THÈSE DE DOCTORAT DE L UNIVERSITÉ PARIS VI. Présentée par. Gillian Boccara

Transcription

1 THÈSE DE DOCTORAT DE L UNIVERSITÉ PARIS VI Spécialité : OCÉANOGRAPHIE-ATMOSPHÈRE-ENVIRONNEMENT Présentée par Gillian Boccara Laboratoire de Météorologie Dynamique École Polytechnique Université Pierre et Marie Curie Pour obtenir le grade de DOCTEUR de l UNIVERSITÉ PIERRE ET MARIE CURIE Sujet de la thèse ÉTUDE DE LA DYNAMIQUE DE LA BASSE STRATOSPHÈRE POLAIRE À L AIDE DES DONNÉES VORCORE Soutenance le 22 octobre 2008, devant le jury composé de : Vladimir Tseitline LMD Président Daniel Cariolle CERFACS Rapporteur Hennie Kelder KNMI Rapporteur Vincent Cassé Météo-France Examinateur Francis Dalaudier SA Examinateur Peter Preusse Forschungszentrum Jülich Examinateur François Vial LMD Directeur Albert Hertzog LMD Co-directeur

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3 i REMERCIEMENTS Je tiens à remercier chaleureusement mes directeurs de thèse, Albert Hertzog et François Vial, pour m avoir encadré pendant cette thèse, et pour avoir toujours été disponibles pour répondre à mes nombreuses questions. Je voudrais également remercier les membres de mon jury de s être penché sur mon travail, en particulier Daniel Cariolle et Hennie Kelder qui ont accepté d être rapporteurs, mais également Vincent Cassé, Francis Dalaudier, Peter Preusse et Vladimir Tseitline. Je remercie Hervé Le Treut de m avoir accueilli au sein du Laboratoire de Météorologie Dynamique. Merci à Katial Laval, de m avoir accueilli dans l école doctorale des sciences de l environment. Je remercie également Francis Dalaudier et Riwal Plougonven pour avoir suivi mon travail en tant que comité de thèse, et pour leurs suggestions destinées à approfondir mon travail. Merci également à tous ceux qui de près ou de loin, m ont aidé ou aiguillé dans mon travail, Thomas Dubos, Philippe Drobinski, Hélène Chepfer, Vincent Noel, Laurent Menut, Martial Haeffelin. Merci encore à tous les membres du LMD à Polytechnique qui ont contribué à faire de ma thèse une experience enrichissante: doctorants, CDD, permanents, Marie Claire Lanceau, Martine Roux et Eliane Rier. Merci enfin aux membres du "bureau", Tamara, Clément, Yohann, Fabien, Cindy, sans qui le quotiden n aurait pas été le même... Pour terminer, je souhaite également remercier ma famille et mes amis au soutien infaillible, et Laurie of course.

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5 TABLE DES MATIÈRES iii Table des matières 1 Introduction générale La stratosphère Dynamique de la stratosphère Importance de l ozone Importance des ondes de gravité dans l atmosphère moyenne Paramétrisation de l effet des ondes de gravité dans les modèles de circulation générale Observation des ondes de gravité Enjeux de la thèse Théorie des ondes de gravité Conservation de la quantité de mouvement, de la masse et de l entropie Conservation de la quantité de mouvement Conservation de la masse Conservation de l entropie Linéarisation Interaction entre ondes de gravité et écoulement moyen Réponse des BPS aux ondes de gravité Études théoriques et numériques antérieures Les oscillations naturelles Les oscillations induites par les ondes de gravité Outil mathématique : l analyse en ondelettes Étude théorique et numérique des ondes de gravité

6 iv TABLE DES MATIÈRES Article : Estimation of Gravity-Wave Momentum Fluxes and Phase Speeds from Quasi-Lagrangian Stratospheric Balloon Flights. 1: Theory and Simulations Précisions concernant la méthodologie Études complémentaires Simulations Limites de l analyse La campagne de ballons pressurisés Vorcore Historique de l observation par ballons Observation d ondes de gravité par des ballons pressurisés Récapitulatif de la campagne Vorcore Article : Stratéole/Vorcore Application à la campagne Vorcore Estimation du flux de quantité de mouvement transporté par les ondes de gravité Application de la méthodologie à la campagne Vorcore Article : Estimation of Gravity-Wave Momentum Fluxes and Phase Speeds from Quasi-Lagrangian Stratospheric Balloon Flights. 2: Results from the Vorcore Campaign in Antarctica Discussion Comparaison interhémisphérique Article : Quasi-Lagrangian superpressure balloon measurements of gravitywave momentum fluxes in the polar stratosphere of both hemispheres Précision des analyses et réanalyses stratosphériques Analyses et réanalyses Article : Accuracy of NCEP/NCAR reanalyses and ECMWF analyses Précisions concernant la méthodologie Interpolation dans les analyses et réanalyses Calcul des trajectoires

7 TABLE DES MATIÈRES 1 7 Paramétrisations des ondes de gravité Paramétrisations dans les modèles de circulation générale Ondes orographiques Ondes non-orographiques Calculs des flux à partir des paramétrisations Méthodologie Paramétrisation des ondes orographiques (Lott and Miller, 1997) Paramétrisation des ondes non-orographiques (Hines, 1997a,b) Impact simultané des deux paramétrisations Conclusion 159 Bibliographie 163 Liste des abbréviations 177

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9 1 Chapitre 1 Introduction générale Le changement climatique, initié par les activités anthropiques depuis la révolution industrielle, est en passe de devenir un défi majeur du XXIème siècle, d un point de vue social, politique, économique et humain. De ce fait, la communauté scientifique, qui a mis en évidence ce changement, est régulièrement sollicitée pour expliquer, quantifier et prévoir ses conséquences à court et moyen termes. Une telle coopération entre les pouvoirs politiques et la communauté scientifique a eu un précédent lors de la signature du protocole de Montréal en Dans les années 1970, des équipes scientifiques ont mis en cause l effet potentiel de constituants chlorés industriels sur le cycle de l ozone (Molina and Rowland, 1974), mais ce n est qu en 1985, lorsque le "trou" dans la couche d ozone a été mis en évidence (Farman et al., 1985), que les pays ont conduit des négociations fermes en vue d interdire ces substances. Ce succès scientifique et politique a marqué l avènement d une prise de conscience effective des conséquences de nos modes de vie sur la planète. Par la suite, au "Sommet de la Terre" à Rio en 1992, les fondations du protocole de Kyoto et la nécessité pour les états de s engager dans la lutte contre le changement climatique ont été posées. Dans ce contexte, le Laboratoire de météorologie dynamique (LMD) participe activement à l étude du climat, en mettant au point des techniques d observations avancées, par exemple les ballons pressurisés dans la stratosphère, et des outils de modélisation comme le modèle de circulation générale LMDz. Notre thèse s intéresse spécifiquement à la basse stratosphère polaire, située entre 10 km et 20 km

10 2 CHAPITRE 1. INTRODUCTION GÉNÉRALE d altitude, qui est fortement influencée par le changement climatique et qui joue un rôle important dans le rétablissement de la couche d ozone. 1.1 La stratosphère Cette couche de l atmosphère, entre km et 50 km, est située au dessus de la troposphère où prend place la totalité des phénomènes météorologiques. La stratosphère est une couche stratifiée relativement stable car elle possède un gradient vertical de température positif lié à la présence d ozone, qui réchauffe la stratosphère en absorbant les rayons ultraviolets du soleil. Si le grand public est plus concerné par l évolution de la troposphère, la communauté scientifique s est progressivement rendue compte de l influence que peuvent avoir les échanges dynamiques et chimiques à la tropopause, désignés sous la forme de couplage troposphère-stratosphère. Des études récentes ont montré que les échanges dans les deux sens devaient être considéré (Baldwin et al., 2001). L échange d espèces chimiques traces à fort potentiel radiatif est représentatif de l impact radiatif que peuvent avoir ces deux couches l une sur l autre : d une part, l ozone stratosphérique peut pénétrer la haute troposphère lors de foliations de tropopause (Danielsen et al., 1987), et d autre part des espèces traces comme la vapeur d eau, le méthane ou d autres gaz à effet de serre peuvent s introduire dans la stratosphère au niveau de la tropopause tropicale (Holton et al., 1995) et peuvent aussi avoir un impact sur la chimie de l ozone. Les échanges dynamiques se font en partie par la propagation d ondes atmosphériques de la troposphère à la stratosphère. Il existe différents types d ondes qui sont caractérisées par des échelles spatiales et temporelles très différentes : les ondes d échelle planétaires (ondes de Rossby) dont la longueur d onde horizontale atteint plusieurs milliers de kilomètres, les ondes équatoriales (ondes de Kelvin, ondes de Rossby-gravité) qui sont observées uniquement dans les latitudes tropicales, ou encore les ondes de gravité qui sont de plus faibles échelles spatiales et temporelles et qui possèdent un grand nombre de sources (orographie, convection, ajustement géostrophique, cisaillement) (Holton, 1992). Toutes ces ondes peuvent interagir avec l écoulement moyen en cédant leur énergie et leur quantité de mouvement. Elles se propagent verticalement depuis la troposphère où elles sont principalement

11 1.1. LA STRATOSPHÈRE 3 engendrées et influencent l atmosphère moyenne lorsqu elles sont soumises à des instabilités et qu elles déferlent. Jusqu à récemment, comme la troposphère contient 90% de la masse de l atmosphère, il était admis que seule la troposphère pouvait influencer dynamiquement la stratosphère et non l inverse. En réalité, la stratosphère peut influencer la troposphère par le biais du «downward control» (Haynes et al., 1991) selon lequel le forçage engendré par le déferlement d ondes dans l atmosphère moyenne va déterminer la circulation méridienne moyenne à des altitudes plus basses. En respectant la conservation de la masse, la circulation moyenne va engendrer des mouvements verticaux qui influencent les distributions de température à des altitudes plus basses. Dans l hémisphère nord, plusieurs études ont démontré la propagation vers le bas d anomalies de températures et de vents zonaux, un phénomène qui correspond à l Oscillation Arctique (Thompson and Wallace, 1998, 2000; Baldwin and Dunkerton, 1999) et des phénomènes similaires correspondants à l Oscillation Antarctique ont également été observés dans l hémisphère sud (Thompson et al., 2005). Au sein de l atmosphère moyenne (stratosphère et mésosphère), Garcia and Boville (1994) ont montré que le déferlement d ondes de gravité dans la mésosphère polaire exerce une influence sur les températures de la stratosphère à des altitudes de l ordre de 30 km Dynamique de la stratosphère La circulation zonale de la stratosphère présente une alternance entre une circulation d est pendant l été et une circulation d ouest pendant l hiver. Lorsque l hiver s installe, la circulation d ouest s intensifie à cause des forts gradients de températures qui existent entre l Équateur et les hautes latitudes, de sorte qu au dessus du pôle d hiver, un fort tourbillon s installe depuis la mésosphère jusqu à la stratosphère. L air à l intérieur du vortex est isolé des moyennes latitudes par ces vents d ouest et le bord du vortex constitue une barrière étanche quasi-infranchissable pour les particules d air (McIntyre, 1989; Chen, 1994). L isolement de l air à l intérieur du vortex et son refroidissement radiatif, bien qu il soit associé à une subsidence adiabatique des particules d air (voir cidessous), engendre des températures extrêmement froides à l intérieur du vortex. La circulation méridienne, également appelée circulation de Brewer-Dobson, est décrite par une ascension des masses d air au dessus de l Équateur, suivie d une migration vers les hautes latitudes puis une subsidence dans les moyennes et les hautes latitudes. Le gradient en latitude du forçage

12 4 CHAPITRE 1. INTRODUCTION GÉNÉRALE thermique (lié au rayonnement solaire) ne permet pas d expliquer cette distribution des masses d air. La figure 1.1, extraite de Plumb (2002), illustre l importance du déferlement des ondes synoptiques dans la haute troposphère et la basse stratosphère, des ondes planétaires dans la stratosphère (McIntyre and Palmer, 1984) et des ondes de gravité dans la mésosphère. En effet, le moment angulaire des particules d air diminue lors de leur déplacement vers les pôles et seul le forçage par les ondes atmosphériques permet d expliquer cette perte de moment angulaire (Plumb, 2002). Le déferlement de ces ondes engendre des forces de trainées à différents niveaux de l atmosphère moyenne cruciales pour la circulation méridionale moyenne et influence la distribution de température dans la stratosphère (Shepherd, 2002). FIG. 1.1 Circulation de Brewer-Dobson forcée par les ondes : S pour le déferlement des ondes synoptiques, P pour les ondes planétaires et G pour les ondes de gravité (Plumb, 2002) Importance de l ozone Au sein du vortex polaire d hiver, des réactions chimiques de destruction de l ozone peuvent avoir lieu mettant en jeu des espèces traces comme les composants chlorés et bromés produits par les activités industrielles et les oxydes d azote issus de la combustion et des émissions d avion.

13 1.1. LA STRATOSPHÈRE 5 Cette destruction a un impact important sur toute la biosphère car l ozone absorbe les rayons ultraviolets du soleil nocifs à la vie. Ces réactions ont lieu lorsque la température devient inférieure à 190 K, et que des nuages stratosphériques polaires (NSP) se forment (Lowe and MacKenzie, 2008). A la surface de ces nuages, des réactions de chimie hétérogène entre les composants halogénés et des cristaux d acide nitrique (créés à partir des oxydes d azote) libèrent des atomes de chlore ou de brome actif. Au printemps, avec le retour du soleil, des réactions photochimiques entre ces atomes et les molécules d ozone conduisent à une destruction catalysée de l ozone (Solomon, 1999). Dans l hémisphère nord, cette destruction est limitée, car la propagation depuis la troposphère d ondes de Rossby de forte amplitude forcées par la topographie (Himalaya, Rocheuses) perturbe ou peut briser le vortex et ainsi provoquer un réchauffement rapide de la stratosphère, ce qui empêche les températures d atteindre le seuil de formation des NSP. Dans ce cas, l air n est plus confiné dans le vortex et se mélange à l air des moyennes latitudes. Ce phénomène est connu sous le nom de "réchauffement stratosphérique soudain" (Schoeberl, 1985b). En revanche, ce phénomène est plus marqué dans l hémisphère sud, car le vortex est peu perturbé par la propagation d ondes et les températures sont inférieures à 190 K chaque hiver. Ces épisodes de destruction sont documentés exhaustivement par l Organisation Météorologique Mondiale (OMM) qui publie annuellement des rapports analysant la destruction de la colonne d ozone (par exemple WMO, 2005). Si, en première approche, la destruction de l ozone apparaît comme un processus purement chimique, celle-ci est influencée par des mécanismes dynamiques comme les perturbations du vortex induites par les ondes de Rossby, les réchauffements stratosphériques soudain, et les perturbations de températures induites par les ondes de gravité (Carslaw et al., 1998). Ces auteurs ont mis en évidence le rôle des ondes de gravité forcées par la topographie (ondes de montagne) qui peuvent induire des diminutions locales de la température de l ordre d une dizaine de degrés permettant d atteindre la température nécessaire pour la formation des NSP.

14 6 CHAPITRE 1. INTRODUCTION GÉNÉRALE 1.2 Importance des ondes de gravité dans l atmosphère moyenne Le rôle des ondes de gravité dans l atmosphère moyenne est multiple. Ces ondes sont nécessaires pour expliquer la circulation méridienne moyenne dans la stratosphère, elles jouent un rôle essentiel dans la destruction de l ozone en permettant la formation de NSP, et elles jouent également un rôle dans le mélange des particules d air lorsqu elles déferlent. Or le changement climatique a une influence sur la chimie de l ozone et la circulation méridienne moyenne. Dès lors, les ondes de gravité doivent être intégrées dans les modèles numériques construits par la communauté scientifique pour prévoir le climat à court, moyen et long termes. L observation des ondes de gravité est également nécessaire pour documenter les impacts et comprendre les mécanismes physiques impliqués dans la génération, la propagation et la dissipation des ondes de gravité. Par exemple, dans le cas de la destruction de l ozone, les campagnes European Arctic Stratospheric Ozone Experiment (EASOE), et THird European Stratospheric Experiment on Ozone (THESEO) ont combiné des observations spatiales, des sondages ozone, des mesures par avion, des mesures par lidar et des mesures de montgolfières infra rouges pour étudier les processus dynamiques impliqués dans la destruction de l ozone Paramétrisation de l effet des ondes de gravité dans les modèles de circulation générale La communauté scientifique a mis au point des modèles numériques de circulation générale (MCG) permettant de reproduire et d étudier les caractéristiques de la circulation générale de l atmosphère. Il existe un certain nombre de MCG couramment employés pour les prévisions météorologiques à court et moyen termes ou pour des contributions à des études climatologiques à plus long terme, par exemple pour les rapports du Groupe d experts intergouvernemental sur l évolution du climat (GIEC). Le rapport du GIEC publié en 2007 montre que le changement climatique provoquera un réchauffement global de la troposphère et un refroidissement global de la stratosphère (GIEC, 2007). Or, de tels changements auront un impact sur le rétablissement de l ozone stratosphérique et seront dépendants des différents couplages qui existent entre la troposphère et stratosphère liés notamment à la propagation d ondes atmosphériques et dont les MCG doivent tenir compte.

15 1.2. IMPORTANCE DES ONDES DE GRAVITÉ DANS L ATMOSPHÈRE MOYENNE 7 Les modèles mis au point par les centres météorologiques opérationnels représentent l atmosphère de la surface jusqu à la stratopause ou la mésopause avec des mailles de l ordre du degré. Ils incluent diverses paramétrisations pour représenter les processus physiques et dynamiques sous-maille essentiels, comme la convection, les précipitations ou les ondes de gravité. Comme les ondes de gravité agissent à des petites échelles spatiales et temporelles, elles ne sont pas explicitement résolues par les MCG. Garcia and Boville (1994) ont montré que si les ondes de gravité ne sont pas paramétrées, les modèles simulent au dessus du pôle d hiver des températures bien plus froides que celles observées, en particulier dans l hémisphère sud. Dès lors, la plupart de ces modèles utilisent des paramétrisations d ondes de gravité pour prendre en compte leur impact correctement. Les paramétrisations d ondes de gravité distinguent généralement les ondes orographiques des ondes non orographiques. Les ondes orographiques sont engendrées par le vent sur les montagnes ce qui facilite leur observation et leur analyse (par exemple Peltier and Clark, 1979; Schoeberl, 1985a; Ralph et al., 1992). En revanche, les ondes non-orographiques sont plus difficiles à modéliser car leur répartition est globale et leurs mécanismes de formation sont moins bien compris. Comme la formation, la propagation et la dissipation des ondes de gravité sont des phénomènes complexes, les paramétrisations ont des difficultés à reproduire correctement leurs impacts. Elles comportent des paramètres libres qui peuvent être ajustés pour correspondre au mieux aux observations d ondes de gravité Observation des ondes de gravité Les observations d ondes de gravité sont essentielles au développement des paramétrisations. Pour décrire avec précision les effets des ondes de gravité, une observation complète de leurs caractéristiques et de leur variabilité temporelle et géographique est nécessaire, mais ces observations sont loin d être triviales. Une difficulté réside dans le fait que les techniques d observations possèdent un filtre observationnel intrinsèque, c est-à-dire qu elles ne sont capables de détecter les ondes de gravité que dans un intervalle de fréquences ou de longueurs d onde donné. Par exemple, pour l instrument spatial Atmospheric InfraRed Sounder (AIRS), la fonction de poids appliquée aux profils verticaux de températures de radiance issus des canaux de fréquences 15µm et 4.2µm a une largeur à mi-hauteur de

16 8 CHAPITRE 1. INTRODUCTION GÉNÉRALE 12 km. Les ondes de gravité dont la longueur d onde est inférieure à 12 km ne peuvent donc pas être détectées (Alexander and Teitelbaum, 2007). Par opposition, les analyses d ondes de gravité faites à partir de radiosondages ne peuvent résoudre que les ondes de gravité dont les longueurs d onde verticales sont inférieures à 7 km parce que les profils troposphériques sont analysés séparément des profils stratosphériques (Wang et al., 2005). Les principales techniques d observations des ondes de gravité sont les suivantes : 1. Les instruments transportés par satellites permettent d obtenir des profils verticaux de températures ou de températures de radiance avec une couverture quasiment globale. Selon la manière dont ils observent l atmosphère, au nadir ou au limbe, ils vont observer une gamme différente de longueurs d onde et de fréquences (Wu et al., 2006). Les instruments AIRS et Advanced Microwave Sounding Unit-A (AMSU-A) effectuent des observations au nadir ce qui les rend sensibles à des ondes de gravité dont le rapport des longueurs d ondes verticales et horizontales λ z λ h est grand. Des instruments comme CRyogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA), ou HIgh Resolution Dynamics Limb Sounder (HIRDLS) font des observations au limbe de sorte qu ils ont une bonne résolution verticale et détectent surtout des ondes de gravité pour lequelles λ z λ h est faible. L instrument CHAllenging Minisatellite Payload (CHAMP) permet également d obtenir des profils de températures à partir d occultations radio de signaux Global Positionning System (GPS) (Hei et al., 2008). 2. Les lidars Rayleigh permettent d obtenir des profils verticaux de température ou de densité dans la haute stratosphère et la basse mésosphère avec une résolution verticale de 1 km (par exemple Wilson et al., 1991). Les études par lidar Rayleigh ont permis de dégager un cycle saisonnier de l énergie avec un maximum en hiver et un minimum en été pour quelques sites donnés, en majorité dans les moyennes latitudes. Ce type d observation permet d obtenir localement une bonne couverture temporelle. 3. Les radars permettent également d obtenir des climatologies pour des sites fixes (surtout dans les moyennes latitudes), dans la basse stratosphère, dans la mésosphère et la basse thermosphère (par exemple Vincent and Reid, 1983; Tsuda et al., 1990). Comme pour les observations par lidar, la bonne couverture temporelle est limitée au seul site de mesure. 4. Les radiosondages permettent d observer des ondes de gravité jusqu à 25 km. Comme les stations de radiosondages sont nombreuses, des climatologies peuvent également être dérivées

17 1.3. ENJEUX DE LA THÈSE 9 (Allen and Vincent, 1995). Cependant la résolution temporelle de ces mesures est faible, avec au plus deux radiosondages par jour. 5. Les ballons pressurisés de longue durée, qui font l objet de notre thèse, permettent des observations dans la troposphère ou la stratosphère sur des zones géographiques étendues pendant plusieurs mois. Ces observations permettent de renseigner les cycles saisonniers et annuels des ondes de gravité, mais également de déterminer leur répartition géographique et de tenter de comprendre leurs mécanismes de formation, de propagation et de dissipation. 1.3 Enjeux de la thèse Le projet Stratéole/Vorcore a été initié par le LMD et le Centre National d Études Spatiales (CNES) en association avec Météo-France et l Université de Californie Los Angeles (UCLA) pour étudier la dynamique stratosphérique dans le vortex polaire à l aide de ballons pressurisés stratosphériques (BPS) de longue durée (Vial et al., 1995). Le but était d étudier la porosité du bord du vortex et d observer l érosion et la rupture du vortex au printemps, c est-à-dire lorsque le retour du soleil permet la destruction catalysée de l ozone. La campagne Vorcore a eu lieu entre septembre 2005 et février 2006 à partir de la station de Mc- Murdo en Antarctique (Hertzog et al., 2007). Pendant les vols, des observations de pression, de température et de position (latitude, longitude, altitude) ont été effectuées toutes les 15 minutes. L échantillonnage fin de ces données, la longue durée des vols (deux mois en moyenne), ainsi que la distribution des observations sur une région géographique étendue, permettent de documenter les ondes de gravité se propageant dans la basse stratosphère polaire. L objectif principal de cette thèse est d étudier les ondes de gravité se propageant au dessus de l Antarctique dans le vortex polaire à partir des observations enregistrées par les BPS. A l aide de ces observations, nous allons fournir des informations pertinentes pour contraindre les paramétrisations d ondes de gravité existantes. Les données Vorcore documentent de manière dense une zone peu observée et peuvent également

18 10 CHAPITRE 1. INTRODUCTION GÉNÉRALE être comparées à des analyses et réanalyses produites par des centres météorologiques opérationnels. En effet, pour que les prévisions des modèles se rapprochent le plus de la réalité, des données issues de satellites ou de radiosondages sont assimilées dans les prévisions pour produire des analyses. En outre, plusieurs centres météorologiques produisent des réanalyses, en utilisant un modèle fixe, un système d assimilation constant, et en intégrant toutes les données réalisées pendant l intervalle des réanalyses (en général plusieurs dizaines d années). Ces analyses et réanalyses sont couramment utilisées pour conduire diverses études sur des processus chimiques et dynamiques ou pour dégager des tendances climatologiques (Peixoto and Oort, 1996). Dans la mesure où ces analyses servent d états fiables de l atmosphère (et nous ferons cette hypothèse dans certains chapitres de la thèse), il est indispensable de connaître leur précision et plusieurs études ont été réalisées pour estimer quelles analyses étaient plus proches de l état l atmosphère en utilisant des données indépendantes ou en comparant les modèles les uns aux autres (par exemple Keil et al., 2001; Manney et al., 2003). La thèse est structurée comme suit: tout d abord, nous reprendrons les approches théoriques classiques utilisées pour décrire les ondes de gravité dans le chapitre 2, puis dans le chapitre 3, nous détaillerons la méthodologie développée pour déduire les caractéristiques des ondes de gravité pouvant perturber les ballons pressurisés. Dans le chapitre 4, nous présenterons les données enregistrées pendant la campagne Vorcore et dans le chapitre 5 nous montrerons les résultats obtenus en appliquant cette méthodologie aux données Vorcore. Dans le chapitre 6, nous examinerons la précision d analyses et de réanalyses stratosphériques, en les comparant avec les données de température et de vent obtenues lors de la campagne Vorcore. Dans le chapitre 7, nous comparerons les résultats du chapitre 5 avec ceux obtenus en appliquant une paramétrisation des ondes orographiques et des ondes non-orographiques à des analyses opérationnelles. Enfin, nous concluerons et nous examinerons les perspectives qui peuvent être apportées à ce travail.

19 11 Chapitre 2 Théorie des ondes de gravité Ce chapitre pose le cadre théorique classique utilisé pour décrire les ondes de gravité. Les équations développées ici serviront ensuite à modéliser la réponse des BPS aux perturbations induites par les ondes de gravité. Les ondes de gravité ou de flottabilité se propagent verticalement et horizontalement dans l atmosphère depuis leurs sources situées principalement dans la troposphère. Celles-ci sont nombreuses (topographie, ajustement géostrophique, cisaillement, convection et plus généralement instabilités diverses) et produisent des ondes possédant des caractéristiques distinctes, en fonction des processus physiques en jeu, et localement des échelles spatiales et temporelles. Par exemple, les ondes de montagne, qui sont forcées par l orographie, ont une vitesse de phase quasiment nulle et des longueurs d onde horizontales comprises entre 10 km et 100 km. Leur longueurs d onde verticales sont étroitement liées à l orographie locale, au vent moyen et à la fréquence de Brunt-Väisälä (Bacmeister et al., 1990). De même, les ondes produites par ajustement géostrophique dépendent considérablement des échelles spatiales et temporelles du forçage. Par exemple, le spectre fréquentiel des ondes de gravité excitées va dépendre de la durée du forçage appliqué. Pour des forçages longs, les ondes dont la période est plus courte que la durée de forçage sont coupées (Vadas and Fritts, 2001). Enfin, les ondes engendrées par la convection profonde ont généralement des fréquences élevées (McLandress et al., 2000; Alexander et al., 2000). En se propageant, les ondes de gravité transportent de l énergie (cinétique et potentielle) et de la

20 12 CHAPITRE 2. THÉORIE DES ONDES DE GRAVITÉ quantité de mouvement jusqu à la stratosphère et la mésosphère où elles déferlent, interagissant ainsi avec l écoulement moyen. 2.1 Conservation de la quantité de mouvement, de la masse et de l entropie Une onde de gravité est une onde transverse pour laquelle, suite à un déplacement, une particule d air va osciller autour de sa position d équilibre, sous l effet de 2 forces : la gravité et la poussée d Archimède. Nous reprenons ici les équations décrivant les perturbations des composantes zonales u, méridiennes v et verticales w de la vitesse, du champ de pression P, de densitéρet de température potentielle θ dues aux ondes de gravité, en s inspirant de Fritts and Alexander (2003). On suppose que les ondes de gravité induisent des perturbations de faible amplitude dans une atmosphère stratifiée et peuvent être décrites en linéarisant les équations du mouvement, de la conservation de la masse et de l entropie Conservation de la quantité de mouvement Sous forme vectorielle, la seconde loi de Newton ou conservation de la quantité de mouvement s écrit : d U dt = 2 U Ω 1 ρ P+ g + X (2.1) où U= (u,v,w) est le vecteur vitesse, Ω est la vitesse angulaire de rotation de la Terre,ρ est la densité, P est la pression, g est la gravité et X= (X,Y,Z) représente un forçage extérieur. Dans l équation ci-dessus, les forces agissant sur la particule d air sont le gradient de pression (poussée d Archimède) et la gravité. Le premier terme du membre droit de l équation 2.1 représente la force apparente de Coriolis liée à la rotation de la Terre.

21 2.1. CONSERVATION DE LA QUANTITÉ DE MOUVEMENT, DE LA MASSE ET DE L ENTROPIE13 En projetant selon les axes (x,y,z) dirigés respectivement vers l est, le nord, et la verticale locale, l équation 2.1 s écrit : Du Dt f v+ 1 p ρ x = X (2.2) Dv Dt + f u+ 1 p ρ y = Y (2.3) Dw Dt + 1 p ρ z + g = Z (2.4) où D/Dt est la dérivée particulaire, f = 2Ωsinφ est le paramètre de Coriolis (φ est la latitude) Conservation de la masse En appliquant la conservation de la masse à une particule d air en mouvement, on obtient l équation de continuité : 1 Dρ ρ Dt + u x + v y + w z = 0 (2.5) Conservation de l entropie Enfin, l équation thermodynamique d une particule d air en mouvement s écrit : Dθ Dt = Q (2.6) où θ = T ( ) R ps cp (2.7) p T est la température, p s est une pression de référence égale à 1000 hpa, R = 287 J kg 1 K 1 est la constante des gaz parfaits pour l air et c p = 1004 J kg 1 K 1 est la chaleur spécifique à pression constante. Q est le terme de forçage radiatif.

22 14 CHAPITRE 2. THÉORIE DES ONDES DE GRAVITÉ Linéarisation Les équations 2.2 à 2.7 peuvent être linéarisées autour d un état moyen et hydrostatique, avec un vent horizontal uniforme (u,v,0). Nous supposons que la température potentielle θ, la pression p, et la densitéρ(pour laquelleρ =ρ 00 exp( (z z 0 )/H) oùρ 00 =ρ(z 0 ) est la densité de référence au niveau z 0, et H 7 km est la hauteur d échelle) ne varient que selon z et que le forçage extérieur est nul (X = Y = Z = 0) : Dw Dt D Dt Du Dt f v + ( ) p = 0 (2.8) x ρ Dv Dt + f u + ( ) p = 0 (2.9) y ρ + ( ) p 1 ( p )+g ρ z ρ H ρ ρ = 0 (2.10) ( D θ )+w N2 Dt θ g = 0 (2.11) ( ρ où la dérivée particulaire D/Dt s écrit : ρ )+ u x + v y + w z w H = 0 (2.12) θ θ = 1 ( ) p c 2 ρ (2.13) s ρ ρ D Dt = t + u x + v y où c 2 s = pγ/ρ est la vitesse du son dans l air,γ = c p c v, c v = 717 J kg 1 K 1 est la chaleur spécifique à volume constant et N est la fréquence de Brunt-Väisälä : N 2 = g dθ θ dz Dans la stratosphère, on obtient N s 1, en prenant une valeur moyenneθ = 500 K et dθ dz 20 K km 1, ce qui correspond à une période de l ordre de 5 minutes. Enfin, en se plaçant dans l hypothèse Wentzel-Kramers-Brillouin (WKB), pour laquelle les propriétés de l atmosphère changent peu dans une échelle comparable à la longueur d onde, on recherche une solution de la forme : ) (α) = (u,v,w, θ θ, p [ ρ,ρ = (ũ,ṽ, w, θ, p, ρ).exp i(kx+ly+mz ωt)+ z ] ρ 2H (2.14) où k, l, m sont les nombres d onde respectivement zonal, méridien et vertical, etω est la fréquence de l onde dans le référentiel lié à la Terre. Le terme e z 2H assure la conservation de l énergie et des

23 2.1. CONSERVATION DE LA QUANTITÉ DE MOUVEMENT, DE LA MASSE ET DE L ENTROPIE15 flux verticaux, en compensant la diminution exponentielle de la densité. Les équations 2.8 à 2.13 peuvent ainsi s écrire : i ˆωũ f ṽ+ik p = 0 (2.15) i ˆωṽ+ f ũ+il p = 0 (2.16) ( i ˆω w+ im 1 ) p = g ρ (2.17) 2H i ˆω θ+ N2 w = 0 (2.18) g ( i ˆω ρ+ikũ+ilṽ+ im 1 ) w = 0 (2.19) 2H θ = p c 2 s ρ (2.20) où ˆω =ω ku lv est la fréquence intrinsèque de l onde, c est à dire la fréquence observée dans le référentiel du vent moyen. Par convention, ˆω est choisie positive. Équation de dispersion Les équations 2.15 à 2.20 peuvent être exprimées sous la forme d un produit : (M) t α = 0 (2.21) Pour que l équation 2.21 admette une solution non trivialeα, le déterminant de M doit être nul. L équation de dispersion ainsi obtenue lie les paramètres spatiaux à la fréquence de l onde et s écrit : m H 2 = (k2 + l 2 )(N 2 ˆω 2 ) ( ˆω 2 f 2 ) (2.22) Comme le membre de gauche est une somme de carrés, le membre de droite doit être positif, et on en déduit que f < ˆω < N. Aux moyennes latitudes, la période intrinsèque des ondes de gravité est donc comprise entre quelques minutes et 16 h, alors qu aux pôles, la période maximale des ondes de gravité est proche de 12 h. A l équateur, la force de Coriolis disparaît et les ondes de gravité peuvent donc avoir des périodes très longues, ce qui rend complexe la distinction entre les ondes planétaires, les ondes de gravité et les ondes équatoriales. On distingue les ondes de gravité pures qui combinent hautes fréquences ( ˆω f ) et faibles longueurs d onde des ondes d inertie-gravité qui associent basses fréquences et grandes longueurs d onde (Holton, 1992). Elles sont ainsi influencées par la force de Coriolis ce qui rend les trajectoires des particules d air elliptiques. On peut les observer dans les hautes latitudes où la force de

