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Storm Surge

Permanent Link: http://ufdc.ufl.edu/UFE0021997/00001

Material Information

Title: Storm Surge Influence of Bathymetric Fluctuations and Barrier Islands on Coastal Water Levels
Physical Description: 1 online resource (167 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: adcirc, barrier, bathymetry, circulation, coastal, coupled, flooding, hurricane, island, modeling, setup, storm, surge, swan, waves
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Coastal and Oceanographic Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The impact of hurricanes on coastal communities has been highlighted in recent years. As researchers, our goal is to better understand the physics and mechanisms that create and drive storm surge from hurricanes. To achieve this goal, both analytic and complex numerical modeling techniques, as well as historical data, are used to test the effects that selected parameters have on the total surge levels. The focus of this work is on bathymetric properties, and how they can affect the water levels at the coast. An automated, 2D coupled wave-surge modeling system was developed using the SWAN and ADCIRC models. The system is calibrated using historical data as well as both analytic and complex numerical modeling techniques. As further validation, the coupled model system is used to perform flood level predictions along the Mississippi coast. The forcing from the momentum flux due to wave breaking is an important component to the modeling system. As such, time is taken to explore and validate the methodology used to include this physical process. The SWAN model is used to compute the flux in radiation stresses. Once adopted, the system is employed to test the sensitivity of the surge levels at the coast to variations in the bottom contours. A suite of bottom perturbations is tested for different sloped bottom profiles in the 1D cases. The domain for the 2D tests is the Gulf of Mexico, with the bathymetry varied offshore of Mississippi, Alabama and the Florida panhandle. The accuracy in surge predictions can be retained with a RMS difference of less than 4.6% of the unperturbed value when the bottom variation is less than 60% of the water depth. The significance of variations decreases in depths greater than 30 m. Outside the 30 m depth contour highly resolved bathymetric data is not required to accurately compute the surge levels at the coast. In the extreme case of a perturbation that breaks the surface, 100% or greater of the water depth, the variation from the surge calculated on the undisturbed profile is more significant. For the 1D cases, an idealized profile is used as the model domain. The 2D simulations employs a bathymetric data sets that are representative of the Mississippi coast both with and without barrier islands. If the island is not overtopped, the surge at the coast is lowered with the presence of barrier islands. For a wind speed of 50 m/sec, the island should be at least 3.5 m above the mean water level to reduce the chances of overtopping. In addition to the height of the island being important, the seaward facing slope of the island should be steeper than 1:100 in order to be an effective block to surge levels. The work presented in this dissertation has helped to gain a more complete understanding of the role bathymetry plays in coastal storm surge. With the modeling system developed, we can more readily simulate storms. This ability allows the researcher to test parameters and evaluate their significance in a more efficient manner.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Slinn, Donald N.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0021997:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021997/00001

Material Information

Title: Storm Surge Influence of Bathymetric Fluctuations and Barrier Islands on Coastal Water Levels
Physical Description: 1 online resource (167 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: adcirc, barrier, bathymetry, circulation, coastal, coupled, flooding, hurricane, island, modeling, setup, storm, surge, swan, waves
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Coastal and Oceanographic Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The impact of hurricanes on coastal communities has been highlighted in recent years. As researchers, our goal is to better understand the physics and mechanisms that create and drive storm surge from hurricanes. To achieve this goal, both analytic and complex numerical modeling techniques, as well as historical data, are used to test the effects that selected parameters have on the total surge levels. The focus of this work is on bathymetric properties, and how they can affect the water levels at the coast. An automated, 2D coupled wave-surge modeling system was developed using the SWAN and ADCIRC models. The system is calibrated using historical data as well as both analytic and complex numerical modeling techniques. As further validation, the coupled model system is used to perform flood level predictions along the Mississippi coast. The forcing from the momentum flux due to wave breaking is an important component to the modeling system. As such, time is taken to explore and validate the methodology used to include this physical process. The SWAN model is used to compute the flux in radiation stresses. Once adopted, the system is employed to test the sensitivity of the surge levels at the coast to variations in the bottom contours. A suite of bottom perturbations is tested for different sloped bottom profiles in the 1D cases. The domain for the 2D tests is the Gulf of Mexico, with the bathymetry varied offshore of Mississippi, Alabama and the Florida panhandle. The accuracy in surge predictions can be retained with a RMS difference of less than 4.6% of the unperturbed value when the bottom variation is less than 60% of the water depth. The significance of variations decreases in depths greater than 30 m. Outside the 30 m depth contour highly resolved bathymetric data is not required to accurately compute the surge levels at the coast. In the extreme case of a perturbation that breaks the surface, 100% or greater of the water depth, the variation from the surge calculated on the undisturbed profile is more significant. For the 1D cases, an idealized profile is used as the model domain. The 2D simulations employs a bathymetric data sets that are representative of the Mississippi coast both with and without barrier islands. If the island is not overtopped, the surge at the coast is lowered with the presence of barrier islands. For a wind speed of 50 m/sec, the island should be at least 3.5 m above the mean water level to reduce the chances of overtopping. In addition to the height of the island being important, the seaward facing slope of the island should be steeper than 1:100 in order to be an effective block to surge levels. The work presented in this dissertation has helped to gain a more complete understanding of the role bathymetry plays in coastal storm surge. With the modeling system developed, we can more readily simulate storms. This ability allows the researcher to test parameters and evaluate their significance in a more efficient manner.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Slinn, Donald N.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0021997:00001


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STORMSURGE:INFLUENCEOFBATHYMETRICFLUCTUATIONSANDBARRIERISLANDSONCOASTALWATERLEVELSByROBERTJ.WEAVERADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2008 1

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c2008RobertJ.Weaver 2

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ToJacqueline,Moose,Chaos,PerandZoe 3

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ACKNOWLEDGMENTSThankstoallthosewhohelpedmelearnhowtoquestionandhowtoresearchsolutionsoverthepast7years.Iwouldliketoacknowledgemyadviser,DonSlinnandmycommitteemembers,BobDeanandMaxSheppard,whoassistedmethroughmymaster'sandstuckwithmeformyPhD,aswellasAshishMehtaandClayMontaguewhoservedonmyPhDcommittee.ThankstotheNOPP'ers:HansGraber,VinceCardone,AndrewCox,BobJensen,NeilWilliams,ScottHagen,andGeoSamuels.Itwasanhonortobeapartofsuchagroupofneresearchers.IwouldalsoliketoacknowledgeAlanNiedoroda,HimangshuDas,andChrisReedatURS.AlargeportionoftheworkthatwentintothisdissertationwascompletedwiththefundingandguidanceoftheURSteam.TheskillsIlearnedwhileworkingontheFloodMapprojecthavebetterpreparedmeformyfuture.Iwouldliketothankmyocematesfortheinterestingandhelpfuldailydiscussionsthathavehelpedusallimproveourgraspofthesubjectmatter.Andnally,Iwouldliketoacknowledgemywifeandherpatiencewithmethesepast7years. 4

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TABLEOFCONTENTS ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 7 LISTOFFIGURES .................................... 8 LISTOFSYMBOLS .................................... 12 ABSTRACT ........................................ 14 CHAPTER 1INTRODUCTION .................................. 16 1.1HurricaneStormSurge ............................. 18 1.1.1WindSet-Up ............................... 19 1.1.2WaveSet-Up ............................... 20 1.2ResearchObjectives ............................... 23 2COUPLEDWAVE-SURGESYSTEM ....................... 25 2.1Introduction ................................... 25 2.2SWANWaveModelandConguration .................... 26 2.2.1BathymetricData ............................ 27 2.2.2NestedGridSystem ........................... 28 2.2.3WindandWaveBoundaryConditionsData ............. 29 2.3ModelSystemDescription ........................... 30 2.4SampleApplication:HurricaneKatrina .................... 33 2.5CalibrationandValidation ........................... 35 2.5.1ComparisontoStormWaveBuoys ................... 36 2.5.2ComparisonofSWAN,STWAVE,andDean's1Dmodel ....... 38 2.6ChapterSummary ............................... 42 3VALIDATIONOFWAVESET-UP ......................... 66 3.1Introduction ................................... 66 3.2WaveForcingSensitivityTests ......................... 68 3.2.1Introduction ............................... 68 3.2.2ModelDescription ............................ 69 3.2.3BoundaryConditionTests ....................... 70 3.2.4WaveForcingTests ........................... 72 3.3NielsenTests .................................. 74 3.3.1Introduction ............................... 74 3.3.2ModelDescription ............................ 74 3.3.3Results .................................. 75 3.4HurricaneOpal ................................. 76 5

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3.4.1Introduction ............................... 76 3.4.2ModelDescription ............................ 77 3.4.3Results .................................. 77 3.5HurricaneKatrina ............................... 78 3.5.1Introduction ............................... 78 3.5.2ModelDescription ............................ 79 3.5.3Results .................................. 79 3.6ChapterSummary ............................... 81 4BATHYMETRICSENSITIVITYTESTS ..................... 100 4.1Introduction ................................... 100 4.2Methodology .................................. 101 4.2.11DTests ................................. 101 4.2.22DTests ................................. 104 4.3Results ...................................... 106 4.3.11DResults ................................ 106 4.3.22DResults ................................ 107 4.4ChapterSummary ............................... 108 5IMPACTOFBARRIERISLANDSONCOASTALSTORMSURGE ...... 129 5.1Introduction ................................... 129 5.21DBarrierIslandSimulations ......................... 129 5.3MississippiCoastBarrierIslandTest ..................... 131 5.4ChapterSummary ............................... 135 6CONCLUSIONS ................................... 158 6.1CoupledWave-SurgeSystem .......................... 158 6.2SensitivityofWaveSet-Up ........................... 158 6.3BathymetricSensitivity ............................. 159 6.4BarrierIslands ................................. 160 6.5Summary .................................... 161 REFERENCES ....................................... 162 BIOGRAPHICALSKETCH ................................ 166 6

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LISTOFTABLES Table Page 3{1Resultsfromwavesensitivitytests ......................... 82 3{2Nielsentestparameters ................................ 82 3{3Nielsentestresults .................................. 83 3{4Opaltestparameters ................................. 84 3{5Opaltestresults ................................... 84 3{6SummaryofKatrinaresults ............................. 84 3{7Setupasafunctionofwaveheight ......................... 85 5{1Tablesoftheapproximatevalues,S,forslope=1:S,oftheseawardfaceoftheislandperturbation ................................ 137 7

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LISTOFFIGURES Figure Page 2{1VisualizationofwaveamplitudeandoodingalongtheMississippicoastduringHurricaneKatrina .................................. 44 2{2Post-KatrinacoastalbathymetryusedinthewavemodeldevelopedfromURSandNGDCdatasets. ................................. 45 2{3Computationaldomainsusedinthewaveset-upmodelingapproach. ...... 46 2{4Flowchartofwaveset-upmethodology. ...................... 47 2{5LocationsforcomparisonofHSfortheHurricaneKatrinarunswithandwithouttheadditionofsurgelevelstothewavemodel. .................. 48 2{6ComparisonofthesignicantwaveheightsfortheHurricaneKatrinasimulationswithandwithouttheadditionofsurgelevels .................... 49 2{7SignicantwaveheightspredictedduringHurricaneKatrinainthebasinscalegrid. .......................................... 50 2{8SignicantwaveheightspredictedduringHurricaneKatrinaintheregionscalegrid. .......................................... 51 2{9WaveheightandwaveforcepredictionsforHurricaneKatrina .......... 52 2{10LocationofNOAAwavebuoysintheGulfofMexico. ............... 53 2{11ComparisontowavebuoyresultsduringHurricaneKatrina005atBuoys42003and42007. .................................. 54 2{12ComparisonofwavemodelandbuoydataduringKatrina05atBuoys42019and42040. ....................................... 55 2{13ComparisontowavebuoyresultsduringHurricaneGeorges1998atBuoys42002and42007. ................................... 56 2{14ComparisonofwavemodelandbuoydataduringHurricaneGeorges998atBuoys42003and42040. ............................... 57 2{15MaximumsignicantwaveheightspredictedforGeorges998andKatrina05 58 2{16ComparisonofresultsfromSTWAVEandSWANforsteady50m/ssouthwind. 59 2{17Locationof1DtransectsforSWAN{STWAVEcomparisonsinthemiddleofcoastalzone7crossingthebarrierisland. ...................... 60 2{181DversionsofSWANandSTWAVEcomparisons. ................. 61 2{19ComparisonofSWAN,STWAVEandDean's1Dmodel .............. 62 8

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2{20Cross-shoreforcedistributionandtotalintegraloftheforcesCase2 ...... 63 2{21Cross-shoreforcedistributionandtotalforceintegralsCase3 ......... 64 2{22Resultsforset-upofthethreemodelsSWAN,STWAVE,andDean's1D ... 65 3{1Proleandplanviewofthebathymetryusedforthewaveforcingsensitivitytests 86 3{2Schematicofthe1Dmodeltests ........................... 87 3{3Qualitativesketchofthe2Dmodeltests ...................... 88 3{4Contourplotsofthe3boundaryconditiontestresults .............. 89 3{5WatersurfaceelevationproleforBCtestsatcenterlineofdomain ....... 90 3{6Watersurfacecontourwithcurrentstreamlinesforsteadywindtests ...... 91 3{7Watersurfacecontourwithcurrentstreamlinesfor10-kmand70-kmwide2Dsteadywindtests ................................... 92 3{8WatersurfaceelevationproleforsteadywindtestscomparedtoSWANandDean1Dmodels ................................... 93 3{9ResultsofTest1.1solidlinesandTest1.2brokenlines ............ 94 3{10ResultsofTest1.1solidlinesandTest1.3brokenlines ............ 95 3{11ResultsfromthreeOpaltests ............................ 96 3{12HurricaneKatrinamaximumwaveheightinregionandcoastaldomains ..... 97 3{13MaximumwaveheightandwaveforcinginthecoastaldomainforHurricaneKatrinasimulation .................................. 98 3{14Maximumwaveset-upelevationforHurricaneKatrinaaspredictedbymodelingsystem ......................................... 99 4{11Dbathymetricprolesandcorrespondingsurge .................. 110 4{2Coastalsurgeprolescalculatedwithwindforcingaloneandwithwindandwaveforcing. ..................................... 111 4{31Dbathymetricandsurgeprolesforslope1:100 ................. 112 4{4Bathymetricdisplacementsandsurgeprolesforinitialslope1:50 ........ 113 4{5Bathymetricdisplacementsandsurgeprolesforinitialslope1:100 ....... 114 4{6Locationoftheperturbedsitesnearthe15mand25mcontourlevelsotheFloridaandAlabamacoasts. ............................ 115 9

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4{7Bathymetriccontoursfor20%perturbedsitesnearthe15mand25mcontourlevels. ......................................... 116 4{8Locationoftheperturbedsitesnearthe5mand15mcontourlevelsotheMississippicoast. .................................. 117 4{9Bathymetriccontoursforthe20%perturbedsitesnearthe5mand15mcontourlevels. ......................................... 118 4{10 0vsamplitudeforthecaseofinitialslope1:100 ................. 119 4{11 0vsamplitudeonbottomslope1:50 ........................ 120 4{12 0vsamplitudeonbottomslope1:100 ....................... 121 4{13Expectedvaluesof 0forindicatedamplitudes ................... 122 4{14Combinedlikelihoodforall20,40and60%perturbations ............. 123 4{15RMSDvs.disturbanceamplitudeforallperturbations .............. 124 4{16SurgeresponsestoalteredbathymetriesalongtheAlabama/Floridacoast. ... 125 4{17Dierenceinsurgeresponsestoalteredbathymetriesatthe15mand25mcontouralongtheAlabama/Floridacoast. .......................... 126 4{18SurgeresponsestoalteredbathymetriesalongtheMississippicoast. ....... 127 4{19DierenceplotofthesurgeonthealteredbathymetriesforMississippicoast. .. 128 5{1Bathymetricprolesforeachsimulationwithcenterofperturbationlocated10kmoshore .................................... 138 5{2Bathymetricprolesforeachsimulationwithcenterofperturbationlocated20kmoshore .................................... 139 5{3Bathymetricprolesforeachsimulationwithcenterofperturbationlocated30kmoshore .................................... 140 5{4Surgeprolesforeachsimulationwithcenterofperturbationlocated10kmoshore ........................................ 141 5{5Surgeprolesforeachsimulationwithcenterofperturbationlocated20kmoshore ........................................ 142 5{6Surgeprolesforeachsimulationwithcenterofperturbationlocated30kmoshore ........................................ 143 5{7 0vsamplitudeforthecasex0=10km ...................... 144 5{8 0vsamplitudeforthecasex0=20km ...................... 145 10

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5{9 0vsamplitudeforthecasex0=30km ...................... 146 5{10Combinedhistogramofsurgelevellikelihoodforallbarrierislandcongurations. ............................................. 147 5{11BathymetriccontoursofcoastalMississippidomainsforbarrierislandtests. .. 148 5{12Cross-shoretransectsforcomparisonof2Dsimulationto1Dtests ........ 149 5{13Comparisonofcross-shoredepthcontoursbetweenthe4transectsfromthe2Dsimulationandthe1DplanarslopeGaussianislandtestcases. ......... 150 5{14Comparisonofcross-shoresurgeprolesbetweenthe4transectsfromthe2Dsimulationandthe1DplanarslopeGaussianislandtestcases. ......... 151 5{15SnapshotofsurgesimulationresultsforHurricaneKatrinaattime,t=2005/08/2911:45UTC ...................................... 152 5{16SnapshotofsurgesimulationresultsforHurricaneKatrinaattime,t=2005/08/2915:45UTC ...................................... 153 5{17SnapshotofsurgesimulationresultsforHurricaneKatrinaattime,t=2005/08/2922:00UTC ...................................... 154 5{18Thedierencebetweenthebarrierislandcaseandthenobarrierislandcaseattime,t=2005/08/2911:45UTC ........................... 155 5{19Thedierencebetweenthebarrierislandcaseandthenobarrierislandcaseattime,t=2005/08/2915:45UTC ........................... 156 5{20Thedierencebetweenthebarrierislandcaseandthenobarrierislandcaseattime,t=2005/08/2922:00UTC ........................... 157 11

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LISTOFSYMBOLSGreeksymbols freesurfacedisplacement. 0 freesurfacedisplacementonunperturbedprole. breakingconstant. b meansurfacedisplacementatbreaking. densityofwater. a densityofair. frequency. st standarddeviation. stx standarddeviationinx-direction. sty standarddeviationiny-direction. xx surfacewindstress. zx)]TJ/F23 11.955 Tf 9.298 0 Td[(h bottomshearstressinx-direction. zx surfaceshearstressinx-direction. wavedirection.Romansymbols A Amplitudeofgaussiandisturbance. C wavecelerity. Cd surfacedragcoecient. Cg wavegroupvelocity. E totalaverageenergyperunitsurfacearea. Fx bodyforce. Fy bodyforce. g gravitationalacceleration. h waterdepth. H waveheight. 12

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hb waterdepthatbreaking. H0 oshorewaveheight. HRMS rootmeansquaredwaveheight. HS signicantwaveheight. H1 3 waveheightforwhichone-thirdofthewavesarelarger. Hbrms rootmeansquarewaveheightatbreaking. Hm0 waveheight. n)]TJ/F24 7.97 Tf 6.586 0 Td[(heta ratioofbottomstresstosurfacestress. SVD VanDornwindstressformula. Sxx radiationstressinthex-direction,x-directedcomponent. Sxy radiationstressinthex-direction,y-directedcomponent. Syx radiationstressinthey-direction,x-directedcomponent. Syy radiationstressinthey-direction,y-directedcomponent. t time. U10 meanwindspeedtakenat10metersabovethesurface. Wc criticalwindspeed. x crossshoredirectioncomponent. x0 x-locationofcenterofgaussiandisturbance. y0 y-locationofcenterofgaussiandisturbance. WS windspeed. 13

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophySTORMSURGE:INFLUENCEOFBATHYMETRICFLUCTUATIONSANDBARRIERISLANDSONCOASTALWATERLEVELSByRobertJ.WeaverMay2008Chair:DonaldN.SlinnMajor:CoastalandOceanographicEngineeringTheimpactofhurricanesoncoastalcommunitieshasbeenhighlightedinrecentyears.Asresearchers,ourgoalistobetterunderstandthephysicsandmechanismsthatcreateanddrivestormsurgefromhurricanes.Toachievethisgoal,bothanalyticandcomplexnumericalmodelingtechniques,aswellashistoricaldata,areusedtotesttheeectsthatselectedparametershaveonthetotalsurgelevels.Thefocusofthisworkisonbathymetricproperties,andhowtheycanaectthewaterlevelsatthecoast.Anautomated,2Dcoupledwave-surgemodelingsystemwasdevelopedusingtheSWANandADCIRCmodels.Thesystemiscalibratedusinghistoricaldataaswellasbothanalyticandcomplexnumericalmodelingtechniques.Asfurthervalidation,thecoupledmodelsystemisusedtoperformoodlevelpredictionsalongtheMississippicoast.Theforcingfromthemomentumuxduetowavebreakingisanimportantcomponenttothemodelingsystem.Assuch,timeistakentoexploreandvalidatethemethodologyusedtoincludethisphysicalprocess.TheSWANmodelisusedtocomputetheuxinradiationstresses.Onceadopted,thesystemisemployedtotestthesensitivityofthesurgelevelsatthecoasttovariationsinthebottomcontours.Asuiteofbottomperturbationsistestedfordierentslopedbottomprolesinthe1Dcases.Thedomainforthe2DtestsistheGulfofMexico,withthebathymetryvariedoshoreofMississippi,AlabamaandtheFlorida 14

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panhandle.TheaccuracyinsurgepredictionscanberetainedwithaRMSdierenceoflessthan4.6%oftheunperturbedvaluewhenthebottomvariationislessthan60%ofthewaterdepth.Thesignicanceofvariationsdecreasesindepthsgreaterthan30m.Outsidethe30mdepthcontourhighlyresolvedbathymetricdataisnotrequiredtoaccuratelycomputethesurgelevelsatthecoast.Intheextremecaseofaperturbationthatbreaksthesurface,100%orgreaterofthewaterdepth,thevariationfromthesurgecalculatedontheundisturbedproleismoresignicant.Forthe1Dcases,anidealizedproleisusedasthemodeldomain.The2DsimulationsemploysabathymetricdatasetsthatarerepresentativeoftheMississippicoastbothwithandwithoutbarrierislands.Iftheislandisnotovertopped,thesurgeatthecoastisloweredwiththepresenceofbarrierislands.Forawindspeedof50m/sec,theislandshouldbeatleast3.5mabovethemeanwaterleveltoreducethechancesofovertopping.Inadditiontotheheightoftheislandbeingimportant,theseawardfacingslopeoftheislandshouldbesteeperthan1:100inordertobeaneectiveblocktosurgelevels.Theworkpresentedinthisdissertationhashelpedtogainamorecompleteunderstandingoftherolebathymetryplaysincoastalstormsurge.Withthemodelingsystemdeveloped,wecanmorereadilysimulatestorms.Thisabilityallowstheresearchertotestparametersandevaluatetheirsignicanceinamoreecientmanner. 15

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CHAPTER1INTRODUCTIONStormsurgeistheriseinwaterlevelscausedbythepresenceofanatmosphericdisturbance.Thedisturbancecouldbeassociatedwithastrongfrontalsystemmovingacrossabodyofwateroralowpressuresystem,eithertropicalorextratropical.Thelattercasesaretermedeithertropicalorextratropicalcyclones.Tropicalcyclonesformmainlyinthetropics,atlatitudeslessthan30.0degnorthandsouth.Themaindierencebetweentropicalandextra-tropicalcyclonesisthemeansbywhichtheyaregeneratedandsustained.Theextratropicalstormsarecausedbytemperaturedierencesintheatmosphere.Thestormoccurswhenhighpressure,coolerair,andlowpressure,warmerairsystemsinteract.Atropicalcycloneisfueledbytheheatexchangebetweenthewarmoceansurfaceandthecoolupperatmosphere.Theworkpresentedinthisdissertationiscenteredaroundstudiesoftropicalcyclones.InNorthAmerica,tropicalcyclonesarecalledhurricanes.Theyhaveothernamesaroundtheworld;willy-willyinAustralia,typhooninthePacicRim.Nomatterwhattheyarecalled,tropicalcyclonesareaforceofnaturetoberespected,studiedandunderstood.Thedamagefromthesestormscancrippleanation,asHurricaneKatrinadidtotheUnitedStatesin2005.HurricaneKatrinawasthethirddeadliesthurricaneintheUnitedStatessince1900,thedeadliestsince1977 Knabbetal. 2005 .Katrinaisresponsibleforanestimated80billiondollarsinlosses.Inmoderntimes,therehasbeenareductioninthelossoflifeassociatedwithhurricanes,howeverthecostfromdamagecausedbythestormsincreasesasmorepeopleandindustrypopulatethecoastlines.Tropicalcyclonesarelow-pressuresystemsthatforminthetropicsandarenotassociatedwithafrontalsystem.StormsystemscanformoverWestAfrica,andtravelovertheAtlantic,orthesesystemscanformoutatsea.Largethunderstormstormcellsarearequirementfortheformationofthelowpressuresystem.Theprocessstartsattheairseainterfaceandisdependentonthevaporpressures.Whenthetemperature 16

