The Zonal Mean Structure of Clouds and Haze on Saturn from Cassini/CIRS Observations

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Title:
The Zonal Mean Structure of Clouds and Haze on Saturn from Cassini/CIRS Observations
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Lin, Hsin-Jung
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Doctorate ( Ph.D.)
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University of Florida
Degree Disciplines:
Physics
Committee Chair:
Matcheva, Katia Ivandva
Committee Members:
Fry, James N
Detweiler, Steven L
Tanner, David B
Ge, Jian

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atmosphere -- cassini -- cirs -- cloud -- haze -- retrieval -- saturn
Physics -- Dissertations, Academic -- UF
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Physics thesis, Ph.D.
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Abstract:
Clouds and haze can be used as a tracer for the dynamic activities and seasonalcirculation of Saturn’s atmosphere. The vertical distributions of clouds and haze canalso provide a strong constraint on the chemical and physical process of the planet.Furthermore, knowledge of the composition of Saturn’s atmosphere also contributes to information about the models of the Solar System formation as well as the evolutionof the gas giants. The vertical distribution of clouds and haze on Saturn has beenresearched from ground-based, space-based and spacecraft observations. In thiswork, we use the Cassini/CIRS mid-infrared MIRMAP data from 2005 to 2008 duringthe Prime Mission to study the latitudinal distribution of clouds and haze both in thesouthern and northern hemispheres. We develop a retrieval algorithm and provide erroranalysis for temperature and clouds/haze retrievals.
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In the series University of Florida Digital Collections.
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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, 2012.
Local:
Adviser: Matcheva, Katia Ivandva.
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by Hsin-Jung Lin.

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UFE0044960:00001


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THEZONALMEANSTRUCTUREOFCLOUDSANDHAZEONSATURNFROM CASSINI/CIRSOBSERVATIONS By HSIN-JUNGLIN ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2012

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c 2012Hsin-JungLin 2

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Tomyfamilyandfriends 3

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ACKNOWLEDGMENTS IwouldnothavenishedmyPh.D.programwithoutthehelpandsupportfrommy parents,advisors,committeemembers,professorsandmanyfriends. Iwouldliketoexpressmydeepestgratitudetomythesisadvisor,Dr.Katia Matcheva,forkindlyrecruitingmeintheendofmythirdgraduateyear;Iwouldlike tothankDr.Matchevaforhersupport,encouragementandrelentlesspatienceduring thepastthreeandhalfyears.Iwouldalsoliketothankmycommitteemembersinthe physicsdepartment,Dr.DavidTanner,Dr.JamesFryandDr.SteveDetweiler,aswell astheexternalcommitteememberintheastronomydepartment,Dr.JianGe,fortheir adviceonmydissertationandresearch.Myappreciationalsogoestomyprevious advisor,Dr.GuidoMueller,andcolleaguesinLIGOforteachingmetothinkcriticallyand puttheoryintopractice. IwouldalsoliketothankDr.JohnSabin,Dr.RobertDeSerio,andMr.Charles Parks,forassistingmetoovercomelanguagebarrierandhelpingmedealwithstudent issueswhileIwasateachingassistant.AspecialthanksisgiventoDr.JohnSabinfor hisbeingmysubstitutingcommitteememberduringmynalexamination. Thankstothestaffinthephysicsdepartment,especiallyPamMarlin,David Hansen,JanetGermany,MartinMeder,andKristinNicholaforhelpingmeprepare forallthenecessarypaperworkandsolvingITproblemssoIwouldbeabletofocuson myresearch.IwouldalsoliketoshowmygratitudetoPamMarlinforalwaysmaking surethatIgotpaidandregisteredfortheincomingsemesterontime. Iamgratefultomyparentsandmanyofmyfriendsfortheirsupportandforkeeping mesanethroughthesedifcultyears:myparentsforalwaysencouragingmetopursue mygoal;Tzu-YiTsaiforbeingmybestfriendof15yearsandhelpingmeovercome allthedifcultiesinmylife;Hsiu-ShanLiuforgoingtothefootballgameswithmefor twoseasons;TzuTing(Helen)Linforbeingaloyalrunningpartnerandalwaysbeing willingtohavedinnerwithme;TuckerRinggerasabuddyandabikingpartner;Jeffery 4

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HoskinsandRichardOttensforshowingmeAmericanculturesaswellasdraggingme awayfrommyworkforsomethingfunwheneverIneededabreak;KatherineDooley forsupportingmeremotelyfromLouisianaandfromGermany;Shih-FenYeh,Hsuan Hsu,RyanWong,JackChenandShizukoOkusaforcookingmealsformeandplaying Algricolawithme;WenyaWangforpassingtheinformationaboutDr.Matcheva'ssearch foraPh.D.studentsoIcouldbeintroducedtothewondersofplanetaryscience;many internetfriendswhowerealsoworkingontheirgraduatedegreesforaccompanyingme duringtheyearsofmyPh.D.studies. Intheendoftheacknowledgements,IwanttogivemyspecialthankstoTzuTing (Helen)LinandKatherineDooleyforspendingcountlesshourseditingmydissertation. 5

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 8 LISTOFFIGURES ..................................... 9 ABSTRACT ......................................... 12 CHAPTER 1INTRODUCTION ................................... 13 1.1Overview .................................... 13 1.2MotivationsfortheResearch ......................... 14 1.3OutlineoftheDissertation ........................... 16 2OBSERVATIONSANDDATAANALYSIS ...................... 18 2.1Cassini/CIRSOverview ............................ 18 2.2DataAnalysis .................................. 20 2.2.1MIRMAPObservations ......................... 20 2.2.2CoveragesandEmissionAngles ................... 21 2.2.3SensitivityStudyoftheData ...................... 22 2.2.4BrightnessTemperatureMapsat1392cm 1 ............. 25 2.2.4.1Globalbrightnesstemperaturesfrom2005to2007 .... 25 2.2.4.2Latitudinalvariationsofbrightnesstemperatures ..... 27 2.2.4.3Calibrationanddataquality ................. 29 3RETRIEVALALGORITHMANDNUMERICALMODEL .............. 69 3.1Introduction ................................... 69 3.2ForwardModel ................................. 69 3.3RetrievalMethod ................................ 72 3.4FunctionalDerivativeMatrixK ......................... 75 3.4.1 K ij fortheTemperatureRetrievals ................... 76 3.4.2 K ij fortheClouds/HazeRetrievals ................... 77 3.5ErrorAnalysis .................................. 79 ErrorAnalysisforCloud/HazesRetrievals .................. 80 4TEMPERATURERETRIEVAL ............................ 82 4.1Introduction ................................... 82 4.2ResultsandDiscussion ............................ 84 4.2.1StratosphericTemperature ....................... 84 4.2.2TroposphericTemperatureandTemperatureKnee ......... 85 6

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5CLOUDRETRIEVAL ................................. 103 5.1Introduction ................................... 103 5.2NumericalExperiment ............................. 104 5.3 2 MinimizationApproach ........................... 106 5.4CloudRetrievalResultsandDiscussion ................... 108 6SUMMARY ...................................... 119 REFERENCES ....................................... 122 BIOGRAPHICALSKETCH ................................ 126 7

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LISTOFTABLES Table page 1-1ObservedpropertiesofSaturn,JupiterandEarth. ................ 17 2-1SummaryoftheCIRSMIRMAPsusedinthiswork ................ 33 2-2Spectralrangeusedforthetemperatureandcloudinversions. ......... 35 2-3600cm 1 ....................................... 35 2-41304cm 1 ...................................... 35 2-51392cm 1 ...................................... 35 8

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LISTOFFIGURES Figure page 2-1CIRSFocalPlaneLocations. ............................ 36 2-2NoiseEquivalentSpectralRadianceforFP3andFP4at2.8cm 1 spectral resolutionduringJupiterencounterin2000. .................... 37 2-3MIRMAPcoveragein2005. ............................. 38 2-4MIRMAPcoveragein2006. ............................. 39 2-5MIRMAPcoverageofSaturn'snorthernhemispherein2007. .......... 40 2-6MIRMAPcoverageofSaturn'ssouthernhemisphereatlatitudesbetween7 S and80 Sin2007. .................................. 41 2-7MIRMAPcoveragein2009. ............................. 42 2-8MIRMAPcoveragein2010. ............................. 43 2-9EmissionanglesofMIRMAPobservations. .................... 44 2-10ReferenceatmosphericstructureofSaturn. .................... 45 2-11Synthesizedspectrumbasedonthereferenceatmosphericstructure. ..... 46 2-12Pressurelevelofunityopticaldepthinnadir-viewinggeometry. ......... 47 2-13Sensitivitystudytotheabundanceofphosphine. ................. 48 2-14Sensitivitystudytotheabundanceofammonia.(1000-1200cm 1 ) ...... 49 2-15Sensitivitystudytotheabundanceofammonia.(1350-1490cm 1 ) ...... 50 2-16Brightnesstemperaturemapat1392cm 1 from2005MIRMAPobservations inthesouthernhemisphere. ............................. 51 2-17Brightnesstemperaturemapat1392cm 1 from2007MIRMAPobservations inthesouthernhemisphere. ............................. 52 2-18Brightnesstemperaturemapat1392cm 1 from2006MIRMAPobservations inthenorthernhemisphere. ............................. 53 2-19Numberofradiancesat1392cm 1 averagedforbrightnesstemperaturecalculation in2005. ........................................ 54 2-20Numberofradiancesat1392cm 1 averagedforbrightnesstemperaturecalculation in2007. ........................................ 55 9

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2-21Numberofradiancesat1392cm 1 averagedforbrightnesstemperaturecalculation in2006. ........................................ 56 2-22Zonalmeanbrightnesstemperatureat1392cm 1 from2005to2007. ..... 57 2-23Zonalmeanbrightnesstemperatureat1392cm 1 ofthesouthernhemisphere in2005and2007. .................................. 58 2-24Zonalmeanbrightnesstemperatureat1392cm 1 in2005comparedwiththe modeledbrightnesstemperatureretrievedfromthereferenceatmosphere withoutcloudsandhazes. .............................. 59 2-25Discontinuityinthebrightnesstemperatureat1392cm 1 .(2005MIRMAP observations) ..................................... 60 2-26Discontinuityinthebrightnesstemperatureat1392cm 1 .(2007MIRMAP observations) ..................................... 61 2-27NumberofspectrausedinMIRMAPobservationsat60 Sin2005forcold calibration(DeepSpace). .............................. 62 2-28NumberofspectrausedinMIRMAPobservationsat60 Sin2005forwarm calibration(Shutterclosed). ............................. 63 2-29Variancesofthezonalmeanbrightnesstemperatureofthesouthernhemisphere in2005. ........................................ 64 2-30Variancesofthezonalmeanbrightnesstemperatureofthenorthernhemisphere in2006. ........................................ 65 2-31Variancesofthezonalmeanbrightnesstemperatureofthesouthernhemisphere in2007. ........................................ 66 2-32SpectraoftheMIRMAPobservations009A007and009B007inFP3spectral range. ......................................... 67 2-33SpectraoftheMIRMAPobservations009A007and009B007inFP4spectral range. ......................................... 68 3-1Flowchartoftheretrievalalgoritm. ......................... 81 4-1Initialtemperatureprolesfortemperatureretrievals. ............... 88 4-2ContributionfunctionforCH 4 at27 Sin2005. ................... 89 4-3ContributionfunctionforH 2 at27 Sin2005. .................... 90 4-4Temperatureproleat27 Sin2005afterthesecondstageoftemperature retrieval. ........................................ 91 10

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4-5Temperatureproleat77 Sin2005afterthesecondstageoftemperature retrieval. ........................................ 92 4-6Partialspectrum(1200-1400cm 1 )at27 Sin2005aftertherststageof temperatureretrieval. ................................ 93 4-7Partialspectrum(1200-1400cm 1 )at77 Sin2005aftertherststageof temperatureretrieval. ................................ 94 4-8Partialspectrum(590-750cm 1 )at27 Sin2005afterthesecondstageof temperatureretrieval. ................................ 95 4-9Partialspectrum(590-750cm 1 )at77 Sin2005afterthesecondstageof temperatureretrieval. ................................ 96 4-10Spectrumat27 Sin2005aftertemperatureretrieval. .............. 97 4-11Spectrumat77 Sin2005aftertemperatureretrieval. .............. 98 4-12Temperatureproleat27 Sin2005aftertherststageoftemperatureretrieval. 99 4-13Temperatureproleat77 Sin2005aftertherststageoftemperatureretrieval. 100 4-14Retrievedtemperatureofsouthernhemispherein2005. ............. 101 4-15Retrievedtropospherictemperaturekneein2005. ................ 102 5-1Cloudabsorptioncoefcientofthenumericalexperiment. ............ 111 5-2Opticalthicknessofthenumericalexperiment. .................. 112 5-3Resultsof 2 minimizationapproach. ........................ 113 5-4Cloudretrievalresults(a). .............................. 114 5-5Cloudretrievalresults(b). .............................. 115 5-6Cloudretrievalresults(c) .............................. 116 5-7Retrievedcloudwithuncertainties. ......................... 117 5-8Spectrumoftheretrievedcloud. .......................... 118 11

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy THEZONALMEANSTRUCTUREOFCLOUDSANDHAZEONSATURNFROM CASSINI/CIRSOBSERVATIONS By Hsin-JungLin December2012 Chair:KatiaI.Matcheva Major:Physics Cloudsandhazecanbeusedasatracerforthedynamicactivitiesandseasonal circulationofSaturn'satmosphere.Theverticaldistributionsofcloudsandhazecan alsoprovideastrongconstraintonthechemicalandphysicalprocessoftheplanet. Furthermore,knowledgeofthecompositionofSaturn'satmospherealsocontributes toinformationaboutthemodelsoftheSolarSystemformationaswellastheevolution ofthegasgiants.TheverticaldistributionofcloudsandhazeonSaturnhasbeen researchedfromground-based,space-basedandspacecraftobservations.Inthis work,weusetheCassini/CIRSmid-infraredMIRMAPdatafrom2005to2008during thePrimeMissiontostudythelatitudinaldistributionofcloudsandhazebothinthe southernandnorthernhemispheres.Wedeveloparetrievalalgorithmandprovideerror analysisfortemperatureandclouds/hazeretrievals. 12

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CHAPTER1 INTRODUCTION 1.1Overview Saturn,withitsmagnicentringsystemand62naturalsatellites,isthesecond largestplanetintheSolarSystem.Itismostlycomposedofmolecularhydrogen ( 96.3% 2.4% ),helium( 3.25% 2.4% )andmethane( 4500 2000 ppm);itsmeanbulk densityis687kg/m 3 ( Williams 2012 ). Saturnrotatesextremelyrapidlyatarateof10hoursand32minutesperrevolution ( AndersonandSchubert 2007 )with26.73 obliquitytotheorbit( Williams 2012 ).The rapidrateofrotationcausesSaturntobeanoblatespheroid,andthisobliquitysimilarto theEarth 1 drivesSaturn'sseasonalcycleintheatmosphere.Themeandistancefrom SaturntotheSunis9.5AU 2 ( Irwin 2009 ),theresultantsolarirradiance(ux)is14.99 W/m 2 ,andtheeffectivetemperature 3 is82.4K.TheeffectivetemperatureofSaturn issignicantlysmallerthantheobservedmeanbolometrictemperature 4 (95K).This indicatestheemittedthermalenergyofSaturnexceedstheabsorbedsolarenergy, whichcanbeexplainedbyinternalheatsources. 5 ThecompositionandverticalstructureoftheatmosphericpropertiesofSaturnare similartothoseonJupiter,theothergasgiantinthesolarsystem.Acomparisonofthe 1 Earthhas23.44 obliquity. 2 1AU =1.494 10 8 km. 3 Theeffectivetemperatureofaplanetistheblackbodytemperatureatwhichsolar radiationisbalancedbytheemittedradiationoftheplanet. 4 Thebolometrictemperatureisthemeanblackbodytemperatureatwhichtheplanet actuallyradiates. 5 Onepossiblesourceoftheinternalheatisduetotheinternaldifferentiationof helium( Irwin 2009 ). 13

