedbytheaccuracyofthebathymetryavailableforaregion.FortheKaneoheBaySWANmodel,availablebathymetryresolutionwashighfornear‐shorelocations,butwascoarseroffshore(50metergridspacing).Additionally, offshore boundary conditions specified in the model validation were comprised ofparameterized, constant significant wave height, peak period, and mean wave directionparameters; wave frequency and direction spectrum was generated from these parameters.Specification of offshore boundary conditions in this manner precluded the inclusion of wavespectrafrommultipledirectionsormultipledominantfrequencies(i.e.bi‐modalwavespectra).
ResultsModelutilitywasdemonstratedbyrunningthenestedSWANmodelforasamplerangeoftypicalwaveconditions.Offshore,coarsegrid(100mgridspacing)boundaryconditionscomprised1,2,3,and4mwaveheights atpeakperiodsof 6, 8, 10,12, and14 s andoriginating frommeanwavedirectionsof0°,30°,60°,90°,and330°.Theresultingcoarsegridmodeledwavespectrawerethenspecifiedforeachgridpointinthefinergridmodel(20mgridspacing)andallowedtopropagateintoshore.Thenestedmodelwasrunwithandwithoutobstacles(WECdevices)tobettercomprehendboththeexistingcondition(i.e.noWECdevice)waveconditionsandthosethatmaybepresentwhenaWECdevice (orWECarray) is installed.Formodelrunsthat includedsimulatedWECdevices,anarrayofthreeobstacleswassimulated(Figure2).Thelocationoftheshallowwaterberthandthe
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approximatelocationofthetwodeeperwaterberthswereprovidedbytheNavy.Eachobstaclewasapproximately 20m in length (due to grid size constraints) andwas located nearWEC sites ofinterest(Table2).Modelobstaclereflectionandtransmissioncoefficientsweresetto0.0and0.0,respectively.Atotalof200nestedmodelrunswereconducted(100withoutobstaclesand100withobstacles).
Table2.LocationsofthethreeobstaclesforSWANmodelruns.Obstaclenumber Latitude(°N) Longitude(°W) Depth(m)
1 21.4656 157.751 332 21.4726 157.755 523 21.4784 157.749 86
Figures4through6areexamplesofmodeledsignificantwaveheight fornestedSWANrunswithoffshoreboundaryconditionsignificantwaveheightsof1,2,3,and4mandpeakwaveperiodsof6s(Figure4),10s(Figure5),and14s(Figure6).Meanwavedirectionwasheldconstantat0°forthese12modelruns.Figures7‐10illustratemodelpredictionswithvaryingmeanwavedirections;the peakperiodwas a constant (10 s) for the results shown in these images. The array of threeobstacleswasincludedintheSWANmodelrunsshowninFigure4‐10.
Figure4.SWANsimulatedsignificantwaveheightwithmodelinitiationparameters:MWD=0°;Tp=6s;andHs=1m(upperleft),2m(upperright),3m(lowerleft),and4m(lowerright).Theboldlinedenotestheshorelineandcontourlinesfor10m,20m,30m,and40mareshown.Themodel
obstacles,shownaswhitesquares,arenottoscale.
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Figure5.SamecaptionasFigure4butTp=10s.
Figure6.SamecaptionasFigure4butTp=14s.
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Figure7.SWANsimulatedsignificantwaveheightwithmodelinitiationparameters:MWD=30°;Tp=
10s;andHs=1m(upperleft),2m(upperright),3m(lowerleft),and4m(lowerright).
Figure8.SamecaptionasFigure7butMWD=60°.
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Figure9.SamecaptionasFigure7butforMWD=90°.
Figure10.SamecaptionasFigure7butforMWD=330°.
The effects of obstacle inclusion on the near‐shore study area wave climate were evaluated bycomparingmodeloutputswith andwithout obstaclesatnine (9)discretemodeloutput locations(Table3).
