Dr Virginie Marécal

Dr Geneviève Sèze

Dr Sergey M Khaykin

Prof Peter

H Haynes

Dr Jérémie Burgulat

Dr Jean-François Rysman

Dr Mélanie Ghysels

Prof Gerhard Held

Prof Jean-Pierre Pommereau

Prof Georges Durry

Dr Aurélien Podglajen

Keywords: Couche de la tropopause tropicale, overshoots convectifs, vapeur d'eau stratosphérique, BRAMS, TRO-Pico, GOES-12, MHS, Aura MLS, TRMM, évaluation de modèle, bilan de masse Tropical tropopause layer (TTL), overshooting convection, stratospheric water vapor, BRAMS, TRO-Pico campaign, GOES-12, MHS, Aura MLS, TRMM, radio sounding, mesoscale model evaluation, mass budget. vii

This dissertation work wouldn't have been accomplished

Introduction générale

La vapeur d'eau (VE) prend une partie centrale dans l'équilibre radiatif et les processus physiques et chimiques dynamiques de la haute troposphère -basse stratosphère (UTLS). Il peut également influencer l'équilibre de l'ozone stratosphérique, qui permet d'entretenir la vie sur Terre. Bien que l'air stratosphérique ne contienne que 0.001% d'eau de sa masse totale, l'abondance de la VE peut influencer de manière significative l'équilibre radiatif et chimique de l'atmosphère terrestre et même la température de surface à l'échelle décennale. Grâce à la libération de chaleur latente pendant la condensation, elle peut moduler la circulation globale de l'atmosphère, et donc le climat global. En raison de présence infime de VE dans la basse stratosphère, ce qui rend très difficile sa mesure précise, un grand débat a persisté sur les tendances stratosphériques de VE et ses conséquences sur le climat mondial jusqu'à la fin du XXe siècle. Même aujourd'hui encore, les processus liés à l'abondance de la VE stratosphérique sont encore débattus.

L'humidité stratosphérique est contrôlée par l'interaction de processus complexes se produisant principalement dans l'UTLS tropical correspondant au mécanisme de transport entre la troposphère et la stratosphère. Principalement, la majeure partie de la VE pénètre dans la couche de transition entre la troposphère et la stratosphère, appelée couche de tropopause tropicale (TTL), et se propage vers les pôles et vers le haut dans la stratosphère avec la circulation Brewer-Dobson (BDC). En outre, il existe des preuves d'interaction entre la BDC et l'oscillation quasi-biennale (QBO) dans la ceinture équatoriale, un changement de direction du vent avec une période de 27 -29 mois. La TTL est reconnue comme la «passerelle» vers la stratosphère. Les constituants chimiques appauvrissant l'O 3 transitent par la TTL vers la stratosphère. Plus particulièrement, les conditions de froid extrême dans la TTL provoquent la déshydratation des masses d'air entrant dans la stratosphère, par condensation solide puis sédimentation des particules de glace (on parle de piège froid), et ces conditions peuvent donc déterminer la quantité de VE entrant dans la basse stratosphère. Un autre facteur, à savoir la convection tropicale profonde, pourrait jouer un rôle dans l'entrée de la VE dans la basse stratosphère. Les systèmes convectifs sévères dépassant le niveau de flottabilité neutre -les overshoots, sont reconnus pour relier les conditions de surface aux altitudes de la TTL, et sont connus pour jouer un rôle dans le transport vertical des traceurs vers la stratosphère via le TTL. Ces overshoots peuvent parfois atteindre la basse stratosphère, en injectant des particules de glace qui peuvent sublimer dans la stratosphère avant de retomber dans la troposphère. En outre, la convection tropicale est connue pour être la source d'ondes atmosphériques (par exemple, des ondes d'inertie-gravité), dont on montre qu'elles peuvent jouer un rôle sur les champs de température dans la TTL. EIles peuvent ainsi moduler la durée de vie de la particule de glace dans cette couche. Cependant, parmi ces interactions de différents mécanismes, les facteurs contribuant à l'humidité stratosphérique ne sont pas encore bien compris. Cela pourrait être lié à notre compréhension insuffisante des mécanismes physiques et chimiques ix régissant la TTL, donc de l'humidité stratosphérique. Les processus à grande échelle et à petite échelle qui contrôlent le bilan de la VE dans la TTL sont d'une importance primordiale pour l'impact climatique des tendances de vapeur d'eau stratosphérique.

Ainsi, les recherches sur la TTL se sont intensifiées depuis plus d'une décennie. Les lacunes dans la compréhension ou la quantification de l'impact des overshoots convectifs sur la TTL (principalement sa partie stratosphérique) à grande échelle sont en grande partie dues au manque de mesures à fine résolution par satellite, avion et ballon permettant d'étudier les processus clé au sein de la TTL. En particulier, les overshoots stratosphériques se produisent à des échelles horizontales de quelques km 2 dont le signal en vapeur d'eau est peu détectable. De plus, les panaches d'air provenant d'overshoots stratosphériques sondés par les satellites sont trop fins par rapport à la résolution verticale des instruments. En l'absence de mesures précises et bien résolues à l'échelle globale, notamment de mesures continues pendant longtemps, il est presque impossible de conclure avec précision sur les mécanismes existant dans la TTL et leur contribution sur la VE stratosphérique, en particulier dans un monde où les changements climatiques sont rapides. Une autre façon d'appréhender une meilleure connaissance du rôle global des overshoots est la simulation numérique. Cependant, l'inconvénient majeur est l'absence de modèles climatiques globaux qui pourraient prendre en compte de manière réaliste les overshoots stratosphériques, dont l'échelle est bien inférieure à la résolution des modèles. Des études de modélisation ont déjà montré un accord au moins qualitatif sur la distribution de vapeur d'eau stratosphérique à grande échelle, sans prendre en compte les overshoots. Il en est déduit que les overshoots stratosphériques ne sont pas le processus principal expliquant l'abondance de la VE. Pour autant, l'approche inverse n'a jamais été réalisée à grande échelle et rien ne prouve que le rôle des overshoots soit négligeable.

Cette dissertation propose un double cadre pour faire progresser notre compréhension du transport de vapeur d'eau vers la basse stratosphère dû aux overshoots aux tropiques, et ses rétroactions à long terme sur le système climatique global. Premièrement, nous réalisons une simulation d'une d'une saison humide complète en utilisant le modèle mésoéchelle BRAMS, couvrant une grande partie de l'Amérique du Sud tropicale. La zone d'altitude d'intérêt y est la TTL. Cette simulation ne tient pas compte des overshoots stratosphériques (ci-après nommé SOC) puisque nous choisissons une résolution du modèle ne permettant pas de les résoudre explicitement. Cette simulation est ensuite évaluée pour d'autres caractéristiques typiques de la TTL. La majeure partie de ce travail s'appuie sur les mesures par instruments sous ballon dans le cadre de la campagne de terrain TRO-Pico, un projet ANR français qui vise à étudier l'impact de la convection profonde sur le bilan de l'eau dans la TTL. Dans le même but, nous utilisons également les mesures du rapport de mélange H 2 O extrait de l'Aura MLS, des informations sur les overshoots détectées par MHS, la pluie accumulée déduites des observations du satellite TRMM, les mesures de sommets de nuages par le satellite GOES-12, et des mesures de températures et de vents par une série de radiosondage à différents endroits du Brésil. Dans cette partie du travail mon objectif est double : Premièrement, je veux démontrer que le modèle BRAMS est un outil adéquat pour modéliser la TTL à l'échelle continentale, et par conséquent un outil adéquat pour estimer l'impact de SOC sur la vapeur d'eau stratosphérique dans une étude future où l'impact des overshoots sera forcé dans le modèle. Deuxièmement, en supprimant la contribution de SOC dans la simulation, je veux déduire un rôle relatif possible des SOC par rapport à

Introduction

Water vapor (WV) takes the central part in the radiative equilibrium and the dynamical physical and chemical processes of the upper troposphere-lower stratosphere (UTLS). Most importantly, it can influence the stratospheric ozone equilibrium, which supports the living beings on the Earth. Albeit the stratospheric air is deemed to possess only ∼0.001% H 2 O of its total mass, the abundance of WV can influence significantly the whole radiative and chemical equilibrium of the Earth's atmosphere, and even the surface temperature on a decadal timescale. Through the latent heat release during the condensation, it can modulate the global circulation of the atmosphere, and therefore the global climate. Due to its minuscule presence in the lower stratosphere, which makes it quite challenging to make a proper WV measurement, nobody was really agreed on the stratospheric WV trends, and its consequences on the global climate until the late 20th-century. Even today also, the processes linked to the stratospheric WV abundance are debatable.

Stratospheric humidity is controlled by the interplay of complex processes occurring mostly in the tropical UTLS corresponding to the transportation mechanism between the troposphere and the stratosphere.

Primarily, most of the WV enters through the interfacing layer between troposphere and stratosphere, known as the tropical tropopause layer (TTL), and spreads poleward and upward further into the stratosphere along with the Brewer-Dobson circulation (BDC). Furthermore, there is evidence of interaction between the BDC and the quasi-biennial oscillation (QBO) in the equatorial belt. The TTL is acknowledged to be the 'gateway' to the stratosphere. The potential O 3 depleting chemical constituents pass through the TTL to the stratosphere. Most notably, the extremely cold conditions in the TTL causes the dehydration of the air mass entering to the stratosphere, known as the freezing-drying (cold trap) mechanism, and therefore such conditions can determine the amount of WV entering to the lower stratosphere.

Another factor, which is the tropical deep convection, could play a role in WV entry to lower stratosphere.

Severe convective system overpassing the level of neutral buoyancy, sometimes the lower stratospherestratospheric overshooting convection (SOC), is admitted to link the surface conditions to the TTL. SOC is observed to play a role in the vertical transportation of tracers to the stratosphere via the TTL. These overshoots can sometimes penetrate the lower stratosphere, injecting ice particles which could sublimate in the stratosphere. Furthermore, the tropical convection is known to be the source of atmospheric waves (e.g., inertia-gravity waves), which are shown to play an impact role in the temperature field of the TTL.

They can modulate the lifetime of ice particle within the TTL. However, among these interplay of different mechanisms, their contributing factors towards the stratospheric humidity are not well understood so far.

This could be affiliated with our insufficient understanding of the physical and chemical mechanisms governing the TTL. The large-scale, as well as, small-scale processes controlling the WV budget in the TTL, xiii are of prime importance for the global climate studies, and attract more research to be carried out on the TTL.

The gaps in understanding the impact of SOC on the TTL at large-scale are mostly due to the glaring lack of comprehensive satellite-, aircraft-and balloon-borne measurements of the processes within the TTL. Without global-scale measurements, importantly continuous measurements for a long time, it is almost impossible to conclude precisely on any mechanism occurring within the TTL and its contribution towards the stratospheric WV, especially in a changing climate world. Another way would be the numerical simulations. Then, the key drawback could be the lack of extensive climate models who could reproduce the limited available observations akin to the overshooting convection. Then, it becomes an arduous task to comprehend the processes governing the TTL composition and dynamics that could be affiliated with the overshooting convection and the stratospheric WV. Given the fact that the numerical modeling based studies and modern theories have been shown to simulate a qualitative overview of WV variability within the TTL, and its transport and climatic feedback, none of them have quantified the role of WV being transported to the stratosphere due to SOC at a large-scale and its long-term aftermath on global climate system.

This dissertation prescribes a twofold framework to advance our understanding of the WV transportation to the lower stratosphere, particularly by the SOC in the tropics, and its long-term feedbacks on the global climate system. Firstly, we make a simulation of a typical TTL for a full wet season using the BRAMS mesoscale model, covering a large tropical region of South America. We absent the SOC in the modeled TTL by incorporating a relatively coarse horizontal grid-point resolution, so that the model wouldn't be able to reproduce it. This simulation is then evaluated for other typical features of the TTL. The major part of this work takes advantage of the balloon-borne measurements retrieved from the apparatuses flew in the frame of TRO-Pico field campaign, a French ANR project which aims at studying the impact of deep convection on the TTL's WV budget. For the same purpose, we also use the measurements of H 2 O mixing ratio retrieved from the Aura MLS, information about the overshooting cells detected by the MHS, rainfall accumulation from the TRMM satellite observation, cloud top measurements from the GOES-12 satellite observation, and radio sounding measurements at different places over Brazil from the upper-air database. This part of the work is twofold. First, we demonstrate the BRAMS model is an adequate tool to simulate the TTL at a continental scale, and consequently an adequate tool to nudge the impact of SOC on the stratospheric water vapor in a future study. Secondly, by removing the contribution of SOC in this simulation, inferences are drawn on a possible relative role of SOC with respect to other large-scale processes.

Secondly, we investigate the stratospheric overshoot upscaling issue in a complementary approach : the cloud scale simulation, with the same mesoscale model. The goal is to extract from the same model as in the first step, the key physical parameters that will help us to define a way to force the impact of SOCs on the stratospheric water at large-scale. The parameters we focus on are mostly related to ice particles (the type of hydrometeor injected, ice mass flux, mass budget in the stratosphere, etc.) We again take advantage of the TRO-Pico campaign to simulate an observational case of SOC. The TRO-Pico measurement will help in validating the model outputs. In order to estimate the sensitivity our parameters to the model setup, several simulations of the same case are proposed. All these elements will help in defining the best forcing option of SOCs in a large scale simulation without explicit overshoot, keeping in mind that the xiv simulation from the first step of this thesis work could be used as a reference simulation for upscaling the impact of SOC. This dissertation comprises of five chapters and four appendices. The structure is as follows. Chapter 1 introduces the fundamentals of the Earth's atmosphere, including the advent of meteorology, climatology and general circulations. It also discusses the tropical weather system and the current state of our understanding of various physical mechanisms governing the TTL, and thus the WV budget. We discuss briefly the current state of numerical simulations relevant to our problem.

Chapter 2 elaborates the methodology we develop to make further advancement in the aforementioned problems discussed. Chapter 2 mostly includes the description of our numerical experimental set updescription of the BRAMS mesoscale model and the modifications done relevant to our problem, the TRO-Pico campaign including all the apparatuses utilized in our study (e.g., Pico-SDLA, FLASH-B, RS92), S-Band Radar, upper-air PTU radio sounding measurements from six different positions over Brazil, and satellite-borne observations (e.g., GOES-12, Aura MLS -Microwave Limb Sounder, MHS -Microwave Humidity Sounder, TRMM -Tropical Rainfall Measuring Mission) within our domain of interest. Their measurement criteria are also briefly discussed, then the application of these datasets to evaluate the simulations.

Chapter 3 comprises of the first step of our advancement in understanding the impact of SOC on the WV budget of the TTL. It includes a publication led by me and Dr. Rivière with the collaborations from several laboratories within France and abroad. This article is published in JGR-Atmosphere, which reports about the validation of the BRAMS mesoscale model at a continental scale during a wet season corresponding to the TRO-Pico campaign measurements. In the frame of this article, we discuss the importance of SOC, and why it is necessary to upscale its influence on the stratospheric water vapor budget. We give the analyses carried out in order to incorporate the satellite-borne observations and PTU radio soundings retrieved from the upper-air database as a supplement material to the publication.

Chapter 4 comprises of the second step of our dissertation, and discusses the preparation of a sub-grid scale forcing of ice hydrometeors into the lower stratosphere above 380 K isentrope, i.e., the over-world stratosphere. This preparation work is based on the cloud scale simulation of a SOC case during TRO-Pico and its analysis. The observational case is presented, and several simulations of the same case are described and validated. Key parameters to help us set a forcing scheme of the impact of SOC on stratospheric water is extracted from the simulations and discussed.

Chapter 5 concludes this dissertation by revisiting each chapters' outlooks. We also discuss the future work to be done in the continuity of this thesis work that is the application of the key results of chapter 4 into the reference simulation presented and validated in chapter 3.

Liste des Figures

1.1 A schematic diagram of the generalized distribution of the temperature and pressure, representing different layers present within the Earth's atmosphere. The layers are defined according to the change in their ambient thermodynamical composition which varies with altitude. The lowermost layer is known as the troposphere, which determines mostly the weather conditions, then the upper layer is stratosphere. The composition of this (ozone) layer is very important to sustain life on the Earth. Then further high in altitude, there exist mesosphere, thermosphere, and exosphere. There are three relatively warmer layers, i.e., near the surface, at 50 km à 60 km, and at ∼120 km altitude. They are separated by relatively two colder layers, i.e., at 10 km à 30 km, and at 80 km à 100 km altitude. These altitudes can differ slightly from the equator to the poles. Courtesy : https: //www.britannica.com/science/atmosphere. . .

1.6

The ozone hole time evolution over 30 years of satellite observations. The color scale is in Dobson units, varies from navy-blue to red at a scale of 0 -500. The histogram below indicates the number of contributions to the ozone measurements for each satellite with time starting from 1980s to 2010s. Courtesty : https://www.nasa.gov. . . . . . . . . . . . .

1.7

The structure of the QBO -extracted from [START_REF] Baldwin | The quasi-biennial oscillation[END_REF]. (a) The time evolution of the vertical cross-section of the monthly-mean zonal (u) wind (m s -1 ) corresponding to years of 1964 -1990, after the removal of the seasonal cycle. The red color represents the positive westerly winds, and the counterpart is shown with blue color. (b) The dynamical overview of the QBO during the winter in the northern hemisphere. The orange arrows depict the propagation of various atmospheric waves at the tropics, driving the QBO upward. The contour (black) lines refer the difference in the zonal winds between easterly and westerly phases of the QBO. Here, the QBO phase is defined at 40 hPa equatorial wind. . . . . . . . xxi 1.8 (a) The meridional supply of air mass between the troposphere and the stratospherethe Brewer-Dobson circulation (BDC). The dotted lines refer to the isotherms over the globe, and the solid lines corresponds to the circulation towards the summer and winter poles, respectively, from the equatorial belt, envisaged by keeping track of H 2 O budget [START_REF] Brewer | Evidence for a world circulation provided by the measurements of helium and water vapour distribution in the stratosphere[END_REF] and by keeping track of O 3 budget by [START_REF] Dobson | Origin and distribution of the polyatomic molecules in the atmosphere[END_REF]. Courtesy : http: //birner.atmos.colostate.edu/bdc.html. (b) The recent depiction of the BDC playing role in sending H 2 O, H 2 and CH 4 , i.e., the greenhouse gases to the lower stratosphere -extracted from [START_REF] Ravishankara | Water vapor in the lower stratosphere[END_REF]. The left inlet shows the H 2 O mixing ratio variation with altitude at midlatitude, which reveals the enhancement up to 7 ppmv in the lower stratosphere (∼70 hPa). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9 (a) A version of TTL envisaged by [START_REF] Holton | Stratosphere-troposphere exchange[END_REF], with the dynamics controlling the transport mechanism occurring between 1000 hPa à 10 hPa pressure levels. The TTL is denoted by the thick line, other lines correspond to the isentropic surfaces. high clouds within the domain of the simulation during the FMOP. X is a random variable corresponding to the percentage of occurrence of high clouds (>10.0 km). Abscissa depicts X from the numerical simulation of REF 1 , while the ordinate represents X from three different sources, i.e., from the REF 1 simulation (black line), and from GOES-12 observations, but using CTTH_Height+CTTH_Effect (red) and CTTH_Height (blue), respectively. . . . . . 3.21 A schematic diagram of extracting vector format satellite gridded data to raster gridded format using a particular cell size, i.e., size of each individual pixel. As such, for our case, the cell size of 0.04 • is transformed into 0.18 Ice+liquid concentration color contour varies from 0 g kg -1 à 4 g kg -1 . . . . . . . . . . . . . . 4.12 BRAMS total water (ice, liquid and vapor) content in g kg peut faire le lien entre les constats observés à l'échelle locale et l'impact que l'on peut en déduire à l'échelle globale ou continentale. Nous passons en revue l'état de la modélisation de la TTL à différentes échelles, et notamment permettant de mieux quantifier l'impact des overshoots. L'essentiel des travaux a été consacré à la modélisation à l'échelle du nuage des overshoots stratosphériques permettant de mieux quantifier leur impact à l'échelle locale. Pourtant, une assez grande variabilité des résultats est observée selon les études.