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observedpropertiesofthetwogasgiants,SaturnandJupiter,withEartharelistedin Table 1-1 1.2MotivationsfortheResearch TheatmosphereofSaturnisobservedtobemeteorologicallyactiveandhighly convective.Cloudshavebeenusedastracersforthedynamicactivitiesofgasgiants. Thevariationsofchemicalcompoundsaswellastheopticalpropertiesofcloudsand hazeprovideinformationofSaturn'satmosphericdynamicprocessandseasonal circulation.Thepressurelevelofcloudandhazelayersissensitivetothemixing ratiosofthechemicalcompounds.Theverticaldistributionofcloudsandhazeinthe troposphereandinthestratospherewillprovideastrongconstraintonthephysicaland chemicalprocessintheatmosphereofSaturn. Inaddition,studyingSaturn'satmosphericstructuredoesnotonlyassistusto obtainknowledgeofgasgiants,butitwouldalsoimproveourcurrentunderstandingof meteorologicalphenomenaobservedonEarth.Furthermore,theunderstandingofthe compositionofSaturn'satmospherealsoprovidesconstraintsonmodelsoftheSolar Systemformation,whicharethefoundationsforexoplanetaryresearch. OurunderstandingofthecloudsandhazeonSaturnhasoriginatedmostlyfrom ground-basedobservationsandspace-basedobservations,suchastheHubbleSpace Telescope.Inaddition,informationretrievedfromspacecraftmissions,likeVoyager1, Voyager2,andtheCassini-Huygensmission,hasalsoofferedsignicantcontributions tothestudyofSaturn. EquilibriumCloudCondensationModel( Atreyaetal. 1999 ; Weidenschillingand Lewis 1973 )predictsthattherearethreelayersofcloudsintheatmosphereofSaturn. Thesethermochemical-predictedcloudlayersareanaqueous-ammoniacloudbased atthepressurelevelof20bar,anammoniumhydrosuldecloudatthepressurelevel ofabout6bar,andatopammoniaicecloudwithabaseataround2-barpressurelevel withthecondensiblevolatilestakenas5 solar( AtreyaandWong 2005 ). 14

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Abovethetopclouddecklocatedat1-2barpressurelevel,numerousstudies (e.g., KarkoschkaandTomasko 1992 ; 1993 ; 2005 ; Munozetal. 2004 ; Ortizetal. 1996 ; Stametal. 2001 ; Temmaetal. 2005 )illustratethatthereisastratospherichaze layerofparticleswithasmallradiusof r # 0.1 $ 0.2 m atthepressureof1-100 mbar,andthereisatropospherichazelayerwithparticlesizeof r % 0.5 m fromthe tropopause(near100mbar)downtothetopoftherstcondensationclouddeckat1.52.0barwithpossibleaerosol-freegapsinbetween. Stratospherichazeparticles(ethane,acetylene,andotherhydrocarbonproducts) presumablyoriginatesfromphotolysisprocessofmethane( Irwin 2009 ).Tropospheric hazeisexpectedtoformfromthecondensationoftheammoniagas;iftheatmospheric verticalmixingisefcient,cloudscanextendtotheupperboundaryoftheconvective region,whichisatabout500-600mbar( Bzardetal. 1984 ).However,nospectral signatureofsolidammoniahasbeenobservednear3 m ,wheresuchfeaturewouldbe expected( Kerolaetal. 1997 ). Kerolaetal. ( 1997 )indicatethatthetopmosttropospheric aerosolsarenotmadeofpureammoniaice,whichmayhaveprovidedtheexplanation fortheabsentspectralfeature.Comparedwiththestratospherichaze,thetropospheric hazeisconsideredtohavealargeropticaldepthanditspressurelevelexistsovera widerrange. Regardlessofthedifferentopticalpropertiesanddiverseformingmechanism ofbothhazelayers,boththetroposphericandstratospherichazelayersshow hemisphericalasymmetrybetweenthenorthernandsouthernhemispheresonSaturn. Tropospherichazeshowsstronghemisphericalasymmetryduetoseasonallyvarying photochemicalandcondensationprocessescombinedwithaerosolmicrophysical processes( Stametal. 2001 ),anditsconcentrationandthicknessvarylatitudinally.The stratospherichazealsohasseasonalasymmetryforhavingalargeropticaldepthinthe fallhemispherethaninthespringhemisphere( Munozetal. 2004 ). 15

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Differentdata-analysismodelsandretrievalmethodshavebeenusedtoextract informationabouttheverticaldistributionandcompositionofSaturn'satmosphere. However,thenumberofthecloudandhazelayers,theopticalpropertiesofthevertical proles,aswellasthepresenceoftheaerosol-freegapbetweenlayersarenotfully constrainedfromthepreviousobservations.Forthepurposeofprovidinganalternative analysiswithadifferentspectralrangeandretrievalmethod,weuseCIRSMIRMAP dataoftheCassini-Huygensmission( Flasaretal. 2004 )withamid-infraredspectral rangecenteredat1392cm 1 andaretrievalalgorithmusedin Matchevaetal. ( 2005 )to retrievetheverticalstructureofthecloudsandhazeonSaturn. 1.3OutlineoftheDissertation Thisworkisfocusedon27 latitudesinthesouthernhemispherein2005duringthe PrimeMission(2004-2008)oftheCassinimissionimmediatelyafterSaturn'ssouthern summersolstice.WewilldescribetheMIRMAPdatasetsandseveralparametersused inthisworkinChapter 2 .Thenumericalmodelsusedfortemperatureandcloudretrieval aredescribedinChapter 3 .Retrievedresultsforthetemperatureandthecloudsare discussedinChapter 4 andChapter 5 ,respectively. 16

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Table1-1. ObservedpropertiesofSaturn,JupiterandEarth. PropertySaturn Jupiter Earth Solardistance[AU] 9.5 5.2 1 Siderealorbitalperiod[yr] 29.5 11.9 1 Equatorialradius[km]60268 71492 6378 Meandensity[kg/m 3 ] 700 1330 5515 Equatorialsurfacegravityat1bar[m/s 2 ] 9.1 23.1 9.81 Siderealday10hr32min # 9hr55min23hr56min (SystemIII)(SystemIII) Obliquity26.73 3 23.5 Bolometrictemperature[K] 95 124 255 Equilibriumradiatingtemperature[K] 82 110 255 Numberofnaturalsatellites # 62 67 1 Planetaryringsystem Yes Yes No Datareference: Irwin ( 2009 ) & AndersonandSchubert ( 2007 ) Williams ( 2012 ) # NASAplanetaryfactsheetsforSaturn,Jupiter,andEarth. 17

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CHAPTER2 OBSERVATIONSANDDATAANALYSIS 2.1Cassini/CIRSOverview TheNASA-ESAjointCassini-HuygensorbiterlaunchedinOctober1997.Ithada shortybyofJupiterinDecember2000withaclosestapproachofapproximately136 Jupiterradii( Flasaretal. 2004 ),anditthenenteredtheSaturniansystemin2004.In July2004,theHuygensProbeseparatedfromtheCassiniOrbiteraftertheSaturnOrbit Insertion(SOI)andenteredtheatmosphereofTitantomakeinsitumeasurements duringanapproximately150minutedescentinJanuary2005.InJuly2004,theCassini Orbiterstartedtherstfour-yearPrimeMissiontouroftheexplorationofSaturn,its rings,satellites,andmagnetospherevia75orbitsaboutSaturnandcloseybysofits satellitesalongwithmanyradioandsolaroccultations.Aftercompletingasuccessful four-yearPrimeMissionin2008,atwo-yearextendedmissionnamedEquinoxMission (EM)andaseven-yearExtended-ExtendedMission(XXM)calledSolsticeMission(SM) wereinitiatedinJune2008andinSeptember2010separately.Withthetimespanof thesemissions(abouthalfoftheSaturnyear),weareabletoobservetheseasonal variationsintheSaturniansystem. TheCassiniOrbiterisathree-axisstabilizedspacecraftdesignedfor27diverse scienceinvestigations( Flasaretal. 2004 ).Itcarries12onboardinstrumentsincluding fouropticalremotesensinginstruments(CompositeInfraredSpectrometer,Imaging ScienceSubsystem,UltravioletImagingSystem,andVisibleandInfraredMapping Spectrometer),twomicrowaveremotesensinginstruments(CassiniRadarandRadio ScienceSubsystem),andinstrumentsforparticles,wavesandeldsstudies(Cassini PlasmaSpectrometer,CosmicDustAnalyzer,IonandNeutralMassSpectrometer, Magnetometer,MagnetosphericImagingInstrument,andRadioandPlasmaWave Science).TheCassiniMissioninvestigatesthephysical,chemicalaswellastemporal propertiesofSaturn,itsrings,icysatellites,magnetosphere,andthelargestmoonTitan. 18

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TheCompositeInfraredSpectrometer(CIRS)isaninfraredFourierTransform Spectrometer(FTS)amongoneofthe12instrumentsonboardtheCassiniOrbiter. ItsdesignisbasedontheVoyagerInfraredInterferometerSpectrometer(IRIS)with extendedfar-infraredcoverage,improvedsensitivityandspectralresolution.CIRS measuresthethermalemissioninwavenumberfrom10to1400cm 1 (1mmto7 m) withaselectablespectralresolutionfrom0.5to15.5cm 1 ( Flasaretal. 2004 ).The far-Infraredspectrumismeasuredwithapolarizationinterferometerwithafocalplane labeledFP1(5-695cm 1 )consistingoftwothermopiledetectorswitha3.9mradField ofView(FOV).Themid-infraredpartofthespectrumismeasuredwithaconventional MichelsoninterferometerwithtwofocalplanesFP3(570-1125cm 1 )andFP4(1025 -1495cm 1 ),bothofwhichiscomposedofa 1 10 arrayofHgCdTedetectors,with 0.273mradFOV.Figure 2-1 showstheCIRSeldofviewsprojectedonthesky. CIRShasbothnadir-viewingandlimb-viewingcapabilitytoperformdifferent observations.Thelimb-viewingcapabilityallowsCIRStoprovideverticalprolesof atmosphericvariableswithhighlyresolvedresolutionofonescaleheightorbetterin thestratosphereandthemesosphere.Inthisgeometry,thesensitivitytotheminor constituentsisenhancedduetothelongabsorberpathsviewedagainstacoldspace background.Theverticalresolutionofnadirsoundingisverylimited.However,the advantageisthatthenadir-viewinghasbetterhorizontalspaceresolutionwithlesscloud andaerosolinterferences. CIRS,withthevariablespacecraft-to-Saturnrange,isnotonlyabletoprovide verticalprolesofthetargetscienticobjectives,butitalsohasthecapacitytoconstruct globalmapsoftemperatureandchemicalcompositiontostudythesouthernand northernhemisphericasymmetryduetotheinclinationoftherotationalaxis.In addition,withabouthalfoftheSaturnyeartimespanofthecombinedPrimeMission 19

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andtheextendedmissions, 1 CIRScanalsoobservetheseasonalvariationofSaturn's atmosphericconstituents. 2.2DataAnalysis 2.2.1MIRMAPObservations InordertoretrievethecloudandhazeprolesintheatmosphereofSaturn, wechooseaseriesofSaturnmappingobservationsbyCIRSknownasMIRMAPs fromFebruary2005toJune2010.MIRMAPobservationusedinthisworkacquired thermalemissionfromSaturn'satmosphereatasinglelatitudewith2.8cm 1 spectral resolutionforroughlyoneSaturndaywhiletheplanetrotatedbeneaththespacecraft. Thespacecraftkeptadistanceof25-40Rs(radiusofSaturn)fromtheplanet,withthe longaxis(Zaxis)oftheCIRSarrayspointingtowardthepoleofSaturn( Cassini/CIRS 2012 ),givingaspatialresolutionof 1.1 to 1.7 Fletcheretal. ( 2009 )calculatedthe eldsofviews(FOVs)byscalingthefootprintoftheinstrumenttodegree-latitudesat theequator,andthesecalculationsshowedtheFOVsofMIRMAPobservationsfrom 2005to2008areabout0.75 -1.6 .Eachdatasetcontainsatleastathousandspectra calibratedwithabout50to100deepspacespectra.TheNoiseEquivalentSpectral Radiance(NESR)isthesignalforwhichthesignal-to-noiseratio(SNR)isunity( Flasar etal. 2004 ).TheNESRofthedatawith2.8cm 1 spectralresolutionforFP3andFP4 donotvarysignicantlywithfrequency(seeFig. 2-2 ),andwecanusetheaveraged NESRforerroranalysis.TheaveragedNESRis 7.811314 10 9 Wcm 2 sr 1 (cm 1 ) 1 forFP3andis 1.601580 10 9 Wcm 2 sr 1 (cm 1 ) 1 forFP4respectively.Asummaryof theMIRMAPobservationsfrom2005to2010islistedinTable 2-1 1 Cassini-HuygensmissionsstartedinJuly2004,shortlyafterSaturn'ssouthern summersolstice(October2002),untiltheendoftheCassiniSolsticeMissioninMay 2017,whichwillbeafewmonthspastSaturn'snorthernsummersolstice. 20

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2.2.2CoveragesandEmissionAngles MIRMAPdatacollectedduringthePrimeMissionweremeasuredwhilethe spacecraftwassittingatthenear-equatorialorbit,andtheemissionanglesforthe observationsvariedfrom0 toaround75 .Latitudinalcoverageforbothhemispheres werebuiltupoverthespanofafewmonths.Thesouthernhemispherecoverage wasobtainedin2005,2007and2009,whilethenorthernhemispherecoveragewas obtainedin2006,2007and2010.Fig. 2-3 to 2-8 showtheFP4MIRMAPcoverage from2005to2010. 2 Inthesegures,asetofvecloseparallellinesinthesamecolor representthecoverageofaindividualobservationsequence. DuringeachMIRMAPobservation,CIRSusesoneoffourpre-programmed observationmodescalledPAIRSwhenprocessingsignalscollectedfromeach mid-infraredfocalplane.Althoughthereare10detectorseachforFP3andFP4, CIRShasonlyvesolid-state'channels'forpost-detectionsignalprocessing( Nixon 2011 ).Hence,thereareexactlyvedatapointsineacharrayofthefocalplanethatcan beprocessedatatime.WhenPAIRSmodeisactivated 3 ,10detectorsofeachfocal planearedividedinto5pairs.Ineachpair,thesignalsofindividualdetectorswouldbe combinedbeforebeingprocessed.Therefore,aswecanseeinFig. 2-3 asanexample, thereare5datalinesperlatitudinalbandforasingleobservation(showninthesame color)whenthespacecraftisscanningovertheplanet. SaturnorbitsaroundtheSunevery29.5Earthyears,soatmosphericproperties willnotshowlargescaleseasonalvariationsintheMIRMAPobservationsfrom2005 to2007.Whencomparingthedatafrom2005,2006,and2007MIRMAPobservations withthosefrom2009and2010,thedatafrom2005to2007havebettersouthern andnorthernhemisphericalcoverages.Withthedatacoveragesof85 S-75 N 2 FP3coveragesandemissionanglesaresimilartothoseofFP4. 3 DatabaseIDCode1-5forFP3,and36-40forFP4 21

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inthesethreeyears,weareabletoobservethehemisphericalasymmetryofthe atmosphericpropertiesinthebeginningoftheCassiniPrimeMission(rightafter Saturn'ssouthernsummersolstice).However,consistencyoftheemissionangles withinthesamelatitudinalbandsisimportantifweneedtoco-addtheapodizedspectra fromdifferentMIRMAPobservations.Whenexaminingthelatitudinalvariationsofthe brightnesstemperaturesatparticularwavenumbers,wealsoneedtotakeemission anglevariationsintoconsideration.Fig. 2-9 showsthattheemissionanglesin2007for Saturn'snorthernhemispheredonotincreasesteadilyalonglatitudes,andtheyhave abouta20 discrepancycomparedwith2006MIRMAPdataatmid-latitudes.Therefore, whenanalyzingthehemisphericalasymmetryofbrightnesstemperature,datafromthe northernhemispherein2007willnotbeincluded. 2.2.3SensitivityStudyoftheData Toconstructtheglobaltemperaturemapsandtoretrievetheverticalclouds/haze prolesofSaturn'satmosphere,weneedtoselecttheappropriatespectralrangefrom thenadirmid-infraredmeasurements.WerstexaminedthesensitivityofSaturn's thermalemissiontoanumberofatmosphericparameters,includingmixingratiosand opticaldepthofhydrogen(H 2 ),methane(CH 4 ),ammonia(NH 3 ),phosphine(PH 3 ),and hydrocarbons,suchasC 2 H 2 andC 2 H 6 .Fig. 2-10 presentsthereferenceatmosphere structureofSaturn,showingthevolumemixingratiosofsomemainatmospheric constituents(excludingH 2 ,CH 4 ,andHe)varyingwithpressure.Otherconstituentssuch asH 2 O,GeH 4 ,CO,AsH 3 andCO 2 donotcontributemuchtothemid-infraredspectrum andwereneglectedfromthereferencemodel. Thereferencephosphineverticalproleisbasedonrotationallineobservationsby Ortonetal. ( 2000 ; 2001 ).ThePH 3 volumemixingratiois 7.4 10 6 at645mbarand dropslinearlyinlog-logscaletoavalueof 4.3 10 7 at150mbarduetophotolysis.The referenceverticaldistributionofammoniafollowedresultsfromVoyager2by Courtin etal. ( 1984 ).NH 3 saturatesatpressuresnear1.3bar,anditsabundancedecreases 22