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atthesurfaceoftheoceanwaterisgreatenough,thewatervaporizesandthesurfaceairmixeswiththewarmwatervapor.Theairwillbewarmedbytheoceantothepointthatitwillbegintorise.Thesurfacewatertemperaturesintheoceanmustbeatleast26to27C.Warmmoistairrisesfromtheoceansurface.Thesystemsgenerallyformwherethereisanatmospherictrough,wherecooldryairconvergesanddescendsfromtheupperatmosophere.Asthewarmerhumid,surfaceairrises,coolerdryerairisdrawnintowardsthecenterofthelowpressure.Alongthewaythisinowingairpicksupmoistureandbecomeswarmedbytheoceansurface.Warmmoistairrisesfromtheoceansurface.Asthemoistairrises,thetemperatureoftheaircoolsduetoexpansion.Eventually,thecriticaltemperaturewillbereachedwherethemoisturecondensesoutoftheair,creatingawarmingeect.Theprocessdescribedaboveisknownaslatentheatexchangeandisthefuelingmechanismfortropicalcyclones SimpsonandRiehl 1981 .Thiswarmingwillcauseatemperaturegradientintheupperatmosphere,whichsustainsthetropicalcyclone.However,thisaloneisnotenoughtocreateahurricane.Therearelittleunderstoodperturbationsthatwillpushalargestormtowardbecomingatropicalcyclone.Itcouldbeawesterlywindonthesouthernsideofthestormoraneasterlywindonthenorthernside.Perhapsatroughintheupperatmospherepressurescausesthewindstofavorgenerationofahurricane.Ifthestormislocatedatalatitudegreaterthanabout8degreesNorthorSouth,thestormsystemswillbeaectedbytheCoriolisforceandarotationwillbegin.Therotationiscylonic,counter-clockwise,inthenorthernhemisphereandclockwiseinthesouthernhemisphere.HurricanegenerationisacomplexprocessandactiveareaofresearchintheUnitedStates.Ourresearchdealswiththeeectsofthehurricanesandnottheirgeneration.FluctuationsintheNorthAtlanticOscillation,NAO,causeregionalvariationinthefrequencyofhurricanes Elsneretal. 2000 .Thisvariationcomplicatesthepredictionofhurricanes.AnnuallywendthatmoststormsandthemostpowerfulstormsoccurinthelatesummermonthsofAugustandSeptemberinthenorthernhemisphere.Itisatthis 17

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timethattheoceanwatersareattheirwarmest.However,thereseemtobelargertimescalesthatinuencethenumberofhurricanes.Theoccurrenceandintensityofhurricanesalsouctuatesatdecadalandmillennialtimescales.Stormsurgemodelinghasprogressedgreatlysincepeoplebegantostudyandpredicthurricanes BodeandHardy 1997 .Themodelingcommunityhasprogressedfrom1Dto2Dto2.5Dandnallyto3Dmodelingmethods.Eachsystemofmodelingisavaluabletooltounderstandingthephysicsofstormsurge.Withtheexponentialincreaseincomputingpower,wenowhavetheabilitytorunforecastandhindcastsimulationsonaPCatourdesk.BothPC'sandmultiprocessorsupercomputersareemployedinordertosimulatestormsandstormsurge.Itiscurrentlyfeasibletoemployacoupled2Dmodelingsystemtoforecasthurricanesinreal-timeusingasupercomputer Graberetal. 2001 2006 .1.1HurricaneStormSurgeIntheUnitedStatesofAmerica,tropicalcyclonesareclassiedbasedonthemaximumsustainedwindspeedusingtheSar-SimpsonScale.Tobeclassiedasahurricane,maximumsustainedwindspeedsof74mphm/sarerequired.Stormsurgeistheriseinwaterlevelduetohurricanes.Therearethreemaincausesofstormsurge:windset-up,waveset-up,andtheinversebarometriceectofthelowcentralpressureofthestorm.Thesurfaceoftheoceanunderthestormwillreacttothepressureandwind.Thewatersurfacedirectlyunderthestormwillriseslightlyduetothepressuredierenceintheatmosphere.Overdeepwaters,therewillbeapproximatelya1cmriseinwaterlevelforeachmillibardropinpressure Anthes 1982 .Thewindwillpushabulgeofwateroutinfrontofthestorm,andserveasthemechanismforgeneratinglargewaves.Thethreattocoastalcommunitiesfromahurricaneincludeshighwindscausingdamage,wavesbreakingonstructures,aswellascoastaloodingcausedbythestormsurge.Therearemanybooksandpapersthatseektoexplainthegenerationandstructureofhurricanes SimpsonandRiehl 1981 ; Anthes 1982 ; Emanuel 1991 .As 18

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thestormconvergesonthecoast,theinversebarometricpressureeectisampliedduetoconvergenceinshallowwater.Thebulgefromthewindtransformsintoalargeset-upasthewaterinfrontofthestormispushedtowardland.Asthedepthdecreasesthereisnooutletforthewatertoreturntotheseasoitwillbuildupagainstthecoast.Additionally,thewavesgeneratedbythewindswillbreakastheyapproachthecoast.Thechangeinmomentumduetowavebreakingalsoforcesariseinthemeansealevel.Thetideswillalsoplayaroleintheeectofthehurricaneonthecoast.Stormtideisthecombinationofthesurgewiththetide.Ifthestormmakeslandfallduringhightide,theeectisahigherwaterlevelthanifthesurgehitstheshoreduringlowtide.1.1.1WindSet-UpThewindset-upiscausedbythewindblowingacrossthesurfaceofthewateroverhundredsofsquarekilometers.Asthedepthgetssmallertheeectofthewindstressincreases.Windstressoverashallowwideshelfwillproducealargerset-upthanthesamewindstressoveranarrowerordeepershelf.Thesteadystate,one-dimensionalsolutionforwind-inducedsealevelrise DeanandDalrymple 1991 isshowninEq. 1{1 .@ @x=n)]TJ/F24 7.97 Tf 6.587 0 Td[(hetazx wgh+{1AsseeninEq. 1{1 ,inthedeeperwaters,whenh,theslopeoftheseasurfacegoestozero.Inthedepth-averagedapproximation,nearacoastinsteadystate,thehorizontalvelocityiszeroandthebottomshearstressvanishestherefore;n)]TJ/F24 7.97 Tf 6.586 0 Td[(heta=1.Momentumtransferattheair-seainterfaceproduceswind-generatedwaves.Thistransferofmomentumiswhatdrivesthewindset-upandhasbeenstudiedextensively GeernaertandPlant 1990 ; Donelanetal. 1993 ; Donelan 1998 .Thewindstressisusuallyapproximatedaszx=aCdjU10jU10whereaisthedensityofair,U10isthemeanwindspeedtakenat10metersabovethesurface,andCdisthedragcoecient.Thedragcoecientdependsonseasurfaceroughnessandatmosphericstratication,andhasamagnitudeontheorderof10)]TJ/F22 7.97 Tf 6.586 0 Td[(3.Therearemanydierentrecommendedformsforthe 19

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dragcoecient,Cd.TherangeofvalidityofthedierentformulasforCddependsonwindconditions,andotherfactors.Therehasbeenrelativelylittleresearch,however,intowhatformulationwouldbestsuithurricanewindandseaconditions.Itisdiculttomakeopenoceanmeasurementsduringhurricaneconditions.Mostequationsproducebyextrapolatingfromdataanincreasingdragcoecientwithincreasingwindspeed.Thisformulationtsdatasetsatlowerwindspeeds.Butwhenthestrengthofthewindsbecomeslarge,>30m=s,thetopsofthewavescanbeshearedandtherelativewavesurfaceroughnesschanges.Thesurfaceoftheoceanthenmoveslikeasheet,analogoustoaslipboundarycondition.Onepossibilitycurrentlybeingdebated,isthatathigherwindspeedsthedragcoecientlevelsoasthewavesareshearedoatthecrests,andthenetmomentumimpartedtothewatercolumnbeginstolevelo.Therehasbeenarenewedinterestintheformulationforthewindstresscoecientinrecentyears. Powelletal. 2003 and Donelanetal. 2004 foundthatthesurfacedragcoecientbecomessaturatedatawindspeedof33m/s.Themaximumvaluesforthedragcoecientfromthesestudiesareapproximately2:510)]TJ/F22 7.97 Tf 6.586 0 Td[(3.Workby Jensenetal. 2006 determinedthatabetteragreementinthecomputedwaveheightswasachievedwhenacapwasplacedonthedragcoecient.Researchgroups,likeOceanWeather,Inc.seektoimproveontheirmodelsforhurricanewindprediction.Theresultisaneverimprovingstateofwindcalculation,whichwillincreaseourabilitytodevelopmoreaccuratesurgepredictionschemes.1.1.2WaveSet-UpWaveset-upiscausedbythetransferofmomentumorradiationstressbackintothewatercolumnaswavesbreak.Aswavesshoal,theygainmomentum,whichisreleasedbackintothewaterwhentheybreak.Therstevidencethatperhapswavescouldforceariseinsealevelattheshorewasfoundafterananalysisofdamagefroma1938hurricanethatimpactedtheeastcoastoftheUnitedStates.Itwasfoundthatsurgelevelsontheopencoastwere1mhigherthanwaterlevelsonarelativelyprotectedshoreline Holman 20

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andSallenger 1985 .Existingsurgemodelscouldnotaccountforthisdierenceinwaterlevels.Itwassuggestedthattheadditionalincreaseofwaterlevelwascausedbythewavesbreaking.Followupworkby Fairchild 1958 ; Saville 1961 conrmedthehypothesisthatthewavescausedanincreaseinthewaterlevelsatthecoast.Savillewasabletomeasuretheset-downandthesubsequentset-upduringwavegrowthandbreaking,respectively.Atthispoint,acuriosityinnaturehadbeenrecreatedinthelaboratory,howevertherewasnotheoreticalexplanationforwhatwasbeingobserved.Thepioneeringworkonradiationstresstheorywasdevelopedinthelate1950'sandearly1960'sby Longuett-Higgins 1953 ; Longuett-HigginsandStewart 1962 1963 1964 and Whitham 1962 .Followinguponthedevelopmentofwaveradiationstresstheory,researchersattemptedtovalidatethetheoreticalsolutioneitherintheeldorinlaboratoryexperiments. Bowenetal. 1968 foundthattheirresultsfromtestsinawavechannelagreedwiththeassumptionsofthetheoryquitewell.Itisthetransferofwavemomentumtothewatercolumnthatforcesachangeinthemeanwaterlevel.Nearthecoast,wavemomentumuxisbalancedbyapressuregradientassociatedwithachangeinthelocalwaterdepth.Aswavemomentumincreasesinthepresenceofnon-breakingwaves,themeanwaterlevellowers.Thisphenomenoniscalled'set-down'.Asbreakingcommences,thewaveenergyandmomentumdecrease,resultinginareductionoftheradiationstresscarriedbythewaves.Thesestressesforceperunitareaareimpartedintothewatercolumn.Therapidreductionofwaveradiationstressnearthecoastforcesariseinmeansealevel,called'waveset-up'.Themomentumtransferredfromthewavestothewatercolumnproducesanopposinghydrostaticpressuregradient.Duringstormevents,theresultingriseinwaterlevelcanplayamajorroleinstormsurge. 21

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Thesteadystatesolutionforwaveset-upoveramildlyslopingbottomisgivenbyEq. 1{2 DeanandDalrymple 1991 :d dx=)]TJ/F15 11.955 Tf 31.836 8.088 Td[(1 gh+ dSxx dxwhere,Sxx=Encos2+1)]TJ/F15 11.955 Tf 11.955 0 Td[(0:5 {2 Wherenistheratioofwavegroupvelocitytowavecelerityn=Cg C.Theproblemcanbefurthersimpliedbyassumingthewavesareshorenormalinshallowwater,overabathymetrywithstraightandparallelcontours.TheequationforradiationstresscanbereducedtoEq. 1{3 :Sxx=3 2E=3 16gH2RMS{3Thewaveheightcanbeassumedtobeafractionofthetotalwaterdepth,H=h+ ,where,thebreakingcoecient,rangesfrom0.3-1.2.Applyingthesesimplications,itcanbeshownthat,attheshore,theequationforthesurfacedisplacementcanbeapproximatedbyEquation 1{4 : = b+32 8 1+32 8hb{4Accordingtolineartheory,theeectivechangeinwaterlevelfromasteadytrainoflinearwavesapproachingnormaltotheshoreonagentlyslopingbottomisabout19%ofthebreakingwaveheightfor=0:73.Thevaluemayincreaseordecreasedependingonbathymetricprole,nonlineareects,dissipativeforces,2Dsystemsandwaveobliquity.Theeectofwaveradiationstressonseasurfaceelevationforsimpleandcomplexforcingconditionsisexamined.Thegoalistoincreaseunderstandingoftherolethatwavesplayinstormsurge.Waveforcescausedbygradientsinthewave-inducedradiationstressesareanimportantcomponentofatypicalstormsurge.However,theeectsofwavebreakingandtherelatedset-uparehighlylocalized.Theycreateastaticwaveset-upthatcannominallyamounttoasmuchas10to15%ofthesurgelevelsontheopencoast,and 22

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potentiallymoreinsidebaysandestuaries,astheresultingsurgeconverges.AlongtheopenGulfcoastthewaveset-upcomponentofthestormsurgeisvariableinspaceanddependsontheconditionsofeachindividualstorm.Asthestormandassociatedsurgepropagateinland,thespatialdierencesofthewaveset-upbecomemoreobvious.Duetotheuncertaintyofthepathofanygivenstorm,andthefactthatundertherightcircumstanceswavescancontributemorethan10%ofthetotalwaterlevelfromastorm,theseeectsmustbeanintegralpartofeachindividualcomputedstormsurge.1.2ResearchObjectivesThegoaloftheresearchisthreefold: Developandtestacoupledwave-surgemodelingsystem Improveunderstandingofwaveset-up Gainabetterunderstandingoftheinuenceofsmall-scalebathymetricuctuationsandbarrierislandsonstormsurgeToaccomplishtheabovegoals,aseriesofanalyticalcalculationsandsimplenumericalstudiesareperformed.Thesetestsandstudiesprovideabetterunderstandingoftheprocessesatwork.Theideasarethenexpandedintotwodimensions.Acoupled2Dwaveandcirculationmodelingsystemusingthewavemodel,SimulatingWavesNearshore,SWAN Holthuijsen 2000 ,andtheAdvancedCirculationModelADCIRC Luettichetal. 1992 tocalculatethewaterlevelsisdeveloped,testedandimplemented.Thecoupledsystemiscalibratedandtested.ThemostrigoroustestingofthesystemcamefromitsuseintheFederalEmergencyManagementAgencyFEMAMississippiCoastFloodAnalysisStudy,wherethemethodologywaschallengedanddefended.Invalidatingthemodelingsystem,anextensivein-depthstudywasperformed,lookingintohowwaveforcesandset-uparecomputednumerically.Boththeanalyticandthenumericalmodeledwaveset-upresultsarecomparedforavarietyofphysicalandforcingsituations.Additionally,thenumericalmodelswerevalidatedagainstavailabledata.Thenumericalsolutionsaremeasuredagainstthetheoreticalpredictions,laboratorystudies,eldstudiesandavailablehistoricdatasetsfromvariousstormevents. 23

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Usingthecoupledmodelingsystemalongwithanalytictheoryand1Dmodels,theimpactthatbathymetricvariationhasonstormsurgevaluesatthecoastisexamined.Theseideasarethentakentothenextlevel,investigatingtheimpactofbarrierislandsoncoastalstormsurge.Usinginsightfromstudiesofwaveset-uponcoralreefs, Gourlay 1996a b ,itisexpectedthatthevariationwillhavenoaectonthewavesifthecrestoftheperturbationissucientlysubmerged.Also,iftheislandissucientlyhighenoughoutofthewaterthatitisnotovertoppedbythesurge,thewaterswillbecompletelyblocked.Inthiscase,thesurgethatreachesthemainlandislocallygeneratedoverarelativelyshortfetch.Forthe2Dcases,theabilityforthewatertoescapelaterallyshouldreducetheset-upfromthewaves.Thepurposeofthisresearchistobetterunderstandthephysicalprocessesthataecttheelevationofwateratthecoast.Toachievethisgoal,historicaldataisused,aswellasbothanalyticandcomplexnumericalmodelingtechniques,totesttheeectsthatselectparametershaveonthetotalsurgelevels.Thecoupledmodelingsystemwillbeintroducedrst,followedbyavalidationofthewaveset-upapproach.Next,thebathymetricvariationsareexamined.Afterinsightintotheeectsofbathymetricvariationsisgained,testswillberuntodetermineunderwhatcircumstancesbarrierislandsprovideprotectionfromstormsurge.Finally,theresultswillbesummarized. 24

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CHAPTER2COUPLEDWAVE-SURGESYSTEM2.1IntroductionThedamagecausedfromstormsurgesandwavesgeneratedbyhurricanescanbecompletelydevastating.Inaneorttobetterunderstandhowthesurgeiscreated,theforcingmechanismsthatcausetheincreaseinwaterlevelsarestudied.Oneofthosemechanisms,havingreceivedlittleattentionuntilrecentyears,isthewaveforcingcomponent.Waveforces,causedbygradientsinthewave-inducedradiationstresses,areanimportantcomponentofatypicalstormsurge.Theseforcescreateastaticwaveset-upthatcannominallyamounttoasmuchas10to15%ofthemeasuredCoastalHighWaterMarksCHWMsontheopencoast.Typicallystormsurgepredictionmodelshaveusedonlyatmosphericforcingdataandcalibratedthemodeloutputtomatchhistoricwaterlevels.Thoughthisapproachgivesrelativelygoodresults,amoreaccurateapproachusedinarecentNOPPprojectentitled,Real-TimeForecastingSystemofWinds,WavesandSurgeinTropicalCyclones Graberetal. 2001 ,couplesapredictionofthewaveforcesintothecirculationmodelforcingterms.Theresultsobtainedusingacoupledmethodincreasesthepredictiveabilityofthesurgemodel.Tofurtherincreaseaccuracy,asystemofdynamiccouplingbetweenthesurgeandwavemodelisdeveloped.Thecoupledsystemrstproducesatimeseriesofwaveestimatesonthestillwaterlevelusingthewindinputs.Wavemomentumforcingcomponentsthenservetoforcethecirculationmodel,alongwiththeatmosphericforcingdata.Aninitialsurgelevel,forthefulldurationofthesimulation,isproduced.Thisrstestimateofthewaterlevelsisthenusedtoraisethewaterinthewavemodelforasecondwavecalculation.Thesewaterlevelsaresentbacktothewavemodel,andasecondseriesofwavepredictionsiscalculated.Amoreaccuratewaveclimateissimulatedandtheseforcesarethenusedtoforceanalrunofthecirculationmodel.Thewaveforcesfromthesecondmodelrunarereadintothecirculationmodelforthenalsurgesimulation.Thismethodallows 25

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foroodingandthepredictionofwavesoveroodedland.Additionally,theresponseofthewavesfromtheincreasedwaterlevelsinshallowwateriscaptured.ResultsfromastudyforFloridaDOT, Sheppardetal. 2007 ,revealedthatmorefrequentcouplingdoesnotsignicantlychangetheresultingsurgelevels.Itwasfoundthatthereisnosignicantchangeintheresultingwaveeldbetweenrunningbothmodelssimultaneously,dynamicallycouplingtheresultseverythreehours,andtwowaycouplingrunningthemodelsseparatelyandusingtheresultsfromeachmodelasinputsfortheother.Thesystemcanberuninparallelforanydesireddomain,givenacomputationalmeshforeachnumericalmodel.ThismodelingsystemwasusedinarecentstudybytheFederalEmergencyManagementAgencyFEMAtosupporttheHazardMitigationTechnicalAssistanceProgramHMTAP.TheMississippiCoastalFloodHazardProjectTO-18wasassignedunderthiscontract.IntheFEMAstudy,waveeldswerecalculatedwiththeW aveA ctionM odel,ThirdGeneration,WAM-3GindeepwaterandwiththeSimulatingWavesNearshoreSWANmodelinshallowwater.ThepurposeofthisprojectwastodeveloprevisedmapsofthecoastaloodzonesasdenedbytheNationalFloodInsuranceProgram.Theprimarycomponentofthemappingwasthedeterminationofcoastaloodinghazardelevationsfor10%,2%,1%and0.2%probabilityofbeingequaledorexceededalongtheMississippicoast.Thedevelopmentofthecoastaloodinghazardelevationatanylocationrequiresanestimateofthestormsurgeelevationandanassociatedwaveheight.ThesurgeelevationsweredevelopedbysimulatingstormsusingthecirculationmodelADCIRC.2.2SWANWaveModelandCongurationTheSWANmodelisathirdgenerationspectralwavemodel.Itincludesmanyphysicalprocessestoobtainarealisticestimateofrandomwaveelds.TheprimaryinputeldsforSWANarethebathymetry,thewindelds,andthewaveboundaryconditions.TheSWANmodelisaphaseaveragedmodel,forsimulationofwavesin 26

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shallow,intermediateordeepwater,andwasdevelopedbythesamegroupthatdevelopedtheWAMmodel.SWANincludesphysicalrepresentationsofwaveattenuationduetobottomfriction,shelfslopedependentdepthlimitedbreaking,unsteadywaveeldsdevelopment,bathymetricandcurrentwaverefraction,wavediraction,andsub-gridobstacles.Waveenergytransferfromdierentwavefrequencybandsiscalculatedbyspecictriadandquadrupletwave-waveinteractions.Includedinthewavemodelaresub-modelsforthephysicsofsteepnesslimitedbreakingwavewhitecappingaswellasexponentialwind-wavegrowth.AsamplesnapshotofthewaveeldinthecoastaldomainduringasimulationofHurricaneKatrinanearlandfallisplottedinFigure 2{1 .SWANmodelversion40.51,aphase-averaged,fullplanemodel,wasusedforthisstudy.Themodelhasbeenextensivelycalibratedandpublishedintheopenandrefereedliterature Risetal. 1994 ; Booijetal. 1996 ; Holthuijsenetal. 1997 1993 ; Risetal. 1999a b ; Hsuetal. 2005 ; ZijlemaandvanderWesthuysen 2005 .SWANwasimplementedwith72directionalbinse.g.,with5degreedirectionalwavespectralbinsandwith26frequencybinsfrom0.0314to0.4177Hzcoveringwaveperiodsbetweenapproximately32secondstodownto1secondthelastfrequencybinforthehighestfrequencywavesisnominallyat2.4secondperiods,butrepresentswaveswithperiodsfrom0.0to2.4seconds.Thetimestepwas15minutesandthemodeldatawasoutputevery30minutes.Inadditiontothespecicationofsomenumericalparameters,SWANrequires: 1. bathymetry 2. boundaryconditions 3. windelds 4. agridsystemEachoftheseisdescribedbelow:2.2.1BathymetricDataThecoupledsystemrequiresasetofdomains.Anysourceforbathymetricdatacanbeusedtopopulatethedomains;however,thequalityofthedatashouldbethoroughly 27

