Journal of Geophysical Research-Planet, vol 104, pages 24,155 … · 2003. 2. 5. · Journal of...

Journal of GeophysicalResearch-Planet, vol 104,pages24,155-24,176,1999

Improved general circulation models of the martianatmosphere from the surface to above 80 km

FrancoisForget,Frederic Hourdin,RichardFournier,�

ChristopheHourdin,andOlivier Talagrand

LaboratoiredeMeteorologieDynamiqueduCNRS,Universite Paris6, Paris

Matthew Collins,�

StephenR. Lewis andPeter. L. Read

Atmospheric,OceanicandPlanetaryPhysics,Departmentof Physics,Oxford University, Oxford,England,UnitedKingdom

Jean-Paul Huot

EuropeanSpaceResearchandTechnologyCentre,EuropeanSpaceAgency, Noordwijk, Netherlands

Abstract. We describea setof two “new generation”generalcirculationmodelsof the Martian atmospherederived from the modelswe originally developedintheearly1990s.Thetwo new modelssharethesamephysicalparameterizationsbut usetwo complementarynumericalmethodsto solve theatmosphericdynamicequations.Theverticalresolutionnearthesurfacehasbeenrefined,andtheverticaldomainhasbeenextendedto above 80 km. Thesechangesareaccompaniedbytheinclusionof state-of-the-artparameterizationsto bettersimulatethedynamicalandphysicalprocessesnearthe surface(boundarylayer scheme,subgrid-scaletopographyparameterization,etc.) andat high altitude(gravity wave drag). Inaddition,radiative transfercalculationsandtherepresentationof polarprocesseshavebeensignificantlyimproved.Wepresentsomeexamplesof zonal-meanfieldsfrom simulationsusingthemodelat severalseasons.Onerelatively novel aspect,previously introducedby Wilson [1997], is that aroundnorthernwinter solsticethestrongpoleto polediabaticforcing createsa quasi-global,angular-momentumconservingHadley cell which hasno terrestrialequivalent.Within sucha cell theCoriolis forcesacceleratethewinter meridionalflow towardthepoleandinducea strongwarmingof the middle polar atmospheredown to 25 km. This winterpolarwarminghadbeenobservedbut not properlymodeleduntil recently. In fact,thermalinversionsaregenerallypredictedaboveone,andoftenboth,polesaround60-70km. However, the Mars middle atmosphereabove 40 km is found to bevery model-sensitive andthusdifficult to simulateaccuratelyin the absenceofobservations.

�Now at Laboratoired’Energie Solaireet Thermiquede l’Habitat, Uni-

versite PaulSabatier, Toulouse,France.�Now at Hadley Centrefor Climate Predictionand Research,United

KingdomMeteorologicalOffice,Bracknell,England.

1. Introduction

Most of what is currentlyknown aboutthe climateandthegeneralcirculationof theatmosphereof Marsstill comefrom the spacecraftmissionsof the 1970s. Unfortunately,theseobservationaldatalackedthetemporalandspatialcov-

1

2 FORGETET AL.

erageneededto fully characterizethe generalcirculationof the atmosphere,and for several yearsthe detailsof thegeneralcirculationhave beenderivedfrom numericalsimu-lationsperformedwith generalcirculationmodels(GCMs)adaptedfrom the modelsusedfor weatherforecastingandclimate studiesfor the Earth. On Mars, GCMs have suc-cessfullyreproducedmostof theavailableobservationsandhave thusbeenvery usefulin analyzingandinterpretingthedata. They have alsobeenusedto predict the behavior ofthe Martian atmosphereand climate in regionswherefewobservationaldatawereavailable,in particularto predictthebehavior of planetarywavesandmeridionalcirculations.

A new eraof spacecraftexplorationof Mars is now be-ginning. More than ever, generalcirculation modelsareneeded. On the onehand,thesemissionswill greatly ex-tendthequantityof observationsof theMartianclimate,andGCMsarethebesttoolsto analyzeandinterpretthesedata.For instance,theThermalEmissionSpectrometer(TES)andPressureModulatedInfrared Radiometer(PMIRR) instru-mentsof theMarsGlobalSurveyorprogramareatmosphericsounderswhich mostly measureatmospherictemperatures,rather than winds or pressure. Interpretingthe exact na-ture of the observed structurewill be possibleby directlycomparingthedatawith theGCM predictionsor by assim-ilating the datainto the modelsusingthe powerful dataas-similation schemeswhich have beendevelopedfor Earth’smeteorologyandclimatology, asdemonstratedfor MarsbyLewis et al. [1996]. On the otherhand,the designof fu-turemissionsrequiresa goodknowledgeof theMartianen-vironmentandits variability (for aerobraking,aerocapture,descentandlanding,instrumentspecification,etc.).Becausethey areableto providea completethree-dimensionaltime-dependentatmosphericstate,carefully validatedGCMs arethebesttoolsavailablefor theseaspectsof missiondesign.

For thesepurposes,very sophisticatedmodels,account-ing for all theprocessesthoughtto affect theMartianmete-orology, areneeded.To developsucha model,two groupsfrom the Laboratoirede MeteorologieDynamique(LMD,Paris)andthesub-Departmentof Atmospheric,OceanicandPlanetaryPhysicsat Oxford University (hereafterAOPP,Oxford)havejoinedtheirefforts,with thesupportof theEu-ropeanSpaceAgency, CentreNationaldeRechercheScien-tifique (CNRS),andthe U.K. Particle PhysicsandAstron-omy ResearchCouncil. A “new generation”GCM hasbeendeveloped,basedlargely on the modelspreviously devel-opedseperatelyby thetwo groups,but in which mostof theschemeshavebeenimprovedor redesignedandnew param-eterizationsadded.The primarypurposeof this paperis topresenta detaileddescriptionof the resultingmodel. Someresultsillustrating the GCM performanceshave also beenincludedat the endof the paper. More detailedanalysisof

the Martian climate and further comparisonsof the GCMresultswith the availableobservationsare to be publishedelsewhere(see,for instance,Forget et al. [1998b] ; otherpapersarein preparation).In particular, this new GCM hasbeenusedto producea Martianclimatedatabase,presentedin a companionpaper[Lewis et al., this issue]alongwithsomecomparisonswith theavailableobservations.

2. Background

Comprehensivegeneralcirculationmodelingof theMar-tian atmospherebegan with Leovy and Mintz [1969] whosuccessfullyadaptedthe thenrecentlydevelopedterrestrialGCM of theUniversityof California,Los Angeles(UCLA)to Martian conditions. The model predictedatmosphericcondensationof CO� andthepresenceof transientbaroclinicwaves in the winter midlatitudes. Later developmentsofthis modelweremadeat NASA AmesResearchCenterandhave provideda numberof insightsinto our understandingof theMartianclimate[see,e.g.,Pollack et al., 1981,1990;Haberleet al., 1993b;Barneset al., 1993,1996;Murphyetal., 1995;Hollingsworthet al., 1996].

In 1989theLMD terrestrialclimatemodelwasadaptedtoMarsby developinga new radiative transfercode[Hourdin,1992a]and a self-consistentparameterizationfor the con-densationandsublimationof CO� . This modelwasthefirstto simulateafull Martianyearwithoutany forcingotherthaninsolation[Hourdin etal., 1993,1995]. It wasableto repro-ducein a very satisfactory way the seasonaland transientpressurevariationsobservedby the Viking Landers[Hour-din et al., 1995;Collins et al., 1996].

More recently, a similar effort wasinitiatedjointly at theUniversitiesof ReadingandOxford in theUnitedKingdom.A spectralsolver wasusedin conjunctionwith a simplifiedsetof physicalparameterizations.Original resultswereob-tainedonthedynamicalregimeof baroclinicwaves[CollinsandJames, 1995;Collins et al., 1996]andon theboundary-currentnatureof thelow-level cross-equatorialbranchof theHadley Circulation[Joshiet al., 1994].

At aboutthe sametime, a new GCM wasdevelopedatthe GeophysicalFluid Dynamic Laboratory(GFDL) withinclusionof a physicalpackagesimilar to theAmesmodel.Themodelwasusedto studytherole of thermaltides[Wil-son and Hamilton, 1996], and, separatelyfrom Forget etal. [1996] (who obtainedthe sameresultsat LMD at thesametime), indicatedthe importanceof extendingthe ver-tical coverageof GCM modelingto createa polarwarming[Wilson, 1997].

In 1995,at the initiative of theEuropeanSpaceAgency,who wereseekingan environmentalmodelfor missionde-sign on Mars, the LMD andAOPP, Oxford, teamedup to

IMPROVED MARTIAN ATMOSPHERICMODELS 3

develop the modelpresentedhereandthe climatedatabasedescribedin the companionpaperby Lewis et al. [this is-sue].

3. Model Dynamics

Thecoreof anatmosphericgeneralcirculationmodel isthehydrodynamicalcodededicatedto thetemporalandspa-tial integrationof theequationsof hydrodynamics.Thispart,which is basedon a rathergeneralformulation of the hy-drostaticprimitiveequationsof dynamicalmeteorologyonasphere,canbeadapteddirectly from terrestrialmodels.Twodistinctformulationshavebeendevelopedsofar: (1) afinitedifferencesor grid pointmodelbasedonthediscretizationofthehorizontaldomainfieldsona latitude-longitudegrid and(2) aspectralmodel,in whichthehorizontalmodelfieldsarerepresentedby a truncatedseriesof sphericalharmonics.

Each of theseformulationsoffers advantagesand dis-advantageswith regard to accuracy and numericalperfor-mance,andboth approachesareemployed at variouscen-tersfor climatemodelingon Earth.As for Mars,sincebothformulationshadbeenpreviously usedat LMD (grid pointmodel)andAOPP(spectralmodel),we choseto keepbothkinds asoptionsin order to estimatethe likely uncertaintyarisingfrom certaintypesof modelingerrors.