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morerapidlythanPH 3 withaltitudeduetocondensationandphotolysisintheupper troposphere( Fouchetetal. 2009 )andalmostbecomesnegligibleattropopause.The verticaldistributionsofC 2 H 2 andC 2 H 6 areassumedbasedontheresearchby Moses andGreathouse ( 2005 )toincreasewithaltitude.ThevolumemixingratioofHe/H 2 isa xedvalueof0.135basedontheVoyager/IRISresultfrom200-600cm 1 by Conrath andGautier ( 2000 ).Theoreticalmodelspredictedthatmethanedoesnotcondenseand iswell-mixedthroughoutSaturn'satmosphere.Inourmodel,weassumedthevolume mixingratioofCH 4 /H 2 is 5.3 10 3 basedontheretrievedresultby Fletcheretal. ( 2009 ). Combiningthecompositionprolesmentionedabovewithanapriorivertical temperatureprolefromVoyager/IRISobservations( Courtinetal. 1984 ),wethen cangenerateasyntheticmid-infraredspectrumshowninFig. 2-11 .Thissynthesized spectrumshowsthespectralfeaturescontributedbydifferentatmosphericspecies.For example,C 2 H 2 ,C 2 H 6 andCH 4 havestrongemittingfeaturesat625-825cm 1 ,700-900 cm 1 and1150-1350cm 1 respectively,whilstPH 3 andNH 3 appearinabsorption relativetothebackgroundcontinuumbetween900-1200cm 1 VerticaltemperatureprolesofSaturncanberetrievedfromthe 4 methaneband at1200-1400cm 1 andS(1)andS(2)collision-inducedabsorption(CIA)lineswith thetranslationalcontinuumfrom590to700cm 1 .Themethaneemissiveregion providesinformationonlowerstratospherictemperaturesatfewmbarinnadir-viewing observations.Temperatureinformationintheuppertroposphereandthetropopauseat fewhundredmbarcouldbeextractedintheCIAcontinuumregion. TheEquilibriumcloudcondensationmodel(ECCM)predictedthat,onSaturn,the topammoniaicecloudbaseislocatedataround2barwiththecondensiblevolatiles being 5 solar( AtreyaandWong 2005 ).Thisisdeeperthanthetopcloudbasein Jupiterduetothecoldertemperature.Toobtaininformationontheaerosoldistribution abovethetopcloudlayer,weneedtondspectralregions,whereCIRScanprobeas 23

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deepaspossibleinnadir-viewingmodebasedonthereferenceatmosphericstructure ofSaturn.Wethenfurtherconstructaguretoinfertheunityopticaldepthatdifferent wavenumbersinnadir-viewinggeometry,whichprovidesinformationofdeepestprobing pressurelevelbasedontheknownatmosphericconstituents.AsshowninFig. 2-12 thedeepestprobingwavenumbersarepresentedintheregionsbetween1100and 1200cm 1 aswellasintheregionbetween1390and1450cm 1 .CIRScanpotentially samplearound900mbarat1392cm 1 and600mbarbetween1100-1200cm 1 ina clearatmosphereofSaturn,assumingtherearenoinuencesfromcloudsandhaze. Duetotheincreasingemissionanglesofhigherlatitudes,thealtitudesatthesame spectralregionsthatCIRScansamplewouldbecomehigher.Nevertheless,CIRSisstill abletoprobeasdeepas700mbarand500mbarwithinthesetwodeepprobingregions respectively. Theatmosphericopacityofthespectrumbetween1100and1200cm 1 ismostly providedbytheabsorptionofphosphineandammonia.TheabundanceofPH 3 and NH 3 variessignicantlyastheresultoftheglobalatmosphericcirculationandthe localatmosphericdynamics,andthereforetheabundanceofthesetwoconstituentsis notwellconstrained.Weperformedaseriesofsensitivityexperimentssimilartothe sensitivitystudiesin Matchevaetal. ( 2005 )toexaminehowthespectrumbetween 1100and1200cm 1 varieswiththemixingratiosofPH 3 andNH 3 .ThespectrainFP4 spectralrangeshowninFig. 2-13 ,Fig. 2-14 andFig. 2-15 presenthowthespectra varyifweweretosetthemixingratioonetenthortentimesthereferencePH 3 orNH 3 abundances.PH 3 emissionbetween1100and1200cm 1 issignicantlymodiedby thechangeoftheabundance.Thischangeoftheabundanceshasalmostnoeffect onthespectrumatwavenumberlargerthan1250cm 1 asshowninFig. 2-13 .The changeofNH 3 abundancewouldalsomodifythespectrumat1000-1200cm 1 and theregionlargerthan1460cm 1 asshowninFig. 2-14 and 2-15 .TheNH 3 spectrum modicationisnotassignicantasthatofPH 3 duetothesmallmixingratiointhe 24

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uppertroposphere,butitisstillsensitivetothemixingratiovariation.Therefore,the unconstrainedabundancesofbothconstituentsmakethedeepprobingregionbetween 1100and1200cm 1 hardtoextractusefulinformationforverticalcloudandhaze structures.Itisalsodifculttolookforanylatitudinalorglobalvariationsofthecloud properties. Thenarrowspectralwindowcenteredat1392cm 1 isfreeofinuenceofammonia andphosphine.Thespectrumnear1392cm 1 isonlyconstructedbytheCH 4 andH 2 gaseousabsorbers( Flasaretal. 2004 ),whosemixingratiosarewell-mixedthroughout Saturn'satmosphereandarewellstudied.Inourwork,wechooseaspectralwindow between1389and1395cm 1 forcloudsandhazeretrievals. Spectralregionsusedfortemperatureandcloud/hazeinversionsinthisworkalong withrelatedinformationarelistedinTable 2-2 2.2.4BrightnessTemperatureMapsat1392cm 1 2.2.4.1Globalbrightnesstemperaturesfrom2005to2007 BrightnesstemperaturemapsofSaturn'ssouthernhemispherefrom2005and2007 CIRSMIRMAPobservationsat1392cm 1 areshowninFig. 2-16 andFig. 2-17 ,and themapfrom2006observationsofthenorthernhemisphereisshowninFig. 2-18 .The thermalemissionofSaturn'satmosphereisnotexpectedtovarymuchseasonallyin oneyear,andaveragingthecalibrateddatawouldeliminatethetemporalatmospheric uctuations.Toobtaintheseyearlybrightnesstemperaturemaps,weco-addedand averagedthecalibratedintensitiesat1392cm 1 withinrectanglesof4 inlatitude and6 inlongitude,with2 latitudinaland1.5 longitudinaloverlappingbetweenthe adjacentrectangles.Whiteblocksinthesemapscorrespondtoregionsofdatawithlow signal-to-noiseratioorregionscontainingnodata.Thetemperatureisdecreasingwith altitudeinthetroposphere;alowbrightnesstemperatureat1392cm 1 indicatesthatthe emissionoriginatesatalowerpressurelevel(higheraltitude).Inthiswork,weassume 25

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thatthehorizontaltemperaturevariationsat1392cm 1 areverysmallnearthepressure levelatwhichCIRSissensitive. ThebeltandzonestructuresonSaturnarelessclearthanthoseonJupiter,sowe donotseeclearboundariesforzonesandbeltsintheglobalbrightnesstemperature mapsasexpected.However,thesebrightnesstemperaturemapsstillrevealseveral interestingproperties,whicharelistedbelow. Inthemapfrom2005(Fig. 2-16 ),thebrightnesstemperatureisslightlyincreasing towardstheequatorintheequatorialregionatlatitudeslessthan15 S.Thelowest brightnesstemperatureisobservedbetween15 Sand65 Sinthelowandmid-latitudes. Forlatitudeshigherthan65 S,thebrightnesstemperatureissignicantlyhigher comparedwiththatinthelowandmid-latituderegions;andthebrightnesstemperature inthepolarregionisabout10-15Khigherthanthatintheequator.Ifwetakethe viewinggeometryintoconsideration,thetropospherictemperaturewouldbedecreasing withtheelevatedemissionangletowardthepolewiththeemissionangleminimumat8 in2005(Fig. 2-9 ),whichmakestheunexpectedincreasingbrightnesstemperatureat higherlatitudesevenmorepronounced.Thepresenceofhighstratosphericabsorbers maybethereasonforthelargeamountoftemperatureincreaseathighlatitudes. Themapin2007(Fig. 2-17 )presentsbandsofhigherbrightnesstemperature centeredat10 S,30 S,55 S,and78 Swithabout5Khighercomparedtothe neighboringlowertemperatureregions.Thetemperatureisnotincreasingtowards thepolarregionforlatitudeshigherthan65 Sasseeninthemapof2005.With nodataatlatitudeshigherthan80 Sandnofurtherdataanalysis,wearenotable todetermineifthehighbrightnesstemperaturebandlocatedat78 Sindicatesan increasingtemperaturetrend,orifitissimplyalocalbandstructureathighlatitudes. Thesebandorbeltfeaturesshowninthe2007mapmaybecorrespondingtothezonal motionsintheuppertroposphere,ortheycouldsimplybearesultsoftheuctuations duetotheco-addedspectrafromdifferentobservations.Anothercausefortheobserved 26

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latitudinalvariationsmayberelatedtothecalibrationoftherawdata,anditwillbe discussedinsection 2.2.4.3 Throughacomparisonofthesouthernhemispheremapsfrom2005and2007(Fig. 2-16 andFig. 2-17 )tothenorthernhemispheremapfrom2006(Fig. 2-18 ),wecan observethatthebrightnesstemperaturesonaverageinthenorthernhemisphereare colderthanthoseinthesouthernhemisphere.Thisislikelyduetomoresolarinsolation onthesouthernhemisphereimmediatelyaftersouthernsummersolstice.Themapin 2006alsoshowsnoclearbandorbeltstructuresat1392cm 1 2.2.4.2Latitudinalvariationsofbrightnesstemperatures Toseethelatitudinalvariationofthezonalmeanbrightnesstemperatures(ZMTb) of1392cm 1 basedonobservationsfrom2005to2007,weaveragedallthemeasured radianceofthesameyearat1392cm 1 withina4 latitudinalbandcenteredateach latitude.Wethenconvertedthemeanradiancetoameanbrightnesstemperaturevia Planckfunction.Thenumberofentriesintheaveragedradianceat1392cm 1 foreach latitudeisshowninFig. 2-19 ,Fig. 2-20 andFig. 2-21 InFig. 2-22 ,wecanseethelargescaleasymmetryofbrightnesstemperaturein thenorthernandsouthernhemispheresduetotheseasonaleffect( CessandCaldwell 1979 ).TheZMTbinthenorthernhemisphereisabout5K,onaverage,colderthanthat inlowandmid-latitudesofthesouthernhemisphere.Forlatitudeshigherthan60 S inthesouthernhemisphere,thereisasignicantelevationtowardsthepolarregion in2005.In2007,ZMTbisalsoincreasinginasimilarmannerforlatitudeshigherthan 70 S.ThehighestZMTbinthesouthernhemisphereisabout10Kwarmerthanthe ZMTbattheaveragelevelinthenorthernhemisphere. IfwecomparetheZMTbin2005withthatin2006inFig. 2-22 ,itseemslikeinthe northernandsouthernhemispherestherearesmallscalevariationssymmetricwith respecttotheequator,whichmayberelatedtoSaturn'ssymmetriczonaljetsystemand theringshadoweffect.TheZMTbin2005andin2007shouldshowsimilarbehavior 27

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becausethetwo-yeartimespanisrelativelyshortwhencomparedwithafullSaturnyear (29.7Earthyears),andwillnotcausemuchchangeintheinsolationofthesouthern atmosphere.However,Fig. 2-23 showsthattheZMTbsarenotcorrelatedlatitudinallyin 2005and2007,whichshouldshowsimilarpatternsifthevariationsareduetothesame globalatmosphericcirculationonSaturn.Therefore,thesmallscalelatitudinalvariations mayhaveresultedfromsystematicmeasurementerrorsorcausedbynoise. InordertoanalyzetheverticaldistributionofthecloudsandhazeinSaturn's atmosphere,wefocusonthelatitudeswherethedatamayprovideclearinformation aboutaerosols.Werstranseveralquicktemperatureretrievals 4 fordifferentlatitudes andcomparedthecalculatedbrightnesstemperatureat1392cm 1 withtheobserved latitudinalZMTbin2005,asshowninFig. 2-24 Theexpectedzonalbrightnesstemperatures(bluelineinFig. 2-24 )arecalculated fromthespectrumgeneratedfromtheretrievedverticaltemperatureprolesatdifferent latitudes,assumingthattherearenocloudsorhazeintheatmosphere.At1392 cm 1 ,theemissioncomesfromapressureleveldeeperthan500mbars,wherethe temperaturevarieswithheightfollowingthedryadiabaticlapserate.Iftheemission angleofthemeasurementisconstant,thenthecalculatedtemperatureat1392cm 1 shouldbeahorizontalstraightline,whichcorrespondstothetemperatureatcertain heightinaclearatmosphere.Iftheemissionangleincreaseswithlatitude,theretrieved brightnesstemperaturedecreasestowardsthepolarregionasshowninFig. 2-24 becausetheemissioncomesfromhigheraltitudesinthetroposphere. Forlatitudeshigherthan70 S,theobservedZMTbisabout5-8Kwarmerthanthe expectedbrightnesstemperatureassumingnocloudsoratmosphericaerosols,while theobservedZMTbisabout10Kcolderthantheexpectedoneatlowandmid-latitudes. 4 Detailsoftheforwardmodelandtheretrievalalgorithmwillbediscussedinthe followingchapter. 28

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Lowerobservedtemperaturesthantheexpectedonecanbeexplainedbythepresence ofcloudsorhazeintheuppertroposphere;warmerthanexpectedtemperaturesare possiblyduetohazeinthelowerstratosphereatpressurelessthan100mbarwherethe temperatureishigher. Theobservedbrightnesstemperaturemapimplieddiversephysicspropertieswhich mayindicatedifferentverticalstructuresofcloudsandhazeforlowandmid-latitudes comparedtohigh-latitudes.Toverifythestatementsabove,weusetheMIRMAP observationsin2005toperformcloudinversionsat27 Sforlowandmid-latitudesas wellas77 Sforhighlatitudes.Theinversionmodelandtheretrievedresultswillbe discussedinthefollowingchapters. 2.2.4.3Calibrationanddataquality Calibrations .Afteracarefulexaminationofthebandandbeltstructuresshown intheglobalbrightnesstemperaturemapinFig. 2-16 andFig. 2-17 ,wecanseethat thereistemperaturediscontinuityatlatitudescenteredat5 S,19 S,43 Sand60 S inthe2005data,whilein2007,therearealsodiscontinuitiescenteredat13 S,20 S, 50 Sand60 S.ThoseregionsareboxedandshowninFig. 2-25 andFig. 2-26 .Aftera carefulinspectionoftheapodizedspectraandotherinformationcorrespondingtothe calibrations,wefoundthatthosebrightnesstemperaturediscontinuitiesmayberelated tothecalibrationoftheinstrument. ThearraydetectorsofFP3andFP4areoperatedatthetemperaturerangeof 75Kto80K,andthistemperatureisdifferentfromtheoperatingtemperatureofthe interferometer,whichisaround170K.Forcalibrationofmid-infraredspectra,CIRShas tousedeepspacereferenceinterferogramsataround2.7K(cold)andinternalshutter referenceinterferogramsat170K(warm)whentheshutterisclosed.Thecalibration methodalsorequriesFouriertransformsandtheuseofcomplexpowerspectra,which makesthecalibrationchallenging.Thedetailofthecalibrationalgorithmisbeyondthe 29