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checked.Indeepwater,thebathymetrydoesnotmattertothewaveeld.Ifthewaterisdeeperthanabout200metersthenthewavesarenotinuencedbythewaterdepth.Itisimportanttoperformaqualitycheckonthecoastalandnearshorebathymetrydata.Problemswiththecoastaldatashouldberesolvedbeforeusingthemodelsystem.Forthetestsofthemodelingsystem,thedomainsarefocusedontheMississippicoastline.Theoceanbathymetry,notshown,andcoastaltopography,showninFigure 2{2 ,weretakenfromtwosources,theNationalGeophysicalDataCenterNGDCandfromtheURSADCIRCgrid,whichincorporatedthehighresolutionLIDARsurveydata.TheURSADCIRCgridwasdevelopedbyURSCorps.foruseintheMississippiCoastalFloodHazardProject.Anyavailablebathymetricdatacanbeassimilated,eithermanuallyorthroughtheuseofsoftwaresuchasTecPlot,toproduceabestestimate.InthecoastalzonethebathymetryinthewavemodelswasinterpolatedfromthehigherresolutionURSADCIRCgridtooneofthenestedcoastaldomainsdescribedinSection 2.2.2 .ThereferencelevelwasNAVD88.2.2.2NestedGridSystemTheSWANmodelwasimplementedonasetofnestedgrids,withresolutionsrangingfrom10km,to2.5km,andthendowntoapproximately160m.Thisnestingsystemwasdesignedtooptimizegridresolutionandsimulationtime.ThethreelevelsofwavedomainsusedareshowninFigure 2{3 .ThebasindomainisshowninFigure 2{3a ,withthelocationoftheregiongridshowninthispanelbytheredbox.Atthecoarsestresolution,thebasindomaincoveredtheentireGulfofMexicowithagridresolutionof0.1degreesorapproximately10km.Insetinthisgureisthesecondgridleveltheredboxinthegureisthesecondgridlevel,anditisexpandedinFigure 2{3b .IntheLouisiana-Mississippiregiongrid,agridresolutionof2.5kmwasimplemented.TheregiondomainisshowninofFigure 2{3b ,withthelocationofthecoastaldomainsshowninthealternatingredandblackboxes.InthecoastalMississippiregion,9coastalgridswereusedtocoverthedesireddomaincoastline,eachwith160mgridspacinginthe 28

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x-direction,and180mgridspacinginthey-directionbothare0.00166667degreesatthislatitude.TherearelimitationsofthewavemodelSWANthatonlyallowforamaximumnumberofcomputationalpointsinadomain.ThecoastalzonewasrepresentedinordertoconstrainthesystemtotherequirementsofSWANandtoenableoptimizedruntimes.Eachcoastalgridhad301x151gridpointsandextendedapproximately54kmintheoshoredirectionand24kminthealongshoredirection.ThecoastalgridsareshownintheinsetofFigure 2{3b ,overlappedby2.4kmoneitherside.Theresultsintheoverlappingregionswereblendedbyweightingthesolutionclosesttoitsinteriordomainfromonetozero,linearlydependingonitsdistancefromtheinteriorofthedomain.2.2.3WindandWaveBoundaryConditionsDataThemodelingsystemwasdevelopedtoimplementwindandatmosphericdataforcinggeneratedbyOceanWeather,Inc.OWI.WindandpressureeldsfromOWIwereusedtodrivethesurgeandwavemodels.Modicationscanbemadetoallowforalternatesourcemeteorologicalinputswithoutinterferingwiththeperformanceofthemodelingsystem.WaveboundaryconditionscanbegeneratedforeachdomainusingtheSWANmodeloutputfromarunonacoarsermesh.TheSWANmodelcanbeimplementedonabasinscaletogenerateboundaryconditionsfortheregionmesh.Similarly,thesimulationresultsfromtheregionmeshcomputationprovidetheboundaryconditionsforeachofthecoastaldomains.Alternatively,thesystemwasadaptedtobeusedwithboundaryconditionsprovidedbydeepwaterwavemodels.FortheFEMAtests,deepwaterwaveswerecalculatedusingtheWAM-3GThirdGenerationWaveActionModel; Komenetal. 1994 ,implementedbyOceanWeatherInc.OWI.OWIprovidedwavespectraontheregiondomainboundariesdescribedbelow.Thewavespectraweregivenin15degreedirectionalbinsandfor26frequenciesat15minutetimeintervalsoverthecourseofusuallythreedaylonghurricanes.Thebasinwaveeldwascalculatedona10kmgrid0.1degree.Thesewavespectrawere 29

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interpolatedinspectraldensityspaceontothehigherresolutionwavegridsdegreedirectionalspectraandhigherresolutionspatialcoverage.2.3ModelSystemDescriptionTheinteractionbetweenastormsurgeandwavegenerationisahighlycoupledprocess.Thewaveheightsandperiodsdependonthesurgeheighti.e.,waterdepthandthesurgeheightdependsontheradiationstressgradients,whicharedependentonthewaterdepth.Ideally,afullycoupledmodelsimultaneouslyincludingsurgeandwavesimulationscouldbeused.However,thereisnomodelcurrentlyavailableforapplicationsinthisstudyandthereforeaniterativeapproachusingseparatesurgemodelsandwavemodelshasbeenemployed.Theattentionofthisworkisrestrictedtothestatic,ortimeaveraged,waveset-up.Thereisasecondcomponentofthewaveset-up,calledthedynamicset-upor'surfbeat',associatedwithdierentwavepackets.Largerwavegroups,maylastforafewminutes,andcauselargerwaveset-upforashortduration.Thesewavegroupsarefollowedbysmallerwavegroups,thatwouldhavelessassociatedwaveset-up.Theaveragingtimeintervalis15minutes,andthewavemodelisforcedwith30minuteaveragedwinds,andthereforeproducingtheaveragewaveset-up,fromtheaveragewaveelds.Theoveralliterativeschemeforthecouplingmethodinvolvesrapidlycomputingasequenceofwaterlevelsalongthewholecoastandcalculatingthecoastalwaveeld.Thisprocessisdoneforeachstorm,andsimulatedbyusingtheADCIRCmodelonarelativelylowresolutiongrid.ThisexistingmodelisconguredfortheMississippicoastusingagridwithabout58,000nodes.Themodelatthisstepdoesnotprovideforoverlandpropagationofthesurge,butexperiencesimulatingallthehurricanesforthelast5yearsintheAtlanticandGulfofMexicohasshownthatitreliablyoutputsthewaterdepthsoverthewholenearshorezoneatxedtimeintervals.Theselesaretheninputtoa2DwavepropagationandbreakingmodelSWAN.OutputlescontaintheradiationstressgradientsforeachgridpointinthehighresolutionADCIRCgridandevery30 30

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minutes.ThelecontainingtheradiationstressproleistheninputtothedetailedADCIRCgrid00,450nodesthatdoesprovideforoverlandpropagationofthesurge.Thisdetailedmodelhasmuchmorestringentcomputationalrequirementsandrunsmoreslowlythantheothertwomodels8KADCIRCandSWANthataretobeusedforeachstorm.ThisdierenceincomputationalrequirementsmeansthattheschemetopreparetheradiationstressgradientinputlescanbeimplementedfasterthantherunsofthedetailedADCIRCmodel.Inotherwords,theprojectschedulesoftheresearchteamcouldbemaintainedbecausethemorecomputationallyintensivemodelsetstheoverallrateofprogress.Thewind,wave,andsurgemodelsarelinkedatmanylevels.First,thewavemodelSWANisrun,forcedwiththehurricanewinds,assumingnosurgeispresentonthebasinGulfofMexicoandregionLouisianatoAlabamadomains.Second,acoarseresolution8,000elementADCIRCsimulationisrun,forcedwithboththewindandpreliminarywaveeldstoestimatethewaterelevations.Third,theSWANmodelisrunontheregiondomainandthenonthe9CoastalMississippigridswithhighresolutionapproximately160m.ThemaindierenceinthesecondimplementationofthewavemodelisthatthewaterelevationsfromthelowresolutionADCIRCgridareincludedinthetotalwaterelevations.Thewaveeldsarealsocalculatedovertheoodedlandregions,assumingthattheoodlevelsareabletoachieveahydrostaticbalanceintheinlandareas.Thewaveeldsfromthe10gridsarethenreassembledandthewaveforcesthatactonthewatercolumnarethencalculatedandinterpolatedontothehighresolution00,450nodesADCIRCgridforthecoastaloodingstudies.Anadvantageofthismethodologyisthatthewaveforcesthatproduceset-uparenotoverestimated.Theyarespatiallyandtemporallyvaryingusingthebeststate-of-the-sciencemethodologies.Thecomputationalcost,isrelativelysmalltoaddthewavecomponents,comparedtothecostofcalculatingthetotalstormsurge.Theonlyinputsrequiredforthecoupledmodelingsystemarethetimeandspatiallyvaryingwindeldsandthebathymetry.Themoreaccuratethewind 31

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elds,themoreaccuratetheresultingtotalsurgeandset-uppredictions.Inpreviousimplementationsofthismethodology,theOWIandH-Windwindeldshavebeenusedwithconsiderablesuccess.Aowchartofthewaveset-upmethodologyisshowninFigure 2{4 .Thesystemhas16majorsteps: 1. MergeNGDCandURSbathymetries. 2. RunWAMforthebasin.Interpolatethewaveboundaryconditionsfortheregiongrid. 3. Calculateradiationstressgradientsonthebasin.optional 4. RunSWANontheregion. 5. Calculateradiationstressgradientsontheregion. 6. RunADCIRConthe58Kelementgridwithwaveforcesfrom3and5above. 7. RunADCIRCwiththe58Kelementgridwithnowaveforcesoptionalstepusedindevelopment. 8. Calculatecoastalwaveset-uponshorelineandinland. 9. Extrapolatethecoastalwaterlevelsinlandusingahydrostaticapproximation. 10. RunSWANagainontheregiongridwithoodlevelsactive. 11. Calculatetheradiationstressgradientsontheregiongrid. 12. RunSWANonthe9coastaldomains. 13. Calculatetheradiationstressgradientsonthemergedcoastalandregiongrids. 14. Interpolatethenalwaveforceeldsontothe900,450elementADCIRCgrid,makingafort.23forcingle. 15. RerunthelowresolutionADCIRCgridifdesiredoptional. 16. Determinecoastalset-upalongshorelineonlowresolutiongridoptional.Anadditionalstepintheprocessistodecreasethemagnitudeofthewaveforcesinvegetatedareas.Thismethodologyfollowstheanalysisof DeanandBender 2006 thatshowedwaveattenuationinvegetatedareasresultedinareductionofmomentumtransfertothewatercolumn.Forlinearwaves,frictionallossestothetrees,bushesorgrassescoulddecreasetheradiationstressgradientsby2/3dependingontherelativewaterdepthstotheheightofthevegetation.Fornon-linearwaves,thereductioninmomentumtransfertothewatercolumnwouldbegreater.ThemodelingsystemhasbeencompletelyautomatedusingshellscriptingandisoperableonanyUnixplatform.Thesystemofcalculationswasimplementedona1000processorDepartmentofEnergyIBMSupercomputerandonasuiteofsingleanddualprocessorLinuxworkstations.Thesystemisnearlyplatformindependent.It 32

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compilesalloftheopensourcemodelslocallyonthecomputers,includingSWANandADCIRC,andallofthe20orsointerfacingprogramsthatarewritteninFortran.TheonlychangesnecessaryonanewplatformarerelatedtothenecessarycompileragsandbatchsubmissionsystemtosubmitthesimulationstothemainCPU.Inthenalimplementation,thecoupledlow-resolutionADCIRCandSWANsystemrunsinapproximately3daysofCPUtimeonasingleprocessorcomputer,orinabout3hoursofrealtimeona32processorcomputerfora3dayhurricanesimulation.TypicalproductionontheDepartmentofEnergy,DOEsystemwereapproximately5simulationsperday.Onthesystemof12CPU'sdedicatedtothisprojecttheproductionratewasapproximately4simulationsperday.2.4SampleApplication:HurricaneKatrinaInthissection,anexampleofresultsfromanimplementationofthewavemodelingsystemforthecaseofHurricaneKatrinaisshown.First,sampleresultsofthewaveeldareshownonthebasingridtheGulfofMexico,thenresultsontheregiongridLouisianatoAlabamaandthenresultsonthehighresolution,coastalMississippigrids.Inordertoillustratethenecessityofincludingthecouplingofacirculationmodelwiththewavemodel,SWANisrunforHurricaneKatrinabothwithandwithoutmodiedwaterlevels.ExaminingtheresultsofthefourpointsplottedinFigure 2{5 ,theadditionalwaterlevelswillsignicantlyalterthewaveclimateinthecoastalwaters.Figure 2{6 isaplotofthesignicantwaveheightforthefourpointswhoselocationsweregivenabove.Ineachoftheplots,thereisasignicantdistinctionbetweenthetwocases,withandwithoutwaterlevels.Thedierenceinwaveheightcanbeasmuchas3m,asseeninFigure 2{6a .Point43,Figure 2{6b ,remainsmostlydryandwithoutanywavesunlessthesurgelevelsareaddedtothewavemodel.Figurs 2{6c and 2{6d ,showhowthewaveheightcanmorethandoublewhenthesurgewatersareaddedtothewavecomputation.Havingestablishedtheneedtoincludethewaterlevelsinthewave 33

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modelforthisdomain,theresultsofthefullycoupledsystemforHurricaneKatrinaareexamined.Figure 2{7 isaplotofthespatialdistributionforasnapshotintimeofthesignicantwaveheightsduringHurricaneKatrina.Thesignicantwaveheight,HS,istheaverageheightofthe1/3largestwavesinthespectrum,ormoreexactlythisisalsocalledHm0whichisfourtimesthesquarerootofthezerothmomentofthewaveenergydensityspectrum.Thewavespropagateawayfromthecenterofthestormfasterthanthewinds,andreachtheshorebeforethestrongwindsofahurricanearrive,oftencausingsignicantwaveset-uppriortothelandfallofthestorm.Indeepwater,waveheightsofapproximately21marepredictedneartheeyeofthehurricane.WavemodelresultsontheregiondomainnearthepeakofHurricaneKatrinaareshowninFigure 2{8 .Thisgridresolutionis2.5km.Thelargestwavesoccuroutsideofthebarrierislands.Thelowlyingtopographyisoodedwithwaterduringthecourseofthesimulation.ThissimulationisusedpredominantlytofeedaccurateboundaryconditionstothenestedhighresolutiongridsshowninFigure 2{9 .InFigure 2{9 a ,thesignicantwaveheightsareshownascalculatedduringstep12ofthemodelingsystemthatincludescoastaloodingandmodelcouplingwithADCIRC.Thewaveforcesradiationstressgradientscalculatedinthecoastaldomainstep13inthemodelingsystemdescribedaboveareplottedinFigure 2{9 b .WenoteforcompletenessthatinanextensivestudyconductedpreviouslyfortheFloridaDepartmentofTransportation,itwasshownthatthereisgenerallylessthana1%changeofthewaveandwatereldsthatwouldresultifathirditerationofwaveandoodcouplingisconducted Sheppardetal. 2007 andthereforemakingitunnecessarytoincludeanyadditionaliterations.Thepeakwaveheightsinmeters,Figure 2{9 a ,andpeakwaveforcestransferredtothewatercolumn,Figure 2{9 b ,inthemergedcoastaldomains,illustratehowthewavesbehaveothecoastofMississippi.TheunitsADCIRCrequiresforthewaveforcearem2=s2,whichisstress,N=m2,dividedbythedensityofwater,andrepresents 34

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thevelocitycomponentoftheenergy.Theseguresaretypicalofresultsfromalloftheproductionruns.Thepeakwaveforcesoccuroutsidethebarrierislands.Therearestrongtwo-dimensionalaectstoboththewaveeldsandthewaveforces.Therearetwomajorsurfzones.Theonejustoutsidethebarrierislandsisabout2kmwide,andiswellresolvedinboththewavemodelwithabout15gridpointsandinthestormsurgemodelgrid,whichhasapproximately80mgridresolutionthere.Surfzoneresolutionwasfoundtobeanimportantconsideration.Thesurfzoneneedstoberesolvedbyapproximately10gridpoints,inordertorepresentaccuratelythemomentumtransferbetweenthewaveandsurgeelds.Thesecondsurfzone,ofcourse,occursimmediatelyadjacenttotheshoreline.Otherregionsofstrongvariabilityareevidentinthewaveforceplot.Someofthesevariabilitiesarecausedbydredgedshippingchannelsthataremuchdeeperthanthesurroundingbathymetry.Thedeeperwaterallowsmuchlargerwavestopropagateanddevelop.Astheserefractintoshallowerwater,theybegintobreakandtransfermomentumtothedepthaveragedwatercolumn.Wavespenetratethroughthechannelsbetweenthebarrierislandsandthenrefractandspreadouttheirenergythroughthechannels.Wavesofapproximately15marepredictedwelloutsideofthebarrierislands.ThewavesreforminMississippiBay,betweentheislandsandshore,overadistanceofapproximately15-20km.Thesewavesarebothfetchlimitedanddepthlimited,andtypicallyhaveamplitudesofunder4m.Thelongestwaveperiods,inexcessof10secondsaregenerallyrestrictedtooutsideofthebarrierislands.Wavesreforminsidethebarrierislands,andevenduringovertoppingoftheislandsasoccurredduringKatrina,thereislittlepenetrationofthelongperiodwavesacrosstheshallowwateroverthebarrierislands.2.5CalibrationandValidationThemodelingsystemdevelopedcanbemodiedtorunwithanywaveandcirculationmodel.Thesystemcanberunonmanydierenttypesofcomputationalplatforms.The 35

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systemisusedtogaininsighttosomephysicalprocessesthatcanaecttheheightofthesurgeatthecoastduringastormevent.Therstuseistoassesstheeectbathymetricvariationswillhaveonthesurgeatthecoast.Theresultsfromtheprevioustestalongwithmorein-depthtesting,isusedtoinvestigatetheimpactofbarrierislandsonthesurgelevel.ForthesecondtestthefocusisontheMississippicoastwherethebarrierislandsareapproximately20kmoshore.However,beforeresultsfromthesetestscanbeconsideredtobereliable,themodelingsystemmustrstbevalidated.ThereisanextensivebodyofliteratureindicatingthatbothWAMandSWANarestate-of-the-artmodelsforpredictingwavesaccuratelyincoastalwaters.SWANisacommonlyusedandacceptednearshorewavemodel,anditscapabilitieshavebeendemonstratedandvalidatedinmanypublishedarticlesandreports Risetal. 1994 ; Booijetal. 1996 ; Holthuijsenetal. 1997 1993 ; Risetal. 1999a b ; Hsuetal. 2005 ; ZijlemaandvanderWesthuysen 2005 .Themodelhasbeenfoundtoagreewiththeory,labmeasurements,andelddataunderawidevarietyofcircumstances.Twomethodswereusedformodelvalidation.First,twohistoricalhurricanesthatimpactedthemodeldomainweresimulated,andmodelpredictionswerecomparedtodatafromvariousbuoystoindicatethelevelofagreementwithmeasurements.Second,comparisonsweremadebetweenthetwosimilarspectral,phase-averaged,two-dimensionalcoastalwavemodels,SWANandSTWAVE,andthoseresultswerecomparedtoasophisticatedone-dimensionalmodelthathasbeenpreviouslycalibratedagainsthurricanewavedata.2.5.1ComparisontoStormWaveBuoysTheNationalOceanographicandAtmosphericAdministrationNOAAmaintainsanumberofwavebuoysintheGulfofMexicoandtheinformationisavailableonlineattheNationalDataBuoyCenterwebsiteNDBCURL:http://www.ndbc.noaa.gov/.ThelocationsofseveralofthesebuoysareindicatedinFigure 2{10 .VerygoodagreementhasbeenfoundbetweentheOWIdeepwaterwavemodelandthedeepwaterwavebuoys,andtheyhavecalibratedthatmodelagainsteveryhurricanepossiblethroughoutrecorded 36

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historyoverthelast20yearsintheirroleofconductinghurricanemodelingforoshoreoilplatformdesign.Twoofthebuoysareintheregionofprimaryinterest,andallofthebuoyswereusedforcomparisonswithmodelpredictionsforHurricanesGeorges1998andKatrina05.Figures 2{11 and 2{12 showtheagreementbetweenthemodelpredictionsandtheNDBCbuoysduringHurricaneKatrina.Buoy42007,Figure 2{11b ,isofprimaryinterestbecauseitislocatedinshallowwaterjustoutsideofthebarrierislandsinoneofthehighresolutioncoastaldomains.Buoy42040,Figure 2{12b ,isalsointheregiondomain,locatedoutsideofthebarrierislandchain.Notethattwoofthebuoys,42003Figure 2{11a and42007Figure 2{11b ,bothmalfunctionedduringthepeakofthestorm,andsofurthermodelvalidationcannotbeobtained.Theagreement,howeverwasverygooduntilthebuoysfailed.Themodelresultsmatchthetrendofincreasingwaveheight.Agreementfarawayfromthestorm,atBuoy42019Figure 2{12a ,showshowthemodelperformswellthroughouttheentiredomain.Themeasuredpeakwaveheightsarewellmatchedbythemodelpredictionatmostbuoysinthedomain.Sincethewavemomentumuxisafunctionofthewaveheightsquared,andthemaximumuxinthedomainisofgreatestinterest,goodagreementisdeterminedbytheabilitytomatchthepeakwaveheightsandthetrendasthewavesareincreasinganddecreasing.OnlyBuoy42040givesdisappointingagreementduringKatrina.Themodelsunderpredictthepeakwaveheightbyapproximately4meters.Peakmeasuredwaveheightsareapproximately17matthisbuoy,butthemodels,bothWAMandSWANonlypredictabout12or13m.NotethatnosurfzonewavegaugeswereavailableforcomparisonwiththeSWANresultsforthehurricanes.Figures 2{13 and 2{14 showsimilarresultsforHurricaneGeorges,thelargesthurricaneof1998.Forthishurricane,onlyBuoy42007Figure 2{13b stoppedrecording.Thisbuoy'sreadingsatthepeakofthemeasurementsarenottrusted,astheyleveloforsometimejustbeforethebuoyfails.Favorableagreementwasobtained 37

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betweenthemodelpredictionsandthebuoydataatallofthebuoys.Themodelandthedatacomparefavorablyovertheentiredomain;farawayfromthepathofthestorm,atBuoy42002Figure 2{13a ,andindeepwateratBuoy42003Figure 2{14a .Here,agreementwithBuoy42040Figure 2{14b ismuchbetter.Thereareseveralpossibleexplanations,weoertwothatarelikely.First,thewavepredictionsareonlyasaccurateasthewindeldsthatwereused,becausetheyhavesomemarginofuncertainty.However,themorelogicalexplanationisthattheeyeofthestormpassednearlydirectlyoverthisbuoylocationforHurricaneGeorges,wherethewaveheightagreementwasexcellent,butforHurricaneKatrina,thisbuoywasontheedgeofthehurricane'sstrongwindswherethewaveheightgradientsarelarge.Asmallerrorinstormpathwillresultinalargedierenceinwaveheight.Maximumsignicantwaveheightsofover21mwerepredictedbytheWAMandSWANmodelsatlocationsotherthanthosemeasuredatthebuoys.TheswathofthepeakobservedsignicantwaveheightsforHurricanesKatrinaandGeorgesareshowninFigure 2{15 .ExaminingthepathofthestormsclearlyindicatesthattheeyeofthestormpasseddirectlyoverBuoy42040forGeorgesFigure 2{15a butpassedtothewestforKatrinaFigure 2{15b .Sensitivitiesofwavepropagationorsmalldierencesbetweenthemodeledwindeldontheedgeofthestormcouldeasilyaccountforthemodel-datadiscrepanciesatBuoy42040forKatrina.2.5.2ComparisonofSWAN,STWAVE,andDean's1DmodelSimplecomparisonsbetweenSWANafull-planemodelandSTWAVEahalf-planemodelareconducted,andtheresultsarecomparedwithaone-dimensionalwavemodelinordertobetterunderstandthedierencesandsimilaritiesintheresponsesofthethreemodels.Thetestsconductedhereusedsteadywindelds.Figure 2{16 showstheresultingwaveeldsandwaveforcesobtainedbyimplementingasteady50m/swindfromthesouthontheMississippi-LouisianaregiondomainusingSWANandSTWAVE.ThewaveheightspredictedbySTWAVE,Figure 2{16 a ,growmoreslowlyawayfromthe 38

