ozone depletion, chlorine activation and water vapor...

Ozone depletion, chlorineactivation and water vaporobserved in Spitsbergen

Dissertationzur ErlangungdesGradesDr. rer. nat.derUniversiẗatBremen

vorgelegt vonIngo WohltmannApril 2002

BerichteausdemInstitut für Umweltphysik– Band0herausgegebenvon:

Dr.Georg HeygsterUniversiẗatBremen,FB1, Institut für Umweltphysik,Postfach330440,D-28334BremenURL http://www.iup.physik.uni-bremen.deE-Mail [email protected]

Prüfer: Prof.Dr. KlausKünzi,Prof.Dr. JohnBurrows

c�

2001IngoWohltmann

Contents

1 Physicsand Chemistry of the Atmosphere 131.1 Compositionof theAtmosphere . . . . . . . . . . . . . . . . . . 131.2 Physicsof theAtmosphere . . . . . . . . . . . . . . . . . . . . . 151.3 Dynamicsof theStratosphere. . . . . . . . . . . . . . . . . . . . 181.4 OzoneChemistry . . . . . . . . . . . . . . . . . . . . . . . . . . 211.5 OzoneDistribution . . . . . . . . . . . . . . . . . . . . . . . . . 291.6 ChlorineMonoxideandWaterVapor . . . . . . . . . . . . . . . . 311.7 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2 Instrument 332.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.2 RadiativeTransfer. . . . . . . . . . . . . . . . . . . . . . . . . . 342.3 AbsorptionCoefficients . . . . . . . . . . . . . . . . . . . . . . . 362.4 InstrumentDescription . . . . . . . . . . . . . . . . . . . . . . . 40

2.4.1 QuasiOptics . . . . . . . . . . . . . . . . . . . . . . . . 402.4.2 AntennaandMixer . . . . . . . . . . . . . . . . . . . . . 422.4.3 IntermediateFrequency Chain . . . . . . . . . . . . . . . 442.4.4 AcoustoOpticalSpectrometer. . . . . . . . . . . . . . . 452.4.5 BremenRadiometer . . . . . . . . . . . . . . . . . . . . 45

2.5 MeasurementPrinciple . . . . . . . . . . . . . . . . . . . . . . . 452.5.1 TotalpowerMethod . . . . . . . . . . . . . . . . . . . . . 462.5.2 ReferenceBeamMethod . . . . . . . . . . . . . . . . . . 47

3 Retrieval 493.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.2 OptimalEstimation . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2.1 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . 513.2.2 Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.2.3 Nonlinearities. . . . . . . . . . . . . . . . . . . . . . . . 54

3.3 Retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3

3.3.1 GeneralFeatures . . . . . . . . . . . . . . . . . . . . . . 553.3.2 ForwardModelFeatures. . . . . . . . . . . . . . . . . . 593.3.3 Moist WeatherConditions . . . . . . . . . . . . . . . . . 72

3.4 WaterVapor, Spitsbergen . . . . . . . . . . . . . . . . . . . . . . 733.4.1 A SimpleApproach. . . . . . . . . . . . . . . . . . . . . 733.4.2 LogarithmicRetrieval . . . . . . . . . . . . . . . . . . . 743.4.3 ReferenceBeamSpectra . . . . . . . . . . . . . . . . . . 753.4.4 ContinuaandLine Wings . . . . . . . . . . . . . . . . . 773.4.5 Frequency Shift andSelf Broadening . . . . . . . . . . . 78

3.A CovarianceMatrices . . . . . . . . . . . . . . . . . . . . . . . . 803.B LogarithmicDistribution . . . . . . . . . . . . . . . . . . . . . . 80

4 OzoneDepletion 834.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.4 MeteorologicalSituation . . . . . . . . . . . . . . . . . . . . . . 894.5 OzoneDepletionin 1999/2000 . . . . . . . . . . . . . . . . . . . 944.6 Comparisonwith OtherTechniques . . . . . . . . . . . . . . . . 100

4.6.1 Match . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.6.2 TracerMeasurements. . . . . . . . . . . . . . . . . . . . 1014.6.3 Vortex AveragedMeasurements. . . . . . . . . . . . . . 1044.6.4 SLIMCAT . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.7 Accuracy of theHeatingRates . . . . . . . . . . . . . . . . . . . 1084.8 TheGeneralPicture . . . . . . . . . . . . . . . . . . . . . . . . . 1124.9 ChlorineActivation . . . . . . . . . . . . . . . . . . . . . . . . . 1154.10 Denitrification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1234.11 Effecton OzoneLoss . . . . . . . . . . . . . . . . . . . . . . . . 1254.12 OzoneDepletionin 2000/2001 . . . . . . . . . . . . . . . . . . . 1274.A Integrationof LossRates . . . . . . . . . . . . . . . . . . . . . . 1314.B DoubleConvolution . . . . . . . . . . . . . . . . . . . . . . . . . 1334.C ErrorAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1334.D Convolutionof IndependentMeasurements. . . . . . . . . . . . 135

5 Water Vapor Columns 1375.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1375.2 Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1375.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1385.4 Correction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1405.5 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Used Publications

Partsof this thesiswerepublishedin� Klein, U., Wohltmann,I., Lindner, K. andKünzi, K. F.: Ozonedepletionand chlorine activation in the Arctic winter 1999/2000observed in Ny-Ålesund.J. Geophys.Res., 107, accepted,2002.

5

Abstract

This work discussesmeasurementsof the groundbasedmicrowave Radiometerfor AtmosphericMeasurements(RAM), theretrieval of desireddataproductsandtheir interpretation.The radiometeris operatedat the Arctic stationof the Net-work for theDetectionof StratosphericChange(NDSC)atNy-Ålesund,Spitsber-gen(78.9� N, 11.9� E). It measureswatervaporat22GHz, ozoneat142GHzandchlorinemonoxideat 204GHz.

Thefirst partof thiswork concentratesonthedataretrieval. A summaryof themostrecentstatusof the retrieval softwareis given asa referenceandto reflectsomenew additions. A specialfocus lies on the water vapor retrieval, whichprovedto beunexpectedlydifficult to implement.

The secondpart dealswith the determinationof ozoneloss rates,chlorineactivation anddenitrification. A methodto determineloss ratesfrom the mea-surementsof theRAM hasbeendevelopedandimprovedover thelastfour years.Here,ozonelosscalculationsfor the winters1999/2000and2000/2001arepre-sented,accompaniedby a comparisonto other techniques,a mathematicalex-aminationof themethodandan error analysis,including theeffectsof differentdiabaticheatingrates,mixing, thedefinitionof thevortex edge,altituderesolutionandotheraspects.

Measurementsof chlorinemonoxide,denitrificationandreservoir gasesarepresentedand examinedin the context of the current understandingof ozonechemistry. It is shown by modelcomparisonsthatthegeneralaspectsof chemistryseemto bewell understood.It is alsopointedthatthereremainsomeconsiderableuncertaintiesin measurementsaswell asin themodelassumptions.

Thethird partexaminesthepossibilitiesof retrieving troposphericwatervaporcolumnsfrom themeasurementsof theradiometer. Whenthetroposphericwatervaporbiasis measuredattwo differentfrequencies,thecalculationof thecolumnsis straightforwardandanestablishedmethod.Thestudyhereconcentrateson theeffectsof precipitationandcloudsandpossibilitiesto correcttheoccurringerrors.

7

Intr oduction

Microwave radiometersbuilt in Bremen,Germany, have beenmeasuringstrato-spherictracegasesfor almosta decadenow. Looking back,a wealthof measure-mentsandscientific resultshasresultedfrom our researchactivity. First ozonemeasurementshavealreadybeenconductedin 1992,andcontinuousobservationsbeganin 1994in Ny-Ålesund,Spitsbergen(79� N, 12� E). In thefollowing years,moreandmoreinstrumentshavebeenadded.In themoment,ozoneprofiles,chlo-rinemonoxideprofiles,troposphericwatervaporcolumnsandstratosphericwatervaporprofilesaremeasured.Ny-Ålesundis partof theprimaryArctic stationoftheNetwork for theDetectionof StratosphericChange(NDSC),wheretheinstru-mentsareoperatedin cooperationwith theAlfred WegenerInstituteof PolarandMarineResearch(AWI) in Potsdam,Germany, andtheInstituteof EnvironmentalPhysics(IUP) in Bremen.Main goalof theNDSCis theidentificationof changesin the ozonelayer andthe examinationof their causes.Therefore,a continuousseriesof ozonemeasurementshasbeenrecordedat Ny-Ålesundandusedto inferozonedepletion. Equally relevant are the measurementsof chlorinemonoxide,which is an importantspeciesin the chemistryof ozonedepletionand can beusedto testtheunderstandingof theunderlyingchemicalmechanisms.Chlorinemonoxideis obtainedby only half adozenof instrumentsin theArctic, with verylimited spatialandtemporalcoverage,makingobservationsveryvaluable.A sim-ilar situationexists for watervapor, which is importantfor the radiationbalancein thestratosphereandthetrendin ozonedepletion.

Thestoryis continuedwith new radiometersatBremen(53� N, 8� E),Mérida,Venezuela(8� N, 71� W), andSummit,Greenland(72� N, 38� W). Theradiometerin Bremenis measuringozoneatmid latitudessince1999,while theinstrumentinVenezuelawill beoneof thefirst radiometersmeasuringtracegasesin thetropicsandis locatedin morethan4500m altitudeto reducetheinfluenceof watervapor.Theextremelydry locationof Summitin theArctic, situatedin morethan3000maltitude,is ideally suitedfor theobservationof rarelymeasuredspeciesthatonlyshow upathigh frequencies,wheretheatmosphereis nearlyopaqueunderhumidconditions.For example,thefirst continuousmeasurementsof N2O andHNO3 intheArctic will becarriedoutat Summit.

9

Ny−AlesundNy−Alesund

BremenBremen

MeridaMerida

SummitSummit

Microwaveradiometersmeasurethethermallyinducedradiationof atmosphe-ric tracegasesanddeduceprofile informationfrom thepressurebroadenedformof theemissionlines. A greatadvantageto otherinstrumentsis thepossibility tomeasurein thepolarnight andthehigh temporalresolutionof themeasurements.Theinstrumentsarealsoalmostindependentof weatherconditions.Hence,acon-tinuousmeasurementseriesfor ozoneandwatervaporandregular observationsof chlorine monoxideprovide the opportunityof long term trend analysesandcontinuingobservationsof Arctic ozoneloss.

Purposeof this work is the retrieval andinterpretationof the numerousdataproductsof theradiometers,with aspecialfocusonozonedepletion.Thedetermi-nationof anthropogenicozonedepletionhasbeena key topic in atmosphericsci-encesin thelastdecade.Thisdevelopmentwasinitiatedin 1985,whenFarmanetal. discovereda strongozonedeficit in thesouthernpolarregion in spring,whichwasapparentlycausedby anthropogenicinfluences.In thenineties,asimilarphe-nomenoncouldalsobeobservedin theArctic. In thefollowing, thepolitical andpublic interestinducedby the harmful effectsof increasingultraviolet radiationandtheimpactof ozoneon theclimatechangecatalyzeda tremendousamountofscientificresearchactivity. In an unprecedentedevent in environmentalpolitics,this ledto aworldwidebanonchlorofluorocarbons,whichweremaderesponsiblefor theozonedecline.A detailedoutlineof thehistoryof ozonedepletionis givenin thefirst chapterof this thesis,which leadsusto a summaryof thecontentsofthis work.

