JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104,NO. D21, PAGES 26,597-26,609,NOVEMBER 20, 1999
The contribution of mixing in Lagrangian photochemical predictions of polar ozonelossover the Arctic in summer 1997 T. DuncanFairlie,•,2R. BradleyPierce, 3 Jassim. A. A1-Saadi, 3 WilliamL. Grose, • James M. Russell Ili, 4 MichaelH. Proffitt, '•,6andChristopher R. Webster, 7 Abstract. Measurementsfrom the HalogenOccultationExperiment,togetherwith assimilatedwinds, temperatures, and diabaticheatingratesfrom the NASA Goddard
dataassimilation office,are usedin the NASA LangleyResearch Centertrajectoryphotochemical modelto computephotochemistry alongthree-dimensional air parcel trajectories for theNorthernHemisphere for theperiodMarchthroughSeptember 1997. Thesecalculations providea globalperspective for the interpretation of constituent measurements madefromtheER-2 platformduringthePhotochemistry of OzoneLossin the ArcticRegionin Summeraircraftcampaign.An importantcomponent of the model is a parameterization of sub-grid-scale diffusivemixing. The parameterization usesan "n-member mixing"approach whichincludesanefficiencyfactorthatenhances themixing in regionswherestraindominatesthe large-scaleflow. Model predictionsof 03 andCH4 are comparedwith in situ measurements madefrom the ER-2. Comparisonof the in situdatawith modelpredictions, conducted with andwithoutdiffusivemixing,illustrates the contributionthat irreversiblemixing makesin establishing observedtracer-tracer correlations. Comparisons madefor anER-2 flightin lateApril 1997showthatirreversible mixingwas importantin establishing observedtracer-tracer correlations duringspring 1997.Comparisons madein lateJune1997,whenfilamentsof verylowN20 andCH4 were observed,indicatethat remnantsof air from the polarvortexsurvivedunmixedin the low stratosphere 6 weeksafterthebreakupof thepolarvortexin May. The resultsdemonstrate thatthe sub-grid-scale mixingparameterization usedin themodelis effectivenot only for strongmixingconditions in latewinterandearlyspring,butalsofor relativelyweakmixing conditionsthat prevailin summer. 1. Introduction
The NASA LangleyResearchCenter(LaRC) POLARIS theory team used a three-dimensional trajectory-photoThe Photochemistry of OzoneLossin the ArcticRegion chemical model to investigate the large-scale verticaland in Summer(POLARIS) aircraftcampaign,whichwas conmeridional distribution of the stratospheric ozone lossdurductedfrom March to September1997, was designedto ing Northern Hemisphere summer 1997. The trajectory calinvestigatethe relative contributionsof NOx, HOx, C1Ox, culations were initialized with data from the Halogen OcandBrOx in accountingfor observedozonelossin the low (HALOE) instrument onboardtheUpstratosphere during late spring,summer,and early fall in cultationExperiment
northernhigh latitudes[Newmanet al., thisissue].The mis- per AtmosphereResearchSatellite(UARS) andusedwinds sionconsisted of a seriesof measurement flightsby theER-2 anddiabaticheatingratesfrom theNASA Goddarddataassimilationoffice (DAO). These calculations,which we call high-altitudeairplane,basedprimarilyin Fairbanks,Alaska. "HALOE air masspredictions," providea three-dimensional hemisphericcontextfor the interpretationof in situ constituentmeasurements madealongtheER-2 flighttrack,and • ScienceandTechnology Corporation, Hampton,Virginia. yield estimatesof the photochemical productionof ozone 2Nowat NASA LangleyResearch Center,Hampton,Virginia. and of the relative contributionsto ozone loss due to NO.•, 3NASALangleyResearch Center,Hampton,Virginia. 4Department of Physics,HamptonUniversity,Hampton,Vir-
ginia.
HOx, C1Ox,andBrOx. The ER-2 measurements provide animportant validationtestfor theHALOE air masspredic-
tions. 5NOAA AeronomyLaboratory, BoulderColorado. 6Alsoat CooperativeInstitutefor Researchin Environmental The work describedin this paperfocuseson an imporScience,Universityof Colorado,Boulder. tant aspectof the LaRC trajectory-photochemical model, 7JetPropulsion Laboratory, Pasadena, California. namely,the incorporation of a diffusivemixingparameter-
Copyright1999by theAmericanGeophysical Union. Papernumber1999JD900111. 0148-0227/99/1999JD900111
$09.00
izationthat is designedto representconstituent massexchangebetweenneighboringair parcels. The Lagrangian approachconsidersall traceconstituents to be transported withinconstant-mass parcelsof air;thecentroidof eachpal'26,597
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cel is advectedby griddedwindsinterpolated to the parcel position.This approachhasthe advantage that all species move as one, and the transportis not affectedby the numericaldispersion or dissipation thatafflictsEulerianadvectivetransport algorithms.However,distortion of air parcels by shearsin the real atmosphere ultimatelyundermines the basicassumption of distinct,definable,constant-mass air parcels.The inclusionof a mixingparameterization thatallowsconstituent massexchangebetweenneighboring parcels providesa meansto continuallyreestablish the conceptof coherentair parcels[Waltonet al., 1988]. The studypresentedhere focuseson comparisons of 03
time of eachair parceltrajectory[Pierceet al., this issue]. Initial values of 03, CH4, HC1, NO, NO2, and H20 mix-
ing ratio and sulfateaerosolsurfacearea density(SAD) for the photochemical calculations are determined from the HALOE measurements. The initializationof the remaining chemicalconstituents is describedby Pierce et al. [thisissue].