Les travaux de modélisations proposés dans le cadre de cette thèse se veulent un pas supplémentaire dans la quantification du rôle des overshoots en mettant l'accent sur le lien entre l'échelle locale et l'échelle continentale.

The Atmosphere

Origin of the Earth's atmosphere dates back to the pioneering treatise of [START_REF] Laplace | Exposition du système du monde (cercle-social[END_REF] in which the Laplacian model depicts that our solar system was condensed out of an interstellar cloud of gas and dust -the 'primordial solar nebula' [START_REF] Descartes | Principia philosophiae[END_REF] about 4.6 × 10 9 years ago. Then, Johannes Kepler, a key figure during the scientific revolution of 17th-century, used the observational data of planets' positions gathered by Tycho Brahé and put to the fore the planetary motion of the Solar system. As per the formulation of the Keplerian accretion disk, the Sun takes the central position at one of the foci of the elliptical disk, and the newly formed planets start revolving around it according to their stable center of mass (gravity) positions [START_REF] Kepler | New astronomy[END_REF][START_REF] Russell | Kepler's laws of planetary motion : 1609-1666[END_REF][START_REF] Voelkel | Johannes Kepler and the new astronomy[END_REF]. The Sun holds ∼99.8%

of the total mass of our solar system, and its size is so enormous that about 1 × 10 6 number of Earths could fit within it. After Mercury and Venus, the Earth is the third closest planet that revolves around the Sun at a distance of about 1.5 × 10 8 km. With the progress in time, the Earth's atmosphere is believed to be formed by the release of compact volatile compounds from its surface due to the revolving motion [START_REF] Berger | Stability of the astronomical frequencies over the earth's history for paleoclimate studies[END_REF][START_REF] Ruddiman | Earth's Climate : past and future[END_REF]. Albeit the little thickness of the atmosphere in comparison to the Earth's radius (only ∼1% of the radius), it can be divided into two domains, i.e., the lower atmosphere, which extends from surface up to the stratosphere (∼50 km) and known for meteorology, and the upper atmosphere, which is known for aeronomy [START_REF] Barry | Atmosphere, weather and climate[END_REF].

Exploration of the Earth's atmosphere has a very extensive history involving both observation and theory. The emergence of major scientific activities to explore the atmospheric composition call attention to the expositional work of Aristotle known as «Meteorologica» [START_REF] Lee | Aristotle : Meteorologica[END_REF], which was written around 340 BC. It is the first known proof of advent of meteorology that gave rise to the word 'meteorology'. Scientific measurements started possibly after the invention of appropriate instruments, where most of them had complex long-term evolution. As such for the temperature measurements, Galileo Galilei invented the thermometer in the early 1600s, but the precise measurements were available only during the early 1700s

after the vital scientific inventions by Daniel-Gabriel Fahrenheit and Anders Celsius. Similarly for the pressure measurements, the inventions brought by Evangelista Torricelli -the barometer and Blaise Pascal during 1640s ; for the relative humidity measurements, the invention of hygrograph by Horace-Bénédict de Saussure (1780), and then the advent of few fundamental principles proposed by Robert Boyle (1660) and Jacques Charles ( 1802), all together put to the fore the concept of different thermodynamic parameters and their variability within the atmosphere. The combined use of thermometer and barometer allowed the attempts to make further progress in investigating the structure of the atmosphere. Depending on the vertical variability of these thermodynamic parameters, mainly on the basis of temperature, the atmosphere is then conveniently divided into several numbers of well-marked horizontal layers [START_REF] Barry | A brief history of the terms climate and climatology[END_REF]Chorley, 2009, Salby, 2012]. A schematic diagram is shown in Figure 1.1.

Inventions of appropriate instruments and formulations of new theories or hypotheses spawned the atmospheric research works to two different leagues, where one (theoretical) group purely relies on the concepts of Meteorologica, and the second (observational) group promotes the astronomical events to make atmospheric predictions [START_REF] Neves | A short critical history on the development of meteorology and climatology[END_REF]. During the commencement of modern-era (last quarter of 18thcentury), the innovative experiments accomplished by [START_REF] Cavendish | Experiments on air. by henry cavendish, esq. frs & sa[END_REF], [START_REF] Lavoisier | Traité élémentaire de chimie : présenté dans un ordre nouveau et d'après les découvertes modernes[END_REF], [START_REF] Priestley | Observations on different kinds of air. by joseph priestley, l ldfrs[END_REF] to investigate the atmospheric composition led to the discovery of several major components of the The lowermost layer is known as the troposphere, which determines mostly the weather conditions, then the upper layer is stratosphere. The composition of this (ozone) layer is very important to sustain life on the Earth. Then further high in altitude, there exist mesosphere, thermosphere, and exosphere. There are three relatively warmer layers, i.e., near the surface, at 50 km à 60 km, and at ∼120 km altitude. They are separated by relatively two colder layers, i.e., at 10 km à 30 km, and at 80 km à 100 km altitude. These altitudes can differ slightly from the equator to the poles. Courtesy : https://www.britannica.com/science/atmosphere. [START_REF] Kasting | Earth's early atmosphere[END_REF][START_REF] Zahnle | Earth's earliest atmospheres[END_REF]. However, the current Earth's atmosphere is little congruous with the earlier stage atmosphere and composed of N 2 (78%) mostly. This is only because, it is chemically non-reactive, non-condensable, non-water soluble, hence most of the outgassed N 2 is accumulated in the atmosphere.

Among other components, O 2 (21%) and Ar (0.9%) are significant. Apparently adopting to the postulations made on the photosynthetic processes, the Earth's biosphere is developed. It took about 400 × 10 6 years to fulfill the current level of O 2 , and the level is balanced by the photosynthesis and respiration activities, and decay of organic carbon processes [START_REF] Canfield | The archean sulfur cycle and the early history of atmospheric oxygen[END_REF][START_REF] Canuto | Oxygen and ozone in the early earth's atmosphere[END_REF][START_REF] Cloud | The biosphere[END_REF][START_REF] Farquhar | Atmospheric influence of earth's earliest sulfur cycle[END_REF].

Water vapor (WV) is also a very essential and integral part of the atmosphere [START_REF] Finlayson-Pitts | Chemistry of the upper and lower atmosphere : theory, experiments, and applications[END_REF]. Majority of the WV was supposedly condensed into Oceans and rivers ; nonetheless, from where does this water come is still an enigma. The remaining vapor is believed to be present in the atmosphere as clouds out of the primordial atmosphere [Abe andMatsui, 1986, Kasting et al., 1988]. Due to the greater density of water in comparison to air, thus a higher specific heat, it is interesting to note that only the top 10 cm à 15 cm of Ocean water contains as much heat as does the total atmosphere. Furthermore, during the evaporation and condensation processes, the heat energy of water is translated into the kinetic energy of H 2 O molecules and the subsequent condensation in a cloud releases kinetic energy that returns back as heat energy -the exchange of latent heat [START_REF] Black | Lectures on the Elements of Chemistry : Delivered in the University of Edinburgh[END_REF]. Therefore, the amount of water that can be stored in vapor/gaseous state depends on the temperature of the ambient air. The condensation process of warm moist air mass releases a large amount of latent heat, hence increasing the vertical instability of the air masses. This phenomenon corresponds to the process known as convection, in which heated air mass expands, decreases the air mass density and rises, and then resulting in precipitation, whereas cooled air mass contracts and the resulting increase in the density leads to the subsidence [START_REF] Houze | Convection in gate[END_REF]. The potential energy gradients produce such type of thermally forced motions corresponding to the exchange of potential (thermal) and kinetic energy at large-scale in the atmosphere. In particular, the differential heating of low and high latitudes is the mechanism which drives both the atmospheric and Oceanic circulations, i.e., the global atmospheric circulation -discussed in subsequent sections.

The Sun-Earth Link

About 51% of the energy coming from the Sun reaches the surface of the Earth in the form of short-wave radiation (insolation). The land surface or the Ocean surface are continuously being heated, and subsequently, they re-radiate this heat as long-wave thermal radiation. During the 1830s, Schmidt calculated the net heat gain and loss by the Earth's surface for each latitude by the incoming and outgoing solar radiation, respectively. Then, the increased heating of tropical regions in comparison to the higher latitudes became apparent. Following the work of Schmidt, [START_REF] Meech | On the relative intensity of the heat and light of the Sun upon different latitudes of the Earth[END_REF], [START_REF] Wiener | Ueber die stärke der bestrahlung der erde duch die sonne in ihren vershiedenen breiten und jahreszeiten[END_REF], and [START_REF] Angot | Etude sur les vendanges en france[END_REF] calculated the amount of insolation received by the outer limits of the Earth's atmosphere at all altitudes. [START_REF] Milankovitch | Development and validation of a time-lag correction for vaisala radiosonde humidity measurements[END_REF], [START_REF] Simpson | Further studies in terrestrial radiation[END_REF] calculated the values of the insolation balance of the Earth's atmosphere based on their theoretical calculations. These calculations put to the fore the importance of this extraterrestrial contribution to modulate the Earth's atmosphere. However, the solar radiation received by the Earth was only accurately measured since the satellite-era of 1990s [START_REF] Trenberth | Earth's global energy budget[END_REF]. A schematic diagram is given in Figure 1.2 to represent aforementioned energy balance.

There are many pieces of evidence of a link between the evolving Sun and the variability in Earth's atmosphere, where the hypotheses are made on observations and numerical model simulations. Importantly, the solar variability [START_REF] Güdel | The sun in time : Activity and environment[END_REF] such as, total solar-irradiance (TSI), solar UV irradiance, solar energetic (wind) particles, (galactic) cosmic rays are succinctly influential on the Earth's atmospheric conditions [START_REF] Adem | On the theory of the general circulation of the atmosphere[END_REF][START_REF] Stocker | Climate change 2013 : the physical science basis : Working Group I contribution to the Fifth assessment report of the Intergovernmental Panel on Climate Change[END_REF]. As is acknowledged so far, the Earth's hydrological cycle and sea surface temperatures (SSTs), heating budget of the upper and the middle atmosphere and their dynamical coupling with the troposphere [START_REF] Claud | The effect of the 11-year solar cycle on the temperature in the lower stratosphere[END_REF][START_REF] Hood | Effects of solar uv variability on the stratosphere[END_REF][START_REF] Keckhut | The 11-year solar-cycle effects on the temperature in the upper-stratosphere and mesosphere : Part i-assessment of observations[END_REF][START_REF] Van Loon | The influence of the 11-year solar cycle on the stratosphere below 30 km : A review[END_REF],

the chemistry of the middle and the lower atmosphere, the important stratospheric ozone budget and the processes linked to its balance therein [START_REF] Forster | Changes in atmospheric constituents and in radiative forcing. chapter 2[END_REF][START_REF] Haigh | The sun and the earth's climate[END_REF][START_REF] Shindell | Solar cycle variability, ozone, and climate[END_REF], are being modulated by the solar variability. Furthermore, some great inventions of instruments promoted the attempts to identify and measure the composition of trace gases in the atmosphere at a scale of 10 6 parts of a volume air mass. Keeping track of their variability in the atmosphere at a time scale corresponding to the solar variability (e.g., decadal scale) leads to the conclusion that atmospheric composition is evolving globally [START_REF] Solomon | Climate change 2007-the physical science basis : Working group I contribution to the fourth assessment report of the IPCC[END_REF][START_REF] Stocker | Climate change 2013 : the physical science basis : Working Group I contribution to the Fifth assessment report of the Intergovernmental Panel on Climate Change[END_REF].

Global Atmospheric Circulation

Halley [1686] proposed a (thermal) theory based on convection in order to explain the association of easterly trade winds (northeasterly in the northern hemisphere and southeasterly in the southern hemisphere) with the low-level convergence in the equatorial belt -the place of greatest heating on the Earth by solar radiation generating a low-pressure zone. These air flows are compensated by the return air mass aloft, moving towards the subtropical zone, which causes the formation of high-pressure zone/jet near the horse latitudes 1 . Towards the pole, outside the region of convection, the subsidence of air mass occurs due to the cooling associated with the downward motion and subsequently feeds the northeasterly and southeasterly trade winds at the surface. However, during that time period, this proposed mechanism spawned two major questions : firstly, 'which mechanism produces high-pressure zone/jet in the subtropics', and secondly, 'what was responsible for the circulation of the westerly winds (westerlies) towards the poles at this high-pressure zone' ? Around the 1880s, the first global mean sea-level map was proposed by Léon-Philippe Teisserenc de Bort, showing the vital low and high-pressure zones, i.e., cyclones and anticyclones, respectively. Nevertheless, the theory proposed by Edmond Halley was able to explain the origin of the Asian monsoon, which is based on the differential distribution of temperatures over land and

Ocean surfaces. This is because the land captures less energy from the incoming solar radiation due to its higher reflectivity. It heats up and cools down faster in comparison to the Oceans ; consequently, the continental pressure varies differently than the Oceanic ones due to the variable seasonal heating. The seasonal variations in the thermal structure of the equator got recognized much later. [START_REF] Hadley | Concerning the cause of the general trade-winds : By geo. hadley, esq ; frs[END_REF] explained the deflection of winds in a rotating globe, i.e., to the right in the northern hemisphere, and to the left in the southern hemisphere, respectively. George Hadley put to the fore the Earth's rotational motion playing a role in the direction possessed by an air mass, as it moves upward relative to the surface. His work was mostly based on the analogy of the thermal circulatory mechanisms to make advancement in explaining the existence of the trade winds 2 . Then using the mathematical hypotheses proposed by [START_REF] Coriolis | Mémoire sur les équations du mouvement relatif des systèmes de corps[END_REF] on the motion of revolving bodies on the Earth, [START_REF] Ferrel | An Essay on the Winds and the Currents of the Ocean. Cameron & Fall[END_REF] developed the first three-cell model of hemispherical atmospheric circulations, proposing a mechanism for the origin of high-pressure zone/jet in the subtropics, i.e., ∼ ± 35 • latitudes. Later, the relationship between the pressure variability and the trade wind directions are demonstrated by [START_REF] Buys | Note sur le rapport de l'intensité et de la direction du vent avec les écarts simultanés du baromètre[END_REF]. A schematic diagram is given in Figure 1.3 to explain briefly these circulations.

In Figure 1.3a, the aptness of upper cold air to subside in the subtropics -near the horse latitude, and the increasing influence of the deflective (Coriolis) force on upper air moving towards the pole above westerlies belt builds up a high pressure zone, i.e., the subtropical jets/highs at the subtropics. The thermally dominated Hadley cells use to modulate the trade wind belt of these subtropical jets moving towards the intertropical convergence zone (ITCZ) -discussed in subsequent sections. During the poleward motion of air masses from horse latitudes, they get favorable conditions to move further towards the higher latitudes (shown in red arrows on top of the three-cell). In both the hemispheres, the westerlies comprise 1. Horse latitudes or subtropical jets are situated at subtropical latitudes (within 30 • à 38 • ), both in northern and southern hemispheres, respectively, where the high-pressure zone -an area of anticyclone modulates the atmospheric circulation, subsequently suppressing the rainfall and cloud formation, and possesses variable winds mixed with calm winds.

2. The trade winds are the prevailing pattern of easterlies in the tropics, counterpart of westerlies in the midlatitudes, within the lower atmosphere near the Earth's equator. The trade winds flow mainly from the northeast in the northern hemisphere, and from the southeast in the southern hemisphere, respectively. N-S), and trade winds and westerlies in an idealized conditions (e.g., the equinox). (b) the vertical cross-section of these circulations starting from the equator to the north-pole. Courtesy : https://www.seas.harvard.edu/climate/eli/research/equable/hadley.html of this airflow. The highly variable northern margin of the westerlies (shown in yellow line) is situated at the latitudes, where the westerlies are weakened by polar air mass moving towards the equator -known as polar front [START_REF] Bergeron | Wellen und Wirbel an einer quasistationären Grenzfläche über Europa[END_REF]. In Figure 1.3b, the upward and downward motions of all these overturning circulations are shown explicitly for the northern hemisphere, depicting the division of the troposphere into regions of essentially closed wind circulations. The heat propagation from the equator to the pole sinks at ∼30 • latitude, where the Hadley cell ends. These three-cell motions are responsible for the easterly trade winds in the tropics and dominate the tropical weather patterns. [START_REF] Held | Nonlinear axially symmetric circulations in a nearly inviscid atmosphere[END_REF] delineated the dynamics of these circulations through a simplified model.

Climatology

Humboldt [1817] was the first to determine the global temperature map of mean annual isotherms for the northern hemisphere. Later, [START_REF] Dove | Temperaturtafeln nebst Bemerkungen über die Verbreitung der Wärme auf der Oberfläche der Erde und ihre jährlichen periodischen Veränderungen : eine in der Akademie der Wissenschaften gelesene Abhandlung[END_REF] published his calculations on the monthly mean temperature maps ; [START_REF] Loomis | Contributions to meteorology ; being results derived from an examination of the observations of the united states signal service and from other sources[END_REF] made the global precipitation map employing the mean annual isohyets3 ; De Bort [1884] published his work on annual and monthly global maps of cloudiness. Albeit the lack of detailed measurements over the Ocean surface (∼71% of the Earth's total surface area), the later 19th-century illustrated much progress on climatic research, which was concerned mostly with pressure, temperature and wind distributions. During that time, [START_REF] Hann | Handbuch der klimatologie[END_REF] published his three-volume handbook on climatology, which remained standard until the first quarter of 20th-century. Afterward, it was replaced by the book of [START_REF] Köppen | Handbuch der klimatologie[END_REF]. All these works allowed to classify the climates regionally.