Thebasicprinciplesof stratosphericphysicsandchemistrywill beexplainedin the first chapter, while the secondintroductorychaptercontainsa descriptionof the instrumentand the fundamentalsof radiative transfer. The third chapter

dealswith the retrieval of desireddataproductsfrom the measuredspectra. Asummaryof themostrecentstatusof theretrieval softwareis givenasareferenceand to reflect somenew additionsnot publisheduntil yet. Specialattentionisgiven to the new watervaporretrieval, a speciesthat proved to be unexpectedlydifficult to implement.Althoughnovalidatedprofilescouldbeobtainedyet,somepromisingdevelopmentsareshown. The detailedreview of the physicalmodelandof the changesin the retrieval codehopefully will lay the foundationfor asuccessfulretrieval in thefuture.Thedevelopmentof anew retrieval for theozoneradiometerin Bremenandthechlorinemonoxideradiometerin Spitsbergenshallalsobementionedhere.

Thefourth chapterpresentscalculationsof ozonedepletionandexaminesthechemistryof ozoneloss. Countlessstudieshave beencarriedout aiming at abetterunderstandingof ozonedepletionover the last few years. Examplesarethe EASOE (1991/1992)and SESAME (1994/1995)campaignsand especiallythe American-Europeanjoint effort SOLVE/THESEOin the winter 1999/2000,which is presentedherein detail.A wide varietyof differenttechniqueshasbeendevelopedto determinateozonelossratesin the past. Many of themhave beenemployedduringtheSOLVE/THESEOcampaign,givinganexcellentopportunityto comparedifferenttechniquesandto assesstheir errors. A methodfor thede-terminationof ozonelossratesfrom themeasurementsof theozoneradiometerinSpitsbergenis describedandappliedto thedatafrom thewinters1999/2000and2000/2001.Cumulativelossesof 1 � 2 � 0 � 4ppmand0 � 4 � 0 � 3ppmareinferredforthe two winters. The agreementbetweentheseresultsandthe findingsof othermethodsis shown to begood,consideringthelargeuncertaintiesof all techniques.Sincea detailederroranalysiswasmissingsofar for our method,it is conductedin additionto thepracticalcomparison.Effectsof altituderesolution,thechoiceof theobservedperiod,theinfluenceof thevortex edgedefinition,differentheat-ing ratesor mixing andprincipaldifferencesin theseveralmethodsarediscussed.Furthermore,a mathematicalexaminationof themethodis performed,leadingtotheintroductionof apassiveprofile in theozonedepletioncalculations.

Thecomputationof ozonelossrateswouldnotbecompletewithoutaphysicalinterpretationof the data. Measurementsof chlorinemonoxide,reservoir gases,nitratespeciesanddenitrificationareshown to develop a chemicalscenarioforthewinter. Resultsarecomparedto theSLIMCAT model,whichencompassesthecurrentknowledgeof stratosphericphysicsandchemistry(asfar ascomputation-ally possible),anddiscrepanciesarediscussed.Especially, differencesin chlorineactivationareobserved,which areattributedto uncertaintiesin thedenitrificationschemeandtheformationmechanismfor stratosphericcloudsin themodel. Thesurprisinglygoodagreementof theozonelossratesof themeasurementsandthemodelis alsoexamined. It is shown that the generalaspectsof ozonedepletionarequalitatively well understood,but that thereremainsomequantitative uncer-

tainties.Thelastchapterexaminesthepossibilitiesof retrieving watervaporandliquid watercolumnsfrom the radiometermeasurements.Sincethe radiometerswerenot explicitly built to measurethis quantities,this is a nice additionto thevariety of our measurements.The focus herelies on the effectsof cloudsandprecipitationandmethodsof correctingoccurringerrors.Finally, thework is con-cludedwith asummaryof all results.

In hopefor apleasantreading,IngoWohltmann

1 Physics and Chemistr y of theAtmosphere

1.1 Composition of the Atmosphere

Theatmosphereof theearthformedlong agofrom gasesescapingfrom theinte-rior of the earthandthe biosphere.It is composedmainly of nitrogen(78.1%),oxygen(20.9%)andsomenoblegases(0.9%). The remainderconsistsof sev-eral tracegases.Themoststriking featureof theatmosphereis thesharpdropofpressurewith altitude.It canbeexplainedby thehydrostaticequilibriumbetweengravity andthepressuregradient

∂p� ∂z �� ρg (1.1)wherep is pressure,z is altitude,ρ is thedensityof air andg is thegravitationalacceleration.In regardto thepressure,theidealgaslaw states

p � ρRT� mmol (1.2)whereT is thethermodynamictemperature,R � 8 � 31Jmol 1K 1 is theuniversalgasconstantandmmol is themassof NA � 6 � 022 1023 molecules.Combinationof Equation1.1and1.2yieldsthebarometriclaw

p � z�� p0exp �� z� H � (1.3)undertheassumptionthatT is constant.p0 is thereferencepressureat sealevel,which is usuallysetto 1013hPa. ThepressurescaleheightH � RT �� mmolg� hasavalueof about7 km.

The atmospherecan be divided in several layersdistinguishedby differentphysicalproperties,seeFigure1.1.Thetroposphereis thelowermostlayer, markedby a negative vertical temperaturegradientdueto adiabaticmotions,which willbe explainedbelow. Most of the weatherphenomenatake placein the tropo-spheredue to the dynamically imbalancedsituationconnectedwith a negative

13

14 1 Physics and Chemistry of the Atmosphere

180� 200� 220 240 260� 280� 300�Temperature [K]�0

20

40

60

80

100

Alti

tude

[km

]

Troposphere� TropopauseStratosphere

Stratopause�MesosphereMesopause

Thermosphere�

Figure1.1: Layersof the atmosphere.The temperatureprofile is typical of a subarcticwinteratmosphere.

temperaturegradient.Thetropospherealreadycontainsmorethan50%of all airmolecules.We will focuson the next layer of the atmosphere,the stratosphere,extending from roughly 8 km to 50 km in the polar winter. The stratosphereis marked by a positive temperaturegradientcausedby diabaticheating,whichleadsin turn to a dynamicallystablesituationwith low verticalwind speeds.Thestratosphereis dynamicallyandchemicallyisolatedfrom thetropospherethroughthetropopause(definedby theWorld MeteorologicalOrganizationasthealtitudewherethetemperaturelapseratefirst decreasesbelow 2 K � km in a 2 km altituderange). Furtherlayersarethe mesospherewith a negative temperaturegradientandthevery hot thermosphere.Thelayersfrom the troposphereup to themeso-sphereform thehomosphere,wheregasesarein thermalequilibrium.

Tracegasesaregaseswhich arehighly variablein time andspace.Althoughtheir amountscanbevery low, they usuallyhave agreatimpacton thephysicsoftheatmosphere.Their abundancecanbemeasuredin severalways.Numberden-sity givesthenumberof moleculespervolume. Volumemixing ratio is theratioof thenumberof moleculesof theobservedspeciesto thenumberof moleculesof

1.2 Physics of the Atmosphere 15

all species.It canbecalculatedfrom thenumberdensityn of thegasby

x � nkBT � p (1.4)wherekB � 1 � 38 10 23 J� K is Boltzmann’s constant. It is often measuredinpercent,partspermillion (ppm)or partsperbillion (ppb). Sincevolumemixingratiosareconservedundermovements,they arenormallyusedin mostanalyses.Finally, the columnof a tracegasis given by the vertical integral of the num-ber density. Ozonecolumnis often measuredin DobsonUnits, where1 DU isgivenby 2 � 69 1016 molecules� cm2, correspondingto anozonelayerof 0.01mmthicknessatseapressure.Ozonecolumnis importantfor theamountof ultravioletradiationreachingthesurfaceof theearth.

1.2 Physics of the Atmosphere

Generalaspectsof the physicsof the atmospherewill not be repeatedhere,be-causethey canbefoundin numeroustext books.Instead,we will concentrateonsomeconceptsusedfrequentlyin this thesis.

At first, wewill introducetheconceptof anair parcel.An air parcelis definedasanentityconsistingof ever thesameair moleculesmoving aroundin theatmo-sphere.If somepropertyx of theparcel,like its velocity or pressure,is changedlocally for an observer moving with the parcel(Lagrangianviewpoint) and thechangeis givenby ∂x� ∂t, thechangefor anobserver standingat a fixedposition(Eulerianviewpoint) is

DxDt

� ∂x∂t

� uacosϑ

∂x∂ϕ

� va

∂x∂ϑ

�w

∂x∂z

(1.5)

in sphericalcoordinates.u is thezonalwind here,v is themeridionalwind, w istheverticalwind, ϑ is latitude,ϕ is longitudeanda is theradiusof theearth.Thederivative D � Dt is calledthe substantive derivative. Note that by definition, themixing ratio of anair parcelcannotbechanged.

Next, wewill establishausefulcoordinatesystemthatsimplifiesthefollowingdiscussions.It consistsof potentialtemperatureinsteadof altitudeandpotentialvorticity insteadof horizontalcoordinates.A thermodynamicprocesswithout thesupply of externalheatis calledadiabatic. In the stratosphere,most processescanbeconsideredadiabaticon thetimescaleof a few days.For longertimescalesradiative heatinghasto be considered.Potentialtemperatureis a quantityof anair parcelthatremainsconstantunderadiabaticconditions.It is definedas

Θ � T � p0p � 2� 7 (1.6)


wherep0 is anarbitraryreferencepressureandT andp aretemperatureandpres-sureof the air parcel. Θ is the temperaturethe air parcelwould have if it weremovedadiabaticallyto thereferencepressurelevel. Theconservationof potentialtemperatureexpressesthe fact that increasingpressureincreasesthe temperatureof an thermally isolatedair parceldue to the transformationof work into heat.Sincepotentialtemperaturenormally increasesmonotonicallywith altitudeanddoesnot vary very rapidly in horizontaldirection, it canbe usedinsteadof thez coordinate,cancelingany vertical adiabaticmovements.Surfacesof constantpotentialtemperaturearecalled isentropes.In the lower stratosphere,25 K po-tential temperaturecorrespondto about1 km altitudedifference,with the475Kisentropiclevel situatedaround20km altitude.On thescaleof a few days,air inthestratospheremovesonly on isentropicsurfaces.

It canbe shown that an air parcelthat is moved adiabaticallyandverticallyfrom its original position will continueits movementwhen the actualverticaltemperaturedecreaseis higherthanthediabatictemperaturedecrease(instabilityagainstconvection)andwill beforcedbackto its originalpositionwhentheactualtemperaturedecreaseis lower thanthe adiabaticdecreaseor thereis a tempera-tureincrease(stabilityagainstconvection).Thisexplainsthedynamicdifferencesbetweentheconvective troposphereandthestratosphere.