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scopeofthisdissertation.Interestedreadersmaywishtoreferto Flasaretal. ( 2004 ) and Carlson ( 2001 )forfurtherinformation. DuringtheMIRMAPobservations,FP3andFP4areviewingbothcoldandwarm targetsperiodically.Ifwetakebrightnesstemperaturecenteredat60 Sin2005 MIRMAPsasanexample,thelatitudinalcoveragebetween53 Sand66 Saremainly fromtwoMIRMAPobservations,004MIRMAP1392A039and004MIRMAP1392B039. Thecolderbrightnesstemperaturebetween150 and330 inlongitudecorresponds tothedifferentcoldcalibratingsequencesasshowninFig. 2-27 ,whilethewarm calibrationsequencesshowninFig. 2-28 appeartocontributelittletothediscontinuityin thebrightnesstemperaturebands.Otherbrightnesstemperaturediscontinuitiesarealso relatedtodiscontinuityofthecoldorwarmcalibrationduringobservations.However, wealsonoticedthatnotallthediscontinuitiesinthecalibrationwillcauseadiscontinuity inthebrightnesstemperaturezonalbands.Warmcalibrationsappeartohaveless inuenceonthesediscontinuitiescomparedtothecoldcalibrations. Toshowthevariancesofthebrightnesstemperatureforeachlatitude,werst averagedalltheradiancesinablockof4 inlatitudeand6 inlongitudewith1.5 longitudinaloverlapping.Fromthere,weconvertedthemeanradiancesintothe brightnesstemperatureat1392cm 1 usingthePlanckfunction.Thebrightness temperaturevarianceforeach4 latitudinalbandisthestandarddeviationbasedon theaveragedresultsof237blocksalongthesamelatitudinalband.Redverticallinesin Fig. 2-29 andFig. 2-31 showthevariancesofthezonalmeanbrightnesstemperaturein thesouthernhemispherein2005and2007;Fig. 2-30 showsthevariancesofthezonal meanbrightnesstemperatureinthenorthernhemispherein2006.In2005,thevariance isfrom2Kto10KasshowninFig. 2-29 ,andthevarianceissmallerforhigherzonal meanbrightnesstemperaturesathigherlatitudesinthesouthernhemisphere.In2006, asshowninFig. 2-30 ,thevariancesofthezonalmeanbrightnesstemperatureinthe northernhemispherearemuchlarger,anditmaybearesultofthelowsignal-to-noise 30

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ratiosfortheseobservations.In2007,Fig. 2-31 illustratesthatthevarianceisfrom 2.5Kto16.5K,andthevarianceissmallerforzonalmeanbrightnesstemperatures higherthan125K.Thelargevarianceintheseguresindicatesthatthesmallmeridional variationsofthezonalmeanbrightnesstemperaturemaybeaconsequenceofa systematicerrororduetothelowsignal-to-noiseratiosduringthemeasurements. DataQuality .HgCdTedetectorarraysofFP4areexpectedtohavethehighest performancenear80Kinthespectralrangeof7-9 m .However,asshowninthe gurein Flasaretal. ( 2004 ),theaveragebandpassspectralresponseofthese10 detectorsisunitycenteredaround1200cm 1 ,andtheresponsedecreasesto0.8near 1400cm 1 .Hence,thesignal-to-noiseratioforthesedetectorsofFP4aresmallernear 1392cm 1 TochecktheMIRMAPdataquality,weuseobservations009A007and009B007 in2005and050028and050B028in2007toseeifthezonalmeanbrightness temperaturesareconsistentforconsecutiveobservations.Intheexperiment,we chose27 Sasanexample.Foreachobservationlistedabove,weusedthreedifferent methodstocalculatethezonalmeanbrightnesstemperatureat600cm 1 ,1304cm 1 and1392cm 1 ,respectively. MethodAistocalculatetheaveragedbrightnesstemperaturebyusingallthe radianceswithina4 latitudinalbincenteredat27 S,whichisthestandardprocedure forcalculatingthezonalmeanbrightnesstemperatureinourwork.MethodBisto calculatethemeanintensitiesinsmallrectanglescenteredat27 Sof4 inlatitudeand 6 inlongitudewith1 longitudinaloverlapping.Andtheaveragebrightnesstemperature isthencalculatedbasedonthepositiveaveragedintensitiesinthoserectangles. MethodCissimilartomethodB,butinsteadofusing4 x6 rectangles,weused4 x4 squaresforthemeanbrightnesstemperature.TheexperimentresultsarelistedinTable 2-3 ,Table 2-4 andTable 2-5 31

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Forthesethreedifferentwavenumbers,ifthemeasurementhadgoodlongitudinal coverage,thenmethodA,BandCwillprovidesimilaraveragedbrightnesstemperatures. Themeasurementsusedforcalculationcoveredapproximately360 inlongitude,andfor eachobservation,themeasurementlastforaboutoneSaturnday.Ideally,theaveraged zonalradiancesatthesamelatitudebandshouldnotvarydramaticallyforconsecutive measurements.Forthewavenumberat600cm 1 and1304cm 1 ,thedifferencesofthe averagedbrightnesstemperaturescenteredat27 Softwoconsecutiveobservations arelessthan1Kin2005andlessthan2.5Kin2007.However,at1392cm 1 ,which isthespectralregionforcloudretrievals,thedifferencesbetweentheconsecutive observationsareabout5Kinboth2005and2007. Fig. 2-32 andFig. 2-33 showthespectraat27 Softhe2005observations009A007 (redline)and009B007(greenline)intheFP3andFP4spectralrange,respectively.The generalshapeofthespectrainFP3andinFP4aresimilarforbothobservations.Those spectramatchespeciallywellinthemethaneemissionregionbetween1150and1350 cm 1 .However,asthesignal-to-noiseratiodecreasestowardsthespectraledgeofeach focalplane,thespectraoftheseconsecutiveobservationsarenotconsistent. Basedontheresultsshownabove,MIRMAPdataat27 Swillhavesmallererror barsfortemperatureretrievalsifonlydataat590-700cm 1 and1250-1350cm 1 are used.However,theuncertaintiesforinversionsofcloudsandhazewillbelargeifdataat thewavenumberlargerthan1350cm 1 areused. 32

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Table2-1. SummaryoftheCIRSMIRMAPsusedinthiswork ObservationsSequenceYearDurationLatitudeStartSCETEndSCETRange(km) Covered 003SA MIRMAPA001S08200519hr30m40 S-60 S110904246011091126602204100 003SA MIRMAPA003S08200511hr30 S-50 S110915856011091981602424737 003SA MIRMAPB003S08200511hr30 S-50 S110923416011092737602528366 004SA MIRMAPA039S09200511hr50 S-70 S110967600011097156002590282 004SA MIRMAPB039S09200511hr50 S-70 S110975160011097912002509606 006SA MIRMAPA004S10200510hr50m71 -85 S111423324011142722402438399 007SA MIRMAPB004S10200511hr71 -85 S111431100011143506002449009 008SA MIRMAPA006S11200511hr40m60 S-80 S111707874011171207402090136 008SA MIRMAPB006S11200510hr17m60 S-80 S111716634011172033602248117 009SA MIRMAPA007S11200510hr25m26 -33 S111862884011186663402042730 009SA MIRMAPB007S11200511hr26 -33 S111870384011187434402192441 010SA MIRMAPA008S12200511hr10 S-30 S112027614011203157402191238 010SA MIRMAPB008S1220058hr30m10 S-30 S112035120011203818002306071 011SA MIRMAPA009S12200511hr0 -20 S112165200011216916001682126 011SA MIRMAPB009S12200511hr0 -20 S112173612011217757201933113 012SA MIRMAPA002S13200512hr17m0 S-10 S112346382011235034202237457 012SA MIRMAPB002S1320059hr42m0 S-10 S112354092011235805202341344 023SA MIRMAPA010S19200611hr5 N-15 N114560280011456424003025640 023SA MIRMAPB010S20200611hr45m5 N-15 N114568920011457315002810285 023SA MIRMAP011S20200620hr29m15 N-25 N114712458011471983202875805 025SA MIRMAPA012S21200611hr25 N-35 N115112292011511625202730276 025SA MIRMAPB012S21200611hr26 N-34 N115120842011512480202478734 026SA MIRMAP013S21200621hr26m34 N-47 N115272438011528015402915013 026SA MIRMAP014S22200611hr30m55 N-65 N115430880011543502002621692 028SA MIRMAP015S23200612hr45m46 N-54 N115749270011575386001935292 030SA MIRMAP036S24200621hr30m66 N-73 N116117160011612490002063491 33

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Table 2-1 .Continued. ObservationsSequenceYearDurationLatitudeStartSCETEndSCETRange(km) Covered 046SA MIRMAP024S31200721hr14m10 S-30 S118219590011822723402264004 047SA MIRMAPB024S31200711hr0 -20 S118230930011823489002299727 048SA MIRMAP025S31200720hr30m30 S-50 S118400892011840827202881444 048SA MIRMAP026S32200721hr30m40 S-60 S118538226011854596602352865 049SA MIRMAP027S33200711hr30m50 S-70 S118894800011889894002676443 050SA MIRMAP037S34200721hr30m60 S-80 S119055546011906328602779837 050SA MIRMAP028S34200711hr20 S-40 S119153874011915783402127765 050SA MIRMAPB028S34200711hr20 S-40 S119161752011916571202336377 112SA MIRMAP001S50200921hr10m43 N-48 N124415412012442303201490000 118SA MIRMAP001S53200923hr17m36 S-48 S125402838012541122002632500 122SA MIRMAP001S55200922hr41m4 S-4 N125980308012598847402405000 122SA MIRMAP002S55200915hr40m12 S-19 S125997588012600845402010000 123SA MIRMAP001S55200923hr00m27 S-34 S126140676012614895601920000 125SA MIRMAP001S56201020hr55m26 N-34 N126414870012642240001970000 126SA MIRMAP001S57201022hr25m40 S-50 S126661578012666964802335000 129SA MIRMAP001S58201023hr11 N-19 N127002294012701057402345000 130SA MIRMAP001S59201020hr55m46 N-58 N127302282012730981202551500 132SA MIRMAP001S60201023hr45 S-55 S127615542012762382202278000 34

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Table2-2. Spectralrangeusedforthetemperatureandcloudinversions. RetrievedPropertySpectralrangePressurerange parameter (cm 1 ) (mbar) TemperatureCH 4 1250-1350 0.3-5 TemperatureH 2 590-700 80-300 Clouds/hazegraycloud1389-1395 300-800 Table2-3. 600cm 1 2005observations2007observations 009A007009B007050028050B028 A93.83K94.01K94.32K91.60K B93.83K93.99K94.08K91.59K C93.83K93.99K94.07K91.56K Table2-4. 1304cm 1 2005observations2007observations 009A007009B007050028050B028 A142.54K142.07K141.94K142.58K B142.54K142.07K141.97K142.55K C142.52K142.07K141.97K142.56K Table2-5. 1392cm 1 2005observations2007observations 009A007009B007050028050B028 A118.97K123.78K126.39K131.20K B118.21K122.90K125.90K131.06K C118.69K122.78K125.84K131.04K 35

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Figure2-1. CIRSFocalPlaneLocations.FP1isthefar-infraredinterferometerwithFOV of3.9mrad,anditcoversthespectralrangefrom5to695cm 1 .The mid-infraredinterferometerscontainstwofocalplanearraysFP3(570-1125 cm 1 )andFP4(1025-1495cm 1 ).Eacharrayhas10detecterswith0.297 mradFOV.ThisgraphistakenfromtheFig.3inCIRS FOV OVERVIEW.pdf ofthePDSarchiveco-s-cirs-234-tsdr-v31.Thisgraphisalsoshownin Flasaretal. ( 2004 ) 36

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1e-09 1e-08 1e-07 1e-06 1e-05 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 Spectral NESR [W m -2 sr -1 / cm -1 ] Wavenumber [cm -1 ] Noise Equivalent Spectral Radiance (NESR) FP3 2.8 cm -1 FP4 2.8 cm -1 Figure2-2. NoiseEquivalentSpectralRadianceforFP3andFP4at2.8cm 1 spectral resolutionduringJupiterencounterin2000.CalculationofNESRis describedin Flasaretal. ( 2004 ). 37

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Figure2-3. MIRMAPcoveragein2005.Ineachobservation,thespacecraftscanned overalatitudinalbandwith5activedetectors(shownas5horizontallines withthesamecolor).Linescenteredatdifferentlatitudesbutshowninthe samecolor(forexample,5horizontalreddatalinescenteredat70 Sand5 horizontalreddatalinescenteredat5 S)arefromseperateobservations measuredatdifferentsequences.In2005,MIRMAPobservationscovered thelatitudesbetween0 and85 SinthesouthernhemisphereonSaturn. 38

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Figure2-4. MIRMAPcoveragein2006.MIRMAPobservationsin2006coveredSaturn's northernhemisphereatlatitudesbetween5 Nand73 N. 39

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Figure2-5. MIRMAPcoverageofSaturn'snorthernhemisphereatlatitudesbetween 8 Nand65 Nin2007. 40

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Figure2-6. MIRMAPcoverageofSaturn'ssouthernhemisphereatlatitudesbetween 7 Sand80 Sin2007. 41

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Figure2-7. MIRMAPcoveragein2009.In2009,theMIRMAPobservationscoveredthe equatorialregionbetween5 Sand5 N,andthelatitudinalregionbetween 10 Sand50 S. 42

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Figure2-8. MIRMAPcoveragein2010. 43

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Figure2-9. EmissionanglesofMIRMAPobservationsfrom2005to2010.TheCassini spacecraftisneartheequatorialregionforMIRMAPobservations,therefore, theemissionanglesincreasewithlatitudes. 44

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0.01 0.1 1 10 100 1000 1e-10 1e-09 1e-08 1e-07 1e-06 1e-05 0.0001 0.001 Pressure [mbar] Mixing Ratio NH 3 PH 3 C 2 H 2 C 2 H 6 Figure2-10. ReferenceatmosphericstructureofSaturn.Thevolumemixingratiosof ethaneandacetyleneincreasewithheight,basedonthestudyby Moses andGreathouse ( 2005 ).Thereferencephosphineverticalprolesisbased onrotationallineobservationsby Ortonetal. ( 2000 ; 2001 ).Thevertical distributionofammoniafollowedresultsby Courtinetal. ( 1984 ).Chemical constituentssuchasH 2 O,GeH 4 ,CO,AsH 3 ,andCO 2 donotcontribute muchtothemid-infraredspectrumandwereneglectedfromthereference model. 45

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1e-11 1e-10 1e-09 1e-08 1e-07 600 700 800 900 1000 1100 1200 1300 1400 1500 Intensity [Wm -2 sr -1 /cm -1 ] wave number [cm -1 ] Reference spectrum Figure2-11. Synthesizedspectrumbasedonthereferenceatmosphericstructure.This gureshowsthespectralfeaturescontributedbydifferentatmospheric species.C 2 H 2 ,C 2 H 6 andCH 4 havestrongemittingfeaturesat625-825 cm 1 ,700-900cm 1 ,and1150-1350cm 1 ,respectively.PH 3 andNH 3 appearinabsorptionrelativetothebackgroundcontinuumbetween 900-1200cm 1 46

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!" !"# !"## !"### !$## !%## !&## !'## !"### !""## !"(## !")## !"*## !"+## ,-.//0-.!1234-5 647.8023.-!192:"5 !" # $" % &" % ' # ( )%*'+,-+.) '+.+ '+ /!012 Figure2-12. Pressurelevelofunityopticaldepthinnadir-viewinggeometry.The atmosphericmodelassumesaclearatmospherebasedonthereference atmosphericstructureinFig. 2-10 .Horizontallinesindicatethespectral rangescontributedbythechemicalconstituents. 47

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90 95 100 105 110 115 120 125 130 135 140 145 1050 1100 1150 1200 1250 1300 1350 1400 1450 Brightness Temperature [K] Wavenumber [cm -1 ] 2005 CIRS MIRMAP observation Reference atmosphere 0.1 x reference PH 3 10 x reference PH 3 Figure2-13. Sensitivitystudytotheabundanceofphosphine. 48

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90 95 100 105 110 115 120 125 1000 1050 1100 1150 1200 Brightness Temperature [K] Wavenumber [cm -1 ] 2005 CIRS MIRMAP observation Reference atmosphere 0.1 x reference NH 3 10 x reference NH 3 Figure2-14. Sensitivitystudytotheabundanceofammonia.(1000-1200cm 1 ) 49

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114 116 118 120 122 124 126 128 130 132 134 136 1360 1380 1400 1420 1440 1460 1480 Brightness Temperature [K] Wavenumber [cm -1 ] 2005 CIRS MIRMAP observation Reference atmosphere 0.1 x reference NH 3 10 x reference NH 3 Figure2-15. Sensitivitystudytotheabundanceofammonia.(1350-1490cm 1 ) 50

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80 90 100 110 120 130 140 Brightness Temperature [K] Tb at 1392 cm -1 (2005S MIRMAPs) 0 50 100 150 200 250 300 350 Longitude -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Planetographic Latitude Figure2-16. Brightnesstemperaturemapat1392cm 1 from2005MIRMAP observationsinthesouthernhemisphere. 51

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80 90 100 110 120 130 140 Brightness Temperature [K] Tb at 1392 cm -1 (2007S MIRMAPs) 0 50 100 150 200 250 300 350 Longitude -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Planetographic Latitude Figure2-17. Brightnesstemperaturemapat1392cm 1 from2007MIRMAP observationsinthesouthernhemisphere. 52

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80 90 100 110 120 130 140 Brightness Temperature [K] Tb at 1392 cm -1 (2006N MIRMAPs) 0 50 100 150 200 250 300 350 Longitude 0 10 20 30 40 50 60 70 80 Planetographic Latitude Figure2-18. Brightnesstemperaturemapat1392cm 1 from2006MIRMAP observationsinthenorthernhemisphere. 53

