A Large Spectrum of Free Oscillations of the World Ocean Including the Full Ocean Loading and Self-attraction Effects

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.