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Table3.Locationsofnine(9)outputpointsforevaluatingeffectsofWECdevices(i.e.obstacles).Outputpoint# Depth(m)* Latitude(°N) Longitude(°W)
1 20 21.4672 157.7592 20 21.465 157.7553 25 21.464 157.7494 10 21.4638 157.765 10 21.46 157.7556 10 21.459 157.7497 5 21.461 157.7618 5 21.458 157.7559 5 21.456 157.749
*ApproximatedepthOn average, significant wave heights were 0.02 m smaller, or 1.4% less when obstacles wereincludedinthemodeling.Ingeneral,neitherthewaterdepthnorproximitytoobstaclesappearedtoaffectwaveheightdifferenceswithandwithoutobstacles.Themostobstacleimpactvariability(expressedasstandarddeviation;Table4)wasobservedatoutputlocations6and9,whichwerethenearshore,easternmostlocationsandmostaffectedbywavesapproachingfromtheeast.Table4quantifiesthegeneralstatisticsatallmodeloutputlocations.Percentdifferenceswerecomputedfollowing:
%diff=100*[(Hsw/o–Hsw/)/Hsw/o].WhereHsw/oismodeledHswithoutobstaclesandHsw/ismodeledHswithobstacles.Table4.StatisticsofthedifferencesbetweenHswithandwithoutobstaclesatnine(9)outputpointlocationsfor100nestedmodelruns(modelboundaryconditions:Hs=1,2,3,and4m;Tp=6,8,10,12,and14s,andMWD=0,30,60,90,and330°).Valuesforthe5mcontour,10mcontour,and20‐25
mcontourarealsoprovided.Outputlocation
Mean Minimum Maximum StandardDeviation
%diff m %diff m %diff m %diff m1 1.08 0.023 0.01 0 2.69 0.097 0.95 0.0262 2.01 0.037 0.94 0.009 4.03 0.114 0.82 0.0233 0.68 0.013 0 0 3.41 0.099 0.95 0.0194 1.20 0.024 0.02 0 2.62 0.094 0.80 0.0235 2.0 0.038 0.19 0 3.11 0.098 0.74 0.0256 1.65 0.029 0 0 6.32 0.148 2.23 0.0407 1.10 0.017 0.01 0 2.35 0.056 0.74 0.0148 1.50 0.025 0.04 0 3.11 0.069 0.91 0.0179 1.26 0.018 0 0 5.96 0.104 1.94 0.0285m 1.29 0.020 0 0 5.96 0.104 1.19 0.02010m 1.62 0.030 0 0 6.32 0.148 1.26 0.029
20–25m 1.26 0.024 0 0 4.03 0.114 0.91 0.023Visualresultsforsignificantwaveheightdifferences(Hswithoutobstacles‐Hswithobstacles)areshowninFigures11‐14.
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Figure11.Evaluationoftheeffectsofanobstaclearrayonthenearshorestudyarea(obstacles–whitesquares–arenottoscale).Themodelinitiationparameterswere:MWD=0°;Tp=10s;andHs=1m(upperleft),2m(upperright),3m(lowerleft),and4m(lowerright).Theboldlinedenotestheshorelineandcontourlinesfor10m,20m,30m,and40mareshown.Modeloutputlocationsareindicatedbywhitecirclesandarenumberedintheupperleftpanel(seeTable3foradditionaldescription).ThedifferencesbetweenSWANsimulatedsignificantwaveheightwithoutandwith
obstaclesforeachoutputlocationareindicatedontheleft‐handsideofeachpanel.
Figure12.SamecaptionasFigure11butforMWD=30°.
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Figure13.SamecaptionasFigure11butforMWD=60°.
Figure14.SamecaptionasFigure11butforMWD=90°.