The photochemicalmodule includesa Lagrangianformulationof sub-grid-scale mixing, which providesan additional tendencyfor each air parcel'schemicalcomposition. We haveusedan "n-membermixing"formulation, similarto thatusedby Waltonet al. [1988], comprising a tendency, plusanefficiencyfac- CH4 constituentcorrelationsobtainedfrom measurements relativelyweakbackground madefrom the ER-2 platformandHALOE air masspredic- tor designedto accountfor enhancedmixingdueto sheartionsat ER-2 flight altitudes.Suchconstituent correlations straindeformationof the large-scaleflow field [see,e.g., 1963].The mixingtendencyis givenby havebecomea ubiquitoustool for identifyingthe originof Smagorinsky, air masses, andfor distinguishing conservative fromnoncon-
servative processes thataffecttracermixingratios[ Waugh et al., 1997, and referencestherein]. We useO3 - CH4 correlationsfrom differentER-2 flights,togetherwith HALOE
•-•ck-
T
T
air masspredictions conducted with and withoutmixing, whereck is the mixing ratio of the kth trajectory,6• and to assessthe contributionof diffusivemixing to observed 6• areaverages of themixingratiosfor thekthparceland constituent correlations. In a companion paper,HALOE air its nearestneighbors,T is the timescalefor background submassrepresentations of thetimeevolution of meridional and grid-scalemixing,A is a free parameter,and Q > 0 is the altitudinaldistributionsof ozonemixing ratio, photochem- efficiencyfactor. The valuesof T andA are 60 daysand
icalproduction, andrelativelosses duetoNOx,HO.•,C1Ox, 8 8-•, respectively. Thesevaluesarechosen to providea andBrO.•arepresented [Piercee! al.• thisissue]. rangeof mixingtimescales,from 60 daysto onlya few days The formatof thepaperis asfollows.Section2 contains (dependingon the distributionof Q), and are basedon esa description of themodelandtheobservational datausedin timatesof mixing time scalesobtainedin previousstudies thisstudy.A description of thepostprocessing andreduction [Pierce and Fairlie, 1993; Pierce et al., 1994]. The sensiof model data is also given. The resultsof the studyare tivity of the modelresultsto changesin theseparameters is
presented in section3. Discussion andconcluding remarks discussed in section4. Neighborhood averages 6• and6• are givenin section4. differin that6• is constructed onlywith"likeneighbors," i.e., parcelsflaggedas "vortex"or "nonvortex,"whereas• is constructed with all neighboringparcels. This is to pre2. Model and Data Description vent the efficiencyfactor Q from causingexcessivemixing The modelusedin thisstudyis theNASA Langleythreebetweenpolar vortexand midlatitudeair parcels(seelater dimensional (3-D) trajectory-photochemistry model. The discussion of Figure 2). The coincidencecriterionfor intrajectorycomponent is a 3-D globaltrajectory modelthat cludingneighboringparcelsin theneighborhood averages is usespotentialtemperature as a verticalcoordinate [Pierce +/- 5ø of longitudeand +/- 4ø of latitude. Currently,only andFairlie, 1993;Pierceet al., 1994, 1997]. Thephotochemthoseparcelsoriginatingon the sameisentropiclevel are ical component hasbeendeveloped fromtheLaRC chemi- considered aspotentialneighbors. caltransport model(CTM) [Eckman etal., 1995].Air parcel The efficiencyfactor Q providesa quantitativemeasure
trajectories areinitializedat thetimeandlocationof occul-
of the relative contribution of strain and rotation on fluid
tationmeasurements madeby the HALOE instrument[Rus- elementsin an Eulerian referenceframe. Q is definedby sell et al., 1993]. Sixty-daytrajectoriesare calculatedus- 2Q - D:DW: W, whereD is the rate-of-deformation
ingdailyaveraged windsanddiabaticheatingratesobtained tensor, D from6-hourlyobjectiveanalyses providedby theDAO. Tra-
••(L + Lt ), W is thespinor vorticity tenI(L sot,W - • - Lt ), L is thevelocitygradient tensor,
jectoryhistoryinformation accumulated overthelifetimeof eachtrajectory includes 3-D position, solarzenithangle,and L = u X7, and the operator":" denotesthe tensorscalar overheadcolumnozone,at 3-hourintervals.Overheadcol- productT: D = T• D• [see,e.g.,Malvern,1969].When umnozoneis determined fromdaily,3-D, potentialvorticity Q is positive,strainpredominatesand fluid elementsare Bra(PV) - mappedHALOE ozonedistributions [Pierceet al., stretched;whereQ is negative,rotationpredominates. chet et al. [1988] and Mc•'lliams [1984] used Q for studthisissue].Thetrajectory historyinformation is fedintothe photochemical component of the model. Thephotochem-ies of quasitwo-dimensionalturbulenceto distinguishreical modulecomputes a time historyof mixingratiosand gionsof positiveQ, wherestretchingof fluid elementsleads
photochemical production andlosstendencies foreachof toincreased vorticity gradients, fromregions ofnegative Q 20 chemical familiesandindividual species overthelife- comprising stablerotational flow. Theyargued thatin re-
FAIRLIE ET AL.: CONTRIBUTION OF MIXING IN LAGRANGIAN PREDICTIONS
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gionsof positiveQ the lengths of line elements ultimately ter which makes direct, simultaneousmeasurementsof N20, 1
increaseat a rate ezp(Q5 t), whichrelatesQ to the local HC1, CH4, andNO2. The detectionlimits are 0.05 ppbvfor Liapunovexponent[Ottino, 1989]. Haynes[1990], who NO2 and HC1, 0.2 ppbv for CH4, and 0.1 ppbv for N20. usedQ to examinesimulations of the stratospheric circu- Measurementaccuracyis reportedas 5 - 10%. lation, found that closed circulations tend to be associated