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boundaryanddonotreachthemagnitudeofthosepredictedbySWAN.InSWAN,thewavesgrowfasterandbecomelarger,Figure 2{16 c .Therearemanysimilaritiesbetweenthebasicwaveelds.Theshelfregionsaredominatedbydepthlimitedbreaking,andthemodelresultsaresimilarinthoseregions.Onestrikingdierenceisevidentfromtheforcevectors.Thewindisblowingduenorth,andSTWAVE,Figure 2{16 b ,givesalmostalloftheforcevectorsorientedduenorth.SWAN,Figure 2{16 d ,hasamoresignicantrefractionmodel.Inthecoastalzonesthistrendisevidentinregionsnearthebarrierislands,andattheshorewhererefractionismoreimportant.Asimpletestisdesignedtoexamineboththewavemodelpropertiesaswellasthewaveinducedset-upproducedbythemodels.Thedomainforthistestisatransectfromcoastaldomain7.Figure 2{17 isapairofcontourplotsofthewaveheightresponsefromtheHurricaneKatrinasimulationincoastaldomain7.Priortothestormenteringthedomain,Figure 2{17 a ,thebarrierislandandthestillwaterlevelareevident.Thecoastlinetakesonamuchmorecomplexform,andthebarrierislandbecomesmostlyovertoppednearthepeakofthestorm,Figure 2{17 b .A1DtransectofthebathymetryisextractedalongtheMississippishelfasindicatedinFigure 2{17 b .ThebathymetryisplottedinFigure 2{18a .Thewaterdepthisapproximately15mattheoshoreboundary,thex-axisisgiveninmeters,withtheoshorelocatedatapproximately890,500metersandthebarrierislandslocatedatabout913,000meters,orabout23kmshorewardoftheoshoreboundary.Threeseparatetestswereconductedonthiscross-shorebathymetryproleusing1DversionsofSTWAVEandSWAN.Theseresultswerealsocomparedtoastandard1Dmodel,developedbyDr.RobertG.DeanandbasedonacombinationofShoreProtectionManual CERC 1984 andCoastalEngineeringManual CERC 2003 methodology.TherearethreetestcasesshowninFigures 2{18 to 2{22 .ThewavesareinitializedattheoshoreboundarywithaJONSWAPspectra. 39

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Case1,50m/swindtothenorthandoshoresignicantwaveheightof7.89mwithpeakspectralwaveperiodof10sec Case2,zerowindandthesame7.89moshoresignicantwaveheightwithpeakspectralwaveperiodof10sec Case3,50m/swindtothenorth,andoshorewaveheightof0mEachmodelhasdierentwindandwaveinputparameterizationsaswellasdierentwavebreakingmodels.Thesethreetestsaredesignedtoillustratethedierentresponsesfromeachofthesefeatures.Thecross-shoredistributionofthewaveheightforCase1isillustratedinFigure 2{18b ThewaveheightspredictedbySTWAVEblacklineandSWANbluelinearequitesimilar.Wavesbegintobreakimmediatelyandcontinuebreakingacrosstheshelf.STWAVEissettobegindepthlimitedbreakingwhentheratioofHStothewaterdepthis0.6.SWANhasamoresophisticated,slopedependentdepthlimitedbreakingcriteria.Thewavesdecayfromapproximately8mto4mbeforedepthlimitedbreakingplaysasignicantrole.Thenataroundawaterdepthof5m,thewavesinbothmodelsdroporapidlyinthesurfzoneoutsideofthebarrierislands.ThesurfzoneinSWANiswiderthanthatinSTWAVE,thatis,thewavesbeginsteepbreakingfartheroshore.Allthreemodelspredictwaveheightdistributionsinfairlycloseagreementinsidethesurfzone.Thedecayinwaveheightsfrom8mto4misnotcausedbydepthlimitedbreaking,butratherbysteepnesslimitedbreaking.Asthewavespectrumbecomessaturated,andthewavesshoalinintermediatedepthwater,theyshorteninwavelengthandcausethewavecreststosteepenandbreakmoreregularly.Thisprocesstransfersmomentumtothewatercolumn,butthetransferhappensindeeperwaterthanwouldoccurifdepthlimitedbreakingwereoperative.Thewaveradiationstressesareproportionaltothewaveheightsquared.Hence,alargeportionofthewavemomentum,istransferredtothewatercolumninrelativelydeepwater,allowinglessmomentumtocontributetotheset-upinshallowerwater.Figure 2{19 showsthecross-shorewaveheightdistributionsforCases2and3.ResultsforCase2,Figure 2{19a ,showthatSWANhasamorerobustwaveshoaling 40

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componentthanSTWAVE.Itisevidentthatallthreemodelshandlethezoneofdepthlimitedbreakinginsimilarfashions,butthattheyhaveverydierentwind-wavegrowthmodels,withthe1Dmodelhavingthelargestwind-wavegrowth,Figure 2{19b .STWAVEhasthelargeststeepnesslimitedbreakingsinkterminthewaveactionequation,andSWANstartsbreakingwavesinthesurfzonesoonerthantheothermodels,becauseitincludesashelfslopedependentdepthlimitedbreakingcriteria.Additionaltests,notincludedhere,showedthatonsteeperslopes,SWANpredictslargerwavebreakinginthesurfzonethanSTWAVE.Thepresentslopeof15mchangeindepthover8kmisaslopeofapproximately1:500,orarelativelymildlyslopingshelf.Thecross-shoredistributionsofthewaveforcesandofthecross-shoreintegralofthetotalaccumulatedforceareshownforCase2inFigure 2{20 andforCase3inFigure 2{21 .Thesetwocasesillustratethemainpoints.ForCase2,Figure 2{20a showsthatSWANpredictslargerwaveforcesinthesurfzonethanSTWAVE,because,asseeninFigure 2{19a ,thewavedecayisosetbyagreateramountofshoaling.Thisshoalingleadstoalargerwaveheightjustbeforedepthlimitedbreakingoccurs.Thereislesslossofwavemomentumbysteepnesslimitedbreakingfartheroshore.ThisalsomeansthattherewillbearegionofmorepronouncedsetdownfortheSWANtest.InFigure 2{20b ,astheintegralofthewaveforcesdecreasespriortodepthlimitedbreaking.Thetotalintegralsgivesimilarvaluesforbothofthe2Dmodels.ForCase3,theSWANsurfzonestartsfartheroshore,Figure 2{19b .STWAVEpredictsahigherpeakx-directedforce,Figure 2{21a .However,sinceSWANbeginstobreaksooner,thereisawiderzoneofforcingcomingfromtheSWANmodel.ThetotalintegralofwavemomentumtransferredtothewatercolumnbetweenSWANandSTWAVEarenearlyidenticalFigure 2{21b .Forallcases,the1Dmodelgivesalargertotalintegral.Thepositiveforcesareisolatedinordertoillustratethedierencesintheshorewardmomentumuxbetweenthe3models.Figures 2{20 and 2{21 showthatthe1Dmodelwillyieldmuchhigherwaveset-upbecausethewind-wavegrowthmodel 41

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produceslargerwavesthanthoseofthespectralwavemodels.Inthiscase,thepeakvaluesoftheforcefromSTWAVEinthesurfzoneareabouttwiceaslargeasthepeakvaluesoftheforcefromSWAN.Figure 2{22 isasummaryplotoftheset-upoutsidethebarrierislandsforCases1through3.ForCase1,STWAVEpredictslargertotalset-upthanSWAN,Figure 2{22a .ForCase2,SWANpredictssomewhatlargertotalset-upoutsidethebarrierislandthanSTWAVE,Figure 2{22b .ForCase3,SWANandSTWAVEpredictthesametotalset-upwithinafewpercent,Figure 2{22c .Insummary,themodelsaresomewhatdierentinthateitheronecangivelargervaluesofset-upthantheotherdependingondetailsofthewindandoshorewaveamplitudesandtheshelfbathymetry.Both2Dmodelsgiveverysimilarresults,usuallywithinabouttenortwentypercentofeachother.The1Dmodelhasmanysimilarproperties,butoftenpredictsset-upabouttwiceaslargeasthe2Dspectralmodels,whenrunin1Dmode.Theresultsfromthe1Dmodelcanbeadjustedtomorecloselymatchthe2Dresultsbyreducingthevalueforthebreakingconstant,,to0.4.Theprimarydierencesarethewind-wavegrowthmodelandthesteepnesslimitedbreakingsub-models.IfthebreakerheightindexinSTWAVEissetto0.42insteadofthedefaultvalueof0.6,theresultsforwaveheightandset-upbetweenSWANandSTWAVE,forthisparticularbathymetry,becomeverysimilar.Thisadjustmentwouldbejustiableonamildslopingshelf.2.6ChapterSummaryThetwo-dimensionalspectralwavemodelSWANSimulatingWavesNearshorewasusedtocalculatewaveeldsandwaveradiationstressgradientsonanesteddomainsystem.TheresultswerecoupledwiththestormsurgemodelADCIRC.Themodelwasextensivelyvalidatedandtestedonthreevalidationrunsandimplemented,fortheURSFEMAMississippiCoastalFloodMappingStudy,in228productionrunsfordierenthurricanesstrikingtheMississippiCoast. 42

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Themodelingsystemwasveriedbycomparingwaveheightresultstooshorewavedata,andcomparingsurgeresultstoCoastalHighWaterMarks.Aremainingchallengeistovalidatethewaveset-upestimatesthatareincorporatedinthemodelingsystem.Waveset-upisdiculttomeasureandhardtoextractfromexistingelddata.SWANoutputsthewaveforcingcomponents,however,thisdatamustbethoroughlyexaminedtoensurethesystemproducesaccuratepredictions.InthenextChapter,itwillbeshownbycomparisontolaboratoryandelddata,thatthemethodchosentocomputethewaveforcingcomponentsisjustiedandacceptable. 43

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Figure2{1.AvisualizationofthewaveamplitudeandoodingalongtheMississippicoastduringHurricaneKatrina,lookingnorthaccrosstheMississippiDelta.TheplotiscenterednearLongBeach,MS.Thewarmercolorsindicatehighersignicantwaveheight,withthescaleinmeters,from6.0mdowntozero.Thelandisplottedinbrown.Atthistimeallofthebarrierislandsarebeingovertopped,andmuchoftheMississippicoastisinnundated. 44

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Figure2{2.Post-KatrinacoastalbathymetryusedinthewavemodeldevelopedfromURSandNGDCdatasets.Coolercolorsindicatedeeperwaters,warmercolorsindicateland.Thezerocontourcoastlineisoutlinedinblack,andtheuntisareinmeters. 45

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a bFigure2{3.Computationaldomainsusedinthewaveset-upmodelingapproach.aGulfofMexicogridregion.bBlowupoftheredsquarefroma.ItincludestheLouisiana,MississippiandAlabamacoastlines.bAlsoincludesthelocationsofthe9overlappingcoastalgrids.Theunitsofwaveheightareinmeters.Thexandy-axisaretransformedintotheCartesianmodeldomain,andthoseunitsarealsoinmeters. 46

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Figure2{4.Flowchartofwaveset-upmethodology.Thisowchartgoesstep-by-stepthroughtheprocessesusedtocoupleandrunthewaveandcirculationmodels.Theresultofthisprocessiscoastalwaveandsurgepredictionsonagivendomain. 47

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Figure2{5.LocationsforcomparisonofHSfortheHurricaneKatrinarunswithandwithouttheadditionofsurgelevelstothewavemodel. 48

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aPoint72 bPoint43 cPoint42 dPoint41Figure2{6.ComparisonofthesignicantwaveheightsfortheHurricaneKatrinasimulationswithgreenlineandwithoutbluelinetheadditionofsurgelevels.aComparisonatpoint72.bComparisonatpoint43.cComparisonatpoint42.dComparisonatpoint41.Theadditionofwaterlevelstothewavemodelallowsforalargerwaveheighttobesustainedateachpoint. 49

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Figure2{7.SignicantwaveheightspredictedduringHurricaneKatrinainthebasinscalegrid.Theunitsofwaveheightareinmeters.Thexandy-axisaretransformedintoCartesianmodeldomain,andthoseunitsarealsoinmeters. 50

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Figure2{8.SignicantwaveheightspredictedduringHurricaneKatrinaintheregionscaledomain.Theunitsofwaveheightareinmeters.Thexandy-axisaretransformedintoCartesianmodeldomain,andthoseunitsarealsoinmeters.TheMississippiandLouisianacoastareinnundatedandwavesarebeingcalculatedontheoodwaters. 51

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Figure2{9.WaveheightandwaveforcepredictionsforHurricaneKatrina.aWaveheightsinmetersinthecoastaldomainfromtheSWANsimulationsforHurricaneKatrina.bMaximumvaluesofthewaveforcesunitsofm2=s2inthecoastaldomainduringtheKatrinasimulationinthemergedcoastaldomains. 52

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Figure2{10.LocationofNOAAwavebuoysintheGulfofMexico. 53

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a bFigure2{11.ComparisontowavebuoyresultsduringHurricaneKatrina005atBuoysa42003andb42007. 54

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a bFigure2{12.ComparisonofwavemodelandbuoydataduringKatrina2005atBuoysa42019andb42040. 55

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a bFigure2{13.ComparisontowavebuoyresultsduringHurricaneGeorges998atBuoysa42002andb42007. 56

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a bFigure2{14.ComparisonofwavemodelandbuoydataduringHurricaneGeorges98atBuoysa42003andb42040. 57

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a bFigure2{15.MaximumsignicantwaveheightsinmeterspredictedforKatrina005andGeorges998.aMaximumsignicantwaveheightsduringHurricaneGeorgesandbHurricaneKatrinaduringthesimulationsinthebasinmodeldomains. 58

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Figure2{16.ComparisonofresultsfromSTWAVEandSWANforsteady50m/ssouthwind.aSignicantwaveheightaspredictedbySTWAVE.bWaveforcespredictedbySTWAVE.cSignicantwaveheightpredictedbySWAN.dWaveforcespredictedbySWAN.Theunitsofthesignicantwaveheightsareinmeters,andtheunitsoftheforceareinpascals,theordinateandabscissaareshowninthegridindex. 59

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Figure2{17.Locationof1DtransectsforSWAN{STWAVEcomparisonsinthemiddleofcoastalzone7crossingthebarrierisland.aSignicatwaveheightpredictedattimet=08/28/200500:00.bSignicatwaveheightpredictedattimet=08/29/200515:30andtransectlocationfor1Dtests.Theunitsofwaveheightareinmeters. 60

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a bFigure2{18.1DversionsofSWANandSTWAVEcomparisons.aPlotofthebathymetryproleusedineachtestrun.bHSproleforeachofthethreemodelsusingtheforcingconditionsoutlinedinCase1.Thex-axisplotsthecross-shorelocationinCartesiancoordinateswithunitsinmeters. 61

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a bFigure2{19.ComparisonofSWAN,STWAVEandDean's1DmodelforanowindCase2andbzerooshoreboundaryconditionCase3simulations.Thex-axisplotsthecross-shorelocationinCartesiancoordinateswithunitsinmeters. 62

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a bFigure2{20.aCross-shoreforcedistributionandbtotalintegraloftheforcesforthethreemodelsappliedinonedimensiontoCase2.Thex-axisplotsthecross-shorelocationinCartesiancoordinateswithunitsinmeters.TheunitsforforceareN=m2 63

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a bFigure2{21.aCross-shoreforcedistributionandbtotalforceintegralsforthe3modelsofCase3.Thex-axisplotsthecross-shorelocationinCartesiancoordinateswithunitsinmeters.TheunitsforforceareN=m2 64

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a b cFigure2{22.Resultsforset-upinmetersofthethreemodels;SWAN,STWAVE,andDean's1D,aCase1,bCase2,cCase3.Thex-axisplotsthecross-shorelocationinCartesiancoordinateswithunitsinmeters.Theunitsforwaveset-uparemeters. 65

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CHAPTER3VALIDATIONOFWAVESET-UP3.1IntroductionOneofthephysicalcontributorstostormsurge,especiallyduringhighenergystormssuchashurricanes,isthewaveset-up.Theforcesimpartedbythewavesintothewatercolumnforceagradientintheseasurfaceelevation.Untilrecently,itwasnotcommonpracticetoincludewavepredictionswhencalculatingtheincreaseinwaterlevelsfromhurricanes.Recentwork,overthepastyears,hastakenadeeperlookintotherolewavesplayinhurricanestormsurgegeneration.Inordertomoreaccuratelyrepresentthephysicsofstormsurge,itisimportanttoincludethewaveforcingcomponents Weaver 2004 ; WeaverandSlinn 2004 2006 ; Graberetal. 2006 ; Niedorodaetal. 2007 .TheSWANmodel Holthuijsen 2000 isusedtocalculatethewaveeld.Thismodelcomputesthewaveforcesinspectralspace.Thewaveforceiscomputedbycalculatingthedissipationinthewaveeld.Priortobreaking,excessmomentumbuildinginthewavecausesaset-downintheseasurfaceelevation.Asthewavesbreak,themomentumisreleasedbackintothewatercolumnandthisforcesaset-up.Whenthisbreakinghappensindeepwater,theeectismuted.Ina2Dmodeltheforceisdepthaveraged.Innature,aswavesbreaksomeofthemomentumistransferredintoturbulenceandheatgenerationthroughviscousshearstresses.Indeepwater,aportionofthemomentumistransferredintosurfacecurrentsandeddygeneration RappandMcIvill 1990 .Inshallowwater,themajorityofthemomentumtransfrerredintothewaterforcesachangeinthemeanwaterlevel.TheamountofwaterlevelchangeisexpressedbyEquation 1{2 .Momentumuxrepresentedbythegradientintheradiationstressesisthedrivingcomponentoftheset-upequation.ThexandycomponentsofthewavemomentumtransferareexpressedinEquations 3{1 and 3{2 .Fx=[)]TJ/F23 11.955 Tf 10.494 8.088 Td[(@Sxx @x)]TJ/F23 11.955 Tf 13.151 8.088 Td[(@Sxy @y]3{1 66

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Fy=[)]TJ/F23 11.955 Tf 10.494 8.088 Td[(@Syy @y)]TJ/F23 11.955 Tf 13.151 8.088 Td[(@Syx @x]3{2Inspectralspacetheradiationstresscomponentsaredenedas:Sxx=Z10Z20ncos2+n)]TJ/F15 11.955 Tf 13.15 8.088 Td[(1 2E;dd {3 Sxy=Syx=Z10Z20nsincosE;dd {4 Syy=Z10Z20nsin2+n)]TJ/F15 11.955 Tf 13.15 8.087 Td[(1 2E;dd {5 Theradiationstressesareafunctionofthetotalenergyinawave.Thetotalaverageenergyperunitsurfaceareais,inturn,afunctionofthewaveheight,Equation 3{6 .E=1 8gH2rms{6Forcomparisonofthemodelresultsandtheorytonature,arepresentativebreakingwaveheightisrequired.Undernormalconditionsalonganaveragebeach,thisisnotdicult.Anobservercanlookatthenearshoreseaandvisuallypickoutwherethewavesbegintoshoal,wherethesurfzonebeginsandwherethelargestwavesarebreaking.Typicallyinthesecasesthereisaniteregionofbreakingwithinafewhundredmetersofthecoastline.Thisisnotthecaseforhighlyenergetichurricanegeneratedseas.Forhurricanegeneratedseas,thereisnoclearsurfzoneasdescribedabove.Insteadthe'surfzone'canbetensofkilometerswide.InthecaseofHurricaneKatrina,measuredwaveheightsinexcessof20metersexistedhundredsofkilometersoshore.Atabout50kmoshorethewaveheightshadreducedbymorethanhalf.Overawidesurfzonethereisasignicantamountofsteepnesslimitedbreakingwhitecappingandturbulencegeneration.ThedepthaveragedresponseoftheseasurfacetomomentumexchangeindeepwaterisnegligiblesincethetotalstressisdividedbythewaterdepthEquation 1{2 .Indeepwater,excessmomentumgoesintoforcingasurfacecurrent.Aneddyisgenerated,asthemomentumisleftbehindbythewavegroup.Accordingto Rappand 67

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McIvill 1990 ,"Morethat90%oftheenergylostfromthewaveswasdissipatedwithinfourwaveperiods."Themomentumfromwaveswouldbetransferredintothewatercolumn.Whenevaluatingtheperformanceofthewavemodelandthemodelingsystem,resultsneedtobemeasuredagainstabreakingwaveheightthatrepresentsthewaveheightatthetimeofstrongdepthaveragedshorewardmomentumuxintothewater.Anoshore,deep-waterwave,withaheightof20m,willspillandbreakdowntoan8to9mwaveatthetimeofstrongshallowwaterbreaking.Themomentumexchangedduringthistransitionlikelyforcedturbulenceandheatgenerationaswellassurfaceandeddycurrents.Oneshouldbecondentthatthephysicsoftheproblemarerepresentedcorrectly.InordertohaveincreasedcondenceinthecoupledmodelingsystemdescribedinChapter 2 ,asuiteofsimulationsaimedattestingtheresponsevariabilityofthewaveset-uptoavarietyofmodelingconditionsisperformed.Theresultsofthesetestswillhelptobetterinterprettheresultsoftheremainingtestcases.Themodelsystemistestedforthreecases: Aeldstudythatmeasuredwaveset-up MeasureddatafromHurricaneOpal DatafromHurricaneKatrinaResultsfromthesimpliedmodeltestslistedaboveshouldfallwithinthescatterofthedataasmeasuredorrecorded.Ifthesetestresultsareacceptable,onecanbecondentthatthewavesandwaterlevelsduringextremestormshavebeenrepresented.3.2WaveForcingSensitivityTests3.2.1IntroductionAsarststeptoimprovingunderstandingofwaveforcing,asuiteoftestsaredevelopedusingtheSWANandtheADCIRCmodels.Testsarerstperformedtodeterminethemodelsensitivityofthewaveforcingtoboundaryconditions,spatialuniformityandtemporaluniformityintheinputforcing.Oncevariationintheresponsetotheabovementionedconditionsisevaluated,themodelingsystemisfurthertested, 68

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comparingmodelresultstoeithereldstudiesordatacollectedduringandafterhurricaneevents.3.2.2ModelDescriptionThisstudyisfocusedonunderstandingtheresponsevariationsfortwocases,1Dand2D.Modelresponseisexaminedforthefollowingthreevariations: Boundaryconditions Steadyforcingandunsteadyforcing SpatiallyuniformforcingacrossentiredomainandvariedforcingacrossaportionofthedomainThedomainusedfortheabovelistedtestsisshowninFigure 3{1 .ThebathymetryusedisslightlysteeperthanthatfoundotheMississippicoast.Anaverageslopeof1:1700isused,otheMississippicoasttheaverageslopeiscloserto1:2000.Thedomainhasamaximumdepthof30mlocated50kmfromthemeanwaterlevel,andthereisadrylandportiontoallowforoodinganddrying,Figure 3{1 a .Thedomainextends180kmalongshore,Figure 3{1 b .Theset-upresponsefromSWANiscomparedtoacoupledSWANandADCIRCsystemandcomparebothtoa1DanalyticmodeldevelopedbyDean.This1Dmodelisbasedonsimplewavetheoryforbreakingwavesonarelativelysteepslope.Themaindeterminingvariableinthe1Dtheoryisthebreakerconstant,kappa,=Hb hb.TheequationforthemeanwatersurfacedisplacementattheshorelineisgivenbyEquation 3{7 .Theformulationofthisequationisgivenin DeanandDalrymple 1991 .=b+32=8 1+32=8hb{7Thegoalistorstverifythatthemodelproducessimilarresultstowhatthetheorypredicts.Oncethemodelshavebeenreconciled,thetestslistedinthebeginningofthissectionwillcommence.Therearefourvariationsusedforthesetests. 1. 1Dwithsteadywinds Uniformwindof50m/sectimeandspace ZerooshorewaveBC 69

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9m,10secoshorewaveBC 2. 1Dwithunsteadywinds Uniformwindthroughoutdomainspace Gaussianwindproleintimewithapeakwindof50m/sec 9m,10secoshorewaveBC 3. 2Dwithsteadywinds Forcingof50m/seconly70kmswathalongshorew/centerat90km Forcingof50m/seconly10kmswathalongshorew/centerat90km ZerooshorewaveBC 9m,10secoshorewaveBC 4. 2Dwithunsteadywinds Forcingof50m/seconly70kmswathalongshorew/centerat90km Gaussianwindproleintimewithapeakwindof50m/sec ZerooshorewaveBC 9m,10secoshorewaveBCSeeFigure 3{2 forasketchofthe1DmodelcongurationandFigure 3{3 forthedescriptionofthe2Dmodelingsystemdescribedinthelistabove.Foreachtestcase,theSWANmodelisrunrst,beingforcedbywindandifapplicableoshorewaveboundaryconditions.TheresultsfromtheSWANrunarethenconvertedintoinputfortheADCIRCmodel.ThecirculationmodelisonlyforcedwiththewaveforcingcomponentsprovidedbySWAN,anddonotincludethecontributionduetowindstressesoratmosphericpressures.Thisallowstheattentiontobedirectlyfocusedonthewavecontributionstothesurge.3.2.3BoundaryConditionTestsThersttestlistedabove,withuniformsteadyforcingandzerooshorewaveboundaryconditions,isusedtotestthesensitivityofthemodelingtotheboundaryconditionsusedinthecirculationmodel.ADCIRCisrunwiththreedierentboundaryconditionsforthewatersurfaceattheboundaries: 1. sideandoshoreboundariesallopen 2. sideandoshoreboundariesallclosed 3. sideboundariesclosedandoshoreboundaryopenTheresultsoftheBoundaryConditiontestsareshowninFigure 3{4 70