Thegrid point dynamicmodelis basedon theLMD ter-restrialmodeldescribedby SadournyandLaval [1984]. Thediscretizationschemeconservesbothpotentialenstrophyforbarotropicnondivergent flows [Sadourny, 1975] and totalangularmomentumfor constantsurfacepressureaxisym-metricflow. Thelatterpropertywasnot includedin theorig-inal terrestrialversionbut was found to be very importantfor simulatingtheMartianatmospherein orderto avoid spu-rious progradezonalwinds in equatorialregions[Hourdin,1992b].Themodelis typically runwith a regularresolutionof 64 � 48 grid pointshorizontally, correspondingto 3.75

�latitude by 5.625

�longitude. However, in its presentver-

sion,thegrid pointscanbearbitrarilyspreadin bothlatitudeandlongitude. This offers the possibilityof zoomingin ona givenpartof theglobeto studythelocal meteorology, forinstance,ataspacecraftlandingsite.At high latitudeafilteris appliednearthesingularityin thegrid at thepolein orderto satisfy the Courant-Friedrichs-Lewy numericalstabilitycriterionwithout going to anexcessively small timestep.Intheoriginalversionof thedynamicalcodeaclassicalFourierfilter wasused,but we foundthatbecausetheMartianpolaratmosphereappearsto bemuchmoredynamicallyunstablethantheEarth’spolaratmosphere,a moreefficient formula-tion (basedon thegroupingof adjacentgridpointstogether)wasnecessaryto avoid numericalinstability.

TheAOPPspectralsolverwasoriginally developedat the

University of Reading[Hoskinsand Simmons, 1975] andalsoconservestotal angularmomentum.A triangulartrun-cation in spectralspaceat total wavenumber31, with thenonlineartermscalculatedon a 96 � 48 real spacegrid, istypically used.

In the vertical, both models use the terrain-following� coordinatesystem( � is pressuredividedby surfacepres-sure)in finite differenceform. Twenty-five levels aretypi-cally used,with themiddleof thefirst threelayerslocatedataltitudesof about4,19,and44m [seeLewisetal., thisissue,Table3]. Comparedto the previous versionsof the model[seeHourdin et al., 1993,Table1], the vertical resolutionnearthesurfaceis substantiallyenhanced,allowing a muchbetterrepresentationof theatmosphericboundarylayer(seesection6.1). Similarly, themiddleof thetop layerhasbeenextendedfrom 60 km up to about100 km. This extensionnot only allows us to explore the meteorologicalregime atthesealtitudes,but wefoundthatadeepermodeldomainal-lows for thefull developmentof theHadley circulationandwasthusnecessaryto properlysimulatetheMartianclimatebelow 50km. This is discussedfurtherin section8.

In both the grid point andspectralmodels,nonlinearin-teractionsbetweenexplicitly resolved scalesand subgrid-scaleprocessesareparameterizedbyapplyingascale-selectivehorizontaldissipationoperatorbasedon an � time iteratedLaplacian

�. For the grid point model, for instance,this

canbewritten �� diss! �#"%$ ! � &' where "%$is thesmallesthorizontaldistancerepresentedin themodeland diss is thedissipationtimescalefor a structureof scale"%$ . A similar operatoris applied to the spectralmodelfields in spectralspace. Theseoperatorsare necessarytoensurethe grid point modelnumericalstability andto pre-venta build up of energy at thetruncationlimit of thespec-tral model. In practice,theoperatoris separatelyappliedto(1) potentialtemperature,(2) thedivergenceof theflow, and(3) its vorticity. We respectively use �(�*) , �(�+� , and�,�-) in thegrid point model.In thenominalversionof thespectralmodel,however, �.�(/ is usedfor the threefields,following theguidelinesgivenby MacVean[1983].

In the upper levels a spongelayer is also usedin bothmodelsin anattemptto reducespuriousreflectionsof verti-cally propagatingwavesfrom themodeltop. Unlike thetra-ditionalRayleighfriction formulation,this operatesasa lin-eardragsolelyon theeddycomponentsof thevorticity anddivergencefields andis not scale-selective. The timescaleson which it operatesare typically half a day, 1 day, and2daysat thethreeuppermostlevels,respectively.

4 FORGETET AL.

4. Radiative Transfer

The radiative transfer through the Martian atmospherecanbe affectedby the presenceof CO� gas,mineraldust,watervapor, waterice particles,andCO� ice particles.Theradiative effects of ozone should generally be negligible[Lindner, 1990;Zurek et al., 1992]. This sectiondescribeshow the effects of gaseouscarbondioxide and suspendeddustare includedin the modelat solarand infraredwave-lengths.The radiative effectsof watervaporareneglected,sincethecoldMartianatmospherecannotsustainmorethana few tensof precipitablemicrometersof water. In reality,watervaporcouldslightly increasethegaseousinfraredab-sorptionof theloweratmospherein thenorthernhemispherein summer[Savijarvi, 1991]. However, theassociatederrorshouldbesmallcomparedto theuncertaintiesrelatedto thedustradiative propertiesandspatialdistribution. Similarly,theeffect of waterice cloudsis neglected.Waterice cloudscanbecomeoptically thick on Mars,but their occurrenceisthoughtto bequite limited in spaceandtime. Nevertheless,new measurementsmaymotivatethedevelopmentof watercloudparameterizationsin thefuture.Thepossibleradiativeeffectsof CO� iceparticlesduringthepolarnighthavebeenparameterizedseparately, asexplainedin section7.

4.1. CO � Gas

4.1.1. Thermal infrared. Thetreatmentof absorptionandemissionby the strongCO� 15-0 m bandis describedby Hourdin [1992a].Theradiative transferequationis inte-gratedusingthewidebandmodeldevelopedby Morcretteetal. [1986]. In its currentversiontheschemeaccountsfor theDopplerbroadeningof the molecularlines at low pressure(significantabove 50 km) but not for departuresfrom localthermalequilibrium (LTE) (thoughtto be significantabove70-80km, nearthe top of the model). Work is ongoingtoincludenon-LTE effectson cooling in themodel. TheCO�15-0 m band,extendingfrom 11.5to 20 0 m, is divided intotwo widebandsrepresenting(1) thecentralstronglyabsorb-ing part(14.2-15.70 m) and(2) thewings.

4.1.2. Near-infrared absorption. Atmosphericheatingdueto absorptionof solarradiationin thenear-IR bandsofCO� is negligible below 30 km but becomesconsiderableabove 50 km. A simpleparameterizationhasbeenincludedwhich is similar in its effect to heatingratesobtainedinradiative transfercalculationsperformedby Lopez-PuertasandLopez-Valverde [1995] which includenon-LTE effects.At pressure132��54�676 Pa andfor a meanMars-Sundistance8 2 �9�7:<;7) AU, theheatingratecorrespondingto azerosolarzenithangle( 0=�>6 ) is takento be��?�� @132BA 8 2BAC6 ! �5�B: / K dayDFE (1)

The heatingrateat otherpressures1 , Mars-Sundistance8 ,andzenithalangle0 is thencomputedasfollows:��?�� @1GA 8 AH0 ! � ��?�� @132BA 8 2BAC6 ! � 8 �28 � I 1321-J0K�L�7M 1 NLTE1 ! DNE (2)

where 1 NLTE is a pressurebelow which non-LTE effectsaresignificant(1 NLTE �O6P: 676Q47; Pa) and J0 the cosineof thesolarzenithanglecorrectedfor atmosphericrefraction(weuse J0=�R�S�L�%)7)�T70 � MU� ! �V�%)7)7; ! � EHW � ). Theeffectof non-LTE isastrongdecreaseof theheatingabove80km. In theory, thissimpleparameterizationis not completelyconsistentsincetheCO� heatingis justaddedto otherheatingtermswithoutreducingthesolarflux availablefor dustandsurfaceheatingbelow. However, thecorrespondingmaximumreductionofthesolarincidentflux is alwayslowerthan1.5%,well belowthe level of other uncertaintiesrelatedto the dust and thesurfaceproperties.

4.2. Dust

4.2.1. Solar radiation. As in theoriginalversion[Hour-din et al., 1993, 1995], the radiative transferequationac-countingfor theabsorptionandscatteringof solarradiationby the dust is basedon the numericalschemeof Fouquartand Bonel [1980]. This codewasoriginally developedforthe LMD terrestrialGCM andis currentlyusedby the op-erationalmodelof theEuropeanCentrefor Medium-RangeWeatherForecasts(ECMWF). The upward anddownwardfluxesareobtainedfrom thereflectancesandtransmittancesof thelayers,computedusingtheDelta-Eddingtonapproxi-mation.

The availablestudiesof Martian dustoptical propertieshavesuggestedthatthesingle-scatteringpropertiesarechar-acterizedby anabruptchangearound0.5 0 m nearthepeakof the incidentsolarflux andthatmultispectralcalculationswereessentialto obtainaccurateresults[Ockert-Bell et al.,1997]. Sincedetailedmultispectralcalculationswould betoo expensive in a GCM, we usetwo broadbands(0.1-0.50 m and0.5-5 0 m). In order to make useof spectraldustproperties,we spectrallyaveragethem in eachwidebandto obtainmeanscatteringcoefficients(extinctioncoefficientJXZY\[^] , single-scatteringalbedo J_ , andasymmetryparameterJ` ). Thefollowing ponderationlawsareused:

JXZY\[^] � acbedb�f�g b XihLj�k\l b�mQnaob db f�g bpmVn (3)

J_ � a bedb f g b XZY\[^]ql b _ brmQna b db�f g b XZY\[^]ql bpmVn (4)


J` � a b db f g b X Y\[^]ql b _ b ` b mQnaob db%f�g b XZY\[^]ql b _ b�mQn (5)

where g b is thePlanckfunctionat 6000K (representingthesolarradiance)and n E and n � arethewavelengthsat theboundariesof theband.

