A Large Spectrum of Free Oscillations of the World Ocean Including the Full Ocean Loading and Self-attraction Effects (Hamburg Studies on Maritime Affairs)

ThisbookdependsonadissertationpreparedattheDepartementofGeosciencesat theUniversityHamburg. ItwasacceptedbytheDepartementwiththegradesumma cumlaudein2008. IwouldliketothankmyacademicadvisorProf. Dr. WilfriedZahelforhisconstant supportandforthelongandconstructivediscussions. Further,IwouldliketothankProf. Dr. Jur .. genSundermann .. forintroducingmeto theInternationalMaxPlanckResearchSchool. TheInternationalMaxPlanckResearchSchoolforMaritimeAffairsandinparticu larProf. Dr. Dr. h. c. Jur .. genBasedowandhisco directorsarethankedforgivingme theopportunitytoperformthisstudyinHamburg. IacknowledgethecomputationalsupportoftheDKRZandNEC,especiallythe helpfulcommentsofKlausKetelsenandJens OlafBeismann. LastbutnotleastmanythankstomywifeJanaSillmannandmysonDariusfor givingmethetimeIneededforthisstudyandprovidingajoyfulandlovinghome. ThisworkhasbeenfundedbytheInternationalMaxPlanckResearchSchoolfor MaritimeAffairsattheUniversityHamburg. Hamburg,August2008 MalteMuller .. Contents Abstract…1 1 Introduction…3 2 TheoryandModel …7 2. 1 Theory …7 2. 1. 1 SecondaryForces:TheLoadingandSelf AttractionEffect . 8 2. 1. 2 TheEquationsofMotionandtheEquationofContinuity…11 2. 1. 3 EnergyBalance…1 4 2. 1. 4 ParameterizationoftheLSA AnAnalyticalApproach …16 2. 2 Model…18 2. 2. 1 TheImplicitlyRestartedArnoldiMethod…19 2. 2. 2 TheParallelizationwithMPI …21 2. 2. 3 ThePerformanceoftheModel…21 3 TheFreeOscillations…23 3. 1 GravitationalModes…23 3. 1. 1 The? value…24 3. 1. 2 TheIn?uenceoftheLSA …25 3. 1. 3 TheAntarcticKelvinWave…30 3. 1. 4 NewModes…30 3. 1. 5 TheSlowestModes …31 3. 2 VorticityModes…32 3. 2. 1 TopographicalVorticityModes…32 3. 2. 2 PlanetaryVorticityModes…34 4 SynthesisofForcedOscillations…39 4. 1 TidalDynamicsandtheIn?uenceofLSA…40 4. 1. 1 TheProcedureofTidalSynthesis…40 4. 1. 2 LSA effectonForcedOscillations…45 4. 1. 3 TheSynthesisoftheSemidiurnalandDiurnalTides…50 xi xii Contents 4. 2 IntegrationoftheSolutionsofaTidalModelwithAssimilationof Data…55 4. 2. 1 NewExpansionCoef?cients…55 4. 2. 2 NewFrequenciesandAdjointEigenfunctions …59 4. 2. 3 Results…61 4. 2. 4 Summary…70 4. 2. 5 Discussion…71 5 Conclusion …73 Figures…75 Tables…101 Appendix…105 ListofSymbols …109 References…113 Index …1 17 Abstract AnewsetofbarotropicfreeoscillationsoftheWorldOceaniscomputedwithex plicitconsiderationofdissipativetermsandthefulloceanloadingandself attraction effect(LSA). Thissetcontainsfreeoscillationsthatdidnotappearinthespectraof previousstudies. Furthermore,theexpansiontowardslongerperiods(165hours) yieldsnewglobalplanetarymodes. Altogether169freeoscillationsarecomputed withperiodslongerthan7. 7hours. Ofthese,71aregravitationalmodes,92areto pographicallycontrolledvorticitymodes,and6areplanetaryvorticitymodes. The in?uenceoftheLSAisinvestigatedforallthreekindsofmodeswithrespectto changesintheperiodsandinthespatialstructureoftheseasurfaceelevationand thehorizontalmasstransports. Inparticular,formodesinthesemi diurnalanddi urnalperiodrange,theparameterizationoftheLSAisanalyzed. Forthefreeoscillationsintheperiodrangefrom9to40hoursthecorresponding adjointsolutionsarecomputedandusedtosynthesizesemidiurnalanddiurnaltides ofseconddegree. Sincethesefreeoscillationsaredeterminedwithandwithoutcon siderationofthefullLSA effect,thisstudyallowsforadetailedanalysisoftheLSA onthedynamicsofoceantides,e. g. anphysicalexplanationisgivenfortheinduced phasedelaycomputedbyoceantidemodels. Further,thesynthesisgivesaspectral compositionofcertainwellknowntidalfeaturesandpairsoffreeoscillationsare identi?ed,diminishingtheircontributioneitheronaglobalorlocalscale. Further,semidiurnalanddiurnaltidalsolutionsofatidalmodelwithassimilation ofdataareintegratedintheprocedureofsynthesizingtides.