During the inter-war periods, the emergence of a number of climatic ideas became significant, which were not brought to complete accomplishment until the last half of 20th-century. Among them, the work of [START_REF] Fedorov | Das klima als wettergesamtheit (climate as totality of the weather)[END_REF], [START_REF] Nichols | Frequencies of weather types at san jose, calif[END_REF] on the application of using frequencies on various weather types, the work by [START_REF] Gorczyński | The aridity coefficient and its application to california[END_REF][START_REF] Gorczyński | Aridity factor and precipitation ratio and their relation to world climates[END_REF] on the concepts of variability of temperature and rainfall pattern, and the work by [START_REF] Geiger | Das klima d. bodennahen luftschicht[END_REF] on micro-climatology4 , are notable. A detailed history of the terms climate and climatology can be found in [START_REF] Barry | A brief history of the terms climate and climatology[END_REF]. Since the commencement of satellite-era, it became possible to analyze largely assembled global climatic data in order to assess them for the regional-scale generalizations.

Tropical Weather

The climatic evolution described by various theoretical and observational studies promoted the attempts further to understand the regional-scale weather system. It became very important during the last half of 19th-century to utilize them as a forecasting tool for the sailors to predict the directions of the easterly trade winds and the storms. [START_REF] Espy | The philosophy of storms[END_REF] put to the fore a comprehensible convection theory of energy production in cyclones with the release of latent heat as a vital source. Concurrently, [START_REF] Dove | The Law of Storms : considered in connection with the ordinary movements of the atmosphere[END_REF] published a book on the theory of cyclones, stating that the energy for the cyclonic patterns was produced by converging flow of air masses. [START_REF] Ley | The relation between the upper and under currents of the atmosphere around areas of barometric depression[END_REF] proposed a 3D view of a low-pressure cyclonic system having a cold air segment/zone close to a sharp discontinuity in temperature pattern and penetrating into a warmer ambient zone. [START_REF] Abercromby | On the reduction of wind records[END_REF] gave an explanation on the storm systems akin to a pattern of closed isobars with typical associated low-pressure systems. Albeit the cyclonic system energetics were unclear then, an opaque picture of the link between the generation of midlatitude storms and the mixing of warm tropical air masses with cool polar air masses, due to the latitudinal gradients of incoming solar radiation and outgoing terrestrial radiation, was emerged by the end of 19th-century. Afterward, [START_REF] Seilkopf | Maritime meteorologie[END_REF] coined the term 'jet-stream' that denotes a narrow streak of high velocity upon the observation of upper westerlies winds. The typical jet-stream characteristics come in line with the Rossby waves 5 [START_REF] Rossby | The layer of frictional influence in wind and ocean currents[END_REF]. The Rossby wave exists due to the combination of meridional temperature gradients and the rotation of the Earth, i.e., the Coriolis force. This wave is a large-scale wave system whose size is about thousands of kilometers horizontally, and several kilometers vertically. As a consequence of these studies, mostly which are able to explain the frontal depression of the midlatitude, the tropical region (mostly ∼ ± 20 • around the equator), comprising ∼50% of the surface area of the globe, attracted then for the better understanding of the weather variability, therefore the global climate. In the tropics, the temperature discontinuities of the air masses rely on moisture differences, and the weather pattern therein results mostly from the strong convectional features, such as the tropical cyclones and the ITCZ.

Intertropical Convergence Zone (ITCZ)

The intertropical convergence zone (ITCZ) comprises of a band of clouds consisting of showers and occasional thunderstorms, encompassing the Earth near its equator [START_REF] Gray | Global view of the origin of tropical disturbances and storms[END_REF]. The solid band of clouds can expand for many hundreds of kilometers (semi-continuously) around the globe and could be observed as broken smaller line segments. The convergence of the northeast trade winds in the northern hemisphere with the southeast winds from the southern hemisphere spawns the ITCZ. At this convergence point, the trade winds force the air masses to move upward into the atmosphere, thus forming the ITCZ clouds. It is known to be a quasi-stationary zone varying latitudinally with a displacement of ∼5 • annually above the Pacific and Atlantic Oceans, respectively. Elsewhere depending on the season, it can possess a larger displacement between 17 • S to 8 • N in January, and 2 • N to 27 • N in July akin to the southern and northern monsoon seasons, respectively [START_REF] Sikka | On the maximum cloud zone and the itcz over indian, longitudes during the southwest monsoon[END_REF]Gadgil, 1980, Sultan and[START_REF] Sultan | Abrupt shift of the itcz over west africa and intra-seasonal variability[END_REF].

The seasonal displacement of the ITCZ and the impact of other convective influences put to the fore the southeast Asian monsoon as the most significant global weather phenomenon [START_REF] Webster | Monsoon and enso : Selectively interactive systems[END_REF].

Furthermore, it can also appear as a convergence zone in westerly monsoon flow. The monsoon westerlies tend to have easterlies trades towards the poles. The shear line partitioning the monsoon westerlies from easterlies is known as the 'monsoon trough', and is an important region for tropical cyclone formation.

The trade winds convergence line has large vertical wind shear at the ITCZ. When monsoon westerlies are present, the upper-level subtropical ridge lies on top of the low-level monsoon shear line. During the summer in the northwestern Pacific Ocean, the ridge above the monsoon trough is called the subequatorial ridge. This configuration of trade easterlies overlain with westerlies and monsoon westerlies overlain with easterlies gives a vertical wind shear (seasonally averaged) with westerly shear on the poleward side and easterly shear towards the equator. A schematic representation is given in Figure 1.4, explaining its typical 5. The Rossby wave is named for Carl G. Rossby, an early atmospheric research scientist. Observations of waves characteristics (e.g., Rossby waves) in the tropical trade winds began in the Caribbean sea during the 1940s, while the structure of the cloud clusters corresponding to the storms came into light around the 1970s due to the satellite-borne observations, which were proven to be valuable then to detect the formation of hurricanes over the tropical regions in the Oceans. The investigations expanded further in order to conclude a relationship between the south Asian monsoon mechanism and the subtropical jet-streams.

Global Walker Circulation

The pioneering work of [START_REF] Walker | Correlation in seasonal variations of weather-a further study of world weather[END_REF] on the detection of southern oscillation reports on the eastwest fluctuation of the atmospheric pressure, and the resulting rainfall between Indonesia and the eastern Pacific Ocean. The work of [START_REF] Troup | The 'southern oscillation[END_REF] proposed a direct toroidal circulation mechanism to put to the fore the variations observed in southern oscillations and attributed it with the variations in the southeasterly trade winds in the south Pacific Ocean and the consequent variations in the cyclonic vortex formed in the western Pacific Ocean. [START_REF] Rogers | The association between the north atlantic oscillation and the southern oscillation in the northern hemisphere[END_REF] published the connection between southern oscillation occurring over the Pacific Ocean, India Ocean and the western Atlantic Ocean, respectively, with the North Atlantic oscillation occurring over the Atlantic Ocean. All these research works depict the hypothesis proposed by Gilbert T. Walker, stating that there exists a teleconnection, i.e., the connection between climatic conditions and the widely separated regional conditions. A schematic diagram is shown in Figure 1.5, describing this circulation pattern. [START_REF] Mcgregor | Recent walker circulation strengthening and pacific cooling amplified by atlantic warming[END_REF]. The Walker circulation highlights the air mass aloft over the warm western Pacific Ocean as well as the tropical Africa and South America continents during the summer. This pattern is modulated by the solar radiation and the latent heat released by the heavy rainfall activity corresponding to the storms in the tropics. The uplifted air mass gradually settles down in the eastern Pacific Ocean, Atlantic Ocean, and the western Indian Ocean, respectively. Walker circulation depicts well the patterns observed during ENSO (El Niño-Southern Oscillation) events, i.e., El Niño and La Niña [START_REF] Holton | El Niño, La Niña, and the southern oscillation[END_REF].

Obviously, by the end of 20th-century, the existence of global climate system received acknowledgment.

The two-century long research work can be concluded with five subsystems to represent the global climate, viz., atmosphere -rapidly changing system, ocean -possesses greater thermal inertia and modulate the atmospheric variations, snow and ice covers, and land surface types, i.e., the lithosphere and the biosphere. Now, the natural variability is not only due to the external variable forcing by the Sun, but also depends on the nonlinear feedback mechanisms which coexist within the system itself. Major feedbacks comprise of the role of snow and ice layers reflecting the incoming solar radiation, and the atmospheric water vapor absorbing the re-radiation from the Earth's land and ocean surfaces. This can be stated as such, with the increasingly warmer conditions of the Earth, the atmospheric water vapor abundance increases, thus increment of greenhouse gas results in warming the Earth further. Similarly, clouds can play a complex role by reflecting the short-wave radiation, and furthermore by trapping the outgoing long-wave radiation.

It raises the total amount of energy directed towards the surface, thereby inducing a rise in the surface temperature. The natural greenhouse effect is primarily responsible for increasing the Earth' mean surface temperature from about 255 K à 288 K [Bailey et al., 2002, Seinfeld and[START_REF] Seinfeld | Atmospheric chemistry and physics : from air pollution to climate change[END_REF]. However, even today also there exist uncertainties in determining the future climate warming, because of the positive and negative feedback mechanisms in the climate system. The vital role of greenhouse gas feedbacks and their impact on the «stratospheric ozone» budget are of prime importance of investigation, and as such debatable so far [START_REF] Eyring | Sensitivity of 21st century stratospheric ozone to greenhouse gas scenarios[END_REF][START_REF] Forster | Changes in atmospheric constituents and in radiative forcing. chapter 2[END_REF] -detailed discussions are in subsequent sections.

In order to delineate the evolution of global warming conditions in more detail, atmospheric scientists then started investigating the variabilities brought by greenhouse gases in the tropospheric and the stratospheric compositions, respectively. This dissertation indirectly aims at the lower stratospheric compositions and its forcing factors. [START_REF] Fabry | L'absorption de l'ultra-violet par l'ozone et la limite du spectre solaire[END_REF] were the first to discover the presence of O 3 layer in the stratosphere. Later, [START_REF] Chapman | Bakerian lecture. some phenomena of the upper atmosphere[END_REF], [START_REF] Gowan | The effect of ozone on the temperature of the upper atmosphere. ii[END_REF], [START_REF] Maris | The upper atmosphere[END_REF] put to the fore the life-supporting role of the ozone layer, depicting its ability to absorb the ultraviolet radiation. O 3 is being produced by the photolysis of the O 2 molecules in the stratosphere by ultraviolet radiation, thus generating a layer which attains its apogee at 20 km à 25 km altitude. This layer shields the living beings on the Earth from the harmful ultraviolet radiation coming from the Sun. Apparently, the presence of O 3 in the atmosphere plays a paradoxical role.

Odyssey of Stratospheric Research

Its presence in the stratosphere protects living beings from ultraviolet radiation, whereas its presence in the troposphere can create very unfavorable life-supporting conditions [START_REF] Forster | Changes in atmospheric constituents and in radiative forcing. chapter 2[END_REF][START_REF] Jacob | Heterogeneous chemistry and tropospheric ozone[END_REF][START_REF] Marenco | Evidence of a long-term increase in tropospheric ozone from pic du midi data series : Consequences : Positive radiative forcing[END_REF][START_REF] Monks | A review of the observations and origins of the spring ozone maximum[END_REF].

Discovery of Ozone Hole

In the last quarter of 20th-century, the sudden discovery of 'ozone hole' in Antartica [START_REF] Farman | Large losses of total ozone in antarctica reveal seasonal ClOx/NOx interaction[END_REF][START_REF] Solomon | The mystery of the antarctic ozone "hole[END_REF][START_REF] Solomon | On the depletion of antarctic ozone[END_REF]] drew everyone's attention, and atmospheric scientists became very watchful towards the O 3 budget equilibrium on the stratosphere. Before this, [START_REF] Stolarski | Stratospheric chlorine : a possible sink for ozone[END_REF] made a report on the stratospheric ozone destruction. 30 years of satellite observations of ozone hole time evolution is shown in Figure 1.6.

The O 3 destruction is primarily related to the anthropogenic emissions of chlorofluorocarbons (CFCs) -work as an atmospheric thermal insulator, and halogen compounds that can photolyze to produce those radicals which can destroy the O 3 in the stratosphere. The complex compounds from the chlorine reservoir that exists during the polar winter undergo heterogeneous reactions on the surface of the aqueous sulfate aerosols and polar stratospheric clouds (PSCs) to form reactive compounds. These compounds can photolyze upon the arrival of spring to produce the chlorine monoxide radicals in the presence of sunlight.

The oxides of chlorine and bromine have the ability to destroy ozone in catalytic cycles at a scale of 10 5 O 3 molecules per Cl atom [START_REF] Crutzen | Nitric acid cloud formation in the cold antarctic stratosphere : a major cause for the springtime 'ozone hole[END_REF][START_REF] Logan | An analysis of ozonesonde data for the troposphere : Recommendations for testing 3-d models and development of a gridded climatology for tropospheric ozone[END_REF][START_REF] Molina | Heterogeneous chemistry on polar stratospheric clouds[END_REF][START_REF] Solomon | Stratospheric ozone depletion : A review of concepts and history[END_REF][START_REF] Staehelin | Ozone trends : A review[END_REF]. The abundance of other greenhouse gases in the upper troposphere, e.g., CO 2 , CH 4 , N 2 O, O 3 and many halogen group compounds, also drew attention then [START_REF] Wang | Inadequacy of effective co2 as a proxy in simulating the greenhouse effect of other radiatively active gases[END_REF]. Prior to the ozone hole discovery, [START_REF] Levy | Normal atmosphere : Large radical and formaldehyde concentrations predicted[END_REF] communicated that the budget of O 3 in the upper troposphere and lower stratosphere (UTLS) is dominated by the photochemistry of hydroxyl radical (OH -) in the presence of NOx -nitrogen oxides, CFCs, CO and water vapor. This contradicts the previous hypothesis made on the stratosphere-troposphere exchange (STE) across the extratropical tropopause [START_REF] Danielsen | Stratospheric-tropospheric exchange based on radioactivity, ozone and potential vorticity[END_REF][START_REF] Regener | The vertical flux of atmospheric ozone[END_REF]. Therefore, the O 3 budget in the UTLS is a topic of great concern and disputable so far [Lelieveld andDentener, 2000, Stuber et al., 2001].

The very recent study of [START_REF] Solomon | Emergence of healing in the antarctic ozone layer[END_REF] reports about the ozone hole recovery after forbidding the halocarbons under the 1987 Montreal Protocols and its subsequent amendments. Since then, the CFC concentrations have been observed to decline. Putting aside the anthropogenic causes of CFCs and other hydrocarbons and halogen compounds, the N 2 O emission is a big source of producing ozone-destroying NOx radicals in the stratosphere [START_REF] Ravishankara | Nitrous oxide (n2o) : The dominant ozone-depleting substance emitted in the 21st century[END_REF]. However, there are many ongoing debates on the impact role of NOx and water vapor on the O 3 budget in the UTLS [START_REF] Johnston | Reduction of stratospheric ozone by nitrogen oxide catalysts from supersonic transport exhaust[END_REF]. Apparently, NOx turns out to be the more impacting one, though the impact of water vapor cannot be ignored [START_REF] Shindell | Climate and ozone response to increased stratospheric water vapor[END_REF]. The elevated climate forcing parameters can induce additional warnings to the ozone levels by influencing the stratospheric temperature and water vapor concentrations, respectively. It is observed that the increasing levels of greenhouse gases can warm the Earth, and concurrently the energy conservation depicts that they can also generate a net cooling effect in the stratosphere. [START_REF] Thompson | Recent stratospheric climate trends as evidenced in radiosonde data : Global structure and tropospheric linkages[END_REF] report about the mean stratospheric temperature decrement by ∼0.75 K on a decadal scale at ∼35 km altitude since 1979, while the cooling rate is even higher (2.5 K per decade) at ∼50 km altitude. The variability of PSCs and sulfate aerosols and their ability to initiate the catalytic processes involving halogen compounds are modulated by the temperature. Thus, the cooler stratospheric conditions in the stratosphere and the warmer surface conditions can produce more degree of freedom for halogen activation. Subsequently, it can promote the polar ozone destruction due to the catalytic processes caused by chlorine and bromine radicals. Two decades-long research confirms that the Arctic ozone loss is strongly modulated by the ambient stratospheric temperatures. During the winter-spring seasons of the year 2011, the Arctic ozone loss manifests this connection, where the extremely cold temperature led to ∼80% of the ozone loss within 18 km à 20 km altitude range [START_REF] Manney | Unprecedented arctic ozone loss in 2011[END_REF]. During this event in March 2011, a striking feature was observed regarding a very cold vortex temperature, which was about ∼3.0 • C colder than March 1997. Hence, it can be concluded that a small fluctuation in the threshold temperature for sulfate aerosol activation can significantly escalate the O 3 destruction processes in the stratosphere.

The climatic forcing corresponding to the increment of the greenhouse gases plays an important role to increase the stratospheric water vapor levels. The concerns raised over H 2 O abundance in the stratosphere is because its abundance could lead to the production of OH -radicals in the stratosphere, and this is well known to destroy O 3 in the catalytic process. Near the poles, increased water vapor level in the stratosphere can enhance the formation rate and persistence of the PSCs [Toon et al., 1989b]. [START_REF] Kirk-Davidoff | The effect of climate change on ozone depletion through changes in stratospheric water vapour[END_REF] show that a 1 ppmv increment of H 2 O mixing ratio can increase the threshold temperatures for PSC activation by ∼1 • C. Further, this can cause an enhancement in the spatial and temporal extent of the polar ozone loss. Furthermore, [START_REF] Anderson | Uv dosage levels in summer : Increased risk of ozone loss from convectively injected water vapor[END_REF] report that the deep convective outflow can raise the H 2 O mixing ratio up to 12 ppmv in the mid-latitude stratosphere, which can potentially activate the catalytic ozone loss process by the aqueous sulfate aerosols, leading to ∼25% of ozone loss within a very short timescale of few weeks. The severe overshooting convection can also transport very short-lived species (VSLS) corresponding to halogen group into the stratosphere, which would enhance then the feasibility of stratospheric ozone loss. Furthermore, the rise in global surface temperature is observed to elevate the frequency of overshooting events [START_REF] Liu | Global distribution of convection penetrating the tropical tropopause[END_REF]. Consequently, a significant local scale ozone loss could be instigated. Therefore, an increment in stratospheric water vapor budget akin to overshooting convection plumes stands high as a foreseen threat to global ozone loss. It is very certain that H 2 O could be one among several factors to the total O 3 budget in the lower atmosphere (UTLS). Recent modeling based and observational studies depict the significant role of water vapor budget in the UTLS, modulating the global temperature [START_REF] Dessler | Stratospheric water vapor feedback[END_REF][START_REF] Held | Water vapor feedback and global warming[END_REF].