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0 5000 10000 15000 20000 25000 30000 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Number of Data Planetographic Latitudes Number of data averaged in 2005 Figure2-19. Numberofradiancesat1392cm 1 averagedforbrightnesstemperature calculationin2005. 54

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0 5000 10000 15000 20000 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Number of Data Planetographic Latitudes Number of data averaged in 2007 Figure2-20. Numberofradiancesat1392cm 1 averagedforbrightnesstemperature calculationin2007. 55

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0 5000 10000 15000 20000 0 10 20 30 40 50 60 70 80 90 Number of Data Planetographic Latitudes Number of data averaged in 2006 Figure2-21. Numberofradiancesat1392cm 1 averagedforbrightnesstemperature calculationin2006. 56

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116 118 120 122 124 126 128 130 132 134 -80 -60 -40 -20 0 20 40 60 80 Temperature [K] Planetographic Latitudes Observed Tb 1392 cm -1 in 2005 Observed Tb 1392 cm -1 in 2006 Observed Tb 1392 cm -1 in 2007 Figure2-22. Zonalmeanbrightnesstemperatureat1392cm 1 from2005to2007. 57

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120 122 124 126 128 130 132 134 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Temperature [K] Planetographic Latitudes Observed Tb 1392 cm -1 in 2005 Observed Tb 1392 cm -1 in 2007 Figure2-23. Zonalmeanbrightnesstemperatureat1392cm 1 ofthesouthern hemispherein2005and2007. 58

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115 120 125 130 135 140 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Temperature [K] Planetographic Latitudes Observed brightness temperature in 2005 Modeled brightness temperature without cloud/haze Figure2-24. Zonalmeanbrightnesstemperatureat1392cm 1 in2005comparedwith themodeledbrightnesstemperatureretrievedfromthereference atmospherewithoutcloudsandhazes.Themodeledbrightness temperature(blueline)decreaseswithincreasingemissionanglesat higherlatitudes. 59

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!"# !$# !%## !%%# !%&# !%'# !%(# )*+,-./011!20340*5.6*0!789 2:!5.!%'$&!;3 <% !=&##>?!@AB@CD1E !# !># !%## !%># !&## !&># !'## !'># FG/,+.6H0 <$# <"# # <(# <'# <&# <%# !# DK5/0.G,*54-+;!F5.+.6H0 Figure2-25. Brightnesstemperaturemapat1392cm 1 from2005MIRMAP observationsinthesouthernhemisphere.Rectangularboxeslabelthe discontinuityregionsofthebrightnesstemperatureat1392cm 1 60

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!"# !$# !%## !%%# !%&# !%'# !%(# )*+,-./011!20340*5.6*0!789 2:!5.!%'$&!;3 <% !=&##>?!@AB@CD1E !# !F# !%## !%F# !&## !&F# !'## !'F# GH/,+.6I0 <$# <"# <>#
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70 70.5 71 71.5 72 0 50 100 150 200 250 300 350 Number of spectra used for calibration Planetographic Longitude Cold Calibration 004A039 Deep space 004B039 Deep space Figure2-27. NumberofspectrausedinMIRMAPobservationsat60 Sin2005forcold calibration(DeepSpace). 62

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7 7.5 8 8.5 9 9.5 10 0 50 100 150 200 250 300 350 Number of spectra used for calibration Planetographic Longitude Warm Calibration 004A039 Shutter closed 004B039 Shutter closed Figure2-28. NumberofspectrausedinMIRMAPobservationsat60 Sin2005forwarm calibration(Shutterclosed). 63

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105 110 115 120 125 130 135 140 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Brightness Temperature [K] Planetographic Latitudes 2005 MIRMAP Figure2-29. Variancesofthezonalmeanbrightnesstemperatureofthesouthern hemispherein2005. 64

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105 110 115 120 125 130 135 140 0 10 20 30 40 50 60 70 80 Brightness Temperature [K] Planetographic Latitudes 2006 MIRMAP Figure2-30. Variancesofthezonalmeanbrightnesstemperatureofthenorthern hemispherein2006. 65

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105 110 115 120 125 130 135 140 -80 -70 -60 -50 -40 -30 -20 -10 0 Brightness Temperature [K] Planetographic Latitudes 2007 MIRMAP Figure2-31. Variancesofthezonalmeanbrightnesstemperatureofthesouthern hemispherein2007. 66

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92 94 96 98 100 102 104 106 108 110 112 114 600 650 700 750 800 850 900 Temperature [K] Wavenumber [cm -1 ] CIRS009SAMIRMAPA007PRIME CIRS009SAMIRMAPA007PRIME Figure2-32. SpectraoftheMIRMAPobservations009A007and009B007inFP3 spectralrange. 67

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70 80 90 100 110 120 130 140 150 1050 1100 1150 1200 1250 1300 1350 1400 1450 Temperature [K] Wavenumber [cm -1 ] CIRS009SAMIRMAPA007PRIME CIRS009SAMIRMAPA007PRIME Figure2-33. SpectraoftheMIRMAPobservations009A007and009B007inFP4 spectralrange. 68

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CHAPTER3 RETRIEVALALGORITHMANDNUMERICALMODEL 3.1Introduction Forsatellite-basedremotesoundingobservations,weneedtorelyoninverse methodstoretrievetheatmosphericpropertiesbecausethedesiredphysicalquantities arenottypicallydirectlymeasurable.ToobtaintheverticaldistributionofSaturn's atmosphericproperties,suchastemperatureandclouds/hazeproles,werstacquire infraredspectrafromtheCassiniOrbiterwithremotesoundingtechniques.Wethen comparetheobservedspectrumwithasyntheticonegeneratedbyaforwardmodel withinitialphysicalparameters.Newsyntheticspectrawillbegeneratedwithdifferent setsofvaryingphysicalparameters,andtheretrievedatmosphericproleswillbe providedbytheparametersthatbesttsyntheticspectra.Aschematicdiagramofthe retrievalprocessisshowninFig. 3-1 .Adetaileddescriptionoftheforwardmodeland theretrievalalgorithmwillbediscussedinthefollowingsections. 3.2ForwardModel Theforwardmodelisthekeycomponentwhichconvertsphysicalparametersto spectrumintheretrievalalgorithm.Thismodelnotonlyhastoincludealltherelevant physics,butitmustalsobenumericallyefcienttoreducethecomputingtime. Inanon-scatteringhomogeneousatmosphere,themeanradiance I ( ) emittedto spacebetweenfrequencies and canbecalculatedas I ( )= B ( T 0 ) T r (0)+ $ 0 B ( T ( z )) d T r ( z ) d z d z (31) where T r ( z ) isthemeantransmittancefromthealtitude z tospaceatfrequency B ( T ( z )) isthemeanPlanckradianceattemperature T ,and T 0 isthetemperatureata referenceheight.Forrockyplanets,thereferenceheightistheground;forgasgiants,it isusuallythe1-barpressurelevel.Themeantransmittance T r betweenthefrequency 69

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interval and + canbecalculatedas T r ( m )= 1 + exp $ m # j k j ( % ) $ d % (32) where m isthetotalabsorberamount,and k j istheabsorptioncoefcientofthe j thline. TocalculatethesyntheticspectrumfromEq. 31 and 32 ,aline-by-linemodel, whichcomputestheabsorptionofeachindividualspectralline,isconsideredthemost accurateforwardmodel.Linedataareprovidedfromthestandardlinedatabases,such asHITRAN( Rothmanetal. 2005 )orGEISA( Jacquinet-Hussonetal. 2005 ).The individualabsorptionsneedtobecalculatedforthedifferentpressuresandtemperatures ( Irwinetal. 2008 ).Thespectralrangesofinterestareusuallylarge,andtherequired spectralresolutionforEq. 32 toresolvetheindividuallineshapesismuchsmaller thanthespectralinterval ,whichresultsinsubstantialamountofcomputingtime. Therefore,theline-by-linemodelisunrealisticforretrievalpurposes. Tobalancebetweenefciencyandaccuracy,acorrelated-kmethod( Goodyetal. 1989 ; LacisandOinas 1991 ; Liou 2002 )isusedasaforwardmodelinourwork.With thecorrelated-kmethod,wecancalculatethemeantransmittancebasedongrouping theabsorptioncoefcients k insteadofintegratingoverthefrequencyintervalstosave computingtime. Themeantransmittanceinanon-scatteringhomogeneousatmosphereisnot dependentontheorderoftheabsorptioncoefcientsforagivenspectralrange.We canrewriteEq. 32 astheintegrationoverthe k spacewiththefraction f ( k ) ofthe frequencydomain.Thenewmeantransmittanceequation,therefore,becomes T r ( m )= $ 0 f ( k )exp( $ km )d k (33) Furthermore,ifwedeneasmoothsingle-valuecumulativefunction g ( k ) as g ( k )= k 0 f ( k % )d k % (34) 70

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whichincreasesmonotonicallyin k space,thenEq. 33 canberewrittenas T r ( m )= 1 0 exp( $ k ( g ) m )d g (35) where k ( g ) iscalledthek-distributionfunction. k ( g ) istheinversefunctionof g ( k ) ,andit isasmoothfunctionin g space. ComparingEq. 32 withEq. 35 ,wecanseethatEq. 32 requiresasmall frequencyinterval d inanumericalintegrationtoacquireoptimalresolutionbecause k ( ) isarapidlychangingfunctionof ;Eq. 35 usesfewerstepsandlargerinterval d g because k ( g ) isaslowlyincreasingfunction.Therefore,byintegratingovertheg-space, wecansavenumericalcomputingtimebyusingthecorrelated-kmethodfortheforward model. Forcomputationalpurposes,weneedtoapproximateEq. 35 bydiscretizingitas T r ( m )= N # i =1 exp( $ k i m ) g i (36) whereNis20inourworktobalancethecomputationalspeedandtheaccurate samplingofthek-distribution. k i isthek-distributionvalueatthe i thpointand g i is thecorrespondingweight.However,arealatmosphereisnothomogeneousbecause thetemperatureandpressurevarywithheight.Wecantreattherealinhomogeneous atmosphereasseveralstackedhomogeneouslayers.Themeantransmittancealongthe paththroughMlayerscanbewrittenas T r ( m )= N # i =1 exp $ M # j =1 k ij m j $ g i (37) Asaresult,thediscretizedmeanradiancethroughMlayersintheinhomogeneous atmospherecanbewrittenas I ( )= N # i =1 % B ( T 0 ) T ri ,1 + M # j =1 B ( T j )( T ri j +1 $ T ri j ) & g i (38) 71

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Beforeapplyingthecorrelated-kmethodintheretrievalalgorithmtocalculatethe spectruminaparticularspectralregion,weneedtorstcalculate k ( g ) toformaset ofk-tablescorrespondingtothespecicplanetandtheinstrument.Thek-tablesare obtainedfromlinedataandmustincludeallthespectralactivegaswithinthefrequency rangeofinterested.Detailedcalculationsarebeyondthescopeofthisdissertation,and interestedreaderscanreferto Irwinetal. ( 1999 ; 2006 ). 3.3RetrievalMethod Therelationshipbetweenthemeasurement y andtheproleofinterest x canbe describedbyaforwardfunction f ,sothat y = f ( x ) .However,notonlyisthephysics oftheforwardfunctionnotfullyunderstood,buttherearealsomeasurementand experimentalerrors.Thus,theactualrelationshipbetweenthemeasuredquantity andthedesiredprolecanbewrittenas y = F ( x )+ F istheforwardmodel,which describesthephysicsofthemeasurement,basedonourknowledgeofatmospheric radiationtheorywithapproximationsasdescribedinSection 3.2 istheerror correspondingtothemeasurement,whichincludessystematicandrandomerrors. ToderivetheverticaltemperatureproleandtheclouddistributioninSaturn's atmosphere,weusetheinfraredradiationemittedfromthetopoftheatmosphere measuredbythespacecraftCassini/CIRSorbitingaroundSaturn.Theproblemswe trytosolveareill-posednon-linearproblems,anditisnearlyimpossibletondexact solutionswiththepresenceofthemeasurementerror.Therefore,ndingareasonable solutionthattstheobservationwithintheexperimentalerrorsistheessentialtask. Inthiswork,weuseamulti-stagelinearinversiontechnique,whichisdescribed indetailby Matchevaetal. ( 2005 ), Conrathetal. ( 1998 ), Rodgers ( 1976 ; 2000 )and RodgersandConnor ( 2003 ).Theinversionmethodisoutlinedbelow. Let X ( z ) betheproleofanatmosphericparameterwewishtoretrieveatagiven height z ,and I ( ) isthemeasuredradiance,whichisafunctionofthewavenumber .Atmosphericparameters X ( z ) canbetemperature,gasmixingratios,orcloud 72

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absorptioncoefcient.Inamulti-stageinversion, X ( z ) isretrievedsequentiallytoavoid non-uniquenessproblemsarisingfromthecorrelationofvariables( Fletcheretal. 2009 ). Discretizingthecontinuousprolesintohundredsoflevelsandretrievingthe solutionswithvectorsandmatriceshelptoavoidthetediousnumericalcalculation.We candiscretize X ( z ) into n verticallayersand I ( ) into m wavenumberswithinthechosen spectralrange.Thenon-linearproblemcanalsobesimpliedbylinearizingtheforward modelaboutareferenceatmosphericstate X 0 ( z ) ,andtherelationshipbetweenthe measuredradianceandtheprolebecomes I ( i )= F i ( X 0 ( z j ))+ n # j =1 # F i ( X ( z )) # X ( z j ) ( X ( z j ) $ X 0 ( z j ))+ $ i (39) and i =1,2,... m ; j =1,2,... n where F i istheintensityoftheoutgoingthermalradiationatwavenumber i measured fromthetopofanopticallythickatmospherebasedontheradiativetransfertheory,and F i ( X ( z ))= $ 0 # T r ( z ) # z ( B ( i z )d z (310) Uponreplacing F i ( X 0 ( z j )) with I 0 ( i ) ,Eq. 39 becomes I i = n # j =1 # F i ( X ( z )) # X ( z j ) X j + $ i (311) where I i = I ( i ) $ I 0 ( i ),! X j = X ( z j ) $ X 0 ( z j ). (312) Inourdiscretizedequation, z isadimensionlessaltitudedenedas z = $ ln p p 0 (313) withareferencealtitude z 0 =0 at p 0 =1000 mbar. 73

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Denethefunctionalderivativematrix K withcomponents K ij = # F i ( X ( z )) # X ( z j ) (314) thelinearradiativeequationEq. 311 thencanbewrittenas I = K X + (315) The m n matrix K issometimesreferredtoastheweightingmatrix,theJacobian, thekernel,thesensitivitykernel,thetangentlinearmodel,ortheadjointintheinverse methodliteratures( Rodgers 2000 ).Thepropertiesandthedetailedmathematical derivationof K correspondingtotheradiationtheorywillbediscussedinSection 3.4 I isacolumnvectorinam-dimensionalmeasurementspace,while X canbe thoughtofasacolumnvectorinan-dimensionalstatespace.Therefore,tosolveEq. 315 istodetermineamappingbackfromthemeasurementspaceintothestatespace. Eq. 315 canbesolvedbyminimizingacostfunction Q denedas Q =( I $ K X ) T E 1 ( I $ K X )+ % a T a (316) E isthemeasurementerrorcovariancematrix.ThesuperscriptTintheequationabove denotesmatrixtransposition,andtheparameter % reectstherelativeweightofthe initialguessforthesolutioninthenalresult.Columnvector a containstheexpansion coefcientsandexpands X inasetofbasisvectors.Therelationshipbetween X and a is X = Ha (317) where H isamatrixwhosecolumnsarethebasisvectors. Withtheminimizationofthecostfunction Q X canbeestimatedas X = SK T ( KSK T + % E ) 1 I (318) 74

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S = HH T isatwo-pointcorrelationmatrixofthebasisvectorsandisdenedas S ij =exp ) $ ( z i $ z j ) 2 2 c 2 (319) where c isthecorrelationlengthinscaleheights.Weuse c =0.5 forthetemperature inversionsand c =0.01 forthecloudinversionsinthiswork. Ineachiteration,thefunctionalderivativematrix K iscalculatedfortheestimation of X tomodifytheradiance I .Thisprocedureisrepeatediterativelyuntilasetof requirementsissatised. 3.4FunctionalDerivativeMatrixK Intheretrievalmodel,functionalderivativematrix K ,denedasEq. 314 ,is thematrixwhosecomponentsaretherateofchangeoftheradiancewithrespectto changesintheatmosphericvariables.Toobtain K intheretrievalmodel,wecanadjust theatmosphericvariableateachlayerandcalculatetheentirespectrum,andthen dividecalculatedchangeintheemissionbythechangeoftheatmosphericproperty. Thisapproachisstraightforward,however,itrequiresmultiplecalculationsofthe spectrumforeachiteration;thiswouldresultinaratherslowandinefcientretrieval process. Analternativeapproachistocalculate K analyticallyatthedeepestsubroutine level,startingfromEq. 310 withtransmittanceatwavenumber i denedas T r ( i z )= e 1 # ( z ) (320) isthecosineoftheemissionangleand & ( z )= $ z Y ( z % )d z % = $ !$ Y ( z % ) ( z % $ z )d z % (321) istheopticaldepthatheight z Y ( z ) isthedimensionlesscloudabsorptioncoefcient. Thedetailedderivationsof K ij forthetemperatureretrievalandthecloudretrieval arediscussedinthefollowingsections. 75