24 16 CHAPITRE 2. THÉORIE DES ONDES DE GRAVITÉ Coriolis a un effet notable sur les trajectoires des particules d air, et nous verrons dans le chapitre 4 que des ondes d inertie-gravité ont été observées pendant la campagne Vorcore. Relations de polarisations Enfin, en combinant les équations 2.15 à 2.20, des relations de polarisations peuvent être dérivées liant les perturbations ũ, ṽ, w, p. Par exemple, pour les perturbations des composantes de vitesse verticale et zonale, et les perturbations de pression et des composantes de vitesse zonale, on obtient : ( w = m i ) ( ˆω ˆω 2 f 2 ) 2H N 2 ˆω 2 ũ (2.23) ˆωk+ i f l ( ˆω 2 f 2 ) p = ũ (2.24) ˆωk+ i f l Vitesse de groupe et de phase La vitesse de groupe verticale intrinsèque correspond à la vitesse à laquelle l énergie est transportée. Elle est définie comme : ĉ gz = ˆω m. En manipulant l équation 2.22, ˆω peut être exprimée en fonction de m. En dérivant alors par rapport à m, on obtient : ˆω m = mˆω (k 2 + l 2 )( f 2 N 2 ) k 2 + l 2 + m (2.25) 4H 2 Le terme ( f 2 N 2 ) est négatif, aussi pour des ondes se propageant vers le haut (ĉ gz > 0), m doit être négatif. La vitesse de phase intrinsèque s écrit : ĉ = ˆω k k 2 de la composante horizontale de ĉ h s écrit donc : où k h = k 2 + l 2. où k = (k,l,m) est le vecteur d onde. Le module ĉ h = ˆω k h (2.26) La direction horizontale de propagation de l ondeψ est colinéaire au vecteur d onde horizontal : ψ = arccos( k k h ) (2.27) Un des objectif de cette thèse est de retrouver ĉ h etψàpartir des données enregistrées par les BPS durant la campagne Vorcore. 2.2 Interaction entre ondes de gravité et écoulement moyen Lors de leur propagation, les ondes de gravité sont susceptibles de devenir instables et ainsi de déferler. Cette interaction des ondes de gravité avec l écoulement moyen permet d expliquer un

25 2.2. INTERACTION ENTRE ONDES DE GRAVITÉ ET ÉCOULEMENT MOYEN 17 certain nombre de processus atmosphériques comme le minimum de température observé dans la haute mésosphère polaire en été (Garcia and Solomon, 1985), ou l oscillation quasi-biennale (OQB) (Baldwin et al., 2001). FIG. 2.1 Moyenne zonale de la température en janvier de la surface à la mésopause d après les données COSPAR International Reference Atmosphere (CIRA-86). Les observations (figure 2.1) montrent que la distribution de température dans la mésosphère n est pas en équilibre radiatif. Pendant l été, la température de la mésopause dans les hautes latitudes est inférieure de plus de 50 K à celle dans l hémisphère d hiver alors que ce dernier ne reçoit aucun rayonnement solaire. De plus, la figure 2.2 montre un fort ralentissement du vent zonal au niveau de la mésopause. Des études comme celles de Garcia and Solomon (1985) ont montré que ces deux phénomènes sont étroitement liés au déferlement des ondes de gravité. Plus précisément, le déferlement des ondes de gravité freine la circulation zonale et entraîne une circulation méridienne du pôle d été au pôle d hiver (Hamilton et al., 1995; Holton, 1992). Cette circulation s accompagne d une ascendance (et d un refroidissement adiabatique) au dessus du pôle d été qui vient expliquer les températures extrêmement froides observées. Le deuxième processus majeur qui prend place dans la stratosphère tropicale dont l interprétation fait intervenir des ondes atmosphériques est l OQB. La figure 2.3 illustre l alternance entre circulation moyenne zonale d ouest et d est, sur des périodes comprises entre 24 et 30 mois dans la stratosphère tropicale. L OQB s établit d abord à une altitude d environ 30 km puis se propage

26 18 CHAPITRE 2. THÉORIE DES ONDES DE GRAVITÉ FIG. 2.2 Vent zonal moyen en janvier et en juillet de la surface à la mésopause d après les données CIRA-86. vers le bas dans la stratosphère (Naujokat, 1986). Le transfert de quantité de mouvement nécessaire à l entretien de la circulation est assuré par la propagation d ondes de gravité, de Kelvin, et de Rossby-gravité (Lindzen and Holton, 1968; Holton and Lindzen, 1972; Dunkerton, 1997). L interaction des ondes de gravité avec l écoulement moyen a été étudiée théoriquement par Eliassen and Palm (1961); Boyd (1976); Andrews and McIntyre (1976). En effectuant les moyennes eulériennes des équations 2.2 à 2.7, les effets des ondes sur la circulation moyenne peuvent être mis en évidence, par exemple pour la projection zonale, on obtient : [ ] u u t + v y f + w u z X } {{ } effets dus à la circulation moyenne = (v u ) y 1 ρ 0 (ρ 0 w u ) z } {{ } effets dus aux ondes (2.28) Cependant, ces moyennes ont tendance à se compenser entre elles. Andrews and McIntyre (1976) ont redéfini les termes moyens de circulation résiduelle v et w, ce qui permet d exprimer directement l influence des ondes sous la forme de la divergence d un flux F = (0,F (y),f (z) ) appelé flux d Eliassen-Palm : u t + v [ u y f ] + w u z X = 1 ρ 0.F (2.29)

27 2.2. INTERACTION ENTRE ONDES DE GRAVITÉ ET ÉCOULEMENT MOYEN 19 FIG. 2.3 Section verticale des vent zonaux moyennés par mois sur les îles de Canton (janvier 1953-août 1967), les îles des Maldives/Gan (septembre décembre 1975) et Singapour (janvier avril 1985), extraits de Naujokat (1986). F (y) =ρ 0 ( u z v θ /θ z v u ) (2.30) F (z) =ρ 0 {[ f u y ]v θ /θ z w u } (2.31).F = F(y) y + F(z) z (2.32) Dans le cas d une onde linéaire, d amplitude stationnaire, adiabatique et non dissipative, cette divergence est nulle et l onde n interagit pas avec l écoulement moyen. Si la divergence est non nulle, les ondes transfèrent une partie de leur quantité de mouvement ce qui peut freiner ou accélerer l écoulement moyen. On distingue plusieurs raisons pour lesquelles une onde devient instable et se dissipe : Alors que la densité diminue avec l altitude, l amplitude de l onde augmente exponentiellement grâce au terme e z 2H tiré de l équation Les effets non linéaires négligés en première approximation deviennent importants, conduisant les isentropes à se déformer de manière

28 20 CHAPITRE 2. THÉORIE DES ONDES DE GRAVITÉ irreversible, entraînant mélange, turbulence et dissipation: l onde déferle (Andrews et al., 1987). La condition de stabilité peut être quantifiée par le nombre de Richardson qui permet d estimer l importance relative de la stabilité verticale et du cisaillement vertical : Ri = N2 ( du dz )2 Pour Ri < Ri c = 1/4, l écoulement est instable et l onde déferle. Dans les paramétrisations d ondes de gravité, l estimation de Ri peut être un diagnostic pour le déferlement de l onde (Lindzen, 1981), voir le chapitre 7. Lors de la propagation d une onde de gravité, si sa vitesse de phase devient égale à la vitesse de l écoulement moyen, l onde peut également devenir instable. A ces niveaux dits "critiques", le nombre d onde vertical devient infini et l onde peut être absorbée par l écoulement moyen dans le cas du déferlement, ou réfléchie (Drazin, 1982; Breeding, 1971; Whitten and Riegel, 1973; van Duyn and Kelder, 1982). Si la vitesse de phase de l onde ĉ approche la vitesse de l écoulement u par le haut (ĉ > u), le déferlement de l onde va conduire à accélerer l écoulement. Au contraire, si ĉ approche u par en dessous, celui-ci sera freiné. Ainsi, les caractéristiques de l écoulement moyen jouent un rôle déterminant dans la propagation et la dissipation des ondes de gravité. La figure 2.4 montre un profil de vent superposé à des ondes de gravité se propageant vers le haut. Au fur et à mesure de la propagation, les ondes dont la vitesse de phase se rapproche de la vitesse de l écoulement moyen vont saturer et déferler. Les ondes dont la vitesse de phase est toujours supérieure à la vitesse de l écoulement moyen pourront se propager plus haut et ne déferleront que lorsque leur amplitude deviendra trop grande, dans la mésosphère. Les ondes de montagne ont la particularité d être stationnaires (c 0 ms 1 ), et si la vitesse de l écoulement moyen est toujours différente de zéro au dessus de l altitude à laquelle elles sont générées, elles pourront également se propager jusqu à la mésosphère. Si l on se place à 10 hpa, les ondes dont la vitesse de phase est comprise entre 2 et 6 m/s sont absentes. On dit qu elles ont été "filtrées" par l écoulement, car à des altitudes plus basses, leur vitesse de phase a été proche de la vitesse de l écoulement ce qui les a forcées à déferler. En reprenant les équations 2.30 et 2.31 pour le cas des ondes d inertie-gravité, on peut simplifier

29 2.2. INTERACTION ENTRE ONDES DE GRAVITÉ ET ÉCOULEMENT MOYEN 21 FIG. 2.4 Vent zonal moyenné sur la période septembre-décembre 2000 entre 80 o S et 90 o S d après ERA-40. Les lignes en pointillées désignent la tropopause et la stratopause. Les flèches indiquent schématiquement la propagation verticale d ondes de gravité et les zones hachurées dénotent le déferlement des ondes. Voir le texte pour plus de détails. l expression de F. Comme l équation 2.14 définit une onde plane infinie, le terme F (y) ne varie pas en fonction de la latitude. Cependant, comme nous le verrons dans le chapitre suivant, nos simulations représentent les ondes sous la forme de paquets d onde et non d ondes planes. Nous pouvons toutefois supposer que les variations de F (y) sont négligeables sur la durée du paquet d onde.en négligeant u y utilisant la définition de N 2 et l équation 2.18, l équation 2.31 s écrit : F (z) =ρ 0 (1 f 2 et en ˆω 2)u w (2.33) Le flux d Eliassen-Palm, ne dépend donc que de z, et notre méthodologie va chercher à estimer le termeρ 0 u w grâce aux données récoltées par les BPS.

30 22 CHAPITRE 2. THÉORIE DES ONDES DE GRAVITÉ Résumé Nous avons vu dans ce chapitre les paramètres essentiels caractérisant les ondes de gravité. A partir des données enregistrées pendant la campagne Vorcore, nous allons estimer la vitesse de phase intrinsèque horizontale ĉ h, la direction de propagationψet le flux vertical de quantité de mouvement ρ 0 u w transporté par les ondes de gravité. Ces grandeurs sont à rapprocher de la paramétrisation développée par Alexander and Dunkerton (1999) qui calcule le forçage des ondes de gravité en fonction de la distribution de la vitesse de phase intrinsèque (voir le chapitre 7).

31 23 Chapitre 3 Réponse des BPS aux ondes de gravité : étude théorique et numérique Ce chapitre détaille la méthodologie développée pour dériver des caractéristiques des ondes de gravité à partir des séries temporelles enregistrées par les BPS. L étude théorique qui suit s appuie sur les équation développées dans le chapitre précedent et sur des travaux théoriques et numériques antérieurs, en particulier Massman (1978); Nastrom (1980); Hertzog and Vial (2001a). Afin de valider notre approche, des simulations reproduisant les séries temporelles de pression et de vent ont permis de tester la méthode et sa robustesse. 3.1 Études théoriques et numériques antérieures Dès les années 1960, la réponse théorique des ballons préssurisés à des mouvements verticaux a été étudiée, par exemple Angell and Pack (1962); Booker and Cooper (1964); Hirsch and Booker (1965). En effet, si les ballons sont des bons traceurs des mouvements horizontaux, ils ne reproduisent pas parfaitement les mouvements verticaux. Les mouvements verticaux des ballons pressurisés peuvent être liés à différents types d oscillations :

32 24 CHAPITRE 3. RÉPONSE DES BPS AUX ONDES DE GRAVITÉ les oscillations naturelles qui sont un mode d oscillation propre, les oscillations diurnes liées à la température de l hélium dans l enveloppe (quand la température du gaz augmente pendant la journée, la surpression à l intérieur de l enveloppe augmente également ce qui conduit à une expansion du gaz et de l enveloppe, et donc à une diminution de la densité) ou encore les oscillations causées par un vent vertical potentiellement lié aux ondes de gravité. L enveloppe d un BPS est quasiment inextensible afin que le volume du ballon reste constant. Dans cette hypothèse et en se plaçant dans l approximation des gaz parfaits, le ballon se déplace sur des surfaces de densité constante. En outre, le BPS est en équilibre stable, c est-à-dire que s il est déplacé verticalement, il aura tendance à revenir sur cette surface isopycne. Toutefois, dans ce cas, la trajectoire du BPS ne sera plus strictement isopycne. Dans la stratosphère, comme le forçage radiatif est faible, on considère que les particules d air se déplacent le long des isentropes. Un des objectif de cette étude théorique est donc de trouver une relation entre le déplacement vertical isentrope d une particule d air induit par une onde de gravité et le déplacement vertical correspondant d un ballon isopycne ainsi que de modéliser le comportement d un BPS lorsqu il s éloigne de la surface isopycne. Hirsch and Booker (1965) ont été parmi les premiers à modéliser la réponse d un ballon pressurisé à une onde sinusoïdale se propageant verticalement. Ils se sont placés dans l hypothèse où la force de frottement est en équilibre avec la force de flottabilité et que les effets dus à l inertie sont négligeables. Ils ont trouvé un déphasage entre la trajectoire du ballon et la trajectoire de la particule d air, ainsi qu une sous estimation par le ballon de l amplitude de l onde (15%). Ces résultats préliminaires, bien qu ils ne prennent pas en compte toute la physique du ballon, ont été qualitativement vérifiés dans les travaux qui suivirent. Puis, ce travail a été complété par des observations, des simulations et des approches théoriques dont nous allons maintenant reprendre les principaux résultats, en particulier ceux obtenus par Massman (1978) et Nastrom (1980). Les principales forces verticales qui s exercent sur le ballon sont : la force de flottabilité dynamique liée à l accélération de l air 1, la force de frottement 2 et la force de flottabilité statique 3. L équation décrivant le mouvement du ballon dans la verticale s écrit (Nastrom, 1980) : (M b +ηm a ) 2 z t 2 = (M a +ηm a ) w a 1 ( ) z } {{ t } 2 ρ ac d A b t w z a t w a g(m b M a ) } {{ } } {{ } (3.1)

33 3.1. ÉTUDES THÉORIQUES ET NUMÉRIQUES ANTÉRIEURES 25 où M b correspond à la masse du ballon (enveloppe + gaz + équipement), M a la masse de l air déplacé, ρ a la densité de l air ambiant, V le volume du ballon, z le déplacement vertical du ballon par rapport à son niveau d équilibre, w a la vitesse verticale de l air, A b =πr 2 l aire de la section transversale du ballon, C d 0.5 le coefficient de frottement lié à la géométrie du ballon, η le coefficient de masse additionnel lié à la géométrie du ballon. Dans le cas des BPS, le ballon est sphérique doncη = 1 2. Les études théoriques et numériques ont examiné particulièrement les oscillations naturelles et les oscillations induites par les ondes de gravité auxquelles sont soumises les ballons Les oscillations naturelles Les oscillations naturelles sont un mode d oscillation propre autour de la position d équilibre du ballon. Dans l hypothèse où toutes les forces sont nulles sauf la force de flottabilité statique, l équation 3.1 se simplifie : (M b M a) 2 z dt 2 = g(m b M a ) (3.2) A la position d équilibre, M a = M b, et l équation 3.2 peut s écrire : 2 z dt 2 = 2 3 gρ av M b M b (3.3) Le membre de droite peut être exprimé sous la forme d un oscillateur harmoniqueω 2 n(z z 0 ), où z 0 est la hauteur du niveau de densité à l équilibre etω n correspond à la fréquence des oscillations naturelles (Levanon et al., 1974; Massman, 1978). Le terme ρ av M b M b dépend à la fois de la variation de densité et de pression. Cette dernière entraîne une modification de la surpression et une contraction ou une expansion du volume. En utilisant l équation des gaz parfaits et la relation hydrostatique, le terme ρ av M b M b peut être exprimé sous la forme : ρ a V M b M b ( g = R + dt dz )( 1+K P T 0 ) (z z 0 ) (3.4)

34 26 CHAPITRE 3. RÉPONSE DES BPS AUX ONDES DE GRAVITÉ ( ) où P correspond à la surpression à l équilibre, K = 1 dv V d p température de l air, g R = = 34.2 o C km 1 et dt dz terme K P est petit par rapport à 1 (Sommeria, 1970),ω n peut s écrire : ω n = la compressibilité isotherme, T 0 la T le gradient vertical de température. Comme le [ ( g 2 3 g R + )] dt 1 2 dz (3.5) T 0 Dans la stratosphère, les valeurs moyennes de dt dz et T 0 permettent d obtenir une estimation de la période des oscillations naturelles : dt dz +1 K km 1 et T 0 209K; on obtient une période de l ordre de 200 secondes, ou 3 minutes. Dans la stratosphère, la période de Brunt-Väisäla est proche de 5 minutes, donc les oscillations naturelles ont des périodes inférieures à celles correspondant aux ondes de gravité Les oscillations induites par les ondes de gravité Les études de Massman et Nastrom ont cherché une solution analytique à l équation 3.1 en effectuant les simplifications suivantes : La masse du ballon est égale à la masse de l air déplacé, M a = M b, sauf dans le terme de flottabilité statique pour lequel même des faibles différences peuvent avoir un effet important. Le déplacement vertical isentrope peut être relié au déplacement du ballon isopycne grâce à un termeκintroduit par Massman : κ = g C p + dt dz g R + dt dz où g C p est le gradient vertical adiabatique de température pour l air sec : 9.8 K km 1. Dans notre cas où dt dz 1 K km 1,κ = R+1 dt C p Ainsi, dans le cas où dz = 0, la définition du termeκcorrespond à la définition issue de la thermodynamique classique,κ = R C p. Dans Massman (1978), le déphasage entre le ballon et la surface isentrope, et le rapport entre l amplitude du déplacement du ballon et celui de l isentrope sont calculés à l aide de 1. Dans les séries temporelles étudiées, ces mouvements ont été filtrés par l échantillonnage de 15 minutes. Cependant, la pression était également enregistrée toutes les minutes et le signal de ces oscillations a pu être observé comme nous le verrons dans le chapitre 5.

35 3.1. ÉTUDES THÉORIQUES ET NUMÉRIQUES ANTÉRIEURES 27 FIG. 3.1 Figures tirées de l article Massman (1978). techniques de perturbations. La figure 3.1 montre le déphasage (à gauche) et le rapport des amplitudes (à droite) en fonction d un facteurεpour différentes valeurs deκ : ε =ω 2 ζ Z a /ω 2 n oùωest la fréquence de l onde de gravité,ζ = ρ aa b C d 3M b = 10 2 π , m 1 avecρ a = 10 2 kg m 3, R = 10 m. Z a, qui correspond à l amplitude de l onde en mètres, est de l ordre du mètre. Ainsi, pour des périodes comprises entre 1 h et 14 h (ω n >>ω), le termeεest faible. Or, selon la figure 3.1, le déphasage est compris entre 0 o et 25 o pourε < 2. Nastrom a suivi une démarche similaire en ajoutant au raisonnement les variations de densité engendrées par les ondes de gravité. Il a calculé le déphasage et le rapport d amplitudes en fonction d un paramètreω 2 qui dépend de la stabilité de l atmosphère N 2 et du gradient vertical de température. Il trouve un déphasage de plus de 60 o et un rapport d amplitudes proche de 0.5. Ces résultats sont valables pour des périodes inférieures à 1 heure, mais restent qualitativement très informatifs. Ces deux études présentent des résultats similaires qualitativement. Pour les ondes de gravité dont la période est longue (supérieure à une heure), les ballons se rapprochent asymptotiquement d un traceur isopycne parfait, en conservant un certain déphasage. Les périodes des ondes de gravité étudiées dans cette thèse sont toutes supérieures à une heure, c est pourquoi notre méthodologie

36 28 CHAPITRE 3. RÉPONSE DES BPS AUX ONDES DE GRAVITÉ prend en compte le déphasage éventuel du ballon par rapport à la surface isentrope compris entre 0 o et 30 o, et emploie un terme constant reliant le déplacement de la surface isentrope à celui de la surface isopycne. 3.2 Outil mathématique : l analyse en ondelettes FIG. 3.2 Décomposition en ondelette de l énérgie cinétique en fonction du temps et de la période pour une simulation comportant une onde de gravité. En pointillé, le cône d influence. L algorithme que nous avons développé utilise l analyse en ondelettes (Torrence and Compo, 1998) pour détecter les ondes de gravités dans les séries temporelles de perturbations de pression et de vitesse. Cet outil mathématique, développé au début des années 1980, permet de décomposer un signal temporel en temps et en fréquence à partir d une ondelette "mère". Celle-ci est compressée (ou dilatée) puis translatée afin de couvrir tout le domaine de la fonction décomposée. Le facteur de

37 3.2. OUTIL MATHÉMATIQUE : L ANALYSE EN ONDELETTES 29 translation détermine sur quel intervalle du domaine de définition de la fonction on se place alors que le facteur d échelle calibre le domaine fréquentiel. Dans cette étude, l ondelette de Morlet a été utilisée. Cette ondelette complexe est réprésentée par un paquet d onde et s exprime sous la forme: ψ(t) =π 1 4 exp ( 1 2 t2 )exp (i2π f 0 t) (3.6) où f 0 est la fréquence centrale de l ondelette. Le choix d une ondelette complexe permet d évaluer les différences de phase entre les perturbations de vent et de pression. Comme nous le verrons dans la partie 3.3, la méthodologie développée s appuie spécifiquement sur ces différences de phase. La figure 3.2 représente la décomposition en ondelettes de l énergie cinétique pour une simulation de 10 jours qui comprend une onde dont la période 7 h. Le cône d influence (en pointillé) correspond à la période maximum qui n induit pas d effet de bords. Les points situés à l extérieur du cône d influence ne sont pas pris en compte dans l analyse, au risque d introduire des erreurs. L onde est facilement identifiable par un pic d energie autour du temps t 0 au centre du paquet d onde. L onde (et son énergie cinétique) se projette sur des ondelettes de périodes comprises entre 5 h et 11 h. Cet étalement dans le plan des fréquences explique que les périodes des ondelettes utilisées soient comprises entre 1 h et 24 h. Le minimum est lié à l échantillonnage utilisé dans les observations (15 minutes), alors que le maximum a été choisi pour éviter des pertes d énergie. En effet, si la période de l onde est proche de la période inertielle, l onde se projetera sur des ondelettes dont la période est plus longue (jusqu à 20h), il faut donc en tenir compte au risque de sous-estimer l énergie (et la quantité de mouvement) transportée par une onde. Dans les simulations, l onde est représentée par un paquet d onde, comme l ondelette de Morlet, et on peut donc parler de filtre adapté. Néanmoins, pour des ondes de gravité se propageant verticalement et à travers la surface isopycne sur laquelle se déplace le ballon, il est raisonnable de penser que les perturbations enregistrées par le ballon s apparentent à un paquet d onde.

38 30 CHAPITRE 3. RÉPONSE DES BPS AUX ONDES DE GRAVITÉ 3.3 Étude théorique et numérique des ondes de gravité Article : Estimation of Gravity-Wave Momentum Fluxes and Phase Speeds from Quasi-Lagrangian Stratospheric Balloon Flights. 1: Theory and Simulations Cet article développe l étude théorique qui permet d exprimer la vitesse de phase horizontale intrinsèque ĉ h, la direction de propagation horizontaleψ et le flux de quantité de mouvement dans la direction de propagation de l ondeρu w à partir des perturbations de pression, de vitesse et de température enregistrées par les BPS. L article présente les simulations réalisées ainsi que l algorithme utilisé pour retrouver ĉ h,ρu w etψ. Dans le cas d une onde de gravité, l algorithme retrouve précisémentψ, il sous-estimeρu w de 14% en particulier pour les ondes de hautes fréquences, et la restitution de ĉ h produit une distribution très dispersée. Dans le cas plus réaliste où plusieurs paquets d onde sont inclus dans les simulations, la restitution deρu w tend à se dégrader au fur et à mesure que les paquets d onde se superposent dans le plan temps-fréquence intrinsèque. La restitution précise deψpermet d obtenir les distributions deρu w etρv w, respectivement les flux de quantité de mouvement zonaux et méridiens. Cet article a été accepté en mars 2008 à Journal of Atmospheric Sciences. Dans la suite de la thèse il est désigné sous la forme Boccara et al. (2008b).

39 3042 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 65 Estimation of Gravity Wave Momentum Flux and Phase Speeds from Quasi-Lagrangian Stratospheric Balloon Flights. Part I: Theory and Simulations GILLIAN BOCCARA AND ALBERT HERTZOG Laboratoire de Météorologie Dynamique, Université Pierre et Marie Curie, École Polytechnique, Palaiseau, France ROBERT A. VINCENT Department of Physics, University of Adelaide, Adelaide, Australia FRANÇOIS VIAL Laboratoire de Météorologie Dynamique, École Polytechnique, Palaiseau, France (Manuscript received 11 December 2007, in final form 17 March 2008) ABSTRACT A methodology for estimating gravity wave characteristics from quasi-lagrangian observations provided by long-duration, superpressure balloon flights in the stratosphere is reviewed. Wavelet analysis techniques are used to detect gravity wave packets in observations of pressure, temperature, and horizontal velocity. An emphasis is put on the estimation of gravity wave momentum fluxes and intrinsic phase speeds, which are generally poorly known on global scales in the atmosphere. The methodology is validated using Monte Carlo simulations of time series that mimic the balloon measurements, including the uncertainties associated with each of the meteorological parameters. While the azimuths of the wave propagation direction are accurately retrieved, the momentum fluxes are generally slightly underestimated, especially when wave packets overlap in the time frequency domain, or for short-period waves. A proxy is derived to estimate by how much momentum fluxes are reduced by the analysis. Retrievals of intrinsic phase speeds are less accurate, especially for low phase speed waves. A companion paper (Part II) implements the methodology to observations gathered during the Vorcore campaign that took place in Antarctica between September 2005 and February Introduction Corresponding author address: Albert Hertzog, Laboratoire de Météorologie Dynamique, École Polytechnique, F Palaiseau CEDEX, France. albert.hertzog@lmd.polytechnique.fr Temperatures in the extratropical middle atmosphere differ greatly from radiative equilibrium values (Andrews et al. 1987). The observed departures result from a global pole-to-pole circulation in the middle atmosphere driven by planetary and gravity wave breaking in the stratosphere and mesosphere (Holton et al. 1995). Because of their shorter spatial and temporal scales, as well as their small amplitudes in the lower atmosphere, gravity waves (GWs) are more difficult to observe than planetary waves. In particular, there are relatively few observations of the global-scale distribution of GWs available, despite their importance in the dynamics of the middle atmosphere (e.g., Nastrom and Fritts 1992; Fritts and Nastrom 1992; Allen and Vincent 1995). In the past few years, however, modern spaceborne observations have significantly improved our knowledge of the GW field in the middle atmosphere. For example, limb observations of infrared (Fetzer and Gille 1994; Eckermann and Preusse 1999; Preusse et al. 2002) and microwave radiances (Wu and Waters 1996; McLandress et al. 2000; Jiang et al. 2004), nadir observations (Wu 2004; Eckermann and Wu 2006; Alexander and Barnet 2007), as well as GPS radio-occultation techniques (Steiner and Kirchengast 2000; Tsuda et al. 2000; Ratnam et al. 2004; Baumgaertner and McDonald 2007), provide important insights into the distribution of GW potential energy on a global scale. Nevertheless, a GW quantity that is still poorly measured on a global scale is the momentum flux, although DOI: /2008JAS American Meteorological Society

40 OCTOBER 2008 B O C C A R A E T A L it is a quantity required to constrain GW effects in atmospheric general circulation models (Charron et al. 2002; McLandress and Scinocca 2005). Some GW momentum fluxes measurements have been obtained at a few widely spaced locations around the globe with radar or in situ airborne observations (e.g., Vincent and Reid 1983; Tsuda et al. 1990; Fritts et al. 1990; Alexander and Pfister 1995). Recently, the first global observations of absolute GW momentum fluxes in the lower stratosphere were obtained during two oneweek duration campaigns using the Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA) instrument (Ern et al. 2004, 2006). Furthermore, Alexander et al. (2008) derived absolute momentum fluxes from the High Resolution Dynamics Limb Sounder (HIRDLS) observations in May Longduration flights of superpressure balloons in the lower stratosphere provide an additional method by which GW momentum fluxes can be derived on global scales (Massman 1981; Hertzog and Vial 2001; Vincent et al. 2007). The balloon technique complements satellite observations by providing an independent estimation of absolute GW momentum fluxes. Importantly, directional fluxes, which cannot be measured using current spaceborne technology, can be derived with the balloon technique. Here we review and extend the methodology used to extract GW information from observations obtained during long-duration balloon flights. In contrast to Hertzog and Vial (2001), we take into account that superpressure balloons do not perfectly follow constantdensity (isopycnic) surfaces and assess this effect in the retrieval of GW momentum fluxes. Furthermore, we derive an expression for computing GW phase speeds from the balloon observations. Last, we carefully quantify the accuracy with which GW characteristics are retrieved from such datasets. In a companion paper (Hertzog et al. 2008), the methodology described in this study is applied to the dataset collected during the 2005 Stratéole/Vorcore campaign, during which 27 superpressure balloons were launched from McMurdo, Antarctica (77.8 S, E) (Hertzog et al. 2007). During the campaign, the scientific payload carried by each balloon recorded every 15 min the air temperature and pressure, as well as the balloon s 3D position. Since superpressure balloons are very good tracers of horizontal motions in the atmosphere (Massman 1978), the horizontal positions provide information on the horizontal wind velocities during the flights. The methodology described in this study can, in principle, be used with any quasi-lagrangian balloon flight. However, the reported uncertainties in the derived GW properties are specifically valid for the Vorcore observations since they depend on, among other things, the observational noise and sampling rate. The following section reviews the theoretical basis behind the retrieval of GW characteristics from longduration balloon observations. The important point of such observations is that the balloons move with the wind so that the GW disturbances observed by the balloons are made in a Lagrangian frame of reference. The method used to estimate momentum fluxes, as well as wave phase speeds, from those observations is presented. Section 3 describes the numerical simulations undertaken to estimate the accuracy of our GW retrievals. Specifically, we generated time series containing a number of GW packets with known characteristics, similar to those recorded during real balloon flights. The algorithm used to analyze these simulated time series or the real ones is also described in this section. Section 4 is devoted to comparisons of the retrieved GW characteristics with those imposed in the simulated time series. We consider in particular the retrieval of absolute as well as zonal and meridional momentum fluxes and phase speeds as these parameters are arguably the most important in GW drag parameterizations. The limits of the GW retrievals are also discussed. The main results of this study are summarized in the final section. 2. Theory Here, the relationships between the various meteorological parameters measured by superpressure balloons (SPBs) when they encounter gravity wave packets are examined. Based on these equations, the methodology used to infer GW properties is developed in two steps: first, we consider that SPBs drift on constantdensity (isopycnic) surfaces (Massman 1978), and then take into account the effect of small departures from a perfect isopycnic behavior, as suggested in Nastrom (1980). In particular, Nastrom showed that the balloon vertical displacements may have a small phase shift relative to those of an isopycnic surface. In both cases, we assume that SPBs are perfect tracers of the horizontal wind (Hertzog et al. 2007). a. The balloon as a perfect isopycnic tracer Figure 1 illustrates (in solid) the vertical displacement of an isopycnic surface induced by a gravity wave. We assume here that the balloon always remains on this surface. Let A (altitude z 0 ) be a point where the waveinduced density disturbance vanishes. At A, the density therefore simply reduces to the background atmospheric density (z 0 ). Let B be a point where the ver-

41 3044 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 65 FIG. 1. Vertical displacements of an isopycnic surface generated by an Eulerian disturbance in air density induced by a gravity wave (solid line). In A, 0, whereas in B, 0 (see text for further details). A perfect isopycnic balloon will drift on the isopycnic surface, whereas according to Massman (1978) the vertical displacement of real balloons (dashed) may be slightly shifted relative to the isopycnic surface. tical displacement of the isopycnic surface is nonzero, where the prime denotes a wave disturbance. The density at B is z 0 z 0 z 0. By definition, it is equal to the density at A so that at first order of the wave disturbance: z 0 z 0 z z 0. Solving for the vertical displacement of the isopycnic surface yields where z 0 z H z 0 z 0, H 1 z is the density scale height. The wave-induced pressure perturbation in B is obtained as in (1): p z 0 p z 0 p z p z 0. Hence the pressure perturbation observed by the balloon (i.e., the Lagrangian pressure perturbation) at B is, to first order, p l B p z 0 p z 0 p z 0 p z, where the index l denotes Lagrangian disturbances. It should be noted that the second-order Stokes correction to the Lagrangian-mean pressure has been neglected in this equation. The Lagrangian pressure perturbations measured by the drifting balloon are therefore the sum of two components: (i) the Eulerian perturbation caused by the wave p (z 0 ), hereafter referred to as p w, and (ii) a contribution associated with the vertical gradient of the background pressure p/ z, hereafter referred to as p g. Similar equations can be written for the velocity perturbations, but we assume in the following that u g u/ z and g / z are small with respect to the Eulerian perturbations (see, e.g., Hertzog and Vial 2001). From now on, a complex notation is used for the wave disturbances with primed quantities denoting the complex wave amplitudes. The following developments rely on the classical GW equations derived in Fritts and Alexander (2003). Thus, the horizontal momentum equations can be used to find a relation between the Eulerian pressure disturbance and the velocity perturbation in the direction of propagation of the wave u : p w ĉ u, where 1 f 2 / ˆ 2 (with f the inertial frequency and ˆ the intrinsic frequency of the wave) and ĉ is the horizontal intrinsic phase speed of the wave (i.e., ĉ ˆ /k h, where k h is the horizontal wavenumber). The vertical momentum equation [Eq. (17) in Fritts and Alexander (2003)], on the other hand, relates the Eulerian pressure and density perturbations: i ˆ w im 2H 1 p w g, where w is the vertical velocity perturbation, and m is the vertical wavenumber. Owing to the sampling period of 15 min used during Vorcore, we cannot resolve the highest frequency part of the gravity wave spectrum. The motions that we are interested in are therefore to a good approximation hydrostatic, and we can safely ignore the first term on the left-hand side of (7). Assuming that the background pressure is in hydrostatic equilibrium, p g can be expressed as p g g. Combining (3) with (7) and (8), p g can be expressed in terms of p w, so the Lagrangian pressure perturbation becomes p l 1 2 imh p w. 9 Using (6) the Lagrangian pressure perturbation can then be related to the velocity perturbation in the wave direction of propagation: 6 7 8

42 OCTOBER 2008 B O C C A R A E T A L p l 1 2 imh ĉ u. 10 It is interesting to note that for a typical GW vertical wavelength of 3 km in the polar lower stratosphere (Allen and Vincent 1995) (i. e., m rad m 1 ) and with H 6 km, the imaginary part of (10), which is associated with p g, dominates the real part so that p l and u are essentially in quadrature, whereas the Eulerian pressure disturbance is in phase with u. Forming the covariance of p l with u, one obtains p l u * ĉ u 2 2 imh ĉ u 2, 11 where the asterisk denotes the complex conjugate. The horizontal intrinsic phase speed of the wave can thus be computed from this covariance: vertical displacement of a balloon ( b ) can slightly lead that of the isopycnic surface. We now study the effect of this small shift. Let ( 0) be the small angle by which the balloon leads the isopycnic surface (see also Fig. 1): b e i 1 i. The expression for p g is modified accordingly: p g pg 1 i, while p w is unchanged to first order. The resulting new expression for the Lagrangian pressure perturbation becomes p l 1 2 mh i mh 2 pĉ u. 18 ĉ 2 u 2 R p lu *, 12 Now mh k /2 for typical values of m and H so that, when forming the covariance with u, where R stands for the real part. To obtain an expression for the wave absolute momentum flux, we first use the polarization relation between w and u (Fritts and Alexander 2003): w i 2H m ˆ 2 f 2 k h N 2 u, 13 where N is the buoyancy frequency. Using (11) R w u * ˆ HN I p lu 2 *, 14 where I stands for the imaginary part. Note that we are only interested in the real part of the momentum flux as it is the only contribution that does not vanish when averaged over a wave period. Simple calculus shows that the multiplicative term on the right-hand side in the previous equation depends on the vertical gradient of background temperature, so 1 HN 1 2 g g R T z g c p T z, 15 where R and c p are, respectively, the perfect gas constant and specific heat at constant pressure per unit mass of air. Equations (14) and (15) are equivalent to (11) in Hertzog and Vial (2001). b. Real balloon In high static stability conditions, such as those encountered in the stratosphere, superpressure balloons behave asymptotically as isopycnic tracers (Massman 1978). Nevertheless, Nastrom (1980) showed that the p l u * 1 2 mh ĉ u 2 imh ĉ u Hence the imaginary part is not modified by the phase shift, and the wave momentum flux can still be estimated using (14). On the other hand, estimation of the wave intrinsic phase speed now requires knowledge of. To estimate from the balloon data, we consider the density recorded by the balloon; namely, Using (3) and (16) gives b z z z b z. b z z 1 i H z z z H z z i z to first order. Hence, the Lagrangian density perturbation is Using (6) and (7) gives l b i. l m 2H i ĉ u g Forming the covariance of with u and taking the real part yields R l u * m ĉ u 2 g ; 25

43 3046 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 65 hence, can be determined via gh R u * I p l u *. 26 Once is estimated, the velocity perturbation can be computationally shifted to retrieve the intrinsic phase speed of the wave: ĉ 2 u R p l u 2 e i *. 27 The algorithm used to analyze the long-duration balloon dataset therefore uses (14) and (27) to estimate both the momentum flux and the intrinsic phase speed of the observed GW packets. It ultimately relies on the estimation of phase differences between the observed velocity and pressure time series. 3. Simulations and the retrieval algorithm In this section, we discuss numerical simulations that were conducted to assess the validity of our retrievals of GW characteristics from the SPB dataset. We then present in more detail the algorithm used to analyze the observations. a. Numerical simulations of balloon observations A three-dimensional model was constructed to simulate the balloon observations. It consists of a background isothermal atmosphere, with a constant buoyancy frequency (N rad s 1 ) and a mean eastward flow of 10 m s 1 that is representative of conditions during Vorcore. One or several gravity wave packets, each propagating upward in the atmosphere, were linearly superimposed onto this background. GW polarization relations (Andrews et al. 1987; Fritts and Alexander 2003) were used to compute the waveinduced disturbances in horizontal velocity, pressure, temperature, and density. Wave wave and wave mean flow interactions were ignored. GW characteristics, such as the phase constant, intrinsic period 2 / ˆ, azimuth of propagation, intrinsic phase speed ĉ, and time corresponding to the center of the wave packet t c, were chosen randomly within the ranges detailed in Table 1. The wave packets had a Gaussian envelope, with full width at half maximum (FWHM) proportional to the intrinsic period of the wave so that the wave packets always had the same number of oscillations ( 3). Finally, a phase shift ( ) between the balloon vertical displacement and that of the isopycnic surface was randomly chosen from a homogeneous distribution between 0 and 0.5 rad and assigned to each wave packet so as to simulate the departure of the balloon from TABLE 1. Gravity wave characteristics used in the simulations. The longest period used corresponds to the inertial period at 60 latitude. isopycnicity. From the randomly chosen parameters the horizontal and vertical wavenumbers were derived as and Parameter k h ĉˆ m N2 ˆ 2 ˆ 2 f k 2 2 h 1 4H The negative value of the vertical wavenumber means that the waves were propagating upward. The amplitudes of the wave-induced disturbances in horizontal velocity along the directions of propagation were chosen so as to be consistent with the horizontal kinetic-energy density spectrum displayed in Hertzog and Vial (2001) and Hertzog et al. (2002). In particular, the wave amplitude scales as ˆ 1 in our simulations. The vertical momentum flux transported by the wave packets is computed analytically from the wave parameters and the Gaussian envelope. For some simulations, the combination of parameters generated unstable waves. In the real atmosphere, such wave-generated instabilities will significantly reduce the wave amplitudes. Simulations that included unstable waves were therefore discarded. To determine whether a wave packet would be unstable, we used a similar threshold to that advocated by Fritts et al. (2006); namely, z 0.1, Range Phase at origin ( ) 0 2 Horizontal angle of propagation ( ) 0 2 Intrinsic period (2 / ˆ ) h Intrinsic phase speed (ĉ) m s 1 Time of occurrence (t c ) day Envelope type Gaussian FWHM of the envelope / ˆ Phase shift of balloon response ( ) (rad) 30 where is the amplitude of the wave-induced vertical displacements of air parcels and z is the vertical wavelength. Simulations that contained quasi-inertial wave packets ( ˆ 1.1f) or wave disturbances that occurred too close to the beginning or end of the simulated flights (i.e., those for which less than two periods could be observed in the simulated time series) were also removed from further analysis.