withnegativeQ, whilepositiveQ is associated withregions 3. Results of "planetary-wave breaking"[McintyreandPalmer,1983] Figure1 showsa mapof reversedomainfilled (RDF) poin whichstirringof vortex-edge andmid-latitudeair occurs. tential vorticity (PV) at 500 K for 0000 UT on April 27, Efficientstirringpromotesdiffusivemixing acrossbound1997. The map was producedusinga trajectorymapping ariesbetweendifferentair massesby increasinginterfacial technique,usingtrajectoriesinitializedon a uniform 1ø by area [Aref and Balachander,1986]. Thus Q > 0 is chosen
l ø grid and 5-day back trajectories(for detailsof PV reto providean enhancement (abovebackground) of parameversedomainfilling, see, e.g., Fairlie et al. [1997]). The terizedmixing for regionswhereefficientstirringis anticmap illustratesthe circulationin the lower stratosphere for ipated. For quasi-horizontal, two-dimensional flow on the the ER-2 flight from Fairbanks,Alaska, on April 26. The rotatingEarth,Q normalizedby theEarth'sradiusis given stratospheric polar vortex is characterized by an extensive, by
elongatedregionof high PV, extendingfrom the Kamchatka Peninsula in eastern Russia across the Arctic to Scandinavia.
The vortexhas developedtwo distinctcycloniccenters,as evidencedby separatecyclonicswirlsofhigh-PV air in each lobe of the elongatedvortex. The polar vortexwas excep(2) tionally long-livedin early 1997 and was characterized by recordlow temperatures[Coy et al., 1997] and recordlow where u and v are the horizontalwind componentsin ozone values [Newmanet al., 1997]. Smaller regionsof the longitudinal()0 and meridional(4•) directions[Haynes, high-PV air in midlatitudes(Figure l) havePV valuescharacteristicof the polarvortexedgeair. Daily mapsof PV and 1990;Fairlie, 1995]. The trajectory-photochemical modelwas integratedfrom wind vectors indicate that air masses have been torn from March 19 to September22, 1997, extendingover the en- the vortex edge, in the courseof planetary-wavebreaking, intomidlatitudes.Superimposed onthemap tire POLARIS time period. HALOE air masstrajectories andtransported were initialized on eachof 12 isentropiclevels (425, 450, in Figure 1 is the rangering andflight track of the ER-2 for 475, 500, 525, 550, 600, 700, 800, 900, 1000, and 1200 the flight of April 26. The flight originatednearthe center by generK) for over 1800 HALOE occultations madeduringthe PO- of a large anticycloniccirculation,characterized LARIS period. The numberof air parcel trajectoriesin ally low PV, whichalsoenclosessomeair fromlow latitudes the model varies as the integrationproceedsbecausenew andfrom the vortexedge.The aircraftflew northfrom FairHALOE measurementsare continually introduced,while banks,penetratingtheedgeof thepolarvortexbeforereturntrajectoriesolderthan 60 daysare removed.Time histories ing to Fairbanks. Figure 2 showsa corresponding map of Q at 500 K for of mixingratiosandphotochemical productionandlosstendencies were saved for each of 20 chemical families and in0000 UT, April 27. Q > 0 is used as an efficiencyfacof sub-grid-scale mixing,asdedividualspecies,at 1-hourintervalsoverthe lifetimeof each tor for theparameterization air parceltrajectory.The accumulationof the HALOE air scribedabove.The cycloniccentersat eitherend of the poby regionsof negativeQ, as is masschemicalcharacteristics for 188 days,at 1-hourtem- lar vortexare distinguished poral resolution,constitutes a large amountof data. Data the anticyclonecenteredover Alaska at this time. Largest reductionis achievedby daylightaveragingthe constituent positivevaluesof Q are found in regionsof strongcurvature on the outerflank of thejet surrounding the polar vorcharacteristics for eachparcelfor eachday. the edgeof the polar vortex,but Resultsfrom the model are comparedwith O3 and CH4 tex. Q = 0 approximates measurementstaken by the National Oceanic and Atmo- someregionsof positiveQ lie insidethe vortex and stradsphericAdministration (NOAA) Dual-BeamUV-Absorption dle the vortexedge. Specifically,positiveQ is foundin the OzonePhotometer(NOAA O3) andtheJetPropulsion Labo- regionbetweenthe two cycloniclobesof the polar vortex ratory Aircraft Laser Infrared AbsorptionSpectrometer wheresmall-scalefilamentarystructureis beinggenerated (ALIAS) instruments flownontheER-2 airplane.The NOAA by strongshearstrainin the flow. Kinematicstudies[e.g., O3 instrument[Projfitt and McLaughlin, 1983; Projfitt et Pierce and Fairlie, 1993; Pierce et al., 1994] have idential., 1989] makesin situ measurements of ozoneby mea- fied a kinematicbarrierto large-scalemixingnearthe edge suringthe absorptionof 254-nm radiationpassingthrough of the polar vortex. To preventanomalousenhancedmixa pair of identicalabsorption chambers.For a 1-sresponse ing betweenvortex and nonvortexair parcels,we use the time, the precision(minimumdetectableconcentration) is attributesof both PV and Q to delineatethe polar vortex. 1.0 x 10TMmolecules cm-3 . Thereported accuracy is 3% Q is integratedaroundcontoursof constantPV; air parcels plusprecision.The ALIAS instrument[Websteret al., 1994] with potentialvorticityP are flaggedas vortexair parcels is a high-resolution scanning tunablediodelaserspectrome- whenever P > PVmin, where PVmin is the lowest PV value
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0
2
4
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B
RDFPV(10• K m2 k(::j-'S") Figure 1. NorthernHemisphere orthographic mapof reverse-domain-filled (RDF) potentialvorticity(PV) at 500 K for 0000 UT, April 27, 1997. The mapwasproducedusingtrajectorymappingwith 5-dayback trajectoriesandwindsobtainedfromNASA GoddardSpaceFlightCenter(GSFC) dataassimilation office
(DAO)analyses. Unitsare10-•Km2kg-1s-1.