Choosingtheexactradiativepropertiesto beusedby themodel remainsproblematic,however. On the one hand,this is dueto the factsthat the dustsingle-scatteringprop-ertiesmay vary with altitude,season,andhorizontalloca-tions and that the variouspropertiesobtainedby the dif-ferent paststudiesmay not be representative. In particu-lar, it is likely that in someconditions,the dust particlescanget coatedby water ice [Colburn et al., 1989; Ockert-Bell et al., 1997]. On the other hand,the radiative trans-fer resultswhich areof importancefor GCM (e.g.,heatingrates)areunfortunatelyextremelysensitive to thedustprop-erties.For instance,thedustsingle-scatteringalbedo_ atso-lar wavelengthis thoughtto bequitehigh, typically around0.9. An uncertaintyof s 5% then correspondsto an erroron theheatingrateof about s 50%. Dustopticalpropertieshave beenderived from surfaceobservations(landers)andfrom orbit. Among the first kind of data,oneof the mostcompletedatasetsis the spectralsingle-scatteringproper-ties extrapolatedover the solarwavelengthsby Ockert-Bellet al. [1997] from the Pollack et al. [1995] Viking Landerdata.Thesedataappearto beconsistentwith themorerecentPathfinderobservations[Markiewiczetal., 1999].However,dataobtainedfrom downlooking observation performedinorbit from above the atmosphereseemto give slightly dif-ferentsresults. Wavelength-averageddust propertieswerederivedby ClancyandLee[1991]on thebasisof their anal-ysis of the Viking orbiter infraredthermalmapper(IRTM)emission-phase-functionmeasurements.Theseobservationsyieldedbrighterdustproperties,with ahighersinglescatter-ing albedoanda lower asymmetryparameter(Table4.2.1).This may result from to the fact that smallerdustparticlesaresampledfrom aboveor that theobservationincludestheeffectsof clouds.In practice,Clancy andLee’sdustparame-terscorrespondsto slightly coldertemperaturesthanwith theOckert-Bell dustparameters.Until betterdatafrom theup-comingMartianmissionsaremadeavailable,we have beenusingboth kinds of datain the model(Table4.2.1). How-ever, the resultspresentedin this paperas well as in thecompanionpaperby Lewis et al. [this issue]wereall ob-tainedusingClancyandLee’s [1991]dust.

4.2.2. Thermal infrared. In theoriginalversionof themodel,scatteringof thermalinfraredradiationwasnottakeninto account.Thisassumptionis madein mostEarthstudies.On Mars,suchanassumptionis reasonablewithin theCO�15-0 m bandbecauseof thestrongisotropy of the radiation

0t

1u 2v

3w

4x

5y

6z192

194

196

198

200

202

Sur

face

Tem

pera

ture

(K

)

{

Dust visible Optical depth

WITH scattering|NO scattering

Figure 1. Daily averagedsurfacetemperaturecomputedatViking Lander1 site (22

�N) at winter solstice( }�~��()B4�6 � )

asa function of dustopacity (resultsobtainedwith a one-dimensionalradiative-convectiveversionof thegeneralcir-culationmodel(GCM) physicalpackage).Scatteringof in-fraredradiationby the airbornedusttypically increasestheincidentIR flux to thesurfaceoutsidetheCO� gaseousbandby 10-20%.This resultsin a warmingof thesurface.

emittedby the gaseousatmosphere(Y. Fouquart,personalcommunication,1991). However, we found that at otherwavelengthsthe infrared radiationscatteredby the atmo-sphericdustbackto the surfacecanbe nonnegligible (Fig-ure1), thuschangingthesurfaceandatmospherictempera-ture.

We have thereforeincludeda radiative transferschemethat accountsfor multiple scatteringby dustparticlesout-side the CO� 15-0 m band. It is basedon the two-streamhemisphericmeansourcefunction codedescribedby Toonet al. [1989]. The infraredspectrumoutsidethe CO� 15-0 m bandis divided into two widebands,onefor the 9-0 msilicate band (5-11.5 0 m) and one for the rest of the in-fraredspectrum(20-200 0 m). Until moreaccuratedataaremadeavailable,we usea setof syntheticsinglescatteringspectralpropertiesof the Martian dust specificallyformu-lated for this GCM anddescribedby Forget [1998]. Thismodelwasdevelopedby modifying the long-standingToonet al. [1977] dust model (basedon the optical propertiesof a clay samplecalledMontmorillonite 219b) in order toaccuratelymatch the Mariner 9 observationsof the 1971globalduststormateveryIR wavelength,withoutrestrictionto any particularhypothesisfor theactualdustcomposition.In eachwideband,wavelength-integratedmeandustsingle-scatteringpropertieswerecomputedusing(3), (4) and(5),with g b beingthe blackbodyintensityat 215 K, a typicalmeantemperatureon Mars (Table 4.2.1). This discretiza-

6 FORGETET AL.

Table 1. AveragedAtmosphericDust Single ScatteringParametersUsedin the Solar and Thermal Infrared RadiativeTransferCodein theCurrentVersionof theModel with theInfraredto Visible OpacityRatio ��C� m �% �2�� C�� m setto 2.

Band, 0 m JX Y\[^] � X Y\[^] �#6P: �Q4%0 m) J_ J`Solarradiation(1)a 0.1-0.50 m 0.878 0.665 0.819

0.5-5 0 m 1.024 0.927 0.648

Solarradiation(2)b 0.1-0.50 m 1.0 0.920 0.550.5-5 0 m 1.0 0.920 0.55

Thermalradiationc 5-11.6 0 m 0.253 0.470 0.52811.6-200 m 0.405 0.541 0.55120-2000 m 0.166 0.370 0.362

Resultspresentedin this paperwereobtainedusingsolarradiationproperties(2).�Computedfrom Ockert-Bell et al. [1997].�Computedfrom ClancyandLee[1991].�Computedfrom Forget [1998].

tion in two widebandswasfoundto introducelessthan10%errorcomparedto a moresophisticatednarrowbandcompu-tation. In the15-0 m band,absorptionby thedustis addedtothe absorptionby CO� , usinga meanabsorptionparameterJXZ�C�� R�H�r� J_ ! JX Y\[^] , with J_ and JX Y\[^] computedasabove.

The scalingof dustopacity in the infraredcomparedtothe visible is alsoa key parameterof the dustmodelsinceit controlsthelocal radiative balanceof theatmosphereandthe surface. This ratio is highly sensitive to the actualdustsizedistribution,which is poorly known sinceeachspectralregionis sensitiveto differentparticlesizes[seeZurek1982;Forget, 1998]. In the original model a ratio of about1.2hadbeenused,following Pollack et al. [1979] as in mostotherexisting Mars GCMs then[e.g., Pollack et al., 1990;Wilson and Hamilton, 1996]. However, measurementsofthedustopticaldepthmadeseparatelyat solarandinfraredwavelengthsat thesametime andlocationsuggesta visible(0.67 0 m) to infrared(9 0 m) ratio of about2-2.5 [Martin,1986; Clancyet al., 1995]. In the baselineversionof themodelwe thereforescalethedustopacities from theratio ��C� m �% �2�� C�� m ��) (Table4.2.1).

4.2.3. Dust spatial distribution. In the baselinever-sionof themodel,thedustmixing ratio is prescribedandthedustis not transportedby winds(otherversionsof themodelincludethis capability[Forget et al. 1998a]).Thedustmix-ing ratio is takento beconstantin the lower atmosphereupto a level above which it rapidly declines,consistentwiththe availablespacecraftobservations. Following Pollack etal. [1990], mostGCMs (including the previous versionofthis model)have usedthe dustvertical distribution derivedby Conrath [1975] from considerationsof particlesedimen-tation andeddymixing. The dustmassmixing ratio was

definedasa functionof pressure1 ; thatis, �� 2��N� �F�L�p��132��1 ! � 1,��1&2 �� 2 1,��1&2 (6)

where �2 is a constantdeterminedby the prescribedopti-cal depthat the referencepressurelevel 1&2��4�676 Pa and� is a constantthat determinesthe shapeof the function.Conrath [1975] estimated�R�+6P: 676Q4 during dust storms,but Pollack et al. [1990] (andfollowing mostotherGCMs)used��6P: 67/ , thoughtto representmoretypicalconditions.In reality, observationsat the limb by the cameraaboardMariner 9 [AndersonandLeovy, 1978] andViking [Jaquinet al., 1986] have shown that the dustvertical distributionstronglyvarieswith spaceandtime,with dustconfinednearthe surfacein the polar regionsor reachingvery high alti-tudesin the tropicsduring duststorms.Representingthesevariationswith (6) by varying � would have led to an un-realisticverticaldistribution. We thereforeuseda modifiedversionof (6): Z�> �2N��6P: 676Q4¡ ¢�r�£�@132��1 !�¤ ��2&¥^¦ WC§�¨3©#ª�«¬&® 1,��132 (7)

where ¯ max is the altitude(km) of the top of the dustlayer.Equation(7) matches(6) under the conditionsfor whichthe later was originally designedby Conrath( �°�*6P: 676V4 ,¯ max �±4�6 km) but remainsrealistic for thinner dust lay-ers [seeLewis et al., this issue,Figure 3]. The climato-logical altitude of the top of the dust layers can be de-duced from the analysisby Anderson and Leovy [1978]and Jaquin et al. [1986]. To first order, thesemeasure-mentscanbe summarizedandrepresentedby the function¯ max �°�B6�M>��²o³�´SµN�¶} ~ �£�e�76 � ! �·)7)3�¶³�´¸µ�¹ ! � , with } ~ bee-ing thesolarlongitudeand ¹ beinglatitude.Thisequationis


currentlyusedin mostof oursimulations.However, weusu-ally keepthereferencemixing ratio 2 constanthorizontallyover theplanet.Indeed,althoughslight spatialvariationsofthedustopticaldepthhavebeenmeasuredby Martin [1986]andMartin and Richardson[1993], no simpledependenceon latitudeor longitudecanbedetermined.