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3.4.1 K ij fortheTemperatureRetrievals Forthetemperatureretrieval,therateofthechangeofradiancewithrespecttothe changeofthetemperatureis # F i # T j = # F i ( i z ) # T ( z j ) = $ 0 # # T ( z j ) ) # Tr ( i z ) # z B ( i T ( z )) d z = $ 0 # 2 Tr ( i z ) # T ( z j ) # z B ( i T ( z ))d z + $ 0 # B ( i T ( z )) # T ( z j ) # Tr ( i z ) # z d z (322) B ( i T ( z )) isthePlanckradianceattemperature T atwavenumber i .Thepartial derivative # T r ( i z ) # z = $ 1 e 1 # ( z ) #& # z = $ 1 T r ( i z ) #& ( z ) # z (323) Theequationabovebecomes # F i # T j = $ 0 # # T ( z j ) ) $ 1 Tr ( i z ) #& ( z ) # z B ( i T ( z ))d z + $ 0 # B ( i T ( z )) # T ( z j ) # Tr ( i z ) # z d z = $ 0 $ 1 ) # Tr ( i z ) # T ( z j ) #& ( z ) # z B ( i T ( z ))+ Tr ( i z ) # 2 & ( z ) # T ( z j ) # z B ( i T ( z )) d z + $ 0 # B ( i T ( z )) # T ( z j ) # Tr ( i z ) # z d z (324) Thersttermvanishesbecause Tr ( i z ) and & ( z ) areindependenton T ( z j ) ,and # B ( i T ( z )) # T ( z j ) ( =0 76

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onlywhen z j = z .Thefunctionalderivative K ij fortemperatureretrievalatwavenumber i atheight z j becomes K ij = # F i # T j = # B ( i T ( z )) # T ( z j ) # Tr ( i z ) # z d z (325) 3.4.2 K ij fortheClouds/HazeRetrievals Weuseasimilarapproachtocalculatethefunctionalderivative K ij forcloud retrievals.However,insteadofusingthechangeoftheabsorptioncoefcient Y j atthe height z j ,wechosetousethechangeofthe ln Y j asthedenominator.Solvingfor ln Y j inthecloudretrievalswilleliminatethepossibilityofresultinginunphysicalsolutions duetomathematicalconsistency.Itwillavoidthenegativeabsorptioncoefcient Y j inthesolution,sothattheopticaldepth & c woulddecreasemonotonicallywithheight. Moreover,manyatmosphericparameters,suchaspressure,massanddensity,vary exponentiallywithaltitude.Consequently,usinglogarithmicvariableswouldalsomake thenumericalcomputationlessdemanding( Matchevaetal. 2005 ). K ij forcloudretrievalsisderivedas K ij = # F i ( i z ) # ln Y j = Y ( z j ) # F i ( i z ) # Y ( z j ) = Y ( z j ) $ !$ # # Y ( z j ) ) # Tr ( i z ) # z B ( T ( z )) d z = Y ( z j ) $ !$ + # 2 Tr ( i z ) # Y ( z j ) # z B ( T ( z ))+ # Tr ( i z ) # z ! !" 0 # B ( T ( z )) # Y ( z j ) d z = Y ( z j ) $ !$ # # Y ( z j ) ) $ 1 Tr ( i z ) #& ( z ) # z B ( T ( z )) d z = $ Y ( z j ) $ !$ ) # Tr ( i z ) # Y ( z j ) #& ( z ) # z + Tr ( i z ) # 2 & ( z ) # Y ( z j ) # z B ( T ( z ))d z (326) 77

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Thepartialderivatives #& ( z ) # Y ( z j ) = $ !$ # # Y ( z j ) [ Y ( z % ) ( z % $ z ) ] d z % = $ !$ # Y ( z % ) # Y ( z j ) ( z % $ z )d z % + $ !$ Y ( z % ) ! !" 0 #' ( z % $ z ) # Y ( z j ) d z % = ( z j $ z )d z j (327) and # T r ( i z ) # Y ( z j ) = $ 1 e 1 # ( z ) #& ( z ) # Y ( z j ) = $ 1 & ( z ) T r ( i z ) #& ( z ) # Y ( z j ) = $ 1 & ( z ) T r ( i z ) ( z j $ z )d z j (328) Eq. 326 canbewrittenas K ij = $ Y ( z j ) $ !$ $ 1 & ( z ) Tr ( i z ) ( z j $ z )d z j #& ( z ) # z B ( T ( z ))d z $ Y ( z j ) $ !$ Tr ( i z ) # 2 & ( z ) # z # Y ( z j ) B ( T ( z ))d z = $ Y ( z j ) $ !$ ) $ 1 & ( z ) Tr ( i z ) #& ( z ) # z d z ( z j $ z )d z j B ( T ( z )) $ Y ( z j ) $ !$ Tr ( i z ) # # z [ ( z j $ z )d z j ] B ( T ( z ))d z = $ Y ( z j ) $ !$ d Tr ( i z ) B ( T ( z )) ( z j $ z )d z j $ Y ( z j ) $ !$ Tr ( i z ) [ $ ( ( z j $ z )d z j ] B ( T ( z ))d z = $ Y ( z j ) $ !$ d Tr ( i z ) B ( T ( z )) ( z j $ z )d z j + Y ( z j ) $ !$ Tr ( i z ) ( ( z j $ z ) B ( T ( z ))d z j = $ Y ( z j ) $ !$ d Tr ( i z ) B ( T ( z )) ( z j $ z )d z j + Y ( z j ) Tr ( i z j ) B ( T ( z j ))d z j (329) 78

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Thediscretizedfunctionalderivative K ij atheight z j atwavenumber i forthe clouds/hazeretrievalis K ij = # F i # ln Y j = Y ( z j ) z / B ( i T ( z j )) Tr ( i z j ) $ m # q = j B ( i T ( z q )) Tr ( i z q ) 0 3.5ErrorAnalysis Toestimatetheuncertaintyintheretrieved X prole, X j isallowedtovarysothat thechangeofradiance I i islimitedwithintheobservationalerror.ForFP3(570-1125 cm 1 )andFP4(1025-1495cm 1 ),observationalnoiseispresentinthemeasured spectra,deepspacecalibrationspectraandwarmcalibrationspectra.Followinga similarapproachin Teanbyetal. ( 2006 ),theexpectederrorof N spectrainthezonal meanaveragewith N w warmcalibration(shutterclosed)spectraand N c coldcalibration (deepspace)spectracanbewrittenas ) 2 = 2 NESR N 2 + 2 NESR N 2 w + 2 NESR N 2 c (330) where NESR isthemeanNoiseEquivalentSpectralRadiance(NESR).TheNESRs ofFP3andFP4varyslowlywithwavenumbersandareassumedtobeconstant. Theaveragedvaluesof NESR are 7.811314 10 9 Wcm 2 sr 1 (cm 1 ) 1 forFP3and 1.601580 10 9 Wcm 2 sr 1 (cm 1 ) 1 forFP4. Inourwork,theobservationalerrorwithintheselectedspectralrangeisdominated bythecalibrationspectrabecausethetypicalnumberof N isabout4000-10000,and thenumberofcalibrationspectraisusuallylessthan100.Thereforetherelationship betweenthechangeoftheradiance I i andthevaryingamountof X j canbewritten basedonEq. 311 andEq. 314 as | ( I i | = 1 1 1 1 1 n # j =1 K ij ( X j 1 1 1 1 1 ) 2 2 NESR N 2 w + 2 NESR N 2 c = ) calibration (331) 79

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and i =1,2,... m ; j =1,2,... n Foreachaltitude z j andwavenumber i ,Eq. 331 shouldbesatisedindependently;for each i and j ,itcanbeshownas | K ij ( X j | ) ) calibration (332) Foreachaltitude z j ,ifweletthefunctionalderivative K qj bethelargestamongstthe spectralrangeofinterest( | K qj | % | K ij | ),then | K qj | willprovidethebestsensitivityinthat layer j .Eq. 331 canthenbewrittenas | ( X j | ) ) calibration | K qj | = X j (333) j =1,2,... n X j istheuncertaintyoftheretrievedatmosphericparameter X j ataltitude z j withinthe retrievalspectralrangeduetotheobservationalandcalibrationnoise. Erroranalysisforcloud/hazesretrievals Theatmosphericparametersolvedfromtheretrievalmodelforcloudsandhazeis thelogarithmicoftheabsorptioncoefcient Y ,sotheuncertaintyoftheretrievedresults atheight z j canbederivedfromEq. 333 with X j =ln Y j ,where | ( X j | = | ( ln Y j | = 1 1 1 1 ( Y j Y j 1 1 1 1 ) ) calibration | K qj | (334) Theuncertaintyoftheretrievedabsorptioncoefcientforcloudsandhazeatheight z j is Y j = | ( Y j | = | Y j | | K qj | ) calibration (335) j =1,2,... n 80

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!"#$%#&'("&)* +,-./).01'23)1.#45 ("&06,'3/,201%*'3%#%5).)#2 7"53%#)' $0./'"82)#9)&' 23)1.#45 :-0.0%*'3%#%5).)#2 ;%'3#0"#0'%.5"23/)#01' 2.#41.4#)< !"#$%&"'"()* +,)%+-". !"#$%&"'"() (/)*+,)%+-". =).#0)9)&'#)24*.' $0./'./)'8)2.'>. Figure3-1. Flowchartoftheretrievalalgoritm. 81

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CHAPTER4 TEMPERATURERETRIEVAL 4.1Introduction Toacquiretheverticaldistributionandopticalpropertiesofthecloudsandhaze atvarioussouthernlatitudesin2005,werstconstructthetemperatureprolesina clearatmosphereonSaturn'ssouthernhemisphere.Inthiswork,weusecalibrated mid-infrareddatafromCassini/CIRSMIRMAPobservationslistedinTable 2-1 .We averagetheradiancesover4degreesinlatitudewith2degreesoverlappingbetween theadjacentzonalbands.Themeanemissionangleswithinthelatitudinalbandsare alsocalculatedwiththeaverageradiances.Wethenobtaintheretrievedtemperature prolewiththeuseoftheretrievalalgorithmdescribedinSec. 3.3 byminimizingthe differenceswithinthedenedspectralrangebetweentheobservedspectrumandthe syntheticspectrumgeneratedbyaninitialtemperatureprole. Fig. 4-1 showstheinitialtemperatureprolesusedfortheforwardcalculation togeneratethesyntheticspectrum.Forlowandmid-latitudes,weusetheretrieved prole(redcurvein 4-1 )fromVoyager/IRISobservationsby Courtinetal. ( 1984 ) andthemodiedone(greencurvein 4-1 )astheinitialtemperatureproles.Forhigh latitudes,theinitialprole(bluecurveinFig. 4-1 )isabout20Kwarmeratpressures lessthanafewmbarsinthestratospherecomparedwiththetemperatureprolefrom theVoyager/IRISobservations.Thewarmerstratospherictemperatureisduetohigh emissionanglesathighlatitudes.Theseinitialtemperatureprolesareinterpolatedonto agridof200pointsbetween0.01mbarand5barpressurelevels.Forlayersbelowthe tropopausewithpressureslargerthan500mbar,weassumethetemperatureincreases withthedryadiabaticlapserateasthepressureincreases. Intheforwardcalculation,weusethecorrelated-kmethod( Goodyetal. 1989 ; LacisandOinas 1991 ; Liou 2002 )describedinSec. 3.2 tocalculatetheabsorption spectraofCH 4 (1150-1600cm 1 ),NH 3 (600-1600cm 1 ),PH 3 (800-1350cm 1 ), 82

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C 2 H 2 (625-825cm 1 and1250-1400cm 1 ),C 2 H 4 (825-1150cm 1 ),andC 2 H 6 (750 -900cm 1 ).Thelatitudinaldependentgravityiscalculatedbasedonequationsby AndersonandSchubert ( 2007 )varyingfrom12.07m/s 2 atthepoleto9.03m/s 2 atthe equator.WeassumethevolumemixingratioofHe/H 2 is0.135( ConrathandGautier 2000 )andtheCH 4 /H 2 volumemixingratiois 5.3 10 3 ( Fletcheretal. 2009 ). Theelementofthefunctionalderivativematrix K forthetemperatureretrieval modiedfromtheoneby Matchevaetal. ( 2005 )isderivedinSec. 3.4.1 andshownas K ij = # B ( i T ( z j )) # T ( z j ) # Tr ( i z j ) # z j d z (41) where B ( i T ( z j )) isthePlanckradianceattemperature T atwavenumber i T r ( i z j ) istheatmospherictransmittancefromthetopoftheatmospheredown tothelayer z j atthewavenumber i isthecosineoftheemissionangle,and d z is thedifferencebetweenlayer z j and z j +1 .Theuncertainty X j fortemperatureretrievalat altitude z j withintheretrievalspectralrangeis X j = 1 | K qj | 2 2 NESR N 2 w + 2 NESR N 2 c (42) j =1,2,... n where K qj isthelargestfunctionalderivativeamongstlayer j ,and K qj givesthebest sensitivity. N w and N c arethenumberofspectrainwarmandcoldcalibrations, respectively,and NESR isthemeanNoiseEquivalentSpectralRadiance(NESR). Inthiswork,weuseatwo-stageretrievalfortemperatureinversions.Thecollisional-induced absorption(CIA)ofH 2 inthespectralrangeof590-700cm 1 isusedtoextract informationaboutthetemperatureproleintheuppertroposphere,whereasthe methaneemissioninthespectralrangeof1250-1350cm 1 isusedtoretrievethe temperatureproleinthestratosphere.Thenormalizedcontributionfunctions(functional derivatives)ofH 2 andCH 4 innadir-viewinggeometryareshowninFig. 4-2 andFig. 4-3 TheredregionsinFig. 4-2 andFig. 4-3 indicatetheregionswheretherateofchangeof 83

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observedradiancewithtemperatureisthegreatest.Aswecanseeinthesetwogures, thepressurerangesensitivetotheH 2 absorptionsisintheuppertropospherebetween 40and500mbarwiththepeaksensitivityoccurringnear100mbar;thepressurerange sensitivetotheCH 4 emissionsisinthestratospherebetween0.1and20mbarwith thepeaksensitivityaround5mbar.Temperatureiswell-constrainedwithinthesetwo sensitivepressureregions.Outsidetheconstrainedpressurerange,theretrieved temperaturewillfollowtheinitialguessduetothelackofdirectinformation.Forhigher latitudes,thepeaksensitivitytotheH 2 absorptionswouldslightlyshifttohigheraltitudes withlowerpressuresduetotheincreasingemissionangles. 4.2ResultsandDiscussion WeuseMIRMAPobservationsin2005fortemperatureinversionstoanalyzethe verticaltemperaturedistributionandthelatitudinalvariationsofthetemperatureinthe southernsummerhemisphereonSaturn. Fig. 4-4 andFig. 4-5 presenttheretrievedverticaltemperatureprolesat27 Sand 77 Sin2005.Theshadedregionsindicatetheuncertaintiesoftheinversionsandthe redlineistheinitialtemperatureprole.Fig. 4-6 andFig. 4-7 showthespectraafter rst-stageretrieval(CH 4 ).Inthesetwogures,wecanseetheretrievedspectraare veryclosetotheobservedspectrainbothlatitudeswithintheselectedspectralregion between1250and1350cm 1 .Forthesecond-stageretrieval(H 2 ),despitethesmall variationsintheobservedspectra,theretrievedspectra(bluelines)tthegeneraltrend oftheobservedspectra(redlines)withinthespectralrangebetween590-700cm 1 asshowninFig. 4-8 for27 SandFig. 4-9 for77 S.Thecomparisonoftheobserved spectraandtheretrievedspectraafterrst-andsecond-stageinversionswithintheFP3 andFP4spectralrange(600-1500cm 1 )areshowninFig. 4-10 andFig. 4-11 4.2.1StratosphericTemperature Stratospherictemperaturesbetween1and10mbararedevelopedintherststage ofthetwo-stagetemperatureretrieval,whichareshowninFig. 4-12 andFig. 4-13 ,with 84