Potentialvorticity is a quantityconservedunderadiabaticandreversiblecon-ditions andthereforecanbe usedasa tracerfor air masses.Its advantageoverchemicaltracersis the fact that it canbe calculatedfrom wind, temperatureandpressure,which are easily available for the whole globe. Potentialvorticity istheproductof thethicknessof the isentropesandthecurl of thewind field in anabsolutecoordinatesystem

P � g∂Θ∂p

� ζp � f � (1.7)whereg is the gravitational acceleration,∂Θ � ∂p is the changeof potentialtem-peraturewith pressureandthe last term is the curl of the wind field, alsocalledabsolutevorticity. Theabsolutevorticity is composedof theplanetaryvorticity fandthe relative vorticity ζp of thewind field. f is givenby 2 �Ω � sinϑ, whereΩis theangularvelocity of theearth.ζp is thecurl of thewind field relative to theearthsurface,which is givenby

ζp � 1acosϑ � ∂v∂ϕ � ∂ � ucosϑ �∂ϑ � (1.8)Theconservationof potentialvorticity is connectedwith thefact thattheangularmomentumof arotatingair massmustbeconserved.If theair massis stretchedinverticaldirection,theangularvelocity mustincrease.Potentialvorticity is mea-suredin unitsof PVU � 10 6 K m2kg 1s 1. It decreasesfrom thecenterto the

1.2 Physics of the Atmosphere 17

edgesof the low pressureareanormally found in the Arctic winter stratosphere(whichwewill comebackto soon)andthereforecanbeusedasahorizontalcoor-dinate.Sometimes,equivalentlatitudeis usedasacoordinateinsteadof potentialvorticity. Theequivalentlatitudeof a potentialvorticity contouris definedasthelatitudeit wouldhave if theenclosedareawouldbecircularandcenteredover thepole. Equivalentlatitudehastheadvantageof beinglessinfluencedby shorttimefluctuationsin theabsolutevaluesof potentialvorticity.

Finally, let usalsohaveashortlook ontheequationsgoverningthedynamics.In equilibrium, the horizontalwind is determinedby the balanceof the Coriolisforcewith thehorizontalpressuregradient

f u �� 1a

∂Z∂ϑ

(1.9)

f v � 1acosϑ

∂Z∂ϕ

(1.10)

whereZ is the geopotentialaltitude of a given pressuresurface. Wind blowsparallelto theisobaresin equilibrium,sothat thepressuregradientis conserved,which is called geostrophicwind. Combinationof the barometriclaw and theequationsfor thehorizontalwind yields

f∂u∂z

�� RaH

∂T∂ϑ

(1.11)

f∂v∂z

� RaHcosϑ

∂T∂ϕ

(1.12)

Thesearetheequationsof thethermalwind, connectinga horizontaltemperaturegradientwith anincreasein wind speedwith altitude.Finally, theverticalwind isdrivenby thediabaticheatingrateQ, givenasthediabaticallyinducedtemperaturechangepertime

w � Q � ∂T∂t

(1.13)

andtheconservationof massis describedby thecontinuityequation

1acosϑ

�∂u∂ϕ

� ∂ � vcosϑ �∂ϑ � � 1ρ0 ∂ � ρ0w�∂z � 0 (1.14)

with ρ0 � exp �� z� H � beingameanair density.


Figure1.2: Brewer-Dobsoncirculation.Thethin horizontallinesdenoteisentropiclevels.Seethetext for adetailedexplanation.Adaptedfrom [Holton etal., 1995]

1.3 Dynamics of the Stratosphere

Comparedto the troposphere,thedynamicsof thestratospherearequitesimple.Due to the positive temperaturegradientin the stratosphere,convection is notlikely. The temperaturegradientis causedby the absorptionof sunlightby theozonelayer, which is virtually identicalin extentwith thestratosphere.Thever-tical movementsin the stratosphere,which arevery slow (some10 m per day),areconnectedto diabaticprocesses,which in turn arecausedby adiabaticmove-mentsinducedby planetarywaves.In thetropicsthereis anupwellingmovementanddiabaticheatingin the sunlight,while at the polesthereis an downwellingmovementanddiabaticcoolingwhich is especiallyprominentat thewinter polein the dark polar night. At the sunlit summerpole, movementis virtually non-existent. For continuity reasonsa polewardmotion of air developsin thewinterhemisphere.This meanmeridionalmovementis calledBrewer-Dobsoncircula-tion. A sketchof this circulationis givenin Figure1.2. Theoverturningtime forthecirculationcell is about5 years.

We will turn to thehorizontalcirculationnow. Thethermalgradientfrom theequatorto thewinterpoleimpliestheformationof a low pressureareain thepolar

1.3 Dynamics of the Stratosphere 19

Polar vortex at 475 K February 17, 2000

0E

0

10

20

30

40

50

60

Pot

entia

l vor

ticity

[PV

U]

Figure1.3: Polarvortex at February17, 2000at 475K. Potentialvorticity asa tracershows the distinction betweeninner andouter vortex air masses.The inner andoutervortex edgeis markedby thick lines.Thepositionof BremenandNy-Ålesundis markedby dots.A minor warmingdisturbstheshapeandpositionof thevortex.

region,calledthepolarvortex. At thevortex edge,abandof strongwesterlywindscanbefoundaccordingto theequationsof thethermalwind, which is calledthepolarnight jet. In theinnervortex air is virtually isolatedfrom air massesoutsidethevortex dueto thenearlygeostrophicair motionat theedge.An examplefortheappearanceof thepolarvortex canbefoundin Figures1.3and1.4.

Interestingly, theBrewer-Dobsoncirculationis not causedby radiationin theendand it is not even purely diabatic. In the so calledsurf zone,which is sit-uatedbetweenthe polar vortex andthe tropics,air is turbulently mixed in hori-zontaldirectionby planetarywavespropagatingvertically from the troposphere.Thewave breakingof theseeddiestakesmomentumout of themovementsin thestratosphereandleadsto a decelerationof thewesterlywindsprominentin thesealtitudes.In turn this leadsto a dynamicallyandthermodynamicallyimbalancedsituation. Air from the mid latitudes,which is too warm for thepoles,is drawnpolewardsincedynamicforcesarenot balancedwith theCoriolis forceanymore.It begins to move downwardfor continuity reasons,andwarmsup adiabatically,pushingtemperaturesabovetheirradiativevaluesanddriving thediabaticcooling.Strongdownwelling is connectedwith a weakvortex, high stratospherictemper-aturesin polar regions and high wave activity and vice versa. Becauseof the



0E

190/41.0

195/44.9

200/49.1

205/53.5

210/58.2

215/63.2

220/68.5

225/74.1

230/80.0

Tem

pera

ture

[K] /

Pre

ssur

e [h

Pa]


0E

0

10

20

30

40

50

60

Win

d sp

eed

[m/s

]

Figure1.4: Temperature,pressureandwind for the polar vortex at February17, 2000.Left panel: Temperatureandpressure,which hasthesameisolinesat isentropes.Rightpanel: Wind speed(contours)andwind direction(arrows). The inner andoutervortexedgeis marked by thick lines. The positionof BremenandNy-Ålesundis marked bydots.

distributionof land,seaandmountainsthat influencewave activity, theAntarcticvortex is usuallymuchmorestablethantheArctic vortex.

During particularlystrongwave breakingeventsthe momentumtaken fromthe vortex canleadto a breakdown of the wind system.This is calleda suddenstratosphericwarming,becauseit is associatedwith a prominentrise in temper-atureinsidethevortex. Often, thepolarvortex canrecover from a warmingandbuild upagain.But in spring,whensunlightcomesback,thevortex splitsupor isdestroyedentirely.

It is oftendiscussedwhatprocessesarecausallyconnectedwith theformation,stabilityanddurationof thevortex andthecorrespondinglow temperatures,sincea stableand cold vortex is connectedwith high ozonedepletion. Suggestionsincludecorrelationswith the negative radiative forcing due to increasingwatervaporanddecreasingozone,wave activity of planetarywavesin thetroposphere,the Quasi-BiennalOscillationof the tropical stratospherewinds in east-westdi-rection(QBO), the North-Atlantic Oscillation(NAO) andmany more. It seemscertainthat thereis a connectionbetweentemperaturesandwave activity [New-man et al., 2001], sinceMarch vortex temperaturesand Januarywave-inducedheatfluxesarehighly correlated.Waveactivity maybeweakeneddueto couplingto the greenhouseeffect, which could obstructthe propagationof troposphericwaves in the stratosphere.In turn, this could lead to a colderandmore stablevortex in thefuture.

1.4 Ozone Chemistry 21

1.4 Ozone Chemistr y

Althoughozonehasa mixing ratio of only a few ppm,it is a very importanttracegas. The absorptionof harmful ultraviolet radiationin the stratospheremakeslife on earthjust possible,andthestratospherewould not evenexist without thediabaticheatingof theozonelayer. Ozoneformsby thephotolysisof molecularoxygen:

O2�

hν � O � O λ � 242nm (1.15a)O�

O2M� O3 (1.15b)

whereM is anair moleculeneededfor theconservationof momentum.Similarly,it is destroyedby photolysisat greaterwavelengths:

O3�

hν � O2 � O � 3P� λ � 1100nm (1.16a)O3

�hν � O2 � O � 1D � λ � 310nm (1.16b)

The excitedstateO � 1D � canrelax to the groundstateO � 3P� by collision. Sinceozoneandoxygenatomsrapidlyinterchangewith eachother, thelifetime of ozoneitself is short,while only the following reactionsproducea net lossin the long-livedoddoxygen,thesumof O andO3:

O�

O3 � O2 � O2 (1.17a)O�

OM� O2 (1.17b)

Reactions1.15to 1.17form theChapmancycle,which waspostulatedin [Chap-man,1930]. It leadsto an equilibrium statefor ozonemixing ratiosdependingon altitudeandseason.It turnedoutquickly thattheChapmanreactionsoveresti-matedtheozonecontentof theatmosphere.This inconsistency wassolvedby thediscoveryof catalyticreactionsof theform

X�

O3 � XO � O2 (1.18a)XO

�O � X � O2 (1.18b)

O�

O3 � O2 � O2 (1.18c)The radicalX canbe recycled many timeswithout beingdestroyed. Thus,evensmall amountsof the radicalscandestroy muchlargerabundancesof ozonedueto the catalyticnatureof the cycles. The mostimportantcatalysatorsX areOH[BatesandNicolet,1950],NO [Crutzen,1970],Cl [StolarskiandCicerone,1974]


andBr [Wofsy et al., 1975]. The mostsignificantnaturalcatalyticcycle in thelowerandmiddlestratosphereis theNO cycle,while theOH cycle is dominatingin theupperstratosphere.Themainanthropogeniccycle is theCl cycle.

Sourcegasesfor theradicalsareN2O for NO andH2O andCH4 for OH. Thesesourcegasesaremainly of troposphericorigin andarepartially photolysedin thestratosphere.N2O andthe sumof H2O andCH4 areonly minorly changedbythe productionof the radicalsin the lower polar stratosphereandcan thereforebe usedas tracers,which we will take advantageof later. Sourcegasesfor ClandBr areman-madechlorofluorocarbons.Chlorofluorocarbonsaredecomposedphotochemicallyin thestratosphereandquickly form gaseslike HCl or HF. In-terestingly, fluor playsno role in ozonedepletion,sinceHF is verystableandcanalsobeusedasa tracertherefore.

The catalyticcyclesare deceleratedby reactionsof the radicalswith them-selves,for example:

ClO�

NO2M� ClONO2 (1.19a)

BrO�

NO2M� BrONO2 (1.19b)

NO2�

OHM� HNO3 (1.19c)

Cl�

HO2 � HCl � O2 (1.19d)Cl

�CH4 � HCl � CH3 (1.19e)

ClO�

HO2 � HOCl � O2 (1.19f)ClO

�NO � Cl � NO2 (1.19g)

ThechemicallyinactivegasesClONO2 andHCl producedby someof thesereac-tionsarecalledreservoir gases,sincethey storetheozonedestroying radicalCl.Otherproductsthatwe will show to play a role soonareHNO3 andthereactiveHOCl.