forwhich J•PV Q < -10 8--1. Thismethod isused todis- ences therein; Plumb andKo,1992].Thein situmeasuretinguishvortexand non-vortexair parcelsat all isentropic mentsof O3 andCH4 arepositivelycorrelated for CH4 vallevelsthroughout thePOLARIS period.At 500 K on April. uessmallerthan 1.0 ppmv,characteristic of air in thepolar 27 (Figure 2), air definedas vortexair is enclosedby the vortexthat hasbeensubjectto chlorine-catalyzed ozonedeheavysolid contour.The efficiencyfactorO is appliedus- pletion [Pierceet al., 1997]. A negativecorrelationexists ing meanmixingratiosdeterminedfrom "like" neighboring for CH4 valuesgreaterthan 1.2 ppmv,characteristic of midparcelsonly (Equation(1)). latitudeair. BetweenCH4 valuesof 1.0 and 1.2 ppmv,O3 Figure3 showsa scatterplot of O3 versusCH4, obtained valuesare relativelyflat. This air characterizes the collarof from NOAA O3 and ALIAS measurements madealongthe high ozonethat surrounds the polarvortexat this time; the ER-2 flighttrackonApril 26, togetherwithHALOE air mass relativeuniformity of O3 valuesin this CH4 intervalsugpredictionsfrom the trajectory-photochemical model. Both geststhatmixingof vortex-edge air andmidlatitudeair has sets of data are restrictedto potentialtemperaturesrang- occurred[see,e.g., Waughe! al., 1997]. Fragmentsof highing from 495 to 525 K, which includesmostof the ER-2 PV air observedin midlatitudes(Figure 1) are symptomatic breakingthatenhances suchmixing. flight altituderange. Tracer-tracer correlations of this kind of theplanetary-wave havebeenusedto distinguish theimpactof nonconservative The HALOE air masspredictionsfor thisflight day capprocesses on constituent mixingratios(e.g.,photochemistry turethepositivecorrelationfor CH4 valuessmallerthan 1.0 and diffusivetransport)from conservativeprocesses(e.g., ppmv, where air massesclusterinto two distinctcompact nondiffusivetransport),by identifyingdeviationsfrom nor- populations:onewith lowerandonewith higherozonevalmally compactrelationships [Waughet al., 1997, andrefer- uesthanthe populationsampledby the ER-2. (We notethat
FAIRLIE ET AL.: CONTRIBUTIONOF MIXING IN LAGRANGIAN PREDICTIONS
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Q (s Figure 2. NorthernHemisphereorthographic mapof theefficiencyfactorQ at 500 K for 0000 UT, April
27. Unitsares-• . Theheavysolidcontour encloses "polarvortexair,"definedby Q integrated around PV contours(seetext for details).
HALOE samplesall longitudes,whereasthe ER-2 longitude samplingwas severelylimited for this flight. Pierce et al. [1997] found considerablelongitudinalvariability for HALOE ozonemeasurements in the polar vortex during March 1997.) The HALOE air massesalsocapturethe negativecorrelationfor CH4 valuesgreaterthan 1.2 ppmv. For CH4 valuesbetween1.0 and 1.2 ppmv,the HALOE air masspredictionsof O3 are in goodquantitativeagreement with the NOAA O3 measurementsmade from the ER-2.
Figure 4 showsa corresponding scatterplotthat displays the sameER-2 databut showsHALOE air masspredictions that excludethe impact of diffusivemixing. The HALOE predictionsshowconsiderably morescatterthanthosefrom the simulationthat includesdiffusivemixing (Figure3). In addition, O3 mixing ratios are substantiallyoverestimated whendiffusivemixing is excluded,particularlyfor CH4 values smallerthan 1.35 ppmv. This is especiallytrue for CH4 values between 1.0 and 1.35 ppmv, where O3 values are overestimated by as much as 25% comparedwith the simulation that includesdiffusivemixing. The differencebetween the two predictionsillustratesthe accumulated im-
pact of the parameterizedmixing on O3 and CH4 mixing ratiosbetweenMarch 19 andApril 27. The improvementin predictiveskill demonstrated by the simulationthatincludes mixing (Figure 3), supportedby observations of large-scale stirringdue to planetary-wavebreaking(Figure 1), strongly suggeststhat mixing betweenvortex-edgeand midlatitude air duringMarch andApril 1997playeda significantrole in establishingthe O3 versusCH4 correlationsobservedfrom the ER-2 on April 26. In mid-May thepolarvortexbrokeapartintothreedistinct circulationsas part of the dynamicallydriven final warming thatled to the establishment of summertimeanticyclonic conditionsovernorthernhigh latitudes.Successive mapsof PV (not shown)showair from within thesecirculationsbeing stretchedinto elongatedair massesand stirredinto the surroundingair. ' We now considerthe ER-2 flight that took placeon June 26, somesix weeksafterthebreakupof thepolarvortex.The ER-2 flew northto sampleair thathad experiencedcontinuous sunlightover the last severaldays;it thenflew acrossa strongsolarexposuregradientthat lay to the southof Fair-
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Figure 3. Scatterplot ofNOAA 0 3 versusAircraftLaserInfraredAbsorptionSpectrometer (ALIAS) CH4, obtainedfrom measurements madealongtheER-2 flighttrackon April 26 (light crosses), togetherwith HALOE airmasspredictions of 03 andCH4 fromtheNASA LangleyResearch Center(LaRC) simulation with diffusivemixingfor 0000 UT April 27 +/- 2 days(darkpluses).The HALOE air massdatashown arelimitedto 45ø - 90øN andto potentialtemperatures rangingfrom495 - 525 K.