5. Surface Processes

Surfacetemperatureevolution is governedby thebalancebetweenincomingfluxes(directsolarinsolation,thermalra-diationfrom theatmosphereandthesurfaceitself,andturbu-lent fluxes)andthermalconductionin thesoil. Theparam-eterizationof this lastprocessis basedon thesophisticated11-layersoil modeloriginally developedfor theLMD Mar-tianGCM (describedby Hourdin etal. [1993]). A verticallyhomogeneoussoil is assumed,andthespatiallyvaryingsoilandsurfaceproperties,thatis, thermalinertiaandalbedo,arecurrentlybasedon the Viking IRTM observationsanalyzedby PalluconiandKieffer [1981](thermalinertia)andPleskotandMiner [1982] (albedo)extendedto thepolarregionsus-ing therecentresultsfrom Paigeetal. [1994]andPaigeandKeegan [1994]. It hasbeensuggestedthat the thermalin-ertiadeducedby Palluconi andKieffer [1981] maybeover-estimateddueto weaknessesin theretrieval model[HaberleandJakosky, 1991]but it is retainedfor thepresentin theab-senceof morereliableinformation.Moreaccuratedatafromthe upcomingmissionswill be adoptedas soon as avail-able.A third mapis usedby themodelfor thesurfaceorog-raphy. The accuratemeasurementsfrom the Mars OrbiterLaserAltimeter (MOLA) aboardMarsGlobalSurveyor willbe usedassoonaspossible.This paperwaswritten beforethesedataweremadeavailable. Threedatasetswerethenavailablefor modelers: the Mars Consortium[Wu, 1978],the U.S. GeophysicalSurvey digital elevationmodel(oftencalledDTM ; seeDavies[1992]), andthe eigth-degreeandordersphericalharmonicmodelderivedfrom radioocculta-tion databy Smithand Zuber [1996]. The choicebetweenthesedatasetsremainedcontroversial.Thesimulatedzonal-meanfieldspresentedin this paperwereobtainedusingtheDTM dataset,which accountsfor fine structuresnot repre-sentedin SmithandZuber’s [1996] smoothtopographyandwhich providessomeinformation in the southernpolar re-gion, wheretheMarsConsortiummapsufferedfrom a lackof data.In fact,suchzonal-meanfieldsarenotverysensitiveto the detailsof the topography, andalmostsimilar figureswouldhavebeenobtainedwith theotherdatasets.

6. Subgrid-Scale Dynamics

6.1. Turbulent Diffusion in the Planetary BoundaryLayer

Accuratedescriptionof near-surfaceconditionsis an in-creasingrequirementfor Martian GCMs in order to pre-dict accuratesurfacedrags,dustlifting, tracertransport,andnear-surfaceconditionsfor missiondesign.In turn, Mars isa challengingplanetfor parameterizationof boundarylayerdynamics,theveryshallow (about100m) andstronglystrat-ified nocturnalboundarylayerevolving during the day in averydeepandfully convectivelayerof severalkilometers.

As in mostGCMs,boundarylayerdynamicsis accountedfor by a turbulent closureschemebasedon the conceptofturbulentviscosityplusa convective adjustementin caseofunstabletemperatureprofiles. The turbulent mixing of anystatevariable º (horizontalwind componentsor potentialtemperature)is computedas��º�� » ��¯G¼ » ��º��¯ (8)

where ¼ takesdifferentvalues¼�½ and ¼¿¾ for �¢ÀÁAHÂ ! and Ã ,respectively. In thebottomlayertheturbulentsurfaceflux isgivenby »VÄÆÅ�Ç E �¶º E �Èº 2 ! , where º E and º 2 arethevariablevaluesin thefirst atmosphericlayerandat thesurface( º 2 �6 for winds), Ç E is the wind velocity in the first layer, andÄ Å is thedragcoefficient. Becauseof thesmalldepthof thefirst layer( ¯ ErÉ T m),wecanassumethatthewind profileinthefirst metersabove thesurfaceis logarithmicandsimplyuse Ä Å ��ÊÌËÍ µ §§HÎGÏ � (9)

where Ë is the von Karmanconstant( Ë �*63: T ) and ¯ 2 isthe roughnesscoefficient. We assumethat ¯ 2 �Ð6P: 6P� meverywhereon Mars, assuggestedby Suttonet al. [1978]for theViking Landersites.

Theschemehasbeenrecentlyimprovedby introducinganew parameterizationfor ¼ ½ and ¼ ¾ basedon Mellor andYamada’s [1982] unstationary2.5-level scheme. With re-spectto the original Mellor and Yamadascheme,we usea modified set of stability functions derived by Galperinet al. [1988] to solve somenumericalinstability problemsin the scheme,and the computationof the turbulent mix-ing length is replacedby Blackadar’s [1962] law, ÑH�¶¯ ! �Ë ¯V��L��M Ë ¯Q��ÑÒ2 ! , whereÑÒ2 is areferencelengthscalethatwefixedto a valueof 160m.

Computationof mixing coefficientsis basedon anequa-tion for theevolutionof theturbulentkineticenergy(TKE) Ó :��Ó�� ÔÑRÕ3Ö ½V×�½ M Ö ¾�×i¾ � �Ø EVÙ M ��¯ ¼�Ú ��Ó��¯ (10)

8 FORGETET AL.

with ��°Û )7Ó (11)Ü �5Ý Õ ��À��¯ Ù � M Õ ��Â��¯ Ù � (12)

× ½ � Ñ � � Ü � (13)

×i¾ �5� Ñ � � `Ã%2 ��Ã��¯ (14)

Ö ½ � Þ E M Þ � ×i¾�L��M Þ Ô × ¾ ! �L�ßM ÞGà × ¾ ! (15)

Ö ¾ � ÞÁá��M Þ Ô × ¾ (16)Ö Ú � Þ � (17)

Thecoefficients Þ andØ E take the constantvalues( Þ E ,Þ � , Þ Ô , Þ�à , Þ á , Þ � , Ø E ) =(0.393,-3.09,-34.7,-6.13,0.494,

0.38, 16.6). Here Ã%2 is the meanpotential temperature.Within this context, the correspondingturbulent diffusioncoefficients are ¼ ½ �â �Ñ Ö ½ for velocity, ¼ ¾ �± �Ñ Ö ¾ forpotentialtemperature,and ¼ Ú �� Ñ Ö Ú for TKE.

Figures2aand2cshow resultsfrom one-dimensional(1-D) simulationobtainedwith this modelwith thesameverti-cal discretizationasfor 3-D GCM simulations.Theverticalwindandtemperaturestructuresaresimilarto thoseobtainedby Haberleetal. [1993a]with astrongdecreaseof theplan-etaryboundarylayerheightat night andanassociatednoc-turnal jet with wind magnitudes20% above the large-scalegeostrophicwind.

In thereferenceparameterizationpresentedabove,weusean implicit time schemeexceptfor ¼ . However, evenwiththis classicalimplementation,themodelrequiresverysmalltime steps(hereabout1000timeslongerthanin theGCM),especiallyat night. The instability in thosestronglystrati-fiedconditionswasattributedto thestrongcouplingbetweenwind shearandTKE: for largetimesteps,theTKE evolutioncannotbe estimatedwithout taking into accountthe windshearreactionduring the time step. We thereforederivedasimplifiedbut muchmorerobustparameterizationin whichanestimationof thewind shearevolutionundertheeffectofTKE is introducedin the computationof TKE. This evolu-tion is givenby

Õ � Ü�&� Ù § l k � � ��¯ � � ¼ ½ l § l k Ü § l k ! (18)

For fixedvaluesof fluxes ¼ ½ Ü at thetwo neighboringlev-els,(18) givesa simpleestimationof the local couplingbe-tweenTKE andwind shear. In thestablelimit ( '��ã 0) and

neglectingturbulentdiffusionof Ó , thesystemof equations(10)-(17)reducesto��Ó�&� � �ÔÑ Ê � Þ �Þ Ô Þ�à�ä¾ Î�å ¾å § Ü � MæÞ áÞ Ô � �Ø E Ï (19)

and the resultingcoupledsystemof (18) and (19) can besolvedanalyticallyin thestationarycase( �N��&�ç��6 in equa-tions).

In practice,for alargetimestep � suitablefor theGCM,

theTKE is updatedin two steps:Ü �§ l k¢èNéçkÁê Ü �§ l kÖ ½ l § l k ×�½ l § l k Õ �Ø E � Ö ¾ l § l k × ¾ l § l k Ù (20)

and Ó Ô W �§ l k¢èNéçk ê Ó § l kÛ )�ÑH�#¯ ! Ü § l k¢èNéçkÕ �#¯ è �ë¯ ! ¼ ½ l §�ì l k Ü §�ì l k M>�¶¯��ë¯ D ! ¼ ½ l §^í l k Ü §^í l k¯ è �î¯ D Ù (21)

where ¯ D and ¯ è are the altitudesof the layer below andabove,respectively.

Stationaritymeansthat thetime constantsfor turbulenceareshorterthanthe time step,which is approximatelytruehere. However, the stableapproximationis not valid fordaytimeconditions,but, then,themixing is essentiallydoneby convection. Undersuchconditionsthe Mellor and Ya-mada[1982]parameterizationis probablynotvalid anyway.The derivation of the schemeandanalysiswill be detailedin a forthcomingdedicatedpaper. Nevertheless,we showheresomecomparisonsof the GCM parameterizationwiththe full parameterizationpresentedpreviously. Figures2band2d show 1-D simulationresultsusingthis approximateprocedurewith the standardGCM time step(48 stepsperday).Convergencewith thereferencesimulation(Figures2aand2c)is satisfactorywith the exceptionof the strongday-nighttransitionduringwhichall statevariablesundergovari-ationswhich arefasterthantheGCM time stepandsocan-not be fully reproducedby the approximateparameteriza-tion. This convergenceis themainargumentfor thevalidityof thesimpifiedGCM scheme.

In Figure3 in situhigh-frequencymeasurementsobtainedby the Viking Lander1 in spring are comparedwith 1-Dmodel results. Thesemeasurementswere madeat 1.6 mabove the surface, whereasthe center of the first GCMlayer is around4 m. This altitude differencedoesnot al-low an exact comparison,especiallyfor the wind at night,whenstratificationis verystrongimmediatelyabovethesur-face. Anothermajor sourceof differencesbetweenmodelandobservationsis theconvective adjustment,which is not


REFERENCE MODEL (MY2.5) APPROXIMATE GCM MODEL

Local time (h) Local time (h)

Local time (h) Local time (h)

Figure 2. (Figures2aand2b ) Horizontalwind meanvelocity (m sDNE ) and(Figures2c and2d ) standarddeviation of windstrength dueto turbulence(m sDNE ) simulatedby thereferenceMellor andYamada[1982]2.5model(left) andtheproposedparameterization(right) useablewith theGCM’s30 minutetimestep.Resultsin bothcaseswereobtainedwith a1-D versionof theGCM physicalpackagefor conditionsat theViking Lander1 site (22

�N) in spring( } ~ �RTQ; � ). Themodelis forced

thermallyby radiation(visible dustopacity: 0.5; surfacealbedo:0.32;surfacethermalinertia: 290J m D � sDNEHW � K DFE ) anddynamicallyby a geostrophicwind of 7 m sDNE .