In 1985,Farmanetal. discoveredastrongozonedeficit in thesouthernvortexin spring(Figure1.5,upperpanel).It eventurnedout thatthis deficit hadexistedunnoticedsincethe mid-seventies.The word ozonehole wascoinedquickly bythepressandcatalyzeda vivid public discussionabouttheharmfuleffectsof theultraviolet radiationnormallyabsorbedby ozone.Thestronglossof ozonein thepolar springthat causesthe Antarctic ozonehole cannotbe explainedsolely bycatalyticreactions.It is a matterof factnow, thattheozoneis destroyedwith thehelp of heterogenousreactionssettingfree chlorinefrom the reservoir gasesonthesurfaceof polarstratosphericcloudsthatform in thepolarnight.

Firstsuggestionsfor thesemechanismswerealreadypublishedayearlater, forexampleby CrutzenandArnold [1986]or Solomonetal. [1986]. They blamedthe


1950� 1960 1970 1980� 1990 2000Year!100

150

200

250

300

350

400T

otal

ozo

ne [D

U]"

Figure1.5: Decreaseof ozonecolumnsin the lastdecades.Upperpanel: Averagetotalozonecolumnsfor OctoberoverHalley Bay, Antarctica.Dotsadaptedfrom Farmanetal.[1985], diamondsfrom JonesandShanklin[1995] andvon König [2001]. Lower panel:Averagetotal ozonecolumnsbetween63# and90# N for Marchfrom differentsatellites.Adaptedfrom Newmanetal. [1997,2002].


anthropogenicallyproducedchlorofluorocarbons,whichdecomposeinto reservoirgasesandfurtherinto radicalsthroughheterogenousreactionsin thestratosphere,for destroying theozonelayer. Pioneeringwork in thisdirectionhadalreadybeendonein the seventiesby Molina andRowland [1974]. The productionof chlo-rofluorocarbonswasstoppedthereuponby internationalagreementdocumentedin the MontrealProtocol[1987] andits adjustments.However, dueto the slowtransportin the stratosphereand the stability of chlorofluorocarbonsin the tro-posphere,chlorineloadingis expectedto reachits peakjust around2000. Addi-tionally, dueto horizontalmixing in thetroposphereandtheBrewer-Dobsoncir-culation,chlorofluorocarbonsandtheirproductsareveryuniformly distributedinthestratosphere.Ironically, chlorofluorocarbonswereusedwidely in theindustry(e.g. in refrigeratorsor asaerosolpropellants),just becausethey werechemicalinert andhadno harmful effectson theenvironmentandhealth. In the nineties,a phenomenonsimilar to theozonehole,but lesspronounced,couldalsobeob-served in theArctic [Newmanet al., 1997]. As canbeseenin Figure1.5, lowerpanel,theamountof ozonelossis highly dependenton thetemperaturesandvor-tex developmenthereandoftenmaskedby diabaticdescent.

The processesleadingto the ozoneholewill be discussedin somemorede-tail now. During the polar night, whenthe polar vortex forms, the influx of airmassesfrom lower latitudesis suppressed,andthe lack of sunlightleadsto verylow temperaturesin thelowerpolarstratosphere.Polarstratosphericclouds(alsocalled PSCs)form hereundercertaintemperatureand pressureconditionsandmixing ratiosof their constituents.Typically, they canbe found between16 to27 km, wherethey aregeneratedfrom watervapor, gaseousnitric acid and thebackgroundsulfateaerosol.Nitric acid is mainly producedby reaction1.19c,sothata decelerationof thenaturalcatalyticcyclesis connectedwith a accelerationin theheterogenouschemistry. At athresholdtemperatureof approximately195Kat the475K isentropiclevel, polarstratosphericcloudsof TypeIa canform, con-sistingof solid HNO3 $ 3H2O (nitric acid trihydrateor NAT) particleswith radiiof about1 µm. Solid particlescanalsobe formedby sulphuricacid tetrahydrate(SAT) below 215K, but theseparticlesplaynorole in chlorineactivation.TypeIbcloudsconsistof liquid ternaryH2O� HNO3 � H2SO4 solutions(STS)andform attemperaturesof about191K. Below 188K, polarstratosphericcloudsof TypeIIthatarecomposedof iceparticleswith radii of about10µm canexist.

Thereis still somedebateregardingtheformationandcompositionof strato-sphericclouds. An overview of themostrecentunderstandingis givenby Koopet al. [1997],seealsoFigure1.6.A typical formationpathis theuptakeof HNO3by liquid H2SO4 particlesto form STSparticles(path1 � 3 � 5). Ice particlescan form subsequentlyfrom the STS particles,coveredby NAT, SAT or a liq-uid STScoating(path7 � 9 � 10). Solid NAT particlescannormallyonly formthroughco-condensedNAT oniceparticles(path14or 12 � 25). Theassumption


% &' (

) *

+ , - %/.%0% %1&%/' % (

%1) % *% ,

&0&& (

&0)& +

243/57698;:=@?243/57698;:=A?243/57698B:=@? 5AC4D

E9C4D5AC9D24EF6HG0:=A?293157698B:=A? E4C9D243/5I6J8;:=A?

KMLON29EP6 G :=A?243/57698;:=@? KMLONE9C4D243/57698B:=@? KMLONE9C4D5AC9D

QSROT;UWV &A%1)YXQIZST;UWV % - )�X

QI[ \^]V % ,0, XFigure 1.6: Formationof polar stratosphericclouds. Arrows show possibleformationpaths.Dashedpathsareonly possibleunderspecialcircumstances.Adaptedfrom Koopetal. [1997].


thatNAT particlescanonly form below thefrost point is unsatisfactory, becausetheobservedextentof NAT cloudsis not compatiblewith this supposition.Thus,someotherexplanationshave beenproposed,for examplethe creationof NATthroughHNO3 $ 2H2O (NAD). A new developmentis the discovery of so-calledNAT rocks[Fahey et al., 2001]with radii of up to 10µm. Theformationof theseparticlesis still not clear, but the may be formedwithout the help of ice parti-cles. Anotherpoint of discussionis the influenceof mesoscalecloudsformingovermountainrangesin comparisonto synopticclouds.More informationcanbefoundfor examplein [Koopet al., 1997]or [Drdla et al., 2002].

Onthesurfaceof thepolarstratosphericclouds,severalreactionsfreechlorineandbrominefrom thereservoir gases:

ClONO2�

HCl � Cl2 � HNO3 (1.20a)ClONO2

�H2O � HOCl � HNO3 (1.20b)

BrONO2�

H2O � HOBr � HNO3 (1.20c)HOCl

�HCl � Cl2 � H2O (1.20d)

HOBr�

HCl � BrCl � H2O (1.20e)N2O5

�H2O � HNO3 � HNO3 (1.20f)

N2O5�

HCl � ClNO2 � HNO3 (1.20g)Additionally, NOx (thesumof NO, NO2 andtheirnighttimereservoir 2N2O5), isconvertedto HNO3 andremovedfrom thegasphase,impedingthedeactivationofClO by reaction1.19a.ThepartitioningbetweenHCl andClONO2 at thebegin-ning of thewinter is to someextent importantfor the timing of theactivationofchlorine,sincetheabove reactionshave differenttime scalesandalsodependonthe typeof thecloudsurface. Activation is fastestwhenHCl andClONO2 havethesamemixing ratio,sincereaction1.20ais themostrapidone.

If theparticlesin thecloudsarelargeenough,sedimentationwill setin, remov-ing NOx from the altitudelayersof the clouds. The sameis true for the HNO3directlyproducedby thereaction1.19cwhichcouldreactbackto NOx through

HNO3�

hν � OH � NO2 (1.21a)HNO3

�OH � NO3 � H2O (1.21b)

The removal of NOx by meansof sedimentation,which is calleddenitrification,will lengthentheprocessof ozonedepletion,becauseit is mademoredifficult forClO to returnto its reservoir gases.While denitrificationis quitecommonin theAntarctic,it hasonly beenobservedsporadicallyin theArctic. Denitrificationcanbe connectedwith dehydrationin caseof ice particlescoatedwith NAT, or canhappenjust with NAT particles,whereNAT rocksbecomevery effective dueto


theirhighfall velocities.Denitrificationwithoutdehydrationwasobservedseveraltimesin theArctic, whichis anotherhint thatNAT particlesdonot form indirectlythroughice clouds.SmallNAT particlesor STSparticlesarelesslikely to causedenitrificationdueto their lower fall velocities.

Massive ozonelosswill only startwhensunlightreappearsin the precondi-tionedstratosphereenablingcatalyticcyclesto destroy ozonein largequantities.TheClO cycle cannotexplain theozonelossratesdueto thelack of atomicoxy-gen.Ozoneis ratherdestroyedby thecycle

2Cl�

2O3 � 2ClO � 2O2 (1.22a)ClO

�ClO

M� Cl2O2 (1.22b)Cl2O2

�hν � ClOO � Cl (1.22c)

ClOOM� Cl � O2 (1.22d)

2O3�

hν � 3O2 (1.22e)discoveredby Molina andMolina [1987]. Thechlorineradicalsarephotochem-ically producedfrom thechlorinespecieson theright sideof the reactions1.20.The chlorinemonoxideoriginatingfrom the reactionwith ozone1.22ais storedin the dimer Cl2O2 at night, andis convertedto chlorinedioxide whensunlightcomesback.This leadsto a diurnalcycle in ClO with low mixing ratiosat night.A similar cycleexistsfor bromine:

Cl�

O3 � ClO � O2 (1.23a)Br

�O3 � BrO � O2 (1.23b)

BrO�

ClO � Br � ClOO (1.23c)ClOO

M� Cl � O2 (1.23d)2O3

�hν � 3O2 (1.23e)

The brominecycle makes up for abouta third of the depletionof the chlorinecycledespitethelow abundancesof brominein thestratospherebecausebromineis lesstightly boundthanchlorine[Solomon,1999].

Consideringall effects,the strongestozonedepletionis usuallyfound in thealtitudelayersaround20km. This happensto bejust thealtitudewherethepeakconcentrationscanbefound.A summaryof theozonedestructioncycle is shownin Figure1.7. In earlywinter, mostof thechlorineis storedin thereservoir gases.When temperaturesdecreasein the polar night, polar stratosphericcloudsfree


1

2

3O

3

Time

VM

R [p

pm]

Winter Spring

0

0.5

1

1.5

2

2.5

3

ClO+2Cl2O

2

Sun→

HCl

PSCs↓

ClONO2

VM

R [p

pb]

Figure1.7: Ozoneholechemistry. Adaptedfrom Websteretal. [1993].

chlorine from the reservoir gases.With the sun comingback in spring, ozoneis destroyed by the catalyticcyclesshown above. Eventually, the air warmsupandthe vortex is destroyed. In the following, air rich in NOx is mixed in frommid latitudes,NOx is setfreeagainfrom thevanishingstratosphericcloudsandproducedphotochemicallyby reaction1.21a.Thus,thecyclewill finally cometoastopvia thereactions1.19.Sincereaction1.19ais muchfasterthanthereactionsproducingHCl, deactivationoccursmainly into ClONO2, which only later in theyearreachesequilibriumwith HCl.