banks.AnalyzedPV at 500 K for June26 (notshown)shows little variabilityin middle and high latitudesof the Northem Hemisphere;at the sametime, absolutevaluesof Q are small, indicatinga weak isentropiccirculationin the low stratosphere andweakmixing. Figure 5 showsa scatterplotof O3 and CH4 from the NOAA O3 andALIAS instruments on theER-2 for theflight of June26, togetherwith the HALOE air masspredictions valid for the sameday. Most of the ER-2 datapointsare clusteredbetweenCH4 - 1.2 and 1.35 ppmv and between O3 = 2.0 and 2.8 ppmv. This clusteringis symptomaticof relativehomogeneityin constituentmixing ratios,i.e., well-
Filaments of low CH4 and low NeO were also observedin
the Observations from the Middle Stratosphere (OMS) balloonplatform[Hermanet al., 1998]. HALOE air masspredictionsfor the ER-2 flight day clusterat CH4 valuesnear 1.2 ppmv and O3 valuesnear2.6 ppmv, in relativelygood agreementwith the observations.In addition,the HALOE predictionscapturesomeof the low CH4 filamentarystructurewith CH4 valuesaslow as0.6 ppmv. Exclusionofparameterized mixingtendencies in themodel haslessof an impactontheair masspredictions for theflight of June26 thanwasthecasefor April 26. Figure6 showsthe corresponding scatterplotfrom the simulationthat excludes mixing. The vastmajorityof HALOE air massesclusterin the sameregionof O3 - CH4 spaceas is foundfor the simulation with mixing (Figure 5). However, Figure 6 shows that withoutmixing, HALOE predictionsretainair masses with CH4 valuesexceeding1.4 ppmv and more air masses with CH4 valuesbelow0.9 ppmv.Thesevaluesare characteristicof tropicalandpolarair masses,respectively, andthe
the low stratosphere aboveFairbankson June30, 1997from
retention of these values in the model is inconsistent with the
mixed air. However, the ER-2 ALIAS instrumentalso ob-
servedsomefilamentsof very low CH4 values(0.6 ppmv) duringthe courseof the flight. Theseare distinguished in Figure5 by narrowstructures extendingfrom themaincluster of pointstowardlow CH4, with relativelyuniform O•.
FAIRLIE ET AL.: CONTRIBUTION OF MIXING IN LAGRANGIAN PREDICTIONS
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Figure 4. As for Figure3, exceptHALOE air masspredictions withoutparameterized diffusivemixing (i.e., chemistryonly) are shown.
ER-2 observations. Mixing of tropicalandpolarair masses 7 showsa contourmapof PV at 500 K forMay 20, 1997.Suwith midlatitude air masses moves these constituent values perimposed onthemaparethepositionsofHALOE occultatowardsthemainclusterof pointsin Oa - CH4 space(Figure tionsonthisday,grayscalecodedby HALOE CH4. Highest 5). PV air massesare remnantsof the polar vortex,remaining The low CH4 structures,shownin both the ALIAS obser- afteritsbreakup.In particular,a smallcyclonicvortex,cenvationsandthe HALOE air masspredictions(Figure5), are terednear70øN, 70øW,andcharacterized by PV > 0.4, has characteristic of air from the polarvortex.However,the sur- beenidentifiedasa remnantof thepolarvortexusingsuccesvival of unmixedremnantsof thepolarvortexsolongafter sivedailymapsofPV. HALOE sampledthiscycloneonMay its breakupin mid-May is unexpected.Waughet al. [ 1997], 20 and foundCH4 valuesas low as 0.6 ppmv. HALOE air
usingobservations fromthe 1993Stratospheric Photochem- masstrajectories initializedwith theseCH4 valuesac•count observed in theHALOEairmass istryAerosolsand DynamicsExpedition(SPADE)aircraft forthelowCH4structures campaignandcalculations with a strain-diffusion model,es- predictions forJune 26(Figure 5). Thisevidence supports that the low CH4 filamentarystructure0btimatedthatair frominsidetheArcticpolarvortexshould be the hypothesis completelymixedintomidlatitudes withina monthfollow- servedfrom the ER-2 platform on June26 was a remnant ingthebreakupof thepolarvortex.A second possibleorigin ofthepolar vortex thatsurvived unmixed 6 w•eks afterthe for the low CH4 air observedfrom the ER-2 on June26 is a vortexbreakup. ' higheraltitude;the air couldhaverecentlydescended from aloft, whereCH4 valuesare lower. The ALIAS dataalonedo
4. SensitivityAnalysis
notpermitus to distinguish betweenthesepossibilities, but We have demonstrated that the parameterization of diftheoriginof thelow CH4 structure predictedby theHALOE model air masscalculations (Figure5) has.beenestablished. Figure fusivemixing in the LaRC trajectory-pho.tochemical
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Figure 5. Scatterplot of NOAA 03 versusALIAS CH4, obtainedfrommeasurements madealongtheER2 flight trackon June26 (light crosses), togetherwith HALOE air masspredictions of O3 andCH4 from the LaRC simulationwith diffusivemixingfor 0000 UT June27 +/- 2 days(darkpluses).The HALOE air massdatashownarelimitedto 45ø - 90øN andto potentialtemperatures rangingfrom495 - 525 K.