44 OCTOBER 2008 B O C C A R A E T A L FIG. 2. Simulated gravity wave disturbances in pressure (solid, left scale) and in zonal (dashed, right scale) and meridional (dashed dotted, right scale) velocities. Measurement noise is included in the simulated time series and is particularly evident in the pressure disturbance. The simulated flights had a duration of 10 days and started from 60 S. The simulated observations mimic those of the real balloons. In particular, the same 15- min sampling rate was used, and the horizontal velocities were computed through finite differences of successive balloon positions. The simulations were run with and without an additional Gaussian white noise to assess the importance of measurement uncertainties in the analysis. The standard deviations of the added noise correspond to the accuracy of the sensors used on real balloons 0.25 K for temperature, 1 Pa for pressure and 15 m for the horizontal position provided by absolute GPS measurements. An example of simulated gravity wave disturbances is displayed in Fig. 2. This figure highlights the relatively greater importance of the measurement uncertainties in the pressure records compared to those associated with horizontal velocities. It is also noticeable that the zonal velocity fluctuations lead those in the meridional component, consistent with the fact that the balloons are drifting in the Southern Hemisphere. b. Retrieval algorithm In the balloon observations, GWs often appear as individual wave packets. Wavelet analysis techniques were therefore chosen to retrieve GW characteristics since they enable us to account for the nonstationarity of the wave field. Applied to either real or simulated SPB time series, the wavelet technique provides information in time (intrinsic) frequency space. The algorithm uses a complex Morlet wavelet as the retrieval of wave momentum fluxes and phase speeds is based on phase differences between the various time series. The main steps of the retrieval algorithm are as follows: 1. The time series of pressure, horizontal velocity, temperature, and density are decomposed using wavelet techniques. Morlet wavelets with periods ranging between 1 and 24 h are used. This analysis provides complex coefficients that are representative of the energy and phase of the decomposed signal in small time/(intrinsic) frequency bins. The wavelet coefficients are normalized so that the variance of each decomposed signal is recovered when summed over the whole of the modulus of the squared coefficients (Torrence and Compo 1998). From now on, tildes are used to denote wavelet coefficients. For example, p (t i, ˆ j) corresponds to the decomposed pressure time series on the jth wavelet, whose central frequency is ˆ j, in the neighborhood of the ith observation point. 2. To avoid interpreting noise as GWs, wavelet coefficients for which the modulus is smaller than three times the standard deviation of the observational uncertainties are discarded. 3. To determine the horizontal direction of propagation to within an ambiguity of 180, the horizontal velocity coefficients ũ(t i, ˆ j) and (t i, ˆ j) are rotated until the velocity parallel to the rotated direction is maximized. Let ũ and ũ be the respective velocity wavelet coefficients in the parallel and perpen-

45 3048 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 65 observation time. We use [ ˆ c k(t i )] k to denote the set of wavelet frequencies corresponding to these central coefficients. 5. Next, the envelopes of the wave packets are identified. This is done by searching in the frequency space around each ˆ c k(t i ) and selecting the neighboring frequencies for which FIG. 3. Hodograph of the horizontal velocity fluctuations associated with the GW packet shown in Fig. 2. Units are in m s 1. The wave direction of propagation (356 from east) is indicated by the arrow pointing to u. The horizontal velocities projected on this direction and on the orthogonal direction are referred to as u and u, respectively, in the text. dicular directions. The 180 ambiguity is resolved by assuming that wave packets propagate upward in the atmosphere, so the absolute momentum flux R(ũ w*) obtained from (14) is necessarily positive. Figure 3 illustrates this detection for the wave packet shown in Fig. 2. In this case, the input and retrieved direction of propagation are 356 from east. 4. Each wave packet actually projects onto several wavelets, so the central frequency of a wave packet must be known in order to retrieve the momentum flux [see Eq. (14)]. This is achieved by using the polarization relation that links the parallel to the perpendicular velocity disturbances (Fritts and Alexander 2003). Specifically, the wavelet coefficients that satisfy ũ t i, ˆ j i ˆ j f i ũ t i, ˆ j 31 to within an assumed uncertainty (typically 50%) are selected as being associated with the wave packet centers. In (31), f i is the inertial frequency corresponding to the balloon latitude at time t i. This search is only performed among those frequencies that satisfy ˆ j f i, that is, those corresponding to gravity waves. Note that this algorithm can, in principle, detect several wave packet centers at the same R ũ w * t i, ˆ j R ũ w * t i, ˆ c k t i In contrast with the previous step, this latter search is not limited to GW frequencies alone, as the wave packet may project on wavelets with frequencies smaller than the local inertial frequency. The wavelet frequencies selected during this step are those associated with a gravity wave packet, hereafter referred to as ˆ gw (t i ). Figure 4 demonstrates the two last steps for the time series corresponding to the wave packet shown in Fig. 2. The estimated wave envelope is displayed in the left panel in the time frequency plane, whereas the right panel shows the selected frequencies at one specific time. In this case, with only one wave packet in the simulation, the algorithm obviously succeeds in identifying the wave envelope. Some arguably false detections at periods much longer than the wave central period are nevertheless observed. They are, however, of little significance for the GW retrievals since the momentum fluxes associated with these wavelet coefficients are very small. 6. The contribution of the absolute GW momentum flux at time t i to the flight-mean absolute momentum flux is computed by summing over the selected frequencies; that is, j R ũ w * t i, ˆ gw j t i. 33 The phase speeds, on the other hand, are estimated for each of the wave packets present at time t i. Equation (27) is used at the central frequency ˆ c k(t i )to compute the phase speed of each wave packet. This phase speed is then assigned to the frequencies representative of the wave packet envelope. 4. Results Monte Carlo simulations were performed to assess statistically the accuracy of the algorithm used to retrieve GW characteristics. We first present the results obtained with a single gravity wave in the simulated time series and then consider the more realistic situation in which several wave packets are present and may overlap in time frequency space. Unless otherwise

46 OCTOBER 2008 B O C C A R A E T A L FIG. 4. (left) Momentum-flux distribution in time/intrinsic-period space for the time series shown in Fig. 2. The area enclosed by the solid line corresponds to the detected envelope of the wave packet (see text). (right) Cross section of momentum flux vs intrinsic frequency at the time indicated by the solid line in the left panel. The diamond shows the detected central frequency of the wave packet. The frequencies associated with the wave packet are indicated by star symbols. stated, the results presented below refer to simulations that include measurement uncertainties. a. Simulations with one gravity wave packet One thousand time series simulating balloon flights disturbed by one GW packet were numerically generated and analyzed with the algorithms described in the previous section. For each simulation the flight-mean GW momentum flux was retrieved and directly compared to the flight-mean true momentum flux computed from the input wave packet parameters. To estimate the accuracy with which the phase speeds and directions of propagation are retrieved, a flight-mean intrinsic phase speed and direction of propagation were also computed through a momentum-flux weighted average over the selected wavelet coefficients. For instance, the retrieved flight-mean intrinsic phase speed is obtained as do not exhibit any significant bias. On the basis of these Monte Carlo simulations, the standard deviation of the retrievals is 2. The wave propagation directions are well estimated as they rely only on the velocity observations, which have small uncertainties relative to the amplitude of the wave-induced velocity disturbances, whatever the intrinsic frequencies of the wave packets. Figure 6 displays the performance of the analysis in retrieving the flight-mean absolute momentum fluxes. In general, the algorithm succeeds in estimating the momentum fluxes, although a slight systematic underestimation is observed. This underestimation results from the way in which the algorithm selects the wavelet coefficients. Overall, in this case with one gravity wave ĉ i ĉ t i, ˆ gw j t i R ũ w * t i, ˆ gw j t i j i R ũ * t i, ˆ gw j t i j, 34 where the inner sums extend over the frequencies associated with a wave packet at time t i. Figure 5 shows the retrieved propagation directions with respect to the input values. Clearly, the retrievals FIG. 5. Retrieved vs input horizontal direction of propagation of wave packets for simulated flights with one gravity wave.

47 3050 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 65 FIG. 6. (left) As in Fig. 5 but for the flight-mean absolute momentum flux. (right) Ratio of retrieved to input flight-mean absolute momentum flux vs intrinsic period of the wave packets. The thick line indicates the mean ratio over period intervals of 1 h. packet in each simulation, the mean and standard deviation of the ratios between the retrieved momentum flux values and the input values are, respectively, 0.86 and 0.13; that is, the momentum fluxes are underestimated by 14% 13% (1 ). The right panel of Fig. 6 shows the ratio of the retrieved to the input momentum fluxes versus the intrinsic periods of the wave packets. It is noticeable that the momentum flux underestimation occurs mostly at intrinsic periods of a few hours, as well as at periods very close to the inertial frequency. For small periods, the discrepancy results mainly from the finite sampling rate of the balloon observations. As previously mentioned, the retrieval algorithm is based on the estimation of phase differences between time series, which incurs significant inaccuracy when the sampling rate is comparable to the wave period. At quasi-inertial periods, on the other hand, the underestimation results from the small vertical displacements for these wave packets. In this case, the pressureinduced perturbations (i.e., p g ) become comparable to the uncertainty in the pressure measurements, causing a deterioration in the momentum flux retrieval. Arguably, when analyzing real data this latter case is less prejudicial than the former situation as the Eliassen Palm flux is expected to vanish for quasi-inertial waves (Fritts et al. 2006). Importantly, since the wave directions of propagation and absolute momentum fluxes are both well retrieved, the zonal and meridional momentum fluxes, respectively u w u w cos and w u w sin, which are the quantities of interest in GW drag parameterizations, can be estimated from the balloon observations. Typically, the uncertainty in the estimation of the zonal and meridional momentum fluxes is similar to that of the absolute momentum fluxes ( 10%) as the wave directions of propagation are almost perfectly retrieved. The retrieval of the horizontal intrinsic phase speeds is displayed in Fig. 7 for simulations both with and without measurement noise. When the observations are assumed to be perfect, the uncertainty in the retrieved intrinsic phase speeds is relatively small, that is, 12 ms 1 for input phase speeds greater than 20 m s 1. However, the dispersion of the retrieval increases greatly at low intrinsic phase speeds, in which situation a wave is actually perceived as quasi-stationary by the balloon. Therefore, the balloon does not sample adequately the wave packet and the analysis fails. Wave packets with such low intrinsic phase speeds are expected to strongly interact with the mean flow at the level where they are observed and may therefore be of less importance for the forcing of the flow above the balloon float altitude. When realistic measurement uncertainties are included in the simulations, the retrieval of intrinsic phase speed is significantly degraded. The retrieved phase speeds are overestimated by 60% on average, or by 20% if only waves with ĉ 20 m s 1 are considered, and the overall 1 standard deviation of the retrieval is 35 m s 1. There are two main reasons to this deterioration. First, the phase speeds are obtained from the Eulerian component (p w ) of the wave-induced pressure disturbances, which is generally an order of magnitude smaller than its Lagrangian counterpart and thus typically comparable to the uncertainty in the pressure measurement. Second, the phase shift between the

48 OCTOBER 2008 B O C C A R A E T A L FIG. 7. (left) Ratio of retrieved to input horizontal intrinsic phase speed vs input intrinsic phase speeds obtained with the 1-GW simulations without measurement noise. (right) As in the left panel but for the simulations with measurement noise. The thick line indicates the mean ratio over phase speed intervals of 10 m s 1. Note that a logarithmic scale is used on the y axis. balloon vertical displacement and that of the isopycnic surface has to be known to compute the wave phase speed using (27). Now, this estimation relies on the density observations, for which the uncertainties are mostly due to the instrumental noise in the temperature measurement. This significantly impacts the accuracy to which, and consequently ĉ, can be obtained. b. Simulations with multiple gravity wave packets In reality, there can be more than one wave packet occurring at any given time. To study how this situation impacts retrievals, we generated two additional sets of 1000 time series with 2 and 10 wave packets in each simulation, respectively. Figure 8 illustrates the wavelet analysis for one simulation in each of the sets. In the two-gw case shown in that figure, both wave packets are still clearly separated by the analysis. When this happens, the retrievals with the two-wave set are very similar to those obtained with the simulations with one wave packet. It was found that they depart significantly only when the wave packets in the two-wave time series occur less than 12 h apart (not shown). In that case, the FIG. 8. Momentum flux distribution in time/intrinsic period space in the case of (left) 2 and (right) 10 GW packets in the simulated time series. Wavelet coefficients located inside the solid contour are identified as associated with a wave packet.

49 3052 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 65 FIG. 9. Ratio of retrieved to input absolute momentum flux vs ratio of retrieved to input horizontal kinetic energy in the simulated time series with 1 (squares), 2 (triangles), and 10 (diamonds) GW packets. From top to bottom, regression lines are shown for the case studies using 1, 2, and 10 wave packets. The retrieved values are computed from the wavelet analysis by summing over the selected wavelet coefficients (see text for further details). momentum-flux retrieval is slightly noisier and the retrieved momentum flux can, on some occasions, be overestimated. When 10 wave packets are present, some of the wave packets will always overlap in the time/frequency space, as illustrated in Fig. 8. It is consequently more difficult for the retrieval algorithm to detect the envelope corresponding to each of the various wave packets. This results in a further underestimation of the flight-mean momentum flux. Overall, the momentum-flux underestimation estimated from the simulations is thus 14%, 13%, and 23% in the respective cases with 1, 2, and 10 wave packets in the time series. On the other hand, the 1 uncertainty in the estimation of the momentum fluxes does not exhibit any significant dependence on the number of wave packets in the time series and varies between 11% and 13%. It is not possible to use the quoted underestimations to correct results obtained with the real balloon flights since we do not know a priori how many wave packets are present at any given moment in the atmosphere. Nevertheless, we show here that a proxy can be used to determine the amount by which momentum fluxes are underestimated. Namely, the true flight-average GW horizontal kinetic energy can be easily estimated in the balloon observations by applying a high-pass filter (with a cutoff frequency corresponding to the smallest inertial frequency during the flight) to the horizontalvelocity time series, so as to isolate the GW signal. On the other hand, a retrieved flight-average kinetic energy can be computed from the wavelet analysis as 1 2 ti j ũ 2 t i, ˆ j gw t i 2 t i, ˆ gw j t i, 35 where the inner sum extends once again over the wavelet coefficients selected as corresponding to GW packets found at the ith observation record. The proxy is then simply computed as the ratio of the retrieved kinetic energy [obtained from (35)] to the true kinetic energy (estimated with the filtered time series). Figure 9 displays the correlation between the momentum-flux underestimation and the kinetic-energy proxy. Whatever the number of wave packets in the simulated time series, the regression lines are very similar, indicating that this kinetic-energy proxy can be used to estimate by how much our algorithm underestimates GW momentum fluxes. c. Directions of propagation and phase speeds In contrast with the case with one wave packet in the simulated time series, (34) cannot be used to estimate either the retrieved phase speeds or the retrieved directions of propagation when several wave packets are present. Instead, Fig. 10 compares the input and retrieved distributions of the flight-mean density-

50 OCTOBER 2008 B O C C A R A E T A L FIG. 10. (left) Distribution of flight-mean density-weighted absolute momentum fluxes u w as a function of wave direction of propagation in the 1000 simulations with two wave packets: input distribution (gray) and retrieved distribution (black). (right) As in the left panel but for simulations with 10 wave packets. Note that the vertical scale differs between the two graphs. weighted absolute momentum fluxes u w as a function of the directions of propagation. The result is the average over all simulations of the u w ( ) distributions. In the simulations with two GW packets (Fig. 10, left panel), the input absolute momentum fluxes are independent of the wave directions of propagation, as highlighted by the input distribution. There is a clear correlation between the input and retrieved distributions, which indicates that the directions of propagation are still correctly estimated by the algorithm when only two wave packets are present. It is also noticeable that the retrieved momentum fluxes are slightly smaller than the input values. In the simulations with ten GW packets on the other hand, a distinct dependence of momentum flux on the direction of propagation was deliberately imposed (Fig. 10, right panel); namely, the momentum fluxes scale as sin 2 ( /2) (i.e., there are larger westward than eastward fluxes). This nonisotropic distribution allows us to test the reliability of the retrieval by comparing input and retrieved propagation directions. The good agreement observed in the right panel of Fig. 10 demonstrates that wave propagation directions are, indeed, reliably retrieved, even in the case of a large number of wave packets. The distributions of density-weighted zonal momentum fluxes u w as a function of the zonal phase speeds ĉ x are displayed in Fig. 11. As for the directions of propagation, this figure displays the average over all the simulations of the u w (ĉ x ) distributions. In our simulations, the momentum fluxes depend on the intrinsic phase speeds through a ˆ 1 scaling so that the input distributions have more momentum flux at low phase speeds. In the case of the two-wave packet simulations, the retrieved distribution is approximately the same as the input. However, the phase speed retrieval is less accurate at low phase speeds, in agreement with the results obtained with the single-wave simulations. A significant part of the momentum flux is also wrongly attributed to high phase speed waves so that the overall retrieved distribution is somewhat broader than the input distribution. These defects are amplified when 10 wave packets are present in the simulations. In that case, an even more significant amount of momentum flux is attributed to phase speeds larger than the largest phase speed used in the simulations. Nevertheless, the strong anisotropy of the input distribution is correctly reproduced by the retrieval algorithm. 5. Summary A methodology is presented to extract information on GW characteristics from the meteorological observations gathered during long-duration, superpressure balloon flights in the stratosphere. This methodology is based on wavelet analysis techniques that enables GW packets to be identified in the observational time series. When applied to real time series, the wavelet analysis is very useful for studying the geographical distribution of GW activity.

51 3054 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 65 FIG. 11. (left) Distribution of flight-mean density-weighted zonal momentum fluxes u w as a function of intrinsic zonal phase speeds ĉ x for the simulations with two wave packets: input distribution (gray) and retrieved distribution (black). (right) As in the left panel but for the simulations with 10 wave packets. Note that the vertical scale differs between the two plots. Correlations between the velocity and Lagrangian pressure disturbances are used to infer GW momentum fluxes and phase speeds. The method was applied to simulated balloon observations containing up to 10 distinct wave packets. The prescribed wave distributions are generally well retrieved from the simulated observations. Absolute momentum fluxes are well estimated, despite a slight low bias. The underestimation is particularly evident for the highest frequency waves that we can resolve (intrinsic periods of 1 2 h) and is due to the 15-min sampling used during the Vorcore campaign. A proxy aimed at quantifying the overall underestimation can, nevertheless, be easily computed from the balloon observations and can be used to correct the estimated momentum fluxes a posteriori. Since the wave propagation directions are almost perfectly retrieved by our method, the zonal and meridional momentum fluxes are typically estimated with the same accuracy as the absolute momentum fluxes. On the other hand, GW phase speeds are retrieved much less accurately than the momentum fluxes or directions of propagation. In particular, waves with low intrinsic phase speeds are inadequately sampled by the balloons, which induces a significant dispersion in the retrieval. In general, our method tends to overestimate the phase speeds. The methodology described in this article is applied in Hertzog et al. (2008) to the dataset gathered during the Stratéole/Vorcore campaign and enables us to study GW activity above Antarctica and in the Southern Hemisphere midlatitudes. Acknowledgments. AH, FV, and GB acknowledge support of long-duration balloon activities from CNES and CNRS/INSU. RAV acknowledges travel support from the Scientific Visits to Europe Scheme of the Australian Academy of Science and Department of Science and Environment, and the visiting program from École Polytechnique. The authors would also like to thank the two anonymous reviewers who contributed to significantly improve the manuscript. REFERENCES Alexander, M. J., and L. Pfister, 1995: Gravity wave momentum flux in the stratosphere over convection. Geophys. Res. Lett., 22, , and C. Barnet, 2007: Using satellite observations to constrain parameterizations of gravity wave effects for global models. J. Atmos. Sci., 64, , and Coauthors, 2008: Global estimates of gravity wave momentum flux from High Resolution Dynamics Limb Sounder observations. J. Geophys. Res., 113, D15S18, doi: / 2007JD Allen, S. J., and R. A. Vincent, 1995: Gravity wave activity in the lower atmosphere: Seasonal and latitudinal variations. J. Geophys. Res., 100, Andrews, D. G., J. R. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics. Academic Press, 490 pp. Baumgaertner, A. J. G., and A. J. McDonald, 2007: A gravity wave climatology for Antarctica compiled from Challenging Minisatellite Payload/Global Positioning System (CHAMP/ GPS) radio occultations. J. Geophys. Res., 112, D05103, doi: /2006jd Charron, M., E. Manzini, and C. D. Warner, 2002: Intercomparison of gravity wave parameterizations: Hines Doppler-spread

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53 3.3. ÉTUDE THÉORIQUE ET NUMÉRIQUE DES ONDES DE GRAVITÉ Précisions concernant la méthodologie Estimation de la fréquence intrinsèque ˆω Lors de la propagation d une onde de gravité, la surface isopycne sur laquelle se déplace le BPS se déforme et le BPS va osciller à la fréquence de l onde dans le référentiel lié au vent moyen. A partir des perturbations de vitesse et de pression enregistrées, la fréquence intrinsèque peut être estimée très précisément en effectuant la décomposition en ondelettes des perturbations. Seules les observations faites par des ballons isopycnes permettent une estimation directe de ˆω. D autres types d observations permettent de dériver ˆω sous certaines conditions (dans une bande de fréquence donnée) par exemple à l aide de radiosondages (Vincent and Alexander, 2000) et ou d occultations radio de signaux GPS (Gubenko et al., 2008). Dans le cas des radiosondages, l hodographe des perturbations de vitesses zonales et meridiennes est traçé pour dériver les caractéristiques des ondes de gravité. Mais cette méthode peut induire de larges incertitudes (Zhang et al., 2004). Différences avec la méthodologie développée dans Hertzog and Vial (2001b) La méthodologie développée dans Boccara et al. (2008b) vient compléter celle utilisée dans Hertzog and Vial (2001b) pour étudier les ondes de gravité équatoriales. Entre les 2 campagnes (1998 et 2005), la précision des instruments de mesure s est accrue. Par exemple, lors de la campagne équatoriale, l écart type de la mesure de pression était de 10 Pa. Pour la campagne Vorcore, cet écart type est réduit à 1 Pa. Grâce à ces mesures de pression plus précises, la pression a pu être utilisée comme coordonnée verticale. De même, la précision du système de positionnement est passée de 100 m à 15 m. L amélioration de la précision des instruments a donc permis à nos calculs de covariances, et ainsi de ĉ h,ρu w etψd être plus exacts. Dans Hertzog and Vial (2001b), u w est estimé en dérivant w à partir des données de pression. Dans notre approche, les perturbations de pression p sont employées directement dans le calcul de covariances et u w est estimé en utilisant les relations de polarisations entre w et p. Enfin, leur méthode ignore le déphasage éventuel entre les surfaces isopycnes et les mouvements du BPS.

54 46 CHAPITRE 3. RÉPONSE DES BPS AUX ONDES DE GRAVITÉ Calcul de u w à partir des caractéristiques tirées au hasard Cette partie détaille le calcul de u w à partir de la fréquence intrinsèque et de la vitesse de phase horizontale intrinsèque, dans les simulations. La vitesse u s exprime sous la forme : ( ) (t u = u t0 ) 2 0 exp cos( ˆωt) (3.7) σ où u 0 1ˆω est l amplitude de l onde etσcorrespond à la largeur de la gaussienne, égale à la période. En utilisant la relation de polarisation entre u et w (voir l équation 2.23 dans le chapitre 2) et l équation de dispersion, la perturbation de la vitesse verticale peut s écrire : ( ) i ˆω w 2 = 2H m f 2 k h N 2 u (3.8) Dans le terme ( i 2H m), la partie complexe peut être négligée parce qu elle est en quadrature avec u et elle s annule donc lorsqu on effectue la moyenne. La covoariance u w s écrit donc : u w = ˆω 2 f 2 2NT Z + [ ( ) ] t 2 u 2 0 cos 2 t0 ( ˆωt)exp 2 dt (3.9) σ où T correspond au temps de vol, 10 jours. En toute rigueur, l intégrale devrait être faite entre 0 et T. En faisant l hypothèse que l intégrale est nulle en dehors de cet intervalle, on peut l étendre à l infini. Dans le terme u w, l opérateur correspond à une moyenne qui peut être évaluée sur toute la durée du vol (ce qui correspond à notre cas), mais également sur une période ou sur le paquet d onde. En utilisant des intégrales standard, l équation 3.9 devient : u w = ˆω 2 f 2 u 2 π NT ˆω (3.10) Dans les simulations, l équation 3.10 est utilisée pour calculer le flux de quantité de mouvement transporté par un paquet d onde. Dans le cas où plusieurs paquets d onde sont présents, nous avons fait la somme des contributions de chaque paquet d onde.

55 3.4. ÉTUDES COMPLÉMENTAIRES Études complémentaires Par la suite, les limites de nos simulations d ondes de gravité et celles de l analyse appliquée pour en retrouver les caractéristiques ont été étudiées Simulations Nombre d oscillations par paquet d onde Les paquets d onde ont une enveloppe gaussienne dont la largeur à mi-hauteur est égale à la période de l onde. Cela équivaut à trois périodes par paquet d onde environ. Nous allons chercher à déterminer l influence du nombre d oscillations par paquet d onde sur la restitution du flux de quantité de mouvement. Pour cela, des simulations ont été réalisées où, à période fixe (2h, 4h, 6h, 8h, 10h et 12h), l écart type est compris entre 0.3 et 3 fois la période, en augmentant de manière incrémentale. Dans la figure 3.3, le rapport entre le paramètre retrouvé par l analyse et le paramètre s imulé est représenté pour la direction de propagation, la vitesse de phase intrinsèque et le flux de quantité de mouvement. Aucune influence de l écart type sur la restitution n est observée, pour toutes les périodes considérées. Ainsi, les résultats de Boccara et al. (2008b) ne dépendent pas du choix fait d avoir trois oscillations par paquet d onde. Déphasage La partie a décrit le déphasage qui existe entre la trajectoire d un ballon isopycne et une surface isentrope. Dans nos simulations, le déphasage a été tiré au hasard dans l intervalle 0 0,5 rad, d après les résultats de la figure 3.1. Or, le termeεpeut être calculé en fonction de la période (voir la partie 3.1.2) : ε =ω 2 ζ Z a /ω 2 n

56 48 CHAPITRE 3. RÉPONSE DES BPS AUX ONDES DE GRAVITÉ FIG. 3.3 De gauche à droite, la restitution de la direction de propagation, de la vitesse de phase intrinsèque et du flux de quantité de mouvement en fonction de la largeur de la gaussienne pour différentes périodes. oùω n = 1/200 s 1, Z a est de l ordre du mètre, etζ 0.01 m 1. La figure 3.4 montre queεest toujours proche de 0 pour les périodes considérées. Il est donc possible que l intervalle choisi pour le déphasage dans nos simulations excède les bornes du vrai déphasage. Dès lors, la dépendance entre la période et le déphasage aurait pu être incorporée directement dans nos simulations. FIG. 3.4 Variation deεen fonction de la période pour de 2 valeurs de Z a : 1 m et 2 m.

57 3.4. ÉTUDES COMPLÉMENTAIRES Limites de l analyse Repliement de spectre ou "aliasing" L analyse est appliquée à des ondes de gravité simulées dont la période est comprise entre 1h et la période inertielle ( 14 h). Le but de cette partie est d étudier comment sera détectée une onde de gravité dont la période est inférieure à 1h. En particulier, dans le cas d un repliement de spectre, l analyse détectera-t-elle une onde de période plus longue? Mille simulations ont été construites avec une onde de gravité dont la période était comprise entre la fréquence de Brünt Väisälä ( 5 minutes) et 1h. Les ondelettes utilisées dans l analyse avaient des périodes comprises entre 1 heure et 24 heures, comme dans la partie 3.3. La figure 3.5 montre les resultats pour la restitution de la direction de propagation, de la vitesse de phase intrinsèque et du flux de quantité de mouvement. On peut distinguer deux cas : 1. Période inférieure à 40 minutes. Dans ce cas, l algorithme ne détecte pas l onde de gravité dans la mesure où aucun flux de quantité de mouvement n est retrouvé par l analyse. Cependant, pour des périodes proches de 20 minutes, on observe une détection pour la direction de propagation et la vitesse de phase intrinsèque. Mais ces caractéristiques ne correspondent à aucun flux de quantité de mouvement, donc cette "pseudo" détection peut être négligée. FIG. 3.5 De gauche à droite, la restitution de la direction de propagation, de la vitesse de phase intrinsèque et du flux de quantité de mouvement en fonction de la période en minutes.

58 50 CHAPITRE 3. RÉPONSE DES BPS AUX ONDES DE GRAVITÉ 2. Période comprise entre 40 minutes et 1 heure. La direction de propagation est bien retrouvée, la distribution de la vitesse de phase intrinsèque est très dispersée (sous-estimation ET surestimation) et le flux de quantité de mouvement est très sous-estimé (moins de la moitié du flux de quantité de mouvement simulé dans le meilleur des cas). Cette étude permet de conclure que la présence d ondes inférieures à 1h dans les vols de la campagne Vorcore n induira pas de fausse détection par l analyse, car ces ondes sont filtrées par l analyse. Longueur d onde La longueur d onde verticale ou horizontale est un paramètre auquel plusieurs types d observations donnent accès (radiosondages, instruments transportés par satellites, lidar, radar). Ce paramètre a beaucoup été étudié et estimé, par exemple Pfenninger et al. (1999); Steiner and Kirchengast (2000); Wang et al. (2005), et il est donc pertinent de savoir si notre analyse peut l estimer correctement. Dans notre modèle, la longueur d onde horizontale k h peut être théoriquement retrouvée à partir de l équation 2.26, c est-à-dire à partir de la vitesse de phase intrinsèque : k h = ˆω/ĉ h La longueur d onde verticale peut être déduite à partir de k h et de la relation de dispersion : m 2 = (N2 ˆω 2 )k 2 h ( ˆω 2 f 2 ) 1 4H 2 Or, la vitesse de phase intrinsèque est globalement surestimée par l analyse et la distribution de la vitesse de phase retrouvée est très dispersée, avec des surestimations atteignant 100 fois la valeur initiale. Comme la longueur d onde horizontale est directement proportionnelle à la vitesse de phase intrinsèque, elle n est restituée correctement que lorsque ĉ h l est également. Il en va de même pour la longueur d onde verticale qui est aussi proportionnelle à ĉ h. Notre analyse ne permet donc pas pour l instant d estimer les longueurs d onde horizontales et verticales avec une précision suffisante pour apporter des informations pertinentes.