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theCH 4 emissionlinesat2.8cm 1 spectralresolutioninthe1250-1350cm 1 .For pressurelessthan0.1mbarandlargerthan20mbar,theretrievedtemperaturewill tendtofollowtheinitialguessduetolackofinformationforretrievals.Theretrieved temperaturearound5mbarat77 Sisnear160Kandisabout15Khigherthanthe temperatureat27 S. Toseethelatitudinalvariationsoftheretrievedstratospherictemperature,we constructamapthatshowsthetemperatureofSaturn'ssouthernhemisphereretrieved from2005MIRMAPdatasetslistedinTable 2-1 .Ourresultsareconsistentwiththe temperaturestructureanalysisofCIRSdataby Flasaretal. ( 2005 )and Fletcheretal. ( 2007 ),inwhichtheresultisderivedfromfar-infrareddata.AsonecanseeinFig. 4-14 ,thetemperatureincreasesfrommid-latitudestohigherlatitudesforpressure rangebetween0.3mbarand5mbar.Temperatureelevatesslightlyfromlowlatitudes towardtheequator.Thestratospherictemperatureatthepolarregionisabout15K-20K warmerthanthatattheequatoraround2mbarpressurelevel.Thisphenomenonof warmerstratospherictemperatureathigherlatitudesin2005observationsmaybea resultofmoresolarinsolationathigherlatitudesafterSaturn'ssouthernsummersolstice (October,2002). However,asmentionedin Flasaretal. ( 2005 ),Saturn'spolarstratospheric temperaturepredictedbysimpleradiativemodelsshouldonlybewarmerthan theequatorby5Kin2005.Thisisbecausetheradiativerelaxationtimeinthe stratosphereis9.5years,whichresultsintheatmosphericresponselaggingbehind theseasonally-modulatedsolarheatingbyasixthofaSaturn'sorbitalperiod(29.5Earth years).Thewarmerthanexpectedpolarstratospherictemperaturemaybecausedby dynamicalforcingassuggestedby Flasaretal. ( 2005 ). 4.2.2TroposphericTemperatureandTemperatureKnee Tropospherictemperaturesbetween40mbarand500mbarareretrievedatthe secondstageofthetemperatureinversionwiththecollisional-inducedabsorptionofH 2 85

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inthe590-700cm 1 .Forpressurelevelbelow5mbar,thereisnoobviouslatitudinal variationoftheretrievedtemperature.Thetemperatureattropopauseisbetween88 Kand95Kforalllatitudesataround100mbarasshowninFig. 4-14 .Astheradiative timeconstantincreaseswithincreasingpressureindeeperlevelsoftheatmosphere ( ConrathandPirraglia 1983 ),theseasonaleffect( CessandCaldwell 1979 )of thetropospherictemperaturerelatedtoSaturn'sorbitalobliquityislesspronounced comparingwiththestratospherictemperature. Tropospherictemperaturekneeisthechangetothetroposphericlapserate withalocalmaximumintheuppertroposphere( Fletcheretal. 2007 ).Tropospheric temperaturekneeisrstobservedinretrievedtemperatureprolesfromVoyager/IRIS observationsby Haneletal. ( 1981 ; 1982 ),anditislaterconrmedby Fletcheretal. ( 2007 )fromCassini/CIRSfar-infraredandmid-infraredobservations.Temperatureknee isseeninmanyofourretrievedtemperatureprolesatdifferentlatitudes.Thefeatureof thesmallinversionofthetemperaturenear100mbarisshowninFig. 4-5 Fletcheretal. ( 2007 )studiedthelatitudinalvariationsofthetemperaturekneewithFIRMAPdatasets from2004to2006,andthestudyconcludedthatthetemperaturekneebetween150300mbarduringthisobservationperiodislargerinthesouthernsummerhemisphere thaninthenorthernwinterhemisphere.Furthermore,thetemperaturekneeissmaller andhigherintheequator,deeperandlargerintheequatorialbelts,andsmallatthe poles. Fig. 4-15 showsourretrievedresultsfrom2005inthesouthernsummerhemisphere. Ourresultsreectthattropospherictemperaturekneeisdeeperatlow-andmid-latitudes locatedbetween100mbarand200mbar,anditisaround60mbarathigherlatitudes. Wenoticedthatthetemperaturekneeisnotalwaysdevelopedinthetemperature retrievals.Theretrievedtemperaturekneehasacorrelationwiththepeaklocationof thenormalizedfunctionalderivative K (contributionfunction)andtheinitialtemperature proles.Theresultsalsorevealthattheheightofthekneevarieswiththepeaklocation 86

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of K ,atwhichpressurelevelisthemostsensitivetoH 2 absorption. K ishigherathigh latitudesduetoincreasingemissionangles.Withlargeuncertaintiesoftheretrieved resultsintheuppertroposphere,thephysicalexistenceofthetemperaturekneeisstill debatable.Thecauseofthischangeinthelapserateintheuppertropospherestill needstobecarefullyexamined. 87

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0.01 0.1 1 10 100 1000 80 100 120 140 160 180 200 Pressure [mbar] Temperature [K] initial temperature profile A initial temperature profile B initial temperature profile C Figure4-1. Initialtemperatureprolesfortemperatureretrievals.Theinitialtemperature proleA,usedfortemperatureretrievalsatlowandmid-latitudes,isthe retrievedprolefromVoyager/IRISobservationsby Courtinetal. ( 1984 ). TheproleCismodiedfromproleA,anditisusedfortemperature retrievalsathighlatitudes. 88

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1260 1280 1300 1320 1340 Wavenumber [cm -1 ] 0.01 0.1 1 10 100 1000 Pressure [mbar] 0 0.2 0.4 0.6 0.8 1 Figure4-2. ContributionfunctionforCH 4 at27 Sin2005.Thecolorzoneindicatesthe pressurelevel(1-10mbar)atwheretherateofchangeofobservedradiance withtemperatureisthegreatestwithinthespectralregionbetween1250 cm 1 and1350cm 1 inthenadir-viewinggeometry. 89

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600 620 640 660 680 700 Wavenumber [cm -1 ] 0.01 0.1 1 10 100 1000 Pressure [mbar] 0 0.2 0.4 0.6 0.8 1 Figure4-3. ContributionfunctionforH 2 at27 Sin2005.Thecolorzoneindicatesthe pressurelevel(40-200mbar)atwheretherateofchangeofobserved radiancewithtemperatureisthegreatestwithinthespectralregionbetween 590cm 1 and700cm 1 inthenadir-viewinggeometry. 90

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0.01 0.1 1 10 100 1000 80 100 120 140 160 180 200 Pressure [mbar] Temperature [K] initial temperature profile retrieved temperature Figure4-4. Temperatureproleat27 Sin2005afterthesecondstageoftemperature retrieval. 91

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0.01 0.1 1 10 100 1000 80 100 120 140 160 180 200 Pressure [mbar] Temperature [K] initial temperature profile retrieved temperature Figure4-5. Temperatureproleat77 Sin2005afterthesecondstageoftemperature retrieval. 92

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105 110 115 120 125 130 135 140 145 1200 1250 1300 1350 1400 Temperature [K] Wavenumber [cm-1] observed spectrum retrieved spectrum (CH 4 ) retrieved spectrum (H 2 ) Figure4-6. Partialspectrum(1200-1400cm 1 )at27 Sin2005aftertherststageof temperatureretrieval. 93

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110 115 120 125 130 135 140 145 150 155 160 1200 1250 1300 1350 1400 Temperature [K] Wavenumber [cm-1] observed spectrum retrieved spectrum (CH 4 ) retrieved spectrum (H 2 ) Figure4-7. Partialspectrum(1200-1400cm 1 )at77 Sin2005aftertherststageof temperatureretrieval. 94

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90 95 100 105 110 115 600 620 640 660 680 700 720 740 Temperature [K] Wavenumber [cm-1] observed spectrum retrieved spectrum (CH 4 ) retrieved spectrum (H 2 ) Figure4-8. Partialspectrum(590-750cm 1 )at27 Sin2005afterthesecondstageof temperatureretrieval. 95

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90 95 100 105 110 115 120 125 600 620 640 660 680 700 720 740 Temperature [K] Wavenumber [cm-1] observed spectrum retrieved spectrum (CH 4 ) retrieved spectrum (H 2 ) Figure4-9. Partialspectrum(590-750cm 1 )at77 Sin2005afterthesecondstageof temperatureretrieval. 96

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80 90 100 110 120 130 140 150 600 700 800 900 1000 1100 1200 1300 1400 1500 Temperature [K] Wavenumber [cm-1] observed spectrum retrieved spectrum (CH 4 ) retrieved spectrum (H 2 ) Figure4-10. Spectrumat27 Sin2005aftertemperatureretrieval. 97

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80 90 100 110 120 130 140 150 160 600 700 800 900 1000 1100 1200 1300 1400 1500 Temperature [K] Wavenumber [cm-1] observed spectrum retrieved spectrum (CH 4 ) retrieved spectrum (H 2 ) Figure4-11. Spectrumat77 Sin2005aftertemperatureretrieval. 98

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0.01 0.1 1 10 100 1000 80 100 120 140 160 180 200 Pressure [mbar] Temperature [K] initial temperature profile retrieved temperature (CH 4 ) Figure4-12. Temperatureproleat27 Sin2005aftertherststageoftemperature retrieval. 99

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0.01 0.1 1 10 100 1000 80 100 120 140 160 180 200 Pressure [mbar] Temperature [K] initial temperature profile retrieved temperature (CH 4 ) Figure4-13. Temperatureproleat77 Sin2005aftertherststageoftemperature retrieval. 100

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-80 -70 -60 -50 -40 -30 -20 -10 0 Planetographic Latitudes 0.1 1 10 100 1000 Pressure [mbar] 80 90 100 110 120 130 140 150 160 170 Figure4-14. Retrievedtemperatureofsouthernhemispherein2005. 101

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10 100 1000 80 90 100 110 120 130 Presssure [mbar] Temperature [K] 07S 17S 27S 37S 47S 57S 67S 77S Figure4-15. Retrievedtropospherictemperaturekneein2005. 102

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CHAPTER5 CLOUDRETRIEVAL 5.1Introduction Thecloudretrievalisexecutedimmediatelyafterthetemperatureretrievalbyusing anidenticalalgorithmdescribedinCh. 3 withdifferentsetsofinversionparameters 1 ( c and % )andinitialproles.ThecloudretrievalcodeusesaGaussiancloudproleand theretrievedtemperatureproleasinitialconditionstogenerateasyntheticspectrum. ThesyntheticspectrumisthencomparedwiththeobservedspectrumbyCassini/CIRS MIRMAPdatasetsin2005listedinTable 2-1 Inthecloudretrievals,weassumeplane-parallelandagrayabsorbingcloudwitha dimensionlessabsorptioncoefcient Y ( z ) ,whereopticalthicknessofthecloud & c ( z ) at height z isdenedas & c ( z )= $ z Y ( z )d z (51) z isadimensionlessaltitudedenedas z = $ ln p p 0 (52) withareferencealtitude z 0 =0 at p 0 =1000 mbar.Thedimensionlesscloudabsorption coefcient Y atpressure p isthencalculatedas Y ( p )= 3 4 5 4 6 $ d # c dln p if p < p 0 0, if p % p 0 (53) TheinitialGaussiancloudproleisparametrizedwiththreeadjustablevariables :verticalbroadness W ,peaklocationoftheinitialcloud P ,andthemagnitudeofthe absorptioncoefcient A .TheabsorptioncoefcientoftheinitialGaussiancloudisthen 1 c isthecorrelationparameterinscaleheight,and % istherelativeweightofthe initialguessforthesolution. 103

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writtenas Y initial = A exp $ (ln p $ log P ) 2 2 W 2 (54) Duringeachiteration,theretrievalcodewouldmodifytheinitialGaussiancloudstructure untiltherequirementsethasbeenreached. Wesolvefor ln Y insteadof Y toavoidpossibleunphysicalsolutionsconsistent withthemathematicalproblems.Thefunctionalderivative K fortheretrievalofthecloud propertiesusingtheassumptionin Conrathetal. ( 1998 )andfollowing Matchevaetal. ( 2005 )isderivedinSec. 3.4.2 as K ij = Y ( z j ) z / B ( i T ( z j )) Tr ( i z j ) $ m # q = j B ( i T ( z q )) Tr ( i z q ) 0 (55) where B ( i T ( z j )) isthePlanckradianceattemperature T atwavenumber i isthe emissionangle,and Tr ( i z j ) isthetransmittanceatwavenumber i ataltitude z j .The uncertaintyoftheretrievedabsorptioncoefcientforcloudsandhazeatheight z j is Y j = | ( Y j | = | Y j | | K qj | 2 2 NESR N 2 w + 2 NESR N 2 c (56) j =1,2,... n K qj isthelargestfunctionalderivativeamongstthelayer j withthebestsensitivity, N w and N c arethenumberofspectraforwarmandcoldcalibrationsrespectively,and NESR isthemeanNoiseEquivalentSpectralRadiance(NESR). Thespectralrangeforcloudretrievalissettobe1389-1395cm 1 ,ofwhichis adeepprobingspectraregionwithoutinuenceofammoniaandphosphine.The volumemixingratiosandotheratmosphericparametersareleftthesameasthosein temperatureretrievals. 5.2NumericalExperiment Thevalidationoftheretrievalalgorithmfortheclouds/hazehasbeentestedin severalnumericalexperimentssimilarwiththosein Matchevaetal. ( 2005 ).Weinspect 104

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theretrievalalgorithmbyusingvarioussetsofarticialtestcloudsofdifferentgeometric shapes(Gaussiancloud,rectanglecloud,andexponentialcloudwithatbase)at variousheightsandopticalthicknesses.Thesetestcloudsareusedtogeneratetest spectrabasedontheretrievedtemperatureproleat27 Sin2005.Wethenrunthe inversioncodewithinitialGaussiancloudprolesofdifferentsetsofparameterstotthe testspectra.Bycomparingtheretrievedresultswiththetestclouds,wewouldbeable toinvestigatethecorrelationbetweentheinitialguessandthetestclouds,allowingusto constraintheretrievedresultsforfutureretrievalswhentherealclouds/hazestructureis notknown. Resultsofthenumericaltestsdemonstratethat,ifinitialguessescoversthe testcloudrange,thecloudpeaklocationcanbesuccessfullyproducedwithsmall uncertaintiesbytheretrievedcloudstructures.Intheregionswherethereexistweak cloudabsorption(athighaltitudes)orinanopticallythickatmosphere(deeppressure levels),thespectralinformationaloneisinsufcienttodrivethesolutionawayfrom theinitialguess.Thisoccurrenceresultsinlargeuncertaintiesataltitudesawayfrom thecloudpeaks.Ifthetestcloudislocateddeeperatthepressurelevelwherethe atmosphericgasopacityislargerthanunity,orifthetestclouditselfistoothick,wemay notbeabletocorrectlyretrievethecloudpeakandtheopticalthickness. Anexampleofatestcloudwithopticalthicknessisdenedas & c test ( p )= 3 4 5 4 6 & c 0 ( p 0 )( p p 0 ) H / H c if p < p 0 & c 0 ( p 0 ) if p % p 0 (57) anditisshownastheredcurveinFig. 5-1 andFig. 5-2 .Thereferencepressure p 0 is 500mbar,opticalthickness & c 0 is1.0,and H c =0.13 H .Thebaseofthetestcloudisat 500mbar,themaximumabsorptioncoefcientis5,andthebroadnessisbetween280 mbarand500mbar.Theopticalthicknessofthetestcloudincreaseswithdepthfrom 280mbarandbecomesunityatpressuregreaterthan500mbar. 105

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Fig. 5-1 andFig. 5-2 alsoshowtheabsorptioncoefcient Y andopticalthickness & c oftheinitialguesses(greencurves)andtheretrievedresults(bluecurves)with uncertainties(grayzones).TheresultsofanopticallythickinitialGaussiancloud ( P =1000 mbar, W =0.6 ,and A =2 )centeredat1barwithamaximumcloud opticalthickness & c max =3 areshowninthetoppanelsinbothgures.Theresults ofanopticallythininitialGaussiancloud( P =1000 mbar, W =0.6 ,and A =0.5 ) centeredat1barwithamaximumcloudopticalthickness & c max =0.75 areshowninthe bottompanelsinthegures.Theorangehorizontaldashedlinesindicatethepressure levelwheretheatmosphericopacityfor1392cm 1 becomesunitywithoutthepresence ofclouds/hazeinnadir-viewinggeometry.Inthegures,onecanseethatthepeak locationofthetestcloudiswellproducedbytheretrievedcloudstructuresfromboth initialguesses.Theretrievedopticalthickness(bluecurves)isalsoclosetothatofthe testcloudasshowninFig. 5-2 Basedontheresultsofthenumericalexperimentsoftheretrievalalgorithmfor cloudsandhaze,wearecondentthatourcodehasthecapacitytoderivethevertical proleofthecloud/hazewithcarefulselectionsoftheinitialguessclouds. 5.3 2 MinimizationApproach Inordertoexaminetheresultsfromthecloudretrievalsandgatherinformation aboutthepeaklocationaswellasopticalpropertiesoftheclouds/hazeonSaturn,we alsoperformedthe 2 minimizationapproachbyusingaparametrizedcloudstructureto minimizethedifferencesbetweentheobservedandthesyntheticspectra. Asmall 2 valuereectsthatthesyntheticspectrumhasagoodttotheobserved spectrum.Thecalculated 2 valueisdenedas 2 = 1 N N # k =1 ( x ( k ) $ y ( k )) 2 ) 2 x ( k ) (58) modiedfrom Teanbyetal. ( 2006 ). N isthetotalnumberofwavenumberttedinboth spectra, x ( k ) isthemeasuredspectrumwithvariance ) 2 x ( k ) atwavenumber k ,and 106