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Withanoshorewaveboundaryconditionofzerowaveheight,therstresponseofthemodelistogeneratewavesinthedomain.Inthemodels,thiswindgrowthproducesawavestressorientedintheoshoredirection.Thisinterestingresponseisfoundinallofthewavemodelsthatcomputewaveradiationstresses.Thisstresscomputedbythenumericalmodelsisafakestress,astressthatdoesnotoccurinnature.Innaturethewaveheightsareincreasingduetothewindstressattheair-seainterface,notatransferofmomentumfromthewatercolumnintothewave.Itisimportanttomakenoteofthisphenomenon,andrealizethattheset-downandtheoshorecurrentthatispredictedinFigures 3{4 a and 3{4 c areaproductofthemodelandnotreal.Set-downiscausedbyanincreaseinmomentuminthewavecausedbythewaveshoaling,growing,duetointeractionswiththebottom Longuett-HigginsandStewart 1964 ; Bowenetal. 1968 .Circulationmodelscomputethewaterlevelbyexaminingtheenergyinthewave.Theincreaseinenergywaveheightistranslateddirectlyintoawaterlevelresponse.Inthecaseofwind-wavegrowth,however,themechanismforthechangeinwaveheightisfromanoutsideforce,thewindstress.Thisportionofmomentumchangeshouldnotbeincludedinthemomentumbalancethatiscalculatedtocomputethewaveset-down.Futureworkshouldbeperformedtoreconcilethismodeldeciency.TheplotinFigure 3{4 a representstheresultsforthecaseofallboundariesbeingopenandxedatawaterlevelofzero.Suchawatersurfacecontourisnotrealisticforthesideboundarieswhenwehavespatiallyuniformforcinginthedomain.Theconditionforcesaninowingcurrentalongthesideboundariesandanoutowingcurrentalongtheoshoreboundary.ResultsforthecaseofclosedboundariesisplottedinFigure 3{4 b .Thiscasemayberepresentativeoftheresponseinaclosedbasinsuchasalake,howeverthisdoesnotrealisticallyrepresenttheintendeddomainofalong,straightcoastline.TheplotinFigure 3{4 c representstheresultsofthecasewheretheoshoreboundaryisopenandxedatzeroandthesideboundariesareclosed.Thedesiredresultsareobtainedat 71

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thesidesofthedomain,wherethewaterlevelisrepresentativeofwhatisexpectedforacaseofuniformforcingalongalong,straightcoastline.Thepeakvaluesoftheset-upvarybyabout23%atthecenterlineofthedomain,asseeninFigure 3{5 .Byopeninguptheboundariesandallowingcirculation,themagnitudeoftheset-upisreduced.Forhurricanesimpactingacoastline,thereisalwaysatleastoneopenboundary.Forthatreason,boundarycondition3listedaboveisused,wherethesideboundariesareclosedandoshoreboundaryisopenandxedatzero.ThissameboundaryconditionisusedforeachoftheADCIRCrunsforthe4testcases.3.2.4WaveForcingTestsWiththeboundaryconditionssetforthecirculationmodel,the4testslistedaboveareperformed.Surprisingly,therewerenosignicantdierencesbetweenthemaximumwaterlevelsforthestationaryandnon-stationaryforcingsimulations.Forboththe1Dand2Dcases,theresultingmaximumwaterlevelsdieredonlyinthefourthsignicantdigit.The1Dcasewasrunforthefull60hoursinordertoensureequilibrium.Thenon-stationarycasewaveforcewasrampedfromzerouptothefullforce,equaltothestationaryrun,atthe30hourmark,heldconstantfor4hours,andthenrampedbackdowntozerobyhour60.Themaximumwaterlevelwasreachedbyhour34,atwhichtimethemaximumwasequaltotheequilibratedwaterlevelcomputedinthestationaryrun.TherampfunctionwascomputedtocoincidewiththewaveeldgeneratedbyawindeldthatwasrepresentativebothindurationandmagnitudeofthatmeasuredduringHurricaneKatrina.Apreliminarysimulation,usingtheSWANmodelforcedonlywiththerepresentativewindeld,modeledthetimeevolutionofthewaveresponse.Thistimeevolutionwasnormalizedandusedtoscalethewaveforcingusedforthestationaryrun.Themethodensuredthatatthetimeofpeakforcingthemagnitudeoftheforcesbetweenthestationaryandnon-stationaryrunswouldbeequal.AcontourplotoftheresultsforthestationaryrunisshowninFigure 3{6 ,thestreamlinesrepresentingthecurrenteldarealsopresented.Thedierencebetweenthe 72

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1D,Figure 3{6 a ,and2D,Figure 3{6 b ,simulationsis9.2%,from0.340mto0.303m,forthecaseofa2Dforcingswathwidthof70-km.Ifthewidthoftheforcingdomainisreducedinthe2Dsimulationto10km,themaximumsurgeatthecoastisreducedto0.220m,thusproducinga28%reductioninthesurgelevels.Thesurgegeneratedbythewavesissignicantlydependentonthewidthofthewindeld.Thisresultisrelaventtotheeectoftheradiustomaximumwindsinahurricane.Asmallstorm,withasmallradiustomaximumwinds,willhaveareducedresponsefromthewaveelds.Figure 3{7 isaplotoftheequilibratedsurfacelevelwiththecurrentstreamlinesforboththe10km,Figure 3{7 a ,and70km,Figure 3{7 b ,wideforcingcases.TocompletethisstudyacomparisonismadebetweentheresultsfromthewaveforcingteststoresultscomputedusingSWANintrue1Dmodeanda1DmodelbasedontheorydevelopedbyDr.RobertDean.Figure 3{8 isaplotoftheseasurfaceproleresponseacrossthedomainforfourcases.Sincethestationaryandnon-stationarytestsyieldedthesameresults,onlythestationarytestresultsareshown.ThewaveheightaspredictedbySWAN1D,thewaveheightpredictedbyDr.Dean's1Dtheoreticalmodel,andthereferencewaterdeptharealsoplotted.Dr.Dean'smodel,usingavalueof=0:42,andtheSWAN1Dpredictionareinagreement.The1Dtest,uniformforcinginthealongshore,withthewaveforcingcalculatedfromSWANandthewaterlevelcomputedinADCIRCfromthewaveforcingonly,was7%smallerthanthetrueSWAN1Dresult.Theresultofthe2Dcasewherea70kmwideswathwasforcedinSWANandthewaterlevelcomputedinADCIRCfromthewaveforcingonly,was11%smallerthanthe1Duniformforcingcase.ResultsaresummarizedinTable 3{1 .Oneotherresultshouldbenotedregardingthetestsofthenon-stationaryeects.Onecasewassimulatedwherethewindswererampedupfromzerotothemaximumwindvalueusedforthestationarycaseandthenreducedbackdown,followingatemporalprolesimilartothatrecordedduringHurricaneKatirna.Inthiscasethemaximumwaveheightwassmallerthanthatcomputedinthestationarycase.Itfollowsthatthewave 73

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set-upforthiscasewasalsosmaller.However,thereductionisduetothefactthatthewavesdidnotreachthesamemaximumheightasthestationarycase.3.3NielsenTests3.3.1IntroductionTherstsetoftestsdesignedbyDr.RobertG.DeanisbasedonaeldexperimentbyNielsen Nielsen 1988 .TheeldtestsiteisontheAustraliancoastattheTasmanSea.Detailsoftheeldexperimentarethoroughlycoveredinthepapers Nielsen 1988 and Nielsenetal. 1988 .TheNielseneldresultsshowalargescatterinthedata,asdootherlaboratorystudiesofwaveset-up.InadditiontoNielsen,studiesandpapersby Bowenetal. 1968 StiveandWind 1982 HolmanandSallenger 1985 and Stockdonetal. 2006 showadegreeofscatterintheset-upmeasurements.Thegoalistodenetheregionwherethemodelisvalid,andthencomparethemodelresultswithinthisregion.3.3.2ModelDescriptionAsimpliedbathymetryisadoptedforthetests.WaterlevelsandinitialconditionsarechosenthatfallwithintherangeofdataasseenbyNielsenduringhisexperiments.ThetestparametersaresummarizedinTable 3{2 .Thedomainisdiscretizedwith1mspacingbetweencomputationalpoints.SWANallowsforminimalwettinganddryingwithouttheinclusionofaninitialwaterleveldataset.ThevalueinSWANthatdelimitstheextentofwetdomainissetto0.05m.Thismeansthatatdepthslessthan5cm,SWANwilltreatthepointasdry.Thislimitingfactorinthenumericalmodelwillhaveaneectintheinterpretationofthevalidityofthemodeledresults.IntheNielsenstudythereisasignicantincreaseinthewaterlevelinthelast10cmbeforethewaterintersectswiththeland. HolmanandSallenger 1985 ndthatmeasuredshorelinevalueswillalwaysbehigherthanthosecalculatedusingtheoreticalequations.Thisisimpliedbytheideathattheslopeoftheseasurfaceapproachesthebeachfaceasymptotically Bowenetal. 1968 .Inthesenal 74

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fewcentimeters,themeasuredwaterlevelsconvergeasymptoticallytothebeachface.Thenumericalmodelsarenotreliableinthesedepths,assuchweshouldnotcomparetheresultsinthisregion.Sixtestsarerun,andcanbefoundoutlinedinTable 3{2 .Intheseteststhewaveheightsarevariedfrom1mto2m,andtheperiodsaregivenvaluesof8,12and16sec.Thewaterlevelsarealteredby0.5mtosimulatethetidaluctuations.TheeldstudyresultsofNielsenaretakenoveravarietyofconditions.Thoseconditionsoutlinedforthesesimulationsarerepresentedintheresultsmeasuredintheeldstudy.Unfortunately,itisnotknownfromtheNielsenresultswhichdatavaluescoincidewiththeinitialconditionsusedforthesimulations.Forthisreason,thesetestswillbeconsideredreasonablysuccessfuliftheresultsfallwithinthescatteroftheelddata.3.3.3ResultsNielsenstatesthattheshorelineset-upwasapproximately40%oftheoshorewaveheightRMS.Thisvalueischosenastheaverageoftheelddatarepresentingtheintersectionofthewaterandtheland.Thedatausedtoarriveatthisconclusionwascollectedinthelast5cmofwaterdepthbeforethemeasurementsswitchedfrommeasuringmeansealeveltomeasuringthewaterlevelinthewatertable.Thistypeofcomputationisbeyondthecapabilitiesofthenumericalmodelsthatweareusing.SWANdoesnotaccuratelycomputethemaximumelevationofset-upthatwouldoccuratthepointofwaterintersectionwiththeland.Forinstance,inTest1.1,asoutlinedinTable 3{2 ,theSWANmodelstoppedcalculationswhenthewaterdepthreached0.0723m,havingcomputedaset-upof0.212m.Asthewaterinteractswiththebeachface,thereisaresponseinthelastfewcentimetersthatisdependentonthisinteraction.ThisregionistooshallowforourSWANcomputations.Exactscatterlimitsfromthedatacollectedrangedfromlessthan0.05mto0.90m.Thegreatestdensityofdatascatterfromtheelddatafor=Hbrmsrangesfromapproximately0.1upto0.35in 75

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theregionoftotaldepthofapproximately0.05m.Thetestcaseresultsof0.150-0.230marewellwithinthisrangewithanHbrmsof1m.InFigure 3{9 ,theresultsofTest1.1and1.2areplottedtogetherwiththeirrepresentativesimpliedbathymetries.TheresultsofTest1.1and1.3areplottedtogetherinFigure 3{10 .InbothFigures 3{9 and 3{10 itisclearthatthealargeportionoftheset-upoccursjustbeforethewaterintersectstheland.Thisresultshouldbeobviousasthewavesmustbreakhere;thatis,thewaveheightmustgotozeroasthetotaldepthgoestozero.Unfortunately,thesimulatedwaterleveldoesnotcapturethenalpushofthewaterupthebeachfacethatoccursinthelastfewcentimetersofwaterdepth.ThetestresultsaresummarizedinTable 3{3 .ThoughthesevaluesareabouthalfoftheaveragevaluethatNielsenconcludedfortheratio=H0atthedrylandpoint,theyarewellwithinthescatterofvaluesinthedepthrangeof5to10cm.3.4HurricaneOpal3.4.1IntroductionThistestdesignedbyDr.RobertG.Dean,isbasedonthedatacollectedduringandafterHurricaneOpalmadelandfall.OpalmadelandfallatPensacolaBeachintheFloridaPanhandleonOctober4,1995asaCategory3hurricaneontheSar/SimpsonhurricaneScale Mayeld 1995 ; Graumannetal. 1995 .Stormsurgelevelsareestimatedtohaverangedfrom1.5to4.3m,or5to14ft,abovemeansealevel.ThetidegaugeatPanamaCityBeachpier,recordedamaximumwaterlevelof8.3ftorabout2.53m.Adebrislineattheshorewardendofthepierwasmeasuredtobeapproximately18ftor5.49mabovemeansealevel.Thiselevationwillincludetheactualwaveheightatthatlocationcarryingdebrisaswellasthewaveset-upandwindset-upasthewaterreachesthelocallandseainterface.Ithasbeensuggestedthatawaveset-upofapproximately4ftcanbeextractedfromavailabledata.Unfortunately,fromavailabledataitisnotcertainatanyonepointwhatwouldbethecontributionfromthewaves.Onereasonisthatwaveset-upishighly 76

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localized.Additionally,theresponseoftheseasurfacefromthewindeectsisalsospatiallyvariable.Thewindsurgeincreasesasthewaterbecomesshallower,additionallythewaterbeing'blown'andtrappedbytopographicfeaturessuchasbaysandcovescancauselocalizedincreasesinwindsurge.3.4.2ModelDescriptionThewaveheightmeasuredatNDBCBuoy42001peakedat8mwithaperiodofapproximately13sec.FortheOpaltests,asignicantwaveheightof6.1mor20ftisused,withaperiodof9.5sec.TheSWANmodelisrunwithoutwinds,forcedonlybytheoshorewaveconditions.Forthiscase,aproleisextractedfromtheareaaroundthepierwherethewaterlevelrecordingstationislocated.Threetestcasesareexamined.TheparametersforthesetestcasesareoutlinedinTable 3{4 .TheSWANmodelisrunwithoutwinds,forcedonlybytheoshorewaveconditions.Ithasbeenshownthatforthesesimplecasestheset-upcomputedbySWANiscomparabletothatcomputedbyADCIRCforcedwiththewaveforcingfromSWAN.Forthisreason,onlytheSWANmodelisrunforthistest.Thersttestisdesignedtobeperformedwithoutanyinitialwaterlevelconsiderations.Additionally,thewavedirectionalspectraareconnedtoanarrowbandedsectorwhichiscenteredabouttheonshoredirection.Forallthreecases,afullfrequencyspectrumisused,conningthedirectionalspreadingtoanarrowzoneontheorderof2degreesforthersttwotestcasesandusinganaccepteddefaultvalueforthethirdcase.Inthesecondandthirdtests,thewaterlevelinthedomainisincreasedby2.44m,anamountthatisinagreementwiththerecordedwaterlevelsatastationlocatedattheendofPensacolaBeachPier,inPensacolaBeach,Florida Mayeld 1995 ; Graumannetal. 1995 .3.4.3ResultsFigure 3{11 isaplotoftheresultsofthethreetestsforthesimpliedHurricaneOpalsimulation.Theset-upisplottedalongwiththebathymetricandwaveheightprolesfor 77

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thethreecases.Thevaluesfor=H0rangefrom8.8to10.6%.TheresultsaresummarizedinTable 3{5 .TheH0usedinthecomputationoftheratio=H0istheoshorewaveheight,H0=4.3m,14.14ft.Thisvalueisarguable,sincethebreakingthatoccursdowntoabout10ftor3mHSheightisindeeperwaters.Moreintensebreakingcommencesaroundthe10ftor3msignicantwaveheight.Withoutaclearlydened,nitesurfzone,itbecomeschallengingtointerprettheresults.Theratiocouldbecloserto20%dependingonourchoiceforH0.Ifwetakethewaveheightassociatedwiththestartoftheincreasingset-up,lowerlimitoftheset-down,thiswouldrepresentashorewarduxofmomentumfromthewaves.FromFigure 3{11 ,thiswaveheightisapproximatelyHS=15ftor4.57m,translatingtoanHRMSof10.6ftor3.233m,yieldingaratio=H0ofapproximately13to14%fortestcase2.3.Workingwiththeavailabletools,theresultsarereasonablywithintheacceptablerangefortheexpectedvalues.Itischallengingtovalidatethemodelperformancewithoutaccurateeldmeasurementsofwaterlevelsandwaveheightsintheshallow,nearshoreregionwherebreakingispervasive.3.5HurricaneKatrina3.5.1IntroductionHurricaneKatrinawasacatalystforhurricaneresearchintheUnitedStates.Thedesireforaccuratemodelsofthestorm'simpacthaspushedthemodelingcommunitytogainamorecompleteunderstandingofthephysicalprocessesandthewaytheseprocessesareportrayedinthenumericalmodels.Ofparticularinterestisthewavecontributionstothestormsurge.Thestormsurgereached27.8ft,themaximumhighwatermark,atPassChristian,MS Knabbetal. 2005 .Overa20milewideswathcenteredaroundSt.LouisBay,MS,thesurgewasabout24-28ft.Onegoalistodetermineifthedevelopedmethodofpredictingstormsurgeisappropriate,andifso,howmuchofthesurgecanbeattributedtothewavemomentum 78

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forces.Intheprevioussections,itwasshownhowthedevelopedmodelingsystemcomparestotheory,eldstudies,andhistoricdatasets.Inthissection,themodelscapabilitytopredictwaveset-upisevaluated.ThemaximumwaveheightduringHurricaneKatrinawasontheorderof20m,inthedeepwatersoftheGulfofMexico.Intheshallowerwatersofthecomputationaldomain,themaximumwaveheightswereapproximately12to15m.3.5.2ModelDescriptionThepreviouslydescribedcoupledsurgeandwavemodelingsystemisusedtosimulateHurricaneKatrina.ThesystemusestheSWANmodeltocomputeaninitialwaveeldthatisreadintoADCIRCalongwiththemeteorologicaldatatoforceaninitialwaterlevel.AfulldescriptionofthemodelingsystemisgiveninChapter 2 .ThisinitialwaterlevelisthenreadintoSWANinordertocomputeamoreaccuratewaveprediction.Fromthiscoupledsimulation,itispossibletoobtainandisolatethewaveforcingcomponents.ThecirculationmodelADCIRCisthenforcedwithonlythewaveforcingcomponentscomputedusingthewaterlevelsasaninput.Inseparatingoutthewaveforcing,themagnitudeofthewavecontributiontothestormsurgeduringHurricaneKatrinacanbebetterunderstood.Usingthelessonslearnedinthepreviouschapterswillhelpinterpretationoftheresults.3.5.3ResultsTheSWANmodeloutputsresultsinregionofinterest,wheretheresultsareusedasboundaryconditionsforthecoastalregion,whichhasresolutionof160m.Figure 3{12 isacontourplotofmaximumwaveheightsinthecoastaldomainnestedintheregiondomain.Theresultsshowthatthemaximumwaveheightintheregionisabout15m.ThesewaveshavethegreatestimpactontheMississippiRiverDelta,notontheMississippicoast. 79

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Figure 3{13 isaplotofthecoastalMississippidomain.Figure 3{13 a isavisualizationofthemaximumwaveheightsinthecoastaldomain,andFigure 3{13 b isavisualizationofthemaximumwavestressesandthedirectionofthosestressesinthesamedomain.FromtheplotsinFigure 3{13 ,threeregionsofsignicantwaveforcingcanbeidentiedthathaveanassociateddirectionwhichimpliesapossibleimpactontheMississippicoast.Therstregionoccursapproximately40kmoshoreofmainlandMississippi,15-20kmsouthofthebarrierislands,inapproximately30mwaterdepth.Herethewavesaretransformingfrom8to9msignicantwaveheightsdowntoanHSofabout5to6m.ThelargestwavestressesoccurjustGulfwardofthebarrierislands,beginningonly2-3kmoshoreofthebarrierislands.Thisregionisassociatedwiththe5to6mwavesbreakingastheyencountertheshallowwaterGulfwardofthebarrierislands.ThelastregionofbreakingoccursattheshorelineoftheMississippiCoast.Wavesthatpropogatethroughtheislandpassesandthosethataregeneratedlandwardofthebarrierislandswillreachthemainlandcoast,breakandimparttheirmomentumintothewateratthisnalstageofwavebreaking.Thesewavestendtobeinthe2to4mrange.TheeectofeachofthethreeregionsofforcingvisibleinFigure 3{13 canbeseenintheADCIRCresultsofthewaveset-up,Figure 3{14 .TheresultsfromthewaveandcirculationmodelsaresummarizedinTable 3{6 .Thevaluesfor=H0willvaryaccordingtothedistanceoshorethatischosenforwaveheightcomparisons.Thewavesbreaking40kmoshoreoftheMississippicoast,20kmsouthofthebarrierislands,arebreakingin30mwaterdepth.Accordingto RappandMcIvill 1990 ,aportionofthemomentumexchangedinthisregionwillbetransferredintoturbulenceandeddygeneration.Thatportionofthemomentumtransferredfromthosebreakingwaveswillnotreachthecoastline.Ratiosofset-uptowaveheightaresummarizedinTable 3{7 .Attwoofthelocationswherethelandandseameet,thebarrierislandsandtheMississippicoast,=H0iscomputedbasedontwowaveheights.Thesurfzoneinthissimulationisverywide,on 80

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theorderof10'sofkilometerswide.Furthermore,thesiteisveryshallow.TheaverageslopeoshoreofMississippiisapproximately1:2000.Theresultingvaluesfor=H0rangefrom6to14%.Thisrangeofvaluesiswithintheacceptablevaluesforthisratio.3.6ChapterSummaryInconclusion,allofthetestsindicatethatSWANisaccountingforthewavemomentumcorrectly.Thereisaregionattheland-seainterfaceinwaterdepthsofapproximately5cm,inwhichSWANisnotvalid.However,incomparingresultsindeeperwaters,greaterthan10cm,SWANisinagreementwiththeNielseneldstudyndings.Additionally,itwasshownthattheSWANmodelagreeswiththeoryandsimple1Dmodels.Themodelhasbeentestedforawidevarietyofsituations,and,foreachcasestudyreportedhere,therehavebeennoindicatorsthatthemodelhasfailedinreproducingreasonablyagreeableresults.ItwasshowninChapter 2 ,thattheSWANmodelaccuratelypredictsthewaveheightsinthecoastalregionsoshoreoftheMississippitestsite.ResultshereindicatethatifthewaveheightspredictedbySWANaretrusted,thenthereshouldbecondenceinthecalculationsoftheassociatedwaveforcingcomputedbythemodel.Combiningthesendings,theconclusionisdrawnthattheSWANmodelisrepresentingthewaveforcesinamannerwhichisreliableandwithinthelimitsofcurrentdataandtheory.Whencomparedtopublishedstudiesandmeasurableelddata,theresultsfromSWANagreewithintheuncertaintiesinthedata.Astechnologyprogresses,intheforeseeablefuture,therewillbeeldcapabilitiesandprogramstoquantifywaveset-upduringextremeevents,therebyformingabasisforevaluatingthenumericalmodels.Untilthenonemustkeeppressingonwiththebestavailabletechniques,andanopenmind.Themodelingsystemisnowreadytobeputtouseinhelpingtobetterunderstandtherolebathymetricuctuationsandbarrierislandsmayhaveindeterminingthesurgelevelsatthecoastline.Thefollowingchaptersexaminethesetwoquestionsindetail. 81

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Table3{1.Resultsfromwavesensitivitytests.Eachcasewasforcedwith50m/secwindsandwithoshorewaveboundaryconditionsof9mwaveheightand10secperiod. ModelSystemModelTypeSet-Up Dean1D0.367mSWANtrue1Dtrue1D0.366mSWAN/ADCIRCQuasi1D0.340mSWAN/ADCIRC2D,70km0.303mSWAN/ADCIRC2D,10km0.220m Table3{2.Nielsentestparameters TestWaveWaveTideNumberHeightPeriodLevelmsecm 1.11.08-0.51.21.08+0.51.31.016-0.51.41.012+0.51.52.012-0.51.62.012+0.5 82