Regardingthefuturedevelopmentof theozonedestruction,therearetwo di-verging trends.On theonehand,thelower stratospherewasgettingcoolerin thelastdecades[PawsonandNaujokat,1999]dueto enhancedgreenhouse-gascon-centrationsanddecreasingwave activity in the surf zone,enlarging the areaofpolarstratosphericcloudformationandleadingto a morestablevortex breakingup later in theyear. A morestablevortex would not only leadto enhancedozonedepletionbut alsomeanlessdownwardtransportandaccumulationof ozone.Onthe otherhand,the chlorineloadingof the stratosphereis decreasingdueto theProtocolof Montreal.Shindellet al. [1998] have useda circulationmodelwith averysimpleozonechemistry(withoutdenitrification)to makea longtermpredic-tion of ozonedepletionin theAntarcticandtheArctic. They predictthatAntarc-tic ozonelosswill peakin 2010–2020andandwill not bedetectableanymoreby

1.5 Ozone Distribution 29

-60_ -40 -20 0` 20 40 60_ Latitudea

0.1 60.0

1.0 45.0

10.0 30.0

100.0 15.0

1000.0 0.0

Pre

ssur

e [h

Pa]b Altitude [km

]

1c1d 2e2f 3g3h 4i4j

5

k5l

1m2n 2o3p 3q

44

5r 5s6t 6u

6v7 78w 9x

Figure 1.8: Latitudinal distribution of ozonevolume mixing ratios in December. Thecontoursshow themixing ratio in ppm.Takenfrom theclimatologyof FortuinandKelder[1998].

around2050.In theArctic, theinterannualvariability partiallymasksthetrendinozone,but thesituationis roughlycomparablehere.

1.5 Ozone Distrib ution

Theglobalozonedistribution is a resultof bothchemicalanddynamicaleffects.In Figure1.8 themeanozonevolumemixing ratiosfor Decemberareshown asafunctionof altitudeandlatitude. A typical Arctic profile measuredby theRAMcanbe foundsomewhataheadin Figure3.4, page70. While in theupperatmo-spherephotochemistryis so fastthatozoneconcentrationsarein photochemicalequilibrium,transportprocessesaredominatingin the lower atmosphere.Ozoneis producedin themiddlealtitudesof theatmosphere.In high altitudesthe lackof oxygenpreventsthe productionof ozone,while in low altitudesthe ultravio-let light neededfor thephotolysishasalreadybeenabsorbedby ozoneat higherlevels. Thereforeozoneforms a layer in the stratosphere.The main productionareafor ozonewith thehighestpeakvolumemixing ratiosis situatedin thetrop-ics dueto the intenseradiationthere.Paradoxically, the largestcolumnamountsof ozonecanbe found in the high latitudes,seeFigure1.9. This is due to the


Figure1.9: Meanannualcycle of ozonecolumnsasa functionof time andlatitudemea-suredby theTOMS instrumenton boardtheNimbus7 satellitebetween1979and1992.Contourlinesshow thecolumnin stepsof 25DU.

Brewer-Dobsoncirculation,whichveryeffectively carriesozonefrom low to highlatitudesandfrom middleto low altitudes.This is alsoevidentin theozonemix-ing ratioprofiles.While tropicalozoneprofileshaveaprominentpeakandasteeppositive gradientin the lower stratosphere,Arctic ozoneprofileshave a lesspro-nouncedpeak,but alsoa smallergradient.Theozonelayeralsoextendsto loweraltitudesin thepolar region dueto the lower tropopause.Thesetwo effectsleadto highercolumns,sincenumberdensity(asa functionof mixing ratio) falls ex-ponentiallywith altitude.

Seasonalchangesin thecolumnsareverypronouncedin thepolarregions,butmuchlessprominentin the tropics,ascanbe seenin Figure1.9. In winter andspring,ozonecolumnsrisedueto theaccumulationof ozonein thepolarvortexcausedby the Brewer Dobsoncirculation. While the columnsrise to morethan450DU in the northernvortex andhave a maximumabout80� N, the columnsonly rise to about350DU in the southernvortex with a maximumabout60� S.This is dueto thestrongerdownwelling in theweaknorthernvortex andthebetterisolationof air in the strongsouthernvortex. The low columnsaroundOctoberat the southpole mark the ozonehole. The differencebetweenozonecolumns

1.6 Chlorine Monoxide and Water Vapor 31

in southernmid latitudesand the southpolar region is about250DU. To anextentof about50DU, this is anaturaleffectcausedby theisolationof thevortex.The ozonehole chemistrycan lower the columnsby an additional200DU. Incontrast,ozonedepletionin thenorthernvortex is barelyvisibleandsuperimposedby diabaticmovements.

1.6 Chlorine Mono xide and Water Vapor

We will alsohave a shortlook at theotherspeciesmeasuredby theRAM instru-ment. Chlorine monoxideis a tracegaswith abundancesin the ppb range. Atypical chlorinemonoxideprofile measuredby theRAM is shown in Figure3.5,page71. It hasanaturalpeakin theupperstratosphereatabout40km, whichcanbefoundthroughoutthesunlitglobeandis causedby thecatalyticchlorinecycle.Thesecondpeakatabout20km is originatingfrom thechlorinemonoxidedimercycle. It is a clearsignfor ozonedepletionandcanonly beobservedin thepolarspringin sunlight.Night timemixing ratiosarealmostzeroat thesealtitudes.

Watervaporis very variableandcancompriseup to 3% of the atmosphericcompositionin the troposphere.It is responsiblefor many weatherphenomena,andessentialto life on earth.Watervaporis alsothemostimportantgreenhousegasandhasgreatinfluenceon the radiationbalanceof the earth. In the tropo-sphere,watervaporis notchangedby chemistryverymuchandis in arapidcycleof evaporation,transportandprecipitation.Theexponentialdecreaseof waterva-porwith altitudeis causedby condensationthroughadiabaticupwardmovements.Watervaporentersthestratospheremainly in thetropical tropopause,which actsasa freezingtrap for the vapor. Thus, stratosphericwatervapormixing ratiosaremuch lower than in the troposphereand lie about4 ppm. A typical strato-sphericwatervaporprofile measuredby the RAM is shown in Figure3.2. Themostimportantchemicalreactiongeneratingwatervaporin thestratosphereis theoxidationof methane,leadingto a conservationof thequantity2CH4

�H2O and

a minimummixing ratio for watervaporin thelower stratosphere.In additiontothat,watervaporhasa role in ozonechemistryandcoolsthestratosphereradia-tively. Thus,theobservedincreaseof stratosphericwatervaporof about1% peryearleadsto coldertemperaturesin thevortex.

1.7 Literature

Thereis a wealthof literatureon the topic of ozonedepletionandrelateditems,someof whichwill beintroducedhere.Thebulk of thegeneralinformationgivenhereis taken from thesesources.A nice overview of the history, conceptsand


chemistryof ozonedepletioncanbe found in [Solomon,1999],which is a goodpaperto begin with. Theextensive list of referencesthereinis alsoworth a look.Overviewsarealsogivenin thereportsof theWMO [WMO, 1999].Somebooksworthto noteare[BrasseurandSolomon,1986]and[Wayne,1991]for thechemi-calaspectsand[Holton,1992]for thedynamicalaspectsof stratosphericsciences.

2 Instrument

2.1 Overview

The Radiometerfor AtmosphericMeasurements(RAM) is a groundbasedmi-crowave radiometersituatedat Ny-Ålesund,Spitsbergen(78.9� N, 11.9� E). It isoperatedby theUniversityof BremenandtheAlfred WegenerInstituteof PolarandMarine Research(AWI) aspart of the Network for the Detectionof Strato-sphericChange(NDSC).Theinstrumentconsistsof threereceiverssharingacom-monbackend. Eachreceiver passively detectsthethermalemissionof rotationaltransitionsof themeasuredspecies.Thereceiversmeasurea watervaportransi-tion at 22.235GHz,anozonetransitionat 142.175GHzandachlorinemonoxidetransitionat 204.352GHz. The detectedradiationis led througha quasioptics,collectedby ahornantenna,down convertedto anintermediatefrequency, ampli-fied andfed into an acousto-opticalspectrometer. The intensityreceived by thespectrometeris calibratedabsolutelyby comparisonwith hotandcoldblackbod-ies.Volumemixing ratioprofilesof all speciesarefinally obtainedfrom thepres-surebroadenedshapeof therotationallinesusingtheoptimalestimationmethod.

Beforewepresenttheinstrumentsandtheir severalcomponents,we will giveanintroductionto radiativetransferandabsorptioncoefficients.Subsequently, thedifferentpartsof the instrumentsaredescribed.We concludethe chapterwiththedifferentmeasurementtechniquesthatcanbeusedandtheir explanation.Ad-ditionally, we will have a short look at the BRERAM, a microwave radiometermeasuringanozonetransitionat 110.846GHzat Bremen(53� N, 8� E).

GeneralinformationabouttheRAM canbefoundin [Klein, 1993]and[Sinnhu-ber, 1995,1999]. Chlorinemonoxidemeasurementsarealsodescribedin [Raf-falski, 1998] andwatervapormeasurementsin [Lindner, 2002]. Furtherinfor-mationaboutradiative transfer, microwave spectraandmeasurementtechniquescanbefoundin [Janssen,1993],[TownesandSchawlow, 1975]and[Ulaby etal.,1981,1982,1986].

33

34 2 Instrument

2.2 Radiative Transf er

Microwaveradiometersdetectthethermalradiationoriginatingin theatmosphere.A beamof radiationthatcrossestheatmospherecanbe modifiedby absorption,scatteringandemission.Scatteringis negligible underfair weatherconditionsinthemicrowaveregion,sowewill concentrateon emissionandabsorptionhere.

A bodythatabsorbsall incidentradiationis calledablackbody. A blackbodyis alsoa perfectemitter, sincea systemof two identicalblackbodieshasto stayin thermalequilibrium for symmetryreasons.Black body radiationis emittedaccordingto Planck’s law:

Lblackν � T y ν �� 2hν3c2 1exp � hνkBT �z� 1 (2.1)The spectralbrightnessLν is the power per solid angle,emitting areaand fre-quency interval. It will beshown laterthatthis is just thequantityreceivedby theinstrument.T is thethermodynamictemperatureof thebody, h � 6 � 62 10 34 Jsis Planck’s constant,kB is Boltzmann’s constant,ν is the frequency and c �3 108 m� s is the speedof light. For frequenciesin the microwave region,hν { kBT is valid, andPlanck’s law is simplifiedas

Lblackν � T y ν �| 2ν2kBc2 T (2.2)This is theRayleigh-Jeanslaw, which hasthepleasingpropertyof beingpropor-tional to temperature.To obtainthesamebehavior for Planck’s law, wedefinethebrightnesstemperature

TB � T y ν �� hνkB 1exp � hνkBT �}� 1 (2.3)which is virtually identicalwith T in themillimeter wave region. Now we getanexactidentity for all frequencies

Lblackν � T y ν �� 2ν2kBc2 TB � T y ν � (2.4)sothatblackbodyradiationdetectedby theinstrumentcaneasilybeexpressedinbrightnesstemperatures.

In themicrowaveregime,absorptionoccurswhenrotationalstatesof moleculesareexcited by the incomingradiation. Absorptiononly happensat discretefre-quenciescorrespondingto thequantumtransitionsof themolecules,renderingtheatmosphereto a graybodywith frequency dependentabsorption.Theabsorption

2.2 Radiative Transfer 35

coefficient α � zy ν � is definedasthe fraction of the radiationthat is absorbedperunit interval, hence

dLν � α � zy ν � Lν � zy ν � dz (2.5)whereLν is thespectralbrightnessof thebeamwhichshouldnotbeconfusedwiththeblackbodyradiationLblackν . dz is assumedto follow thepathof thebeam.Theabsorptioncoefficient is evidently proportionalto the numberof absorbinggasmolecules,but is alsodependenton thepropertiesof themolecules,asdescribedin the next section. A quantity relatedto α is the opacity, the integral of theabsorptioncoefficient

τ � z1 y z2 y ν �~� z2z1

α � zy ν � dz (2.6)If τ � 0 theatmosphereis transparent,while τ � ∞ meansthattheatmosphereisopaque.