59 3.4. ÉTUDES COMPLÉMENTAIRES 51 Ondes de gravité pour lesquelles 2π 1h < ˆω < N Notre méthodologie permet de résoudre des ondes de gravité dont les périodes sont comprises entre 1 h et 2π/ f 14 h. Comme l échantillonnage des simulations et celui des vols analysés est égal à 15 minutes, la plus courte période théoriquement résolue par l analyse en ondelettes est égale à 30 minutes. Pour rendre la technique plus fiable, la période minimum est fixée à 1 h. La technique ne détecte donc pas les ondes dont la période est comprise entre 2π/N 5 minutes et 1 h. La figure 3.6 montre la densité spectrale du flux de quantité de mouvement dans nos simulations FIG. 3.6 Densité spectrale du flux de quantité de mouvement moyennée sur 10 jours (à gauche) et sur le paquet d onde (à droite). La droite pointillée (à gauche) représente une loi en ˆω 2, et la droite avec tirets (à droite) représente une loi en ˆω 1. en fonction de la fréquence intrinsèque dans 2 cas. La figure de gauche montre le flux de quantité de mouvement moyenné sur la durée du vol simulé (dix jours), alors que la figure de droite montre le flux moyenné sur la durée du paquet d onde. Dans le premier cas, la densité spectrale suit une dépendance en ˆω 2 alors que dans le second cas, elle suit une dépendance en ˆω 1. Selon l article Boccara et al. (2008b), le spectre spécifié suit une dépendance en ˆω 1. Or, le flux de quantité de mouvement estimé par l analyse est moyenné sur le vol, ce qui correspond à la figure 3.6 gauche. Lorsque la moyenne est effectuée sur le vol, la durée temporelle variable des paquets d onde n est pas prise en compte. En revanche, lorsque la moyenne est effectuée sur la durée du paquet d onde, cette caractéristique est prise en compte. Les observations actuelles d ondes de gravité ne permettent

60 52 CHAPITRE 3. RÉPONSE DES BPS AUX ONDES DE GRAVITÉ pas de déterminer si les paquets d onde ont des durées temporelles fixes ou variables. Notre analyse suppose que les paquets d onde ont des durées temporelles fixes, alors que avons imposé des paquets d onde de durées variables. Nous nous sommes donc placés dans une configuration défavorable en terme de rapport signal sur bruit. En effet, nous avons vu que l analyse spécifie un seuil minimum pour ne pas confondre les perturbations dues aux ondes de gravité et celles dues au bruit. Or les ondes de hautes fréquences ont des amplitudes plus faibles (u 0 1ˆω ), et s étendent sur des durées plus courtes que les ondes de basses fréquences. Boccara et al. (2008b) montrent effectivement une moins bonne restitution du flux de quantité de mouvement pour les ondes de hautes fréquences et l échantillonnage a été évoqué pour expliquer cette déterioration. En résumé, la dépendance en ˆω 2 de la densité spectrale du flux de quantité de mouvement, telle qu elle est estimée par l analyse, est en partie liée à la largeur temporelle variable imposée dans nos simulations. En prenant en compte le fait que les paquets d onde ont une durée variable, nous retrouvons bien la dépendance spécifiée en ˆω 1 (figure 3.6 droite). Si l on considére que la dépendance en ˆω 1 est également valable pour des plus hautes fréquences intrinsèques, on peut en déduire le flux de quantité de mouvement transporté par les fréquences non résolues par l analyse : Z 2π 1h f Z N ˆω 1 d ˆω ˆω 1 d ˆω (3.11) 2π 1h Ces deux contributions sont à peu près égales, et l on peut donc déduire que si l on retrouve un certain flux de quantité de mouvement, le flux total sur tout le spectre fréquentiel correspond au double du flux estimé. Résumé Dans ce chapitre, nous avons développé une méthodologie qui permet d estimer le flux de quantité de mouvement, la vitesse de phase intrinsèque et la direction de propagation des ondes de gravité. Elle repose sur les perturbations des champs de vitesse, densité et pression induites par les ondes de gravité et sur les différentes relations qui lient ces dernières. La méthodologie a été testée et validée à l aide de simulations reproduisant les perturbations induites par les ondes de gravité. Notre méthode permet d identifier précisement la direction de propagation d une onde, quelque soit

61 3.4. ÉTUDES COMPLÉMENTAIRES 53 le nombre de paquets d onde présents. Elle sous-estime de 14% le flux de quantité de mouvement dans le cas d un paquet d onde par simulation, et de 23% dans le cas de dix paquets d onde. Cette dégradation de la restitution est liée au fait que les paquets d onde se superposent dans l espace temps-fréquence intrinsèque. La vitesse de phase intrinsèque restituée est en général sur-estimée, et la distribution retrouvée est très dispersée, avec certaines valeurs atteignant cent fois la valeur initiale. Néanmoins, notre approche possède des limites liées principalement à l échantillonnage des observations et à leur précision. Elles ne permettent donc pas d estimer les longueurs d ondes verticales et horizontales qui sont des quantités importantes pour décrire les ondes de gravité.

62 54 CHAPITRE 3. RÉPONSE DES BPS AUX ONDES DE GRAVITÉ

63 55 Chapitre 4 La campagne de ballons pressurisés Vorcore Dans ce chapitre, nous présentons la campagne Vorcore pendant laquelle vingt-sept BPS ont volé dans la basse stratosphère antarctique. Ces données seront ensuite exploitées dans le chapitre 5 en appliquant la méthodologie développée dans le chapitre 3 pour étudier la distribution de flux de quantité de mouvement transportés par les ondes de gravité dans la basse stratosphère. Ces observations sont particulièrement adaptées pour étudier les ondes de gravité car les vols de longue durée associent un échantillonnage fin (15 minutes) et une bonne répartition spatiale et permettent de déduire directement la fréquence intrinsèque. 4.1 Historique de l observation par ballons Jusqu aux années 1970, l observation de l atmosphère s est faite essentiellement grâce aux radiosondages opérationnels, et aux campagnes de ballons de grande échelle. L avènement des satellites a permis une observation plus complète et plus homogène de toute l épaisseur de la couche atmosphérique et a conduit à un abandon relatif des ballons longue durée comme technique d observation. Depuis les années 1960, Le CNES a développé des programmes spécifiques de ballons

64 56 CHAPITRE 4. LA CAMPAGNE DE BALLONS PRESSURISÉS VORCORE dédiés à l observation de l atmosphère et de l espace en mettant à profit les avancées technologiques en termes de télécommunications, de stockage de données, et de positionnement spatial. Aujourd hui, plusieurs types de ballons sont utilisés pour faire des observations dans la troposphère ou la stratosphère. En général, ils sont gonflés à l hélium pour assurer l envol du ballon : les ballons stratosphériques ouverts (BSO) sont destinés à faire des observations atmosphériques ou astronomiques et peuvent embarquer des charges allant jusqu à 3 tonnes. Leur durée de vol n excède pas une journée (sauf dans les hautes latitudes en été où une «journée» peut durer plusieurs jours), car pendant la nuit, la chute de la température entraîne une contraction du gaz et la chute du ballon. Le matériel scientifique est ensuite récupéré et peut être utilisé pour d autres vols. les montgolfières infrarouges. La portance de ces ballons ouverts est assurée par l air chauffé : par le rayonnement solaire pendant la journée, et par le rayonnement infrarouge de la Terre pendant la nuit. Comme ces rayonnements ne sont pas équivalents, la montgolfière vole autour de 25 km la journée et autour de 20 km la nuit et permet d obtenir des profils verticaux de température et d espèces chimiques pendant les transitions jour-nuit. les radiosondages. Ces ballons fermés, lâchés à partir des stations météorologiques, permettent d acquérir des profils verticaux de température, de pression, d humidité et parfois d ozone jusqu à 30 km. Les lâchers de radiosondages ont lieu dans toutes les stations météorologiques, de manière régulière (au moins une fois par jour). De plus, beaucoup de ces stations appartiennent à un réseau mondial opérationnel qui dépend de l OMM. les ballons pressurisés couche limite (BCPL) sont des petits ballons (2 m de diamètre) utilisés pour observer la couche limite troposphérique. enfin les BPS ont la particularité de se déplacer le long de surfaces de densité constante. La pression interne au ballon est toujours supérieure à la pression de l air ambiant et le volume du ballon ne varie que très peu : l enveloppe doit donc être solide et résistante. Historiquement, les ballons de longue durée non guidés ont d abord été utilisés à des fins militaires. Entre novembre 1944 et avril 1945, plus de 9000 ballons-incendies ont été lancés par l armée japonaise sur l océan Pacifique dans l espoir que les vents les amèneraient au dessus des États-Unis où ils causeraient des dommages matériels et des pertes humaines (Arakawa, 1956). En réalité, seuls

65 4.1. HISTORIQUE DE L OBSERVATION PAR BALLONS ballons atteignirent les États-Unis et causèrent la mort de cinq personnes et des dégats matériels mineurs. Dans les années qui suivirent la seconde guerre mondiale, des équipes scientifiques américaines développèrent différents types de ballons pour observer l atmosphère (Lally, 1959). Les ballons pressurisés volaient dans la troposphère autour de 200 hpa, et étaient suivis par des radars pendant quelques heures (Mastenbrook, 1962). Le but premier de ces observations était de renseigner sur la circulation à l échelle globale et synoptique. Au début des années 1960, les ballons pressurisés prenaient la forme de tétrahèdres ("tetroons"), ou de coussins (Booker and Cooper, 1964), pour minimiser le nombre de coutures et limiter le risque de rupture de l enveloppe. Par la suite, les ballons pressurisés développés ont eu une enveloppe sphérique. Des campagnes de ballons pressurisés à grande échelle ont eu lieu dans les années 1970 (Angell, 1972; Morel and Bandeen, 1973; Jullian et al., 1977). Ces campagnes incluaient un grand nombre de BPS permettant l exploration de régions de la stratosphère et de la troposphère qui étaient jusque là mal connues : la bande équatoriale pour la campagne de type Global HOrizontal Sounding Technique (GHOST) en 1970, et l hémisphère sud pour les campagnes Éole en , Tropical Wind, Energy conversion, and Reference Level Experiment (TWERLE) en 1975 et de type GHOST en Ces observations ont permis d obtenir une meilleure connaissance de la circulation en altitude à l échelle globale et synoptique. Les ballons pressurisés transmettaient leur position et leur température (pour les campagnes Éole et TWERLE) par l intermédiaire d un satellite qui les interrogeait quand il les survolait. Ce mode de communication ne permettait pas un échantillonnage régulier, et les données récoltées n étaient pas continues. Durant la campagne TWERLE, certains des ballons avaient été équipés d un système de stockage pour enregistrer des données avec un échantillonnage de 9 minutes. A partir de ces observations, des études sur les ondes de gravité ont pu être conduites (Massman, 1978).

66 58 CHAPITRE 4. LA CAMPAGNE DE BALLONS PRESSURISÉS VORCORE 4.2 Observation d ondes de gravité par des ballons pressurisés Les premières observations d ondes par des ballons isopycnes datent de 1960, durant une campagne de "tetroons" effectuée à partir des Iles Wallops (Angell and Pack, 1962). Les "tetroons" étaient repérés par un radar permettant un échantillonnage de 10 secondes ou 30 secondes. Grâce à cet échantillonnage fin, des oscillations dont les périodes étaient proches de 10 minutes, ont été mises en évidence. Cependant, les vols étaient trop courts (moins de 2 h) pour dériver des résultats quantitatifs. Quelques années plus tard, des ballons isopcynes ont été utilisés pour observer des ondes de montagne (Vergeiner and Lilly, 1970). La première tentative d estimation des caractéristiques des ondes de gravité à partir d observations de ballons isopycnes a été mise en oeuvre par Massman avec les données de la campagne TWERLE (Massman, 1981). Les séries temporelles enregistrées de pression, température et vitesse verticale ont d abord été filtrées pour éliminer les hautes fréquences. Ensuite, les données filtrées ont été traitées individuellement pour identifier des oscillations causées par des ondes de gravité. Ainsi, la période intrinsèque, l énergie et le flux de quantité de mouvement ont pu être estimés. Cependant, cette analyse reste sommaire car elle ne permet pas une détection systématique des ondes et ne prend pas en compte le cas où plusieurs ondes perturbent la trajectoire des ballons au même instant. De plus, les séries temporelles analysées étaient relativement courtes car la mémoire interne des ballons ne pouvait pas enregistrer plus de 8 heures de données, ce qui a limité l étude à des ondes dont les périodes étaient comprises entre 3 et 8 heures. 4.3 Récapitulatif de la campagne Vorcore L article qui suit détaille de manière exhaustive les caractéristiques de la campagne Vorcore. Nous reprenons ici les éléments les plus pertinents de cette campagne pour notre étude. Avant la campagne Vorcore, des campagnes préliminaires ont permis de tester les ballons développés par la division ballon du CNES : depuis Latacunga en Équateur, en 1998 (Vial et al., 2001; Hertzog and Vial, 2001a), et depuis Kiruna en Suède en 2001 et 2002 (Hertzog et al., 2002). Lors de la campagne Vorcore, vingt sept BPS ont été lâchés dans le vortex stratosphérique polaire

67 4.3. RÉCAPITULATIF DE LA CAMPAGNE VORCORE 59 FIG. 4.1 Densité mesurée par le BPS 10. entre septembre et octobre 2005 à partir de la station McMurdo (77.85 o S, o E), en Antarctique. Les nacelles employées lors de cette campagne, utilisent le système de positionnement GPS et réalisent des observations toutes les 15 minutes des variables atmosphériques telles que la pression, la température et la position (longitude, latitude, et altitude). Les données ont été rapatriées par l intermédiaire d une balise Argos. Tous les lâchers ont eu lieu lorsque le vortex était au dessus de la station. Comme l air à l intérieur du vortex est isolé des moyennes latitudes par une barrière de transport, les ballons ont presque tous volé à l intérieur du vortex pendant toute leur durée de vol. De plus, les BPS ont échantillonné de manière tr0ès complète les latitudes au sud de 55 o S, les observations couvrent donc tout le continent Antarctique ainsi qu une partie de l océan Austral. Enfin, les BPS ont échantillonné la stratosphère pendant deux mois en moyenne, certains vols atteignant trois mois de vol. L hypothèse principale de notre approche suppose que les ballons volent sur des surfaces de densité constante. La figure 4.1 montre la densité du BPS 10, qui a volé du 22 septembre au 17 décembre La densité reste bien constante pendant le vol, et les perturbations observées sont inférieures à 2% en terme d amplitude. Dans le panneau agrandi, nous pouvons distinguer des oscillations diurnes qui sont liées à la différence, entre le jour et la nuit, de la température du gaz à l intérieur de l enveloppe, et à l effet de cette différence sur la pression et la densité (voir le chapitre 3). Nous pouvons également discerner des oscillations de plus courtes périodes qui peuvent être associées au bruit de la mesure de température ou aux ondes de gravité. Ainsi, en première approximation, la densité du ballon sur le vol peut être considérée constante, et les perturbations observées vont pouvoir servir à déduire les caractéristiques des ondes de gravité selon la méthode présentée dans

68 60 CHAPITRE 4. LA CAMPAGNE DE BALLONS PRESSURISÉS VORCORE FIG. 4.2 Température potentielle mesurée par le BPS 10. le chapitre précédent. Dans le chapitre 3, l accent a été mis sur le fait que les ballons se déplacent sur des surfaces isopycnes et non isentropes à la différence des particules d air. Or, le vol 27, qui s est déplacé dans le bord du vortex, a été piégé dans un filament de vorticité potentielle qui a été éjecté du vortex à la fin du mois de novembre. Dans ce cas, nous voyons que, sur des échelles de temps de quelques jours, le ballon reproduit bien le déplacement horizontal des particules d air (isentropes). La figure 4.2 montre l évolution de la température potentielle pour le BPS 10. Les fortes oscillations, de l ordre de 20 K, sont causées par la propagation d ondes planétaires. Néanmoins, sur des durées de l ordre de quelques jours, la température potentielle est constante et les surfaces isentropes sont parallèles aux surfaces isopycnes, sur des échelles spatiales supérieures aux ondes de gravité. 4.4 Article : Stratéole/Vorcore - Long duration, superpressure balloons to study the Antarctic lower stratosphere during the 2005 winter Cet article a été publié dans Journal of Atmospheric and Oceanic Technology en Dans la suite de la thèse, il est désigné sous la forme Hertzog et al. (2007).

69 2048 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24 Stratéole/Vorcore Long-duration, Superpressure Balloons to Study the Antarctic Lower Stratosphere during the 2005 Winter ALBERT HERTZOG,* PHILIPPE COCQUEREZ, CLAUDE BASDEVANT, # GILLIAN BOCCARA, # JÉRÔME BORDEREAU, # BERNARD BRIOIT, # ALAIN RENÉ GUILBON, ALAIN ÉRIC JEAN-NOËL VALDIVIA, STÉPHANIE VENEL, AND FRANÇOIS VIAL # * Laboratoire de Météorologie Dynamique, Université Pierre et Marie Curie, IPSL, CNRS, Palaiseau, France Centre National d Études Spatiales, Toulouse, France # Laboratoire de Météorologie Dynamique, École Polytechnique, IPSL, CNRS, Palaiseau, Centre National d Études Spatiales, Aire-sur-l Adour, France (Manuscript received 5 December 2006, in final form 4 April 2007) ABSTRACT In September and October 2005, the Stratéole/Vorcore campaign flew 27 superpressure balloons from McMurdo, Antarctica, into the stratospheric polar vortex. Long-duration flights were successfully achieved, 16 of those flights lasting for more than 2 months. Most flights were terminated because they flew out of the authorized flight domain or because of energy shortage in the gondola. The atmospheric pressure (1-Pa precision) was measured every minute during the flights, whereas air temperature observations (0.25-K accuracy) and balloon positions (absolute GPS observations, 10-m accuracy) were obtained every 15 min. Fifteen-minute-averaged horizontal velocities of the wind were deduced from the successive balloon positions with a corresponding accuracy 0.1 m s 1. The collected dataset (more than independent observations) provides a thorough high-resolution sampling of the polar lower stratosphere in the Southern Hemisphere from its wintertime state up to the establishment of the summer circulation in December January. Most of the balloons stayed inside the vortex until its final breakdown, although a few were ejected toward the midlatitudes in November during filamention events associated with an increase in planetary wave activity. The balloons behaved as quasi-lagrangian tracers during the first part of the campaign (quiescent vortex) and after the vortex breakdown in early December. Large-amplitude mountain gravity waves were detected over the Antarctic Peninsula and caused one flight termination associated with the sudden burst in the balloon superpressure. 1. Introduction Shortly after the discovery of the Antarctic ozone hole by Farman et al. (1985), the dynamical isolation of air parcels located well inside the stratospheric polarnight vortex was identified as a key factor in the processes that led to ozone depletion (McIntyre 1989). Since then, it has been acknowledged that besides chemistry, dynamics play a major role in determining the geographical structure, intensity, and variability of the ozone hole (e.g., WMO 2003, and references therein). In the late 1980s and beginning of the 1990s, however, the degree of isolation of air parcels located in Corresponding author address: A. Hertzog, Laboratoire de Météorologie Dynamique, École Polytechnique, F Palaiseau CEDEX, France. hertzog@lmd.polytechnique.fr the inner vortex, as well as how they could eventually be transported to the midlatitude stratosphere and be irreversibly mixed there, was not fully understood. In this context, Vial et al. (1995) suggested that a set of quasi-lagrangian, balloonborne observations could be very useful to document the dynamics and chemistry in the otherwise poorly observed Southern Hemisphere (SH) polar stratosphere in winter. This project, named Stratéole, consisted in launching 200 superpressure balloons (SPBs) able to fly for a few months at about 50 and 70 hpa in and around the polar vortex. Those balloons actually have the property to stay on constant-density (isopycnic) surfaces (e.g., Levanon et al. 1974), and thus to provide a good estimate of the motions of stratospheric air parcels that are isentropic to first order. In the 1960s 70s, a number of superpressure balloon flights already demonstrated the potential interest of those devices for scientific pur- DOI: /2007JTECHA American Meteorological Society

70 DECEMBER 2007 H E R T Z O G E T A L poses. For instance, the Global Horizontal Sounding Technique (GHOST; ), Éole ( ), and Global Atmospheric Research Programme (GARP)- related Tropical Wind, Energy Conversion, and Reference Level Experiment (TWERLE; 1975) campaigns together flew hundreds of superpressure balloons in the SH upper troposphere (Lally et al. 1966; Morel and Bandeen 1973; TWERLE Team 1977). Flight durations longer than 3 months were frequently achieved. At the same time, about 50 stratospheric flights of superpressure balloons (float level between 50 and 18 hpa) were also performed (Angell 1972; Schumann 1980; Olivero et al. 1984). Though the dataset gathered during those early flights allowed the documenting of characteristics of the atmospheric dynamics that were unaccessible to the contemporary techniques, the lack of global communication and positioning systems significantly limited the observation frequency and accuracy. The situation changed in the 1980s, and Stratéole proposed to benefit from the assets of global-scale superpressure balloon flights and from modern, satelliteborne communication and positioning systems to provide an unprecedented in situ sampling of the polar stratosphere. However, the project had to cope with a number of logistic and technological difficulties, and in the late 1990s it was decided to split Stratéole into two separate phases: the first one, called Vorcore, was devoted to the study of the vortex core and needed a few tens of balloons only. After several years of development and test campaigns, the Vorcore campaign finally took place in McMurdo, Antarctica, in August October The original scientific objectives were refined in light of our current knowledge of the ozone hole, but the technological preparatory campaigns confirmed that the originality of the Vorcore observing system could provide new insights into stratospheric dynamics (Vial et al. 2001; Hertzog and Vial 2001; Hertzog et al. 2002b). More specifically, the Vorcore goals now include the study of gravity wave activity in the SH high latitudes, the characterization of the dispersion regime inside the vortex core, the quantification of ozone depletion rates in spring, and the assessment of the operational analysis accuracy. This paper is aimed at presenting the observing system used during Vorcore, as well as the main features of the observation set that has been collected during the campaign. It is organized as follows. Section 2 describes the Vorcore balloons and briefly reviews their physics. The scientific and technological observations performed by the payload are also presented in this section. Section 3 is devoted to the campaign itself. It gives details on the flight configuration used during Vorcore, the set of flights performed during the campaign, and the various events that caused their terminations. Section 4 reviews more precisely the Vorcore dataset. In particular, the geographical distribution of the observations and the balloon behavior in the stratospheric flow are emphasized. The last section is devoted to the presentation of foreseen developments for long-duration superpressure balloon flights and to their possible implications for the study of the stratosphere. 2. Observation technique a. Superpressure balloons 1) BALLOON CHARACTERISTICS AND LAUNCHING TECHNIQUE The balloons used during Vorcore are helium filled and have a spherical-shaped, closed envelope. Although their design mainly relies on the main characteristics of the balloons used in the successful 1970s 80s experiments, a dedicated development program had nevertheless been necessary in order to extend the mission capability to winter polar flights and to improve the balloon reliability (Cocquerez et al. 2001). In particular, the envelopes were made of a trilaminate polyester/polyamide film especially designed for the experiment. This film provides high stiffness in flight conditions and is flexible enough at room temperature for manufacturing and packaging. The film stiffness was one of the key design requirements, since it ensures that the balloon volume will stay constant during the flight, even though the helium overpressure inside the balloon may vary (see, e.g., Fig. 1). The film also provides the needed levels of strength and gas tightness for achieving long-duration flights. To sample two density levels in the stratosphere (roughly corresponding to the 50- and 70-hPa pressure surfaces), two balloon sizes were developed: 10- and 8.5-m diameter. This solution was preferred to using only 10-m balloons with some ballast in order to fly at a lower level, since this would have induced more stringent requirements on the gas tightness of the envelopes. A new concept for suspending the payload to the envelope was developed. Whereas the Éole payloads were attached to the balloons with the help of a net, the major feature of this new system was to distribute the loads induced by the payload only at the bottom of the envelope. Finally, the development program also focused on redefining the classical techniques for launching superpressure balloons. This last point was needed to successfully perform launches in the severe polar surface conditions in winter and early spring. In particular, a special effort was devoted to avoiding the need for large and costly dedicated ground infrastructures.

71 2050 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24 envelope, and the environment. This is exemplified in Fig. 1, which shows the helium and air temperatures as well as the superpressure during a 10-day period of one of the Vorcore flights. While the air temperature stays almost constant during that period, the helium temperature (and superpressure) exhibits large daily fluctuations caused by the variations in solar radiation. Furthermore, local drops in superpressure and gas temperature (like, e.g., around days 266 and 270) are caused by variations in the upward infrared radiation due to the presence of high-altitude clouds or to very cold surfaces (i.e., the Antarctic Plateau). Therefore, before the campaign, a mission analysis based on climatological records of temperature, pressure, and radiative fluxes is performed so as to simulate the gas superpressure during the flights. The aim of this mission analysis is to determine the mass of helium that would statistically minimize the risk of balloon burst or depressurization. During Vorcore, this mass significantly varied from the early winter part of the flights to the end of the campaign in late spring, and a compromise between both flight conditions was adopted. FIG. 1. (top) Air (black) and helium (gray) temperatures, and (bottom) helium superpressure observed during a section of Vorcore flight 4. Namely, the balloons are now inflated while lying on an 18-m-long table that can easily be moved from the preparation building to the launchpad when the mean wind velocity is forecast to stay below 4 m s 1 for more than 30 min. The inflation operations are performed outside, which allows the use of a small-height building (see Fig. 5). An inflation bench, based on a sonic-nozzle flowmeter, was also specially designed to work at very low temperatures. 2) BALLOON PHYSICS One of the most critical parameters when flying superpressure balloons is to carefully determine the mass of lifting gas that fills the balloon. The gas amount actually controls the superpressure in the balloon, and one has to avoid both an excess of superpressure that would cause the balloon to burst and a vanishing superpressure that may destabilize the balloon. The maximum superpressure that the balloon can bear is theoretically computed from the mechanical properties of the envelope film and from a stress analysis. But the actual gas pressure during the flight (or, equivalently, the gas temperature once the balloon volume and gas amount are known) results from a complex radiative convective equilibrium between the gas, the balloon 3) BALLOON BEHAVIOR IN THE ATMOSPHERE The goal of the following paragraphs is not to give a complete review of the response of superpressure balloons to atmospheric motions, which has already been done theoretically and numerically elsewhere (e.g., Reynolds 1973; Massman 1978; Nastrom 1980; Hammam 1991). It is rather to recall a few characteristics of those balloon flights that may help to follow the discussions in the next sections. The behavior of superpressure balloons in the atmosphere can safely be decoupled into horizontal and vertical motions. On the horizontal, the most significant force is the aerodynamic drag that prevents the balloon from having a velocity much different than that of the wind. At first order, the equation of horizontal motions actually reads (Vial et al. 2001) d u L 1 dt c u u, where u is the difference between the wind velocity and the balloon velocity, and L c is a characteristic length that scales as the balloon radius and equals 40 m for a 10-m-diameter balloon. Integrating Eq. (1) and averaging over a time period T shows that the averaged-velocity difference cannot exceed L c /T. During Vorcore, the balloon horizontal velocities are averaged over 15 min, and the difference between the balloon and wind velocities over that time period is thus lower than 0.05 m s 1. Superpressure balloons can therefore 1

72 DECEMBER 2007 H E R T Z O G E T A L be considered very accurate tracers of horizontal motions. In contrast, superpressure balloons cannot follow the vertical motions of air parcels: while the balloons have a constant volume (and thus are constrained to stay on isopycnic surfaces), air parcels undergo adiabatic variations of their volume when moving upward or downward. The relative (vertical) displacement of isentropic and isopycnic surfaces therefore determines how Lagrangian superpressure balloons are. For instance, let us consider the response of both surfaces to a local increase in temperature T. The associated increase in potential temperature reads T T 2 and the corresponding vertical displacement of the isentrope is T T. d d dz dz Similarly, the vertical displacement of the isopycnic surface induced by this temperature increase reads T T. d dz Hence, the ratio of both displacements is obtained as r T d dz d dz T Typical values relevant for the Vorcore campaign (i.e., pressure: 60 hpa, temperature: 200 K, and Brunt Väisälä frequency: rad s 1 ) lead to r 4, and air parcels typically undergo vertical displacements 4 times as large as those of the balloons. Based on this simple calculus, Fig. 2 illustrates the motions of isentropic and isopycnic surfaces induced by a small-amplitude atmospheric wave. The disturbances in potential temperature observed by the balloons can be inferred from this figure: local coolings induce negative potential temperature disturbances in the balloon observations. The air parcels, on the other hand, evolve adiabatically and there are obviously no Lagrangian variations in potential temperature. The horizontal axis in Fig. 2 could also be the time in which case the figure FIG. 2. Sketch of the relative displacement of isentropic surfaces (dashed) and isopycnic surfaces (solid) induced by an atmospheric wave (or by the annual cycle of stratospheric temperatures). Three isentropic surfaces (with ) are displayed. Superpressure balloons drift on isopycnic surfaces and see higher (lower) potential temperatures where the local Eulerian temperature disturbance is positive (negative). A horizontal dotted line is shown for reference. grossly illustrates the annual cycle of stratospheric temperature at high latitudes. In winter, the temperatures are lower than the annual mean, and the transition from winter to summer is associated with an increase of potential temperatures in the balloon data. A more complete calculation would, of course, consider the response of isopycnic and isentropic surfaces to pressure disturbances as well. On the one hand, atmospheric waves induce relative pressure disturbances that are one order of magnitude smaller than relative temperature disturbances. On the other hand, applying the same argument as above to a localized pressure disturbance shows that in that case both surfaces undergo almost similar displacements. The previous calculation and Fig. 2 therefore retain the essence of balloon motions with respect to those of air parcels. b. Payload The gondola (named Rumba) used during Vorcore performs the scientific and housekeeping observations, and checks that the balloon flight is safe. The gondola was designed to work in the very cold conditions met during Vorcore (air temperature lower than 90 C), so a 10-cm-thick polystyrene coating isolates the electronics from the environment. Furthermore, the electronics

73 2052 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24 is heated during daytime through a resistor powered by solar generators. The electronics and sensors are powered by nonrechargeable batteries. The energy set was designed to allow 3-month flights, although the gondola consumption may slightly vary from one flight to the other. The gondola mass, including the coating, the batteries, the sensors devoted to atmospheric observations, as well as the straps for the mechanical connection with the flight train, is 10 kg. With the exception of atmospheric pressure, which is measured every minute, all the other observations are performed every 15 min. The data are stored for 24 h in the gondola and sent to the ground via the satelliteborne Argos communication system. The communication bandwidth provided by Argos is very small (typically 30 Kb day 1 ) and determines the sampling frequency. The various sensors used during Vorcore, as well as the processing performed to compensate for potential sensor biases, are now described. 1) PRESSURE The barometer on board the Rumba gondola is a Paroscientific analog pressure transducer (model 216B) with an accuracy of 10 Pa and a precision of 1 Pa. The barometer, which is located inside the gondola, is compensated in temperature down to 54 C. Temperatures inside the gondolas were very rarely colder than 54 C, and hence no further laboratory calibration of the barometers was needed. The pressure is used to monitor the balloon vertical motions in the atmosphere. At the balloon flight level (i.e., atmospheric density 0.1 kg m 3 ), the 1-Pa precision corresponds to a vertical position precision of1m. 2) HORIZONTAL POSITION AND WIND VELOCITIES The balloon horizontal positions are obtained by absolute GPS measurements, with an accuracy of 15 m. With the exception of a few hour-long flight segments at the beginning of the campaign where the temperatures inside the gondolas were very cold, GPS fixes were nominally obtained during the flights. The horizontal wind velocities are deduced from the successive GPS positions by centered finite differences. Since positions are recorded every 15 min, the accuracy on the 15-min-averaged balloon horizontal velocities is 0.02 m s 1. As shown previously, the difference between the balloon and wind horizontal velocities cannot be significantly larger than 0.05 m s 1 during that time interval. Estimates of the 15-min-averaged horizontal wind velocities are thus obtained with an accuracy better than 0.1 m s 1. FIG. 3. Bias of temperature measurements (crosses) for one of the Vorcore flights (flight 13): first thermistor (black) and second thermistor (gray). Corrections subtracted from the raw temperature records (solid lines). 3) TEMPERATURE The air temperature is measured by two independent, 120- m-diameter microbead YSI thermistors that hang 5 m below the gondola. The thermistors are calibrated in the laboratory with respect to a standard Pt100 platine probe down to 80 C. To minimize the daytime radiative heating of the thermistor and its environment, thermistors are aluminized and mounted on small transparent glass plates (Fourrier et al. 1970). The accurate measure of temperature on superpressure balloon flights is, however, particularly difficult: in contrast to classical radiosoundings that continuously ascend in the atmosphere, superpressure balloons move with the wind, and the temperature sensors are poorly ventilated. It has thus been observed that Rumba temperature measurements are warm biased during the day. This is exemplified in Fig. 3, which shows the temperature measurement bias versus solar zenith angles (SZAs) for one of the Vorcore flights. As detailed in Hertzog et al. (2004), that curve is obtained empirically by first computing the derivative of the temperature bias with respect to SZA and then integrating it. In the case of the Vorcore campaign, most of the observations were made at high SZAs, and the temperature bias estimates are therefore more accurate at those solar angles. Figure 3 clearly shows that temperature observations are warmer during day than during night since no diurnal cycle with such an amplitude is expected in the lower stratosphere. The daytime bias may slightly vary from one thermistor to the other due to the proximity of the microbead with the glass plate or to the amount of metal deposited on the plate for the electrical con-

74 DECEMBER 2007 H E R T Z O G E T A L nection between the thermistor and the gondola. However, most of the thermistors exhibit a 1.5-K bias at low SZAs. An exponential is used to fit the daytime bias of each thermistor and then substracted from the raw temperature measurements. After correction, the accuracy of temperature measurements, which can be estimated with the two independent temperature measurements performed on each flight, is found to be 0.25 K during the night and 0.3 K during the day. The temperature accuracy can be further improved by a factor 2 by taking the mean of both thermistor measurements. 4) HOUSEKEEPING PARAMETERS Apart from the previous measurements that are intended for scientific use, Rumba also performs housekeeping observations. In brief, the balloon superpressure and gas temperature are measured by a Honeywell pressure tranducer and a 240- m-diameter YSI thermistor, with respective accuracies of 10 Pa and 0.5 K. The gondola internal temperature, as well as the battery voltage, is also monitored during the flight. 3. Vorcore experiment a. Flight safety and configuration The flight configuration used during Vorcore is shown in Fig. 4. The thermistors are at the bottom of the flight train to avoid the balloon wake. A radar reflector and a flash lamp are used to signalize the flight train when it crosses the airplane space during the ascent and final descent. The end of the flight can be automatically commanded by the gondola as soon as one of the following safety criteria is no longer met: flight domain: the balloon must stay south of 40 S, altitude: the balloon has to fly above 100 hpa, energy: the battery voltage has to be higher than a predetermined threshold, flight length: a maximum lifetime of 110 days is allowed. In that case, the flight train is separated from the balloon and descends with a parachute. The unballasted balloon rapidly ascends and explodes because of the superpressure increase. The flight domain and altitude limitations have been imposed to minimize the probability of flying above populated areas or through airplane corridors. Finally, a secondary redundant device located just above the parachute is also able to FIG. 4. The flight train configuration during Vorcore. check the altitude and flight length criteria and to command the flight termination. b. Balloon campaign The Vorcore campaign took place in McMurdo, Antarctica. McMurdo is actually the only Antarctic basis south of 60 S that can be reached during winter and that provides sufficient logistic capabilities to support such a large balloon campaign. The launching site (77.85 S, E) was located on the sea ice, 300 m in front of the main station, in order to be as much protected as possible from the prevailing southeasterly surface winds that descend from the Antarctic Plateau and circulate around Ross Island. Figure 5 shows the launchpad that consisted of two 25-m-long, semicylindrical Jamesways in which the balloons were prepared before launch, two power generators, a few containers, and a regularly desnowed, 100 m 100 m squared area for the launches. The first launch took place on 5 September and the last one on 28 October. A total of 27 launches were

75 2054 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24 FIG. 5. A 10-m superpressure balloon just after launch. The Vorcore launchpad, with the two dark Jamesways used as preparation buildings, was located 300 m in front of McMurdo on the sea ice. performed during this period. The weather limitations, imposed so as to minimize the risk of damaging the balloon during the final operational phases (i.e., mean surface wind velocity smaller than 4 m s 1 and gusts smaller than 6 m s 1 ), somewhat limited the number of launch opportunities. However, windows long enough to launch the balloons were found on average 66% of the days in September and October. Two consecutive launches were even performed on seven occasions when calm surface conditions lasted for more than 3 h. Details on the 27 flights are given in Table 1. The mean flight duration achieved during the campaign is about 2 months (58.5 days), while the longest flight (flight 8) lasted 109 days. Gondolas running out of energy or balloons crossing the flight-domain boundary were the two main causes of flight terminations. Premature ends of the flights were otherwise principally caused by leaking balloon envelops (3 flights), balloon bursts due to a weakness of the envelops (2 flights), and balloon bursts due to atmospheric gravity waves with dramatic amplitudes (2 flights), as shown below. Figure 6 shows the number of balloons in flight versus time. The launching period extended from the beginning of September to the end of October 2005, at which point a maximum of 21 balloons in flight was reached. In December 2005, this number rapidly fell due to the progressive breakdown of the stratospheric vortex that pushed the balloons toward the limits of the flight domain. Each balloon/gondola typically performs 100 observations per day, so that a total of observations were finally gathered during the campaign. c. Complementary observations Complementary observations associated with the Vorcore campaign have been performed in several Antarctic stations to complement the balloon observations. In particular, an emphasis has been put on ozone observations since no such observations are performed by the Vorcore gondola. To this end, ozone sondes were launched on alert in Davis (68.58 S, E), Marambio (64.24 S, W), McMurdo, and Neumayer (70.65 S, 8.25 W) when superpressure balloons were flying close by. The balloon trajectories in conjunction with the ozone profiles will help to study the ozone depleting rates in the vortex core. Rayleigh lidar observations to document the presence of polar stratospheric clouds were also performed in Davis, Dumont D Urville (66.67 S, E), and McMurdo. Finally, on several occasions when Vorcore balloons were launched from or were flying above Mc- Murdo, a high-resolution vertical profile of aerosol was obtained by the University of Wyoming aerosol counter (Deshler et al. 2003). These aerosol data will be used with the parcel-based history of air temperature provided by superpressure balloons to assess our understanding of microphysical processes in the polar stratosphere.