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Table3{3.Nielsentestresults TestSet-upasaNumber%ofWaveHeight=H0% 1.121.21.221.11.3151.421.91.520.01.623.0 83

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Table3{4.Opaltestparameters TestWaveWaveTideDirectionalityCentralNumberHeightPeriodLevelWaveDirectionHSmsecm 2.16.19.50.0UnidirectionalOnshore2.26.19.5+2.44UnidirectionalOnshore2.36.19.5+2.44CircleOnshore Table3{5.Opaltestresults TestSet-upasaNumber%ofWaveHeight=H0% 2.18.82.210.92.39.9 Table3{6.SummaryofKatrinaresults LocationofDistanceSignicantRMSWaveBreakingWavesOshoreWaveHeightWaveHeightSet-Upkmmmm SouthofIslands4085.660.05BarrierIslands205-63.5-4.20.4-0.5MSBay1-22-30.62-1.00.3-0.4 84

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Table3{7.Setupasafunctionofwaveheight LocationDistance=H0Oshorekm% BarrierIslands207-9BarrierIslands2-39-14MSCoast406-6.5MSCoast209-12 85

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Figure3{1.Proleandplanviewofthebathymetryusedforthewaveforcingsensitivitytests.aProleisapprox.1:1700averageslope,withamax.depthof30mlocated50kmfromthemeanwaterlevel.bThedomainextends180kmalongshore.Theshorelineislocatedatx=50kmandtheunitsareinmeters. 86

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Figure3{2.Schematicofthe1Dmodeltests.Planviewandproleviewschematicofthe1Dmodeltestdomain.Thedomainis50kminthecrossshoreby180kminthealongshore. 87

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Figure3{3.Qualitativesketchofthe2Dmodeltests.Planviewschematicofthe2Dmodeltestdomain.Theactualdimensionsofthetestdomainis50kminthecrossshoreby180kminthealongshoreasseenin 3{1 .Thecentralhighlightedareadesignatestheregionofforcingcenteredinthealongshoreat90km,either70kmor10kmwidedependingonsimulation. 88

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Figure3{4.Contourplotsofthe3boundaryconditiontestresults:aallopen,ballclosed,andcsidesclosedoshoreopen.Theunitsaremetersandthex-axisrepresentsthecross-shoredirectionwhilethey-axisrepresentsthealongshoreextentofthetestdomain.Thestreamlinesindicatethedirectionofthecurrentscalculatedbythemodel.Forcaseb,withalloftheboundariesclosedthesystemwillreachasteadystateconditionwheretheowgoestozero.Thisisshownbytherelativelystationarystreamlines.Thisconditionproducesthehighestset-upinthemodelforthesetests.Casecmostcloselyrepresentstheexpectedresponseforuniformforcingonaninntelengthcoastline.Inallthreecases,theoshoreowandextremelevelofsetdownwouldnotbeseeninnature.Thisisaneectofthemannerbywhichthewavestressesarecomputedinthewavemodel. 89

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Figure3{5.WatersurfaceelevationproleforBCtestsatcenterlineofdomain.Theunitsareinmeters.Theinsetisablowupoftheresultsatthepeakofthesurge. 90

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Figure3{6.Watersurfacecontourwithcurrentstreamlinesforsteadywindtests.a1Dstationaryresultswellafterequilibriumt=60hr.b2Dstationaryrunresultswellafterequilibriumt=60hr.Theunitsareinmeters. 91

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Figure3{7.Watersurfacecontourwithcurrentstreamlinesfor10-kmand70-kmwide2Dsteadywindtests.a10-kmwidewindeldforcingSWANtogeneratethewaveforcingcomponents,andtheresultingresponsefromADCIRC.b70kmwideforcingeld,andtheresultingresponsefromADCIRC.Theunitsareinmeters. 92

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Figure3{8.WatersurfaceelevationproleforsteadywindtestscomparedtoSWANandDean1Dmodels.ThebathymetricproleisplottedalongwiththewaveheightsoftheSWAN1DandtheDeanmodelresults. 93

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Figure3{9.ResultsofTest1.1solidlinesandTest1.2brokenlines.Blacklinesshowbathymetries.BothHSandHRMSareplottedalongwiththeset-upproleacrossthedomain.Thedepthofthedomainistheonlydierencebetweenthesolidandbrokenlinedplots.Theunitsareinmeters. 94

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Figure3{10.ResultsofTest1.1solidlinesandTest1.3brokenlines.Blacklinesshowbathymetries.BothHSandHRMSareplottedalongwiththeset-upproleacrossthedomain.Theinitialwaveperiodistheonlydierencebetweenthesolidandbrokenlinedplots.Theunitsareinmeters. 95

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Figure3{11.ResultsfromthethreeOpalTests.Forthistest,theunitsareinfeet. 96

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Figure3{12.AnestedplotoftheregionandcoastalwaveheightpredictionsforHurricaneKatrina.Thewaveheightsareshowninmeters.TheLongitudesandLatitudesaregivenindegreeseastandnorthrespectively. 97

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Figure3{13.WaveheightandwaveforcepredictionsforHurricaneKatrina.aSignicantwaveheightsinmetersinthecoastaldomainfromtheSWANsimulationsforHurricaneKatrina.bMaximumvaluesofthewaveforcemagnitudeunitsofm2=s2anddirectioninthecoastaldomainduringtheKatrinasimulationinthemergedcoastaldomains.TheLongitudesandLatitudesaregivenindegreeseastandnorthrespectively. 98

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Figure3{14.Maximumwaveset-upelevationforHurricaneKatrinaaspredictedbymodelingsystem.TheLongitudesandLatitudesaregivenindegreeseastandnorthrespectively. 99

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CHAPTER4BATHYMETRICSENSITIVITYTESTS4.1IntroductionTheincreaseinthemeansealevelatthecoastinresponsetoadisturbancesuchasahurricaneisdependentonthebathymetricpropertiesborderingthecoast.Thedepthandwidthofthecontinentalshelfareimportantparametersforcalculatingwindset-upandwaveset-up.Thenearshorecoastalbathymetryisimportantincalculatingtheformationandevolutionofthewavesgeneratedbythewinds,andthuswhencalculatingtheforcesassociatedwiththemomentumuxasthewavesshoalandbreak.CurrentLIDARtechnologiesenablethescientisttomaptheseaooruptothe40-60mdepthcontourdependingontheclarityofthewaterandwavelengthofthelaser, IrishandLillycrop 1999 ; IrishandWhite 1998 .Unfortunately,obtainingandmaintainingcurrentandaccuratebathymetricdatacanbecostlyanddiculttomanage.Acommonquestionforwaveandsurgemodelingis,"howgoodarethebathymetricdata?"Atanygivenlocation,thebathymetricdataavailableandtheactualbathymetrymaynotagree100%.Whenmodelingstormsurge,researchersrelyonaspatiallylargedatasetthatmayhavegapsinportionsofthebathymetricdata.Itisalsopossiblethatthedataprovidedmaybeoutdated,orsimplyerroneous.Thebathymetriccontoursareinaconstantstateofchange,assedimentiscontinuouslytransportedbothinto,outof,andalongthelittoralzones.Duringstorms,signicantamountsofsedimentcanbedisplacedasthecoasterodestoastormprole.Theseamountsofsedimentcanbetransportedoshore.Thewindandwavegeneratedcurrentstransportthemobilizedsedimentalongshore.Duringthelowerenergyeventsthissedimentisslowlymovedbackonshore.Overwashisanotherprocessbywhichsedimentismoved.Theseexamplesillustratethecomplexityofsedimenttransportduringastormevent. 100

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Inthisevaluation,theextenttowhichvariationsinnearshorebathymetryaectthestormsurgeatthecoastisexamined.Ifarangeofuctuationsinthelocalbathymetrycanbeallowedwithoutsignicantlyadjustingtheresultsofthesurgepredictions,researcherscouldpotentiallysavemonthsofeldworkandmillionsofdollars.Inordertoanswerthisquestion,a1Didealizedbathymetryiscreated.ThisbathymetryisalteredbyaddingalocalGaussiandisturbanceatvariousdistancesfromtheshoreline.Awindisdirectedacrossthedomainandawaveeldiscalculated.Fromthis,asurgeproleisgeneratedacrossthedomain.Byalteringthesizeandlocationofthisdisturbanceandrecordingtheeectonthesurgelevelatthecoast,insightisgainedastotheeectsa3Ddisturbancemighthave. Maaetal. 2004 found,inastudyofoshoresandmining,thattheeectsonstormsurgeatthecoastwerenegligible.Thepresenceofasandminingpitonlyalteredthesurgeresultsby0.1cm.Tomoreaccuratelysimulaterealconditions,atwo-dimensionalcoupledmodelingsystemdevelopedbyWeaverandSlinnisused.Thiscoupled2Dmodelingsystemisimplementedtotestthehypothesisalongarealisticcoastline,theGulfCoastfromFloridatoLouisiana.ThewavemodelSWANandtheCirculationmodel,ADCIRC,arecoupledthroughaseriesofscriptsandpre-/post-processingprograms.Givenaninputbathymetricdomain,oraseriesofdomainsfornesting,andaninputmeteorologicalforcing,thesystemwillprocessthewaveandsurgepredictionsfromaninitialpredictiontoanalresult.4.2MethodologyBoth1Dand2Dtestsareperformedinordertogainamorecompleteunderstandingoftheprocesses.Basicanalyticalknowledgeofsurgeiscoupledwitha3rdgenerationwavemodelforthe1Dtests.Thesecondsetoftestsuses2Dmodelingprogramscoupledtogether.Bothsystemsarebrieydescribedbelow.4.2.11DTestsInordertotestthesensitivityofsurgetothequalityofbathymetricdata,a1Dmodelingsystemisemployedrst.Thisquasi-analyticmodelprovidesasolutionforthe 101

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surgeatthecoastusingEquation 4{1 .WherethewaveforcingcomponentiscalculatedusingtheSWANwavemodel Holthuijsen 2000 .@ @x=1 gh+[)]TJ/F23 11.955 Tf 10.494 8.088 Td[(@Sxx @x+n)]TJ/F24 7.97 Tf 6.586 0 Td[(hetaxx]{1Thevalueassignedton)]TJ/F24 7.97 Tf 6.587 0 Td[(hetaforthesetestsis1.25,wellwithintheacceptedrangeof1.15-1.30.Fourlargescalebathymetriesarecreated.Eachbathymetryisasimple,slopingbottom.Thevaluesfortheproleslopesare1 20;1 50;1 100;and1 200.Theseslopesrepresentawidevarietyofbathymetricpossibilities,includingextremes.Figure 4{1a showstheunperturbedbathymetries.Tohaveabaselinedataset,surgepredictionsaregeneratedontheslopedproles.Figure 4{1b showstheassociatedsurgeforeachofthefourslopingbathymetries.Asexpectedtheshallowestbathymetryallowsforthegreatestsurgetobegenerated,sincethewinddrivensurgeisthedominatingcomponent.Thelevelofsurgefollowsthebathymetrywiththeexceptionofthesteepestslope.Theforcesappliedoversteepestslopedbathymetry,1 20,generatethesecondhighestwaterlevelsattheshorelineduetothewaveforcing.Astheslopesbecomesteeper,thewaveset-upbecomeslarger.Figure 4{2 ,isaplotofthelast300mofthecross-shoresurgeproleforthecasesofwindandwaveforcingandthecasesonlyforcedbythewind.Thecontributiontothesurgefromthewaveset-uprangesapproximatelyfromanadditional1.3matthecoast,onthe1:20prole,toanadditional0.6matthecoast,onthe1:200prole.Foreachofthefourproles,asuiteofGaussiandisturbancesarecreated.Thedisturbancesaredenedbytheiramplitudes,theirwidths,andthedistanceoshoreofthepeakofthecurve.Theamplitude,A,isdenedasapercentofthewaterdepthatthechosenpeaklocation,andrangesfrom100%ofthelocalbathymetry,varyingin20%increments.Thewidthisdeterminedusingvevalues,100,500,1000,2500,and5000mforthestandarddeviation,st,inEquation 4{2 .Thelocationofthecenterofthedisturbancemeasuredindistanceoshore,x0,increasesin500mincrementsfrom500mupto5km.Thenalshapeofthedisturbanceiscalculatedusingthesethreeparameters 102

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inEquation 4{2 .disturbance=+Aexp)]TJ/F15 11.955 Tf 9.298 0 Td[(x)]TJ/F23 11.955 Tf 11.956 0 Td[(x02 st2{2Thereareftyprolesusedateachofthetenlocationsoshore,sothatvehundredprolesareusedforeachofthefourinitialslopeddomains,foratotaloftwothousandrealizations.Foreachbathymetricdomain,a50meterpersecondwindissimulated,blowingdirectlyonshore.Thewindstress,xx,iscalculatedusingVanDorn'sformulaforwindstress,Svd,takenfrom DeanandDalrymple 1991 asexpressedinEquation 4{3 .xx=SvdWS2where,Svd=1:210)]TJ/F22 7.97 Tf 6.587 0 Td[(6+2:2510)]TJ/F22 7.97 Tf 6.586 0 Td[(6)]TJ/F15 11.955 Tf 11.955 0 Td[(Wc=WS2and,Wc=5:6m=s {3 ThewindsarethenreadintoSWAN,anda1Dwaveeldiscomputed.Theresultingforcesarethenusedinthecomputationofthesurgealongthebathymetriccross-shoredomain.Thesuiteofdomainsusedforthecaseofthe1:100slopewiththecenterofthedisturbanceat500moshore,isshown,alongwitheachdomains'correspondingsurgelevels,inFigure 4{3 .Representativeplotsofthesuiteofperturbeddomainsfromthe1:50and1:100slopes,andthecorrespondingsurgeproleforeachbathymericprole,areshowninFigures 4{4 ,& 4{5 foroshoredistancesof500m,1000m,2000mand4000m.Eachgurehasfourplotsdieringinthecross-shorelocationoftheperturbationandwaterdepthatthethatlocationintheabsenceofthedisturbance. Figure 4{4a ,located500mfromtheshorelinein10mofwater. Figure 4{4b ,located1000mfromtheshorelinein20mofwater. Figure 4{4c ,located2000mfromtheshorelinein40mofwater. Figure 4{4d ,located4000mfromtheshorelinein80mofwater. Figure 4{5a ,located500mfromtheshorelinein5mofwater. Figure 4{5b ,located1000mfromtheshorelinein10mofwater. Figure 4{5c ,located2000mfromtheshorelinein20mofwater. Figure 4{5d ,located4000mfromtheshorelinein40mofwater. 103

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Foreachcaseitisseen,asexpected,whentheamplitudeofthedisturbanceispositiveandtheproleismadeshallower,thereisagreatersurgelevelpredictedatthecoast.Additionally,whentheperturbationiswide,havingalargestandarddeviation,thereisagreatersurgeresponseattheshoreline.4.2.22DTestsThewavemodelSWANandtheCirculationmodel,ADCIRC Luettichetal. 1992 ,arecoupledthroughaseriesofscriptsandpre-/post-processingprograms.ThesystemisdescribedmorethoroughlyinChapter 2 .Givenaninputbathymetricdomain,oraseriesofdomainsfornesting,andaninputmeteorologicalforcing,thesystemwillprocessthewaveandsurgepredictionsfromaninitialpredictiontoanalresult.Inordertotestthesensitivityofthemodelstothebathymetry,thebathymetricinputsarealtered.Atwo-dimensionalGaussianperturbation,Equation 4{4 ,withamplitudeof20%thebasebathymetricdepthatthecenteroftheperturbationwasappliedtoeachofthechosensites.disturbance=0:20exp)]TJ/F15 11.955 Tf 9.299 0 Td[(x)]TJ/F23 11.955 Tf 11.955 0 Td[(x02 stx2)]TJ/F15 11.955 Tf 13.151 8.088 Td[(y)]TJ/F23 11.955 Tf 11.956 0 Td[(y02 sty2{4Foralloftheperturbations,thealongshorewidthisdenedbystx=4000m,andthecross-shorewidthisdenedbysty=1500m.Wherestxandstyarethestandarddeviationsinthexandydirectionrespectively.Thismethodologyisemployedforthreedepthsatfourlocations,andtwohistorichurricanesareusedasforcingmechanismsforthoselocations.Sensitivitytobathymetricuctuationsistestedclosetothe15mand25mcontoursusingHurricaneIvanforcing,andclosetothe5mand15mcontourusingHurricaneKatrinaforcing.The5m,15mand25mcontourswereselectedbasedonresultsfromthe1Dtests.1Dtestsshowedthatwiththebathymetricanomalycentereddeeperthanthe30mcontour,thesurgeatthecoastwouldnotbesignicantlyaltered.Moreonthedepthdependencyisdiscussedbelow.Thespecicregionsthatarealtered 104

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wereselectedbasedontheproleandtherelevantcoastalcontoursmentionedabove.Thealteredregionsarewithintheinuenceofthestormchosentoforcethatdomain.OnelocationisacoastalregionjustsouthofPensacola,FloridaandeastoftheinlettoPensacolaBay.Thebathymetryatthislocationisvariednearthe25mcontour.ThesecondlocationisjusteastoftheentrancetoMobileBay.Atthislocation,thedepthnearthe15mcontourisaltered.TheselocationsareshowninFigure 4{6 .Figure 4{7 showsthealteredbathymetriccontoursforbothofthelocationsusedwiththeIvanforcing.Figures 4{7 a and 4{7 b showthearealocatedjusteastofMobileBayandFigures 4{7 c and 4{7 d representthearealocatedjusteastofPensacolaBay.Foreachofthesefourtests,HurricaneIvanisselectedtobetheforcingmechanism.Figure 4{8 showsthelocationsofthesiteswhereweperturbedthebottomandforcedthesurgewithHurricaneKatrinawindsandpressures.AlocationinMississippiBaynearthe5mcontourisselected,asisonejustoutsidethebarrierislandchainnearthe15mcontour.Figure 4{9 showsthealteredbathymetriccontoursforbothofthelocationsusedwiththeKatrinaforcing.Figures 4{9 a and 4{9 b arelocatedjustoshoreofGulfport,MSinsideMississippiSoundatabout5mdepthandFigures 4{9 c and 4{9 d arelocatedjustSouthofEastShipIslandatabout15mdepth.Themodiedbathymetryisusedforboththewaveandcirculationpredictions.Therststepoftheofthe2DcomputationalprocessdevelopsthedeepwaterwaveconditionsandtheinitialnearshorewavepredictionsusingSWAN,withnoaddedwaterlevels.TheresultantwaveforcingcomponentsareusedinconjunctionwiththemeteorologicalforcingdatatoruntheADCIRCmodel.Thisinitialwaterlevelisveryclosetotheactualwaterlevel,sincethebulkofthesurgeisgeneratedbythemeteorologicalforcingcomponents.Thesenon-stationarywaterlevelsarethenreadinbythewavemodelSWANateverytimestep.Thenewmoreaccuratewavepredictionswilltakeintoaccounttheincreasedwaterlevels,evenoodedconditions.Thenthenalwaterlevelpredictioniscomputedwiththecoupledwavedataandthemeteorologicaldata. 105

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4.3Results4.3.11DResultsSurgeatthecoastvariesslightlyasaconsequenceoflocalvariationinthebathymetry.TheplotsfromFigures 4{4 and 4{5 ,showtherawresultsforselectedcases.Fromthesewecanseethatforeachcasethebulkofthesimulationspredictthesurgelevelsattheshoretobeveryclosetothatoftheunperturbedslopingbottom.Wedivideeachresultbytheresultfromthecorrespondingunaltereddomain;avalueof1.0correspondstonodierencebetweenthecases.Figure 4{10 showsasampleoutputofthenormalizedmaximumwaterlevelatthecoastalboundaryforeachoftheamplitudesforabottomslopeof1:100,andadistanceoshoreof1500meters.Theresultingsurgewasfoundtovaryby10%foramplitudevariationsthatwerelessthan40%oftheinitialbathymetry.Fluctuationsupto+60%wouldgenerateadierenceatthecoastofatmost+20%.Figure 4{11 andFigure 4{12 showtherelativesurgevs.amplitudeforselectedcases.Therelativesurgevs.thewidthoftheperturbationwasalsoexamined.Thewiderdisturbancesgeneratedagreaterdeviationfromtheunperturbedresult.Inthelimitofaninnitelylargest,thatisifthedisturbancekeptwidening,anewshallower,ordeeper,shelfwouldbecreated.Asthecenteroftheperturbationismovedfartheroshore,therelativedepthincreasesdependingontheaveragebottomslope.Thereisalimitwhere,beyondthisdistance,theeectsofbathymetricuctuationsattheshorebeginstodiminish.Forallcases,thislimitcoincideswithadepthofabout30m.Seawardofthatlimit,theeectsofalteringthebathymetrybegintodiminish.Beyondthatlimititwouldnotbeproductivetoinvestincostlyhighdenitionbathymetrydatacollection.Thelikelihoodoftherelativesurgevaluesisexaminedbygroupingalltheresultstogetherforeachoftheamplitudes.Figure 4{13 showsthelikelihoodfor20%,40%,60%,80%amplitudeuctuations.Forperturbationswithamplitudes20%ofthe 106

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planarslopewaterdepthatthecenteroftheanomaly,Figure 4{13a ,allcasesarewithin5%oftheoriginalsurgevalueswithanRMSdierenceof1.87%.For40%amplitudeuctuations,Figure 4{13b ,nearlyallcasesarewithin10%oftheoriginalsurgevalueswithanRMSdierenceof3.86%.Fortheseamplitudes,eventheextremecasesdonotcreatesignicantdierencesbetweenthesurgevalueatthecoastfromtheunalteredcaseandtheperturbedcases.Astheperturbationsincrease,weseethatthecasesofextremewidthandproximitytotheshorelinestarttoproduceoutliersintheresults.For60%,Figure 4{13c ,allcasesarewithin20%oftheoriginalsurgevalueswithanRMSdierenceof6.79%.For80%,Figure 4{13d ,allcasesarewithin40%oftheoriginalsurgevalueswithanRMSdierenceof12.69%.Withanamplitudeof80%thelikelihoodofgreaterdierencesstartstobecomesignicant.Figure 4{14 showsacompositeplotofthe20%,40%,and60%results.Allresultsfromthese1200casesarewithin20%oftheunperturbedsurgevaluesfortherespectiveplainslopedproles.TheRMSDforthecombineddatais4.59%.Separatingthepositiveandnegativeperturbations,theRMSDisplottedversusamplitudeofprolechangeinFigure 4{15 .DependingonthemaximumacceptableRMSDallowed,arangeofbathymetricvariationscanbeallowedwithoutsignicantlychangingthesurgeresultsattheshoreline.4.3.22DResultsTheMEOWtheMaximumElevationofWatershowsthespatialdistributionofthestormsurge.Thepredictionsarecomparedbyplottingthelocationsofthestormsurgecontourlevels.Theresultsfromthe2Dtestsshowthatthesurgeatthecoastdoesnotvarymorethan+10%whenweperturbthebottomby20%a40%totalchange,andthechangeislocalized.PositiveandnegativeperturbationresultsareplottedontopofeachotherinFigure 4{16 andFigure 4{18 .Theareasdirectlyovertheoshorebathymetrythatwereeitherperturbedtobedeeperorshallowerhaveslightobservableshiftsinthelocationofthecontourlines.Thegreatesteectisseenfromperturbing 107

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nearthe15mcontour.Theareasdirectlyovertheoshorebathymetrythatwereeitherperturbedtobedeeperorshallowerhaveslightobservableshiftsinthelocationofthecontourlines.Thelinesrealignwitheachotherawayfromtheperturbationandclosertotheshorelineasseeninthe1Dresults.Figures 4{17 and 4{19 illustratethedierencesbetweentheresultsofthepositiveandnegativeperturbationsatthefourchosensitelocations.Thereisamaximumdierenceof2cmwherethereisasurgelevelofabout2m.Thisisconsistentwiththemaximumdierencesof10%seeninthe1Dstudy.4.4ChapterSummaryInconclusion,aslongasthelocalbathymetryuctuationiswithin60%ofthewaterdepthoftheaverageslopeoftheshelf,theRMSdierenceinthesurgeatthecoastwillbewithin4.59%.Furthermorethereisnobenetfromexpensiverepeatedsurveysbeyondthedepthatthedistanceofrelativeinuence.Testsindicatethatthiscutoisapproximately30m.ThiscutoiswellwithinthelimitofcurrentLIDARtechnologyevenwhenthewaterclarityisnotperfect.Shorewardofthisdepthofrelativeinuence,DRI,thegreatestdierenceswerefoundbetweenthecomputedsurgefortheperturbedandunperturbedproles.OutsidetheDRIthelocalchangesinbathymetryarenegligible,astherelativesurgeatthecoastgoestoone.The2Dresultsfollowedtheexpectationsderivedfromthe1Dteststudy.Fluctuationsof20%inthebathymetricproleresultedindierencesofnomorethan2.5%betweentheshallowvariationandthedeepvariation.Goodbathymetryisimportanttoaccuratelypredictingbothwavesandsurge.Perfectknowledgeofthelocalbathymetryisexpensivetoobtain,andisconstantlychanging.Aslongasthelargescaleoshorebathymetriccharacteristicssuchasshelfwidthandshelfslopeareknown,thenesmallscaledeviationscanvarylocallywithoutdisruptingthesurgeresultsbymorethana10%RMSD.Thenearshorebathymetrycanbeobtainedby 108