The emissioncoefficient of a gray body like the atmosphereis equalto theabsorptioncoefficient accordingto Kirchhoff ’s law. If we combineKirchhoff ’slaw andEquation2.5,wegettheneteffectof absorptionandemission

dLν � α � Lν � Lblackν � dz �� Lν � Lblackν � dτ (2.7)Integrationgivestheradiative transferequationor Schwarzschildequation

Lν � z0 y ν �~� Lν � z∞ y ν � e4 z∞z0 α zM ν dz� z∞z0

α � zy ν � Lblackν � T � z�0y ν � e zz0 α z ν dz dz (2.8)wherez0 and z∞ are two arbitrary altitudes. If we extend the definition of thebrightnesstemperaturein Equation2.4 to arbitraryradiationby replacingLblackνby Lν, wecansubstitutethepowersby brightnesstemperatures,yielding

TB � z0 y ν �� TB � z∞ y ν � e z∞z0 α z ν dz� z∞z0

α � zy ν � TblackB � T � z�0y ν � e zz0 α z ν dz dz (2.9)We will seesoonthatTB � z0 y ν � is thequantitymeasuredby theinstrument.Thus,we have to know abouttheabsorptioncoefficientsandthetemperatureandpres-sureof theatmosphereto reconstructthemeasurement.A typical spectrumof the

36 2 Instrument

sky in the microwave region is shown in Figure2.1. For a deeperunderstand-ing of theshapeof thespectrum,wewill needmoreknowledgeof theabsorptioncoefficients,which is givenin thenext section.

If we want to calculatewith altitudesinsteadof integratingalongthepathofthe beam,we have to substituteall occurrencesof z with the altitude r and toreplacedz by � dz� dr � dr. For an instrumentwith a pencilbeamantennalookingupundertheangleϑ, theresultis

dzdr

� 1 � r � asin2 ϑ � 2r � a � r2 � a2 (2.10)

if thecurvatureof theearthis considered.Theradiusof theearthis denotedby a.

2.3 Absorption Coefficients

Theinformationaboutthemixing ratioprofileof theobservedspeciesis containedin the absorptioncoefficients. The absorptioncoefficient of the atmospherecanbewrittenas

α � zy ν �� ∑ki

α ki � zy ν � xk � z� (2.11)with k indicatingthemoleculesthatform theatmosphereandi denotingthetran-sitionsof every species.xk is the volumemixing ratio of the speciesandα ki iscalledabsorptioncrosssection.Theabsorptioncrosssectionfor asingletransitionis givenby

α ki � zy ν �� n � z� akiSki � z� Fki � zy ν � (2.12)n is thenumberdensityof air, a is theratio of theisotopethatperformsthetran-sition, S is the line strengthandF is the form factor, which givesthe frequencydependentterm. Thequantummechanicalexpressionfor thecrosssectionyieldsnocleardistinctionbetweenSandF, sotheirdefinitionis somewhatarbitrary. Wewill follow Janssen[1993] here.Thefrequency dependencehasseveralcauses:� Naturalline width� Dopplerbroadening� Pressurebroadening� Frequency shift

2.3 Absorption Coefficients 37

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Figure2.1: Atmosphericspectrumfrom 0 GHzto 400GHzfor asubarcticstandardatmo-sphere,seenfrom thegroundwith anmeasurementzenithangleof 70# . Arrows show thepositionof thespectrameasuredby the22 GHz watervapor, 110GHz ozone,142GHzozoneand204GHz chlorinemonoxideradiometers.Above 400GHz, theatmosphereisopaque.

The naturalline width is causedby the uncertaintyprinciple andis totally neg-ligible for rotationaltransitionsin themicrowave region. Dopplerbroadeningiscausedby the motion of the moleculesof the air relative to the observer. Theresultfor theform factoris

FD � ν �� 1π1� 2γD i exp � � � ν � νiγD i � 2 � (2.13)Thetransitionfrequency is denotedby νi . TheDopplerbroadeningparameterγD iis givenby

γD i � νi � 2kBTmkc2 � 1� 2 (2.14)

38 2 Instrument

141.8 142 142.2 142.4 142.60

1

2

3

4

5

6

7

Frequency [GHz]

Cro

ss s

ectio

n [1

0−3 /

km]

141.8 142 142.2 142.4 142.60

1

2

3

4

5

6

7

Frequency [GHz]

Cro

ss s

ectio

n [1

0−3 /

km]

Figure2.2: Line shapedueto pressurebroadening.Absorptioncrosssectionsfor 10kmand30km altitudefor ozoneat142GHz.

It dependson the temperatureT and the molecularweight mk of the species.Pressurebroadeningis causedby the decreaseof the lifetime of groundstatesand excited statesof the observed molecule,originating from collisions of themolecules. The higher the pressure,the shorteris the time betweencollisionsandthe morethe lifetime is decreased,leadingin turn to an increaseof the halfwidth of the line accordingto Heisenberg’s uncertaintyprinciple. Thus,broadlines originatefrom low altitudesandnarrow lines originatefrom high altitudes(seeFigure2.2). The mostcommonapproachfor the line shapeof the pressurebroadeningis thevanVleck-Weisskopf line shape

FC � ν y νi �� 1π � ννi � 2 � γC i� ν � νi � 2 � γ2C i � γC i� ν � νi � 2 � γ2C i � (2.15)This line shapewasderived by van Vleck andWeisskopf [1945] underthe ap-proximationthat the collisions are sufficiently short and strong. The pressurebroadeningparameterγC i is givenby

γC i � wi � p � pk � � T0T � xi � ws i pk � T0T � xs� i (2.16)wherethe first term describesbroadeningdue to oxygenand nitrogenand thesecondterm describesself broadeningdueto the observed moleculeitself. Theparameterswi , xi , ws i andxs i haveto bedeterminedempirically. T0 is anarbitrar-ily chosenreferencetemperature,andp andpk arethepressuresof theatmosphereandof theobservedspecies,respectively. Nearνi , thevanVleck-Weisskopf line

2.3 Absorption Coefficients 39

shapecanbesimplified:

FL � ν y νi �� 1π γC i� ν � νi � 2 � γ2C i (2.17)This is theLorentzline shape,which is equivalentto theline shapeof a classicaloscillator. The shapeof an atmosphericline nearνi is the convolution of theLorentzline shapeandtheDopplerline shape

FV � ν y νi �J� ∞ ∞ FL � ν � ν y νi � FD � ν � dν (2.18)andis calledVoigt line shape.The integral of the Voigt line shapecanonly becalculatednumerically, seefor example[Drayson,1976].Theline shapeusedforall calculationshereis a combinationof thevanVleck-Weisskopf line shapeandtheVoigt line shape,which is correctfor awide rangeof frequencies:

F � ν y νi �J� � ννi � 2 � FV � ν y νi � � FV � ν y1� νi �/� (2.19)In additionto the broadeningof lines,a shift in the centerfrequency canoccur.Sincethis is only importantfor watervapor, it will betreatedin Section3.4.5.Theline strengthfor a transitionfrom theenergy Ei2 to theenergy Ei1 is givenby

Ski � T �~� 8π3ν2i µ2i gi3hcQk � T � � exp � � Ei1kBT � � exp � � Ei2kBT � � (2.20)whereνi is theline frequency, µi is thequantummechanicaltransitionprobabilityandgi is the weight accordingto the nuclearspin. The partition function Q � T �is in goodapproximationgivenby the productof the vibrational,rotationalandelectronicpartition functions,thusQk � T �F� Qvib k � T � Qrot k � T � Qel k � T � . For ourinstruments,Qel k doesonly play a role for chlorinemonoxide.AssumingEi1 �Ei2 { kBT, weobtaintheformula

Ski � T �~� Ski � T0 � � T0T � qk � 1 1Qvib k � T � exp � bi � 1 � T0T � � (2.21)usedbyJanssen[1993],wheremostspectralparametersweretakenfrom. Thelinestrengthat thereferencetemperatureT0 is definedby Ski � T0 �4� Ski � T0 � Qvib k � T0 �andis tabulatedfor many species.Theparameterbi isgivenby � Ei1 � Ei2 �1�� 2kBT0 � .For theabove formulaQrot k � T �~� Tqk is assumed,whereqk is 0 for anatom,1� 2

40 2 Instrument

for a linear moleculeand3� 2 in any othercase.The vibrationalsumhasto becomputedfrom thefundamentalvibrationalstates:

Qvib k � ∏l

�1

1 � exp �� TklT � � dkl (2.22)The energy of the statesis Ekl � kBTkl anddkl is the degenerationof the states.Finally, theelectronicsumfor chlorinemonoxideis givenby

Qel k � 1 � exp �� Tel k � T � (2.23)with theelectronicstateenergy Eel k � kBTel k.

Themostprominentline spectrain themicrowaveregionarecausedby watervaporwith its strongdipole momentandby oxygen. Although oxygenhasnoelectricdipole moment,its magneticdipole momentandthe large abundanceintheatmosphereleadto ratherstronglines.Nitrogenhasno linesin themicrowaveregion dueto its vanishingdipolemoments.Ozoneexhibits a multitudeof lines,but the line strengthsaresomewhat lower thanfor oxygenor watervaporduetothelower mixing ratios. In additionto the line spectra,watervaporandnitrogencontinuacanbefound. Thewatervaporcontinuumis possiblycausedby devia-tionsof theline shapefrom thevanVleck-Weisskopf line shapefar from thelinecenters,andis to someextentdependenton which linesareexplicitly calculated.Thus,it cannotbeconsideredasa realcontinuum.

2.4 Instrument Description

2.4.1 Quasi Optics

The radiationreceived by the instrumentoriginateseitherfrom the atmosphere,a hot black body, or two differentcold black bodies. Radiationfrom the atmo-sphereentersthelaboratorythrougha styrofoamwindow, which is transparentinthemicrowaveregion. A rotatingmirror is pointedto oneof thesourcesaccordingto a computercontrolledprogramandleadsthe radiationto a quasioptics. Thepurposeof thequasiopticsis to focustheradiationandto restrictthereceivedfre-quency range.Thenamequasiopticsis dueto thesimilarbehavior of microwavesandvisible light, apartfrom somefeatureslikeapronouncedtransversespreadingof the beam. For somemoredetailedinformationaboutmicrowave optics,see[Goldsmith,1998].We will concentrateon theopticsof theozoneradiometerfornow, sinceit is themostcomplicatedone.Theopticsof theotherinstrumentsareanalogous.An outlineof theozonequasiopticsis shown in Figure2.4.

2.4 Instrument Description 41

Figure2.3:Theradiometersin thelaboratoryin Ny-Ålesund.Fromleft to right: Thewatervapor, ozoneandchlorinemonoxidefrontend.Themiddlerackcontainsthebackend.

Someof themirrors in theopticsarejust usedto focusandredirectthe radi-ation,like themirrorsE0 up to E5. But somepartsof theopticsrequirea deeperinvestigation. The first elementof interestis the dichroitic plate D. It is usedto suppressunwantedfrequency contributions in the radiationandconsistsof ametalplatewith concentricholes,which leadto a frequency dependentreflectioncoefficient. Next, the pathlengthmodulatorR3 is usedto suppressFabry-Ṕerotinterferencesin theopticsby periodicallychangingtheopticalpathlengthwith amoving rooftopmirror.