10 FORGETET AL.

180

190

200

210

220

230

240

250

12 17 22 03 08 13

Tem

pera

ture

(K

)ïLocal time (h)

reference model MY 2.5 (z=4m)approximate model GCM (z=4m)

Viking obs. (z=1.6m)

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1

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3

4

5

12 17 22 3 8 13

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d ve

loci

ty (

m/s

)ðLocal time (h)

Reference model MY 2.5 (z=4m) Approximate model GCM (z=4m)


0

0.2

0.4

0.6

0.8

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1.4

1.6

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12 17 22 3 8 13

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d st

anda

rd d

evia

tion

q (m

/s)

ñLocal time (h)

Reference model MY 2.5 (z=4m) Approximate model GCM (z=4m)


Figure 3. A comparisonof Viking Lander1 observationsof temperature,wind meanvelocityandstandarddeviation measured1.6m abovethesurfaceduringsol554( }ß~ß��TQ; � )with resultsfrom the 1-D boundarylayer schemeat about4 m. The model parametersare the sameas in Figure 2.Thehighfrequency Viking datawerekindly providedbyJ.E.Tillman, Viking ComputerFacility (1993).

associatedwith any TKE increasein the presentmodel.This explainsthelow TKE valuessimulatedduringtheday,whereasViking actuallyrecordedwind fluctuationsashighas2 m sDNE . This differencedoesnot alter the meanwindpredictionssignificantly, however. The meanwind veloc-ities predictedby the combinedboundarylayer-convectionschemesseemto matchcloselytheobservations.Morecom-parisonsconcerningthesimulationof variationsin wind di-rectionwith thefull 3-D GCM aregivenby Lewisetal. [thisissue].Altogether, it canbeconcludedthattheproposedtur-bulencemodelallows economicalandrealisticestimationsof most surfaceenvironmentalvariablesand their diurnalevolution.

6.2. Convection

As in theoriginalLMD model,weuseastandardenergy-conservingconvectiveadjustmentschemewhichrapidlymixesheatandmomentumin convectively unstablelayers.To ac-countfor the fact that, in reality, the mixing of momentumdependsupontheactualmassfluxesinvolvedin theconvec-tion, theintensityof themomentummixing is a functionoftheintensityof theinitial verticalinstability [Hourdin et al.,1993].

6.3. Representation of the Subgrid-Scale Orographyand Gravity Waves

Theorographyusedin theGCM is smoothedto thehor-izontal resolutionof the model. Direct effectsof variationsof the orographyon scalessmaller than the grid scaleonthe large-scaleflow areeffectively ignored. Thesesubgrid-scalevariationscan,however, have a significantimpactonthe resolved circulationof the atmosphere,so their effectsshouldbeparameterizedin someway. Morespecifically, thesubgrid-scalemountainscan influencethe large-scale(ex-plicitely resolved)flow in two ways:(1)byproducingaformdragon the flow at low levels and(2) by exciting internalgravity waveswhichcanpropagatein thevertical,break,anddeceleratetheflow farawayfrom themountainsthemselves.We have chosento parameterizethesetwo effectsusing,for(1), thelow-level dragschemeof Lott andMiller [1997]andfor (2) thegravity wave dragschemeof Miller et al. [1989]andBainesandPalmer [1990], which wasitself developedfrom the original schemeof Palmer et al. [1986]. Both oftheseschemesarein currentoperationaluseat theEuropeanCentrefor Medium-RangeWeatherForecasting.Full detailsof the implementationandvalidationof the low-level dragandgravity wave dragparameterizationschemesaregivenby Collins et al. [1997]. The impactof the schemeon theperformanceof themodelis illustratedin section8.3 of thepresentpaper.


HZb

Z Z H/Zb

U

Figure 4. Schematicrepresentationof thelow-level flow be-havior in thesubgridscaleorographicdragparameterizationscheme.Adaptedfrom Lott andMiller [1997].

6.3.1. Low-level drag parameterization. We definethenondimensionalheightof asinglemountain,ò'ó , asò ó �õô òö Ç ö (22)

where ò is the maximumheightof the mountain, Ç is thespeedof the wind incidenton the mountain,and ô is theBrunt-Vaisala frequency.

At smallvaluesof ò ó all theair flowsoverthemountainandgravity wavesare freely generated(seesection6.3.2).Thereis no low-level form dragin this case. At large val-uesof ò ó , part of the low-level air flow goesaroundthemountain,producingasignificantdragonthelow level flow.Figure4 showsa schematicof theflow at large ò ó .

Thedrag ÷ on thelow-level flow canbewrittenas÷=�#¯ ! � � »ZÄ Å ÑH�#¯ ! À ö À ö) (23)

where» is thedensity, ÄÆÅ is adragcoefficientof orderunity,and ÑH�#¯ ! is a lengthscalebasedonthehorizontalscaleof theintersectionof the mountainwith the incidentflow. For anelliptical mountain,thatis,ø � ò��M $ �º � M5ù �Ø � Ø �£º (24)

then Ñ��¶¯ ! �+) Ø I úüû �ë¯¯ (25)

whereúoû

is the upstreamelevation of the lowest isentropethatgoesover themountain.

úüûcanbewrittenasú û �±ò �¶ò ó �ëò óÆý !ò ó (26)

whereò óÆý is acritical nondimensionalmountainheightoforderunity.

In a GCM grid box, thereis oftenmorethanonemoun-tain,andwe musttake accountof this. At a givenaltitude ¯

theintersectionbetweenthemountainsandthemodellayerapproximatesto anellipsoidof eccentricity�¶ºVþA Ø þ ! �ÿ�¶º�A Ø ! Ý úoû �È¯¯�M·0 (27)

where 0 is thestandarddeviation of thesubgrid-scaleorog-raphy(Figure5). Then Ñ��¶¯ ! canbe written approximatelyas Ñ��¶¯ ! �+)�� Ø�� ³ � A�ºß³�´¸µ � ! Ý ú û �ë¯¯�MÈ0 (28)

where�

is theanglebetweentheincidentflow andthenor-mal ridge direction Ã (Figure 5). We note that if } is thewidth of thegrid box, thenfor

� �96 thereare }Æ��)�º ridgesin theboxandfor

� ��) thereare }ß�7) Ø ridgesin thebox.HenceÑH�#¯ ! � } �) Ý ú û �È¯¯�M·0 �� Õ �� ³ �º A ³�´Sµ �Ø Ù (29)

If � is the anisotropy of the orographyand � is the slope(Figure5), we notethat º ê 0�� and ºP� Ø ê � . Hencethemodellow-level dragis÷=�#¯ ! � � Ä Å ��F�#)Z� �8 AC6 ! » �)�0 Ý ú û �î¯¯�M·0�� Õ �� ³ �º A ³H´Sµ �Ø Ù Ç ö Ç ö) (30)

where 8 � �� ³ � � M ��³�´¸µ � �� ³ � � M·³�´¸µ � � (31)

For convenience,andfor consistency with thegravity wavedrag schemedescribedbelow, we substitutethe functiong �� ³ � � M Ä ³�´¸µ � �

, ( g and Ä aredefinedin section6.3.2)

for the expression�� Õ �� ³ �º A ³H´Sµ �Ø Ù . In the GCM the

term ÷��¶¯ ! is evaluatedquasi-implicitly to ensurenumericalstability.

6.3.2. Gravity wave drag. Full detailsof the schemearegiven by Lott and Miller [1997], Miller et al. [1989],BainesandPalmer [1990] andPalmeret al. [1986] but theessentialsarebriefly reproducedherefor completeness.

It is commonin parameterizinggravity wave dragto as-sumea singlegravity wave, with somecharacteristicwave-length, that propagatesfrom the surfaceof the modelonlyin the vertical plane. Schemesthat representensemblesofgravity waves are computationallyvery expensive and, asyet, arelittle testedeven in terrestrialclimatemodels. The

12 FORGETET AL.�� !�"� #��$ %'&)(+*-,.(+/10324*-,.5"0)6"7+8:9�;+<�<+=?>

@BA�C+DFE�GHC�I4J�K-LFJ�I4C"LNMPO"I A�Q�R

S�T U�V�W�V�X�Y"X�ZFW�[\WNY?] ^'_)`+a�bc`+d1e3f4a-b.g"e)h"i+j:k�lNm l+l�n1o

Figure 5. Subgrid-scaleorographyparametersused bythe low-level drag and gravity wave drag parameteriza-tion (see text). These have been calculated from theMars Digital TopographicMap (DTM) [Davies, 1992] at� � �R� � resolutionwith

ø �¢$�A ù ! representingthe orogra-phy within the grid box definedat ô points and pø repre-sentingthe meanorography; 0 � Eó q r � ø �spø ! � , andÃâ� E� �-t ��u ��µZ�¶}Æ� Ü ! , where

Ü � � ø ��$�� ø �� ù and} � E��v �¶� ø ��&$ ! � �£�¶� ø �� ù ! �+w. Theslopeparameter� is

definedby � � � �#� ø ��&$ þ ! � , where$ þ � $ �� ³PÃrM ù ³�´¸µrÃand ù þ � ù �+� ³�Ãî�R$�³�´¸µrÃ . A fourth parameter(notshown) is the anisotropy (shown by Collins et al. [1997]):� �yx �¶� ø �� ù þ ! � ��¶� ø ��$ þ ! � .

vectorsurfacestressinducedby a singlegravity wave gen-eratedby a singleelliptical mountain,of the form givenby(24),canbewrittenas[Phillips, 1984] -� »3Ç ô ò � Ø × � g �+� ³ � � M Ä ³�´¸µ � � A�� g � Ä ! ³H´Sµ �z�+� ³ � !