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varioustechniques,LIDARisoneexample,butneednotbecarriedoutpastthe30-mdepthcontourtoremainwithin10%RMSD. 109

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aOriginalbathymetricproles bSurfaceelevationresponseFigure4{1.1Dbathymetricprolesandcorrespondingsurge.aAcompositeplotofthe4bathymetricproles:20,1:50,1:100,1:200.bCorrespondingsurgeplottedforeachofthe4prolesforcingforsurgecalculationincludeswindandwaveeects. 110

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Figure4{2.Coastalsurgeprolescalculatedwithwindforcingaloneandwithwindandwaveforcing.Thegureplotsthelast300mofthecross-shoresurgeprolegeneratedbywaveandwindeects,andbywindeectsonly,oneachofthefourplanarslopedomains.Waveset-upcontributionstothesurgedecreaseastheslopebecomesmoregradual. 111

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Figure4{3.1Dbathymetricandsurgeprolesforslope1:100.Acompositeplotofallthebathymetricvariationsforthe1Dprolewithaslopeof1:100,andthecenteroftheperturbationlocatedat500metersoshore,plottedwiththecorrespondingsurgeproles.Unitsfordepthandetaaremeters.X-axisplotscross-shorelocationinmeters,withtheshorelineatx=0. 112

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aOrig.D=10m bOrig.D=20m cOrig.D=40m dOrig.D=80mFigure4{4.Bathymetricdisplacementsandsurgeprolesforinitialslope1:50.Centerofdisplacementlocatedat:a500min10mdepth,b1000min20mdepth,c2000min40mdepth,d4000min80mdepth.Unitsfordepthandetaaremeters.X-axisplotscross-shorelocationinmeters,withtheshorelineatx=0. 113

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aOrig.D=5m bOrig.D=10m cOrig.D=20m dOrig.D=40mFigure4{5.Bathymetricdisplacementsandsurgeprolesforinitialslope1:100.Centerofdisplacementlocatedat:a500min5mdepth,b1000min10mdepth,c2000min20mdepth,d4000min40mdepth.Unitsfordepthandetaaremeters.X-axisplotscross-shorelocationinmeters,withtheshorelineatx=0. 114

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Figure4{6.Theplotshowsthelocationsofthe20%Gaussianperturbationsthatwereappliednearthe15mcontourjusteastoftheentrancetoMobileBayand25mcontourleveljusteastoftheentrancetoPensacolaBay.TheinsetboxshowsthelocationofthestudyareawithrespecttotheGulfofMexico.Thehighlightedboxesindicatethelocationsofthetestsites. 115

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Figure4{7.Theplotshowstheresponseofthe20%Gaussianperturbationsthatwereappliednearthe15mand25mcontourlevelsothecoastofFloridaandAlabama.a@15mcontouralteredby)]TJ/F15 11.955 Tf 9.299 0 Td[(20%.b@15mcontouralteredby+20%.c@25mcontouralteredby)]TJ/F15 11.955 Tf 9.299 0 Td[(20%.d@25mcontouralteredby+20%.Thelabelsonthecontourlineshaveunitsofmeters. 116

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Figure4{8.Theplotshowsthelocationsofthe20%Gaussianperturbationsthatwereappliednearthe5mand15mcontourlevelsothecoastofMississippi.TheinsetboxshowsthelocationofthestudyareawithrespecttotheGulfofMexico.Thehighlightedboxesindicatethelocationsofthetestsites.Thedepthatthelocationclosesttotheshorelinevariesfrom3to5m.Thelocationfurtheroshorejustoutsidethebarrierislandisapproximately15mdeep. 117

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Figure4{9.Theplotshowstheresponseofthe20%Gaussianperturbationsthatwereappliednearthe5mand15mcontourlevelsothecoastofMississippi.a@5mcontouralteredby+20%.b@5mcontouralteredby)]TJ/F15 11.955 Tf 9.298 0 Td[(20%.c@15mcontouralteredby)]TJ/F15 11.955 Tf 9.298 0 Td[(20%.d@15mcontouralteredby+20%.Thelabelsonthecontourlineshaveunitsofmeters. 118

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Figure4{10. 0vsamplitudeonbottomslope1:100,withcenterofdisplacementlocatedat1500mfromtheshoreline.Thisplotisrepresentativeofthefollowingplotsofthistype 119

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aOrig.D=10m bOrig.D=20m cOrig.D=40m dOrig.D=80mFigure4{11. 0vsamplitudeonbottomslope1:50.Centerofdisplacementlocatedat:a500min10mdepth,b1000min20mdepth,c2000min40mdepth,d4000min80mdepth. 120

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aOrig.D=5m bOrig.D=10m cOrig.D=20m dOrig.D=40mFigure4{12. 0vsamplitudeonbottomslope1:100.Centerofdisplacementlocatedat:a500min5mdepth,b1000min10mdepth,c2000min20mdepth,d4000min40mdepth. 121

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a20%perturbationamplitude b40%perturbationamplitude c60%perturbationamplitude d80%perturbationamplitudeFigure4{13.Expectedvaluesof 0forgivenamplitudes.aA=20%andcorrespondingRMSD=1.87%,bA=40%andcorrespondingRMSD=3.86%,cA=60%andcorrespondingRMSD=6.79%,dA=80%andcorrespondingRMSD=12.67% 122

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Figure4{14.Combinedlikelihoodforall20,40and60%perturbations.Thecombineddatafromthe20,40and60%perturbations,plottedasahistogram.TheRMSDforall1200casesshownhereis4.59%. 123

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Figure4{15.RMSDvs.disturbanceamplitudeforallperturbations.RMSDbetweenthecalculatedsurgeonthealteredprolesandthesurgecalculatedontheoriginalslopingbottomsforall2000cases.TheRMSDisplottedwithrespecttotheamplitudeofthebathymetricperturbation.Fortheperturbationsthatmaketheproleshallowerthesurgeresponseismorepronouncedthanthosethatmaketheproledeeper. 124

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a bFigure4{16.SurgeresponsestoalteredbathymetriesalongtheAlabama/Floridacoast.ashowsthecomparisonjusteastoftheentrancetoMobileBayandbshowsthecomparisonatjusteastoftheentrancetoPensacolaBay.Bothplotsshowthesurgeresponseofa+20%and)]TJ/F15 11.955 Tf 9.298 0 Td[(20%variationinthebathymetriccontourstoHurricaneIvanforcing.Thelabelsonthecontourlineshaveunitsofmeters.Boththepositiveandnegativeperturbationresultsarecontouredtogether. 125

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a bFigure4{17.Dierenceinsurgeresponsestoalteredbathymetriesatthe15mand25mcontouralongtheAlabama/Floridacoast.aComparisonatthe15mcontourleveljusteastoftheentrancetoMobileBay.bComparisonatthe25mcontourleveljusteastoftheentrancetoPensacolaBay.Bothplotsshowthedierencesurgeresponseofa+20%and)]TJ/F15 11.955 Tf 9.299 0 Td[(20%variationinthebathymetriccontourstoHurricaneIvanforcing.Thelabelsonthecontourlineshaveunitsofmeters. 126

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a bFigure4{18.SurgeresponsestoalteredbathymetriesalongtheMississippicoast.aComparisonatthe15mcontourandbComparisonatthe5mcontour.Bothplotsshowthesurgeresponseofa+20%and)]TJ/F15 11.955 Tf 9.299 0 Td[(20%variationinthebathymetriccontourstoHurricaneKatrinaforcing.Boththepositiveandnegativeperturbationresultsarecontouredtogether.Thetwocontourlinesshowwindowofresultssuchperturbationswouldcreate.Thelabelsonthecontourlineshaveunitsofmeters. 127

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a bFigure4{19.DierenceplotofthesurgeonthealteredbathymetriesforMississippicoast.aShowsthecomparisonatthe15mcontour.bShowsthecomparisonatthe5mcontour.Bothplotsshowthedierencesinsurgeresponseofa+20%and)]TJ/F15 11.955 Tf 9.298 0 Td[(20%variationinthebathymetriccontourstoHurricaneKatrinaforcing.Thelabelsonthecontourlineshaveunitsofmeters. 128

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CHAPTER5IMPACTOFBARRIERISLANDSONCOASTALSTORMSURGE5.1IntroductionTheeectsthatlocalizedchangesinbathymetryhaveonthesurgelevelatthecoasthavebeenpreviouslyexplored.Ifthisideaistakentotheextremecase,theperturbationwouldhavetheamplitudeoftheentiredepthofthewater.Atthispoint,whenthedisplacementisequaltoorgreaterthanthewaterdepth,theperturbationactslikeabarrierisland.Barrierislandscanshieldacoastfromlargewavesandswell.Additionally,assumingthereisnopatharoundtheisland,anditisnotovertopped,thebarrierislandwillalsoblockthewinddrivensurge.Itisexpected,iftheislandhasahigherelevationthantheincreaseinwaterlevel,therewillbenoovertopping,resultinginaminimalincreaseinwaterlevelbehindtheisland.Itisofinteresttodeterminehowmuchshieldingbarrierislandsprovidegivenavarietyofwidths,amplitudes,anddistancesoshore.Mattersbecomecomplicatedintherealworld,asthemodelingsystems,unlikenature,areeither1Doracouplingof2Dwaveandcirculationmodels.Natureisnot1D,norisit2D;however,conclusionsmustbedrawnfromthenumericaltestcasesthatrelatethoseresultstowhatonewouldexpectfromnature.Innature,thewaterwillowaroundthebarrier,andllinbehindtheislandevenifthereisnoovertopping.Evenwithoutcompleteblockage,wehopetoobtainanestimateofthereductionfactorgainedbyhavingabarrierislandapproximately20kmfromthecoastline.5.21DBarrierIslandSimulationsAnextensionofthebathymetricsensitivitytestsincreasestheamplitudesoftheperturbationsbeyondthewaterline.Theperturbationsbecomegreaterthan100%oftheunperturbeddepthatthatlocation.Amplitudesaretestedrangingfrom80%upto190%ofthewaterdepth.Threedistancesfromtheshorelinearechosen,representativeofthebarrierislandsoshorefromtheMississippiCoast.Thelocationselectedforthecenteroftherstdisturbanceis10kmfromthecoast,seeFigure 5{1 .Thedistanceis 129

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thenincreased,anadditional10km,to20kmfromthecoast,Figure 5{2 .Andnally,thecenteroftheislandsismovedtoadistanceof30kmfromtheshoreline,Figure 5{3 .Theoriginalbottomslopeis1:2000;alsorepresentativeoftheslopefoundothecoastofMississippi.ThetestsareperformedinthesamemannerdescribedinChapter 4 .Themodelsarethesame,andtheformulationoftheshapeoftheperturbationsisalsoGaussian,asdescribedinSection 4.2.1 .Theresultsindicateastrongdependencenotonlyontheheightoftheisland,butalsoontheshape.Iftheislandiswideatthebase,meaningthestandarddeviationoftheGaussianusedtogeneratetheislandislarge,thentheislandwillbeovertopped.Theprimaryforceforovertoppingisthewinddrivensurge,duetotheveryshallowwaterscreatedbytheslopeoftheoshorefaceoftheisland.Intheextremecases,thesurgefromthewindsincreasestoovertoptheisland,andtheregionofwaterbehindtheislandisinundated.Thistrendisapparentineachcaseofoshoredistances,Figures 5{4 5{5 ,and 5{6 .Iftheislandisofsuchashapethatitisnotovertoppedandblocksthesurgecompletely,wendthatthesurgelevelsatthecoastarereducedfromthelevelsseenintheunperturbedcase.Forthesecases,whentheislandislocatedclosertothemainland,thesurgelevelsaredecreasedbyapproximately2.5m.Thereductioninsurgeleveldecreasesastheislandismovedfartherfromtheshorelineduetotheincreasedlocalizedfetch.Sincetheshapeoftheislandisdependentonthewaterdepth,theeectsaremorepronouncedfortheislandslocated30kmoshore,Figure 5{6 ,thanwhentheislandsareclosertotheshoreline,Figure 5{4 .Iftherelationshipbetweentheheightoftheislandand=0isexamined,Figure 5{7 ,theislandsclosertotheshorelineappearmorelikelytobeovertopped.However,keepinmindthatforthesecasesamplitudeisafunctionofthewaterdepthattheoshorelocationofthecenteroftheisland.Forthecasewheretheislandiscentered10kmfromtheshore,thedepthisontheorderof5m.Themaximumislandheighttestedatthislocationis4.5mabovemeansealevel.Incontrast,theisland 130

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located20kmoshorehassurpassedthe4.5mabovesealevelheightbythetimethe150%amplitudecaseisreached.Thisislandlocatedat20kmhasamaximumheightabovesealevelof9m.FrominspectingFigures 5{7 5{8 ,and 5{9 separately,itisclearthatforagivenamplitude,thesteepertheoshoreslopeoftheisland,thelesslikelyitistobeovertopped.Furthermore,iftheislandisovertopped,thesurgeatthecoastislowerforthesteeper,narrowerislandthanfortheislandwithawidegraduallyslopingshape.Thisresultisaconsequenceoftherelationshipofthewindsurgetothebottomslope.Thewider,moregraduallyslopingshapedislandshaveagreatereectofincreasingthesurgelevelatthecoastline.Thereisacleargap,seeninFigure 5{10 ,thatrepresentstheprotectionoeredbybarrierislandsiftheyarenotovertopped.Aminimumofa38%reductionwasoeredbybarrierislandsiftheyarenotovertopped.Themaximumprotectioncomputedfromthesetestsisa56%reductioninthesurgelevelsatthecoast.Thisprotectionpercentagewillbereducedasthenumberofdimensionsgoesup.In2D,therewillbeowaroundtheislandsandtheblowdownonthelandwardsideoftheislandwillbereduced.OncetheislandhasblockedthesurgecomingfromtheGulfwardside,thewidthoftheislandhasnosignicantaectonthereductioninsurgelevelsatthecoast.Thelandwardslopeisnotadeterminingvariablewhencalculatingtheprotectionoeredbybarrierislands.Table 5{1 summarizesthevaluesfortheslopeoftheseawardfaceoftheisland.Forslopessteeperthan1:100,theislandsprovidemoreprotectionagainstooding.Astheslopesapproach1:200,weseethatovertoppingbecomesmorelikely.Inordertobemorelikelytoreducethesurgelevelsatthecoast,theGulfwardslopeoftheislandshouldbesteeperthan1:100.5.3MississippiCoastBarrierIslandTestWithnewinsighttosurgebehaviorinthepresenceofbarrierislands,simulationofanhistoriceventisconsidered.Theresultsareobtainedusingtwodomains.Therstdomainistheactualbathymetryandtopography,withrenedresolutionalong 131

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theLouisianaandMississippicoast.Thealtereddomainisasimilardomain,exceptwithoutbarrierislandsseawardoftheeasternpartoftheStateofMississippi.ThedomainsusedinthesesimulationsareshowninFigure 5{11 ;nearlyidenticalexceptforthepresence,Figure 5{11a ,orabsence,Figure 5{11b ,ofbarrierislandsoshoreofeasternMississippi.ThisregionwaschosenduetothemagnitudeanddirectionofthewaveforcingduringHurricaneKatrina.Thewaveforcingcomponentsatthealteredlocationwereshorenormalandrelativelystrongcomparedtoelsewhereinthedomain.NotethatthelocationofmaximumstormsurgeforHurricaneKatrinawaswestofthetestlocation.Thesensitivityofcoastalstormsurgetothepresenceofbarrierislandsistestedbyimplementingatwo-dimensionalcoupledmodelingsystemdevelopedbyWeaverandSlinnanddescribedinChapter 2 .ThewavemodelSWANandtheCirculationmodel,ADCIRC,arecoupledthroughaseriesofscriptsandpre-/post-processingprograms.ThesystemisdescribedmorethoroughlyinChapter 2 ,andisthesamesystemusedinSection 4.2.2 tosimulatetheeectsofsmallscalebathymetricuctuationsonstormsurge.2Dsimulationresultsarecomparedtothe1D,planarslopewithGaussianisland,tests.Fourtransectsareextractedfromthe2Ddomaineachtransectpassingoverabarrierisland,Figure 5{12 .Asitturnsout,the1DstudydomainforthebarrierislandtestcasesmatchesremarkablywellwiththeactualbathymetryothecoastofMississippi.Thecross-shoreproleofthebathymetryforeachofthefourtransectsisplottedalongwiththe1DproleforGaussianislandslocatedat20kmoshore,withastof750mandamplitudesof120%and130%ofthewaterdepth,Figure 5{13a .Forcomparison,thesamefourtransectlocationsareplottedforthe2Dcasewithoutthebarrierislandsandthe1Dprole,Figure 5{13b .Itisimportanttonotethatwheretheactualbathymetryintersectsthecoastlinethereisasteepeningoftheprole.Atabout10kmfromthe1Dtestshoreline,theactualbathymetricproleforthetransectdataindicatesthepresenceofislandsandtheactualshoreline.Thisisnotreectedinthe1Dtestproles.Multiple 132

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perturbationswerenottestedinthe1Dstudy,norwere1Dtestsperformedforanyofthesefourtransects.Thesurgeatthecoastreachesthemaximumvaluesatapproximatelytime,t=2005/08/2915:45UTC.ThesurgeprolealongeachofthefourtransectsisplottedinFigure 5{14 alongwiththeresultsofthe1Dstudyforthetwocasesindicated,.The2Dmodelyieldssimilarresultstothe1Dmodelforthecaseofthebarrierislands,Figure 5{14a .Forthecaseofnobarrierislands,Figure 5{14b ,theactualproleforeachtransectdierstoomuchfromtheplanarslopetodrawanymeaningfulconclusions.Inthisdemonstration,threedierenttimesduringHurricaneKatrina'slandfallareexamined: 1. ood,whenthesurgelevelsareincreasing,t=2005/08/2911:45UTC 2. peak,maximumsurgeelevation,t=2005/08/2915:45UTC 3. ebb,whenthesurgelevelsaredecreasing,t=2005/08/2922:00UTCSnapshotsofthesimulatedsurgelevels,forthedomainwiththebarrierislandsincluded,ateachofthechosentimesareshowninFigures 5{15 5{16 ,and 5{17 .Attimet=2005/08/2911:45UTC,Figures 5{15 ,thereexistsa0.5mto1mdierenceinthewaterlevelsoneithersideofthebarrierislands.Waterlevelsintheregionofinterestarefrom1to3m.Theislandsareholdingbackthesurgeasthewaterisdisplacedtowardthecoast.ThedierencebetweenthesimulationwithislandsandtheonewithoutislandsFigure 5{18a isgreaterthan1mbehindtheislands.Thesurgelevelsatthecoastbehindtheislandsaresignicantlylowerthanthelevelsatthesamelocationsbutwithouttheislandstheretosheltertheshore.Figure 5{18b isaplotofthepercentdierencefromthecaseincludingbarrierislands.Thepercentdierenceisslightlymisleading,aspercentdierenceisdenedtobe-1ifthereiszerosurgeforthebarrierislandcaseandnon-zerosurgeforthecasewithoutthebarrierislandsincluded.And,wehavedenedthepercentdierencetobe1ifthereisnon-zerosurgeforthebarrierislandcaseandzerosurgeforthecasewithoutthebarrierislandsincluded. 133

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ThepeaksurgefromHurricaneKatrinaarrivedatapproximatelyt=2005/08/2915:45UTC,Figure 5{16 .Duetoislandovertoppingafewhoursearlier,thewaterlevelsinsideandoutsidethebarrierislandshaveequilibrated.Thesurgelevelsinthehighlightedportionofthedomainarefrom3to5.5m.Thereisnosignicantdierencebetweenthetwobarrierislandtestcasesatthistime,exceptaroundtheroadwaysandrailwaylines.Thesearerepresentedinthemodeldomainasweirs,andareseenasthedarklinesintheplot.Thereisapondingeectbehindtheweirs,thebarrierislandcasepredictsmorewaterbehindportionsoftwoweirsystemsthanthecasewithoutbarrierislands,whileinfrontofthefeaturesthesimulationwithoutthebarrierislandspredictshigherwaterlevels.Theresultsaredependentonthecomplextopography,asthesurgewatersoodinland,minorchangesintopographycandetermineifandatwhatratealowlyingregionisinundated.Asmallincreaseinsurgeheightmaybeenoughtooodovertopographicalfeaturesandintoalowlyingareathatotherwisewouldnotbeopentoooding.Thiswouldaccountfordierencesbehindthebarrierstructures.TheotherdierenceseeninFigure 5{19a iscausedbyalowerwaterlevelduetoDauphinIsland,ontheeasternportionofourplotteddomain.Figure 5{19b illustratesthepercentdierencewithrespecttothecasewiththebarrierislandsincluded.Asthewaterlevelsrecede,t=2005/08/2922:00UTC,Figure 5{17 ,thereisahigherwaterlevelinthebaybetweentheislandsandthemainland.Thewaterisnotallowedtoreturnasfreelyasitisinthecasewiththeislandsremoved.Bythistimethesurgelevelsinthehighlightedregionofthedomainhavereducedtoabout1to3m.Figure 5{20a illustratesthedierencesinwaterlevelsobtainedbyremovingthebarrierislands.Waterlevelsshorewardoftheislandsareapproximately50%greaterthantheywouldbeiftherewerenoislandspresent,Figure 5{20b .Thesurgewatersaretrappedbytheislandsandhaveanincreasedresidencetime. 134

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5.4ChapterSummaryFromthe1Dtests,thephysicalstructureoftheislandsplayaroleindeterminingwhetherornottheislandisovertopped.Notonlyistheheightoftheislandabovesealevelanimportantfactor,butalsotheslopeoftheseawardfaceoftheisland.Iftheislandhasasteepface,juttingabruptlyoutoftheseaoor,thereislesslikelihoodforovertoppingfromwindset-up.Agentlyrisingislandwithagradualslopingfacewillmorelikelybeovertopped.Thisresultisduetothedependenceofthewindset-uponthebottomslope.Anovertoppedislandhasthepotentialtoaidingeneratingahigherstormsurgethanwouldotherwisebecreated.Ontheotherhand,iftheislandisnotovertopped,thesurgeatthecoastwillbereducedfromthatcomputedwithnoislandinplace.Ifoneweretorecommendconstructinganislandtoserveascoastalprotection,theseawardfaceshouldbeassteepasphysicallypossibletoensurethatnoovertoppingwouldoccur.Ourndingsshowwhatwewouldintuitivelyexpect,thatthecloserthebarriertotheshorelinethelowerthesurgelevelsatthecoast.Thereasonforthisresultisrelativelysimple.Withthesurgeofwaterandthewavescompletelyblockedbytheisland,anyriseinsealevelatthecoastmustbelocallygenerated.Asthebarrierismovedclosertotheshore,theeectivefetchisreduced,thusreducingthewindsurgeandwavegenerationleewardoftheisland.Theresultsfromthe2Dsimulationsreinforcethe1Dpredictions.Weseeduringgrowingsurge,whiletheislandsareexposed,thewaterlevelsbehindtheislandsaresignicantlylowerthanthoseinfrontoftheislands.Thewaterlevelinthebayismorethan20%lowerthanitwouldbeiftheislandswerenotthere.SWANisaphase-averagedmodel,andtherefore,overtoppingeectsfromindividualwavesarenotincludedintheseresults.Oncetheislandshavebeenovertoppedbythesurge,thewaterlevelsquicklyequilibrate.Thereisadurationlimitingfactorthatisevidentfromexaminingthetimehistoryofthewaterelevations.Asthewaterrecedes,iftherearebarrierislandspresent, 135