The most importantelementis the Martin-Puplettinterferometer, which isusedasa bandpassfilter to suppressunwantedfrequency ranges.It consistsofthefixedrooftopmirror R1, themovablerooftopmirror R2 andthewire grid G1.Thewire grid transmitsor reflectstheincomingradiationdependingon its polar-ization.It canbeshown thatif thepathlengthdifferencebetweenthefixedrooftopmirror andthegrid andthemovablerooftopmirror andthegrid is notzero,radia-tion is transformedbetweenthepolarizationswithoutchangingtheoverallpower.Thereforeit is possibleto attenuatethe radiationby addingwire grids aspolar-izationfilters at theexit andtheentranceof theinterferometer. Thewire grid G2

42 2 Instrument

Figure2.4: Quasiopticsof the142GHzradiometer

formstheentranceof theinterferometer, while thewire grid G0 is theexit. If δ isthepathlengthdifference,theattenuationof theincomingradiationis givenby

D � 12 � 1 � cos� 2πδν � c�� (2.24)

whereν is the frequency andc is the speedof light. Dependingon the relativepositionof the wires of the wire grids at the entranceandthe exit to eachotherandthe useof the transmittedor reflectedincomingbeamasa signalbeam,thepolarizationof the signalbeamis rotatedby 90� or left in its original polariza-tion. Thenegativesigncorrespondsto rotatingoperation,while thepositivesigncorrespondsto non-rotatingoperation.Thewire gridsat theentranceandtheexitareorientatedfor non-rotatingoperation.δ is chosenso that transmissionis at amaximumfor ν � νi andat a minimumwherethe largestunwantedcontributionoccurs.

2.4.2 Antenna and Mixer

Thepower perfrequency that is detectedby thehornantenna(save for theeffectof theinterferometer)canbedescribedas

Phorn � 12AeffΩeffLν (2.25)

2.4 Instrument Description 43

whereAeff is theeffectiveantennaarea,Ωeff is theeffectivedetectingangleandLνis theintensityof theradiation.TheEtenduprinciple,which shallnot bederivedhere,states

λ2 � AeffΩeff (2.26)whereλ is the wavelength. Combiningthe Etenduprinciple with the definitionof thebrightnesstemperaturein Equation2.4givesasimplerelationshipbetweenspectralpowerandbrightnesstemperature

Phorn � kBTB (2.27)Sincecommonlyusedamplifiersarenot ableto amplify the frequenciesthatwewish to detect,thesignalis down convertedto anintermediatefrequency. This isachievedby mixing theatmosphericsignalwith themuchstrongersignalof a lo-caloscillatorandpassingit to adevicewith anon-linearresponseof theresultingcurrentto the inducedvoltage. Sucha configurationis calleda heterodynere-ceiver. It canbeshown thattherelationshipbetweenthelocaloscillatorfrequencyνLO, the intermediatefrequency νIF and the amplifiedatmosphericfrequenciesν � n is

ν � n � nνLO � νIF n !#" 0 (2.28)If theintermediatefrequency andthelocal oscillatorfrequency aregiven,severaldiscretesignalfrequenciesareamplifiedat thesametime,giving a superpositionof thespectralpowersof thesinglefrequencies.It canbeshown thatthespectralpowersof thedifferentfrequenciesarenotamplifiedwith thesameefficiency. Theresultingspectralpower is rather

P � ∑n $&% L � νn � TB � νn � (2.29)

wheretheTB arethebrightnesstemperaturesat thedifferentfrequenciesandtheLareproportionalityfactors.Thesignalfrequenciesarecalledsidebands,with ν1giving theuppersidebandandν ' 1 giving the lower sidebandof thefirst order.Both sidebandscanbeusedassignalbands,with theothersidebandbeingthemirror sideband.Thelocal oscillatorfrequency is normallychosennearthelinefrequency to obtaina small intermediatefrequency. Thelocal oscillatorfrequen-ciesare14.235GHz for watervapor, 134.175GHz for ozoneand196.352GHzfor chlorinemonoxide,correspondingto an intermediatefrequency of 8 GHz attheline center. Theuseof theMartin-Puplettinterferometerbecomesclearhere.It canbeusedto suppressat leastoneof theunwantedsidebands,mostoftenthemirror sidebandof thefirst orderis suppressedbecauseit is usuallythestrongest

44 2 Instrument

Figure2.5: Thebackendof theradiometersin Ny-Ålesund

one. Sincethe interferometerinfluencestheproportionalityfactors,they have tobe written asL � νn �(� Λ � νn � D � νn � wherethe Λ areconstantscalledconversionmodesandD is thebandpassof theinterferometer.

We will now give someimplementationdetails. The mixer andthe first am-plifier aresituatedinsidea vacuumchamberandcanbecooleddown to 12K byliquid helium. This is doneto lower the thermalnoisein themeasurement.Themixer consistsof a Schottky diodesituatedbehindthehornantennato which theradiationof a localoscillatorbasingonaGunndevice is coupledby awaveguide.Thezenithangleof theantennais chosento be70� for ozoneandis variable(butsimilar) for chlorinemonoxideandwatervapor. This is a compromisebetweenhigher attenuationof the line in the tropospherewith higher zenith anglesandlower intensityof the stratosphericline with lower zenithangles. The antennapatternis assumedto beapencilbeam.

2.4.3 Intermediate Frequenc y Chain

The first elementof the intermediatefrequency chainis a bandpassfilter with abandwidthfrom 6.8GHz to 8.5GHz. After 22 dB of amplificationthesignalismixedfor asecondtimein orderto transformthesignalto the1.6GHzto 2.6GHzrangeof thespectrometer. Sincethesignalhas1.7GHz bandwidthandthespec-trometeronly 1 GHz bandwidth,the rangefrom 6.85GHz to 7.85GHz andtherangefrom 7.5GHz to 8.5GHz aregivenin turn to thespectrometer. Two local

2.5 Measurement Principle 45

oscillatorswith 5.25GHzand5.9GHzthatcanbeput into thechainalternativelyby a microwaveswitchareusedfor this. Later, thetwo spectraaremergedagain.Finally thesignalis ledthroughanotherbandpassfilter, a33dB amplifier, a22dBamplifier, a power divider (asinput for a powermeter),a microwave switchandaswitchableattenuator. Thelastmicrowaveswitchchangesbetweentheintermedi-atefrequency chainandacombgeneratorusedfor frequency calibration.Thelastelementof thechainis thespectrometer.

2.4.4 Acousto Optical Spectr ometer

The acoustooptical spectrometerdecomposesthe microwave radiationinto itsspectrum. The microwave radiationexcites a transducercoupledto a crystal,which is set into acousticoscillations. That modifies the refraction index ofthe crystal periodically. A laserbeampenetratingthe crystal is diffractedbythe acousticoscillations. The intensity of the laserbeamdiffractedto the an-gle ϑ is proportionalto the intensityof themicrowave radiationat thefrequencyν � ϑncs� λl , wherecs is thespeedof sound,n is themeanrefractionindex andλl is thewavelengthof thelaser. Thelaserlight is detectedby a CCD arraywith1728channels.Althoughthegapbetweenthechannelsis 0.56MHz, theresolu-tion of thespectrometeris only 1.6MHz dueto thescatteringof laserlight.

2.4.5 Bremen Radiometer

The ozoneradiometerin Bremen(BRERAM) wasbuilt in 1997andbeganop-erationalmeasurementsin 2000. It detectsthe rotationaltransitionof ozoneat110.836GHz. Opticsandbackend are similar to the RAM, so we will not gointo detailhere.Measurementquality is somewhat lower in Brementhanin Ny-Ålesund,sincethe measurementsaremoreaffectedby watervaporhere. Moreinformationon the instrumentcanbe found in [Tuckermann,1997]and[Hoock,2000].

2.5 Measurement Principle

Thespectralpower thatis receivedby thespectrometeris composedof two parts.Theactualspectrumis superimposedonthesystemnoiseof theinstrument,whichis usuallymuchlarger thanthedetectedsignal. Thespectralpower Pa of theat-mospherecanbe expressedin termsof brightnesstemperatures,which arepro-portionalto thespectralpower:

Pa � G � TB,a ) TB,sys� (2.30)

46 2 Instrument

Themeasuredatmosphericsignalis denotedby TB,a. G is anamplifyingfactorandTB,sys is the systemnoisetemperaturecorrespondingto the systemnoisePsys �GTB,sys. Thesystemnoiseshouldnot beconfusedwith theactualnoisethatcanbeseenon thespectrum.It is relatedto thesystemnoiseby

σ * TB,sys+∆ν∆t

(2.31)

where∆ν is the frequency resolutionof the instrumentand∆t is the integrationtime. Thesystemnoiseitself canbethoughtof asabiassignalthatis evenpresentwhenno radiationis measured.It originatesfrom several sourceslike thermalnoisein theamplifiersor terminationloadsin theoptics.

2.5.1 Totalpo wer Method

The totalpower methodis usedby the ozoneradiometersin BremenandSpits-bergen. Somemeasurementshave also beencarriedout with the water vaporradiometer, with promisingresults.Themethoddependson a sufficiently strongspectralsignature.All threevariablesin Equation2.30areunknown, so thatad-ditional equationsareneeded.For this reason,a hot anda cold black body aremeasuredin turnwith theatmosphere:

Ph � G � TB,h ) TB,sys� (2.32)Pc � G � TB,c ) TB,sys� (2.33)

TheradiationTB,h andTB,c of theblackbodiesis well known,whenweknow theirphysicaltemperatures.Thus,we obtaina systemof threeequationswith threeunknown variables,which caneasilybe solved. For the atmosphericspectrum,wegain

TB,a � TB,c ) TB,h , TB,cPh , Pc � Pa , Pc � (2.34)Solvingfor thesystemnoise,weget

TB,sys � TB,h , yTB,cy , 1 with y � PhPc (2.35)Let us now have a look at the implementationof the totalpower methodfor theozoneradiometerin Spitsbergen. The hot black body is realizedby a pieceoffoamedplastic at room temperature.The temperature,which is neededin theabove formulas, is measuredby a Pt-100diode. Thereare two different coldblack bodies. The extern cold black body consistsof a dewar vesselfilled with

2.5 Measurement Principle 47

liquid nitrogenat 77 K. The dewar is protectedby a lid, so that the nitrogencannotevaporate.Sincethe radiometermeasuresthe combinedtemperaturesofthe lid andthenitrogen,thetemperatureof the lid is measuredonceperday in acalibrationmeasurement.Theinterncoldblackbodyis situatedinsidethevacuumchamberfor themixerandis notusedin themoment.For thespectra,thehot load,thecoldloadandtheatmospherearemeasuredin turnfor about1s. ThecountsoftheCCDarethensummedupfor 40s. Thetotalpowerformulais appliedto everysingle measurement,and the resultingspectraare integrateduntil a integrationtimeof about200s is reached.

2.5.2 Reference Beam Method

For thevery weaklinesof thechlorinemonoxideradiometerandthemoderatelyweak line of the watervaporradiometer, the referencebeamtechniqueis used.This method,which wasdevelopedby Parrish et al. [1988], hasthe advantageof cancelingany non-linearitiesin the relationshipbetweenspectralpower andbrightnesstemperature.On the otherhand,we loosethe informationaboutthespectralbias,becauseit is implicitly subtracted.The referencebeamtechniqueusesa secondsourceof radiationwhich is adjustedto matchthe spectralpowerof thesignalbeam,but doesnot containthe line. Subtractionof the two spectraeliminatesnon-linearities,but doesconserve the informationthat is containedintheline. In our case,thereferencesourceis asecondbeampointingin adifferentdirectionthanthesignalbeam.Thereferencebeamis attenuatedby anabsorber,usuallyanacryl glassplate,to suppresstheline information.Additionally, asub-stantialamountof radiationis addedby thermalemissionfrom the acryl glassplate. The angleof the signal beamis adjustedin order to matchthe spectralpowersof thesignalbeamandthereferencebeam.