76 DECEMBER 2007 H E R T Z O G E T A L TABLE 1. Summary of Vorcore flights. Flights associated with the same Greek letter were launched consecutively. Flight No. Launch End Duration (day) Balloon diameter (m) Reason for flight termination 1 5 Sep Sep Leaking balloon 2 6 Sep Dec Energy 3 9 Sep Dec Energy 4 9 Sep Nov Flight domain 5 12 Sep Sep Leaking balloon 6 17 Sep Sep Incident on flight train 7 17 Sep Dec Flight domain 8 20 Sep Jan Flight domain 9 22 Sep Sep Balloon burst Sep Dec Flight domain Sep Dec Energy Sep Oct Mountain wave Sep Dec Energy Sep Dec Energy 15 4 Oct Dec Communication lost 16 5 Oct Jan Energy 17 5 Oct Nov Leaking balloon 18 6 Oct Dec Flight domain Oct Jan Energy Oct Oct Mountain wave Oct Oct Balloon burst Oct Dec Flight domain Oct Dec Flight domain Oct Jan Energy Oct Dec Flight domain Oct Nov Flight domain Oct Feb Energy 4. Some characteristics of the Vorcore dataset a. Geographical sampling Figure 7 shows the geographical distribution of the Vorcore observations. Because of the nonstationarity of the stratospheric flow and the long duration of the flights, the balloon flotilla thoroughly sampled the whole Antarctic continent and the ocean up to 55 S. FIG. 6. Number of balloons in flight during the Vorcore campaign (September 2005 February 2006). Note also that the cloud of observations is slightly displaced toward the Atlantic Ocean due to the preferred position of the 2005 vortex. This apparently almost homogeneous sampling nevertheless hides varying geographical features of the observation set associated with the evolution of the stratospheric vortex in the 2005 winter and spring. Those features can be roughly divided into three periods, as shown in Fig. 8. At the beginning of the campaign (September October), the stratospheric vortex was very stable and the flow was almost symmetric about the Pole. The observations performed during this period are associated with almost circular trajectories around the vortex center. In November, the vortex began to be stretched and displaced off the Pole by planetary waves with increasing amplitudes, and the sampling of the stratosphere slightly extends to the midlatitudes. During this month, the vortex center was most of the time located either in the Atlantic or in the western Indian sector of Antarctica, so that the balloons only occasionally flew above the Antarctica Pacific sector. Finally, in December and at the beginning of 2006, the stratospheric vortex broke into several pieces and most of the remaining balloons were ejected toward midlatitudes where some eventually crossed the 40 S parallel.

77 2056 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24 FIG. 7. Geographical distribution of Vorcore balloon observations. The flight domain was limited to latitudes southward of 40 S. Thanks to the long flight duration achieved during the campaign, the Vorcore balloon flotilla therefore documented the 2005 SH stratospheric vortex from its very stable winter state up to its total breakdown in early December. b. Observations with respect to the stratospheric vortex To monitor the positions of the balloons with respect to the vortex, the equivalent latitude of each observation has been computed. The equivalent latitude is the latitude of the parallel that encircles the same polar-cap area as the potential vorticity (PV) contour that passes by the balloon position. The 90 equivalent latitude thus corresponds to the point with the lowest PV in the Southern Hemisphere vortex (the vortex center), while lower equivalent latitudes correspond to midlatitude air. The vortex edge is associated with a strong horizontal PV gradient on an isentropic surface (McIntyre and Palmer 1984), and is therefore computed as the extremum of the first derivative of PV with respect to equivalent latitude (Nash et al. 1996). Here, we used the PV fields provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) operational analyses on 60 vertical levels at horizontal resolution. The differences between the balloon equivalent latitudes and the vortex-edge equivalent latitude are shown in Fig. 9. As mentioned in the introduction, the aim of the Vorcore campaign was primarily to document the small to mesoscale dynamics in the core of the polar stratospheric vortex. Launches were consequently restricted to time periods when the vortex was located above the McMurdo station, and the balloon initial positions are located inside the vortex. As good tracers of air parcel motions, the superpressure balloons did not cross the dynamical barrier associated with the vortex edge during the first two months of the campaign. From October on, nevertheless, the progressive shift of the Vorcore observations toward the vortex edge reflects the regular shrinking of the vortex area that usually occurs in spring. In December, as shown in Fig. 8, the vortex splits in several pieces and finally disappears. At that time, a number of balloons are still located inside the remaining low-pv regions, and the Vorcore observations sample both sides of the vanishing vortices. However, some of the balloons escaped the vortex as soon as mid-november (i.e., much before the vortex breakdown). This was the case of balloon 27, whose positions between 20 and 27 November are reported in Fig. 10. This balloon, which was located close to the vortex edge at the beginning of the period, was embedded in a PV filament that was ultimately ejected from the main vortex. Those kinds of vortex erosion events are responsible for most of the exchange of air masses between the stratospheric vortex and the surf zone and are caused by breaking planetary-scale Rossby waves (McIntyre and Palmer 1983; Waugh et al. 1994; Koh and Plumb 2000; Moustaoui et al. 2003). After 23 November, balloon 27, though outside of the vortex, was still drifting in an air mass with a PV value lower than its surrounding, midlatitude air, and which is furthermore connected by a thin filament to the main vortex. During this period therefore, the balloon stayed in the air mass ejected from the vortex and thus achieved a Lagrangian sampling of the atmosphere. This quasi-lagrangian aspect of superpressure balloon flights is further discussed in the next section. c. Quasi-Lagrangian observations Superpressure balloons do not drift on isentropic surfaces and as such are not perfect tracers of air masses in the stratosphere. Note, however, that although diabatic heating rates are quite low in the stratosphere (typically on the order of 1Kday 1 ), they cannot be neglected on time scales corresponding to long-duration flights, so that even a pure isentropic balloon would not be a perfect tracer of air motion. The above example of balloon 27 nevertheless shows that at

78 DECEMBER 2007 H E R T Z O G E T A L FIG. 8. (top) Geographical distribution of Vorcore balloon observations in (left) September October, (middle) November, and (right) December January. (bottom) Potential vorticity analyzed by ECMWF on the 475-K isentrope on days representative of the three phases of the stratospheric flow during Vorcore: (left) centered vortex, (middle) vortex displaced off the South Pole but still well defined, and (right) vortex broken up in several pieces. The thick white line represents the vortex edge as defined by the Nash et al. (1996) algorithm. The PV color code is the same on the three panels. least on short time scales, superpressure balloon trajectories mimic air-parcel trajectories to a good approximation. To further investigate the quasi-lagrangian aspect of the Vorcore dataset, the air potential temperature measured along two balloon trajectories that are representative of the whole Vorcore flotilla is shown in Fig. 11. In September 2005, the potential temperature of balloon 3 only slightly varies, so that this balloon almost FIG. 9. Difference between the balloon equivalent latitudes and the vortex-edge equivalent latitude. permanently flies on the same isentropic surface. In fact, at that time, the undisturbed state of the vortex causes isentropic and isopycnic surfaces to be roughly parallel to each other in the lower stratosphere. The balloons can therefore be considered Lagrangian tracers to a good approximation at the beginning of the experiment. In October 2005, Fig. 11 shows that balloon 3 potential temperature increases from 450 up to 480 K. This increase results from the progressive warming of the vortex core with the return of the sun and the associated differential displacements of isentropic and isopycnic surfaces. In November, planetary-scale Rossby waves induce large variations of the balloon potential temperatures (up to 30-K amplitude), so that the quasi-lagrangian property of the balloon flotilla is more arguable from mid-october to the beginning of December. Finally, once the balloons escape from the main vortex (as for balloon 27) or after the vortex final breakdown, the potential temperature along the balloon trajectories stays almost constant again. In that last case, the balloons flew in the vicinity of the zero-wind altitude where Rossby waves become evanescent. Once again, the balloons can thus be considered good Lagrangian tracers, which is, for instance, exemplified by balloon 27 (cf. Fig. 10).

79 2058 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24 FIG. 10. Potential vorticity on the 475-K isentrope analyzed by ECMWF at 0000 UTC from 20 to 25 Nov Dark (light) colors are associated with lower (higher) PV values. The thick white line represents the vortex edge. The white cross shows balloon 27 s position at 0000 UTC on the corresponding day. d. An example out of the dataset: The end of flight 12 In this section, the observations performed by flight 11 on 7 October 2005 are analyzed to (i) present the kind of motions that can be studied with the dataset collected during Vorcore and (ii) show how strong atmospheric waves can induce dramatic damages to superpressure balloons. Flights 11 and 12 were launched 20 h apart on 22 September 2005, but were still flying close to each other 12 days after the launch, flight 11 leading flight 12 by about 4 h. The trajectories of both balloons on 6 and 7 October 2005, while the balloons were flying above the northern tip of the Antarctic Peninsula, are shown in Fig. 12. Until 1000 UTC on 7 October, the gondola on board flight 12 was in the nominal flight mode, reporting data every 15 min, and all the balloon and payload housekeeping parameters were nominal. At that time, the balloon was very close to the western coast of the Antarctic Peninsula (see Fig. 12). The next point received from this balloon indicates that the gondola had crossed the 100-hPa flight-domain limit. This point is located on the eastern side of the Antarctic Peninsula, and the altitude reported by the GPS was 3000 m. The vertical velocity of the payload was negative and consistent with a descent under the parachute. The last point received from flight 12 (which is shown by a cross in Fig. 12) indicates that the gondola is just above the sea level. The gondola most likely sank afterward. Air pressure and temperature, as well as helium superpressure inside the balloon reported by flight 11 during its transit over the peninsula, are shown in Fig. 13. The crossing of the peninsula mountains is associated with huge fluctuations of temperature and pressure with, respectively, 17 K and 18-hPa peak-topeak amplitudes. In the center of the disturbance, the balloon performed a vertical excursion of 1500 m in 15 min. Those pressure perturbations in return induced fluctuations of the helium superpressure inside the balloon, which reached 22.7 hpa (i.e., a superpressure at the limit of what a 8.5-m balloon can bear). This disturbance is most likely induced by a gravity wave generated by the tropospheric flow above the peninsula mountains that propagated upward in the stratosphere. Such large amplitude waves have already been reported at high latitudes above topography during winter (e.g., Dörnbrack et al. 1999; Hertzog et al. 2002a). It is thus very likely that balloon 12 also crossed that disturbance 4 h after flight 11. At that time, the sun began to rise and to heat the helium inside the balloon, so that the background superpressure inside balloon 12 already started to increase as it approached the mountains. Furthermore, balloon 12 is a larger balloon (10-m diameter) than balloon 11 and cannot bear superpressures larger than 20 hpa. Embedded in such a

80 DECEMBER 2007 H E R T Z O G E T A L FIG. 11. (top) Air potential temperature measured along balloon 3 and (bottom) balloon 27 trajectories. large amplitude mountain wave, balloon 12 certainly exploded over the peninsula and caused the fall of the gondola. More generally, an increase of gravity wave activity FIG. 13. (top) Air pressure, (middle) temperature, and (bottom) helium superpressure recorded with flight 11 (black) and flight 12 (gray) on 6 7 Oct The 15-min observations are shown with crosses. The gray shading at the bottom of each panel (right scale) represents the elevation overflown by flight 11. (with fortunately smaller amplitudes than those reported above) has been noticed in the Vorcore dataset when balloons were flying in the vicinity of steep topography (i.e., mainly the Antarctic Peninsula and the plateau ocean transition). The dataset collected during Vorcore has a sufficient resolution to document those motions, and the geographical distribution of gravity waves over Antarctica that has been addressed by a few studies only (Allen and Vincent 1995; Pfenninger et al. 1999; Wu and Jiang 2002) will be the subject of forthcoming papers. FIG. 12. Trajectories of flight 11 (black) and flight 12 (gray) on 6 and 7 Oct The last received position of flight 12, while the gondola was at 41 m ASL and descending over the parachute, is indicated by the gray cross on the eastern side of the peninsula. The elevation is represented by contours every 500 m from the sea level. 5. Conclusions and future developments The Vorcore campaign thus proved that superpressure balloons can reliably perform long-duration flights in the very harsh environment typical of the polar lower

81 2060 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 24 stratosphere in winter. A mean flight duration of almost 2 months was achieved, and 16 flights out of 27 were actually longer that 2 months. The balloons were responsible for only 25% of the flight termination. Furthermore, thanks to modern satelliteborne communication and positioning systems, the dataset gathered during this campaign has typically the same size (and much better accuracy) as those of the early 1970s campaigns, although Vorcore only flew 27 balloons versus, for example, 480 during Éole. Vorcore has provided a very valuable scientific dataset, which is original in many respects. For instance, its high resolution and global sampling of the SH polar stratosphere will be very helpful to document the dynamics of that region, from the short-period gravity waves up to the long Rossby planetary waves. Besides, the Vorcore observations were performed in a quasi-lagrangian framework, which is a unique feature that is enabled by superpressure balloons. This characteristic is very useful to compute the momentum flux carried by gravity waves, and hence their potential forcing on the middle atmosphere (Hertzog and Vial 2001). With the help of ozone soundings performed along the balloon trajectories, the quasi-lagrangian observations may also provide new insights on ozone depletion. In the near future, several improvements of the observing system will be addressed in order to further increase its scientific interest. A higher sampling rate will be enabled by the use of satellite phone communications. New instruments aimed at measuring chemical species (e.g., ozone, water vapor) or particles and specially designed to bear the requirements of longduration flights in the lower stratosphere are under development. In parallel, larger balloons (12-m diameter) able to carry heavier payloads (up to 40 kg) have already been successfully tested during tropical flights in Such new systems could be very useful to provide global-scale observations of still poorly sampled regions, such as, for instance, the equatorial lower stratosphere. Acknowledgments. The Vorcore team is much indebted to R. Sadourny and H. Teitelbaum, who first proposed Stratéole, and more generally to all the scientists who supported the project through the ages. The authors are also grateful to the French Space Agency (CNES) and the Institut National des Sciences de l Univers (INSU) for their longstanding support, and to the CNES, Zodiac, and CNRS staff involved in the project. The Vorcore campaign would not have been possible without the involvement of the NSF and of the French Polar Institute (IPEV). The whole NSF and RPSC teams in McMurdo are gratefully acknowledged for their outstanding help during the campaign. The Vorcore team would also like to thank T. Deshler and his team for their friendly support in McMurdo. Finally, the devotion of winter-over personnel who performed Vorcore-related observations in several Antarctic stations is gratefully acknowledged. REFERENCES Allen, S. J., and R. A. Vincent, 1995: Gravity wave activity in the lower atmosphere: Seasonal and latitudinal variations. J. Geophys. Res., 100, Angell, J. K., 1972: Air motions in the tropical stratosphere deduced from satellite tracking of horizontally floating balloons. J. Atmos. Sci., 29, Cocquerez, P., P. Guigue, R. Guilbon, T. Phulpin, M. Durand, J.-P. Lefèvre, M. Eymard, and M. Lafourcade, 2001: Test flights of CNES stratospheric superpressure balloons in experimental Arctic campaigns : Objectives and results. Proc. 15th ESA Symp. on European Rocket and Balloon Programmes and Related Research, SP-471, Noordwijk, Netherlands, European Space Agency, Deshler, T., M. E. Hervig, D. J. Hofmann, J. M. Rosen, and J. B. 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82 DECEMBER 2007 H E R T Z O G E T A L V. E. Suomi, 1974: On the behavior of superpressure balloons at 150 mb. J. Appl. Meteor., 13, Massman, W. J., 1978: On the nature of vertical oscillations of constant volume balloons. J. Appl. Meteor., 17, McIntyre, M. E., 1989: On the Antarctic ozone hole. J. Atmos. Terr. Phys., 51, , and T. N. Palmer, 1983: Breaking planetary waves in the stratosphere. Nature, 305, , and, 1984: The surf zone in the stratosphere. J. Atmos. Terr. Phys., 46, Morel, P., and W. Bandeen, 1973: The EOLE experiment: Early results and current objectives. Bull. Amer. Meteor. Soc., 54, Moustaoui, M., H. Teitelbaum, and F. P. J. Valero, 2003: Ozone laminae inside the Antarctic vortex produced by poleward filaments. Quart. J. Roy. Meteor. Soc., 129, Nash, E. R., P. A. Newman, J. E. Rosenfield, and M. R. Schoeberl, 1996: An objective determination of the polar vortex using Ertel s potential vorticity. J. Geophys. Res., 101, Nastrom, G. D., 1980: The response of superpressure balloons to gravity waves. J. Appl. Meteor., 19, Olivero, J. J., A. W. Shaw, P. R. Williamson, and L. R. Megill, 1984: Mid-stratospheric circulations in the Southern Hemisphere from super pressure balloon trajectories. J. Geophys. Res., 89, Pfenninger, M., A. Z. Liu, G. C. Papen, and C. S. Gardner, 1999: Gravity wave characteristics in the lower atmosphere at South Pole. J. Geophys. Res., 104, Reynolds, R. D., 1973: Superpressure balloons as isentropic/ isopycnic tracers. J. Appl. Meteor., 12, Schumann, A. P., 1980: Carrier balloon trajectories in the stratosphere. J. Appl. Meteor., 19, The TWERLE Team, 1977: The TWERL Experiment. Bull. Amer. Meteor. Soc., 58, Vial, F., and Coauthors, 1995: STRATÉOLE: A project to study Antarctic polar vortex dynamics and its impact on ozone chemistry. Phys. Chem. Earth, 20, , A. Hertzog, C. R. Mechoso, C. Basdevant, P. Cocquerez, V. Dubourg, and F. Nouel, 2001: A study of the dynamics of the equatorial lower stratosphere by use of ultra-long-duration balloons, 1: Planetary scales. J. Geophys. Res., 106, Waugh, D. W., and Coauthors, 1994: Transport out of the lower stratospheric Arctic vortex by Rossby wave breaking. J. Geophys. Res., 99, WMO, 2003: Scientific assessment of ozone depletion: WMO/Global Ozone Research and Monitoring Project Rep. 47, 498 pp. Wu, D. L., and J. H. Jiang, 2002: MLS observations of atmospheric gravity waves over Antarctica. J. Geophys. Res., 107, 4773, doi: /2002jd

83 4.4. ARTICLE : STRATÉOLE/VORCORE 75 Résumé La campagne Vorcore a été un grand succès scientifique et technique, il est le fruit d une collaboration entre la division ballon du CNES et les équipes techniques du LMD qui ont développé les instruments avec le soutien de la National Science Foundation (NSF) et du personnel de la station McMurdo. Les BPS ont volé deux mois en moyenne et ces vols ont permis une observation sans précedent de la basse stratosphère antarctique. L échantillonnage fin a permis d enregistrer plus de observations dans un région jusque là mal documentée. Les BPS ont tous volé à l intérieur du vortex et ils permettent donc une analyse précise de l évolution du vortex justqu à sa rupture et sa dilution. De plus, la manifestation des ondes planétaires comme des ondes de gravité est apparente dans les séries temporelles de température et de vent. Ce jeu de données est donc adapté à l étude d ondes de gravité qui va être conduite dans le chapitre 5.

84 76 CHAPITRE 4. LA CAMPAGNE DE BALLONS PRESSURISÉS VORCORE

85 77 Chapitre 5 Étude des ondes de gravité : application à la campagne Vorcore Dans ce chapitre, la méthodologie détaillée dans le chapitre 3 est appliquée aux données de la campagne Vorcore. La répartition géographique et temporelle des flux de quantité de mouvement totaux et directionnels ainsi que les sources potentielles des ondes de gravité et leur intermittence sont examinées. La distribution du flux de quantité de mouvement en fonction de la vitesse de phase intrinsèque est également étudiée. De plus, ces résultats sont comparés aux flux de quantité de mouvement observés avec les instruments spatiaux CRISTA (Ern et al., 2004) et HIRDLS (Alexander et al., 2008). Des comparaisons interhémisphériques du flux de quantité de mouvement ont également été effectuées en appliquant la même méthodologie à des données enregistrées en 2002 lors d une campagne préparatoire réalisée à partir de Kiruna (68 o N, 20 o E), en Suède.

86 78 CHAPITRE 5. APPLICATION À LA CAMPAGNE VORCORE 5.1 Estimation du flux de quantité de mouvement transporté par les ondes de gravité Comme nous l avons vu dans le chapitre 2, la quantité déterminante pour estimer l interaction des ondes de gravité avec l écoulement moyen est le flux vertical de quantité de mouvement horizontale transporté par les ondes. Ainsi, l estimation de cette quantité a fait l objet de nombreuses études en utilisant différentes techniques d observations : 1. Les radiosondages permettent d estimerρu w dans la stratosphère en étudiant l hodographe des perturbations de vitesses (Chun et al., 2006) ou à l aide d une méthode basée sur les ondelettes (Zink and Vincent, 2001). 2. Dans les observations satellitaires, les ondes de gravité sont détectées en analysant les perturbations des profils de températures ou de températures de radiance dans l atmosphère moyenne. Selon la fonction de poids utilisée par l instrument et le type d observation (nadir ou limbe), certaines parties du spectre en fréquence et en longueur d onde seront plus ou moins bien détectées (Alexander et al., 2008). Parmi les principales études de ce type, on peut noter celles effectuées à partir des observations de l instrument CRISTA (Ern et al., 2004), et celles issues de l instrument HIRDLS (Alexander et al., 2008) qui ont permis d établir des climatologies des ondes de gravité à l échelle globale. Les instruments qui observent au limbe comme CRISTA et HIRDLS induisent une meilleure résolution verticale que ceux qui observent au nadir (Eckermann and Preusse, 2002). 3. Les observations par lidar permettent d estimer le flux de quantité de mouvement dans la haute mésosphère (Gardner and Gulati, 2007). 4. Dans la mésosphère, différents types de radar ont permis d estimerρu w, par exemple Vincent and Reid (1983); Fritts and Vincent (1987); Nakamura et al. (1993); Hocking (2005). 5. Les mesures de luminescence atmosphérique peuvent servir à détecter des ondes de gravité de petite échelle (λ h < 100 km) dans la mésosphère et la basse thermosphère, par exemple Gardner et al. (1999); Espy et al. (2004); Suzuki et al. (2007). 6. Enfin, les ballons pressurisés de longue durée permettent également d estimer le flux de quantité de mouvement. Par exemple, l étude des séries temporelles enregistrées par trois BPS

87 5.2. APPLICATION DE LA MÉTHODOLOGIE À LA CAMPAGNE VORCORE 79 lâchés à partir de Latacunga (Équateur) en août et septembre 1998 ont servi pour estimer le flux de quantité de mouvement transporté par les ondes de gravité dans la zone équatoriale (Hertzog and Vial, 2001b). Les estimations faites à partir de BPS se distinguent des autres car elles permettent d obtenir des observations sur des régions géographiques étendues contrairement aux radars et aux lidars. En outre, elles sont plus directes que les observations faites à partir de satellites ou par les radiosondages, les incertitudes induites par ce type d observation sont donc plus faibles. 5.2 Application de la méthodologie à la campagne Vorcore Article : Estimation of Gravity-Wave Momentum Fluxes and Phase Speeds from Quasi-Lagrangian Stratospheric Balloon Flights. 2: Results from the Vorcore Campaign in Antarctica Cet article présente les distributions de flux de quantité de mouvement obtenues en appliquant la méthodologie développée dans le chapitre 3 sur les données de la campagne Vorcore. Au dessus de la péninsule antarctique, et dans son aval, ainsi que sur la terre d Adélie et au dessus des montagnes transantarctiques, les flux observés sont nettement plus forts que sur le reste de la zone échantillonnée. Les distributions des flux de quantité de mouvement zonaux et méridiens soulignent l importance des ondes de montagne avec des flux se propageant dans la direction opposée à l écoulement moyen. Une critère géographique permet de distinguer les zones où le flux transporté correspond à des ondes orographiques, des zones où le flux provient d ondes non orographiques. L importance des ondes non orographiques a été mise en évidence sur l océan et dans les zones où l orographie ne permet pas la formation d ondes de gravité (faibles gradients topographiques). Enfin, à partir de deux approches différentes, l intermittence des sources a été étudiée. L étude suggère que les sources d ondes non orographiques émettent des ondes de manière continue alors que les sources d ondes orographiques émettent des ondes de manière sproradique. Cet article a été accepté en Mars 2008 à Journal of Atmospheric Sciences. Dans la suite de la thèse, il est désigné sous la forme Hertzog et al. (2008).

88 3056 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 65 Estimation of Gravity Wave Momentum Flux and Phase Speeds from Quasi-Lagrangian Stratospheric Balloon Flights. Part II: Results from the Vorcore Campaign in Antarctica ALBERT HERTZOG AND GILLIAN BOCCARA Laboratoire de Météorologie Dynamique, Université Pierre et Marie Curie, École Polytechnique, Palaiseau, France ROBERT A. VINCENT Department of Physics, University of Adelaide, Adelaide, Australia FRANÇOIS VIAL Laboratoire de Météorologie Dynamique, École Polytechnique, Palaiseau, France PHILIPPE COCQUEREZ Sous-direction Ballon, Centre National d Études Spatiales, Toulouse, France (Manuscript received 11 December 2007, in final form 17 March 2008) ABSTRACT The stratospheric gravity wave field in the Southern Hemisphere is investigated by analyzing observations collected by 27 long-duration balloons that flew between September 2005 and February 2006 over Antarctica and the Southern Ocean. The analysis is based on the methods introduced by Boccara et al. in a companion paper. Special attention is given to deriving information useful to gravity wave drag parameterizations employed in atmospheric general circulation models. The balloon dataset is used to map the geographic variability of gravity wave momentum fluxes in the lower stratosphere. This flux distribution is found to be very heterogeneous with the largest time-averaged value (28 mpa) observed above the Antarctic Peninsula. This value exceeds by a factor of 10 the overall mean momentum flux measured during the balloon campaign. Zonal momentum fluxes were predominantly westward, whereas meridional momentum fluxes were equally northward and southward. A local enhancement of southward flux is nevertheless observed above Adélie Land and is attributed to waves generated by katabatic winds, for which the signature is otherwise rather small in the balloon observations. When zonal averages are performed, oceanic momentum fluxes are found to be of similar magnitude to continental values (2.5 3 mpa), stressing the importance of nonorographic gravity waves over oceans. Last, gravity wave intermittency is investigated. Mountain waves appear to be significantly more sporadic than waves observed above the ocean. 1. Introduction Corresponding author address: Albert Hertzog, Laboratoire de Météorologie Dynamique, École Polytechnique, F Palaiseau CEDEX, France. albert.hertzog@lmd.polytechnique.fr The role of gravity waves (GWs) in forcing the global-scale circulation and the thermal structure of the middle atmosphere has long been recognized (e.g., Holton 1983; Shepherd 2002). Owing to horizontal and vertical scales, respectively km, and 100 m 10 km, that are in general too short to be explicitly resolved by atmospheric general circulation models (GCMs), GW effects on the large-scale circulation have to be parameterized. A wide variety of gravity wave drag (GWD) parameterization schemes, each based on different physical assumptions of the GW field, have been proposed since the early work of Lindzen (1981). However, the GWD parameterizations significantly differ in the way they simulate the GW momentum-flux deposition into the mean flow, so they induce different large-scale responses to a given input wave-source spectrum (Charron et al. 2002; McLandress and Scinocca 2005). These difficulties induce corresponding uncertainties in the chemistry climate simulations of the DOI: /2008JAS American Meteorological Society

89 OCTOBER 2008 H E R T Z O G E T A L stratosphere as the chemical processes responsible for ozone depletion are very dependent on temperature (Eyring et al. 2006). The paucity of GW momentum-flux observations in the atmosphere is known to be a limiting factor in the improvement of GWD parameterizations (e.g., McLandress and Scinocca 2005). Most observations have been obtained by radar technique at widely spaced locations around the globe (e.g., Vincent and Reid 1983; Nakamura et al. 1993). Recently, the analysis of infrared radiances measured from space during the two weeklong Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA) missions provided useful insights into the distribution of GW momentum fluxes at global scale (Ern et al. 2004, 2006). Alexander et al. (2008) similarly derived absolute momentum fluxes from the High Resolution Dynamics Limb Sounder (HIRDLS) observations in May Nevertheless, because of the short duration of these spaceborne datasets and their limited horizontal resolution, new observations of GW momentum fluxes are needed to further constrain GWD parameterizations. The effect of gravity waves on the large-scale structure of the atmosphere is particularly important at Southern Hemisphere (SH) polar latitudes in winter: wave breaking at mesospheric heights induces significant changes in temperature down to the lower stratosphere (Garcia and Boville 1994). Indeed, models that do not represent the correct flux of momentum associated with gravity wave propagation in the SH polar latitudes suffer from strong cold temperature biases that can reach several tens of degrees in the stratospheric vortex (e.g., Hamilton et al. 1995). In spite of the difficulties of performing observations in Antarctica, useful information on GW activity in the SH polar latitudes has been obtained from radiosounding profiles (Allen and Vincent 1995; Pfenninger et al. 1999; Yoshiki and Sato 2000; Yoshiki et al. 2004), MLS and AMSU radiances (Wu and Waters 1996; Wu and Jiang 2002; Wu 2004), and GPS radio occultations (Tsuda et al. 2000; Ratnam et al. 2004a,b; Baumgaertner and Mc- Donald 2007). These studies described the annual cycle of GW potential and/or kinetic energy and reported on enhancements of GW activity associated with disturbances of the stratospheric polar vortex induced by planetary waves. Here we complement these previous studies by providing information on the distributions of GW momentum fluxes and GW propagation directions at SH polar latitudes. Our results are based on meteorological observations gathered during quasi-lagrangian, longduration balloon flights performed during the Vorcore campaign (September 2005 February 2006) (Vial et al. 1995; Hertzog et al. 2007). Such observations have already been used to estimate the momentum fluxes carried by gravity waves (Hertzog and Vial 2001; Vincent et al. 2007). This study, however, will make use of new theoretical developments described in a companion paper (Boccara et al. 2008, hereafter B08). The article is organized as follows: The next section briefly describes the main characteristics of the Vorcore observations and reports on the limits of the dataset relevant to GW studies. The characteristics of the observed momentum fluxes are described in detail in section 3. The wide geographical coverage of balloonborne observations enables us to study the relative importance of orographic and nonorographic waves (section 4), as well as the intermittency of wave activity in the lower stratosphere (section 5). Section 6 briefly discusses some aspects of our results, and the final section summarizes our findings. 2. The Vorcore campaign a. Observations The aim of the Stratéole/Vorcore campaign was to study the dynamics of the lower stratosphere in winter and spring to document the various regimes of the polar-night vortex. The originality of the project comes from the use of quasi-lagrangian devices to sample the atmosphere. These devices are superpressure, heliumfilled balloons that have the ability to remain aloft for several months while being advected by the wind. During Vorcore, 27 such balloons were released from Mc- Murdo, Antarctica (77.8 S, E), between 5 September and 28 October The mean flight duration during the campaign was 59 days, and the longest flight lasted almost four months (109 days). The last flight terminated on 1 February 2006 (i.e., during the SH summer). As discussed in B08, each balloon carried a scientific payload that essentially performed 15-min observations of air temperature and 3D position from which the horizontal velocities of the wind were deduced. The air pressure was also measured, but at a higher rate (every minute) in order to explicitly resolve the balloon s neutral oscillations. Owing to better precision with respect to absolute GPS, the pressure observations are also used to document the vertical motions of the balloons induced by geophysical phenomena (waves, seasonal cycle, etc.) Figure 1 shows the total number of observations in 10 5 longitude latitude boxes. All balloons were released in the stratospheric vortex; therefore, the observations were mostly gathered south of 60 S. While relatively well centered around the pole in September

90 3058 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 65 FIG. 1. (top) Number of observations and (bottom) density of observations in 10 5 longitude latitude boxes, obtained during the whole Vorcore campaign (September 2005 February 2006). and October 2005, the lower-stratospheric vortex moved to the Atlantic sector of Antarctica in November, which explains the higher number of observations in that region. The final warming took place in early December, and after that time the remaining balloons were free to sample the midlatitudes. For safety reasons, however, flights were automatically terminated when the balloons crossed the 40 S parallel, so no observations were gathered equatorward of that latitude. Further details on the campaign, the scientific payload, and the evolution of the stratospheric vortex during the 2005 winter can be found in Hertzog et al. (2007). b. Observational filter As for other observation techniques, observations performed during Vorcore tend to filter out parts of the overall GW spectrum. In the case of observations gathered onboard long-duration balloons that drift with the horizontal wind, the observational filter is best expressed in terms of the GW intrinsic frequency ˆ. The low frequency part of the intrinsic-frequency gravity wave spectrum ( ˆ f, where f is the inertial frequency) is fully resolved by the observations owing to flight lengths that far exceed the longest inertial period in the flight domain (i.e., 19hat40 S). On the other hand, the high frequency part of the GW spectrum, ˆ N, where N is the Brunt Väisälä frequency, cannot be resolved because of the limited sampling rate of the observations. Although the Nyquist period during Vorcore is 30 min, we only computed momentum fluxes for waves with intrinsic periods longer than 1 h. This limit was set to ensure a sufficient resolution of the highest frequency waves studied as our momentum flux estimates critically rely on subtle phase differences between velocity and pressure time series (see B08). This theoretical observational filter is displayed with the thick curve in Fig. 2. For comparison, the typical Brunt Väisälä period (2 /N) during Vorcore was 4 min 40 s. Additional filtering is implicitly produced by the algorithms used to analyze the dataset and to isolate GW packets. As shown in B08, the algorithms result in an underestimation of the wave momentum flux depending on the amount of wave packet overlapping in the time frequency space. B08 reported a 25% underestimation on average when 10 GW packets were present in 10-day-long flights. However, the magnitude of this effect also depends on the wave intrinsic period. This additional effect is shown with the thin curve in Fig. 2. It is up to 50% larger at the highest resolved frequencies and less than 15% for quasi-inertial waves. The GW dispersion relation (e.g., Fritts and Alexander 2003) can be used to convert the long-duration balloon observational filter in terms of horizontal and vertical wavelengths, h and z. Wavelength space is more convenient for most other observational techniques: radiosondes, spaceborne limb sounders, or GPS radio occultations. Since the high frequency part of the GW spectrum cannot be observed with Vorcore observations, the resolved horizontal and vertical wavelengths are not totally independent. The wavelength domain that can be observed by the long-duration balloons with the Vorcore sampling is displayed in Fig. 2. A good approximation to the Vorcore observational limit is z h 12. For comparison purposes, the CRISTA-1 observational domain is also represented in this figure (Preusse et al.