TheeffectsofWECdevices(i.e.obstacles)onnearshorebottomorbitalwavevelocitiesareshowninTable5andFigures15and16.Bottomorbitalvelocitycandecreasebygreaterthan6.5%directlyinshoreoftheobstaclearray(location6)withmodelinitiationparameters:Hs=4m,Tp=10s,and
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MWD = 330°. On average, bottom orbital velocity decreased by 0.007 m/s or 1.4% with theinclusionofobstacles.Table5.StatisticsofthedifferencesbetweenUbotwithandwithoutobstaclesatnine(9)outputpointlocationsfor100nestedmodelruns(modelboundaryconditions:Hs=1,2,3,and4m;Tp=6,8,10,12,and14s,andMWD=0,30,60,90,and330°).Valuesforthe5mcontour,10mcontour,and20‐25
mcontourarealsoprovided.Outputlocation
Mean Minimum Maximum StandardDeviation
%diff m/s %diff m/s %diff m/s %diff m/s1 1.12 0.003 0.01 0 2.99 0.018 1.03 0.0042 2.13 0.005 0.86 0 4.69 0.021 0.96 0.0043 0.61 0.001 0 0 3.24 0.006 0.85 0.0024 1.23 0.006 0.02 0 2.57 0.026 0.82 0.0065 2.07 0.011 0.25 0 3.16 0.031 0.72 0.0086 1.69 0.007 0 0 6.51 0.037 2.28 0.0097 1.11 0.007 0.01 0 2.35 0.022 0.74 0.0058 1.51 0.011 0.05 0 3.10 0.029 0.88 0.0079 1.26 0.008 0 0 5.90 0.045 1.92 0.0125m 1.29 0.008 0 0 5.90 0.045 1.18 0.00810m 1.66 0.008 0 0 6.51 0.037 1.27 0.008
20–25m 1.29 0.003 0 0 4.69 0.021 0.95 0.003
Figure15.Evaluationoftheeffectsofanobstaclearrayonthenearshorebottomorbitalvelocity.Themodelinitiationparameterswere:MWD=0°;Tp=10s;andHs=1m(upperleft),2m(upperright),3m(lowerleft),and4m(lowerright).Theboldlinedenotestheshorelineandcontourlinesfor10m,
20m,30m,and40mareshown.
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Figure16.SamecaptionasFigure15butforMWD=90°.
SummaryThe numericalmodel, SWAN,was used to simulatewave conditions at a potentialWETS site inKaneohe Bay, HI in order to assist with determination of the effects of WEC devices on thepropagationofwavesintoshore.TheSWANmodelwasvalidatedwithCDIPbuoywaveparametermeasurements at Station Mokapu Point. Validation results showed good agreement betweenmodeledandmeasuredsignificantwaveheight,peakperiod,andmeanwavedirection.Anestedmodelwasevaluatedforarangeofoffshore,deepwatersignificantwaveheights(1to4m),peakperiods(6to14s),andmeanwavedirections(330°to90°).TheimpactofWECdevicesonthe study areawas evaluated by simulating an array of threedeviceswithin a nested, finer gridSWANmodeldomain.WECdeviceswererepresentedinthemodelas“obstacles”.DifferencesbetweensignificantwaveheightinthepresenceandabsenceoftheWECdevicearrayovertherangeofspecifiedwaveheights,periods,anddirectionswereassessedatnine(9)locationsnearshoreof thearray.Themaximumpercentdecrease inwaveheightdue to thearrayof threeobstacleswaspredictedtobeapproximately6%at5mand10mwaterdepths(locations6and9).ThisoccurredformodelinitiationparametersofHs=3m,Tp=10s,andMWD=330°forlocation9(5m)andHs=4m,Tp=10s,andMWD=330°forlocation6(10m).Subsequently,bottomorbitalvelocitieswerefoundtodecreasebyabout6%atthesamelocations.It is important to note that this is a very preliminary investigation meant to demonstrate anapproach forassessing theeffectsofWECdevicesonnear‐shorewave fieldsand the subsequentpotential for altering near shore sediment transport. For these initial simulations,WEC deviceswereassumedtocompletelyabsorbtheincidentwaveenergy.Forenvironmentalpurposesthisisavery conservativeestimateandwill lead to themaximumchanges (unrealistically large) inwave
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propagationparameters.Consideringthis,theinitialsimulationsshowthatWECdevicessimulatedin thisway showveryminor changes inwavepropertiesnear shore. Although final conclusionsshouldnotbedrawnfromthis initialstudy,preliminary indicationsshowthat thedeploymentofthreeWECdevicesattheWETStestsitewillhavenegligibleimpactonnear‐shorewaveclimateorshorelineerosion.
ReferencesKomen, G.J., L. Cavaleri, M. Donelan, K. Hasselman, S. Hasselman, and P.A.E.M. Janssen (1994)
DynamicsandModelingofOceanWaves,CambridgeUniversityPress,NewYork,532pp.