Importantly, the stratospheric water vapor contributes to global warming as the main greenhouse gas and can modulate the surface temperatures on a decadal time scale [START_REF] Shine | A comparison of model-simulated trends in stratospheric temperatures[END_REF], Solomon et al., 2010]. The complex physical and chemical processes occurring within the tropical UTLS is demonstrated to play an important role in the stratospheric water vapor abundance [START_REF] Corti | Unprecedented evidence for deep convection hydrating the tropical stratosphere[END_REF][START_REF] Dinh | Effect of gravity wave temperature fluctuations on homogeneous ice nucleation in the tropical tropopause layer[END_REF], Khaykin et al., 2016]. In the tropics, it is being transported to the stratosphere through the tropical tropopause layer (TTL). Comprehending the mechanisms within the TTL, thus the stratospheric water vapor abundance is of prime importance for global climate [Randel andJensen, 2013, Randel et al., 2004].

A clear understanding of the dynamical variability around and at the TTL is very necessary to delineate the troposphere-stratosphere air mass exchange, given the modulation due to the quasi-biennial oscillation (QBO) [START_REF] Schoeberl | Qbo and annual cycle variations in tropical lower stratosphere trace gases from haloe and aura mls observations[END_REF]. One of the major sources causing annual variability in the total ozone and stratospheric water vapor distribution in the atmosphere around the equatorial belt is the QBO [START_REF] Castanheira | Relationships between brewer-dobson circulation, double tropopauses, ozone and stratospheric water vapour[END_REF]. Another major source is the Brewer-Dobson circulation (BDC) [START_REF] Dessler | Variations of stratospheric water vapor over the past three decades[END_REF] -discussed in subsequent sections.

Quasi-biennial Oscillation (QBO)

The quasi-biennial oscillation (QBO) is a phenomenon corresponding to the change in the tropical stratospheric zonal wind (16 km à 50 km) propagation from westerly to easterly wind regimes with a 'quasi-biennial' periodicity averaging approximately 27 -29 months [START_REF] Angell | Quasi-biennial variations in the "centers of action[END_REF][START_REF] Baldwin | The quasi-biennial oscillation[END_REF][START_REF] Yanai | Stratospheric wave disturbances propagating over the equatorial pacific[END_REF]. The oscillating wind regimes are developed at the top of the lower stratosphere (3 hPa à 90 hPa), and propagate downwards at about 1 km per month before dissipating in the TTL. Downward propagation of the easterlies is generally more complex in comparison the westerlies. Among many, one important feature could be the amplitude of the easterly phase, which is almost twice stronger than that of the westerly phase. Furthermore, easterlies dominate at the top of the vertical QBO domain, while westerlies are more likely to be observed at the bottom. This oscillation is shown in Figure 1.7.

In Figure 1.7a, the corresponding radio sounding measurements were carried out at Canton island shown. The contour of the interval is estimated to be 6 m s -1 , having a band varying between ±3 unshaded.

A band-pass filter is used on them in order to retain the periodicity of 9 and 48 months, respectively. In The QBO represents an important source of ozone variability throughout the lower stratosphere [Butchart et al., 2003, Roscoe and[START_REF] Haigh | The sun and the earth's climate[END_REF]. Within the equatorial region, QBO is only confined to the equatorial stratosphere, a region where O 3 is controlled by transportation, as well as by photochemistry.

Below 30 km in the tropics, O 3 is primarily under dynamical control and thus is affected by the circulation modulated by the QBO. Above 30 km, O 3 production is dominated by the photochemical processes. Thus, it responds to the QBO-induced temperature anomalies rather than transportation effects. Total ozone distribution can be influenced by the QBO for two main reasons : the first one could be the influence of the QBO on the temperature structure in the stratosphere, which in turn affects the photochemical balance of the upper stratosphere, while the second one could be the interplay of the QBO [START_REF] Hood | Effects of solar uv variability on the stratosphere[END_REF]Soukharev, 2003, Kinnersley and[START_REF] Kinnersley | Mechanisms for the extratropical qbo in circulation and ozone[END_REF] with the Brewer-Dobson circulation -this slow circulation is discussed in subsequent sections. The temperature fields can modulate O 3 in two ways. Primarily in the upper stratosphere at the tropics, the temperature field modulates the photochemical reaction rates, such that warm temperatures are associated with lower ozone, whereas the colder temperatures are associated with higher ozone levels. Secondly, the temperature can directly influence the circulation by modifying this aforementioned heating and cooling rates. The QBO is acknowledged to be modulated by the solar variability [START_REF] Labitzke | Association between the 11-yr solar cycle, the QBO, and the atmosphere. Part III : aspects of the association[END_REF][START_REF] Labitzke | Associations between the 11-year solar cycle, the QBO and the atmosphere. Part I : the troposphere and stratosphere in the northern hemisphere in winter[END_REF], Loon and Labitzke, 1988[START_REF] Salby | Connection between the solar cycle and the QBO : The missing link[END_REF]. It can modulate the temperature field and the transportation of air mass in and out of the tropics, thus the composition of the tropical tropopause [START_REF] Davis | Interannual variability of tropical tropopause layer clouds[END_REF]. Hence, it is known to be one of the major source playing role in the lower stratosphere variability in the tropics. It can also affect the monsoon rainfall [START_REF] Chattopadhyay | Possible influence of qbo on teleconnections relating indian summer monsoon rainfall and sea-surface temperature anomalies across the equatorial pacific[END_REF], tropical storm activities [START_REF] Shapiro | The relationship of the quasi-biennial oscillation to atlantic tropical storm activity[END_REF], and polar vortex strength [START_REF] Labitzke | Sunspots, the qbo, and the stratospheric temperature in the north polar region[END_REF][START_REF] Lu | Decadal-scale changes in the effect of the qbo on the northern stratospheric polar vortex[END_REF], therefore of greater importance while investigating phenomena related to the tropical climate system.

At this point, we know about the important role of water vapor in stratospheric ozone loss as a greenhouse gas. Now, it is necessary to discuss further other aspects of water vapor. One important point to investigate could be the radiative balance of the atmosphere corresponding to the water vapor budget in the lower stratosphere.

Radiative Influence of Water Vapor

Water vapor not only impacts the atmospheric circulation by releasing latent heat, forming clouds, and varying rainfall patterns, but also it is a dominant natural greenhouse gas in the atmosphere. The amount of moisture in the atmosphere is strongly linked to the temperature, thus very sensitive to the climate changes [START_REF] Ramanathan | The radiative forcing due to clouds and water vapor[END_REF]. [START_REF] Solomon | Contributions of stratospheric water vapor to decadal changes in the rate of global warming[END_REF] determine that a 1 ppmv increment (∼1% per year) of stratospheric water vapor concentration would enhance the rate of surface warming by ∼30%, where the report is based on the observations corresponding to the years of 1980 -2000. Both observations and model studies depict that a slight rise in the tropospheric H 2 O budget can raise the global temperature [START_REF] Dessler | Stratospheric water vapor feedback[END_REF][START_REF] Soden | The radiative signature of upper tropospheric moistening[END_REF]. Consequently, it would result in further warming as H 2 O feedback is observed to be twice the warming caused by CO 2 [START_REF] Held | Water vapor feedback and global warming[END_REF]. As is discussed earlier, the stratospheric H 2 O can induce an impact on the O 3 chemistry as one of the main sources of the OH -radicals [START_REF] Ravishankara | Water vapor in the lower stratosphere[END_REF]. Furthermore, it can also raise the Earth's total energy budget by absorbing the incoming and outgoing radiation, respectively, i.e., the solar down-welling radiation and the planetary up-welling radiation. Thus, stratospheric water vapor contributes significantly to the global climate system. It is very necessary to understand the mechanisms modulating water vapor concentration in the stratosphere in order to predict the future changes and their feedbacks on the changing climate system.

Using global circulation models (GCMs), it is shown that inclusion of water vapor and other climatic feedbacks can produce ∼3.0 • C warming conditions, given that the amount of CO 2 is doubled in comparison to the pre-industrial era [START_REF] Solomon | Climate change 2007-the physical science basis : Working group I contribution to the fourth assessment report of the IPCC[END_REF]. This warmer conditions can be lowered by ∼1.8 • C, without considering the feedbacks due to water vapor and other greenhouse gases. The surface temperature is therefore modulated by the water vapor budget in the UTLS, the zone where H 2 O molecule absorption lines are unsaturated. The H 2 O molecule can absorb the longwave radiation, causing a sharp attenuation in the corresponding wavelengths at the lower troposphere. Hence, the abundance of H 2 O at these pressure levels corresponding to the UTLS could nullify the impact of radiative forcing. Due to this characteristic of H 2 O molecules of following the temperature changes, the climatic feedbacks of the upper tropospheric water vapor (accounts for ∼55% of the greenhouse effect) are well reproduced in the climate models. Increase in the upper tropospheric temperature can lead to the water vapor abundance in positive climatic feedback.

However, the processes modulating the water vapor in the lower stratosphere are not well understood so far. This is the reason why it is very difficult to make the prediction of water vapor concentration at these pressure levels and their radiative feedbacks.

Albeit the lower concentration of water vapor in the stratosphere, observed fluctuations in the H 2 O concentration are now recognized to have an impact on the net radiative forcing and the surface temperatures [START_REF] Held | Water vapor feedback and global warming[END_REF]. One important tool could be to observe the stratospheric water vapor trends on a large time scale (e.g., decadal times scale). However, due to the dryness of stratosphere, it is very difficult to make a proper water vapor measurements in the extremely cold conditions of the UTLS. Thus, the past trends provide unclear information about the processes linked with stratospheric water vapor abundance. Lack of continuity in the measurements could be another drawback, as the results vary over different periods of time, also constrained to limited spatial-scale. Then, the extrapolation to project the results into the future appears to be impractical.

The UTLS region is accepted as the main conduit to inject water vapor into the lower stratosphere, mostly at the tropics by the large-scale ascent of air mass which is known as the Brewer-Dobson circulation.

Furthermore, here at the tropics, H 2 O is transported to the TTL by deep convection (see section 1.6.5), in which the moist air mass undergoes dehydration processes to several tens of ppmv by the condensation and precipitation processes. Then, the slow ascent of air mass above the level of zero radiative heating is also known to play a role in the water vapor variability in the stratosphere. Nonetheless, all these mechanisms involving water vapor trends are still debatable.

Brewer-Dobson Circulation (BDC)

In order to investigate H 2 O abundance in the lower stratosphere, many attempts were carried out to understand the complex mechanisms of the UTLS, and the role they play in its stratospheric water budget. The breakthrough discovery refers to the landmark work of [START_REF] Brewer | Evidence for a world circulation provided by the measurements of helium and water vapour distribution in the stratosphere[END_REF], [START_REF] Dobson | Origin and distribution of the polyatomic molecules in the atmosphere[END_REF] carried out in England. Alan Brewer and Gordon Dobson explained the large-scale meridional circulation of the stratospheric dry air mass, where the air mass ascends into the stratosphere in the tropics to be transported poleward, then gradually cooled air mass subsides at the high latitudes to the troposphere. This is why the tropical air mass contains less ozone than polar air, albeit the ozone production occurs mostly in the tropical stratosphere. They reported about a simple circulation model, known as Brewer-Dobson circulation (BDC), which describes the existence of a slow current in the winter hemisphere which redistributes air masses from the tropics to higher latitudes [START_REF] Butchart | The brewer-dobson circulation[END_REF]. This slow circulation comprises three parts : the first part depicts the rising motion at the tropics from the troposphere to the stratosphere, the second part depicts the poleward transportation in the stratosphere, and the third part depicts the descending motion of the air mass in both the stratospheric middle and polar latitudes. A point to note that the midlatitude descending air mass in the stratosphere is transported back into the troposphere, while the stratospheric polar latitude descending air mass is transported into the polar lower stratosphere [START_REF] Plumb | A "tropical pipe" model of stratospheric transport[END_REF]. A schematic diagram is shown in Figure 1.8, representing the circulation model.

The term 'Brewer-Dobson' circulation was used for the first time by [START_REF] Newell | Transfer through the tropopause and within the stratosphere[END_REF] to explain this global circulation of tropospheric air mass to the stratosphere at the equator and fallback to troposphere again at the poles. At a first glance, the circulation seems to result from the solar heating in the tropics, and cooling in the polar regions, causing a large equator to pole (meridional) overturning as warm tropical air mass rises, while the cold polar air mass subsides. However, these heating and cooling processes do occur, and such a meridional overturning exists in the form of the Hadley circulation [START_REF] Salby | Interaction between the brewer-dobson circulation and the hadley circulation[END_REF]. It is not the specific reason for the existence of the BDC. Indeed, the BDC results from the large-scale wave motions in the extratropical stratosphere. This circulation attributes to the poleward air mass flow in the UTLS during the winter driven by the Rossby wave forcing [START_REF] Plumb | Stratospheric transport[END_REF]. The forcing features from a non-local wave drag originating from the dispersion of upward propagating waves. The Rossby waves with a westward drag can cause a forcing that could drive the air mass towards the poles in order to conserve the angular momentum. This large-scale wave dynamics lifts aloft the air mass from the tropics and forces them to subside in the higher latitudes.

Atmospheric wave dynamics change on a yearly, two-yearly or decadal timescales. These differences produce an inter-annual variability in the wave activity, which can influence the BDC. When a standing planetary-scale wave arrives at the stratosphere, it accumulates its easterly momentum, thus slowing down the westerly wintertime stratospheric jet stream. The aggregation of easterly air mass momentum into the polar stratosphere and the deceleration of the polar jet depict the 'wave breaking' phenomenon. It can induce the stratospheric sudden warming (SSW) [START_REF] Evan | TTL cooling and drying during the January 2013 stratospheric sudden warming[END_REF], where the warmer air mass of the midlatitude, and even of the tropics protrude into the polar region. This results in a thermodynamically imbalanced situation. In the winter lower stratosphere, the circulation in the polar region is downward. This adiabatic descent, thus compression results in such temperatures that are warmer than the corresponding radiative equilibrium value, and further results in producing a slightly warmer radiative balance. Then, the wintertime radiative cooling of the air mass in the polar stratosphere quickly begins. This cooling process of air mass causes subsidence motions, the sinking motion which establishes the meridional overturning from the equator to the pole in the winter hemisphere. That is why the descending air mass in the polar region must be balanced by a poleward flow of air into the same region. Fulfilling the mass continuity requirements, this air mass must come from the tropics. So theoretically, in the absence of any large-scale atmospheric waves modulating the stratospheric compositions and the BDC, the polar region in the middle The meridional supply of air mass between the troposphere and the stratosphere -the Brewer-Dobson circulation (BDC). The dotted lines refer to the isotherms over the globe, and the solid lines corresponds to the circulation towards the summer and winter poles, respectively, from the equatorial belt, envisaged by keeping track of H 2 O budget [START_REF] Brewer | Evidence for a world circulation provided by the measurements of helium and water vapour distribution in the stratosphere[END_REF] and by keeping track of O 3 budget by [START_REF] Dobson | Origin and distribution of the polyatomic molecules in the atmosphere[END_REF]. Courtesy : http://birner.atmos.colostate.edu/bdc.html. (b) The recent depiction of the BDC playing role in sending H 2 O, H 2 and CH 4 , i.e., the greenhouse gases to the lower stratosphereextracted from [START_REF] Ravishankara | Water vapor in the lower stratosphere[END_REF]. The left inlet shows the H 2 O mixing ratio variation with altitude at midlatitude, which reveals the enhancement up to 7 ppmv in the lower stratosphere (∼70 hPa).

of winter would be much colder than it is observed in the reality.

Recalling the earlier discussions about the dependency of the QBO on the atmospheric waves (e.g., gravity waves, Rossby waves, Kelvin waves), the BDC is acknowledged to be related with the variability of QBO due to its wave-like characteristics [START_REF] Flury | Variability in the speed of the brewer-dobson circulation as observed by aura/mls[END_REF]. Therefore, it stands out to be the main mechanism that can lead to the further advancements in the understanding of stratospheric ozone variability, and therefore the stratospheric water vapor budget. Around the equator, the warm and moist air mass moves aloft in the troposphere along the ITCZ, where convectively driven cumulonimbus clouds protrude into the TTL. These convective towers pump air masses, mostly containing ice hydrometeors into the TTL.

Sometimes due to the severity, it can further rise higher to penetrate into the lower stratosphere. Now in this region, most of the dynamics are dominated by the radiative heating where the air mass can be carried further upward by synoptic-scale slow ascent motion. Additionally therein, the BDC generates the poleward motion on these air masses. Subsequently, the cooled dry air mass then sinks back to the cooler regions at subtropics, resulting in subsidence and forming streaks of local high-pressure zones (subtropical jets at horse latitudes), and hence spawning the arid and semiarid climates modulated by the Hadley cell.

The tropical branch of the Hadley circulation is not a continuous dynamical process that occurs at all longitudes, but rather a series of semi-continuous concentrated bands of 'hot towers' of convection. The ITCZ is seen on globally visible clouds, as a thin streak of thunderstorms within ±10 • to the equator.

In addition, the Hadley circulation is responsible for the lower tropospheric easterlies and the upper tropospheric westerlies, respectively. The BDC circulation can extend up to the mesosphere with an aptness of propagation from the summer hemisphere to the winter hemisphere. The mesospheric air mass propagation then results from buoyancy and gravity waves, causing an eastward drag towards the equator forcing in the summer hemisphere and westward drag towards the poles forcing in the winter hemisphere. This circulation pattern leads to the aridity of the stratosphere. Then, this already dried air mass entering the stratosphere through the high and cold tropopause in the tropics, can be dried further until the hygropause. The stratospheric H 2 O concentration is also constrained by the saturation mixing ratio over ice at the coldest temperature fields encountered by the air mass. These coldest fields within the TTL, i.e., the cold-point tropopause (CPT) regulates the stratospheric water vapor concentration [START_REF] Kim | Tropical cold-point tropopause : Climatology, seasonal cycle, and intraseasonal variability derived from COSMIC GPS radio occultation measurements[END_REF], Randel et al., 2006, Wang et al., 2015]. While the processes resulting in the slow air mass upward movement into the stratosphere are acknowledged so far, several other details of this slow upward transport mechanism are the areas of active research currently. The dynamical processes occurring within and near the TTL are therefore of prime importance to make further advancement in understanding the global stratospheric water vapor distribution.