91 OCTOBER 2008 H E R T Z O G E T A L FIG. 2. (left) Theoretical observational filter in terms of wave intrinsic frequency in Vorcore observations (thick line) and an observational filter deduced from Monte Carlo simulations presented in B08 (thin line). Note that the observational filter is defined in terms of momentum flux in the Monte Carlo simulations. (right) Vorcore observational filter in horizontal vertical wavelength space. The gray-colored zone (delimited by the thick line) corresponds to spectral areas that cannot be observed with the Vorcore dataset. Typical values for f and N corresponding to the Vorcore dataset were assumed. For comparison purposes, the CRISTA-1 observational domain is also displayed and corresponds to the half space on the upper right hand side of the thin lines. The dashed area corresponds to horizontal wavelengths that can be resolved by CRISTA-1 if gravity waves propagate at favorable angles with respect to the instrument line of sight (Preusse et al. 2002; Ern et al. 2004). 2002; Ern et al. 2004). The balloon and limb-sounder observational domains are very similar. The main difference lies in the ability of the balloons to observe waves with vertical wavelengths shorter than the CRISTA vertical resolution. [The vertical resolution of recent limb-sounding instruments (e.g., HIRDLS) have, however, been improved, and waves with vertical wavelengths of 2 km can be observed by these new instruments (Alexander et al. 2008).] On the other hand, under favorable observing conditions, CRISTA can detect waves with shorter horizontal wavelengths than the balloons. It can also be noticed that both domains are typically wider than the observational domain of radiosoundings, which typically is 100 m z 8 km (Alexander 1998). 3. Gravity wave momentum flux Exploiting the methodology described in B08, Vorcore flight data are used to estimate gravity wave absolute momentum flux, that is, the vertical flux of momentum along the wave direction of propagation (u w ). Based on the results obtained by Allen and Vincent (1995) and Yoshiki and Sato (2000) in the lower stratosphere, we made the assumption that the observed waves were propagating upward so that this flux is always a positive quantity. The wave propagation direction, relative to east ( ), was identified for each wave packet, and the zonal (u w ) and meridional ( w ) momentum flux were obtained as u w cos and u w sin. In contrast with the absolute momentum fluxes, those latter fluxes are signed quantities: waves propagating either toward the west or the south carry negative zonal or meridional momentum fluxes, respectively. The results presented here were obtained with the 24 longest out of the 27 balloon flights performed during Vorcore. The three discarded flights lasted less than 2 days and were therefore not long enough to allow wavelet analysis. The vertical gradient of background temperature, which is needed to estimate gravity wave momentum fluxes from the balloon dataset [see Eqs. (14) and (15) in B08], was computed from the operational analyses released by the European Centre for Medium-Range Weather Forecasts (ECMWF). According to B08, the 1 uncertainty in the momentum flux values reported below is 11% 13%. The following results are presented in terms of density-weighted momentum flux, that is, 0 u w, 0 u w, or 0 w, where 0 is the mean density along each balloon flight. It is computed from the balloonborne pressure and temperature observations. Density-weighted momentum fluxes have the advantage of being independent of altitude, if the waves propagate without breaking, so that the lower-stratospheric estimates presented here can, in principle, be directly compared with

92 3060 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 65 results obtained at different altitudes. The use of flightmean densities is justified by the fact that the superpressure balloons used during Vorcore drift on constant density surfaces to first order. Typical residual variations of density are generally less than 2%. Balloons with two different sizes were used during Vorcore, resulting in two density flight levels separated by about 1.5 km. Both balloon types have nevertheless been combined in the following results as it is expected that the density-weighted momentum fluxes would not significantly vary over this short vertical range. a. Geographical distribution 1) ABSOLUTE MOMENTUM FLUX To obtain the geographical distribution of the density-weighted absolute momentum flux, we averaged these fluxes in 10 5 longitude latitude boxes. Note that the area covered by each box varies with latitude, so the individual boxes do not contribute equally to the global GW flux. Furthermore, the polarmost boxes, south of 85 S, were merged to increase the statistical confidence in that region. The resulting total number of observations south of 85 S is Figure 3 displays the box-averaged distribution of the density-weighted absolute momentum flux 0 u w. Although the Vorcore observations extend up to 40 S, there are only a few observations per box northward of 50 S. The map therefore extends only up to 50 S. Furthermore, no statistics were computed in boxes with less than 200 balloon observations. Figure 3 reveals a strong heterogeneity of GW momentum fluxes in the southern high latitudes, with the largest fluxes observed above the Antarctic Peninsula and its lee and to a lesser extent above the southern tip of South America. The overall campaign-averaged momentum flux amounts to 2.5 mpa, whereas the campaign-averaged momentum flux above the peninsula locally reaches 28 mpa, exceeding by a factor of 10 the overall mean flux. This confirms the preliminary results of Vincent et al. (2007), which were obtained from only one Vorcore flight. They are also in agreement with previous satellite observations of gravity wave activity above Antarctica that already stressed the importance of the peninsula in the generation of gravity waves (e.g., Tsuda et al. 2000; Wu and Jiang 2002; Ern et al. 2004; Wu 2004; Ern et al. 2006; Baumgaertner and McDonald 2007; Alexander and Barnet 2007). Away from the Antarctic Peninsula and the southern Andes, the momentum fluxes are more homogeneously distributed. Slightly larger fluxes are nevertheless observed above mountainous western Antarctica and to some extent along the Antarctica coastline. On the other hand, most FIG. 3. Box averages of density-weighted absolute momentum flux 0 u w. The boxes are 10 longitude 5 latitude wide. No statistics were computed for boxes with less than 200 observations (dashed line). of the eastern Antarctica plateau is a region of very weak GW activity. This geographical distribution of absolute momentum flux emphasizes the importance of orographic gravity waves at SH polar and subpolar latitudes. In particular, the Antarctic Peninsula and the southern Andes are characterized by meridionally aligned mountain ridges, which are almost perpendicular to the lowlevel eastward flow and are therefore favored regions for the generation of mountain waves. 2) ZONAL AND MERIDIONAL MOMENTUM FLUX The geographical distributions of zonal and meridional density-weighted momentum fluxes are displayed in Fig. 4. Recall that these signed fluxes are representative of the mean wave field and are not easily linked to the absolute momentum flux. For instance, a perfectly symmetric field of waves propagating equally in each direction would produce a net zero zonal or meridional flux, the momentum flux carried by one wave packet being cancelled by that of another wave packet propagating in the opposite direction. On the other hand, the absolute momentum flux of this field, and thus its ability to interact with the mean flow, would be nonzero (see, e.g., Sato and Dunkerton 1997; Hertzog and Vial 2001). In agreement with the results of Yoshiki and Sato (2000) at the Japanese Antarctic station Syowa, the zonal momentum fluxes are found to be predominantly negative (i.e., westward) in the winter lower strato-

93 OCTOBER 2008 H E R T Z O G E T A L FIG. 4. As in Fig. 3 but for (left) zonal and (right) meridional momentum flux. sphere, which means that gravity waves are essentially propagating against the mean eastward stratospheric flow. This feature is particularly emphasized over the Antarctic Peninsula, the southern Andes, and the Ellsworth Mountains, which again suggests that the gravity waves generated there have an orographic origin. Although of smaller amplitudes than over mountainous areas, the oceanic zonal momentum fluxes are also mostly negative. The largest westward oceanic zonal fluxes are observed above the Atlantic and the western Indian Oceans and typically amount to 1 mpa. In contrast with the zonal fluxes, the meridional fluxes exhibit both positive and negative values. The largest northward fluxes are found above the Antarctic Peninsula and are likely to be associated with the main southwest northeast orientation of the mountain ridges there. On the other hand, southward propagating waves are observed above the tip of South America, which is also consistent with the main orientation of the southern Andes. However, the largest negative meridional flux is found on the edge of Antarctica between 140 and 150 E, a region that includes Adélie Land. This region is associated with strong meridional gradients of elevation between the ocean and the Antarctic Plateau and is known as one of the windiest places on earth (Wendler et al. 1997; Parish and Walker 2006). If the waves observed there are also produced by the orography, the southward momentum flux would imply a northward near-surface flow, that is, from the plateau to the sea. This suggests, therefore, that the waves at the edge of the continent can be linked to katabatic winds that are particularly important in this region (Watanabe et al. 2006; Parish and Bromwich 2007). Possible reasons why similar enhancements of meridionally propagating waves are not observed all along the Antarctic coast are discussed further below. b. Temporal variations The results above were obtained using all data acquired during the campaign, from early September 2005 to late January However, several studies have shown that there is a seasonal cycle of GW activity at SH high latitudes (e.g., Pfenninger et al. 1999; Tsuda et al. 2000; Yoshiki and Sato 2000; Ratnam et al. 2004a; Ern et al. 2006; Baumgaertner and McDonald 2007). Based on those studies, GW potential energy appears to maximize in the polar lower stratosphere between September and November (spring), whereas Ern et al. (2006) report smaller momentum flux in November than in August. While this may be due to the interannual variability of wave activity, which is significant in the polar lower stratosphere (Baumgaertner and Mc- Donald 2007), another explanation could be that the GW potential energy is not directly linked to the wave momentum flux, as suggested in Ern et al. (2004) and Alexander et al. (2008). The temporal variation of GW momentum flux during the campaign is shown in Fig. 5. This figure was obtained by computing the mean value of the absolute momentum flux in 10-day intervals starting from the beginning of September Each value therefore combines all observations performed in the corre-

94 3062 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 65 FIG. 5. Ten-day averages of gravity wave absolute momentum fluxes during the Vorcore campaign. sponding interval, whatever the latitudes or longitudes of the balloons. Apart from the first interval, which has few observations, Fig. 5 shows a general tendency of momentum flux to decrease from winter to summer. Typically, momentum fluxes are found to be about twice as large in September October than in December January. However, it should be noted that the precise ratio is difficult to estimate with our observations; it is probably biased by the evolution of the balloon flotilla during the campaign. For instance, the balloons sampled midlatitude regions only after the stratospheric vortex had broken down in early December 2005 (Hertzog et al. 2007). A modest enhancement of GW momentum fluxes is observed, nevertheless, in the first two weeks of December when the 2005 stratospheric vortex broke down, as suggested in Yoshiki et al. (2004). Another interesting feature of the momentum-flux temporal evolution is the peak of activity observed in early October. At that time 14 balloons were already flying and sampling the interior of the stratospheric vortex. In fact, this sudden enhancement of wave activity is due to the encounter of a very strong gravity wave by two balloons above the Antarctic Peninsula (Hertzog et al. 2007). As already mentioned, the peninsula is a favored place for wave generation but, since the balloons flew on several occasions above it during the campaign, this particular increase suggests that some variability of momentum penetrating the lower stratosphere may exist. Such variability can result from changes in near-surface winds that may or may not support wave generation and from changes in atmospheric properties that modulate the wave propagation up to the lower stratosphere. Intermittency of wave activity observed during Vorcore will be further discussed in section 5. c. Phase-speed distribution This section presents results on the distribution of the observed momentum fluxes versus wave phase speeds. B08 showed that wave phase speeds are retrieved with less accuracy than either momentum fluxes or directions of propagation. Thus, although we believe that those results give further insights into the GW field above Antarctica, they certainly require further confirmation. Note also that the phase speed retrieval uses time series of the balloon density. For two of the 24 balloons used in this study (balloons 8 and 16), both thermistors were broken during launching operations. The results presented here are therefore obtained from the remaining 22 balloons. Observational distributions of momentum flux versus phase speed are most directly relevant to the gravity wave drag parameterization developed by Alexander and Dunkerton (1999, hereafter AD99), which uses such a wave spectrum at the source level. Nevertheless, as shown in McLandress and Scinocca (2005), AD99 does not essentially differ from other spectral parameterizations (e.g., Hines 1997a,b; Warner and McIntyre 2001). The distribution of zonal and meridional momentum flux versus intrinsic phase speed are displayed in black and gray, respectively, in the left panel of Fig. 6. Whereas the meridional momentum distribution is almost symmetric with respect to zero phase speed, the zonal distribution clearly exhibits larger fluxes at negative intrinsic phase speeds. This difference between the distributions is consistent with the geographical distribution of zonal and meridional momentum (Fig. 4), which shows a negative net value for the former and no significant tendency for the latter. The largest differences between westward and eastward momentum fluxes occur at relatively low phase speeds. Such behavior is likely to be a signature of mountain waves, which propagate against the mean eastward wind in the vicinity of the Antarctic Peninsula. In part, it may also result from the filtering of eastward propagating waves by upper tropospheric winds (Alexander 1998). In an attempt to provide quantitative numbers from the observed momentum flux distribution versus phase speed, we made an analytic fit to the meridional distribution since it is less subject to wind filtering and thus may be more representative of the source spectrum. AD99 used Gaussian and exponential-like functions to represent their source spectra. A Gaussian function does not fit very well to our observed distribution, so we used the following exponential model: F ĉ y F m sgn ĉ y exp ĉ y ĉ p, 1

95 OCTOBER 2008 H E R T Z O G E T A L FIG. 6. (left) Density-weighted zonal (black) and meridional (gray) momentum flux vs zonal and meridional intrinsic phase speed. An exponential function (dashed) is fitted to the meridional momentum flux distribution (see text). (right) As in the left panel but for momentum fluxes plotted vs ground-based phase speed. where ĉ y is the meridional intrinsic phase speed of the wave. The result of this fit is shown with the dashed curve in Fig. 6. The best estimates for F m and ĉ p are mpa and 92 m s 1 : F m depends on the phase speed resolution (here 10 m s 1 ) chosen to compute the momentum distribution as well as on the sampling by the balloon flotilla of various wave sources and their inherent intermittency. The characteristic intrinsic phase speed ĉ p is found to be significantly larger than the values used in AD99, even for the value used in their broad spectrum. As shown in B08, our algorithm tends to overestimate phase speeds, so the real u w (ĉ x ) and w (ĉ y ) distributions almost certainly contain more momentum flux at low phase speeds than is represented in the left panel of Fig. 6. Consequently, the value of ĉ p derived here should be considered an upper bound to the real atmospheric value. The right panel of Fig. 6 shows the zonal and meridional momentum fluxes versus their respective zonal and meridional ground-based phase speeds. In contrast to the distribution versus intrinsic phase speed, the momentum flux in each bin is a sum of both positive and negative values. This is obvious in the meridional spectrum; waves with small meridional ground-based phase speed (c y 0) carry either positive or negative momentum flux depending on the mean meridional velocity of the wind. As the campaign-averaged meridional velocity is nearly zero, both cases occur equally, and the net meridional flux in the vicinity of c y 0 is small. On the other hand, waves with small zonal ground-based phase speed carry preferentially negative momentum, as the mean zonal wind is directed eastward. Actually, the sign of the net zonal momentum flux changes at c x 20 ms 1, which corresponds to typical values of zonal velocities observed during the campaign. Finally, the largest zonal momentum fluxes are found near c x 0, which once again emphasizes the role of mountain waves. 4. Wave sources GW drag parameterizations used in GCMs generally consist of two distinct contributions associated with waves that are either generated by orographic processes or other processes. In particular, little is yet known about the momentum flux carried by nonorographic waves on a global scale. Numerical simulations tend to show that these waves play an important role in the mean thermodynamic state of the middle atmosphere (e.g., Eyring et al. 2006). Nonorographic waves can be generated by a wide variety of processes: deep convection, midlatitude jets and fronts, geostrophic adjustment, etc. During Vorcore, however, because most observations were gathered at polar and subpolar latitudes, it is reasonable to expect a stronger contribution

96 3064 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 65 of wave sources other than deep convection, which is predominantly expected in the tropics. It is thus of some importance to try to distinguish in the Vorcore dataset the respective role of orographic and nonorographic waves in carrying the momentum fluxes reported in the previous sections. As described in Vincent et al. (2007), the approach that we took was to use a very simple geographical criterion based on the topography gradient computed from the NOAA 5 5 gridded elevation dataset. Each of the geographical boxes that we used previously was thus flagged as orographic or nonorographic depending on the mean of the 10% largest elevation gradient within the box. Typically, most of western West Antarctica, the Antarctic coast and peninsula, as well as the tip of South America were flagged as orographic [see Fig. 3 of Vincent et al. (2007)]. On the other hand, the Antarctic Plateau and the austral ocean (including islands) were flagged as nonorographic. This classification is obviously an oversimplification as nonorographic waves may be produced over areas with steep topography, while orographic waves may propagate over flat terrain and be observed by the balloons there. To limit this last effect, we also flagged boxes located in the direct lee of the Antarctic Peninsula as orographic. We believe that our classification tends to give an upper-bound estimation to the actual momentum flux of orographic waves, whereas the converse is true for nonorographic waves. Figure 7 shows the results of this classification, that is, the latitudinal distribution of zonal-mean densityweighted absolute momentum flux carried by orographic and nonorographic waves, as well as the sum of both contributions. This figure obtained with the whole Vorcore dataset confirms the partitioning of GW momentum fluxes over the Antarctic continent reported in the study of Vincent et al. (2007) based on a single Vorcore flight. South of 70 S about two thirds of the total momentum flux is found over mountainous terrain and, thus, is likely to be associated with orographic waves. In agreement with the geographical distribution of total momentum flux reported above, this zonalmean orographic flux maximizes between 75 and 65 S, which corresponds to the latitudes of the Antarctic Peninsula. The distribution is totally reversed north of 65 S, where the zonal-mean GW momentum flux is almost entirely carried by nonorographic waves. Quite surprisingly, it is even found that the zonal-mean nonorographic momentum flux attains values larger than those associated with the zonal-mean orographic momentumflux above Antarctica. Consequently, the zonal-mean total momentum flux is found to be essentially independent of latitude north of 75 S. The importance of nonorographic waves above the FIG. 7. Latitudinal distribution of zonal-mean density-weighted absolute momentum flux 0 u w carried by orographic waves (thin solid), nonorographic waves (thin dashed), and by both types of waves (thick solid). The wave classification is based on a simple geographical criterion (see text). The latitudes used to plot the distribution correspond to the centers of the geographical boxes (e.g., the polarmost point is plotted at 87.5 S). southern oceans contrasts somewhat with the geographical distribution of total momentum flux displayed in Fig. 3. The discrepancies are explained by the fact that the values displayed in Fig. 3 correspond to local averages of total momentum flux, whereas Fig. 7 shows zonal means. Hence, even though momentum fluxes about 10 times larger than the zonal means are observed above the Antarctic Peninsula, the zonal average significantly reduces the importance of this location. On the other hand, momentum fluxes associated with nonorographic waves are much more zonally symmetric, so the values reported in Fig. 7 are of the same order as the fluxes observed above the oceans, as shown in Fig. 3. Figure 7 also shows that the nonorographic momentum fluxes exhibit significant variations from the South Pole to the southern midlatitudes. Values north of 60 S are 4 to 5 times larger than those south of 70 S. This maximum at the latitudes of the Southern Hemisphere storm tracks (Trenberth 1991) further supports the hypothesis that the nonorographic waves observed during Vorcore were associated with synoptic-scale tropospheric disturbances. Similar enhancements of GW activity were reported by Yoshiki et al. (2004) at Syowa when such disturbances were observed in the vicinity to the station. 5. Gravity wave intermittency An as yet poorly constrained parameter of several GW parameterizations is the so-called GW intermit-

97 OCTOBER 2008 H E R T Z O G E T A L FIG. 8. Intermittency of absolute momentum fluxes computed with (left) the Bernoulli proxy and (right) the percentile proxy (see text). Values close to 1 indicate continuous occurrence; values close to 0 indicate large variability. tency factor, that is, the measure of the probability with which the parameterized wave source effectively generates GW packets. Source intermittency has profound consequences on GW forcing of the mean flow. For instance, for a given long-term mean momentum flux, waves produced by an intermittent source will break lower in the atmosphere than those produced by a steady source (see, e.g., Bühler 2003; Piani et al. 2004). Long-duration balloons, which can stay in the atmosphere for months and sample wide geographic areas, are particularly well suited to characterize the intermittency of the GW field irrespective of the underlying surface or weather conditions. Here, two methods are applied to the balloon dataset to characterize GW intermittency. The first method is very similar to that used by Bühler (2003). It consists of considering wave sources that sporadically emit packets that always have the same amplitude so that the source has on and off phases. Such behavior is mathematically modeled by a random Bernoulli process, and the probability with which the source emits GW, the intermittency, can be computed from the expectation and the variance 2 of the Bernoulli process; that is, This equation is equivalent to (27) in Bühler (2003). In this approach, GW intermittency is thus estimated simply from the expectation and mean of the absolute momentum-flux probability distribution function (pdf) in each of the geographical boxes. It is displayed in the left panel of Fig. 8. Although this is generally the approach used in GW parameterization schemes, it is obviously oversimplified since, more realistically, wave sources generate waves with varying amplitudes. A better proxy of GW intermittency should rely therefore on the whole pdf of the momentum flux distribution rather than on its two first moments (Piani et al. 2004). A first step in that direction is the second approach that we applied to the Vorcore dataset. In this approach, we define the intermittency as 2 p 0.5 p 0.9, where p 0.5 and p 0.9 are, respectively, the 50% (i.e., the median) and 90% percentiles of the momentum-flux pdf in each geographical box. The resulting intermittencies are shown in the right panel of Fig. 8. Although the GW intermittencies obtained with both methods differ in magnitude, the relative variations within each map are well correlated. Actually, the absolute magnitude of the GW intermittency computed with the second method is not very significant as it depends strongly on the quantiles in (3); one could, for instance, use the 80% percentile rather than p 0.9, which would increase 2. What stands out from the two maps in Fig. 8 is that the most intermittent sources, associated with the low- 3

98 3066 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 65 est probability of observation, are found above mountainous areas, such as the Antarctic Peninsula, the Ellsworth Range, and the Antarctic coast in several places, including Adélie Land. In contrast, the probability of observing gravity waves is largest, and the intermittency smallest, above the oceans and to a lesser extent above the Antarctic Plateau. With the orographic classification used in the previous section, one obtains averaged values of 1 that amount to 0.09 over mountainous areas, 0.43 over flat areas, and 0.56 over the oceans north of 60 S. There is thus a clear distinction in the Vorcore observations between orographic waves that possess a very sporadic character and nonorographic waves in the midlatitudes that tend to be much steadier. This result is consistent with the variability of GW activity already noticed above the Antarctic Peninsula and also with previous findings from satellite observations and mountain wave modeling, which display large day-to-day variability (Eckermann and Preusse 1999; Jiang et al. 2002). If confirmed, such results would thus argue for intermittency parameters that vary with different sources in GWD parameterizations. It should be recognized, however, that intermittency derived from the balloon observations differs in several aspects from the intermittency used in GWD parameterizations. First, the intermittency obtained with the Vorcore observations is representative of the whole GW spectrum (within the observational limits specified above) and only depends on the geographical location. In contrast, the intermittency in AD99 depends on the phase-speed resolution used to represent the GW sources. More importantly, in GWD parameterizations the intermittency is an intrinsic property of a wave source. In our observations, on the other hand, the computed intermittency results from both the source intrinsic intermittency and the filtering of the wave packets by the mean flow. For instance, the propagation of small phase-speed orographic waves up to the balloon altitude depends strongly on the wind profile between the mountains and the balloons. This filtering can a priori have a nontrivial effect on the observed, acting to either increase or decrease it with respect to the wave source intermittency. At this stage it is unclear if wind filtering has a systematic effect and biases the observed intermittency. This possible systematic effect can be assessed in the future with ray-tracing simulations. 6. Discussion FIG. 9. The thick line shows the intrinsic-frequency power density spectrum of absolute momentum flux ( 0 u w / ˆ ) obtained by averaging results from the 24 longest Vorcore flights. The thin lines show the 95% confidence interval. A ˆ 1 law is shown for reference. a. Momentum flux underestimation An important goal is to provide observational estimates of GW momentum fluxes at the Southern Hemisphere high latitudes in order to help improve GW drag parameterizations. However, as stated earlier, our values are likely to underestimate the actual GW flux. The first factor is caused by the algorithm used to compute the momentum fluxes from the balloon observations. Nevertheless, B08 demonstrated that this factor can be estimated from the corresponding attenuation produced in the retrieved GW kinetic energy. Using this proxy, we found that the analysis algorithm underestimates the momentum fluxes by 25% in the Vorcore dataset. As previously mentioned, the raw value of the campaign-averaged absolute momentum flux is 2.5 mpa. Applying the correction factor yields a value of 3.2 mpa for the absolute momentum flux carried by the gravity waves discussed here. Another factor leading to underestimation is caused by the observational filter associated with the sampling rate used during Vorcore. Only the low intrinsic frequency part of the spectrum is addressed in this study. Momentum fluxes carried by waves with intrinsic periods ranging from the Brunt Väisälä period up to 1 h are missed. To estimate the contribution of the highfrequency waves to the total GW momentum flux, we show in Fig. 9 the campaign-averaged wavelet spectrum of absolute momentum flux. This spectrum roughly scales as the inverse of the intrinsic frequency at frequencies higher than twice the (campaign averaged) inertial frequency. If we assume that such scaling is valid up to the Brunt Väisälä frequency, the resolved and unresolved momentum flux should be comparable (to within about 10%):

99 OCTOBER 2008 H E R T Z O G E T A L f 2 1h N ˆ 1 d ˆ ˆ 2 1h 1 d ˆ, given typical values for the buoyancy (2 /N 5 min) and inertial (2 /f 12 h) periods. Notice, however, that there is likely to be more momentum flux in the resolved periods owing to the small enhancement in the spectrum close to the inertial frequency, which is associated with the ubiquitous presence of quasi-inertial waves in the balloon observations (Hertzog et al. 2002). Hence, the upper bound to the total absolute GW momentum flux during the campaign is likely to be about 6.4 mpa. We also note that the spectrum displayed in Fig. 9 exemplifies an important aspect of quasi- Lagrangian observations. At these high latitudes there is a clear separation in the balloon dataset between GW ( ˆ f) and the longer period motions due to planetaryscale Rossby waves for which the energy maximizes at much longer periods than the inertial period. The absence of such scale separation is often an issue in more classical observations such as radiosonde soundings, where a high-pass spatial filter has to be applied to isolate gravity waves. b. Gravity waves generated by katabatic winds Somewhat of a surprise in our results is the near lack of momentum flux enhancement at the border of Antarctica, with the exception of a small region between 140 and 150 E, Adélie Land. The eastern Antarctic coast is actually the location of strong katabatic winds that descend from the Antarctic Plateau to the ocean (Parish and Bromwich 2007), which can favor the generation of orographic gravity waves (Watanabe et al. 2006). Two factors may explain this behavior. First, the Vorcore dataset is mostly representative of late winter and spring conditions. Katabatic winds result from the radiative cooling of near-surface air over the Antarctic Plateau and therefore maximize around the winter solstice. It is possible, therefore, that the balloon flights did not occur at the optimum time to observe orographic waves generated by katabatic winds. Another possible reason for the absence of GW enhancement along the Antarctic coast is the presence of critical levels in the troposphere for orographic waves generated by katabatic winds, preventing them from propagating to balloon flight levels in the stratosphere. Watanabe et al. (2006) reported such critical levels in their GCM simulation of flow over Antarctica. Actually, near-surface winds mainly blow from the south or south-southeast during katabatic wind episodes, whereas the stratospheric flow is mainly eastward. During such periods, the wind therefore veers by at least 4 90 and likely prevents the propagation of orographic gravity waves into the stratosphere. Such filtering of the waves by the mean wind can also explain the low observational probability of wave events over Adélie Land (see Fig. 8): a continuous northward component of the wind from the surface to the stratosphere (implying a disturbed vortex) is needed for the waves generated by katabatic winds to reach the stratosphere. c. Comparison with CRISTA and HIRDLS Apart from long-duration superpressure balloon measurements, there have been only two estimations of GW momentum flux on a global scale. Both of them have been obtained with limb-sounding instruments, either with CRISTA in November 1994 (CRISTA-1) and August 1997 (CRISTA-2) (Ern et al. 2004, 2006) or with HIRDLS onboard Aura in May 2006 (Alexander et al. 2008). The temperature profiles recorded during these satellite missions were used to detect the amplitudes of GW-induced disturbances, as well as the wave vertical and horizontal wavelengths, from which absolute values of GW momentum fluxes were derived. Unfortunately, in both cases, the satellite orbits were such that the spaceborne observations only marginally overlap with those of the Vorcore balloons. In this section, we will nevertheless compare our momentum flux estimates with those obtained during the first CRISTA mission since this dataset was recorded in roughly the same period of the year as the Vorcore campaign. During CRISTA-1, no observations were performed south of 57 S. Therefore, to compare both datasets, only the balloon observations performed in the S latitude band were used. Balloonborne absolute momentum fluxes ( 0 u w ) were furthermore multiplied by (1 f 2 / ˆ 2) to compute the wave pseudomomentum flux, which is the quantity used in Ern et al. (2004, 2006). This operation is easily done with the Vorcore dataset as the wave intrinsic frequencies are directly inferred from the balloon observations. On the other hand, the CRISTA-1 observations were restricted to S and were corrected for aliasing, as described in Ern et al. (2006). Vorcore and CRISTA-1 results are compared in Fig. 10. The campaign-averaged Vorcore pseudomomentum fluxes, as well as those representative of November 2005 to better match the CRISTA period, are shown in this figure. Both momentum flux estimates agree very well. In particular, the signature of the southern Andes (at 70 W) is observed in both datasets. The larger magnitude of the CRISTA pseudomomentum flux in this region possibly results from the relatively poor sampling of that region by the Vorcore balloons (see, e.g., Fig. 3), from the interannual variability of GW

100 3068 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 65 FIG. 10. Longitude distribution of horizontal pseudomomentum flux, i.e., 0 (1 f 2 / ˆ 2) u between 50 and 60 S estimated from the long-duration balloon observations (thick solid) averaged over the whole Vorcore campaign and (thin solid) in November 2005: (thin dashed) estimated from CRISTA-1 radiances at 22 km in November 1994 between 50 and 57 S. activity in the stratosphere, or from an overcorrection for aliasing effects in the CRISTA momentum fluxes. More strikingly, excellent agreement is observed above the Atlantic and Indian Oceans, where Vorcore observations are more numerous than above the Pacific. Such agreement between two very different techniques gives further confidence in the GW momentum flux values reported in this study and in the previous work on CRISTA datasets. Finally, there is also good qualitative agreement between Vorcore and HIRDLS observations, despite the fact that the HIRDLS measurements only extend as far as 60 S (Alexander et al. 2008). Once again, the largest fluxes observed with HIRDLS occur near the southern tip of South America. Over the oceanic regions, the largest fluxes occur over the South Atlantic and Indian Oceans with smallest fluxes over the South Pacific, in good agreement with the balloon findings. 7. Conclusions Characteristics of gravity waves over Antarctica observed during long-duration superpressure balloon flights performed from September 2005 to February 2006 are reported. The observations enable us to derive momentum fluxes carried by the waves in the lower stratosphere. The largest fluxes were found above the mountainous western Antarctica and especially over the Antarctic Peninsula. Over the latter region the time-averaged momentum flux locally reached values 10 times larger than the overall mean momentum flux computed with the balloon observations. Because of its steep orography and of its roughly north south orientation, the Antarctic Peninsula is confirmed as a very active area for the generation of gravity waves and, therefore, is likely to have a profound impact not only on the dynamics of the SH polar stratosphere but also on its chemistry and microphysics (Höpfner et al. 2006; Noel et al. 2008). The signature of waves generated by katabatic winds was found to be rather small except over Adélie Land where a significant enhancement of southward momentum flux was found. Westward zonal momentum fluxes were larger than eastward fluxes, indicating that waves that reached the stratosphere were propagating predominately against the mean flow. On the other hand, meridional momentum fluxes did not display any net contribution. Finally, the momentum fluxes were generally larger at the beginning of the campaign (September October) than at the end (December January). Mechanisms responsible for wave generation were explored. A simple geographic proxy was used to determine whether waves were generated by orographic processes. Mountain waves were found to account for about two thirds of the total momentum flux over Antarctica. Interestingly, we found zonally averaged fluxes over the ocean similar in magnitude to those above the continent, which underlines the importance of nonorographic gravity waves in the SH polar and subpolar latitudes. The intermittency of GW events in the balloon dataset was assessed. Mountain waves were found to be significantly more sporadic than the waves observed above the ocean. Acknowledgments. The authors would like to express their acknowledgements to the CNES programme subdirectorate and to INSU for their longstanding support of the Stratéole/Vorcore project. We are especially indebted to the CNES balloon sub-directorate and to the LMD technical staff for the successful superpressure balloon campaign in Antarctica. The NSF is thanked for its decisive support during the operations in Mc- Murdo. Manfred Ern and Peter Preusse kindly provided the CRISTA data used in the article, as well as useful information on the CRISTA observations. The relief dataset used in this study (etopov5) was provided by NOAA. RAV acknowledges travel support from the Scientific Visits to Europe Scheme of the Australian Academy of Science and Department of Science and Environment, and the visiting program from École Polytechnique. Lastly, the authors thank the two anonymous reviewers who contributed to significantly improve the manuscript. REFERENCES Alexander, M. J., 1998: Interpretations of observed climatological patterns in stratospheric gravity wave variance. J. Geophys. Res., 103,

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103 5.2. APPLICATION DE LA MÉTHODOLOGIE À LA CAMPAGNE VORCORE 97 FIG. 5.3 Variance deρu w. (Alexander et al., 2002)), alors que les ondes orographiques sont émises de manière plus intermittente. Dans le cas de la variance, les zones pour lesquelles la variance est importante coincident avec des zones où quelques valeurs de forte amplitude se démarquent fortement de la moyenne et peuvent correspondre à des sources d ondes orographiques. La figure 5.3 montre la variance moyennée sur des zones de 10 o en longitude et 5 o en latitude, comme dans Hertzog et al. (2008). Les zones où la variance est la plus importante correspondent à des régions montagneuses comme la péninsule antarctique, l ouest de l Antarctique et la terre d Adélie où les vents catabatiques peuvent engendrer des ondes de gravité. Ces résultats sont donc cohérents avec les résultats d intermittence présentés dans Hertzog et al. (2008). Néanmoins, la zone située entre 55 o S et 60 o S, et 50 o E et 60 o E, où la variance est importante, est située dans l océan, ce qui montre que les distributions de variances ne sont pas suffisantes pour déduire l intermittence des sources d ondes de gravité. Distribution deρu w en fonction de la latitude équivalente La distribution deρu w a également été analysée en fonction de la position des BPS par rapport au bord du vortex. En effet, des études comme Baumgaertner and McDonald (2007) ont mis en

104 98 CHAPITRE 5. APPLICATION À LA CAMPAGNE VORCORE FIG. 5.4 Distribution deρu w en fonction de la latitude équivalente du ballon soustraite à la latitude équivalente du bord du vortex. En noir, la moyenne prend en compte toutes les valeurs, en bleu, les points correspondants à des zones montagneuses ont été éliminé. Concernant l axe des abscisses, les valeurs positives correspondent à l intérieur du vortex, et les valeurs négatives à l extérieur du vortex. évidence une augmentation de l énergie potentielle transportée par les ondes de gravité près du bord du vortex. La figure 5.4 montreρu w en fonction de la position du ballon par rapport au bord du vortex (en noir) : c est-à-dire la latitude équivalente du ballon soustraite à la latitude équivalente du bord du vortex. Ces quantités ont été calculées à partir des analyses opérationnelles de l ECMWF en cherchant l annulation de la dérivée seconde de la vorticité potentielle. Les moyennes des flux de quantité de mouvement ont été effectuées sur des intervalles de 2 o en latitude équivalente. Nous observons effectivement une augmentation près du bord du vortex, ainsi qu une valeur forte à l intérieur du vortex. La courbe en bleu dans la figure 5.4 correspond aux points attribués aux zones non orographiques selon le critère détaillé dans Hertzog et al. (2008). Dans ce cas, la valeur extrême disparait ce qui suggère que cette valeur est liée à des fortes ondes de gravité orographiques. Cependant, l augmentation près du bord du vortex, bien que relativement faible, reste présente ce qui suggère que nos résultats sont en accord avec ceux de Baumgaertner and McDonald (2007).