to the improvesthe agreement betweentheHALOE air masssim- impactof mixing is weak. The PDFs corresponding ER-2 observations for April 26 (Figures8a and 8c) are bimodalin CH4, with a strongpeakcenteredaround1.3ppmv thefreeparameters chosenfor themixingparamcterization. anda smallerpeaknear0.9 ppmv,andunimodalin 03, with Figure 8 showsthe probabilitydensityfunctions(PDFs) a peakcenteredaround2.9 ppmv.This reflectsthepresence for CH4 and 03 from ER-2 flight data for April 26 and of two main populations:a midlatitudepopulation(CH4 June26, 1997. The profilesshowthe densityof observa- centeredat 1.3 ppmv) and a polar vortexpopulation(CH4 tionswithin each CH4 or 03 interval as a fractionof the total centeredat 0.9 ppmv). Both populationsare characterized numberof observations.In addition,Figure 8 showsPDFs by intermediate03 values.The polarvortexpopulationhas for five different HALOE air mass simulations. These simfewercountsbecausethe ER-2 spentonly a shorttime in the ulationsare (1) chemistryonly, i.e., no diffusion;(2) back- vicinityof the vortexedgeon April 26. The CH4 minimum of a stronggragrounddiffusiononly; (3) standarddiffusion(T = 60 days betweenthetwo populationsis characteristic andA = 8 8--1);(4) halftheefficiency factor(A = 168--1); dient in CH4 acrossthe vortexedge. The chemistry-only diffusionsimand(5) twicetheefficiency factor(A = 4 s-1). Tohelpin- simulation(simulationl) andthebackground terpretthesePDFs, we note that diffusivemixing tendsto ulation (simulation2) show similar PDFs to one another; homogenizeconstituentdistributions.Its impactis to pro- eachis approximatelybimodalin CH4, with a singlepeak duceor sharpenpeaksin a PDF. (In the limit of totalhomo- in 03 thatis skewedtowardhigher03 valuesthanthe peak geneitya PDF wouldshowa deltafunction).Broadpeaksor in theNOAA 03 PDF (reviewalsoFigure4). 03 PDFsfor simflat PDFs indicatepopulatedintervalsovera wider rangeof boththe chemistry-onlyand the background-diffusion constituent mixingratios,an indicationthattheaccumulated ulationsare broadcomparedwith thoseof the ER-2 obserulationsand observations.We now look more closelyat the sensitivityof theHALOE air masssimulations to changes in
FAIRLIE ET AL.' CONTRIBUTION OF MIXING IN LAGRANGIAN PREDICTIONS
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CH4 (ppbv)
Figure 6. As for Figure5, exceptHALOE air masspredictions withoutparameterized diffusivemixing (i.e., chemistryonly) are shown.
vations.This is a furtherindicationof the inadequacyof the chemistry-onlysimulationin representing the distinctpopulationsof midlatitudeand vortex air sampledby the ER2. The background-diffusion simulationmovesthe 03 peak closerto the observedbut, in general,makesonly a minor improvementoverthe chemistry-onlysimulation. The standardsimulationwith diffusivemixing(simulation 3) showsa muchimproved03 PDF, with a sharppeaksimilar to that displayedby the NOAA 03 PDF (review also Figure 3). The peak is centeredaround3.2 ppmv, 10% higherthan the centralvalue of the NOAA 03 peak. Ozone is generallyoverestimated in the modelat ER-2 altitudes,as is discussed by Pierce et al. [this issue].The CH4 PDF for the standardsimulationshowsa singlepeak at 0.95 ppmv, which corresponds to a clusterof pointswith 03 values around3.2 ppmv (Figure 3). The PDF is unimodal,unlike the PDF of ALIAS CH4, and the median of the distribution
is low comparedwith thatof the ALIAS PDF. Thesedifferencesmay be partly attributedto the increasedsamplingof high-latitudeair parcelsin the HALOE air masssimulation comparedwith the ALIAS observations, buttheyareprobably alsoaffectedby a ratherconservative definitionof a vor-
tex air delimiter(seeFigure2 andassociated discussion). As a result,enhancedmixing of midlatitudeandvortex-edgeair
(via theefficiencyfactor)extends toodeeplyintothevortex edge,erodingthe distinctionbetweenmidlatitudeandvortex air masses.More work is requiredto refineour definitionof the vortexedgebasedon Q andPV. The remainingPDFs illustratethe sensitivityof the sim-
ulationsto changing parameter A in themixingparameterization.Theimpactof doubling A (to 168-1) is to broaden the peaksin the 03 andCH4 PDFs andto displacethemto-
wardhighermixingratios.HalvingA (to4 8- l) sharpens the peaksandshiftsthemtowardlowermixingratios.Theseadjustmentsare minor comparedwith the largeimprovements
madeby introducing thestandard diffusionparameterization to the model(comparesimulations1 and3).