Tropical Tropopause Layer (TTL)

The tropical tropopause is actually not a sharp boundary or a wall between the troposphere and the stratosphere, rather a transition layer having properties intermediate between pure troposphere and stratosphere. Thus, this zone of gradual transition from troposphere to the stratosphere is called tropical tropopause layer (TTL). The TTL starts from the mean convective outflow at ∼355 K isentrope (∼14 km or 150 hPa), and extends up to the highest level of ∼425 K reached by deep convection, a few kilometres above the CPT (∼19 km or 70 hPa) [START_REF] Fueglistaler | Tropical tropopause layer[END_REF][START_REF] Reiter | Stratospheric-tropospheric exchange processes[END_REF]. The CPT is located within the TTL at ∼380 K isentrope level (∼100 hPa). Below the TTL, the radiatively cooled air mass subsides, while its upward motion can be enforced by the moist convection. Above the TTL, the radiatively heated air mass rises aloft with a slow motion into the stratosphere. The TTL is confined to the subtropical high-pressure zones/jets at about 30 • latitudes laterally. However, these boundaries are slightly permeable with isentropic transport in both directions between the TTL and midlatitude lowermost stratosphere [Folkins et al., 1999, Gettelman andForster, 2002]. The interplay of many dynamical activities take place within the TTL in order to maintain an equilibrium in the radiative budget, and the dynamical physical and chemical processes occurring in the lower atmosphere. Importantly, the TTL is also known to induce a significant impact on the water vapor concentration within the layer and above the layer also due to its typical feature of possessing both the convective activities of the troposphere and the stratospheric gradient characteristics of chemical tracers [START_REF] Highwood | The tropical tropopause[END_REF]Hoskins, 1998, Seidel et al., 2001]. A schematic diagram of the TTL is given in Figure 1.9 featuring the typical mechanisms ongoing within. Many of them are understood so far, while several others raise open questions to date. Understanding all such complex processes of the TTL given the fact that H 2 O abundance can influence climate evolution is of prime importance for current generation atmospheric scientists [Dessler et al., 2016, Randel andJensen, 2013].

The lowermost stratosphere is observed to be very dry [START_REF] Brewer | Measurement of absolute humidity in extremely dry air[END_REF][START_REF] Dobson | Bakerian Lecture. Meteorology of the lower stratosphere[END_REF][START_REF] Mastenbrook | Water vapor distribution in the stratosphere and high troposphere[END_REF], but a little change in the concentrations of H 2 O can initiate a slight disturbance in the net radiative heating budget of the Earth's atmosphere [START_REF] Hall | The diurnal cycle of west pacific deep convection and its relation to the spatial and temporal variation of tropical mcss[END_REF][START_REF] Kiehl | Earth's annual global mean energy budget[END_REF][START_REF] Lubin | Effects of clouds and stratospheric ozone depletion on ultraviolet radiation trends[END_REF]. This slight disturbance in the H 2 O concentration becomes significantly visible and stands out as impacting one by investigating the Earth's surface temperature evolution at a decadal scale [START_REF] Solomon | Contributions of stratospheric water vapor to decadal changes in the rate of global warming[END_REF]. Furthermore, it can influence the stratospheric equilibrium of many physical and chemical processes [Gettelman et al., 2002a[START_REF] Thompson | Tropical deep convection and ozone formation[END_REF], as it is acknowledged to play a role in the O 3 layer balance [START_REF] Kirk-Davidoff | The effect of climate change on ozone depletion through changes in stratospheric water vapour[END_REF][START_REF] Lelieveld | Role of deep cloud convection in the ozone budget of the troposphere[END_REF][START_REF] Oltmans | The increase in stratospheric water vapor from balloonborne, frostpoint hygrometer measurements at washington, dc, and boulder, colorado[END_REF]. Therefore, H 2 O turns out to be one among those very few elements which govern the global energy budget of the stratosphere [START_REF] Forster | Stratospheric water vapour changes as a possible contributor to observed stratospheric cooling[END_REF][START_REF] Mlynczak | A detailed evaluation of the stratospheric heat budget : 2. global radiation balance and diabatic circulations[END_REF][START_REF] Oltmans | Increase in lower-stratospheric water vapour at a mid-latitude northern hemisphere site from 1981 to 1994[END_REF].

Current researchers put to the fore the ability of stratospheric water vapor in altering the global climate [START_REF] Forster | Changes in atmospheric constituents and in radiative forcing. chapter 2[END_REF][START_REF] Forster | Assessing the climate impact of trends in stratospheric water vapor[END_REF], and the surface radiative forcing [START_REF] Solomon | Contributions of stratospheric water vapor to decadal changes in the rate of global warming[END_REF].

Water vapor is transported to the lower TTL by the air masses influenced by rapid deep convective activities, which can sometimes overpass the level of neutral buoyancy (LNB) [START_REF] Takahashi | Where is the level of neutral buoyancy for deep convection[END_REF] -the convective overshooting (COV). Within the TTL during the slow ascent motion, the air mass experiences very cold conditions of the tropopause where it enters the stratosphere. Now according to the hypotheses made so far, there are two situations for the air mass in the TTL : firstly, if the water vapor mixing ratio over ice of the air mass exceeds the ambient ice saturation mixing ratio -supersaturation condition, the excess amount of vapor will condense to form ice crystals, and thus sediments out, dehydrating the air mass to the ambient saturation mixing ratio at the CPT encountered on its trajectory -known as the 'cold trap' of freezing-drying mechanism ; secondly, if the ambient conditions are sub-saturated, i.e., the air mass water vapor mixing ratio is less than the saturation mixing ratio, it will keep on hydrating further the trajectory encountered by it, thus leading to a net hydration in the TTL, and will end up with increasing the water vapor concentration. Even if the saturation is not reached during the slow ascent, the H 2 O concentration therein is already low. This is mostly due to the fact that in the TTL, the outflow from The zoomed version of (a), corresponds to the smaller range of altitude from about 13 km à 18 km, which came into light after twodecades of research work [Jensen et al., 2017a]. It mostly depicts the typical high-frequency atmospheric wave induced processes, freezing-drying mechanism, cirrus clouds formation and overshooting convection.

the deep convection removes lots of water vapor by the precipitation process. While vertical velocities in the TTL are of the order about 0.5 mm s -1 , zonal and meridional velocities are typical of the order about 5 m s -1 , allowing air mass to travel large horizontal distances throughout the globe before ascending into the stratosphere [e.g., Fueglistaler et al., 2009, Tissier andLegras, 2016]. In regions of high convective activity, such as the tropical zone of western Pacific Ocean [START_REF] Jensen | Physical processes controlling the spatial distributions of relative humidity in the tropical tropopause layer over the pacific[END_REF], TTL temperatures can be significantly lower than other longitudes -extremely cold conditions. Subsequently, the air mass traveling through these regions are dehydrated further to levels lower than the saturation mixing ratio, where they cross into the stratosphere [START_REF] Holton | Horizontal transport and the dehydration of the stratosphere[END_REF]. Therefore, the variability in the CPT patterns linked with the tropical deep convection [START_REF] Kuang | Convective influence on the heat balance of the tropical tropopause layer : A cloud-resolving model study[END_REF]] is observed to regulate the H 2 O abundance in the TTL [START_REF] Avery | Large anomalies in lower stratospheric water vapour and ice during the 2015-2016 El Nino[END_REF], Randel et al., 2006]. The emission of thermal infrared radiation by H 2 O and CO 2 can also generate extreme cold conditions, and lead in polar regions to the formation of the PSCs [START_REF] Ramaswamy | Fingerprint of ozone depletion in the spatial and temporal pattern of recent lower-stratospheric cooling[END_REF], Toon et al., 1989b].

The concept of thermal constraints on the water vapor entry to the lower stratosphere and the reason behind its aridity originates from the very first H 2 O measurements carried out by [START_REF] Brewer | Measurement of absolute humidity in extremely dry air[END_REF]. It is widely accepted that the stratospheric dryness is due to the large-scale advection of very cold air, drying out the air mass aloft by the freezing-drying mechanism near the hygropause (H 2 O minima above the tropopause) [Jensen andPfister, 2004, Kley et al., 1979]. This is supported by the observed 'tape recorder' signal of annual cycles of H 2 O mixing ratio variability, where the annual cycles of the TTL temperatures are strongly correlated with lower stratospheric water vapor concentrations [START_REF] Hintsa | Spade h2o measurements and the seasonal cycle of stratospheric water vapor[END_REF][START_REF] Mote | An atmospheric tape recorder : The imprint of tropical tropopause temperatures on stratospheric water vapor[END_REF]. The variability in the annual budget of water vapor related with the TTL temperatures is modulated by the large-scale atmospheric waves originating in the troposphere by deep convection and the gradient of Eulerian potential vorticity in the synoptic-scale weather systems [START_REF] Charney | Propagation of planetary-scale disturbances from the lower into the upper atmosphere[END_REF][START_REF] Haynes | On the "downward control" of extratropical diabatic circulations by eddy-induced mean zonal forces[END_REF][START_REF] Tuck | The brewer-dobson circulation in the light of high altitude in situ aircraft observations[END_REF]. Nevertheless, the trajectory models considering only the synoptic-scale temperature fields around the TTL, i.e., the slow ascent and dehydration to the lowest saturation mixing ratio, are good enough to reproduce rather well the stratospheric water vapor concentrations and variability [START_REF] Fueglistaler | Stratospheric water vapor predicted from the lagrangian temperature history of air entering the stratosphere in the tropics[END_REF]. The report of [START_REF] Seidel | Variability and trends in the global tropopause estimated from radiosonde data[END_REF] on the positive trend in stratospheric water vapor, observed during the years 1980 -2004, puts to the fore the anti-correlation with the TTL temperatures during the same period with a negative trend in the temperatures. Soon after, questions pressed on challenging the legitimacy of such strict thermal control, though both trends are associated with large uncertainties [START_REF] Scherer | Trends and variability of midlatitude stratospheric water vapour deduced from the re-evaluated boulder balloon series and haloe[END_REF], Wang et al., 2012]. Furthermore, [START_REF] Read | The roles of convection, extratropical mixing, and in-situ freeze-drying in the tropical tropopause layer[END_REF] report about few other possible mechanisms related to the convective mixing of H 2 O in addition to the synopticscale slow ascent controlling the water vapor entry to stratosphere using a conceptual 2D model. As such, the frequent detection of supersaturation conditions within the TTL makes complicated the concept of rapid condensation related to the saturation mixing ratio over ice at the tropopause.

Another complex picture in the influence of temperature field within the TTL playing role in the stratospheric water vapor is brought by the deep convection in delivering hydrated (or dehydrated) air mass into the TTL, and sometimes to the lower stratosphere. Measurements of HDO in the TTL manifests the significant evaporation of convectively injected ice particles [START_REF] Moyer | Atmos stratospheric deuterated water and implications for troposphere-stratosphere transport[END_REF][START_REF] Payne | Global satellite measurements of hdo and implications for understanding the transport of water vapour into the stratosphere[END_REF]. Furthermore, it is observed that deep convective processes in addition to synoptic-scale slow ascent with condensation and precipitation of ice, are very important processes within the TTL to influence the amount of stratospheric water vapor [START_REF] Dessler | Effects of convective ice lofting on h2o and hdo in the tropical tropopause layer[END_REF]. The investigation of [START_REF] Webster | Water isotope ratios D/H, 18o/16o, 17o/16o in and out of clouds map dehydration pathways[END_REF] on Figure 1.10 gives an overview of the interaction of overshooting convection with the tropopause. It shows the protrusion of very cold air mass above the tropopause, hereafter denoted as convective overshooting (COV). Sometimes, the convective activity is so severe that it enters the stratosphere (>70 hPa), hereafter denoted by stratospheric overshooting convection (SOC). The current concept goes as follows. Firstly, the very cold air mass entering to the TTL encounters further colder ambient temperatures. The air mass detrains from the COV or SOC turrets generating drier conditions within convective outflow. Drying of air mass therein can also be tied to the precipitation from the mean outflow. The convective outflow can mix with ambient air to produce cold pools, viz., mature or dissipating stage of the plume, where it can further dehydrate air transported through that local area (see Figure 1.10 : two temperature minima in the environmental temperatures). Secondly, the hydration mechanism takes place only in the sub-saturated conditions, when the detrained air mass carrying ice particles flows downstream from a cold pool zone in the TTL [START_REF] Ueyama | Dehydration in the tropical tropopause layer : A case study for model evaluation using aircraft observations[END_REF]. Another case could be the picture above the tropopause, where the air mass encounters sub-saturated or under saturated air due to the warmer stratospheric conditions. Evidently, the ice particles being injected into the TTL has potential to directly hydrate the lower stratosphere while bypassing the extreme cold tropopause. This incoming water vapor is then transported upward further, and towards the poles by the large-scale circulations. These mechanisms are observed to occur as high as 425 K isentrope from the ice particles measurements injected by the overshooting plumes and from cloud brightness temperatures [START_REF] Corti | Unprecedented evidence for deep convection hydrating the tropical stratosphere[END_REF][START_REF] Khaykin | Hydration of the lower stratosphere by ice crystal geysers over land convective systems[END_REF], 2016[START_REF] Reus | Evidence for ice particles in the tropical stratosphere from in-situ measurements[END_REF].

Deep convection penetrating the tropopause is also an important factor at midlatitudes, where warmer tropopause temperatures permit deep convection to transport both ice and water vapor in excess of local stratospheric concentrations. Such overshooting convection is acknowledged to contribute significantly to the stratospheric water vapor budget, and observed as high as ∼40% at 380 K isentrope in the midlatitudes [START_REF] Dessler | A reexamination of the "stratospheric fountain" hypothesis[END_REF]Sherwood, 2004, Hanisco et al., 2007].

In order to assess the large-scale impact of lower stratospheric water vapor abundance, and how it may impact the climate system, it is necessary to consider all those processes involved as a whole set of dynamical processes that controls the stratospheric water vapor budget. It is also important to evaluate how those processes may change in the future, which could bring significant impacts. Certainly, whatever possible transportation mechanisms could be subjected to the stratospheric water vapor, as such SOC at the tropics [START_REF] Kley | Transport of water through the tropical tropopause[END_REF][START_REF] Page | Nasa experiment on tropospheric-stratospheric water vapor transport in the intertropical convergence zone, guest editorial[END_REF][START_REF] Robinson | The transport of minor atmospheric constituents between troposphere and stratosphere[END_REF], slow synoptic-scale uplift [START_REF] Dethof | A mechanism for moistening the lower stratosphere involving the asian summer monsoon[END_REF][START_REF] Park | Transport above the asian summer monsoon anticyclone inferred from aura microwave limb sounder tracers[END_REF][START_REF] Sherwood | Tropospheric water vapor, convection, and climate[END_REF], or the impact of convection generated inertia-gravity waves on the TTL temperatures to form ice clouds [START_REF] Jensen | On the importance of small ice crystals in tropical anvil cirrus[END_REF], Schoeberl et al., 2015] by modulating the ice nucleation process [START_REF] Koop | Water activity as the determinant for homogeneous ice nucleation in aqueous solutions[END_REF], diabatic heating rate at the TTL [START_REF] Schoeberl | Simulation of stratospheric water vapor and trends using three reanalyses[END_REF], ice nucleation threshold [START_REF] Spichtinger | Tropical tropopause ice clouds : a dynamic approach to the mystery of low crystal numbers[END_REF], and even the temperature interpolation method across the CPT [START_REF] Kim | A new wave scheme for trajectory simulations of stratospheric water vapor[END_REF], the amount of stratospheric H 2 O abundance is so far delimited to the coldest region within the tropopause [START_REF] Hartmann | The heat balance of the tropical tropopause, cirrus, and stratospheric dehydration[END_REF][START_REF] Houze | Mesoscale convective systems[END_REF][START_REF] Tseng | Tropical tropopause layer cirrus and its relation to tropopause[END_REF]. Moreover, the role of photochemistry in the oxidation processes of molecular H 2 and CH 4 in the stratosphere and the mesosphere cannot be ignored, which could play a role in the stratospheric water vapor budget [START_REF] Harries | Validation of measurements of water vapor from the halogen occultation experiment (HALOE)[END_REF][START_REF] Le Texier | The role of molecular hydrogen and methane oxidation in the water vapour budget of the stratosphere[END_REF][START_REF] Remsberg | Estimates of the water vapor budget of the stratosphere from UARS HALOE data[END_REF][START_REF] Rosenlof | Stratospheric water vapor increases over the past half-century[END_REF]. Nonetheless, the mechanisms responsible for the hydration (or dehydration) of ascending air mass into the stratosphere, and their individual contributions towards the net stratospheric water budget, is still an open question [START_REF] Dessler | A reexamination of the "stratospheric fountain" hypothesis[END_REF][START_REF] Sherwood | On the control of stratospheric humidity[END_REF][START_REF] Sun | An examination of convective moistening of the lower stratosphere using satellite data[END_REF].

Albeit the tropics determine mostly the entry level for water vapor in the stratosphere, processes operating both in the tropics and at midlatitudes possess the ability to alter stratospheric humidity. Thus, it is important to examine processes which may change the TTL temperatures and associated thermal control of water vapor, tropical convection in the TTL both below and above the tropopause, and midlatitude convection above the tropopause. The case of tropical and midlatitude convection should be taken care of separately, as they are modulated by different factors, and hence induce impacts on stratospheric water vapor differently. Apart from the tropical warmer conditions, the rise in the concentration of the greenhouse gases is also observed to increase the continental convective activities in the midlatitudes. The climate models depict the increased moisture content in a warmer climate, which leads to an increase in the frequency as well as the intensity of storms [e.g., [START_REF] Trapp | Transient response of severe thunderstorm forcing to elevated greenhouse gas concentrations[END_REF]. These variabilities could then increase the amount of ice hydrometeors being injected into the tropopause, thus into the stratosphere by convection. This process will lead to the enhancement of the water vapor in the stratosphere, both lower stratosphere and the over-world 6 stratosphere (>380 K isentrope) [START_REF] Holton | Stratosphere-troposphere exchange[END_REF][START_REF] Jensen | Physical processes controlling the spatial distributions of relative humidity in the tropical tropopause layer over the pacific[END_REF]. As the 6. The over-world region is defined above the 380 K potential temperature surface and contains isentropes that are within the stratosphere. The aridity of stratosphere corresponds to this zone, known as the classic stratosphere. The 380 K potential temperature surface is important because, the zone above this surface comprises of the air masses which descend diabatically to the lower altitudes ; simultaneously, the air masses propagates towards the extratropical tropopause as well.

lower atmosphere around the tropopause is a zone of subsidence due to radiative cooling, and the zone of slow ascent due to radiative heating, respectively, the increased water vapor would, therefore, influence the radiative budget. This might not have any impact on the global stratosphere. However, the increased water vapor in the lower stratosphere could be transported isentropically towards the tropics where it can enter the mean circulations, thus hydrating further the lower stratosphere bypassing the CPT [START_REF] Dessler | Mechanisms controlling water vapor in the lower stratosphere : "A tale of two stratospheres[END_REF][START_REF] Dessler | Effect of convection on the summertime extratropical lower stratosphere[END_REF].