105 5.3. COMPARAISON INTERHÉMISPHÉRIQUE Comparaison interhémisphérique Les données Vorcore ont permis d estimer le flux de quantité de mouvement transporté par les ondes de gravité au sud de 50 o S. Or en 2002, cinq BPS ont également été lâchés dans l hémisphère nord lors d une campagne préparatoire à la campagne Vorcore, à partir de la base de Kiruna, en Suède. A partir de ces données, et en utilisant un seul vol de la campagne Vorcore (pour avoir un nombre équivalent de jours de vol), une comparaison des flux de quantité de mouvements transportés aux pôles nord et sud a pu être conduite. Les flux estimés sont plus importants dans l hémisphère sud (3.4 mpa) que dans l hémisphère nord (2.6 mpa), mais ce résultat reste à confirmer car il est peut-être biaisé par un échantillonnage moins complet de l hémisphère nord. De manière générale, les régions les plus actives sont situées au dessus des régions montagneuses. Néanmoins, une partie du flux est transporté au dessus des océans, ce qui suggère que les ondes non orographiques possèdent des sources non négligeable dans les régions polaires. Cet article a été publié dans Geophysical Research Letter en octobre Article : Quasi-Lagrangian superpressure balloon measurements of gravitywave momentum fluxes in the polar stratosphere of both hemispheres

106 Click Here for Full Article GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L19804, doi: /2007gl031072, 2007 Quasi-Lagrangian superpressure balloon measurements of gravitywave momentum fluxes in the polar stratosphere of both hemispheres R. A. Vincent, 1 A. Hertzog, 2 G. Boccara, 2 and F. Vial 2 Received 21 June 2007; revised 15 August 2007; accepted 4 September 2007; published 3 October [1] Superpressure balloons were flown in 2002 and 2005 in the winter polar vortices of both hemispheres. The balloons can drift for months in the stratosphere acting as quasi- Lagrangian tracers of air-parcel motions. The meteorological datasets acquired are used to retrieve small-scale internal atmospheric gravity wave parameters using wavelet techniques. For the first time, gravity wave momentum fluxes are estimated over wide geographical areas and the results will help constrain gravity wave parameterization schemes used in general circulation climate models. The importance of mountain waves is confirmed, with largest fluxes observed in the lee of Greenland and the Antarctic Peninsula. However, significant momentum fluxes are also observed over the oceans, showing the importance of other wave generation mechanisms. Citation: Vincent, R. A., A. Hertzog, G. Boccara, and F. Vial (2007), Quasi- Lagrangian superpressure balloon measurements of gravity-wave momentum fluxes in the polar stratosphere of both hemispheres, Geophys. Res. Lett., 34, L19804, doi: /2007gl Introduction [2] Internal atmospheric inertia-gravity (buoyancy) waves efficiently transfer energy and momentum from source regions in the lower atmosphere to the upper atmosphere and play a role in determining the state of the atmosphere and climate. The decrease of atmospheric density with height produces an exponential growth of wave amplitudes, leading to wave breaking and dissipation. At the solstices the resulting momentum transfer to the mean flow drives a pole-to-pole meridional circulation that profoundly affects the chemical composition and the thermal structure of the middle atmosphere [e.g., Holton et al., 1995]. Gravity waves (GW) are also linked to the formation of polar stratospheric clouds and the associated microphysical processes that play a crucial role in ozone destruction [Eckermann and Preusse, 1999; Höpfner et al., 2006]. GW are generated over a wide range of temporal and spatial scales by a variety of sources, including flow over mountains, convection, flow adjustment and wind shear [Fritts and Alexander, 2003]. Accounting for GW effects in global atmospheric circulation models (GCM) requires understanding of geographical and temporal variability, generation mechanisms and resulting wave characteristics. 1 Department of Physics, University of Adelaide, Adelaide, South Australia, Australia. 2 Laboratoire de Météorologie Dynamique, École Polytechnique, Palaiseau, France. Copyright 2007 by the American Geophysical Union /07/2007GL031072$05.00 [3] GW effects are usually parameterized in models since explicit simulation of a full 3-dimensional wave spectrum and its evolution with altitude is computationally intensive. A variety of parameterization schemes have been proposed that involve a description of the distribution of momentum flux as a function of ground-based phase speed or its equivalent [Hines, 1997; Alexander and Dunkerton, 1999; Warner and McIntyre, 2001]. Such schemes suffer from a lack of observational constraints. The wide variety of tunable parameters means that a model tuned for one set of parameters cannot be used in any prognostic manner [Charron et al., 2002]. [4] Information on GW momentum fluxes on a global basis is difficult to obtain. A variety of techniques that use large ground-based radars, radiosondes and satellite limb sounding or radio-occultation methods have been used [e.g., Eckermann and Preusse, 1999; Tsuda et al., 2000; Ern et al., 2004], but suffer from either poor geographic coverage or require a number of assumptions that cannot easily be tested. Ground and space-based techniques are usually unable to measure the wave intrinsic frequency (the frequency measured in a reference frame moving with the background wind), which determines important wave properties [Gossard and Hooke, 1975]. [5] Measurements made with balloons that drift quasihorizontally with the background wind do not suffer this limitation. The use of superpressure balloons (SPB) to study GW was pioneered by Massman [1981] who analyzed data acquired in the southern hemisphere during the Tropical Wind, Energy Conversion and Reference Level Experiment (TWERLE). At the float level, the gas inside the closed envelope of a SPB is kept at a pressure greater than that of the ambient atmospheric pressure. The balloon always remains spherical during flight and experiences vertical displacements of less than 20 m at sunrise/sunset so it is advected by the horizontal wind on a constant density surface. Here we present recent ultra-long-duration SPB observations that provide measurements of wave fluxes over wide geographical areas in the lower stratosphere of the polar regions of both hemispheres. 2. Observations [6] The balloons used in this study were developed by the French Space Agency (CNES) in the framework of the Stratéole-Vorcore project. Balloons of 8.5-m and 10-m diameter float at respective altitudes of about 17 and 19 km, equivalent to pressure levels of p o 75 hpa and p o 55 hpa in the polar wintertime stratosphere. Six SPB test flights were launched from Kiruna (68 N, 20 E) in the Arctic in early February The longest flight duration achieved during this campaign was 45 days, with most of L of5

107 L19804 VINCENT ET AL.: SPB STUDIES OF GRAVITY WAVES L19804 Figure 1. (a) Trajectories of SPB launched from Kiruna in early February The last flight terminated on March 21. (b) Trajectory of Vorcore SPB-11 (8.5-m diameter) launched on 23 September 2005 from McMurdo. The flight terminated on 26 December. the flights automatically cut-down when crossing 55 N (a limit imposed so as to avoid flying over populated areas). During the Vorcore campaign, 27 SPB were released from McMurdo, Antarctica (78 S, 167 E) between September 5 and October 28, The longest Vorcore flight lasted 109 days and the mean flight duration during the campaign was about 59 days [Hertzog et al., 2007]. [7] Each balloon carried a light gondola to perform scientific observations and to monitor the balloon flight safety. Air temperature and pressure were recorded every 15 min with an accuracy, respectively, of 0.3 K and 1 Pa, the latter value corresponding to vertical displacements of about 1 m. Global Positioning System (GPS) measurements were used to determine balloon location with an accuracy of 10 m in the horizontal and 20 m in the vertical. Zonal and meridional wind speeds along the flight track were obtained by finite differencing of successive 15-min GPS positions to an accuracy of better than 0.1 ms 1. Data were uploaded to the ARGOS satellite system for transmission to ground stations, with the ARGOS bandwidth determining the effective sampling rate. [8] The results presented in this article were obtained from five flights in the Kiruna 2002 campaign and one from the McMurdo 2005 campaign, in order to have about the same number of observation days in both case studies. Trajectories of these flights are shown in Figure 1. All Arctic flights occurred within the polar stratospheric vortex, as well as the major part of the Antarctic flight. This means that orographic (zero phase speed) waves were still able to penetrate into the Antarctic stratosphere and so the seasonal discrepancy between the northern and southern flights is compensated for by the longer duration of the SH vortex. 3. Data Analysis 3.1. Estimation of Momentum Flux [9] As a SPB drifts under the influence of the background wind it experiences perturbations in velocity, pressure and temperature induced by inertia gravity waves. One problem with the present SPB system is that the relatively poor accuracy of the vertical position measurements precludes direct calculation of the vertical velocity and hence a direct estimate of the flux of momentum. Instead we use the crossspectrum between the pressure and horizontal velocity, which can be related to the momentum flux with the assumption that there are only upward-propagating waves in the lower stratosphere. [10] Analysis of the SPB data starts by noting that GW horizontal velocity perturbations are elliptically polarized, with the major axis of the ellipse aligned along the horizontal direction of propagation [Gossard and Hooke, 1975]. Furthermore, the GW pressure perturbation p 0 is due to two components. The first (Eulerian) component is the pressure disturbance induced directly by the wave. The second (Lagrangian) component is caused by the vertical motion in the presence of the background pressure gradient. These two components are in quadrature and both are proportional to uk, 0 the horizontal perturbation velocity aligned with the major axis of the perturbation ellipse. Hertzog and Vial [2001] describe in more detail how the momentum flux is derived from the pressure and horizontal velocity components Wavelet Analysis [11] In practice, the measured fluctuations are caused by the superposition of a wide spectrum of gravity wave packets generated by different sources and propagating in different directions. Wavelet analysis is well suited for extracting the fluxes from the time series of the horizontal velocity and pressure since it decomposes data as a function of intrinsic-period (frequency) and time (space) [Torrence and Compo, 1998; Zink and Vincent, 2001]. Here, the complex Morlet wavelet, which has a Gaussian envelope, was used for its packet-like qualities. [12] Let ~p, ~u and ~v be the respective wavelet transforms of pressure, zonal and meridional velocity. A first selection is performed among the wavelet coefficients to retain only those that pass several criteria, including signal-to-noise ratios larger than a predetermined threshold and intrinsic periods ranging from 1 hour to the local inertial period. [13] The wave directions of propagation are then found by rotating the horizontal axes of the polarization ellipse and maximizing the ratio of parallel ~u k to perpendicular ~u? 2of5

108 L19804 VINCENT ET AL.: SPB STUDIES OF GRAVITY WAVES L19804 Figure 2. (a) Topography in km of the high-latitude Northern Hemisphere. (b) Geographic distribution of densityweighted momentum fluxes in the propagation direction of the waves. (c) Density-weighted zonal and (d) meridional momentum fluxes for the Arctic. (e, f, g, h) Same as for Figure s 2a 2d, but for the high-latitude Southern Hemisphere. Bins with less than 20 observations are left blank in the momentum maps. (aligned with the ellipse minor axis) velocity fluctuations. The local contribution to the momentum flux is then ~u jj ~w* ¼ ^wg p o N 2 I ~p~u jj* : ð1þ where ^w is the intrinsic frequency, g is the acceleration due to gravity, p o the pressure at the float level, N is the buoyancy frequency, I signifies imaginary part, and the asterisk denotes the complex conjugate. [14] Lastly, the mean momentum flux along the flight u 0 jj w0 is recovered by summing the selected individual contributions according to the wavelet Parseval s theorem [Torrence and Compo, 1998]. The same procedure is followed to obtain the mean zonal and meridional components, except that the individual contributions of total momentum flux are first projected on the zonal and meridional directions Numerical Simulations [15] A large number of Monte-Carlo type simulations were performed to test the technique and understand its limitations and uncertainties. Time series were generated by flying balloons through a model that mimicked the observations with realistic noise and sampling rates. Each series contained one or more wave packets that were allowed to propagate in the model. Wave characteristics, such as direction, phase speed and period, were randomly assigned; the only restrictions were that each packet consisted of at least two oscillations and that the amplitude was small enough to preclude wave instabilities. The amplitudes were chosen so that they satisfied observations that show an approximate ^w 2 spectral distribution [Hertzog and Vial, 2001]. [16] It is found from simulations with a single gravitywave packet in each time series that wave directions of propagation are almost perfectly retrieved. Due to the selection performed among the wavelet coefficients, the momentum flux tends to be underestimated on average by about 10% with an uncertainty of about 10%, which is still an order of magnitude better than space-borne estimations [Ern et al., 2004]. The 15-min data rate results in undersampling of the highest-frequency waves (periods 1 hr), and produces poor momentum-flux retrievals for those waves. [17] In practice, however, several wave packets are likely to be present simultaneously, and so time series with either two or ten wave packets were used to evaluate the consequences for the retrieval of wave parameters. In these situations the relations between velocity and pressure wavelet coefficients are modified when wave packets locally overlap in time-frequency space. The analysis tends to discard those coefficients, which leads to further underestimation of momentum fluxes. Typically, 80% of the input momentum flux is retrieved in the 10-wave time series, while the uncertainty is unchanged (10%). 4. Results [18] The retrieved momentum fluxes can be decomposed in a variety of ways, as shown in Figure 2. The geographical decompositions of the density-weighted momentum fluxes in the wave propagation direction appear in Figures 2b and 2f in 5 20 latitude-longitude bins (except around the pole). In the northern hemisphere (NH), the geographical variabil- 3of5

109 L19804 VINCENT ET AL.: SPB STUDIES OF GRAVITY WAVES L19804 Figure 3. (a) Geographical bins assumed to generate only orographic waves (either classical lee waves or waves generated by katabatic flow) (black), and only non-orographic waves (most likely jet and adjustment processes at sub-polar latitudes) (white). (b) Zonal-mean density-weighted momentum fluxes in the propagation direction of the wave (r o u 0 jj w0 ) produced by orographic waves (gray dashed), and non-orographic waves (gray solid). The sum of both fluxes (the zonal-mean total flux) is shown with the black solid curve. The fluxes are plotted at the mean latitude of each latitudinal band. ity is dominated by large fluxes near mountainous regions (Figures 2a and 2b) such as along the edges of Greenland, the Scandinavian Peninsula and Eastern Siberia. In the southern hemisphere (SH) the most active areas are found in the vicinity of the Antarctic Peninsula and the Transantarctic mountains (Figures 2e and 2f), which agrees with satellite observations of wave-induced temperature disturbances [Wu and Jiang, 2002; Jiang et al., 2004; Wu and Eckermann, 2007]. However, significant momentum flux is also observed in oceanic regions and is thus associated with non-orographic gravity-wave sources. The magnitude of the fluxes are clearly different in both hemispheres, with mean values of 3.4 mpa observed in the southern hemisphere compared with 2.6 mpa in the northern hemisphere. This is mostly caused by the momentum fluxes observed above the Antarctic Peninsula that exceed by a factor of 2 the momentum fluxes in every other sampled region. However, this hemispheric contrast may require further confirmation since the NH was not sampled as homogeneously as the SH. In particular, no observations were made in the western hemisphere and therefore potentially significant GW sources were missed, such as the Alaskan Brooks Range. [19] Figures 2c and 2g display the density-weighted zonal momentum fluxes. Strikingly, the zonal momentum flux is negative almost everywhere, which indicates that the vast majority of GW are propagating against the mean eastward flow characteristic of the wintertime stratosphere. The largest westward fluxes are found above or in the lee of major orography, and locally reach 12 mpa over the Antarctic Peninsula. Note that the flux in a given region is both a spatial and temporal average of all the balloon passages in this region (as are all values reported in this article) and may cover both mountainous and oceanic surfaces. Much stronger individual wave packets that had fluxes 50 times larger than the average were locally observed directly above the Peninsula, as also reported from the ER-2 aircraft measurements of Bacmeister et al. [1990]. Away from the mountains, the average zonal fluxes are typically smaller than 3 mpa. [20] The meridional momentum fluxes are displayed in Figures 2d and 2h. In contrast to the zonal momentum fluxes, they are generally smaller in magnitude and both positive and negative values are observed, respectively associated with northward- and southward-propagating waves. The NH values are uniformly small. In the SH significant positive values (10 mpa) are observed in the vicinity of the Antarctic Peninsula (likely associated with the main orientation of the ridges), whereas negative values with smaller magnitudes (3 mpa) are generally found above the southern oceans. [21] A simple geographical criterion is used to distinguish between the relative role of orographic and non-orographic GW momentum fluxes in the SH. Waves observed above areas with steep topography and in their direct lee are assumed to be generated by mountain processes, including waves produced by katabatic winds. The algorithm used to flag the orographic areas is as follows: starting from the NOAA 5 00 x5 00 gridded elevation dataset the gradient of elevation was computed at the same resolution. The mean of the 10% largest gradients were then calculated for each latitude-longitude bin. The bins for which the mean exceeds a (conservative) threshold value of 15 m km 1 were flagged as orographic. A few areas located directly in the lee of major orography (such those to the east of the Antarctic Peninsula) were also included. All waves observed elsewhere are assumed to have a non-orographic origin, probably adjustment, frontal and jet processes at the latitudes considered. Figure 3a displays the areas that are assumed to generate mountain waves. Note in particular the asymmetry between the mountainous West Antarctica and the smoother East Antarctica. [22] The result of this partition of momentum is displayed in Figure 3b. Orographic waves carry about 2/3 of the total momentum flux above Antarctica. Our results therefore confirm the predominance of wave activity over western Antarctica, which has been invoked as a potential factor to explain the PSC asymmetry above the continent [Höpfner et al., 2006]. The largest values of zonal-mean momentum flux associated with orographic waves are observed at latitudes that correspond to the Peninsula. It should be emphasized, however, that the relative decrease of orographic momentum flux between 65 S and 70 S should not be misinterpreted as it may result from the absence of observations in that latitudinal band over the Peninsula. [23] On the other hand, the momentum flux associated with non-orographic waves shows two distinct patterns, 4of5

110 L19804 VINCENT ET AL.: SPB STUDIES OF GRAVITY WAVES L19804 with small values at the highest latitudes, and an abrupt increase north of 65 S. Zonal-mean values of 3 mpa are observed above the Southern Ocean. These oceanic values are strikingly similar to the fluxes produced by orographic waves at the edge of Antarctica and therefore emphasize the importance of non-orographic gravity waves in the global transport of momentum. The mechanism(s) that generates these waves is uncertain, but the predominance of their observation above the oceans obviously means that they have a non orographic origin. Although further confirmation is needed, adjustment of tropospheric disturbances toward geostrophic balance may explain the enhanced observation of GW fluxes at latitudes corresponding to the tropospheric storm tracks [O Sullivan and Dunkerton, 1995]. Future work will examine the relationship between wave fluxes and sources. [24] Acknowledgments. The support of CNES and CNRS/INSU is gratefully acknowledged. The project also benefited from the help of IPEV and from NSF. The Vorcore technological and operational success resulted from the collaboration between the CNES balloon subdirectorate and LMD. RAV acknowledges travel support from the Scientific Visits to Europe Scheme of the Australian Academy of Science and Department of Science and Environment. References Alexander, M. J., and T. J. Dunkerton (1999), A spectral parameterization of mean-flow forcing due to breaking gravity waves, J. Atmos. Sci., 56, Bacmeister, J. T., M. R. Schoeberl, L. R. Lait, P. A. Newman, and B. Gary (1990), ER-2 mountain wave encounter over Antarctica: Evidence for blocking, Geophys. Res. Lett., 17, Charron, M., E. Manzini, and C. D. Warner (2002), Intercomparison of gravity wave parameterizations: Hines doppler-spread and Warner and McIntyre ultra-simple schemes, J. Meteorol. Soc. Jpn., 80, Eckermann, S. D., and P. Preusse (1999), Global measurements of stratospheric mountain waves from space, Science, 286, Ern, M., P. Preusse, M. J. Alexander, and C. D. Warner (2004), Absolute values of gravity wave momentum flux derived from satellite data, J. Geophys. Res., 109, D20103, doi: /2004jd Fritts, D. C., and M. J. Alexander (2003), Gravity wave dynamics and effects in the middle atmosphere, Rev. Geophys., 41(1), 1003, doi: /2001rg Gossard, E. E., and W. H. Hooke (1975), Waves in the Atmosphere, Elsevier, New York. Hertzog, A., and F. Vial (2001), A study of the dynamics of the equatorial lower atmosphere by use of ultra-long-duration balloons: 2. Gravity waves, J. Geophys. Res., 106, 22,745 22,761. Hertzog, A., et al. (2007), Stratéole/Vorcore long-duration, superpressure balloons to study the Antarctic lower stratosphere during the 2005 winter, J. Atmos. Oceanic Technol., in press. Hines, C. O. (1997), Doppler-spread parameterization of gravity-wave momentum deposition in the middle atmosphere. Part 1: Basic formulation, J. Atmos. Sol. Terr. Phys., 59, Holton, J. R., P. H. Haynes, M. E. McIntyre, A. R. Douglass, R. B. Rood, and L. Pfister (1995), Stratosphere-troposphere exchange, Rev. Geophys, 33, Höpfner, M., et al. (2006), MIPAS detects Antarctic stratospheric belt of NAT PSCs cause by mountain waves, Atmos. Chem. Phys., 6, Jiang, J. H., S. D. Eckermann, D. L. Wu, and J. Ma (2004), A search for mountain waves in MLS stratospheric limb radiances from the winter Northern Hemsiphere: Data analysis and global mountain wave modeling, J. Geophys. Res., 109, D03107, doi: /2003jd Massman, W. J. (1981), An investigation of gravity waves on a global scale using TWERLE data, J. Geophys. Res., 86, O Sullivan, D., and T. J. Dunkerton (1995), Generation of inertia-gravity waves in a simulated life-cycle of baroclinic instability, J. Atmos. Sci., 52, Torrence, C., and G. P. Compo (1998), A practical guide to wavelet analysis, Bull. Am. Meteorol. Soc., 79, Tsuda, T., M. Nishida, C. Rocken, and R. Ware (2000), Global morphology of gravity wave activity in the stratosphere revealed by the GPS occultation data (GPS/MET), J. Geophys. Res., 105, Warner, C. D., and M. E. McIntyre (2001), An ultrasimple spectral parameterization for nonorographic gravity waves, J. Atmos. Sci., 58, Wu, D. L., and S. D. Eckermann (2007), Global gravity wave variances from AURA MLS: Characteristics and interpretation, J. Atmos. Sci, in press. Wu, D. L., and J. H. Jiang (2002), MLS observations of atmospheric gravity waves over Antarctica, J. Geophys. Res., 107(D24), 4773, doi: / 2002JD Zink, F., and R. A. Vincent (2001), Wavelet analysis of stratospheric gravity wave packets over Macquarie Island: 1. Wave parameters, J. Geophys. Res., 106, 10,275 10,287. R. A. Vincent, Department of Physics, University of Adelaide, Adelaide SA 5005, Australia. (robert.vincent@adelaide.edu.au) G. Boccara, A. Hertzog, and F. Vial, Laboratoire de Météorologie Dynamique, École Polytechnique, F Palaiseau Cedex, France. (gillian.boccara@lmd.polytechnique.fr; hertzog@lmd.polytechnique.fr; vial@lmd.polytechnique.fr) 5of5

111 5.3. COMPARAISON INTERHÉMISPHÉRIQUE 105 Résumé Dans ce chapitre, nous avons appliqué la méthodologie du chapitre 3 aux données de la campagne Vorcore. Nous avons étudié plusieurs aspects de la distribution deρu w. Si les zones de montagnes semblent être des sources d ondes de gravité prépondérantes, nous avons également mis en évidence l importance des sources non-orographiques au dessus des océans. De plus, l intermittence des sources a été étudiée à l aide de deux approches concordantes, et cette étude suggère que les sources d ondes non orographiques émettent des ondes de gravité de manière continue par opposition aux sources d ondes orographiques qui émettent des ondes de manière sporadique. Ces résultats constituent une contribution importante aux études d intermittence qui sont pour l instant limitées (par exemple Alexander et al., 2002; Bühler, 2003). Enfin, la distribution du flux de quantité de mouvement en fonction de la position des BPS par rapport au bord du vortex a mis en évidence une légère augmentation près du bord du vortex en accord avec les résultats de Baumgaertner and McDonald (2007) sur l énergie potentielle. En résumé, la répartition spatiale et temporelle des BPS a été exploitée de manière complète pour discuter plusieurs aspects de la distribution du flux de quantité de mouvement. Notre méthodologie a donc permis une observation exhaustive des ondes de gravité se propageant dans la basse stratosphère antarctique. Comme nous l avons évoqué dans l introduction, de telles observations sont cruciales pour le développement des paramétrisations d ondes de gravité pour qu elles reproduisent au mieux les flux de quantité de mouvement. Le chapitre 7 va examiner plusieurs paramétrisations et tenter d établir une comparaison avec nos résultats.

112 106 CHAPITRE 5. APPLICATION À LA CAMPAGNE VORCORE

113 107 Chapitre 6 Précision des analyses et réanalyses stratosphériques Ce chapitre présente les résulats d une étude comparant les données de la campagne Vorcore, qui n ont été assimilées par aucun centre météorologique, aux champs de températures, de vitesses zonales et méridiennes issus des analyses opérationnelles du Centre Européen de Prévision Météorologique à Moyen Terme (CEPMMT, que nous allons désigné dans le reste de la thèse sous la forme European Center for Medium-Range Weather Forecasts ECMWF) et aux réanalyses 50-Year National Centers for Environment Prediction-National Center for Atmospheric Research (NCAR/NCEP, NN50) de température, vitesse zonale et vitesse méridionale. En effet, si l objectif principal de Vorcore était d observer les processus dynamiques stratosphériques de petite échelle, la campagne a également permis une observation à fine résolution de l atmosphère pendant près de cinq mois, dans une zone géographique qui reste mal documentée. Une première étude comparative a également été conduite entre les données Vorcore et des observations satellitaires. Les données en température ont été comparées avec les températures extraites des occultations radio faites par l instrument CHAMP/GPS (McDonald and Hertzog, 2008). Les deux jeux de données sont extrêmement proches compte tenu de leurs approches très différentes, car les écarts n excédent pas 0.5 K. De tels résultats renforcent la crédibilité et la fiabilité de nos observations et motivent des études plus exhaustives comme celle présentée dans ce chapitre.

114 108 CHAPITRE 6. PRÉCISION DES ANALYSES ET RÉANALYSES STRATOSPHÉRIQUES 6.1 Analyses et réanalyses Pour dégager des tendances climatologiques à long terme ou étudier des phénomènes physiques et chimiques de moyenne ou grande échelle, deux types de données sont couramment utilisés : les analyses et les réanalyses. Les analyses sont produites en assimilant des observations dans les prévisions issues de modèles de circulation générale et représentent une estimation de l état de l atmosphère qui fournit ensuite un nouvel état initial pour les prévisions (Polavarapu and Shepherd, 2005). La plupart des centres météorologiques produisent des analyses opérationnelles. Parmi eux, on peut citer : le United Kingdom Meteorological Office (UKMO), les NCEP/Climate Prediction Center (NCEP/CPC), et l ECMWF. Par opposition, les réanalyses sont construites en différé, en utilisant une version figée du modèle, un système d assimilation constant et en assimilant toutes les observations archivées de l époque concernée. Les plus connues sont les réanalyses ERA-40, produites par l ECMWF entre 1957 et 2001 (Uppala et al., 2005), et les réanalyses NN50 entre 1957 et 1996 (Kalnay et al., 1996). Le champ d application de ces 2 types de données est large et concerne : les tendances climatologiques à long terme de variables atmosphériques telles que la température, les précipitations, la vapeur d eau. Cependant, il existe des incertitudes concernant la distinction entre les vrais biais et les biais induits par l évolution du système d observation (Bengtsson et al., 2004). le forçage des variables météorologiques utilisées dans les modèles de chimie transport, comme le modèle stratosphérique REactive Processes Ruling the Ozone BUdget in the Stratosphere (REPROBUS) développé au sein de l Institut Pierre Simon Laplace (IPSL), ou le modèle Modélisation de la Chimie Atmosphérique Grande Echelle (MOCAGE) au Centre National de Recherche Météorologique (CNRM). le forçage aux bornes d un domaine régional pour des simulations méso-échelle, tels que les modèles Weather Research and Forecasting (WRF) ou Meso-Northern Hemisphere (Meso- NH). le calcul de trajectoires ou de rétrotrajectoires pour connaître l origine de particules d air (Verma et al., 2007) ou tracer le rapport de mélange d une espèce chimique dans une particule d air, par exemple dans le cas de la méthode MATCH (von der Gathen et al., 1995).

115 6.1. ANALYSES ET RÉANALYSES 109 le calcul de la vorticité potentielle et du coefficient de diffusivité pour identifier les barrières de transport et quantifier le mélange (Haynes and Shuckburgh, 2000). le calcul du flux d Eliassen-Palm et de sa divergence pour estimer l effet des ondes atmosphériques sur l écoulement moyen, par exemple pour diagnostiquer un réchauffement stratosphérique soudain (Newman and Nash, 2005). Ces études nécessitent des champs fiables de variables atmosphériques sur des longues durées. Elles concernent des régions plus ou moins étendues, voire l ensemble du globe. Manney et al. (2005) ont comparé les distributions de température produites par différentes analyses pendant l hiver 2002 en Antarctique, et ont trouvé des différences significatives d une analyse à l autre. Ainsi, la qualité des analyses et réanalyses diffère et il est important de l évaluer. La précision des analyses dépend des trois éléments majeurs suivants : Modèle de circulation générale Les processus physiques comme la convection, les précipitations, la turbulence dans la couche limite ou les ondes de gravité sont paramétrés dans les modèles. Pour chaque processus, une ou plusieurs paramétrisations existent qui sont basées sur des approches physiques différentes. Selon la paramétrisation choisie, les résultats seront différents, voir par exemple Charron et al. (2002) pour les ondes de gravité et le chapitre 7 qui porte sur les paramétrisations des ondes de gravité. Ainsi, la représentation de l atmosphère est plus ou moins proche de la réalité selon les paramétrisations utilisées dans les modèles. De plus, celles-ci dépendent de la résolution horizontale et verticale du modèle. Si les mailles horizontales des modèles sont trop larges, certains phénomènes de petite échelle ne peuvent pas être résolus de manière explicite, par exemple les ondes de gravité (Broad, 2000), ou les précipitations (Zangl, 2007). Plus les modèles possèdent de niveaux verticaux et plus ceux-ci s étendent haut dans l atmosphère, plus les prévisions produites seront précises (Roecker et al., 2006). Par exemple, dans le modèle NCEP (23 niveaux) utilisé pour produire les réanalyses NN50, le niveau le plus haut se situe à 10 hpa, au milieu de la stratosphère, alors qu il se situe à 0.01 hpa à la mésopause dans le modèle ECMWF (90 niveaux). Cette différence associée au fait que le modèle ECMWF contient trois fois plus de niveaux dans la verticale que le modèle NCEP est en corrélation

116 110 CHAPITRE 6. PRÉCISION DES ANALYSES ET RÉANALYSES STRATOSPHÉRIQUES directe avec les analyses plus précises produites par l ECMWF (Manney et al., 2005). Système d observation Les données assimilées sont principalement issues de radiosondages, d instruments transportés par les satellites, de bouées océaniques, d avions, etc... La performance des intruments n a eu de cesse de s améliorer au fil des années et permet de mieux contraindre les analyses et réanalyses. Ainsi, l utilisation systématique de mesures effectuées depuis l espace à partir de la fin des années 1970 a nettement amélioré la qualité des analyses et des réanalyses. Dans le même temps, le nombre de radiosondages a diminué. Or, seuls les radiosondages permettent d obtenir directement des mesures de vents stratosphériques. Ces quantités sont donc moins bien contraintes par le système d observation (Polavarapu and Shepherd, 2005). Sur le continent antarctique, près d une dizaine de stations effectuent des radiosondages régulièrement. Enfin, les observations demeurent plus nombreuses dans la troposphère que dans la stratosphère (voir par exemple Parrondo et al., 2007; Gobiet et al., 2005). Des comparaisons ont été réalisées entre des analyses et des versions améliorées de celles-ci dans lesquelles des mesures d ozone issues des intruments Microwave Limb Sounder (MLS) avaient été assimilées (Dethof and Holm, 2004; Feng et al., 2008). Ces comparaisons montrent une nette amélioration des profils d ozone post-assimilation, et démontrent l importance des données pour la précision des analyses. Une étude similaire a été conduite assimilant des données issues de l instrument Global Ozone Monitoring Experiment (GOME) à l aide d un nouveau schéma d assimilation (Massart et al., 2005). Toutefois, il est important de noter que les observations ont leurs propres limites (biais, écart-type) qui doivent être prises en compte lors de la procédure d assimilation. Schéma d assimilation Les schémas d assimilation incorporent les observations dans les prévisions des modèles en tenant compte du type de donnée (radiosondage, instrument transporté par satellites, etc..) et de ses caractéristiques statistiques. La majorité des centres météorologiques utilisent une assimilation variationnelle tridimensionnelle (3D-var) ou quadridimensionnelle (4D-var). Le terme variationnel témoigne du fait que le schéma essaie de minimiser une fonction J qui estime la différence entre

117 6.2. ARTICLE : ACCURACY OF NCEP/NCAR REANALYSES AND ECMWF ANALYSES111 l analyse et la prévision, et l analyse et les observations. L assimilation 3D-var prend en compte les observations obtenues au moment où s effectue la rectification et, ce faisant, les modifications concernent les trois dimensions de l espace à l instant considéré. Les observations obtenues trop tard ne sont pas prises en compte de manière rétroactive. Les réanalyses NN50 utilisent un schéma 3D-var. En revanche, l assimilation 4D-var prend en compte les observations de manière continue, même à des instants différents de ceux auxquels se fait la rectification. Elle intègre donc également la dimension "temps" en essayant de reproduire les évolutions de l atmosphère entre la prévision initiale et l analyse finale produite. Cette méthode, bien que plus efficace, nécessite des moyens de calculs considérables, de sorte qu elle n est utilisée que par un nombre limité de centres météorologiques (analyses UKMO, ECMWF). Aussi, les évolutions progressives du modèle, du système d assimilation ou des données assimilées tendent à améliorer les analyses et leur précision. 6.2 Article : Accuracy of NCEP/NCAR reanalyses and ECMWF analyses in the lower stratosphere over Antarctica in 2005 Cet article présente une comparaison entre les données de température et de vent enregistrées par les BPS et les champs de température et de vent des analyses ECMWF et des réanalyses NN50. Dans l hypothèse où les données ne sont pas biaisées, nous avons montré que les analyses de l ECMWF sont plus proches des données et donc plus précises que les réanalyses NN50. Le biais en température est de 0.42 K pour l ECMWF et de K pour NCEP. Les biais des champs de vitesses zonales sont de l ordre de 0.1 ms 1 pour l ECMWF et 0.1 ms 1 pour NN50. En étudiant la distribution de ces biais et des écarts-types correspondants en fonction du temps, de la latitude, de la longitude, et de la latitude équivalente, nous avons pu mettre en évidence l homogénéité des analyses de l ECMWF, alors que les réanalyses NN50 sont caractérisées par une grande hétéorogéneité. Néanmoins, nous avons pu lier les larges biais obtenus avec les réanalyses NN50 à une représentation inexacte du vortex polaire. Nous avons également montré qu une grande part de la variabilité

118 112 CHAPITRE 6. PRÉCISION DES ANALYSES ET RÉANALYSES STRATOSPHÉRIQUES (écart-type) est liée à une paramétrisation insuffisante des ondes de gravité. Enfin, à l aide d un calcul de trajectoires, nous avons montré que les champs de vents ne produisent des trajectoires fiables que sur des durées de l ordre de quelques jours. Cet article a été accepté en juillet 2008 à Journal of Geophysical Research. Dans la suite de la thèse il est désigné sous la forme Boccara et al. (2008a).