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thewaterwillbetrappedinthebayandthewaterlevelwillnotdropasquicklyasitdoesinthecaseofnobarrierislands.Ascoastalprotectionfromstormsurge,thephysicalproleoftheislandsisanimportantfactor.Theislandshouldhaveasteepseawardfacingslope,andbetallenoughtowithstandinundationduringthegreaterpartofthestorm. 136

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Table5{1.Tablesoftheapproximatevalues,S,forslope=1:S,oftheseawardfaceoftheislandperturbation.The'o'indicatesiftheislandwasovertoppedduringthesimulation.Eachcolumncorrespondstotheheightabovemeansealevelofthepeakoftheisland.EachrowcorrespondstotheStandardDeviationoftheGaussianislandwidth. DistanceOshore=10km00km=3.11m Amplitude%andHeightAboveMeanSeaLevelmwidth120%130%140%150%160%170%180%190%st1.01.52.02.53.03.54.04.5 10049.21o45.5o42.3o39.5o37.0o34.933.031.3500209.0o194.4o181.8o170.7o160.9o152.2o144.3o137.3o750305.6o285.7o268.3o252.9o239.1o226.8o215.7o205.6o1000441.6o414.6o390.8o369.6o350.5o333.3o317.8o303.6o1500561.0o528.7o500.0o474.2o451.0o429.9o410.7o393.2o DistanceOshore=20km00km=2.10m Amplitude%andHeightAboveMeanSeaLevelmwidth120%130%140%150%160%170%180%190%st2.03.04.05.06.07.08.09.0 10016.7o15.414.313.312.511.811.110.5500112.0o103.7o96.690.384.880.075.771.8750153.8o142.8o133.3o125.0o117.6111.1105.3100.01000207.4o193.1o180.6o169.7o160.0o151.4o143.6136.61500285.7o266.7o250.0o235.3o222.2o210.5o200.0o190.5o DistanceOshore=30km00km=1.35m Amplitude%andHeightAboveMeanSeaLevelmwidth120%130%140%150%160%170%180%190%st3.04.56.07.59.010.512.013.5 10022.020.318.917.616.515.614.713.950083.377.372.167.563.459.956.753.9750123.7o114.8107.1100.494.589.284.580.31000181.8o169.0o157.9148.1139.5131.9125.0118.81500245.1o228.3o213.7o200.8o189.4o179.2170.1161.8 137

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Figure5{1.Bathymetricprolesusedforeachsimulationwiththecenteroftheperturbationlocatedat10kmoshore.Unitsareinmetersandthex-axisplotscross-shorelocation,withtheshorelineatx=0. 138

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Figure5{2.Bathymetricprolesusedforeachsimulationwiththecenteroftheperturbationlocatedat20kmoshore.Unitsareinmetersandthex-axisplotscross-shorelocation,withtheshorelineatx=0. 139

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Figure5{3.Bathymetricprolesusedforeachsimulationwiththecenteroftheperturbationlocatedat30kmoshore.Unitsareinmetersandthex-axisplotscross-shorelocation,withtheshorelineatx=0. 140

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Figure5{4.Surgeprolesforeachsimulationwiththecenteroftheperturbationlocatedat10kmoshore.Unitsareinmetersandthex-axisplotscross-shorelocation,withtheshorelineatx=0. 141

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Figure5{5.Surgeprolesforeachsimulationwiththecenteroftheperturbationlocatedat20kmoshore.Unitsareinmetersandthex-axisplotscross-shorelocation,withtheshorelineatx=0. 142

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Figure5{6.Surgeprolesforeachsimulationwiththecenteroftheperturbationlocatedat30kmoshore.Unitsareinmetersandthex-axisplotscross-shorelocation,withtheshorelineatx=0. 143

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Figure5{7. 0vsamplitude,withcenterofdisplacementlocatedat10kmfromtheshoreline. 144

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Figure5{8. 0vsamplitude,withcenterofdisplacementlocatedat20kmfromtheshoreline. 145

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Figure5{9. 0vsamplitude,withcenterofdisplacementlocatedat30kmfromtheshoreline. 146

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Figure5{10.Combinedhistogramofsurgelevellikelihoodforallbarrierislandcongurations. 0forall1Dbarrierislandtestsplottedasahistogram.Thegapseeninthehistogramrepresentstheminimumprotectiona38%reductionoeredbybarrierislandsfora1Dcaseiftheyarenotovertopped.Themaximumprotectioncomputedfromthesetestsisa56%reductioninthesurgelevelsatthecoast. 147

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a bFigure5{11.BathymetriccontoursofcoastalMississippidomainsforbarrierislandtests.awithbarrierislandsandbwithoutbarrierislands. 148

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Figure5{12.Cross-shoretransectsforcomparisonof2Dsimulationto1Dtests.Eachtransectpassesoverabarrierisland.Thetransectsaredenedas:Greenlocatedat88.7degWestLongitude,Bluelocatedat88.58WestLongitude,Redlocatedat88.47WestLongitude,andOrangelocatedat88.3WestLongitude. 149

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a bFigure5{13.Comparisonofcross-shoredepthcontoursbetweenthe4transectsfromthe2Dsimulationandthe1DplanarslopeGaussianislandtestcases.aBarrierislandcase:cross-shoredistancetocenterofisland=20km,islandamplitude=12%and13%ofthewaterdepthatthatcross-shorelocation,islandwidthstandarddeviation,st=750m.bNobarrierislandcase:wecomparethe2Dresultswiththeplanarslope. 150

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a bFigure5{14.Comparisonofcross-shoresurgeprolesbetweenthe4transectsfromthe2Dsimulationandthe1DplanarslopeGaussianislandtestcases.aBarrierislandcase:cross-shoredistancetocenterofisland=20km,islandamplitude=12%and13%ofthewaterdepthatthatcross-shorelocation,islandwidthstandarddeviation,st=750m.bNobarrierislandcase:wecomparethe2Dresultswiththeplanarslope. 151

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Figure5{15.SnapshotofsurgesimulationresultsforHurricaneKatrinaattime,t=2005/08/2911:45UTC.Duringtimeofgrowingwaterlevels. 152

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Figure5{16.SnapshotofsurgesimulationresultsforHurricaneKatrinaattime,t=2005/08/2915:45UTC.Approximatelytimeofpeaksurge. 153

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Figure5{17.SnapshotofsurgesimulationresultsforHurricaneKatrinaattime,t=2005/08/2922:00UTC.Duringtimeofrecedingwaterlevels. 154

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a bFigure5{18.Thedierencebetweenthebarrierislandcaseandthenobarrierislandcaseattime,t=2005/08/2911:45UTC.aBarrierislandresultsminustheresultsofthenobarrierislandcase.bDierencerepresentedasapercentageofthebarrierislandresults. 155

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a bFigure5{19.Thedierencebetweenthebarrierislandcaseandthenobarrierislandcaseattime,t=2005/08/2915:45UTC.aBarrierislandresultsminustheresultsofthenobarrierislandcase.bDierencerepresentedasapercentageofthebarrierislandresults. 156

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a bFigure5{20.Thedierencebetweenthebarrierislandcaseandthenobarrierislandcaseattime,t=2005/08/2922:00UTC.aBarrierislandresultsminustheresultsofthenobarrierislandcase.bDierencerepresentedasapercentageofthebarrierislandresults. 157

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CHAPTER6CONCLUSIONS6.1CoupledWave-SurgeSystemAcoupledwaveandstormsurgemodelusingSWANandADCIRChasbeensuccessfullydevelopedandextensivelytested.Thecoupledwave-surgemodelingsystemwassuccessfullytestedandimplementedintheFEMAMississippioodstudyandinthestudyofbathymetricperturbationsandbarrierislandeects.Bycouplingthewaveandcirculationmodel,waveandstormsurgepredictionsareimprovedbyproducingmorerealisticwaveconditionsinshallowwatersthathavebeenoodedbystormsurge.Incoastalwaters,wherewaveheightsaredepthlimited,itisimportanttocouplethecirculationmodelwiththewavemodel.Waveheightsattheoshorebuoysarematchedbythemodelresults.Unfortunately,therearenoreliablemeasurementsavailableforcomparisoninthecoastalregion.6.2SensitivityofWaveSet-UpAspartofthevalidationwork,severalvariablesthataectthewaveset-uparetested.Thereareanumberofvariablesthatcanaecttheratioofbreakingwaveheighttowaterlevel: proleslope waterlevel waveperiod widthofthedirectionalspectrumamountofdirectionalspreading 2-DeectssuchaswallsandfocusingLargerwavesbreakindeeperwater.Foramildslopingprole,thewaveswillbreakfarfromthecoast.Additionally,asthewavesshoalandthewavelengthsshorten,thewaveswillbecometoosteepandsteepnesslimitedbreakingwillalterthewavetoamorestableheight.Asteepprolewillallowlargewavestoreachclosertotheshorelinebeforetheybreak.Thecomplexityofwavebreakingismoreproperlyrepresentedinaslopedependentbreakingparameter. 158

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Whennumericallycalculatingthewaveheightsacrossaprole,thedierentmodelswillproduceslightlydierentresults.Theseresultsstemfromthecomplexityofthemodelandthelevelofincludedphysics.TheSWANwavemodelwaschosen,andvalidatedagainst1Dtheorybasedmodelsandagainstmorerealisticdatasetscollectedfrombuoydata.For2Dcases,theresultingwaveforcesareaectedbythewidthoftheforcingwinds,theboundariesofthedomain,andthedirectionalandfrequencydomainofthewavespectraitself.A1Dmodeldoesnottakethesecharacteristicsintoaccount.Thendingsindicatethatgivenasucientlylongdurationofsimilarpeakwaveforcing,thepeaksurgeresultsfromanon-stationarystormwillbethesameasthosefromastationarysimulation.However,anon-stationarysimulationwithequivalentpeakwindsbeingforcedforadurationsimilartothatofHurricaneKatrina,willproducewaveheightslowerthanthosecalculatedforastationaryrun.Thewaveset-upatthecoastisproportionaltothewaveheight,andnotinuencedbythetimeevolutionofthestorm,exceptinthatthewaveheightmaybeafunctionofthedurationofthestorm.6.3BathymetricSensitivityTheeectsofawiderangeofidealizedbathymetricgeometriesonthesurgelevelsweretested.Foreachcase,theresultswerecomparedtothosefortheunperturbedslopedprole.Oncetheheightoftheperturbationsbecomesclosetothedepthofwater,thedierencesinthesurgelevelsbecomessignicant.Deepenedbathymetryproducedverylittlevariationinthesurgeatthecoast,nomatterhowgreattheirdepth.Theperturbationwiththelargerwidths,st,producedagreaterresponsethantheirnarrowercounterparts.Additionally,thelargeramplitudeuctuationsproducedthemostpronounceddierencesinthesurgelevelsatthecoast.Variationsupto60%oftheaveragebottomslopewillproducelessthana5%RMSdierenceinthesurgelevelsatthecoast.Theseperturbationshavediminishingeectsbeyondthe30mdepthcontour.TheseresultsputtheregionofrequiredbathymetricaccuracywithinthelimitsofstandardLIDARsurveyingequipmentandtechniques. 159

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Theresultshighlighttheneedtobefamiliarwiththerequirementsoftheparticulardataneeds.Ifthecoastalwaveclimateisdesired,thenitwouldbeimportanttohavehighlyresolvedbathymetricdata.Ontheotherhand,iftheinterestisfocusedoncoastalsurgelevels,thenthebathymetricresolutionisnotasimportant.6.4BarrierIslandsBarrierislands,astheirnamesuggests,arethecoast'snaturaldefenseagainsttheforcesofthesea.Thestudies,focusedontotalsurge,showthatthereisarangeofresultsdependingonthegeometryoftheisland.Onesignicantvariableistheisland'sdistancefromthecoastline.Thefarthertheislandisfromthecoast,thegreaterthefetchfortheforcingwind,translatingtoahigherwaterlevelattheisland.Foreach1Dtest,a50m/secwindwasused,similartothewindsfromaHurricaneKatrinatypestorm.Inordertoeectivelyblockthetotalsurge,theheightoftheislandshouldbeincreasedasthedistancetotheshoreisdecreased.Resultsindicate,aminimumislandheightofapproximately3.5misrequiredtostopthesurgefromastormwithCategory3strengthhurricanewinds,50m/s,iftheslopewassteepenough.Theslopeoftheislandfacingdeepwaterisanimportantvariable,asistheheightoftheisland.Forcaseswheretheslopeislessthan1:100,theslopeofthefaceoftheforeshorewasgradualenoughthatthewindblewthewaterupthefaceandovertheisland.Inthesecases,thesurgeatthecoastwasgreaterthanthatcalculatedforaplanarslopeprole.Thesteepercasesactedasabarriertothewater,andthesurgeatthecoastwaslessthanwhatwascalculatedforaplanarslopeprole.Resultsindicatethataslopeof1:100isasafevalueforislandslopeforeachofthethreeoshoreislandlocations,aslongastheheightisatleast4mabovemeansealevel.Theheightcanbereducediftheislandislocatedindeeperwaters.Theresultsalsoreinforcethendingsofthewaveset-upsensitivitytests.ForHurricaneKatrina,theislandswereovertoppedformorethan3hours.Thisdurationwaslongenoughforthebaybetweentheislandsandthemainlandtoll.Forthatreason, 160

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thewaterlevelsatthecoastwerenotsignicantlydierentbetweenthecasewiththeislandsandthecasewithout,duringthetimeofmaximumsurge.Priortoandjustafterovertopping,thewaterlevelsinMississippiBay,andalongtheEasternMississippicoastline,arelowerwiththeislandsincludedthanwithouttheislands.Afterthesurgebeginstorecede,wenoticethatthereispondingbehindthebarrierislands.Thiseecttranslatestoalongerdurationofoodwaterswhenthereareislandspresent.6.5SummaryAstateoftheartmodelingsystemforcomputingstormsurgewasdevelopedandtested.Thesystemcouplesawavemodelwithacirculationmodeltoprovidemoreaccuratepredictionsofthechangeinwaterlevelsduetohurricanes.Usingthesystemnewunderstandingandinsightwasbroughttothetopicofcoastalsurge.Theimpactsofsmallscalebathymetricuctuationswerefoundtobenotsignicant.Theaccuracyofsurgecalculationsdependsontheinputwindeld.Theerrorbarsassociatedwiththeinputwindsandpressuresarethedominatingsourceoferror.Errorsattributedtosmallscale,upto60%,bathymetricuctuationsarelessthantheerrorsfromthewindsandpressures.Fluctuationsinwatersdeeperthan30mcontributeevenlesstotheerror,andtherefore,canbeignoredformostsurgecomputations.Asthebathymetricperturbationsbecomemorepronounced,>60%,theaectsonthesurgelevelsatthecoastbecomemoresignicant.Greaterthan100%,theperturbationsbecomeislands.Barrierislandswerefoundtobeabletoprotectthecoastfromstormsurgewiththeproperdimensions.IftheislandisnothighenoughortheslopeoftheGulfwardfaceistoogradual,thentheislandscouldincreasethesurgelevelsatthecoast.Therequiredheightoftheislanddependsontheoshorelocationoftheisland,andthestrengthofthestormfromwhichtheislandisbeingdesignedtoprotectthecoast.Themethodologydevelopedherecanbeusedtoselectandtestthedesigncharacteristicsofthebarrierislands.Table 5{1 providesastartingpointforselectingdesignlocations,elevationsandGulfwardfacingslopesforthebarrierisland. 161

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REFERENCES Anthes,R.A.,1982.TropicalCyclones,TheirEvolutionStructureandEects.AmericanMeterologicalSociety,Boston,Mass. 1.1 Bode,L.,Hardy,T.A.,1997.Progressandrecentdevelopmentsinstormsurgemodeling.JournalofHydraulicEngineering,315{331. 1 Booij,N.,Holthuijsen,L.H.,Ris,R.C.,1996.TheSWANwavemodelforshallowwater.In:Proc.25thInt.Conf.CoastalEngng.Vol.1.pp.668{676. 2.2 2.5 Bowen,A.J.,Inman,D.L.,Simmons,V.P.,1968.Wave'set-down'andset-up.JournalofGeophysicalResearch73,22569{22577. 1.1.2 3.2.3 3.3.1 3.3.2 CERC,1984.ShoreProtectionManual.U.S.ArmyCorpsofEngineers,WaterwaysExperimentStation,Vicksburg,Mississippi. 2.5.2 CERC,2003.CoastalEngineeringManual.U.S.ArmyCorpsofEngineers,WaterwaysExperimentStation,Vicksburg,Mississippi. 2.5.2 Dean,R.G.,Bender,C.J.,2006.Staticwavesetupwithemphasisondampingeectsbyvegetationandbottomfriction.CoastalEngineering53,149{156. 2.3 Dean,R.G.,Dalrymple,R.A.,1991.WaterWaveMechanicsforEngineersandScientists.WorldScienticPress,RiverEdge,NewJersey. 1.1.1 1.1.2 3.2.2 4.2.1 Donelan,M.A.,1998.Air-waterexchangeprocesses.CoastalandEstuarineStudies54,19{36. 1.1.1 Donelan,M.A.,Dobson,F.W.,Smith,S.D.,Anderson,R.J.,1993.Onthedependenceofseasurfaceroughnessonwavedevelopment.JournalofPhysicalOceanography23,2143{2149. 1.1.1 Donelan,M.A.,Haus,G.K.,Reul,N.,Plant,W.J.,Stassnie,M.,Graber,H.C.,Brown,O.B.,Saltzman,E.S.,2004.Onthelimitingaerodynamicroughnessoftheoceaninverystrongwinds.GeophysicalResearchLetters31,L18306. 1.1.1 Elsner,J.B.,Liu,K.-B.,Kocher,B.,2000.Spatialvariationsinmajoru.s.hurricaneactivity:Statisticsandaphysicalmechanism.JournalofClimate13,2293{2305. 1 Emanuel,K.A.,1991.Thetheoryofhurricanes.Annu.Rev.FluidMech.23,179{196. 1.1 Fairchild,J.C.,1958.Modelstudyofwaveset-upinducedbyhurricanewavesatnarragansettpier,rhodeisland.Bull.U.S.ArmyCorps.Engr.,BeachErosionBoard. 1.1.2 Geernaert,G.L.,Plant,W.J.Eds.,1990.BulkParameterizationsfortheWindStressandHeatFluxes.In:SurfaceWavesandFluxesI.KluwerAcademicPublishers,Netherlands,Ch.5,pp.91{172. 1.1.1 162

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Rapp,R.J.,McIvill,W.K.,1990.Laboratoymeasurementsofdeep-waterbreakingwaves.Phil.Trans.R.Soc.Lond.A331,735{800. 3.1 3.1 3.5.3 Ris,R.C.,Booij,N.,Holthuijsen,L.H.,1999a.Athird-generationwavemodelforcoastalregions,partI,modeldescriptionandvalidation.JournalofGeophysicalResearch104,7649{7666. 2.2 2.5 Ris,R.C.,Booij,N.,Holthuijsen,L.H.,1999b.Athird-generationwavemodelforcoastalregions,partII,verication.JournalofGeophysicalResearch104,7667{7681. 2.2 2.5 Ris,R.C.,Holthuijsen,L.H.,Booij,N.,1994.Aspectralmodelforwavesinthenearshorezone.In:Proc.24thInt.Conf.CoastalEngng.pp.67{68. 2.2 2.5 Saville,T.,1961.Experimentaldeterminationofwaveset-up.NationalHurricaneResearchProjectReport50,242{252. 1.1.2 Sheppard,D.M.,Slinn,D.N.,Hagen,S.,2007.Designhurricanestormsurgestudy,nalreport.Tech.rep.,FloridaDepartmentofTransportation,Tallahassee,Florida,USA. 2.1 2.4 Simpson,R.H.,Riehl,H.Eds.,1981.TheHurricaneandItsImpact.LouisianaStateUniveristyPress. 1 1.1 Stive,M.J.F.,Wind,H.G.,1982.Astudyofradiationstressandset-upinthenearshoreregion.CoastalEngineering6,1{25. 3.3.1 Stockdon,H.F.,Holman,R.A.,Howd,P.A.,Sallenger,A.H.,2006.Empiricalparameterizationofsetup,swashandrunup.CoastalEngineering53,573{588. 3.3.1 Weaver,R.J.,2004.Eectofwaveforcesonstormsurge.Master'sthesis,UniversityofFlorida. 3.1 Weaver,R.J.,Slinn,D.N.,2004.Eectofwaveforcingonstormsurge.In:Proc.29thInt.Conf.CoastalEngng.pp.1532{1538. 3.1 Weaver,R.J.,Slinn,D.N.,2006.Real-timeandprobabalisticforecastingsystemforwavesandsurgeintropicalcyclones.In:Proc.30thInt.Conf.CoastalEngng.Vol.2.pp.1342{1348. 3.1 Whitham,G.B.,1962.Mass,momentumandenergyuxinwaterwaves.JournalofFluidMechanics12,135{147. 1.1.2 Zijlema,M.,vanderWesthuysen,A.J.,2005.OnconvergencebehaviourandnumericalaccuracyinstationarySWANsimulationsofnearshorewindwavespectra.CoastalEngineering52,237{256. 2.2 2.5 165

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BIOGRAPHICALSKETCHBorninOklahomaduringtheyear1973,RobertWeaverwasraisedinNorthCarolina.Growingup,hisparentswouldtakehim,hisbrotherandsisteronallsortsoftravels.HerecallsvisitingmanyoftheNationalParksandcampingoutoftheir1971Dodgevan.Theseexperiencesculminatedinamonth-longtriparoundtheUnitedStateswhenhewas10yearsold,whichincludedhikingtheGrandCanyon.ThroughtheseexperiencesRobertgainedrespectfornatureandanabilitytocope,adaptandaccomplishwhateverheputhismindtonishing.RobertbecamecertiedinSCUBAdivingattheageof16whilecarvinghisownpaththroughhighschool.Hespenthis18thbirthdayinEngland,travelingoutsideNorthAmericaforthersttime.Theexperiencewaseye-opening.In1992,hefoundhiswaytocollegeattendingtheUniversityofNorthCarolinaatGreensboro.Asanundergrad,RobertservedaspresidentoftheSocietyofPhysicsStudentsSPS,andwasinductedintoandMEthephysicsandmathematicshonorsocieties.Duringthesummerof1997,Robertspent2weeksinHawaiiasaresearchdiverforthePacicWhaleFoundation,catalogingshandcorallifeat4reefsitesaroundMaui.HislastsemesteratUNC-Greensborowasspentabroad,studyingattheUniversityofStuttgartinGermanyandlearningtheGermanlanguageandculture.WhileinEurope,hewasabletotravelandexperiencedierentcultures,andbroadenhisworldview.RobertgraduatedfromUNC-GinDecember1999,cumlaude,withaBachelorofSciencedegreeinmathematicsandaminorinphysics.AftergraduationRobertspent2yearsinConnecticut,workingatalocalnewspaperandteachingatalocalhighschool.ThoughRobertenjoyedteaching,hefeltthathewasnotreachinghisfullpotential.Lookingforawaytobringtogetherhisloveoftheseaandhiseducationalbackground,Robertdecideditwastimetoreturntoschool.Itwasinthewinterof2000thatheappliedtograduateschoolattheUniversityofFloridaDepartmentofCoastalandOceanographicEngineering.HewasadmittedfortheFall2001semester. 166

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Inadditiontothepast7yearsofresearchandgraduatecoursework,RobertbecamecertiedasaNAUIDivemasterandwasclearedasaScienceDiverfortheUniversityofFlorida.InMayof2004RobertnishedhisMastersofScienceworkattheUniversityofFlorida.Histhesisfocusedonastudyofwaveforcingcontributionstohurricanestormsurge.HequaliedtobeaPh.D.candidatein2005,andbeganworkonhisdissertation.Thethesisanddissertationtopicsbecamemoreimportantasthehurricaneseasonsof2004and2005passed.ThedisasterousresultsofHurricaneKatrinarenewedfocusontheabilitiesofscientiststoforecastandpredictwinds,wavesandsurgelevelsfromhurricanes.Intheyearstofollow,Robertmadeuseofhisnewskills,takingpartinaFEMAprojecttoredrawthecoastaloodmapsfortheStateofMississippi.InMayof2008,RobertnishedhisPh.D.workattheUniversityofFlorida.InadditiontohisPh.D.work,Roberthasfoundedanon-protcorporationwhosemissionistopromoteenvironmentallysoundengineering,businessanddevelopmentpractices.Hisloveoftheocean,natureandsciencebroughtRoberttothispointinhislife,andwillcontinuetodrivethedecisionshemakes. 167