Figures8b and8d showPDFsfor theflightof June26, 1997. The ER-2 PDF for June26 showsa sharppeak in ALIAS CH4, centeredaround1.3ppmv,anda sharppeakat
NOAA 03 of around2.15ppmv,illustrating therelativehomogeneityof theseconstituents alongthe ER-2 flight track. A secondarypeak at 03 of 2.7 ppmv is alsofound(review also Figure 5). The low CH4 filamentarystructure(Figure
26,606
FAIRLIE ET AL.' CONTRIBUTION OF MIXING IN LAGRANGIAN PREDICTIONS
1.4
0.30' ß ß ß
-r
0
1.0
W
o
0.8
0.6
Figure 7. NorthernHemisphereorthographic map of PV at 500 K for May 20, 1997. Units are
10-SKm2kg-•8-•;contour interval is0.1unit.Alsoshown arepositions of HALOEoccultations on 20 May 1997,grayscalecodedby HALOECH4mixingratiosat 500K. Unitsareppmv.
5)isevident inthePDFbythetailoflowCH4values, which Hemisphere(includingthe pole) as the PV
contourdoes. The time seriesillustratesthe evolutionof Q at 500 K over the POLARIS time period,givingan indicationof the spatial andtemporaldistributionof parameterized mixingover the period. Largestpositivevaluesof Q are foundin midlatitudesduringMarchandApril, showingtheprevalence of i.15ppmvforsimulation 5 (A - 4 8-•). Fortheflightof shearstrainin midlatitudesduringlate winter/earlyspring. June26, PDF profilesfor the simulationsare foundto be Largestnegativevaluesareassociated with thepolarvortex, much lesssensitive totheintroduction ofdiffusive mixing northof 60ø equivalentlatitude.After the final warmingin or to changes in the parameters thanwasthecasefor April mid-May,bothpositiveandnegativevaluesof Q fall sharply, 26. For example,theprincipalimpactof enhanced mixing indicativeof a relativelyweakisentropiccirculationthatpreon the 03 PDF is merelyto tightenthepeakat theexpense vailsthroughthesummer.Reducedstrainfollowingthefinal with increased mixingtimescales and of populations in the wings(seealsoFigures5 and6). Its warmingis consistent ,
is populatedby relatively few observations.Each of the HALOE air masssimulationsshowsa singlepeakin both CH4 and 03 PDFs. For 03 the peak is centerednear 2.6 ppmv in eachof the simulations; for CH4 the peakmoves from around1.3 ppmvfor the chemistry-only simulationto
impacton the CH4 PDF is to tightenthepeakandshiftits the extended lifetime of vortex remnants,observedin late June(Figure 5). centralvaluetowardlowermixingratios. The relativeinsensitivity of theHALOE air masssimula-
itons •o,changes inthe diffusive mixing parameterization for 5. Conclusion
the•flightof June26, compared withtheflightof April26,inThis paperdescribesthe use of an "n-member"paramdicatesthatirreversible diffusivemixingwaslessimportant diffusivemixingin Lagrangian duringsummerthanduringspring1997.Mixing timescales eterizationof sub-grid-scale in themodelparameterization arelargelydetermined by the photochemical modelingstudiesof theNorthernHemisphere e,fficiency factor Q.Figure 9 shows atimeseries ofQaver- stratosphere for the 1997POLARIS aircraftcampaign.The ageda/oundPV contours, asa functionof "equivalent lati- parameterization consists of a weakbackground mixingtentude,"at 500 K for March 19 to September 22, 1997. The dencyplus an efficiencyfactorintroducedto simulateenequivalentlatitude(of a PV contour)is definedas the lati- hancedmixingdueto shearin thelarge-scale flow.Compartude that encloses the same fractional area of the Northern
isonsof observedand predicted03 - CH4 correlationsare
FAIRLIE ET AL.: CONTRIBUTION OF MIXING IN LAGRANGIAN PREDICTIONS
(a) CH4 PDF 970426
(b) CH4 PDF 970626
90-45N
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26,607
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Figure 8. Probabilitydensityfunctions (PDFs)for ALIAS CH4 andNOAA 03 fromER-2 flightdatafor April 26 andJune26, 1997.ThePDFsfor fivedifferentHALOE air masssimulations arealsoshown:(1)
chemistry only,(2) background diffusion only,(3) standard diffusion (A = 8 s-i), (4) standard diffusion butwithA= 16s-1, (5) standard diffusion butwithA= 4 s-1 . HALOEairmassdataarelimitedto 45ø90øN,andpotentialtemperatures rangingfrom495 - 525 K.