119 Click Here for Full Article JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, D20115, doi: /2008jd010116, 2008 Accuracy of NCEP/NCAR reanalyses and ECMWF analyses in the lower stratosphere over Antarctica in 2005 G. Boccara, 1 A. Hertzog, 1 C. Basdevant, 2 and F. Vial 3 Received 13 March 2008; revised 16 July 2008; accepted 1 August 2008; published 28 October [1] This article compares the temperature, zonal, and meridional velocities issued by the 50-year National Centers for Environmental Prediction National Center for Atmospheric Research (NCEP-NCAR) Reanalysis (NN50) and European Centre for Medium-range Weather Forecasts (ECMWF) operational analyses with independent observations collected during the Vorcore superpressure balloon campaign. The ECMWF analyses are found to be more accurate than the NN50 reanalyses. In particular, an overall warm bias in the polar Southern Hemisphere lower stratosphere is found in NN50 (+1.51 K), while a cold bias is found using ECMWF analyses ( 0.42 K). The ECMWF temperature bias evolves from winter ( 1.34 K in September) to summer (+0.31 K in January). A common feature of both analyses is the localization of larger discrepancies with respect to the observations for all variables over the Antarctic Peninsula, where orographic gravity waves were observed. More generally, two principal reasons are put forth for explaining the reported differences with the observations: unresolved small-scale pure and inertia gravity waves affecting both analyses and a large-scale misrepresentation of the vortex in NN50. Finally, simulated trajectories are computed starting from the positions of the balloon and advected using the ECMWF and the NN50 velocity fields. The simulated trajectories are compared to the real balloon trajectories. The spherical distance between the real and simulated positions exceeds 1000 ± 700 km on average in just 5 days using NN50 and after 10 days using ECMWF. The distances between the simulated and real balloons are found to increase faster in November and December, owing to the strong Rossby-wave activity in the stratosphere. Citation: Boccara, G., A. Hertzog, C. Basdevant, and F. Vial (2008), Accuracy of NCEP/NCAR reanalyses and ECMWF analyses in the lower stratosphere over Antarctica in 2005, J. Geophys. Res., 113, D20115, doi: /2008jd Introduction [2] Meteorological model forecasts, analyses and reanalyses are often used as reference data sets to study atmospheric processes such as stratospheric ozone depletion or troposphere-stratosphere exchanges, among others. The analyzed temperature field is used in chemistry-transport models to assess several physical and chemical processes such as ozone destruction via the occurrence of polar stratospheric clouds. Furthermore, the wind velocities can be used to compute trajectories and back trajectories. For example, forward trajectories are computed in Match campaigns to assess the ozone loss of an air parcel [von der Gathen et al., 1995]. Conversely, backward trajectories are 1 Laboratoire de Météorologie Dynamique, École Polytechnique, UPMC, Palaiseau, France. 2 Laboratoire de Météorologie Dynamique, École Normale Supérieure, École Polytechnique, Palaiseau, France. 3 Laboratoire de Météorologie Dynamique, École Polytechnique, Palaiseau, France. Copyright 2008 by the American Geophysical Union /08/2008JD010116$09.00 calculated to estimate the turbulent diffusion of an air parcel, and to retrace its history [Legras et al., 2003]. [3] These data sets integrate advanced data assimilation schemes to the model runs, incorporating satellite data and radiosonde profiles. However, there is a net hemispheric contrast in accuracy caused by the lack of monitoring stations available in the Southern Hemisphere (SH) in comparison to the Northern Hemisphere (NH) [Kistler et al., 2001]. In particular, poleward of 40 S, limited data are assimilated into the models [Parrondo et al., 2007] and few stratospheric observations are available [Gobiet et al., 2005] so that the reliability of analyses and reanalyses is best in the troposphere and in the lower stratosphere. Thus, it is very important to assess the accuracy of these analyses and reanalyses in the stratosphere. [4] Studies such as those by Manney et al. [1996, 2003, 2005a, 2005b] have compared temperature analyses and reanalyses produced by different centers, in order to assess their accuracy and their reliability for polar studies. In particular, Manney et al. [2003] found that the occurrence of temperature minima and the volume of polar stratospheric clouds formed are very dependent on the analysis used. Strictly speaking, intercomparison studies only give relative D of15

120 D20115 BOCCARA ET AL.: ACCURACY OF NCEP/NCAR REANALYSES AND ECMWF ANALYSES D20115 pole in September, through October and November when it was highly disturbed and displaced by planetary scale wave activity, until December when it broke down. Twenty-seven SPBs were launched into the stratospheric polar vortex from the station of McMurdo (77 S, 166 E), in Antarctica between 5 September and 28 October. They flew for an average of 2 months, with the longest flight lasting for 109 days. Depending on their size (8.5 m and 10 m diameter), they flew at different pressure levels: around 70 hpa or 50 hpa, which corresponds to the lower stratosphere (17 19 km). Owing to their constant volume, the SPBs have the particularity of drifting on isopycnic surfaces. They are very good tracers of horizontal motions, and therefore exhibit quasi-lagrangian features. [12] The SPB flights were terminated if the power inside the gondola reached a lower bound threshold, or if the SPBs flew north of 40 S. This occurred mainly after mid- December when the vortex had broken down, and the SPBs were no longer confined inside the vortex. [13] The campaign and scientific payload are described in detail by Hertzog et al. [2007]. Briefly, the SBPs carried two temperature sensors, a Global Positioning System (GPS) receiver and a pressure sensor. The data were uploaded onto the ARGOS system for transmission to ground. Measurements were made every 15 min, enabling the computation of the 15-min averaged zonal and meridional velocities. On the basis of calibration studies and comparisons between the two temperature sensors, the temperature is accurate to 0.25 K. Moreover, Vorcore temperatures have been compared to temperatures derived from CHAMP radio occultation and the difference between data sets does not exceed 0.5 K [McDonald and Hertzog, 2008]. According to the manufacturer and careful laboratory calibration, the pressure sensor accuracy is 10 Pa with a 1 Pa precision. The GPS is accurate to 10 m in the horizontal and 20 m in the vertical. This horizontal precision yields a s h 0.02 m s 1 accuracy in the zonal and meridional velocities Analyses ECMWF Analyses [14] At the time of the experiment, the ECMWF spectral model operated a triangular truncation of 511 waves in the horizontal (T511), which corresponds to 40 km grid spacing in latitude and integrated a 4D variational data assimilation scheme [Rabier et al., 2000; Simmons et al., 2005]. This version (cyc29r2) included 60 model levels in the vertical, extending from the surface to 0.1 hpa (about 70 km) [Untch and Simmons, 1999]. The four-daily analyses were retrieved on a grid over all the SH. The gravity wave drag parameterization combines a subgridscale orographic wave drag [Lott and Miller, 1997] and a Rayleigh friction scheme representing the deceleration induced by nonorographic waves. There are known problems to this method as it is linearly proportional to the strength of the winds and therefore acts strongly in regions where the winds are strong. For example, it results in a cold polar bias in the winter and strong westerlies in the midlatitudes [Hamilton, 1995; Hamilton et al., 1999] NN50 Reanalyses [15] The reanalysis system includes the NCEP global spectral model [Kanamitsu, 1989], with 28 sigma vertical levels and a horizontal triangular truncation of 62 waves, equivalent to a 210 km grid. The data assimilation scheme is a three-dimensional variational (3D-VAR) scheme cast in spectral space [Kalnay et al., 1996; Kistler et al., 2001]. The NN50 reanalyses are available four-daily with a grid resolution and on 17 pressure levels ranging up to 10 hpa. An orographic gravity wave drag is implemented on the basis of work by Palmer et al. [1986]. The drag is produced by momentum deposition of small-scale waves, forced by the local orography, at critical levels or at the top of the model Interpolations [16] To compare the data sets, the analyzed temperature, zonal velocity, and meridional velocity were interpolated on the balloon positions. A cubic spline, which extends over six temporal states and eight points in each direction in the horizontal, was used. The logarithm of pressure was used as the vertical coordinate, since the pressure in the balloon data set is more accurate than the GPS altitude. The vertical interpolation also used a cubic spline, extending over seven pressure levels for NN50 from 150 hpa to 10 hpa and over 11 model levels for ECMWF from about 132 hpa to 19 hpa. The levels used for this study correspond to pressure levels: 132, 113, 96, 80, 67, 55, 44, 36, 29, 23, 19 hpa in ECMWF, and 150, 100, 70, 50, 30, 20, 10 hpa in NN50. [17] As an example, Figure 2 shows the zonal and meridional velocities, and the temperature interpolated with the ECMWF analyses and the NN50 reanalyses superposed onto the SPB observations during one flight (SPB7). This SPB flew from 17 September until 18 December. A good agreement is found between data sets, even though the time series exhibit large amplitude disturbances. The close-up of the observed time series illustrates the importance of shortscale disturbances in the observations, which are missed by the analyses partly because of the coarse temporal interpolation. The analyzed zonal and meridional velocities are very close to the observations while clear biases can be identified for the temperature. The NN50 reanalyses are warmer while the ECMWF analyses are slightly colder. This general result will be further detailed in the next section. 3. Comparison Between Data Sets 3.1. General Results [18] The differences between the interpolated analyses and reanalyses and the SPB data were computed for the temperature, zonal and meridional velocities. Figure 3 shows these results as histograms of the differences. The bins used to plot the histograms were respectively 0.25 K and 0.5 m s 1 for the temperature and velocity. NN50 reanalyses exhibit an overall warm bias (+1.51 K) while ECMWF analyses show a cold bias ( 0.42 K), which may be caused by an insufficient parameterization of the gravity wave drag. Indeed, the Rayleigh friction used to mimic the gravity wave drag does not correctly represent the physics involved, such as the deposition of momentum flux at different levels, nor the anisotropy and intermittency of gravity wave sources. This issue will be further examined in section 4. Both analyses represent the zonal and meridional velocities very well. Nevertheless, the ECMWF distribution 3of15

121 D20115 BOCCARA ET AL.: ACCURACY OF NCEP/NCAR REANALYSES AND ECMWF ANALYSES D20115 Figure 2. SPB7 balloon data (black), ECMWF interpolated data (blue), and NN50 interpolated data (red), for zonal velocity, meridional velocity, and temperature. is slightly narrower than that for NN50 (as checked with the c 2 test), indicating a better accuracy of ECMWF winds. The large spacing between levels especially in the stratosphere and the relatively low top level of the NCEP model explains some of the deficiencies of NN50. Our results, compared to previous studies, highlight the fact that the observation system has been improved in the SH [Gille et al., 1996]. Similarly, Manney et al. [2003, 2005a] have found improve- 4of15

122 D20115 BOCCARA ET AL.: ACCURACY OF NCEP/NCAR REANALYSES AND ECMWF ANALYSES D20115 Figure 3. From left to right, histograms of the differences between the interpolated analyses data and the SPB measurements for temperature, zonal velocity, and meridional velocity; for ECMWF (solid line) and NN50 (dashed line). ment in the representation of stratospheric Arctic winters between 1995/1996 and 2003/2004, in ECMWF analyses. Table 1 summarizes the main biases, standard deviations and higher-order moments. According to calibration tests in the laboratory, it is assumed that the observations are unbiased; see section 2.1. Hence, the mean of these differences represent solely the analyses bias. On the other hand, the standard deviations of the differences sum the systematic instrumental errors and the analyses uncertainties, s TOTAL ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2 OBS þ s2 ANALYSES; where s Obs = 0.25 K, for temperature and s Obs =0.1ms 1 for zonal and meridional velocities (s Obs > s h 0.02 m s 1 to increase the confidence levels). Since the values of these systematic errors s Obs are known, equation (1) can be inverted, so that the standard deviations presented in Table 1 only correspond to the analyses uncertainties. [19] The biases for the zonal and meridional velocities are very small, still most of them are significant to 95%. The standard deviations are larger than 2 m s 1 in ECMWF analyses, and 3 m s 1 in NN50 reanalyses. Table 1. Statistics of ECMWF/NN50 Analyses Minus SPB Observation Temperature (K) Zonal Velocity (m/s) Meridional Velocity (m/s) ECMWF NN50 ECMWF NN50 ECMWF NN50 Bias a 0.09 Standard deviation Skewness Excess kurtosis a Not statistically significant. ð1þ [20] A number of studies using satellite data and radiosondes have shown that the analyses biases depend on the altitude in the stratosphere. For instance, using radiosonde temperature profiles from Belgrano (78 S), Parrondo et al. [2007] report on an oscillatory vertical structure of the temperature field in the ECMWF analyses during the 2003 winter. This structure features negative biases at levels ranging from 40 hpa to 15 hpa and from 150 hpa to 65 hpa and positive biases at levels between 65 hpa and 40 hpa. Their results also show that the NN50 reanalyses exhibit a warm bias throughout ranging from 0.5 C to 3 C. Gobiet et al. [2005, 2007] also report on an oscillatory structure of the ECMWF temperature field in the SH winter. Their studies compared radio occultation data from the CHAMP mission with ECMWF analyses since The vertical structure described is consistent with the results from Parrondo et al. [2007]. We now investigate the dependence of the bias with altitude. Indeed, the Vorcore SPBs flew at two different altitude levels depending on their size: 17 km (70 hpa) and 19 km (50 hpa). The statistics were computed for the two levels and the results are summarized in Table 2. The biases Table 2. Statistics of ECMWF/NN50 Analyses Minus Balloon Observation for 8.5-m and 10-m Diameter SPBs Temperature (K) Zonal Velocity (m/s) Meridional Velocity (m/s) ECMWF NN50 ECMWF NN50 ECMWF NN50 Bias: 8.5 m a 0.05 (17 km) Bias: 10 m a 0.15 (19 km) Standard deviation: m Standard deviation: 10 m a Not statistically significant. 5of15

123 D20115 BOCCARA ET AL.: ACCURACY OF NCEP/NCAR REANALYSES AND ECMWF ANALYSES D20115 Figure 4. scale. Number of 15-min observations per latitudinal bin from September to January, in logarithmic and standard deviations are larger at higher altitudes for both analyses: for ECMWF, the bias is colder at higher altitudes, while for NN50, the bias is warmer. For NN50, our results are in good agreement with those from Parrondo et al. [2007]. However, they disagree for ECMWF as the bias evolves from a cold to warm bias at similar pressure levels. These differences, may be due to the different versions of the ECMWF analyses used: cyc26r1 and cyc26r3 for Parrondo et al. [2007] and cyc24r3 through cyc28r2 for Gobiet et al. [2005] while the version cyc29r2 was used in our study Temporal Evolution [21] The previous section reports on results over the whole period which extended between September 2005 and January 2006 and over the whole geographical domain covered by the SPBs. In this section, the temporal evolution of the zonal-mean biases and standard deviations is described. To this end, the statistics were computed for each month, in 5 -latitude bins. Figure 4 displays the number of observations for each month over each latitude interval and shows that there are over 200 observations for every bin but one, which supports the statistical significance of the results computed. The geographical distribution of the SPBs is also illustrated in Figure 4. In September, very few observations are recorded north of 55 S, as the SPBs are confined inside the vortex, which is centered over the pole. In October and November, the observations spread to the lower latitudes. At this time, the strong activity of planetary Rossby waves displaces and distorts the vortex. In December, this strong wave activity leads to the breakdown of the vortex, so that the SPBs are no longer confined and free to drift down to the midlatitudes. [22] Figure 5 shows the zonal-mean ECMWF (top left) and NN50 (top right) temperature biases, as a function of latitude. The corresponding standard deviations are shown in the bottom panels. Figure 6 shows the same for zonal velocity. [23] One interesting feature in Figure 5 is the adjustment of the ECMWF analyses from a cold bias in September ( 1.34 K) to a slightly warm bias in January (+0.31 K) independent of latitude. [24] These results agree with comparisons between ECMWF analyses, NN50 reanalyses and radio occultation data from the CHAMP mission between 2001 and 2004 from June to September, as reported by Nedoluha et al. [2007]. In particular, the absence of latitudinal structure in the ECMWF analysis is consistent with their results. [25] For NN50, the biases are warm for all months, with a relatively smaller bias between 60 S and 70 S. The corresponding standard deviations are larger than in ECMWF analyses. However in both analyses, the biases and standard deviations are smaller in January. Indeed, after the breakdown of the vortex, the easterly summer circulation sets in so that the stratospheric variability and the velocities are smaller. [26] The winter cold bias and the summer warm bias are both consistent with a deficit in gravity wave drag in the ECMWF model. However, the consistently warm bias in NN50 reanalyses cannot be explained through a lacking gravity wave scheme, see section 2.2. [27] Throughout the campaign, the ECMWF zonal velocity biases are very small. Furthermore, the ECMWF biases and standard deviations do not depend on latitude. On the other hand, the latitudinal structure of the NN50 reanalyses exhibits more erratic variations for both means and standard deviations with biases ranging from 2 ms 1 to +5 m s 1. For example in November, the structure in latitude means that the winds in NN50 are too westerly equatorward of 70 S and too easterly poleward of 70 S. Similar features are evident for the rest of the period studied. The meridional velocity statistics are not shown but essentially exhibit the same features as the zonal velocity: small biases and standard deviations for ECMWF, and a strong heterogeneity for both the bias and the standard deviation for NN Longitudinal Structure [28] In the previous section, it was shown that the NN50 temperature biases and standard deviations were randomly 6of15

124 D20115 BOCCARA ET AL.: ACCURACY OF NCEP/NCAR REANALYSES AND ECMWF ANALYSES D20115 Figure 5. (top) Mean temperature differences for (left) ECMWF and (right) NN50. (bottom) Standard deviation of the temperature differences for (left) ECMWF and (right) NN50. Both are plotted according to month, from September to January. distributed in latitude, in particular in November. Further insight into the geographical distribution is given here. [29] The biases and standard deviations are averaged over intervals of 5 in latitude and 20 in longitude. A single box was used for latitudes poleward of 85 S. We used a minimum of 50 observations per box to compute the biases and standard deviations. [30] Figure 7 shows maps of the temperature biases and standard deviations in November. At that time, the temperature and velocity fields are very disturbed, because of the influence of strong planetary Rossby waves as shown by Hertzog et al. [2007, Figure 11]. In Figures 5 and 6, this corresponds to larger biases and/or standard deviations in November for NN50. Figure 7 highlights the coexistence of strong positive and negative biases with a disperse geographical distribution in NN50 reanalyses. A likely reason for this behavior is a misrepresentation of the large-scale structures: the stratospheric vortex and in particular its edge region where gradients are strongest, and therefore large departures can be found. This will be further discussed in section 4.1. It can also be noted that large biases are found at the most equatorward latitudes. As these latitudes correspond to the storm tracks, a possible explanation is that tropospheric disturbances may be misrepresented by NN50 reanalyses. [31] For ECMWF, Figure 7 confirms the overall homogeneous structure of the biases and standard deviations. This supports the hypothesis that large-scale structures are well resolved by the ECMWF analyses. [32] The standard deviation distribution is qualitatively similar to those of the biases (homogeneous for ECMWF, heterogeneous for NN50). Nevertheless, for both analyses, the standard deviations are larger over the Antarctic Peninsula where large amplitude gravity waves were observed during the balloon campaign, [Hertzog et al., 2007]. These events may cause strong temperature disturbances, but are 7of15

125 D20115 BOCCARA ET AL.: ACCURACY OF NCEP/NCAR REANALYSES AND ECMWF ANALYSES D20115 Figure 6. (top) Mean zonal velocity differences for (left) ECMWF and (right) NN50. (bottom) Standard deviation of the zonal velocity differences for (left) ECMWF and (right) NN50. Both are plotted according to month, from September to January. Figure 7. Temperature statistics in November, in boxes of 20 in longitude and 5 in latitude. The two left panels show mean differences for ECMWF and NN50, respectively, and the two right panels show standard deviations for ECMWF and NN50, respectively. Boxes including less than 50 observations are dashed. 8of15

126 D20115 BOCCARA ET AL.: ACCURACY OF NCEP/NCAR REANALYSES AND ECMWF ANALYSES D20115 Figure 8. Raw (dashed line) and filtered (solid line) zonal velocity for SPB7. generally too localized to be properly resolved in the models. 4. Discussion [33] The previous section reviewed the biases and higherorder moments found when comparing the observational data set with the ECMWF analyses and NN50 reanalyses. These errors can be distinguished as being caused by two shortcomings in the models. The first one is due to unresolved small-scale phenomena. This includes disturbances caused by gravity waves, as demonstrated by Vincent et al. [2007], and inertial oscillations. For instance in Figure 1, the cycloidal aspect of the SPB trajectories, which can be observed South of Australia, is typical of such oscillations. The second effect is due to large-scale phenomena, and includes errors due to a misrepresentation of the vortex both horizontally and vertically and the extent and position of the vortex edge Small-Scale Dynamics [34] In order to assess the importance of these small-scale effects, the entirety of the balloon data and the interpolated analyses data were filtered with a low-pass filter with a 15-hour cut-off period which corresponds to the longest inertial period in the balloon data set. Figure 8 shows the zonal velocity recorded by SPB7 over a few days, and the corresponding filtered data. This filtering removes all oscillations caused by pure and inertia-gravity waves, so that the solid line in Figure 8 exhibits oscillations only due to large-scale dynamics. [35] Figure 9 shows the distribution of the differences between the filtered data sets for temperature, zonal velocity and meridional velocity. The small-scale disturbances mainly correspond to the wave oscillations so that their effect should vanish when averaged. Hence, the biases in the filtered time series are not significantly changed, for both the overall bias and the monthly biases (not shown). On the other hand, the standard deviations are greatly reduced. This is particularly true for the zonal and meridional velocities, as the quasi-inertial waves have a strong signature on the velocity fields, and are ubiquitous in the balloon observations [Hertzog et al., 2002]. The distribution of the velocity differences are much more peaked and narrow, in particular for ECMWF, when compared to the histograms in Figure 3. For temperature, the effect is less striking. [36] The difference between standard deviations with or without filtering gives an estimate of the contribution of inertia-gravity waves to the overall analyses standard deviations, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s GWþINERTIAL ¼ s 2 ANALYSES s2 LARGE SCALE; ð2þ where s LARGE SCALE is estimated from the filtered time series, s ANALYSES is the overall standard deviation computed in section 3.1 and s GW+INERTIAL corresponds to the standard deviation induced by inertia-gravity waves apparent in the balloon observations. Table 3 shows the standard deviations associated with inertia-gravity waves for temperature and velocities, for both analyses. The standard deviations associated with small-scale motions have very similar amplitudes for both analyses, suggesting that they both misrepresent the small scales. Furthermore, the standard deviations are much larger for velocities than for temperature. This suggests that quasi-inertial gravity waves make up a substantial part of these standard deviations, as these waves mainly induce disturbances in the horizontal velocities Large-Scale Dynamics [37] Since the large-scale structure of the stratosphere is dominated by the vortex at high latitudes in winter, we study in this section the analyses bias and standard deviation distributions with respect to equivalent latitudes [Butchart and Remsberg, 1986], that is the position of the SPB with respect to the vortex. Namely, for each observation, the 9of15

127 D20115 BOCCARA ET AL.: ACCURACY OF NCEP/NCAR REANALYSES AND ECMWF ANALYSES D20115 Figure 9. From left to right, histograms of the differences between the filtered interpolated analyses data and the filtered SPB measurements, for temperature, zonal velocity, and meridional velocity; using ECMWF (solid line) and NN50 (dashed line). differences between the balloon equivalent latitude and that of the vortex edge (which is defined as the location of the maximum PV gradient) were calculated. The ECMWF fields were used to compute these two parameters, since the previous sections show a better agreement of the ECMWF analyses with the observations. The computation of equivalent latitude was stopped on 14 December, after the vortex has broken down into several pieces. The difference between the balloon observations and the analyzed fields were computed over 5 latitude bins, for each month, using once again a threshold of 50 observations per bin. Figure 10 shows the biases and standard deviations for temperature. [38] Inside the vortex, for ECMWF, the distribution is similar to the one plotted for zonal means (Figure 5), showing an adjustment from colder temperatures in September to warmer ones in December, inside the polar vortex. The mean and standard deviations are almost independent of the position of the SPB with respect to the vortex, which demonstrates that the ECMWF analyses accurately represent the vortex structure and its variability. [39] On the other hand, the results for NN50 show an increase of the biases and standard deviations at the edge of the vortex, in particular in October and November, supporting a misrepresentation of the edge of the vortex by NN50 reanalyses. [40] Furthermore, Table 3 shows the standard deviations due to large-scale dynamics. The standard deviations in the NN50 reanalyses are larger for all variables in particular for the wind fields, confirming that the NN50 reanalyses demonstrate shortcomings concerning the representation of large-scale structures in the stratosphere. These results are consistent with those from previous studies [Manney et al., 2005b] and confirm the deficiencies of NN50 reanalyses. [41] To further illustrate this point, we now consider the vertical structure of the vortex as represented by the ECMWF analyses and NN50 reanalyses near the drifting levels of the SPBs. Figure 11 shows the modified potential vorticity (MPV) [Lait, 1994] on isentropic surfaces situated in the lower stratosphere from 15 November to 15 December. The top and bottom panels of Figure 11 are directly issued from ECMWF analyses at isentropes 430 K and 475 K while the middle panels correspond to an intermediate isentrope (450 K) in the NN50 reanalyses. Given that typical values of the vertical gradient of potential temperature in the lower stratosphere (i.e., 20 K/km), the distance between the successive isentropic levels shown is on the order 1 km. [42] On 15 November the ECMWF defines a sharp vortex edge on both the bottom and top levels, with a large gradient separating the air inside from the air outside the vortex. On the other hand, the NN50 reanalyses shows a more blurred and therefore thicker edge at the intermediate level. Secondly, on 1 December the vortex is breaking down, and the fact that the dissolution is initiated from higher altitudes is evident from the comparison of the two ECMWF maps at 475 K and 430 K. Again, the MPV gradients at the vortex edge are more blurred in the NN50 reanalyses than in both levels in ECMWF analyses. Manney et al. [2005b] found similar results at higher altitudes. [43] These results agree with the equivalent latitude distributions, and plead for some deficiencies in the representation of the vortex in the NN50 reanalyses. This different behavior between analyses is also very likely due Table 3. Standard Deviations due to Small-Scale and Large-Scale Effects and Total Temperature (K) Zonal Velocity (m/s) Meridional Velocity (m/s) ECMWF NN50 ECMWF NN50 ECMWF NN50 s GW+INERTIAL s LARGE SCALE s ANALYSES of 15

128 D20115 BOCCARA ET AL.: ACCURACY OF NCEP/NCAR REANALYSES AND ECMWF ANALYSES D20115 Figure 10. (top) Mean temperature differences for (left) ECMWF and (right) NN50 versus equivalent latitude. (bottom) Standard deviation temperature differences for (left) ECMWF and (right) NN50 versus equivalent latitude. All are plotted according to month, from September to December. to the different resolutions ( for ECMWF and for NN50), and thus the ability of ECMWF analyses to resolve the large gradients associated with the vortex edge. 5. Trajectories 5.1. Method [44] Trajectories and back trajectories are powerful tools to study the transport properties of the troposphere and the stratosphere. For example, many studies have focused on the intrusions of stratospheric air into the troposphere and vice versa [Cristofanelli et al., 2006]. Nevertheless, the accuracy of analyses and reanalyses limits the validity of such studies. The errors in trajectory calculations have been reviewed by Stohl [1998]. The assessment of the total error of trajectories combines a range of errors and is difficult to estimate. Thus, these trajectories last a maximum of 10 days for the Match technique [Morris et al., 2005], and 9 days for Legras et al. [2003] trusting that the cumulative errors due to the biases from the analysis will be limited. [45] We tested this by computing forward trajectories lasting up to 60 days. These simulated trajectories were launched every day at midnight from the current position of the SPBs. The time integration used a fourth-order Runge Kutta method, with a time step of 10 min. This time step was reduced near the pole or when the wind velocity became large. The particularity of the SPBs was that they drifted on isopycnic surfaces, so we computed an average value of the flight density and used this reference density for interpolation. If the simulated trajectory reached latitudes equatorward of 40 S, the trajectory was automatically stopped, as for the SPBs launched during the experimental campaign. We computed the spherical distance between SPB and simulated trajectory, and studied its evolution with time, using both NN50 reanalyses and ECMWF analyses. 11 of 15

129 D20115 BOCCARA ET AL.: ACCURACY OF NCEP/NCAR REANALYSES AND ECMWF ANALYSES D20115 Figure 11. Vertical structure of the vortex (depicted by the MPV fields) as a function of time: columns correspond to the dates 15 November, 1 December, and 15 December. (top and bottom) Two isentropic levels from ECMWF (475 K and 430 K), and (middle) an isentropic level in NN50 (450 K). The color scale is the same for all graphs Results and Discussion [46] Figure 12 presents the mean spherical distance between the SPB position and the simulated position as a function of the simulated flight duration for all simulated flights. The envelopes correspond to the spherical distance of the 25% (and 50%) closest points to the mean spherical distance. The 50% envelope is seemingly asymmetric (this is also true for the 25% envelope albeit less obvious): the distance between the top branch of the 50% envelope and the mean is larger than the distance between the bottom branch and the mean. Indeed the distribution of spherical distance is skewed toward larger distances. For both analyses, we observe a fast growing regime during which the distance increases very rapidly for up to 15 days, and more slowly afterward. After 5 days, the spherical distance between real and simulated positions is larger than 400 km for both analyses. The maximum distances are larger using the NN50 reanalyses than using the ECMWF analyses. The distance reaches 1000 ± 800 km after 5 days and 3000 ± 1400 km after 30 days using NN50 fields. Using ECMWF analyses, the distance reaches 1000 ± 1000 km after 10 days, and 3000 ± 1700 km after about 50 days. So, this result agrees with the previous sections, which concluded that the ECMWF analyses, and especially the wind field, give a better representation of the stratosphere than the NN50 reanalyses. For longer simulations, the distance saturates because of the finite size of the vortex in which the SPBs are trapped, during the winter circula- 12 of 15

130 D20115 BOCCARA ET AL.: ACCURACY OF NCEP/NCAR REANALYSES AND ECMWF ANALYSES D20115 Figure 12. Mean spherical distance (bold line) for (left) ECMWF and (right) NN50 as a function of time since simulated launch. The dotted envelope includes 25% of the closest data points to the mean. The solid envelope includes 50% of the closest data points to the mean. tion. In November and December, this upper bound distance increases as the vortex is stretched by the activity of Rossby waves. [47] Furthermore, the sensitivity of the Match technique to the type of meteorological analysis used was studied by Hoppel et al. [2005]. They compared the ozone loss rates produced using UKMO, NN50 and ECMWF fields and found that the ozone loss rates computed using ECMWF fields were closest to those observed, in agreement with our results. [48] Similar results were obtained when simulated trajectories were computed from the positions of SPBs which flew in January and February 2002 in the NH [Hertzog et al., 2004]. Two growth regimes were observed, and the spherical distances found were smaller for ECMWF (270 ± 230 km after 5 days) and comparable for NN50 (1700 ± 1400 km after 5 days). This highlights the better representation of the NH in the ECMWF analyses. [49] Secondly, the trajectories were separated according to the month during which they were launched. Figure 13 exhibits the two regimes described above for each month, with a switch from one to the other occurring roughly around 15 days as in Figure 12. Two-day averages were performed for smoothing purposes. In agreement with results from section 3.2, the distances are smaller and grow at a slower rate in January. For both analyses, the distances are larger in November and December which are the months when the vortex is highly distorted and displaced owing to the strong Rossby wave activity. The associated large atmospheric variability, as described by Hertzog et al. [2007, Figure 11], is likely to be responsible for the deterioration of the statistics during these months. 6. Summary [50] Observations from the Vorcore superpressure balloon campaign were used to evaluate the accuracy of ECMWF analyses and NN50 reanalyses in the lower stratosphere during the 2005 SH spring. ECMWF analyses were found to agree closely with the observations with virtually no bias on the zonal and meridional velocities and a small cold bias ( 0.42 K) on the temperature. The velocities from the NN50 reanalyses are also very close to the balloon observations although they exhibit larger dispersion. Overall, the NN50 reanalyses displayed a strong warm bias (+1.51 K). [51] For ECMWF, the evolution in time of the temperature biases showed an adjustment from September ( 1.34 K) to January (+0.31 K), independent of latitude. On the contrary, in the NN50 reanalyses, a randomly distributed geographical structure of the bias is observed throughout the campaign with strong positive and negative 13 of 15

131 D20115 BOCCARA ET AL.: ACCURACY OF NCEP/NCAR REANALYSES AND ECMWF ANALYSES D20115 Figure 13. Mean spherical distance (averaged over 2 days) for (left) ECMWF and (right) NN50, by month of launch as a function of time since simulated launch. biases. For both analyses, an increased variability is found over orographic regions such as the Antarctic Peninsula where large-amplitude gravity waves have been observed. [52] It is inferred that two phenomena produce the main discrepancies: the first is caused by the insufficient resolution of pure and inertia-gravity waves in the analyses while the second one is caused by misrepresentations of largescale structures in the NN50 reanalyses. The importance of small-scale dynamics in the time series is showed by filtering the balloon and interpolated data sets with a lowpass filter and reevaluating the biases and standard deviations. Both analyses seem to be affected in a similar way by these shortcomings, although this may be partly due to the coarse temporal interpolation. Indeed, the analyses and reanalyses are output every 6 hours only. [53] To evaluate the misrepresentation of the vortex by the NN50 reanalyses, the temperature biases were estimated as a function of the position of the SPB with respect to the edge of the vortex using the equivalent latitude. Maps of modified potential vorticity also imply a blurred representation of the vortex, also possibly caused by the resolution of the NN50 reanalyses ( ) while the ECMWF analyses are output on a grid. [54] Secondly, we compared the trajectories of the SPBs with isopycnic trajectories computed using ECMWF and NN50 velocity fields. The spherical distance between the real and the simulated positions was computed as a function of the flight time. The ECMWF wind fields produce more accurate trajectories than the NN50, with spherical distance reaching 1000 ± 700 km for NN50 and 400 ± 400 km for ECMWF after 5 days. The distances are largest in November and December, corresponding to the largest part of the Rossby wave activity. [55] This work confirms the fact that NN50 reanalyses are not suitable for polar studies, as previously demonstrated by Manney et al. [2003, 2005a, 2005b]. This study complements Hertzog et al. [2004] in providing a large number of in situ observations to assess the accuracy of analyses and reanalyses in the stratosphere. A new SPB campaign is planned, releasing 12-m-diameter superpressure balloons from McMurdo, Antarctica. Therefore, a similar study will be undertaken to assess any improvements in the model or the assimilating system of these meteorological centers. [56] Acknowledgments. The authors would like to thank two anonymous reviewers for insightful comments. The authors would like to acknowledge the French Space Agency (CNES) as well as the NSF and the French Polar Institute (IPEV) for their longstanding support of the Vorcore campaign. The Laboratoire de Météorologie Dynamique is a member of the Institut Pierre Simon Laplace. References Butchart, N., and E. E. Remsberg (1986), The area of the stratospheric polar vortex as a diagnostic for tracer transport on an isentropic surface, J. Atmos. Sci., 43, of 15

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