The concept developed behind the freezing-drying (cold trap) mechanism occurring in the vicinity of CPT reflects the idea of removal of water vapor from air mass aloft via the overshooting turret by the sedimentation (gravitational settling) process outside the turret. This process produces ice particles because of the extreme cold CPT, which leads to the formation of cirrus clouds [Jensen et al., 2013a]. [START_REF] Jensen | A conceptual model of the dehydration of air due to freeze-drying by optically thin, laminar cirrus rising slowly across the tropical tropopause[END_REF], [START_REF] Newell | A stratospheric fountain ?[END_REF] explain (partially) the formation of cirrus clouds during the slow ascent, and the so-called fountain regions are pinpointed where the temperature field is observed to be extremely cold near the tropopause. There could be several factors playing role in the variability of CPT temperatures, which may evolve differently as greenhouse gas concentrations increase. [START_REF] Seidel | Variability and trends in the global tropopause estimated from radiosonde data[END_REF] report about the decline in the tropopause temperatures by 5 K per decade, as observed during the years of 1980 -2004. However, several other studies do not share the same opinion about this trend. One fact is puzzling that the warming trends in the tropopause tend to warm further the lower atmosphere, causing a higher tropopause ; while stratospheric cooling induces a colder and higher tropopause. Altogether these factors depict the increasing tropopause height, which is already observed [START_REF] Smalley | Contribution of different processes to changes in tropical lower-stratospheric water vapor in chemistry-climate models[END_REF]. However, this effect on tropopause temperature is still questionable. Tropopause temperatures are also modulated by O 3 concentrations, because of its ability to absorb the direct shortwave radiation in the TTL and release of downwelling long-wave radiation in the stratosphere, respectively.

Using a chemistry-climate model, [START_REF] Austin | Long-term evolution of the cold point tropical tropopause : Simulation results and attribution analysis[END_REF] report on the future tropospheric warming, which can exceed from -0.13 ± 0.07 K per decade in the past to +0.254 ± 0.014 K per decade in the future.

They also put to the fore the past decreases in tropical tropopause temperature, which were the result of the O 3 loss. Additionally, the removal of stratospheric chlorine may also lead to an increment in O 3 in the future, increasing tropical tropopause temperatures, and thus the stratospheric water vapor.

Moreover, another key factor could be the strength of the Brewer-Dobson circulation (BDC), which determines the strength of tropical upwelling and associated cooling in the TTL, thus the TTL temperatures. The advent of greenhouse gases increases the temperature gradient in the UTLS, inducing a shift in the thermal wind balance and in the planetary wave activity at mid-latitudes which drives the BDC. This strengthening effect of the BDC in a warmer climate is well represented in the GCMs [START_REF] Butchart | Simulations of anthropogenic change in the strength of the brewer-dobson circulation[END_REF][START_REF] Li | The strength of the brewer-dobson circulation in a changing climate : Coupled chemistry-climate model simulations[END_REF]. [START_REF] Butchart | Simulations of anthropogenic change in the strength of the brewer-dobson circulation[END_REF] put to the fore the increase in upwelling observed over the last decades, which will continue into the future with the same rate. However, as the BDC strength is related to the temperature gradient in the UTLS, past increases in strength may be related to O 3 depletion, which could also raise the temperature gradient. [START_REF] Li | The strength of the brewer-dobson circulation in a changing climate : Coupled chemistry-climate model simulations[END_REF] attribute ∼60% of past increases in upwelling to O 3 depletion, stating that upwelling may continue to increase. If O 3 concentrations stabilize, its future trend will be smaller than that of the past decades. [START_REF] Engel | Age of stratospheric air unchanged within uncertainties over the past 30 years[END_REF] propose from the tracer measurements that there exists no relation in the trend of the stratospheric age of air mass with the BDC strength. [START_REF] Fu | On the seasonal dependence of tropical lower-stratospheric temperature trends[END_REF] suggest that the BDC could be involved in the past tropopause temperature trends based on their observation of anti-correlation between tropical and polar lower stratospheric temperature trends. [START_REF] Dhomse | The relationship between tropospheric wave forcing and tropical lower stratospheric water vapor[END_REF] report about the increased planetary wave activity during the years of 2000 -2005, which comes in line with the observed decline in TTL temperatures and water vapor over the same period.

Nonetheless, supposedly if the strength of the BDC increases in the future, it would lead to colder TTL, and therefore reduced protrusion of water vapor into the stratosphere. [START_REF] Johnson | Isotopic composition of stratospheric water vapor : Implications for transport[END_REF], [START_REF] Pfister | Gravity waves generated by a tropical cyclone during the step tropical field program : A case study[END_REF], [START_REF] Sherwood | A stratospheric "drain" over the maritime continent[END_REF], [START_REF] Sherwood | A model for transport across the tropical tropopause[END_REF] report about the key role of tropical deep convection, which can potentially hydrate (or dehydrate) the TTL locally by rapid updrafts overshooting the LNB. Since the detection of deep convection playing role in the stratospheric water vapor [Danielsen, 1982, Johnston and[START_REF] Johnston | Thunderstorms as possible micrometeorological sink for stratospheric water[END_REF], its long-term impacts on the global climate system still remains questionable. It is very likely that deep convection will increase in the future [START_REF] Knutson | Tropical cyclones and climate change[END_REF][START_REF] Williams | The Schumann resonance : A global tropical thermometer[END_REF], leading to a net enhancement of stratospheric water vapor through convective injection of ice hydrometeors above the tropopause. Several studies report about the perturbation caused by inertia-gravity waves and their link with deep convection. An inertia-gravity wave can induce a cooling effect in the TTL temperatures, and thus forming the cirrus clouds by ice nucleation [START_REF] Dinh | Effect of gravity wave temperature fluctuations on homogeneous ice nucleation in the tropical tropopause layer[END_REF][START_REF] Potter | The role of monsoon convection in the dehydration of the lower tropical stratosphere[END_REF][START_REF] Vömel | Balloon-borne observations of water vapor and ozone in the tropical upper troposphere and lower stratosphere[END_REF]. In fact, it is known to influence the ice nucleation process, sedimentation and cloud fraction in the TTL, depending on which convection can produce a hydrating effect in a sub-saturated condition or a dehydrating effect in a super-saturated condition in the lower stratosphere, respectively [START_REF] Jensen | Can overshooting convection dehydrate the tropical tropopause layer ?[END_REF], Schoeberl et al., 2014, 2015]. In the tropics, increasing seasurface temperatures (SST) due to warmer climatic conditions may lead to the frequent production of deep convection that is capable of penetrating into the TTL. The warmer SSTs allow more convective activation on a short timescale. Using ozonesonde data corresponding to at least two decades, [START_REF] Solomon | On the distribution and variability of ozone in the tropical upper troposphere : Implications for tropical deep convection and chemical-dynamical coupling[END_REF] demonstrate that ozone-depleted air masses in the lower TTL are indicative of convective injection, and have increased in frequency since the 1980s. Gettelman et al. [2002b] report about the convective available potential energy (CAPE), calculated from tropical radiosonde data, which shows a positive trend since the 1970s. On the contrary, [START_REF] Johnson | Changes in the sea surface temperature threshold for tropical convection[END_REF] and [START_REF] Austin | Long-term evolution of the cold point tropical tropopause : Simulation results and attribution analysis[END_REF] raise concerns about the warming conditions of the SSTs and related frequency of deep convective events related to the warming TTL.

Supposedly, the frequency of deep convective events increase in future with the onset of warming climatic conditions, the TTL would then significantly moisten the stratosphere through the evaporation of ice hydrometeors injected to the tropopause by the SOC. Now moving from one to another aspect of convective injection, the raised frequency of cold convective outflow would cool down the TTL, leading to a greater probability of dehydrating the air mass aloft. The equilibrium between these two effects would, therefore, determine the net impact of a potential increment in convective activity on stratospheric water vapor abundance. [START_REF] Rosenlof | Trends in the temperature and water vapor content of the tropical lower stratosphere : Sea surface connection[END_REF] report on the cooling trend of the tropopause that began during 2000s corresponding to the enhanced frequency of cold convective events. They put to the fore the anti-correlation between the warming SSTs trends and cooling tropopause temperature trends during the years of 2000 -2006. Therefore, the convection could be the link between SSTs and the stratosphere, and the increased cooling trend of the tropopause may be an indication of strengthening tropical convection.

The continuing warming of the tropical SST would lead to a stronger convection, and thus an increased convective cooling of the tropopause, decreasing stratospheric water vapor abundance in the future.

Finally, the concluding factors corresponding to the stratospheric water vapor abundance could be listed as follows :

29

-the increasing tropospheric temperatures ; -changes in the stratospheric ozone budget ; -variability in the Brewer-Dobson circulation ; -warming sea-surface temperature akin to the onset of greenhouse gases ; -increasing deep convective activities in the tropics or midlatitudes.

They have the ability to induce significant impacts on the global stratospheric water vapor budget in the future. This dissertation studies the important features of the overshooting convections in the tropics -the stratospheric overshooting convection (SOC) that protrudes the over-world (>380 K isentrope) at a largescale. Furthermore, this work puts the basis of an upscaling work of the impact of SOC on the stratospheric over-world at a grander scale, and subsequently other impacts akin to the global stratospheric water vapor abundance. In order to predict their feedbacks in the future climate, an improved comprehension of these processes and their relative impacts in determining the stratospheric water vapor budget is of prime importance.

Current State of Water Vapor Measurements

It is very important to have accurate and precise H 2 O mixing ratio measurements so that the attempts being carried out to understand the mechanisms controlling the stratospheric humidity would advance further. The frequency of measurements, i.e., the regularity of measurements is also important to understand the short-and long-term trends in the stratospheric water vapor. Currently, many techniques have been used to assess the water vapor variability in the UTLS, involving with the aircraft-, balloon-and satellite-borne measurements.

Since the emergence of the satellite-borne measurements [START_REF] Alcala | Observations of deep convection in the tropics using the tropical rainfall measuring mission (TRMM) precipitation radar[END_REF][START_REF] Avery | Cloud ice water content retrieved from the caliop space-based lidar[END_REF], Read et al., 2007[START_REF] Russell | The halogen occultation experiment[END_REF], and the balloon-and the aircraft-borne measurements [START_REF] Khaykin | Hydration of the lower stratosphere by ice crystal geysers over land convective systems[END_REF], Schiller et al., 2009], or the radar measurements [Comstock andJakob, 2004, Fan et al., 2010],

the study of temporal, spatial and vertical variability of water vapor in the UTLS have been advanced significantly. The SPARC assessments report [START_REF] Kley | Sparc assessment of upper tropospheric and stratospheric water vapour, wcrp 113, world meteorol[END_REF] on the water vapor measurements carried out at 15 different locations using in situ and remote instruments. So far as per the current research status and the reports made on the lower atmospheric water vapor concentrations, the Aura Microwave Limb Sounder (MLS), the Halogen Occultation Experiment (HALOE) on the upper atmosphere research satellite, and Stratospheric Aerosol and Gas Experiment (SAGE) II on the Earth radiation budget satellite provide the measurements of water vapor concentration in the lower level of the UTLS ; while the fluorescence Lyman-α stratospheric hygrometer for balloon (FLASH-B) and Pico-spectromètres à diode laser accordables (Pico-SDLA) -the balloon-borne diode laser spectrometer based on direct absorption infrared lasers, the fast in situ stratospheric hygrometer (FISH), the Harvard Lyman-α photofragment fluorescence hygrometer (HWV) and JPL tunable diode laser hygrometer (JLH) provide water vapor measurements at the highest level of UTLS.

Akin to the Arctic ozone-loss, many big efforts were carried out, and some are going on currently, in the frame of field campaigns to understand the processes linked with the O 3 loss. «SOLVE/THESEO» -(SAGE) III Ozone Loss and Validation Experiment and the Third European Stratospheric Experiment on Ozone [START_REF] Newman | An overview of the solve/theseo 2000 campaign[END_REF] were two major field campaigns during the years of 1999 -2000. The objective of SOLVE/THESEO was to investigate the processes leading to the O 3 loss in the Arctic vortex and the effect on O 3 variability over northern midlatitudes. The measurements carried out during these campaigns curtailed the gaps in our understanding of many key photochemical processes and the variable forms of chlorine which destroy the O 3 . During the winter of January to March 2010, European Union (EU) deployed an experiment called «RECONCILE» from Arena Arctica [START_REF] Ungermann | Crista-nf measurements with unprecedented vertical resolution during the reconcile aircraft campaign[END_REF]. The main aim of the field campaign was to reconcile the key process and involved parameters for an enhanced predictability ozone loss in the Arctic, and its climatic feedback. The RECONCILE campaign put to the fore the variability of the trace gases present in the UTLS for several kilometers below the flight altitude (∼16 km à 19 km) with a vertical resolution of 400 m à 500 m using a limb-sounding technique. Furthermore, the Jet Propulsion Laboratory (JPL) carried out «AAOE» -Antartica Airborne Ozone Experiment, a field campaign, which was dedicated for the measurements of infrared high-resolution solar spectra using JPL Mark IV interferometer onboard NASA DC-8 aircraft [Toon et al., 1989a]. The main objectives of the AAOE campaign were to determine the burdens of O 3 and other greenhouse gases from the solar spectra in Antarctica.

Stratospheric trace gases measurements in the Arctic then drew attention towards the tropical variability in the UTLS. The EU set out the «HIBISCUS» project comprised of a series balloon-borne measurements during the intense convective summers of the years corresponding to 2001, 2003 and 2004 in the State of Saõ Paulo, Brazil [START_REF] Pommereau | An overview of the HIBISCUS campaign[END_REF]. The campaign was comprised of short and long duration balloons and ground-based measurements retrieved from the «TroCCiBras» -Tropical Convection and Cirrus Brazil project [START_REF] Held | Troccibras and its partner projects hibiscus and troccinox : The 2004 field campaign in the state of são paulo[END_REF]. The main objective of this campaign was to investigate the impact of deep convection on the TTL composition. Analyses of the observational meteorological datasets give a comprehensive understanding of the transport of trace gases and ice particles due to intermittent local cold updrafts, strong enough to protrude the lapse rate tropopause up to 420 K à 440 K isentrope in the lower stratosphere, due to overshooting towers. The long duration balloon-borne measurements depict the contrast between the composition of the lower stratosphere over the land surface and Ocean surfaces, respectively, suggesting the significant global impact of such overshooting events. Within the context of investigating the tropical UTLS, another EU field campaign project called «TROCCINOX» -TROpical Convection, CIrrus, and Nitrogen OXides experiment started during January to February 2005, was set out in the State of São Paulo, Brazil in order to assess the impact of the tropical convection on the distribution of trace gases, characteristics of tropical clouds and aerosol particles focusing on the mechanisms governing the TTL [START_REF] Huntrieser | Lightning-produced no x over brazil during troccinox : airborne measurements in tropical and subtropical thunderstorms and the importance of mesoscale convective systems[END_REF], Schiller et al., 2009]. Aircraft-borne trace gas measurements, e.g., NO, NOx, CO and O 3 , were carried out around the altitude up to 13 km with the German research aircraft, named Falcon. The TROCCINOX project provides the meteorological datasets explaining the contribution of lightning-induced nitrogen oxides (LNOx) from tropical thunderstorms, towards understanding and prediction of the nitrogen oxides (NOx=NO+NO 2 ) concentration and photo-chemical O 3 formation in the troposphere. NOx in the presence of oxidized hydrocarbon products (ROx) from non-methane hydrocarbons (NMHC), CO or CH 4 , play an important role as a catalytic agent for the production of O 3 , which is known to be a major greenhouse gas in the upper troposphere. Furthermore, EU started another field campaign project called «SHIVA» (Stratospheric Ozone : Halogen Impacts in a Varying Atmosphere) [START_REF] Sala | Deriving an atmospheric budget of total organic bromine using airborne in situ measurements from the western pacific area during shiva[END_REF] in the western tropical Pacific Ocean to investigate organic very short-lived species (VSLS), relevant for the atmospheric budget corresponding to the total organic bromine. The campaign took place in Malaysia during November to December 2011. The measurements were carried out using the Falcon aircraft operated by the German Aerospace agency -DLR (Deutsches Zentrum für Luft -und Raumfahrt) covering a range of altitudes from the planetary boundary layer up to the ceiling altitude of the aircraft about 13 km. A staggeringly high number of measurements (about 700) were carried out during the campaign, providing various meteorological datasets based on the largest sources of VSLS, viz., various types of marine biota (mostly micro-and macro-algae), and abiotic processes in near-surface Oceanic waters.

SHIVA project addressed their emissions, transport, transformation, and injection to the stratosphere by both experimental and theoretical approaches. In the frame of this project, the importance of VSLS for past, present and future stratospheric ozone were further investigated using global chemical transport models (CTM) and prognostic chemistry-climate models (CCM). Now among the very recent prominent field campaign measurements corresponding to the investigation of mechanisms corresponding to the TTL, «TRO-Pico» [START_REF] Ghysels | Intercomparison of in situ water vapor balloon-borne measurements from Pico-SDLA H2O and FLASH-B in the tropical utls[END_REF], Khaykin et al., 2016] and «ATTREX» (Airborne Tropical TRopopause EXperiment) [Jensen et al., 2017a[Jensen et al., , 2013b] ] The ATTREX project was a long-range (16 × 10 3 km) and high-altitude (20 km) field campaign. These two recent campaigns build a vast source of datasets representing the typical TTL composition and its variability akin to the tropical overshooting convection. This makes them very important resources for further advancement in the understanding of the mechanisms controlling the stratospheric water vapor budget.

Albeit all these measurements in the frame of field campaign projects discussed so far, there exist uncertainties and limits corresponding to the instruments that flew for the measurements carried out within the UTLS, or the very extreme condition of the TTL, or even the locations of measurements. The same constraints could be pertinent for the satellite-borne observations. Thus, there is a glaring lack of detailed information on physics and chemistry of the UTLS akin to multi-layer complex cloud structures, microphysical properties, the interplay of many dynamical activities at different scales with the sharp change in their velocities. Moreover, on top of these the dominant local cloud top properties makes it very difficult for the retrieval of such passive or active sensor measurements onboard satellites, or the balloonborne sensors, or the aircraft-borne sensors. Now, another aspect to understand the complex TTL could be numerical simulations, which could reproduce these obtained measurements at a different time and spatial scales, so that we could use them for the better understanding of the physical mechanisms governing the UTLS by overcoming the limits or uncertainties in the measurements.