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y ( k ) isthesyntheticspectrumatwavenumber k .Thevariance ) 2 x ( k ) ,whichisdened inEquation 330 ,iscalculatedfromtheNoiseEquivalentSpectralRadiance(NESR), thenumberofdataaveragedintheobservedspectrum,thenumberofdeepspace calibratedspectra,andthenumberofthewarmcalibratedspectra. Inthiswork,weusetheMIRMAPobservationsat27 SonSaturnin2005to performthe 2 minimumapproach.Theparametrizedcloudstructureusedtogenerate thesyntheticspectrumisacombinationoftwoGaussiancloudswithpeaksatvarying pressurelevels(0.01-5000mbar),widths(0.1-10),andamplitudesofdimensionless absorptioncoefcients(0-10).Thissix-parametermodeliscapableofsimulating theatmosphereofonlyonecloudandnohazelayers,aswellastheatmosphereof onecloudandahazelayerwithorwithoutaseparatinglayerofcleargas.Awhole rangesurveyforallsixparameterswithlargerintervalswasappliedrsttoconservea signicantamountofcomputingtime.Afterexcludingcombinationsetsofparameters withhigh 2 values,wecalculate 2 valueswithsmallerparameterintervalstoobtain improvedcoverage. Fourgroupsofthecloudprolesprovidesmall 2 values( 1.1 )andare showninFig. 5-3 .TypeAcloud/haze(topleftpanelinFig. 5-3 )isacombinationof adeeperbroadcloud/hazelayerandathinhazelayerlocatedathigheraltitudes. Thestratospherichazelayerisatthepressurelevelbetween0.01and2mbarwith amaximumabsorptioncoefcient Y =0.1 .Thetroposphericcloudspreadsfrom1 mbartofewthousandmbarwiththepeakabsorptioncoefcient Y =2 # 3 ataround 1000mbar.Thecloudopticalthicknessincreasesslowlywithdepthstartingbetween 0.01mbarand1mar,andtherateofincreasingopticalthicknesssuddenlychangesat aroundfewmbar,andbecomeunitybelow100mbar.Thestratospherichazelayerand thetroposphericclouds/hazelayermightbeseparatedbyanaerosolfreegapbetween 1and10mbar.TypeBclouds/haze(toprightpanelinFig. 5-3 )isabroadcloudlayer rangingfrom1mbartofewthousandmbar,anditsopticalthicknessislargerthanunity 107

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atpressurelevelsgreaterthanfewhundredmbar.TypeCclouds/haze(bottomleft panelinFig. 5-3 )issimilartoTypeBclouds/hazeprolewiththemaximumabsorption coefcient Y =1 # 3 at300 # 500mbar.TypeDclouds/haze(bottomrightpanelin Fig. 5-3 )isadeepbroadclouds/hazelayerlocatedintroposphereextendingfrom0.1 mbartofewthousandmbar.Theopticalthicknessincreasesslowlyfrom0.1mbarand becomes0.1atthepressurelevelbetween1marand10mbar;itthenincreasesrapidly withdepthbetween10mbarand100mbar.Nearthetropopause,theopticalthickness becomesunity. Althoughthe 2 minimizationapproachdoesnotshowtherealclouds/haze structureintheatmosphereofSaturn,itstillprovidesinformationaboutthevertical distributionatthelatitudesofinterest.Theresultsofthe 2 minimizationapproachat 27 Sinthesouthernhemispherebasedon2005observationssuggestthattheremay beadeepbroadclouds/hazelayerwithunknownchemicalcompositionthatextends fromthelowerstratosphereatthepressureaboutfewmbartothetropospherewith theopticalthickness & c =1 # 10between100mbarand5000mbar.Apossible opticallythinhazelayermaybelocatedbetween1and10mbaronthetopofthebroad troposphericcloudlayer. 5.4CloudRetrievalResultsandDiscussion AsmentionedinSec. 2.2.4.2 ,thehigherthanexpectedbrightnesstemperatureat latitudeshigherthan70 Sinthesouthernhemispherein2005maybeattributedtothe presenceofcloudsorhazeinthestratosphere.Thelowerthanexpectedbrightness temperatureatmid-andlowlatitudescanbeexplainedbythecloudlayerintheupper troposphere.Inthiswork,weperformthecloudinversionat27 Stoexaminethis assumption. Fig. 5-4 toFig. 5-6 showtheretrievedresultsofdifferentsetsofinitialparameters (peaklocation P ,magnitudeoftheabsorptioncoefcient A ,andtheverticalbroadness W ).Ineachofthesegures,theinitialcloudprolesareshownasthinsolidlines, 108

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andtheretrievedabsorptioncoefcient(leftpanels)andtheretrievedopticalthickness (rightpanels)areshownasthicksolidlines.Aswecanseeinthesegures,anaerosol layerlocatedatuppertropospherebetween10mbarand700mbarisdevelopedduring iterations.Thepeaklocationoftheretrievedcloudstructuremaybelocatedatpressure between20mbarand500mbarasseeninFig. 5-6 .InFig. 5-4 ,afeaturewithasmall absorptioncoefcientisalsodevelopedataround4mbar(bluelines),whichmay indicatethatastratospherichazelayerislocatedatfewmbars. Discussion .Ourretrievedresultsshowthattherearetwotypesofpossible verticaldistributionsofthecloudsandhazeat27 Sin2005.Onepossiblecloud distributioncontainsabroadaerosollayerlocatedbelowthetropopauseat100mbar andextendstodeeperpressureregionatfewthousandmbars.Thisverticaldistribution ofthetroposphericcloud/hazeisconsistentwithpreviousobservations( Karkoschka andTomasko 1993 ; West 1983 ).Theotherpossibleclouddistributionincludesthe troposphericaerosollayerandanopticallythinhazelayerinthestratospherebetween 0.01mbarand10mbar,whichisconsistentwiththeobservationsby Stametal. ( 2001 ) and KarkoschkaandTomasko ( 1993 ). However,theuncertaintiesoftheretrievedclouds/hazeprolesarelarge,asshown inFig. 5-7 ,therefore,theresultscannotbewell-constrained.Theuncertaintiesfor cloud/hazeretrievalscanbeduetothedataqualityissuesdiscussedinSec. 2.2.4.3 in thespectralrangebetween1389cm 1 and1395cm 1 .Wealsonoticedthattheheight oftheretrievedcloudpeakappearstohavesomecorrelationwiththepeaklocationsof theinitialcloudproles,whichshowsthattheretrievedresultsmaybemodel-dependant. AsshowninFig. 5-8 ,whencomparingtheobservedspectrumwiththesynthetic spectraaftertemperatureandclouds/hazeretrievals,onecanseethesynthetic spectrumafterclouds/hazeretrievalcanttheobservedspectrumwithinthenarrow spectralwindowcenteredat1392cm 1 withsmall 2 values.However,thesynthetic spectrumafterclouds/hazeretrievaldoesnotttheobservedspectrumintheneighboring 109

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spectralregionwell.Onepossibleexplanationofthisfailuretottheneighboring spectralregioncanbeduetothelackofinformationoftheethane(C 2 H 6 )absorption coefcientwithinthisspectralrangeintheretrievalcode. 110

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100 1000 0.01 0.1 1 10 Pressure [mbar] test cloud initial guess A retrieved result 100 1000 0.01 0.1 1 10 Pressure [mbar] Cloud absorption coefficient Y test cloud initial guess B retrieved result Figure5-1. Cloudabsorptioncoefcientofthenumericalexperiment. 111

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100 1000 0.01 0.1 1 10 Pressure [mbar] test cloud initial guess A retrieved result 100 1000 0.01 0.1 1 10 Pressure [mbar] Cloud optical thickness test cloud initial guess B retrieved result Figure5-2. Opticalthicknessofthenumericalexperiment. 112

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0.1 1 10 100 1000 0.01 0.1 1 10 Type D Y tau c 0.1 1 10 100 1000 0.01 0.1 1 10 Type B Y tau c 0.1 1 10 100 1000 0.01 0.1 1 10 Pressure [mbar] Absorption coefficient and Optical thickness Type C Y tau c 0.1 1 10 100 1000 0.01 0.1 1 10 Type A Y tau c Figure5-3. Resultsof 2 minimizationapproach. 113

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0.01 0.1 1 10 100 1000 0.001 0.01 0.1 1 10 100 Pressure [mbar] P = 3000 mbar, W = 3 Absorption coefficient A = 0.1 A = 1 0.01 0.1 1 10 100 1000 0.001 0.01 0.1 1 10 100 Optical thickness A = 0.1 A = 1 Figure5-4. Cloudretrievalresults(a). 114

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0.01 0.1 1 10 100 1000 0.001 0.01 0.1 1 10 100 Pressure [mbar] P = 300 mbar, W = 3 Absorption coefficient A = 0.1 A = 1 0.01 0.1 1 10 100 1000 0.001 0.01 0.1 1 10 100 Optical thickness A = 0.1 A = 1 Figure5-5. Cloudretrievalresults(b). 115

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0.01 0.1 1 10 100 1000 0.001 0.01 0.1 1 10 100 Pressure [mbar] P = 30 mbar, W = 3 Absorption coefficient A = 0.1 A = 1 0.01 0.1 1 10 100 1000 0.001 0.01 0.1 1 10 100 Optical thickness A = 0.1 A = 1 Figure5-6. Cloudretrievalresults(c) 116

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0.01 0.1 1 10 100 1000 0.001 0.01 0.1 1 10 100 Pressure [mbar] Absorption Coefficient Y initial guess retrieved cloud profile Figure5-7. Retrievedcloudwithuncertainties. 117

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115 120 125 130 135 140 1320 1340 1360 1380 1400 1420 Temperature [K] Wavenumner [cm -1 ] CIRS observation at 27S retrieved spectrum after T retrieval retrieved spectrum after cloud retrieval Figure5-8. Spectrumoftheretrievedcloud. 118

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CHAPTER6 SUMMARY Thepre-Cassiniknowledgeoftheverticaldistributionsofcloudsandhazeon Saturnisprimarilyderivedfromground-basedandspace-basedobservationsaswell asspacecraftmissionssuchasVoyager1andVoyager2.Thecommoncloudandhaze structuresseeninnumerousstudiesinclude:(a)threecloudlayersatthepressure leveldeeperthan1bar,(b)atropospherichazelayerbetweenthetopammoniaice cloudlayerandthetropopausenear100mbar,and(c)astratospherichazelayeratthe pressurelevelbetween1mbarand100mbar.Inthiswork,weusetheCassini/CIRS mid-infrareddatatoanalyzetheopticalpropertiesofthecloudsandhazeonSaturnto provideanalternativestudyoftheatmosphericstructure. WerstperformthesensitivitystudyoftheMIRMAPdatasetsfrom2005to2008 obtainedduringtheCassiniPrimeMission.Wealsoconstructyearlybrightness temperaturemapstoexaminetheglobalandlatitudinalbrightnesstemperature variationsat1392cm 1 .Thecorrelationofthedataqualityat1392cm 1 andthe calibrationsequencesisalsodiscussedinthisdissertation. Wedeveloptheretrievalalgorithmfortemperateandclouds/hazeinversions.The retrievalalgorithmincludesaforwardmodel,calculationsofthefunctionalderivative matrixanderroranalysis.Themainfunctionoftheforwardmodelistodescribethe physicsoftheproblem.Thecorrelated-kmethodisusedastheforwardmodelto balancetheaccuracyandthecomputationalefciency.Weusearticialcloudstructures totestthevalidationoftheretrievalalgorithmandtoexaminethecorrelationofthe retrievedresultsandtheinitialparameters. 2 minimizationapproachisalsoapplied toobtaininformationofthepossiblepeaklocationandtheopticalpropertiesofthe cloud/hazestructurefortheretrievals. TemperatureRetrievals .Ourretrievedtemperatureprolesinthesouthern hemispherein2005showthat:(a)thestratospherictemperatureatthepressurelevel 119

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between0.3mbarand5mbarisbetween140K-150Kinthelowandmid-latitudes, andthetemperatureisslightlyincreasingtowardtheequator;(b)thestratospheric temperatureelevatesfrommid-latitudestowardthesouthernpolarregion,andthe temperatureatthepolarregionisabout15K-20Kwarmerthanthatattheequator around2mbarpressurelevel;(c)forpressurelevelbelow5mbar,thereisnoobvious latitudinalvariationoftheretrievedtemperature;(d)Thetemperatureattropopausenear 100mbarisbetween88Kand95Kforalllatitudesinthesouthernsummerhemisphere in2005. OurresultsareconsistentwiththetemperaturestructureanalysisofCIRSdataby Flasaretal. ( 2005 )and Fletcheretal. ( 2007 ).Tropospherictemperatureknee( Fletcher etal. 2007 ; Haneletal. 1981 ; 1982 )intheretrievedtemperatureprolesisalso discussedinChapter 4 CloudsandHazeRetrievals .Weuse2005MIRMAPCIRSobservationsat27 S forcloudsandhazeretrievals.Featuresinourresultsshowthat:(a)anopticallythick aerosollayerisdevelopedatthepressurelevelbetween10mbarand700mbar;(b)the peaklocationofthetroposphericaerosollayerislocatedatpressurebetween20mbar and500mbar;(c)apossiblestratospherichazelayerwithsmallopticalthicknessisalso seenatfewmbars. Ourretrievedverticaldistributionofthetropospherichazelayerderivedfrom Cassinimid-infrareddataisconsistentwiththepreviousobservationsby Karkoschka andTomasko ( 1993 )and West ( 1983 ).Theotherpossiblecloud/hazedistribution withatropospherichazelayerandastratospherichazelayerisconsistentwiththe observationsby Stametal. ( 2001 )and KarkoschkaandTomasko ( 1993 ). Discussion .Ourworkprovidestheanalysisoftheverticaldistributionofclouds andhazeinthesouthernsummerhemisphereonSaturnbyusingtheCassini/CIRS mid-infrareddatasets.Thisworkalsoprovidesafoundationforfuturecloudsandhaze researchongasgiantsbyusingmid-infrareddata.Toimproveourunderstandingof 120

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theverticaldistributionofthecloudandhazeprolesonSaturn,severaltaskscan bedoneforfuturereference:(a)Aninclusionofanup-to-dateabsorptioncoefcient ofchemicalcompoundswithinthespectralrangeofinterest,suchasethane(C 2 H 6 ) emissionbetween1300cm 1 and1400cm 1 mayimprovethettingoftheobserved andretrievedspectra;(b)formoreaccuratetemperatureretrievals,informationofother atmosphericproperties,suchastheortho/para-H 2 ratio,isimperative;(c)theCIRSdata releasedinthefuturewithimprovedcalibrationmethodsshouldbeabletodecreasethe uncertaintiesoftheretrievedresultsandprovidebetterresolutionforcloudsandhaze retrievals;(d)datafromdifferentCassiniinstrumentsatdifferentspectralregions(UV, infrared,andvisible)canbetakenintoaccountintheretrievalcodetostudyseasonal andlatitudinalvariationsofclouds/hazeandatmosphericcomposition. 121

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BIOGRAPHICALSKETCH Hsin-JungLinwasborninPingtung,TaiwanandgrewupinsouthernTaiwan.Ze 1 wenttoNationalChiaoTungUniversitymajoringinElectricalandControlEngineering. InsteadofgettingajobasanengineerlikemostNCTUgraduatesdo,Hsin-Jung startedzirPh.DprograminPhysicsattheUniversityofFloridain2006.Afternishing therstyearcourses,zeworkedinLIGO(LaserInterferometerGravitational-Wave Observatory)designingtheMach-Zehnderelectro-opticmodulatorforadvancedLIGO. In2009,Hsin-Jungswitchedtotheeldofplanetarysciences. 1 "Ze"and"zir"aregender-neutralpronouns. 126