If Pr is thespectralpower of the referencebeamandPs is thespectralpowerof thesignalbeam,aderivationsimilar to thetotal powermethodyields

Ps , PrPr

� TB,s , TB,rTB,r ) TB,sys (2.36)

ThesystemnoiseTB,sys hasto bedeterminedin a secondmeasurement.TB,s andTB,r are the brightnesstemperaturesof the signalandreferencespectra,respec-tively.

The line of thechlorineradiometeris soweakthat the referencebeamtech-niqueis notsufficientto obtainspectrawheretheinstrumentalfeaturesaresmallerthantheline. Thus,we take advantageof thestrongdiurnalvariationof chlorinemonoxidein thelowerstratosphereandsubtractnight time measurements,wherealmostno chlorinemonoxideis presentin the lower stratosphere,from day timemeasurements[de Zafraet al., 1989]. Day time is definedas1 houraftersunrise

48 2 Instrument

to 1 hourbeforesunsetin thestratosphereor the2 hoursaroundlocal noonwhenthe day is too short for this condition. Night time is definedfrom 3 hoursaftersunsetto 1 hour beforesunrise. In duskanddawn, chlorinemonoxideis not inphotochemicalequilibrium andexhibits a fastchangein its mixing ratio, with arapid increasedueto photolysisin themorninganda somewhatslower decreasedueto thebackreactionto thedimerin theevening.

3 Retrie val

3.1 Overview

Theaimof theretrieval is to obtainvolumemixing ratiosandotherdesiredquan-tities from themeasuredspectrum.Thespectrumis supposedto besomefunctionof the quantitieswe want to retrieve. Hence,we canobtainthesequantitiesbydeterminingthe inverseof this function. Unfortunately, theinversionis a mathe-matically ill-posedproblemin caseof theradiative transferequation.A standardapproachto solve suchproblemsis the optimal estimationmethod. Thus,sec-tion 3.2dealswith thegeneralapplicationof this methodto our data.

Sections3.3 and3.4 describethedetailedimplementationof the retrieval forthedifferentinstruments.In additionto theexisting softwarefor ozoneandchlo-rine monoxideretrieval in Spitsbergen, somenew retrieval software had to bedevelopedfor the instrumentsbuilt in the last threeyears,namelythe waterva-por radiometerin Spitsbergenandtheozoneradiometerin Bremen.A completerewrite of theexisting retrieval software,which resultedin a muchfaster, easierto useandmorecompleteprogram,wasalsoperformed. All partsof the soft-wareweredevelopedin Matlab, an interpreterlanguagespecializedin matricesandnumericalmathematics.The forward modelsandretrieval methodsfor theozoneandchlorinemonoxideradiometersaredescribedin a generalmannerinsection3.3, togetherwith someexamplesfor spectra,profilesandaltituderangeandresolution. Section3.4 dealswith the challengesposedby the watervaporradiometer. Thewatervaporline is surprisinglydifficult to retrieve, dueto factsastheexponentialdecreasein mixing ratiosanda complicatedline form. Somemethodsof dealingwith theseproblemsor circumventingthemaredescribed,andfirst preliminaryprofilesareshown.

3.2 Optimal Estimation

The optimal estimationmethodis a convenientway to retrieve somesearchedparametersfrom given datathat are a function of theseparameters,especially

49

50 3 Retrieval

if the correspondingmathematicalproblemis underconstrainedor ill-posed. Athoroughdescriptionof the optimal estimationmethodandthe generalproblemof datainversioncanbefoundin [Rodgers,2000].

We assumethat the given data y are somearbitrary function F � x � of thesearchedparametersx and that somestatisticalerror ε is superimposedon thedata:

y � F � x � ) ε (3.1)For example,x maybeavectorof volumemixing ratiosin differentaltitudesandy maybeavectorof brightnesstemperaturesatdifferentfrequencies.Discretizingthesenormallycontinuousfunctionsis necessaryto computeanumericalsolution,but it is alsoconvenientto beableto usematrix algebra.Thevectorvaluedfunc-tion F � x � is calledtheforwardmodelandcontainsthephysicsof theproblem,inour casetheradiative transferequation.Normally, it is only anapproximationtotherealphysicsof theproblem,which maybetoocomplex or unknown.

At first, we will examinethe caseof a linear forward model. We will seelater that themorecommoncaseof a non-linearproblemcanoftenbetreatedbylinearization.Thelinearcaseis givenby

y � F � x0 � ) K � x , x0 � ) ε (3.2)wherex0 is somearbitrarypoint for the time being. The constantmatrix K iscalled weighting function matrix. If we useF � x � , F � x0 � insteadof F � x � andx , x0 insteadof x, which is easilyreversible,weget

y � Kx ) ε (3.3)Usually we have moredatathanretrievedparameters.Thus,at first glance,thisis an overdeterminedsystemof equations,which canbe solved by minimizingthe squareddifference � Kx̂ , y � 2, where x̂ is the estimatedsolution. However,thereareproblemswith this approach.It turnsout that thematrix K is ill-posedin thecaseof theradiative transferproblem,meaningthat thematrix is formallyoverdetermined,but thatits rowsarealmostlinearlydependent.Thussmallerrorsin the data,introducedby noiseor the truncationof numberson the computer,leadto largeerrorsin theresultx̂. An approachto understandthis is to examinethenull spaceof K . Underdeterminedmatriceshaveanull space.If thereis anullspace,therearesolutionsto theequationswhichdonotcontributeto thespectrum

Kxnull � 0 (3.4)andthereforecannot bemeasured.Hence,we canaddan arbitraryvectorfromthenull spaceto a solutionandstill get thesamespectrum,even if we scalethe

3.2 Optimal Estimation 51

vectorwith a very large number. The problemis madeworseby the noiseonthespectrum,which allows for evenmorepossiblesolutions.This leadsto largeoscillationsof the estimatedsolutionaroundthe true stateof the atmosphere,ifnot treatedproperly.

Theapproachtakenin theoptimalestimationmethodis to providevirtual mea-surementsto stabilizethe inversion. We assumethatwe know at leastthemeanx0 andthecovariancesSx of anindependentmeasurementseries,giving ussomea priori knowledgeon theoverall appearanceof our parametersx. Thedefinitionof thecovariancematrix Sx canbe found in Appendix3.A. x0 is calleda prioriprofileandSx is calledapriori covariance.Wenow minimizethedeviationof theresultingprofile x̂ from thea priori profile x0 andthedeviation of thespectrumyfrom thesyntheticspectrumF � x̂ � at thesametime

χ2 � � x̂ , x0 � TS' 1x � x̂ , x0 � ) � F � x̂ � , y � TS' 1ε � F � x̂ � , y � (3.5)weightingthedeviationswith thereciprocalof thecorrespondingerrors.Sε is thecovariancematrix of the errorsin the spectrum,which shouldbe known. Mini-mizing χ2 yields

x̂ � G � y , Kx0 � ) x0 with G � SxKT � KSxKT ) Sε � ' 1 (3.6)This is theoptimalestimationequationfor thelinearcase.

3.2.1 Resolution

Substitutingy � Kx ) ε in Equation3.6 givesa relationbetweenthe trueprofilex andtheestimatedprofile x̂:

x̂ � Ax ) � I , A � x0 ) Gε (3.7)whereA is thesocalledaveragingkernelmatrix

A � GK (3.8)Let ushave a look at therows of this matrix. We look first at thealtitudeswhereenoughinformationaboutthemixing ratiosis hiddenin thespectrum.Here,therowsof theaveragingkernelmatrixoftenhaveaGaussianshapewith apeakatthealtitudeof the retrievedmixing ratio, seeFigure3.1. Thus,the retrievedvolumemixing ratioatagivenaltitudeis aweightedmeanof thevolumemixing ratiosina finite layer. In additionto this, a constantcontribution of thea priori profile isadded.However, thiscontributionis usuallysmallin thealtituderangeconsideredhere.ThetermGε describestheerrorin theprofiledueto errorsin thespectrum.

52 3 Retrieval

10 20 30 40 50 60 70−0.04

−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Altitude [km]

Row

val

ue19.5 km

29.5 km

39.5 km

49.5 km

Averaging kernels

Figure3.1: Averagingkernels. Typical row valuesof four different rows (for ozoneat142GHz). The indicesof the rows are indicatedby the altitude annotatedabove thecurves.

Theshapeof theaveragingkernelsis a measurefor thealtituderesolutionoftheretrieval. Thebroaderthekernelsare,theworseis theresolution.A straight-forward way to definealtituderesolutionis the responseof the retrieval to twodeltafunctionpeaksin the trueprofile. Thesmallestdistancewherethesefunc-tionscanbedistinguishedin theestimatedprofile is thealtituderesolution.It isgiven by the half width of the rows of the kernels. A very similar result is ob-tainedby takingthereciprocalof thediagonalelementsof theaveragingkernels,sincethepeakvaluesareameasurefor thedegreesof freedomperlevel. Altituderesolutionin Figures3.2to 3.5andTables3.1to 3.2is estimatedwith thismethod.

Therearealtitudeswherethereis no sufficient information in the spectrumto retrieve mixing ratios. In this altituderange,thesecondtermof Equation3.7becomessignificantandtheestimatedprofile approachesthea priori values.Thealtituderangeof theretrieval is determinedby thesumof therow elementsof thekernel. If the sumis nearunity, the first term in Equation3.7 is dominantandthea priori hasno contribution. If it is nearzero,theprofile is dominatedby theapriori. Limiting factorsfor thealtituderangearenoise,instrumentaleffectsand

3.2 Optimal Estimation 53

the observed bandwidthfor low altitudesandDoppler broadeningandspectralresolutionfor high altitudes.

A relatedtopic is thesignal-to-noiseratioof themeasurement.If wecomparethe intensity of the line to the measurementnoise,we seethat small lines aremoredifficult to retrievethanlargelines. It is easierto distinguishtheinformationinheritedin the line shapefrom the noisewhenthe line is larger. Thus,altituderesolutionandrangearea functionof thesignal-to-noiseratio. We will seelaterhow wecankeepthesignal-to-noiseratio ataconstantlevel, which is desirable.

Finally, if wewantto compareanindependenthighresolutionmeasurementtoour estimatedprofile,we have to applyEquation3.7 to theindependentmeasure-ment.Weobtainasmoothedversionof themeasurementin ouraltituderesolution.

3.2.2 Errors

Errorsin theestimatedprofile canbedividedin errorsoriginatingfrom thespec-trum propagatinginto the profile, errorsin the forward modelanderrorsduetotherestrictedaltituderesolution.We have alreadyseenthat theerrororiginatingfrom thespectrumis givenby thecovariancematrix

S1 � GSεGT (3.9)All statisticalerrorsshown in thefollowing werecalculatedaccordingto this for-mula. Thealtituderesolutionerrorhasonly to beconsideredif onecomparesanindependentmeasurementthathasnot beentreatedwith Equation3.7 to theesti-matedprofile. If the independentmeasurementhasbeenadjustedto our altituderesolution,this erroris of no interest.It is givenby

S2 � � I , A � Sx � I , A � T (3.10)Wewill notconsiderthiserrorsourcein thefollowing sinceall independentmea-surementshave beenconvolutedto our altituderesolution.Theerrorsin the for-wardmodelcanbedivid

ozone depletion, chlorine activation and water vapor...

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