(32)where g � ��6P:S��²N�=�£6P: 6�T-� � , Ä � 63: TQ²N��M-6P: /N� � , Gis a constantof orderunity, andall theothersymbolsareasdefinedin section6.3.1.Summingoverall mountainsin thegrid box, themodelgravity wave stressbecomes -� »�Ç ô 0 � × � g �� ³ � � M Ä ³H´Sµ � � A�� g � Ä ! ³�´¸µ �{�� ³ � ! :

(33)Wenow considerwhathappenswhenthegravity waveprop-agatesvertically. We assumethat the stressat any level isparallelto thesurfacestressandcanbewritten (� ö ö � Ë »KÇ ô " ø � (34)

whereË � 0 � × ö � g �� ³ � � M Ä ³�´Sµ � � Ae� g � Ä ! ³H´Sµ �z�+� ³ � ! öand " ø canbethoughtof asthevertical isentropicdisplace-ment inducedby the propagatinggravity wave. We thenjudgethe effect of the wave on the meanflow by calculat-ing theminimumRichardsonnumberattainable,that is, theRichardsonnumberthatis “felt by thegravity wave”:

|B}min � |B} �r�9ô " øÇÕ ��M |B} E�W � ô " øÇ Ù � : (35)

Following Lindzen [1981] the saturationhypothesisisemployed. When

|B}min is greaterthansomecritical value|~}\�

, the stressremainsconstantwith height, the gravitywave continuesto propagatevertically, and

|B}min is evalu-

atedat the next model level. This is repeateduntil|~}

min

dropsbelow the critical value|B} �

andthe wave is deemedto havebroken.Thenanew valuefor theisentropicdisplace-ment, " ø , andhencea new valuefor thestress,is calculatedin order to keep

|B}min � |~} �

. The whole processis re-peateduntil the top of the model is reachedand the stressis assumedto be zero,that is, the wavesareassumedto bedissipatedsomewherein theatmosphere.Thetendenciesarecalculatedfrom theverticalderivativeof thestressprofile.

The schemerepresentsstationarywave critical level ab-sorptionsince,whenthe componentof the wind in the di-rectionof thesurfacestressapproacheszero,theRichardsonnumberbecomesvery large,causingthewave amplitudetobecomeverysmall.Thewave is thusabsorbedat thecriticallevel, andthestressis setto zeroabovethecritical line.

7. CO � Condensation and Sublimation

Thetreatmentof this uniquelyMartianprocesshasbeensignificantly improved in the new versionof the model. A


detaileddescriptionanda numericalexpressionof the newschemearegivenby Forget et al. [1998b]. CO� condenseswhenthelocaltemperatureis predictedto fall below thecon-densationtemperature,releasingthe latentheatrequiredtokeepthesolid-gasinterfaceat thecondensationtemperature.Conversely, when CO� ice is heated,it partially sublimesto keepits temperatureat the frost point temperature.Themodelnow allows for thepossiblesublimationof sediment-ing CO� ice particlesin warmeratmosphericlayersastheydescendto the ground. Minor componentsof the energybudgetareincluded(e.g.,thereleaseof potentialenergy byCO� ice particlesduringtheir fall andtheheatconsumptionto warmtheparticlesastheCO� frost temperatureincreaseswith the local pressure).Thesecomponentswerefound tobefar from negligible in practice.Also, a correctionis nowincludedto accountfor the mass,heat,andmomentumre-distribution betweenthemodellayersandbetweenthe lay-ers and the surfacedue to condensationor sublimationin� �.1��^1 2 coordinates.Last,theboundarylayerschemehasbeenmodifiedsothattheturbulentatmosphericmixing takesinto accountthefactthattheatmospherecanneverbecolderthantheCO� frost point.

In the original model,asin every GCM so far, the con-densedCO� wasassumedto precipitateinstantaneouslytothe surface without changingthe propertiesof the atmo-sphereandthe cap. The availableobservationsof the con-densingpolar capssuggestthat reality may be morecom-plex. The Mariner 9 infrared interferometerspectrometer(IRIS) and Viking IRTM instrumentsmeasureda signifi-cantreductionof the infraredflux emittedby the condens-ing capin thepolarnight [Kieffer et al., 1976]. This reduc-tion hasbeenattributedto theradiativeeffectof CO� snow-falls (falling snow particlesor freshsnow deposits).[Forgetet al., 1995]. By affecting the radiative balanceof the po-lar regions, theseCO� snowfalls and depositsare thoughtto significantlydecreasethe amountof CO� condensinginthepolarcapsandthusaffect theglobalclimate[ForgetandPollack, 1996].

To accountfor this process,we mimic the radiative ef-fect of the CO� cloudsand fresh snow by decreasingthesurfaceemissivity � whenatmosphericcondensationis pre-dictedby the model. The detailsof the schemeare givenby Forget et al. [1998b]. In summary, we basedour calcu-lationson simplephysicalconsiderations(radiative transferthroughtheCO� iceparticles,evolutionof thesnow proper-tieson theground). The following governingequationwasadopted: �� R��7:<;��e6 D à � à8 �� M �� L�r�� ! (36)

where ��=�� is the total atmosphericcondensationrate

(a)Brightnesstemperaturesobservedby Viking (K)

(b) Brightnesstemperaturessimulatedby themodel(K)

Figure 6. Examplesof spatialpatternsof the20-0 m bright-nesstemperatures(a) observedby the Viking infraredther-mal mapper(IRTM) in the winter south polar region at} ~ ��B/ � (Reprintedwith permissionfrom Kieffer et al.[1976], Copyright 1976,AmericanAssociationfor the Ad-vancementof Science)and(b) simulatedby themodelwiththeparameterizationof theCO� snowfallswhicharethoughtto locally decreasethe outgoinginfraredflux, thuscreatinglow brightnesstemperaturefeatures( ·� 6P:S� , }�~'� �e)76 � )[from Forgetet al., 1998b].

14 FORGETET AL.

(kg m D � sDNE ) predictedby the GCM, 8 is the meaneffec-tive radiusof theentirelayerof CO� ice particles,and

�is

the characteristictimescaleof snow evolution (particleag-gregationon thesurface).Thevalue 8 wasfixedto 100 0 m,asexpectedfrom microphysicalconsiderations,and

�was

fixedto 0.5day, in accordancewith thetypical timescaleofthe observedlow-emissionzones[Kieffer et al., 1976;For-get et al., 1995]. Without tuning themodelparameters,wehavebeenableto accuratelyreproducethegeneralbehaviorof the low-emissionzonesobserved by Viking in the ther-mal infrared(Figure6), includingtheir temporalandspatialscales,their intensity, their latitudinaldistribution,andtheirsensitivity to thedustinessof theatmosphere[Forget et al.,1998b].

Overall, this new parameterization,usedin combinationwith theDTM topographyandwith allowancefor a varyingatmosphericdustcontent,allows the GCM to simulatetheCO� condensation-sublimationcycle realistically. In partic-ular, theseasonalvariationsof thesurfacepressurerecordedby theViking Landersarereproducedwithoutartificially de-creasingthecondensationrateaswasdonein previousstud-ies [e.g.. Hourdin et al., 1995;Pollack et al., 1993] by re-ducingtheglobalemissivity of thecaps.

8. Model Performance: Mean State of theAtmosphere

In this sectionwe briefly presentthezonalmeancircula-tion simulatedat variousseasonsby the model. We partic-ularly discussthoseaspectof thecirculationwhich arerela-tively new comparedto the referencearticlesfrom the pre-vious models[Haberleet al., 1993b;Hourdin et al., 1993;Wilson andHamilton, 1996]. For eachseason,theseasonalvariation of the amountof dust in the atmosphereand itsdistribution is designedto roughlysimulatetheViking yearswithout the global duststormspeaksof the first year. Thetotalopticaldepthat 700Pa is ¡�>6P:@4�M·6P: / �� ³��¶}ß~ÁM·²76 � !with }�~ beingthesolarlongitude[seeLewisetal., thisissue,Figure2]. Althoughmany simulationshavebeenperformedwith otherdustscenarios,they arenot describedhere. Thedust propertiesat solar wavelenghtsfrom Clancy and Lee[1991]areused.

8.1. Northern Winter Solstice: a Global Hadley Cell

Figure7 showsthegeneralaspectof thezonalmeanther-mal structureand global circulation of the Martian atmo-spherejust after northernwinter solstice. This is a dustyseasonin theViking yearscenario,andthedustvisible op-tical depthat this time in the simulationis around1. Withsuchastrongdiabaticforcing,themeanperformancesof thegrid point andspectralmodelshave beenfound to be very

similar.

The thermalstructurein the lower regions of the sum-mer hemisphereis comparableto the resultsobtainedbyother models[Haberle et al., 1993b; Wilson and Hamil-ton, 1996]. The most striking differencefrom the GCMresultsobtainedin the early 1990sis in the winter polarnight, wherea strongwarmingof the atmosphereis simu-latedbetween25 and80 km above thepole. Sucha warm-ing hasbeenobservedduringnorthernwinter [Theodore etal., 1993;SanteeandCrisp, 1993]. It wasespeciallystrongand its effectspenetratedto relatively low altitudesduringthe secondViking global duststorm,creatingthe so-called“polar warmingevent” detectedby the IRTM 15-0 m chan-nel [Jakosky andMartin, 1987].However, thiswarminghadnever beensuccessfullysimulatedby GCMs until recently,in spiteof thenumerousstudiesundertaken[e.g.,Haberleetal., 1982,1993b; Barnesand Hollingsworth, 1987; Zurekand Haberle, 1988; Barnes, 1990; Hollingsworth, 1992;Theodore et al., 1993]. This was almostcertainly due totheuseof an insufficiently deepdomain.As first shown byWilson [1997]andForgetetal. [1996],raisingthemodeltopbeyond90km altitudeallowsfor thefull developmentof thecirculationandcandramaticallymodify the thermalstruc-turedown to altitudesaslow as20km. In Figure7bonecanseethat the warmingresultsfrom strongmeridionalwindsabove50km which induceaconvergenceof massabovethepolarregion. Thisconvergenceforcesadescentontothepo-lar regionsandanadiabaticwarmingatmuchloweraltitude.