Status of Numerical Simulations

Emergence of Numerical Models

As the satellite-and airborne measurements of the Earth's meteorological composition started unfolding many enigmas of the atmosphere since the last quarter of 20th-century, in order to assess these measurement based studies for further interpretation and advancement our understanding, modeling/simulation-based studies started to emerge. Complementarily, these observational studies created a platform for the advancement of theoretical groups of atmospheric scientists investigating the variabilities in the atmosphere using numerical models. The landmark work of [START_REF] Smagorinsky | General circulation experiments with the primitive equations[END_REF] based on a set of fluid dynamics equations produced the primitive version of general circulation model (GCM). The prescription of dynamical equations therein was adequate enough then to resolve the heat transport from the equator to two poles.

Reproduction of the basic processes such as the moist convection and the cloud formation was at the heart of this model. Subsequently to make progress in the deeper understanding of the coupling of the water cycle and other large-scale circulations, thus their impact role to modulate meteorological conditions [START_REF] Chahine | The hydrological cycle and its influence on climate[END_REF], numerical weather prediction (NWP) [START_REF] Bauer | The quiet revolution of numerical weather prediction[END_REF][START_REF] Tang | The benefits of the met office variable resolution nwp model for forecasting convection[END_REF] model came into play. The main objectives were to reduce the uncertainties in numerical models while estimating the sensitivity of such processes to the meteorological conditions and to adapt to the regional scale variability.

Then, this morphed version of GCM started to incorporate the biosphere and relevant cycles [Sellers et al., 1996a] within the global atmospheric system [e.g., [START_REF] Collins | Development and evaluation of an earth-system modelhadgem2[END_REF][START_REF] Molod | Development of the geos-5 atmospheric general circulation model : evolution from merra to merra2[END_REF], albeit the persisting complexities [START_REF] Stevens | What are climate models missing ?[END_REF]. Commencement of global warming, the rise in greenhouse gas concentration, rise in sea level, and importantly the detection of ozone holes in polar regions have placed a vital question before the atmospheric scientists regarding the future of our global climate [START_REF] Solomon | Climate change 2007-the physical science basis : Working group I contribution to the fourth assessment report of the IPCC[END_REF].

Consequently, the climate change and the weather prediction have gained prime importance through the studies related to the fine-scale (regional) weather to the large-scale (continental) weather, and furthermore to the global weather. As such the development of the parametrization of various atmospheric dynamics is delved in further at various scales in numerical models [START_REF] Prein | A review on regional convection-permitting climate modeling : Demonstrations, prospects, and challenges[END_REF]. The main objectives are to answer the fundamental challenge of scale gap in understanding the typical unresolved phenomena which could be related to the topography or coastlines, or related to convective events.

The numerical models corresponding to the regional scale weather studies are fundamentally computer software that is programmed to describe the fluid motions -for limited region weather models, it is atmospheric circulations based on mathematical equations of motions, given the initial conditions as well as boundary conditions of the domain, i.e., the state of the atmosphere retrieved from the observations datasets of meteorological conditions. These models have the ability to reproduce the past climate, and can also predict the future state of the atmosphere by doing small step size integration backward in time for diagnostic studies and forward in time for the forecast, respectively. The proper representation of water cycle and its coupling with various atmospheric circulations in a regional model lies on its physical parameterization for the better representation, rather than a computationally expensive representation, and the important boundary layer processes prescribed within [START_REF] Stensrud | Parameterization schemes : keys to understanding numerical weather prediction models[END_REF]. For the numerical models, it requires sufficiently high horizontal and vertical grid-point resolution of the simulation to reproduce or forecast typically short-range/scale (mesoscale) weather phenomena in comparison to global scale numerical models. These mesoscale phenomena are tuned by topography, or can be related to convection, where they can represent mostly very short-lived dynamics such as, severe tropical convection, thunderstorms, cold air damming, tropical storms, high-frequency atmospheric waves and cloud cycles [START_REF] Pielke Sr | Mesoscale Meteorological Modeling[END_REF]. The importance of mesoscale models, i.e., a middle-scale numerical model in comparison to a synoptic scale 7 , lies with the fine grid-point resolution simulation, which is able enough to resolve the local scale features.

Current State of Modeling Corresponding to TTL

Numerical models cannot resolve the very fine scale features and processes occurring within the confined grid-points. Thus, mesoscale models cannot resolve the local severe convective flows and swirls. Most of the non-hydrostatic model compromise with the vertical grid-point resolution to make the real-time simulation with comparatively fine horizontal grid-point resolution. In the regional mesoscale models to resolve the convection well, the horizontal grid-point must be of <4 km, and known as convection-permitting models (CPM). Similarly for the large-scale models (LSMs), the horizontal grid-point is generally >10 km [START_REF] Done | The next generation of nwp : explicit forecasts of convection using the weather research and forecasting (wrf) model[END_REF][START_REF] Prein | A review on regional convection-permitting climate modeling : Demonstrations, prospects, and challenges[END_REF]. Importantly, to study a phenomenon like the SOC, horizontal grid-point must be of <1 km and of a few hectometres vertically [START_REF] Dauhut | Large-eddy simulations of hector the convector making the stratosphere wetter[END_REF]. Thus, it is not realistic at all to expect weather models to resolve features like turbulent eddies at this scale, which makes it impractical to upscale its impact of the deep overshooting convection on the TTL H 2 O abundance at a large-scale. Now to address the ensuing problem of the dissertation work, and to advance our understanding by focusing on the better representation of the interplay of general circulation within the TTL with the influence of moist convection, variable cloud structures, convection produced high-frequency atmospheric waves and its interaction with the temperature field [e.g., [START_REF] Dessler | Transport of ice into the stratosphere and the humidification of the stratosphere over the 21st century[END_REF][START_REF] Jensen | Physical processes controlling the spatial distributions of relative humidity in the tropical tropopause layer over the pacific[END_REF][START_REF] Matus | The role of cloud phase in earth's radiation budget[END_REF], we start working with the BRAMS 3D mesoscale model -Brazilian version of RAMS, further details are in Chapter 2. But before going into details of this mesoscale model, it is necessary to give a flashback of other numerical simulation based studies developed relevant to our problem.

The conundrum of ascending air mass intercepting a trajectory of varying saturation mixing ratio over ice represents the uncertainty of hydrating or dehydrating the TTL. Thus, it is important to look at the progress brought by trajectory models relevant to our problem. Several trajectory studies driven by meteorological analyses succeed at least qualitatively in reproducing the stratospheric water vapor variability, rather well in the TTL [e.g., [START_REF] Dessler | Variations of stratospheric water vapor over the past three decades[END_REF][START_REF] Schoeberl | Simulation of stratospheric water vapor and trends using three reanalyses[END_REF] without considering the severe overshooting convection overpassing the LNB. Thus, it is deduced that most of the water vapor entry to the stratosphere is due to an advection-condensation mechanism during the slow ascent towards the very cold tropopause, followed by the sedimentation of ice particles [START_REF] Holton | The influence of gravity wave breaking on the general circulation of the middle atmosphere[END_REF]Gettelman, 2001, Liu et al., 2010b]. This freezing-drying or cold-trap mechanism leads to the dehydration of air entering to the stratosphere at tropics, and particularly very efficient in the Pacific where the CPT is the coldest [Hasebe et al., 2007, Schoeberl and[START_REF] Schoeberl | Dehydration of the stratosphere[END_REF]. It can be concluded from the trajectory-based studies that the CPT in the tropics regulates H 2 O abundance in the lower stratosphere [Randel et al., 2006, Wang et al., 7. Note that scales are defined according to the operation domain -global for entire Earth, regional for continents or states 2015].

As we have already discussed the role of large-scale atmospheric waves on the stratospheric water vapor budget, it is also important to discuss the inertia-gravity wave, which is shown to play a vital role in modulating the water vapor abundance in the TTL conditions recently. Gravity wave plays a key role in the troposphere-stratosphere exchange [START_REF] Fritts | Gravity wave dynamics and effects in the middle atmosphere[END_REF]Alexander, 2003, Holton et al., 1995]. It has a wellobserved influence on the net radiative heating and water vapor exchange that occurs within the UTLS [START_REF] Holton | The influence of gravity wave breaking on the general circulation of the middle atmosphere[END_REF], and also known for its energy dissipation that can heat the ambient atmosphere [START_REF] Kim | Ubiquitous influence of waves on tropical high cirrus clouds[END_REF]. Admittedly, the deep convection in tropics is a major driving force in producing inertia-gravity wave [START_REF] Alexander | The gravity wave response above deep convection in a squall line simulation[END_REF][START_REF] Jewtoukoff | Gravity waves generated by deep tropical convection : Estimates from balloon observations and mesoscale simulations[END_REF]. Recent works of Kim andAlexander [2013, 2015], [START_REF] Schoeberl | The impact of gravity waves and cloud nucleation threshold on stratospheric water and tropical tropospheric cloud fraction[END_REF][START_REF] Schoeberl | Gravity waves amplify upper tropospheric dehydration by clouds[END_REF] put to the fore its significance in the modulation of ice hydrometeors nucleation and water vapor abundance in the TTL.

In contrast to these large-scale processes, COV may penetrate into the stratosphere -the SOC, and injecting ice particles into an environment that is often sub-saturated, leading to the sublimation of ice in the stratosphere and an increase of water vapor. This is concluded both by in situ observations [e.g., [START_REF] Khaykin | Hydration of the lower stratosphere by ice crystal geysers over land convective systems[END_REF], 2016, Schiller et al., 2009] and modeling studies at the convective system scale [e.g., [START_REF] Chaboureau | A numerical study of tropical cross-tropopause transport by convective overshoots[END_REF][START_REF] Chemel | Quantifying the imprint of a severe hector thunderstorm during ACTIVE/SCOUT-O3 onto the water content in the upper troposphere/lower stratosphere[END_REF], Liu et al., 2010a]. The signature of SOC cannot be identified through the satellite-borne WV measurements at the global scale, because of the coarse vertical resolution (e.g., MLS) or the poor precision (e.g., AIRS) to detect local WV enhancement within a narrow range of altitude in the TTL. Consequently, the quantitative role of SOC on the stratospheric water vapor with respect to the large-scale dehydration has not been estimated directly so far. However, the stratospheric water vapor enhancement due to a single event has been estimated to range between 100 t [START_REF] Hassim | A model study on the influence of overshooting convection on TTL water vapour[END_REF], 300 t à 500 t [Liu et al., 2010a] and 2776 t [START_REF] Dauhut | Large-eddy simulations of hector the convector making the stratosphere wetter[END_REF] with a frequency estimation of 13 overshooting events per minute in the tropical belt [START_REF] Iwasaki | Characteristics of deep convection measured by using the A-train constellation[END_REF]. [START_REF] Hassim | A model study on the influence of overshooting convection on TTL water vapour[END_REF] report about the overshooting turrets reaching up to 420 K isentropic surface at the tropics, where they incorporated the WRF mesoscale model with a horizontal grid-point resolution of 1000 m à 250 m following the nested-grid simulation method. Liu et al. [2010a] report about the overshooting turrets reaching up to 400 K isentropic level, where the mesoscale simulations were carried out using the BRAMS mesoscale model with a horizontal grid-point resolution of 20 000 m à 1000 m using a nested-grid simulation. [START_REF] Dauhut | Large-eddy simulations of hector the convector making the stratosphere wetter[END_REF] also report about the overshooting turrets reaching up to 18 km altitude using the Meso-NH mesoscale model. They studied the 'Hector' thunderstorm of Tiwi Islands using a horizontal grid-point resolution of 1600 m à 100 m using a set of simulations. [START_REF] Lelieveld | Stratospheric dryness : model simulations and satellite observations[END_REF] give an estimation of the annual mean of upward H 2 O flux of ∼600 t min -1 across 75 hPa on the tropical belt through the general circulation model ECHAM5/MESSy1 and the HALOE measurements. They also emphasize on the entry of the tropospheric air into the stratosphere in the tropics enforced by large-scale atmospheric waves. [START_REF] Ueyama | Dynamical, convective, and microphysical control on wintertime distributions of water vapor and clouds in the tropical tropopause layer[END_REF] estimate an enhancement of ∼0.3 ppmv of H 2 O across 100 hPa at a large-scale in the southern hemisphere from the trajectory-based studies initiated from convective cloud tops. An indirect signature of the SOC at the global scale can be obtained by studying the diurnal cycle of the Aura MLS H 2 O mixing ratio due to deep convection reaching higher than 100 hPa [START_REF] Carminati | Impact of tropical land convection on the water vapour budget in the tropical tropopause layer[END_REF], highlighting the regions where convection is the most active. This confirms the former results of [START_REF] Liu | Global distribution of convection penetrating the tropical tropopause[END_REF]. But none of these aforementioned studies are able to quantify the direct impact of SOC in the global abundance of stratospheric water vapor so far. Another possible approach to answer this question is the upscaling of SOC from cloud resolving small-scale to larger-scale (e.g., continental scale, or even global scale), with the modeling tools.

Thesis Objectives

After all aforementioned discussions of fundamentals of the Earth's atmosphere, advent of meteorology, climatology, stratospheric ozone-loss, and attention towards the tropical deep convection in regards to the stratospheric water vapor, our thesis motivation, in the frame of an upscaling of the impact of SOC on the stratospheric water vapor at a grander scale (main goal), can be summarized as follows :

-as of the first step, we establish a modeling tool (the BRAMS mesoscale model) that would be utilized for our main goal, which is 'upscaling the impact of SOC on the stratospheric water vapor at a continental scale'. Here, we take advantage of the TRO-Pico campaign balloon-borne measurements, and other satellite-and balloon-borne observations to validate the large-scale simulation of a full wet season over the southern hemisphere (Brazilian scale). The important feature of this simulation is the complete absence of SOC, where we validate the BRAMS model for upscaling study ;

-secondly, we extract several key parameters/features from fine-scale simulations of SOC with the BRAMS model, which will help us to prepare a forcing scheme of SOCs. Here also, we use TRO-Pico campaign balloon-borne measurements, and S-Band radar measurements to validate the fine-scale simulations. This scheme will be used to nudge the impact of SOC in a large-scale simulation, like the one we discuss in chapter 3, to upscale its impact on the stratospheric water vapor at a continental scale. This would be the main essence of this thesis towards upscaling study. This chapter reviews the essential tools used during this dissertation work. In particular, it describes the BRAMS (Brazilian Regional Atmospheric Modeling System) mesoscale model, the tropical version of the American RAMS model. The detailed descriptions, in particular, the essential settings and parameterizations schemes sensitive to this work (convection, microphysics, radiative module), are elaborated. This chapter also describes the main sources of measurements/observations corresponding to the variability in the TTL, used for the validation of the model. At first, the TRO-Pico project campaign is described. This is a field campaign project of small open stratospheric balloons (500 m 3 à 1500 m 3 ) or lightweight balloons (1.2 kg) during a whole wet season, comprising two periods of intensive observation at the peak of the convective season. TRO-Pico aims to better understand and quantify the role of stratospheric overshoots on stratospheric water vapor, on a small-scale, to deduce an impact on a large-scale. The campaign instruments that we describe in priority are the Pico-SDLA laser hygrometer and the Lyman-α FLASH-B hygrometer. We also describe the RS92 radiosonde series during the intensive observation period of the field campaign. We also use the S-Band radar installed at Bauru to infer convective cloud peaks. It is briefly described. Then, we describe the satellite-borne observations, which are relevant to our study, and used to validate our simulations : the cloud top products from the GOES-12 geostationary satellite, the TRMM precipitation measurements, the overshoot climatology (not necessarily stratospheric) by the MHS instrument, and the Aura MLS water vapor measurements. Finally, other radio sounding measurements used for our study are also described, where the measurements are retrieved from different locations over Brazil, from the upper-air database of Wyoming University.

BRAMS

The BRAMS mesoscale model -Brazilian developments on Regional Atmospheric Modeling System [START_REF] Freitas | The Coupled Aerosol and Tracer Transport model to the Brazilian developments on the Regional Atmospheric Modeling System (CATT-BRAMS) -Part 1 : Model description and evaluation[END_REF] is tuned for the tropical meteorology. It is maintained and developed at CPTEC/INPE (Centro de Previsão de Tempo e Estudos Climáticos, Instituto Nacional de Pesquisas Espaciais) using RAMS (version -5.04) [START_REF] Cotton | RAMS 2001 : Current status and future directions[END_REF] //brams.cptec.inpe.br/about/, while its major components can be summarized as follows :

-a mesoscale model that provides the real-time simulations of actual meteorological conditions at any spatial length/scale (generally limited to continental scale study) ; -a compilation of data analysis from the meteorological reanalysis data and satellite or radar observations, which produces the initial conditions to begin the simulation for the mesoscale model ; -a post-processing modeled data visualization and analysis package that can interface with a variety of visualization software utilities (e.g., GrADS : Grid Analysis and Display System).

BRAMS model is a limited-area mesoscale model, but it can be configured to encompass a large area as one of the hemispheres of the Earth for simulating large-scale meteorological systems. This mesoscale model is constructed using the full set of primitive dynamical equations that govern atmospheric circulations, and as an accessory, it can incorporate optional parameterizations for turbulent diffusion, solar-terrestrial radiation, moist processes including the formation and interaction of clouds and precipitating ice-liquid hydrometeors, latent heat exchanges, multiple soil layers, vegetation or deep forestation canopy, surface water, kinematic effects of terrain, and most importantly the tropical deep convection.

In regards to RAMS, BRAMS is deemed completely for the tropics tailored sub-grid scale shallow cumulus and recently developed deep convection parameterization (mass flux scheme) [START_REF] Grell | Prognostic evaluation of assumptions used by cumulus parameterizations[END_REF][START_REF] Grell | A description of the fifth-generation Penn State/N-CAR mesoscale model[END_REF], the SiB (version -2.5, Simple Biosphere Model) sub-model land surface scheme [Sellers et al., 1996a,b] and heterogeneous soil moisture initialization. A point to note here is that BRAMS can be coupled with the Chemistry Aerosol Tracer Transport (CATT) module [START_REF] Longo | The chemistry CATT-BRAMS model (CCATT-BRAMS 4.5) : a regional atmospheric model system for integrated air quality and weather forecasting and research[END_REF] as well, though, for our studies, this is not considered.

General Concept

The three very fundamental principles of physics in any kind of motion, viz., conservation of mass, momentum, and energy are the primary elements, and therefore embedded inside any (atmospheric) modeling system. For atmospheric motions/circulation, they can be expressed in the form of equations of hydrodynamics and thermodynamics [START_REF] Kasahara | Various vertical coordinate systems used for numerical weather prediction[END_REF][START_REF] Lindzen | Dynamics in atmospheric physics[END_REF][START_REF] Van Delden | The dynamics of meso-scale atmospheric circulations[END_REF]]. Pielke [START_REF] Pielke Sr | Mesoscale Meteorological Modeling[END_REF] provides these derivations incorporated within the mesoscale systems, while comprehensive derivations of such nonlinear primitive equations are prescribed in [START_REF] Holton | An introduction to dynamic meteorology[END_REF]. In the ensuing section, a set of equations solved by the BRAMS model are given in their volume averaged form.