madefor two cases:a springtimecase(April 26) for which HALOE originatedin a cyclonicremnantof thepolarvortex, mixing is foundto havea strongimpact,anda summertime whichwas sampledby HALOE afterthe vortexbreakupin case(June26) whenmixing only weaklyaffectsthe results. mid-May. The low CH4 valuessurvivedrelativelyunmixed The success of the Lagrangianair masspredictionsin rep- in the Lagrangianair masspredictions until the endof June. resenting03 - CH4 correlationsfor theseextremesdemon- Thisresultsupports thehypothesis thatthefilamentarystrucstratesthat the diffusivemixingparameterization can per- ture observedfrom the ER-2 on June26 originatedin the formwell in bothstrongmixingandweakmixingregimes. polarvortexand that suchvortexremnantscan surviverelComparisonof observedandpredicted03 - CH4 correla- ativelyunmixedfor up to 6 weeksfollowingthe springtime tionsfor a springtimeflight (April 26) showsgoodagree- breakupof the polarvortex. The laterbreakupof the polar ment betweenobservedand predicted03 valuesfor CH4 vortexin 1997 may accountfor weakerstrainin the largemixing ratios that characterizethe vortex and midlatitude scaleflow, increasedmixingtimescales,and extendedlifeair masses.The inclusionof the sub-grid-scale mixingpa- timesfor vortexremnantscomparedwith thoseestimatedby rameterization in thetrajectorymodelsignificantly improves Waughet al. [ 1997]. Mapsof Q indicatethatthe stretching the agreementwithin the collarregionof high ozonethat effect of the horizontalstrainfield is substantiallyreduced surrounds the polar vortex. This result,togetherwith evi- by vorticity[HaynesandAnglaite,1997]. The survivalof a denceof planetary-wave breakingin successive mapsof PV, coherentcycloniccirculationenclosinglow CH4 values,afdemonstrates thatmixingof vortex-edge air andmidlatitude ter thebreakupof thepolarvortex,is a symptomof reduced flow,whichis likely to haveretarded air in March and April was importantin establishing ob- strainin thelarge-scale the mixing of the air enclosed withinit with themidlatitude servedconstituent correlations observed at theendof April. environment. 03 - CH4 correlations for a summertime flight(June26) It is importantto distinguishbetweenthe effectsof transshow filamentarystructure,characterized by low CH4, mixing on ozonemixing ratiosin againsta background of generallywell mixedair. HALOE port and wave-induced the low stratosphere during POLARIS. This studyprovides air masspredictions for thesameflightcapturethecompact, evidence that wave-induced mixing was importantin dewell-mixedconditions thatwereobserved andsuccessfully correlations observedfrom the ER-2 distinguish thelow CH4 filamentary structure. Althoughthe terminingtracer-tracer mixing was weak origin of the low CH4 observedby the ALIAS instrument platformin spring1997. Wave-induced cannotbeconclusively established, thelowCH4observed by in summer 1997, as is evidencedby the prolongedsur-
26,608
FAIRLIE ET AL.: CONTRIBUTION OF MIXING IN LAGRANGIAN PREDICTIONS I
I
80
=
60
,- 40
u- 20 I
,
0 M
A
j
M
j
A
S
Months Figure 9. Timeseriesof the efficiencyfactorQ averagedaroundPV contours,shownas a functionof
"equivalent latitude"at 500 K for March19 to September 22, 1997. Unitsare 8-]. The equivalent latitude of a PV contour is defined as the latitude that encloses the same fractional area of the Northern
Hemisphere(includingthe pole) as the PV contour.The datahavebeensmoothedin time usinga 5-day
running mean.Negative valuesandvalues exceeding 168-1 areshaded.
vival of vortexfilamentsandonlyminordifferences between air masspredictionswith and without mixing. However, this doesnot indicatethat transportin a mean meridional sensewas unimportant. Pierce et al. [this issue] show that transport-induced changesand photochemical changes to ozonewere of similar magnitudebut generallyopposite sign in northernhigh latitudesfor much of the POLARIS period. This transportcomprisesthe mean meridionaland diabaticcirculations[Rosenlof,this issue]to which tracertracerrelationships,specificallythosethat are independent of potentialtemperature, are insensitive. The successof the air masspredictionsin reproducing much of the observedstructureon April 26 and June26 demonstrates thatthemixingparameterization performswell undertheextremesof strongmixing(April 26) andrelatively weak mixing (June26). This givesus confidencethat the mixing parameterizationcan be usefullyappliedto a wide rangeof conditions.The parameterization is limited, however, by the nonuniformdistributionof air parceltrajectories in the model. Mixing is triggeredonly when neighboringparcels(determinedby the coincidencecriteria)are found.Remappingconstituent valuesto a uniformgridprior to computingdiffusivetendenciescouldhelp alleviatethis limitation,but remappingis itself affectedby a nonuniform
distributionof air parceltrajectories.In addition,further refinement
of the Eulerian
definition
of vortex air used in
the parameterization appearsnecessary.Sucha definitionis neededto representthe existenceof a barrierto large-scale isentropicmixing of vortex and midlatitudeair [Pierce et al., 1994], and to preventanomalousenhancedmixing between vortex and nonvortexair parcelsin the model. The parameterized mixing is sensitiveto this definition,because Q valuestypicallypeaknearthevortexedge.Despiteitslimitationsthe Lagrangianparameterizationof diffusivemixing usedheresignificantlyimprovesthe modelresults,comparedwith thoseobtainedwithoutdiffusivetendencies.In doing so, the parameterizationprovidesthe meansto distinguishand assessthe impactof diffusivemixing on constituentmixing ratiosin the real stratosphere. Acknowledgments. Many thanksto Larry Coy, DavidLamich, and RebeccaOrris for their help with the assimilatedmeteorological analyses.Thanksto Randy May, David Scott,and Bob Herman of the ALIAS team and to Jim Margitan of the NOAA Oa team. Thanksto Bob Herman,Darryn Waugh,and Rich Eckman
for readingthe paperand for very helpfulcommentsand suggestions.
Useful discussions were also held with John Thuburn and
Matt Hitchman. This work was supportedunder NASA's AtmosphericChemicalModelingandAnalysisProgram(ACMAP).
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(ReceivedAugust16, 1998; revisedFebruary1, 1999; acceptedFebruary11, 1999.)