Wilson [1997] first correctlydescribedthe main mecha-nism that controlsthe solsticialzonal-meancirculationandin particularcreatesthe massconvergencein the polar re-gions[seealsoBarnesandHaberle, 1996]. A complemen-tary version is given here. The streamlinesof the meanmeridionalcirculationpresentedin Figure7f show that thecirculation is dominatedby a quasi-globalHadley cell ex-tendingfrom 60

�S almostto thenorthpole.This is aninter-

estingbehavior sinceit hasoftenbeenarguedfor theEarthandalsofor Mars [Haberleet al., 1982;Zureket al., 1992]that the extensionof an inviscid Hadley circulation is lim-ited to thelow andmid latitudesbecauseof theconservationof angularmomentum(an atmosphericparticle leaving thetropicsandconservingits angularmomentumwouldacquirea very high zonalvelocity in the polar region; its polewardmotionwould thusbeinhibitedby theCoriolis andcentifu-gal forcesdetailedbelow). This is not trueon Mars,wherethe solsticialHadley circulationresultsfrom a pole to poleheatinggradient. In particular, there is no reasonfor theascendingbranchof the Hadley cell to lie directly over thesubsolarpoint asis oftenassumed[e.g.,Zureket al., 1992].Thisbranchreacheshigherlatitudesif thethermalforcing isverystrong,for instance,whentheatmospheredustinessin-


��3� o �y� �� oa) b)

c) d)

e) f)

1

Figure 7. Time-meansectionof zonal-meantemperature(K), zonalwind, meridionalwind (m sDFE ), absoluteangularmo-mentum(10� kg m� sDFE ) andmeridionalstreamfunction( ��6 � kg sDFE ) duringearlynorthernwinter ( } ~ �5)B4�6 � �·/7676 � ) assimulatedwith thegrid point model.Thespectralmodelgivesalmostexactly thesamemeanresultsfor this season.Shadedareasin Figures7b-7dshow wheretheCoriolisandcentrifugalforcescontributeto acceleratethemeridionalpolewardmotioninsteadof slowing it asonEarth.Theverticalcoordinateis apseudo-altitudeabovetheground: ¯ �>ò Í µ��@1��^1 2 ! , where1��1 2is thepressurenormalizedby its local valueat thesurfaceand ò a fixedscaleheight ò �R��6 km.

16 FORGETET AL.

creases.In suchconditionsanatmosphericparticleleavingthe high latitudesof the southernhemispherecancrosstheequatorathighaltitudeandreachthehighnorthernlatitudeswhile conservingits angularmomentum.

On thebasisof theseconsiderationsonecanexplain thestrengthof the meanmeridionalcirculationin the northernhemisphereandthusthepolarwarming.Consideranatmo-sphericparticle leaving the southernhemispherefrom lati-tude ¹ 2F� 6 with negligible zonalvelocity. On goingnorth,angularmomentumconservationatlatitude ¹ wouldresultina negative zonalvelocity aslong as

ö ¹ ö � ö ¹ 2 ö (theparticleis thenfartherfrom the rotationaxis thanoriginally) andapositive zonalvelocity at higherlatitudes(

ö ¹ ö � ö ¹ 2 ö ). Thisbehavior is clearly seenthroughoutmost of Figure7c, in-dicatingthatconservationof angularmomentumis approx-imately satisfiedthroughouta large part of the Martian at-mosphere.Suchbehavior is also apparentin the nearco-incidenceof angularmomentumandmassstreamfunctioncontoursin largeregionsof Figures7eand7f. In therotat-ing framethezonalvelocity À inducesanacceleration� ona fluid particle(owing to Coriolis andcentrifugalaccelera-tions)whosenorthwardcomponentis givenby

� �9�rÀç� )��³H´SµÆ¹ M À u �7µ�¹º �A (37)

where º and � are the planetaryradiusand rotation rate,respectively. In the northernhemisphere,if À � 6 , thesetermstend to slow, andultimately stop, the poleward mo-tion of theupperbranchof theHadley circulation. If À � 6in the northernhemisphere,however, � will tend to accel-eratethenorthwardflow (aslong astheCoriolis termdom-inatesthe centrifugalacceleration,which is true whereverö À ö � ö )-�Æº �� ³P¹ ö ). This is the casein a large part of theatmosphere,asindicatedby theshadedregionin Figures7b-7d. There, the fluid particlesin the upper branchof theHadley circulationexperiencea northwardaccelerationdueto � , in additionto thatdueto thegradientof diabaticheat-ing, all theway to thepole.As a result,themeridionalwindshown in Figure7dcontinuouslyincreasesin theshadedareain the direction of Â betweenthe equatorand the À �+6line, wherethesignof thezonalwind changes,resultinginconsiderablemassconvergenceandthusdescendingmotionover thepoleandtheobservedpolarwarming.

If angularmomentumwere to be exactly conserved inthenorthernhemisphere,À � 6 would be foundaslong asfluid particlesin the Hadley cell hadnot crossedthe oppo-siteof thesoutherlylatitude ¹ 2 from which they hadstartedwith negligible zonalvelocity. At higherlatitudes,À wouldbecomepositive, resultingin a smoothdecelerationof themeridionalflow toward the pole. However, we find that Àcan remainnegative all the way to the north pole in Fig-

ure7c. This impliessomedeparturesfrom angularmomen-tum conservationin thetransportby themeridionalcircula-tion, which mustbedueto the interactionwith nonaxisym-metric eddies,leadingto marked changesnot only in thezonalflow, but alsoin themeridionalcirculationitself with aconsequentenhancementof thethermalinversionabove thepole. This impactof thewavescanberoughlyestimatedbyusingsimplifiedversionsof themodel. Simulationscarriedout by removing thegravity wave dragindicatethattheroleof thesewavesis negligible at this season.Simulationsper-formedwith the GCM employing diurnally averagedsolarradiation(i.e., with no thermaltides)exhibit a quasi-globalHadley cell similar to the full modelsimulationsaccompa-niedby a strongpolarwarming,but thereducedwave-meanflow interactiondecreasesthemeridionalwind by about30-50 m sDFE above 70 km in the northernhemisphere.Thecorrespondingpolar warming maximumis slightly shiftedaway from the pole, and temperaturesabove the pole areloweredby 20-30 K between30 and 70 km. Similar re-sultsareobtainedwith a 2-D, axisymmetricversionof themodelwith no planetarywavesat all. This suggeststhat thewave-meanflow interactiondiscussedhereis dominatedbythermaltides,asalsofoundby Wilson [1997].

As on Earth, the thermal structureof the atmospherewithin the Hadley cell is mostly controlled by the dualconstraintsof angularmomentumconservationandthermalwind balance,except in those regions where wave-zonalflow interactionis important. In suchconditionsthe atmo-spherictemperaturecan be far from radiative equilibriumover a largepartof theplanet.This is especiallytruein thenorthernhemispherewherethewarmingoccurs,but alsointhe southernhemisphereduring northernwinter above 50-60 km wherea strongadiabaticcooling may occur. There,the more dust that is in the lower atmosphere,the coolertemperaturesbecomebecausetheHadley circulationis thenmoreintense.In suchconditionstheatmosphericgaswhichis far from radiative equilibrium in the upperbranchof theHadley cell experiencesnetdiabaticradiativeheatingduringits motion, leadingto temperatureswhich aresignificantlyhigherin thesubsidingbranchof theHadley cell wherethepolar warming occursthan the onesat the samepressurelevel in theascendingbranch(Figures.7aand7f).

8.2. Northern Summer

Figure 8 shows the meancharateristicsof the thermalstructureand generalcirculation as simulatedby the gridpointandspectralmodelsshortlyafternorthernsummersol-stice. The thermal forcing at this time is weaker than atnorthernwinter solsticebecauseof the smalleramountofdustin theatmosphere(meanopacityaround0.4in oursim-ulation) and the reducedsolar flux nearaphelion. Conse-


�� o �� oGRID POINT MODEL SPECTRAL MODEL

a) b)

c) d)

e) f)

1

Figure 8. Time-meansectionof zonal-meantemperature(K), zonalwind (m s¡£¢ ) andmeridionalstreamfunction( ¤�¥-¦ kgs¡£¢ )duringearlynorthernsummer( §�¨ª©¬«�¥�¯®¤�°-¥� ) assimulatedwith theLMD grid point andAOPPspectramodels.As inFigure7, theverticalcoordinateis apseudo-altitudeabovetheground.

18 FORGETET AL.

quently, the Hadley circulation is much lessintense. Nev-ertheless,theupperpolaratmosphereexhibits a warmingathighaltitudewhichresultsfrom processessimilar to theonedescribedat winter solstice,thoughmuchweaker. Suchasouthernwinterpolarwarming,however, hasbeenobservedon Mars [Deminget al., 1986]. In thesimulationsthe tem-peratureinversionextendsfarther to the pole in the spec-tral modelthanin thegrid point version,whereasthereis averygoodagreementbetweenthetwo modelsbelow 50km.Furtheranalysisshows that thetheupperpartof theHadleycirculationwhich createsthis warmingis not asinviscid asdescribedbefore and that its extensionpoleward of 50 Sis largely due to wave-meanflow interaction. Planetary,tidal, andgravity waves(seebelow) tendhereto enhancethemeridionalcirculation,mostly by deceleratingthe westerlyjet of the winter hemisphere.It appearsthat the planetaryandtidal waveactivity andtherelatedwave-meanflow inter-actionarestrongerin thespectralmodel,assuggestedby thereducedvelocityof thezonalwind above60km. Sensitivitystudiesperformedwith ±²©´³ in the horizontaldissipationoperatorof both models(seesection3) yieldedsimilar re-sults.This seemsto indicatethatthedifferencebetweenthetwo modelsdoesnot resultfrom this particularscheme.

Figures9eand9f

8.3. Impact of Gravity Wave Drag.

Becausethe diabatic forcing of the meancirculation isweakat that time, northernsummerprovidesan interestingcaseto illustratethe impactof thegravity wave parameteri-zationin theGCM.show thezonalmeanintensityof thedrag(in m s¡£¢ perMartianday)in thefull modelfor this season.Thegravity wave dragis especiallystrongin theupperpartof thezonalwinter jet, wherethecontrastbetweenthemeanflow velocity and the near-zero phasespeedof the waves(towardwhich thespeedof theflow is decelerated)is high.This strongdragresultsfrom the strongsurfacewinds andfrom thefactthatgravity wavescanpropagateverticallyandbreakhigherup within sucha zonaljet. In comparison,theothermaximumobservednear20 N between30 and40 km(5 m s¡H¢ sol¡H¢ ) is alsodueto strongsurfacewinds,but thelowerzonalwind velocitymakesthewavesbrakelowerthanin winter jet, andtheresultingdragis muchsmaller. Conse-quently, the winter jet simulatedby the full modelis about10-20 m s¡H¢ weaker than when the gravity wave schemeis turnedoff (compareFigures8c and 9b). As expected,this additional friction acting on the zonal wind enhancesthemeridionalcirculationtowardthepolearound50-60kmaltitude.This tendsto shift thejet poleward(thusincreasingthezonalwind nearthepolein Figure9d) andenhancesthemassconvergenceat high latitude. Consequently, thegrav-ity wavedragincreasesthestrengthof thepolartemperature

inversionfrom 20 km to the top of the model (Figure9c).Also, the Hadley circulation is globally intensifiedat highaltituderesultingin a strongerretrogradesummerjet (Fig-ure 9d) and an adiabaticcooling of the equatorialmiddleatmosphere(Fig. 9c). It mustbe notedthat the impactofthe gravity wave dragis sensitive to the modelparameters.For instance,in a similar run performedwith Ockert-Bell etal.’s [1997] dustpropertieswhich yield slightly highertem-peraturesin the lower atmosphere,thegravity wave dragisalmostidenticalto the caseshown in Figures9eand9f butit inducesa warmingof thewinter atmosphereabove30 kmapproximatelytwice asstrong.

8.4. Equinox: A Model-Sensitive Upper Atmosphere

Figures10 and11 show therespectivemeanstatesof theatmospherein the model during early northernspring andfall. The low atmosphereis globally in approximateagree-mentwith the resultsof Haberleet al. [1993b]. The gen-eral circulation is dominatedby two progrademidlatitudejets correspondingto the equatorto pole heatinggradientsat low altitudewith asingleHadley cell in eachhemisphere.Above 40 km, however, the atmosphereprovesto be verysensitiveto thekind of dynamicalmodelcore.Nevertheless,for bothseasonsbothversionsof themodelpredictadynam-ically driventemperatureinversionat 60-70km above bothpoles.

During northernspring(Figure10), a strongretrogradejet is simulatedabove theequator. Interestingly, Lellouch etal. [1993] observed suchretrogradewinds usingDoppler-shift measurementsof Martian CO microwave spectra. A-120m s¡£¢ equatorialvelocity near60 km wasestimatedat§ ¨ ©µ¤�« , which is actuallymuchstrongerthanthe time-meanzonal-meanwindsshown in Figure10. However, theequatorialwindsactuallysimulatedat60km arehighly vari-able,rangingfrom 0 to -100m s¡£¢ dependingon longitudeand time of day. Thus the simulationsmay not be signifi-cantly incompatiblewith theobservations,thoughmoreob-servationaldataareneededto confirmthis. Furtherinvesti-gationof thepresentsimulationsshowedthattheretrogradejet totally disappearsin the versionof theGCM employingdiurnally averagedsolar radiation,suggestingthat the mo-mentumflux divergenceassociatedwith thediurnaltidesis amajorfactordriving thejet. A detailedanalysisof thesepro-cessesis ongoingandwill bepublishedin a laterpaper. Theequatorialretrogradejet is strongerin thespectralmodel,in-dicatingthat thethermaltide wave-meanflow interactionismore“efficient” in this version. Similarly, the midlatitudewesterly jets are more clearly closedabove 60 km by thewave-meanflow interactionin thespectralmodel,resultingin strongerpolarinversions.

During northernfall (Figure11) the differencebetween


¶¸·�¹»º�¼ o ½�¾ ¿ ¼ oa) b)

c) d)

e) f)

1

Figure 9. (Figure9a) Meanzonalwind (m s¡£¢ ) and(Figure9b) temperature(K) simulatedby the LMD grid point modelduringearlynorthernsummerwith thegravity wavesschemeturnedoff. (Figures9cand 9d)Correspondingdifferencefieldsfrom thefull model(Figure8), illustratingtheimpactof thegravity wavesin thiscase(Figures9eand9f) Meangravity wavedragon meridionalandzonalwinds(m s¡£¢ sol¡£¢ ) in thefull model.Theverticalscaleis asin Figure7.

20 FORGETET AL.

the tropical middle atmospheresimulatedby the two ver-sions of the model is particularly striking. The spectralmodel shows just a retrogradejet, whereasthe grid pointmodelpredictsa progradejet between60 and90 km. Suchwesterliesat theequator(superrotation)requirecountergra-dient momentumfluxes [Hide, 1969]. Sincethe progradejet totally dissapearsin thediurnally averagedrun, theseap-pearto bealsoprovidedby thethermaltides. However, thereasonfor this importantdifferencehasnot yet beenclearlyidentified.

9. Conclusion

Onthebasisof themodelswestartedto createin theearly1990s,we have developeda “new generation”generalcir-culationmodelof theMartianatmospherebuilt aroundtwocomplementaryversionsof the dynamiccore(finite differ-encesor spectralsolver). Theverticaldomainof themodelhasbeenextendedto above 80 km. This enlargesthe fieldof investigationbut alsoallows themodelto bettertake intoaccountthe influenceof theupperatmosphereon the loweratmospherewhich is found to be far from beingnegligibleonMars.Conversely, theverticalresolutionnearthegroundhasbeensubstantiallyincreased,with a first layer around5 m above the surface. Within this context, state-of-the-artparameterizationshave alsobeenincluded,togetherallow-ing a bettersimulationof the atmospherenearthe surface(boundarylayerscheme,subgrid-scaletopographyparame-terization)andat high altitude(gravity wave drag,spongelayer). In addition, the representationof radiative transfercalculationsand polar processesrepresentationhave beensignificantlyimproved.

The meanperformanceof the model below 40 km isroughly consistentwith previous modelingwork. Onerel-atively novel aspect,however, is that during the dustysea-sonsaroundnorthernwinter solstice,thestrongpoleto polediabaticforcing createsa quasi-global,angular-momentum-conservingHadley cell which extends to the top of themodel. In sucha cell theCoriolis force,which typically de-celeratesthe meanpoleward motion in the terrestrialcase,contributes to an accelerationof the poleward meridionalwind onMars.This inducesamassconvergenceandanadi-abaticwarmingdown to 20 km, which hadbeenobservedbeforebut hadnotbeenproperlyreproducedin modelsuntilrecently. In fact,thepresentstudiessuggestthatthermalin-versionscanalwaysbeexpectedaround60-70km abovethewinter polarregionsnearsolsticeandabovebothpolesnearequinox. However, our experiencewith the presentmodelhasalsoshown thatthethermalanddynamicstructureabove50km is difficult to predict.First, it mustbestatedherethattheaveragedtemperaturesobtainedby themodelin this re-

gion seemslightly too warm comparedto the few observa-tions obtainedin situ by spacecrafts[seeLewis et al., thisissue]or by Earth-basedinstruments[Clancyand Sandor,1998]. Also, we have found that very differentresultscanbeobtainedwhenusingaspectraldynamicalcorecomparedto a grid point model. This seemsto result from strongerwave-meanflow interactionsin thespectralversion,but theactualnatureof the differenceremainsunclear. Generallyspeaking,the Martian upperatmosphereproves to be ex-tremely sensitive to poorly constrainedprocesses,suchasgravity wave drag, horizontaldissipation,upperboundaryconditions,etc. This high sensitivity is probablydueto thestrongcoupling betweenthe Mars lower and upperatmo-spherethroughvertically propagatingwaves(tides,gravity,andplanetarywaves). A large part of this wave activity isable to propagatethroughthe entire modeledatmosphere.Thus,in spiteof a very high modeltop comparedto terres-trial GCMs, the representationof the upperboundarycon-ditions (including, e.g., spongelayer to avoid spuriousre-flection) remainsof key importanceon Mars. All theseun-certaintiesprobablywill not beremovedby theoreticalcon-siderationsalone. Observationsabove 40 km altitude(e.g.,from TES and PMIRR limb data)and even above 80 km(e.g.,from SPICAMonMarsExpress)areneeded.Also, thedirectmeasurementsof equatorialzonalwindsfrom Dopplershifts in microwave spectrallines, from Earth or, ideally,from a spacecraft,would be extremelyuseful,sinceit maynototherwisebepossibleto determinethecirculationin thisregion from observations.

Acknowledgments.

WethankR. T. Clancy, R. M. HaberleandR. J.Wilson for theircommentsandsuggestions.This work wassupportedby theEuro-peanSpaceAgency throughESTECTRPcontract11369/95/NL/JG.

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M. Collins,Hadley Centrefor ClimatePredictionandRe-search,U.K. MeteorologicalOffice, LondonRoad,Brack-nell RG122SZ,England.([email protected])

F. Forget,C.Hourdin,F. HourdinandO.Talagrand,Labo-ratoiredeMeteorologieDynamiqueduCentreNationaldelaRechercheScientifique,Universite Paris6, 4 placeJussieu,75252 Paris Cedex 05, France. ([email protected];[email protected]; [email protected]; [email protected])

R. Fournier, Laboratoired’Energie Solaireet Thermiquede l’Habitat, Universite Paul Sabatier, Toulouse,France.([email protected])

J.-P. Huot,SpaceSystemsEnvironmentandEffectsAnal-ysis Section, EuropeanSpaceResearchand TechnologyCentre,EuropeanSpaceAgency, Keplerlaan1, 2200 AGNoordwijk, Netherlands.([email protected])

S. R. Lewis andP. L. Read,Atmospheric,OceanicandPlanetaryPhysics,ClarendonLaboratory, ParksRoad,Ox-ford OX1 3PU, England.([email protected];[email protected])January22,1999; revisedMay 11,1999; acceptedMay 18,1999.

This preprintwaspreparedwith AGU’s LATEX macrosv4, with theex-tensionpackage‘AGUÚ�Ú ’ by P. W. Daly, version1.5gfrom 1998/09/14.

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