The BRAMS model is well equipped to solve the compressible non-hydrostatic equations [START_REF] Cotton | The colorado state university threedimensional cloud/mesoscale model-1982. part ii : An ice phase parameterization[END_REF]Cotton, 1982] using its multiple grid-nesting schemes, which is used as an asset in the model to solve the equations simultaneously on any number of two-way interaction between computational meshes of increasing spatial-resolution. In order to solve equations exactly with numerical techniques, the solution has to be computed at elementary (molecular) level, which is the most challenging task for the atmospheric scientists so far. To overcome this problem, the conservation equations are used to be integrated over certain specified spatial and temporal scales (discretized system), and of course constrained to the computing sources. An averaging decomposition performed on the conservation equations can be expressed as, Ψ = Ψ + Ψ , where Ψ denotes the dependent variable of the system, Ψ is the averaged value over time and space (i.e., Δx, Δy, Δz, Δt), and Ψ is the sub-grid scale perturbation, which has to be parameterized in the model. Ψ can be defined as, Ψ = (2.1)

In this numerical modeling system, Δt is the time step of integration, while Δx, Δy and Δz are the spatial step size within the grid domain, and it uses forward time differencing method for the thermodynamic variables and leapfrog differencing method for the pressure and velocity components [START_REF] Cotton | RAMS 2001 : Current status and future directions[END_REF].

Equations of Motion

The equations of motion in Cartesian-plane are,

∂u ∂t = -u ∂u ∂x -v ∂u ∂y -w ∂u ∂z -θ ∂π ∂x + fv + ∂(u u ) ∂x + ∂(u v ) ∂y + ∂(u w ) ∂z , (2.2
)

∂v ∂t = -u ∂v ∂x -v ∂v ∂y -w ∂v ∂z advection -θ ∂π ∂y pressure gradient -fu coriolis force + ∂(v u ) ∂x + ∂(v v ) ∂y + ∂(v w ) ∂z turbulent diffusion , (2.3)
where u is the zonal wind speed (x-direction), v is the meridional wind speed (y-direction), and w is the vertical wind speed (z-direction). π is the perturbation form of the Exner function (π) that fluctuates like pressure, viz.,

π = c p p p • κ .
Here, p • = 1013 hPa, c p is the specific heat of dry air at constant pressure, κ = cv cp . c v is the specific heat of dry air at constant volume. In mesoscale models, the pressure gradient is expressed in terms of Exner function. θ is the potential temperature. The subscript '•' denotes the unperturbed value at a reference surface, whereas the ' ' denotes its counterpart -the perturbed value.

And, the vertical momentum equation for the non-hydrostatic condition is

∂w ∂t = -u ∂w ∂x -v ∂w ∂y -w ∂w ∂z -θ ∂π ∂z - gθ θ • buoyancy force + ∂(w u ) ∂x + ∂(w v ) ∂y + ∂(w w ) ∂z . (2.4)

State of Thermodynamics

The prognostic thermodynamic state can be expressed as,

∂θ il ∂t heating rate = -u ∂θ il ∂x -v ∂θ il ∂y -w ∂θ il ∂z horizontal advection + ∂(u θ il ) ∂x + ∂(v θ il ) ∂y + ∂(w θ il ) ∂z turbulent flux divergence + ∂θ il ∂t radiative flux divergence , (2.5)
where θ il is the ice-liquid water potential temperature. This term is emphasized instead of potential temperature to avoid specification of latent heat tendencies. Thus, θ il remains unchanged in the presence of all water phase changes [START_REF] Tripoli | The use of lce-liquid water potential temperature as a thermodynamic variable in deep atmospheric models[END_REF].

State of Mass-continuity

The mass continuity equation enforces the mass conservation as follows :

∂π ∂t = - Rπ • c v ρ • θ • ∂ρ • θ • u ∂x + ∂ρ • θ • v ∂y + ∂ρ • θ • w ∂z , (2.6)
where R refers to the universal gas constant in SI units, θ is the potential temperature in Kelvin, and ρ is the air density. π • , ρ • and θ • are the synoptic-scale reference values of these prognostic variables [START_REF] Pielke Sr | Mesoscale Meteorological Modeling[END_REF].

Equation of Continuity : H 2 O Mixing Ratio

Water species mixing ratio (r n ) is prognosed by

∂r n ∂t = -u ∂r n ∂x -v ∂r n ∂y -w ∂r n ∂z + ∂(u r n ) ∂x + ∂(v r n ) ∂y + ∂(w r n ) ∂z .
(2.7) With this current framework, the non-hydrostatic model is able to integrate predictive equations for the wind field (u, v, w), π, total liquid mixing ratio (r t ), and many more scalars for the ice-liquid microphysics, along with the ice-liquid water potential temperature (θ il ) on a telescopic Arakawa-C gridding system.

Scheme of Kinematic and Thermodynamic Grids

The RAMS model, embedded within the BRAMS, uses the staggered Arakawa-C gridding system [START_REF] Mesinger | Numerical methods used in atmospheric models[END_REF]. All the mass representative variables are situated at the center of the grid-point of the simulation, the meridional velocity (v) is located Δy 2 to the north and South of the center, and zonal velocity (u) is located Δx 2 to the east and west of the grid-point. The X-Y plane of the grid-points uses a polar-stereographic projection, while the Z-direction plane comprises of the σ z terrain-following coordinate [START_REF] Clark | A small-scale dynamic model using a terrain-following coordinate transformation[END_REF], where it can hold the mapping between u and v. A schematic diagram in Figure 2.1 illustrates this method. The vertical grid-point levels can be optimized as per the requirements or can be set to increase geometrically towards the topmost point of the grid. This helps to resolve the boundary layer processes having a fine vertical resolution within the layer itself while compromising with a coarser vertical resolution from the surface to a certain lower altitude below the considered boundary layer and again after the top of that boundary layer until the topmost point of the grid domain for saving the computing resources.

One of the most promising features of BRAMS is that it is capable of incorporating a telescoping nested-grid scheme [START_REF] Walko | An interactive nesting algorithm for stretched grids and variable nesting ratios[END_REF], which enhances the ability of the model to reproduce phenomena involving a wide range of spatial scales. In the grid-nesting system, the parent-grid (PG) covers the full domain of the simulation, while the nested-grids (NG) delve into a smaller domain in comparison to the PG in order to make an intensive investigation of smaller-scale features in atmospheric science by resolving spatial resolution of the grid-points. The full description of this grid-nesting scheme can be found in [START_REF] Clark | Severe downslope windstorm calculations in two and three spatial dimensions using anelastic interactive grid nesting : A possible mechanism for gustiness[END_REF], [START_REF] Clark | Multi-domain simulations of the time dependent navier-stokes equations : Benchmark error analysis of some nesting procedures[END_REF].

On a brief note, this bi-directional interactive grid-nesting scheme of the prognostic1 variables of the model between NGs and PG, and similar mutual communication between multiple nested-grid systems, allows the localized fine grid-points to resolve the compact atmospheric systems of limited small-scale, while simultaneously it can simulate the large-scale atmospheric phenomena also on a coarser grid-points [START_REF] Pielke | A comprehensive meteorological modeling system-RAMS[END_REF]. Thus, the model has neither any lower limit nor upper limit to the domain size or to the mesh cell/grid-point size, and hence it can simulate the micro-scale phenomena, such as tornadoes and boundary layer inter-mixing, as well as sub-micro scale turbulent eddies.

In order to conserve the volume integrals of density-weighted parameters between the grid-points, such as potential temperature and moisture, they are multiplied by their respective densities prior to the communication from PG to NGs and vice versa. Therefore, the NGs follow a shorter time step of integration in comparison to the PG to maintain the simulation stability. Firstly, the PG simulates the prognostic variables at every time step, then the updated values within PG are interpolated both in time as well as in space to match up with the time step and the cell size of its NGs, respectively. Afterwards, the prognostic variables along the boundaries of the NGs grid-points are replaced by the values from the interpolated values of their PG. The NGs are then advanced with the simulation for the prognostic variables in a form of smaller time step units until they catch up with the concurrent simulation time step of their PG.

Finally, the density-weighted prognostic variables over each set of the NG grid-points situated in a single PG grid-point, replace the values of the prognostic variables of that PG grid-points.

Boundary Condition : Incorporation of Reanalysis Meteorological Field

In general, mesoscale models are configured to simulate atmospheric motion on a limited area. Thus, they need an initial condition and grid-point boundary condition to constraint the simulation boundary tendencies by incorporating an artificially enclosed side/wall. It is important to assign values for the dependent variables at the boundary of the domain of the simulation. The main purpose of boundary conditions can be briefed as follows, -to introduce the temporal and spatial evolving parameters to the external forcing into the model domain ;

-to damp the information propagating within the grid-point to the lateral boundary in order to avoid their reflection back into the grid-point.

The treatment of each boundary is different, which can be denoted as top-bottom and lateral boundary conditions, respectively.

Lateral-boundary Conditions

Mesoscale models incorporate two types of lateral-boundary conditions :

-open lateral-boundary -mesoscale perturbations can move into and/or out of the model domain ;

-closed lateral-boundary -mesoscale perturbations are not allowed to enter or exit from the model domain.

The lateral-boundary condition used in the Arakawa-C gridding system follows a radiative condition. This radiative condition minimizes the reflection of outward propagating perturbations within the flow so that it cannot fall back into the model domain. For the east-west boundary, the velocity parameter normal to the boundary of a grid-point is :

∂u ∂t = -(u + c) ∂u ∂x , (2.8)
where u is the zonal velocity, and therefore normal to the eastern-western boundaries of a grid-point. The phase velocity (c) is based on the [START_REF] Orlanski | A simple boundary condition for unbounded hyperbolic flows[END_REF] scheme, and equal to ratio of the model domain height to the Brunt-Väisälä frequency2 (N B ) multiplied by π, where N B is given by,

N B = g θ ∂θ ∂z , (2.9)
and is known to be the static stability of the atmosphere. Here in BRAMS for our study, c is the modified version of [START_REF] Klemp | The simulation of three-dimensional convective storm dynamics[END_REF]. The variables other than the normal velocity are defined by the Δx 2 or Δy 2 away from their normal components with boundaries assigned to zero-gradient conditions, constant inflow and outflow conditions, and radiative outflow conditions. For rest of the variables other than the normal velocity component, the zero-gradient scheme is incorporated. The value of each variable at the boundary is set to the value immediately adjacent to it in the interior, and thus it puts to the fore the zero-gradient condition. It is more useful for the simulations having horizontally homogenous initial conditions.

The BRAMS model could also incorporate a 'cyclic' boundary condition for the north-South direction.

This condition makes the model periodic in the Y-direction, and effectively eliminates the north-south lateral boundaries from the solution. This can be enforced by assigning the values of the dependent variables at one boundary to be identical with the corresponding values at the other end of that boundary [START_REF] Pielke Sr | Mesoscale Meteorological Modeling[END_REF].

Top-boundary Conditions

For a set of non-hydrostatic equations, BRAMS has two options for the treatment of the top-boundary conditions, i.e., a simple wall option at the top, i.e., w = 0, and a Rayleigh friction/sponge-layer at the top of the grid-point to prevent the reflection of gravity waves from the model top into the model grid.

For our case, the [START_REF] Klemp | An upper boundary condition permitting internal gravity wave radiation in numerical mesoscale models[END_REF] gravity wave radiative condition is applied in order to damp them within a sponge-layer at the upper part of the grid and avoid any reflection. In this sponge-layer, an extra term is added to the basic prognostic equations, so that they are nudged towards the horizontally homogenous reference state. It can be expressed as follows :

∂φ ∂t = φ obs -φ m τ , (2.10)
where φ is the model parameter, the subscript 'obs' and 'm' denote observational data and modeled data, respectively, and τ is the nudging time scale and varies linearly with height. Note that a large value of τ can weaken the nudging strength. Usually, a value of 60 s à 300 s is chosen for the top of the domain having a strong effect in damping the gravity waves.

The prognostic field (u, v, θ il , π, r t ) of BRAMS requires meteorological reanalysis data for its grid-point initialization, lateral boundary conditions, and the four-dimensional data assimilation (4DDA) scheme, to start a run by exchanging exterior forcing with the interior. Therefore for our studies, the ECMWF [START_REF] Tremback | Numerical simulation of a mesoscale convective complex : Model development and numerical results[END_REF] observational data analysis package is used for the meteorological input fields of the simulation.

ISAN incorporates a hybrid vertical coordinating system, which is a mixture of isentropic and the terrainfollowing σ z coordinating system. It uses the σ z coordinate in the lowest layer, whose depth (depth of the boundary layer) can be modulated as per the motive of the investigation field. This is to avoid the problem of intersection between the ground surface and isentropic surfaces. It alleviates the problem of the vertical level increment or even decrements in isentropic surfaces (θ) within the planetary boundary layers (PBL). To take advantage of these isentropic coordinates, a transition layer from σ z coordinate to isentropic coordinate is chosen. These data can be accessed over the domain of interest for the simulation and can be interpolated onto the BRAMS polar-stereographic grid-points. This creates a polar pressure coordinate system, where the data are interpolated vertically to the vertical isentropic-coordinate and the terrain-following σ z coordinate.

Modules : Incorporation of Physical Parameterizations

The BRAMS mesoscale model is a set of several sub-models or modules working commensurately to produce the optimal meteorological conditions, which are broadly maneuvered by a turbulent mixing parameterization scheme, convection parameterization scheme, radiation parameterization scheme, surface layer parameterization scheme, and soil and vegetation parameterization scheme. As a whole, they represent a mesoscale simulation. They are briefed in subsequent sections without getting into much detailed mathematical backgrounds.

Module for Eddy Flux

The physics of the model uses the K-theory [START_REF] Smagorinsky | General circulation experiments with the primitive equations[END_REF] to resolve the transportation of the prognostic variables during the turbulent mixing. According to K-theory,

∂u j ∂t turb = ∂ ∂x i -K mi ∂u i ∂x j + ∂u j ∂x i , (2.11) ∂φ ∂t turb = ∂ ∂x i -K hi ∂φ ∂x i , (2.12)
where u i is the speed in i-direction, x i is the i-direction independent variable, φ refers to the scalar parameter of the simulation, K mi is the eddy mixing coefficient for u i , and K hi is the eddy mixing coefficient for φ. The subscripts i and j indicate the direction of motion normal to each other on a plane Cartesian coordinate system.

Module for Convection

Proper parameterization of convective systems is still a challenge to prescribe in mesoscale models in order to achieve a proper representation of their impact and interaction with other physical and chemical processes within any large-scale meteorological system. Fundamentally, this is a method by which atmospheric circulation models account for the convective effects through the redistribution of temperature and moisture in the column of a grid-point of the simulation. Incorporation of such parameterization can prevent the grid-point scale microphysical scheme, i.e., very small scale features from creating unrealistic large-scale convection by reducing the thermodynamic instability, and excessively active low-level cyclogenesis [START_REF] Houze | Mesoscale convective systems[END_REF].

The BRAMS model is equipped with the Grell's convective parameterization scheme for the deep and shallow cumulus convection [START_REF] Grell | A generalized approach to parameterizing convection combining ensemble and data assimilation techniques[END_REF]. This parameterization scheme determines all deep convective clouds as of one size comprising of two steady-state motions, viz., updrafts and downdrafts. It adopts a method where the fractional area coverage of updrafts or downdrafts in the grid-column is not necessary to be of a small-scale. Thus, it is suitable for a grid-point with the horizontal resolution of about 10 km à 12 km. The prescription is such that the mass flux between the levels corresponding to the beginning and ending of updraft or downdraft is considered as constant. The mass flux of the downdraft evolves as a function of the updraft mass flux and the evaporation of the condensate within that convective plume. For the shallow convection, this scheme parameterizes the PBL-forced (energy flux) shallow convection as well as mid-tropospheric shallow convection caused by other sub-grid scale processes due to the radiative cooling [START_REF] Grell | A description of the fifth-generation Penn State/N-CAR mesoscale model[END_REF]. It has a strong lateral mixing, causing no convective downdrafts and precipitation, where the mass flux is calculated by the cloud-work function (A). The cloud-work function calculates the kinetic energy production per unit cloud-base mass flux, i.e., a standard criterion to determine the buoyancy force associated with a cloud ensemble (λ) [START_REF] Arakawa | Interaction of a cumulus cloud ensemble with the large-scale environment, part i[END_REF]. A schematic diagram of this parameterization scheme is given in Figure 2.2.

As such in many cumulus parameterization schemes, the cloud properties are determined by using simplified cloud models, which could lead to several sensitivity issues within the working frames. In case of the Grell's parameterization scheme, the assumptions embedded within can directly influence the vertical distribution of heat, moisture and rainfall accumulation. Mathematically, it can be expressed following the notations as in [START_REF] Grell | Prognostic evaluation of assumptions used by cumulus parameterizations[END_REF], where λ denotes the ensemble type. Then, the entrainment hypothesis of the parameterization is :

μ ue (z, λ) -μ ud (z, λ) = 1 m u (z, λ) ∂m u (z, λ) ∂z , (2.13)
m u (z, λ) = m b (λ)η u (z, λ), (2.14)
where η u is the normalized mass flux. Using the equations 2.13 and 2.14, the steady-state motion of a modeled convective plume could estimate the cloud properties, viz., the liquid water content, moist static energy, mass flux, condensation and evaporation profiles for each ensemble, given the initial condition and closure type for the entrainment and the detrainment mechanisms, respectively. Furthermore, this parameterization scheme can be tuned to adapt several other closure types in order to estimate m b having the information about the amount and position of the convection inside the domain of the simulation. Our study follows the 'ensemble' closure type, where the definition of the cloud-work function (A) follows one type of stable equilibrium that strongly relies on the cloud temperature, ice hydrometeors concentration, precipitation rate and radiative cooling by ice. An equilibrium between the large-scale forcing and the cloud response can be expressed as Putting different criteria to the equation 2.15, other closure types can be derived [see [START_REF] Grell | A generalized approach to parameterizing convection combining ensemble and data assimilation techniques[END_REF]. Here, the ensemble mean of m b is then determined at each time step of the simulation for each grid-point to calculate the optimal feed back value into the 3D model.

A(λ) -A (λ) dt = m b (λ) A (λ) -A(λ) m b (λ)dt , ( 2

Module for Radiation

The [START_REF] Harrington | The effects of radiative and microphysical processes on simulated warm and transition season Arctic stratus[END_REF] short/long wave radiation parameterization scheme is used for our study due to its bi-directional stream interaction with ice-liquid hydrometeors' size spectra. It includes a double moment microphysical scheme having seven different classifications of hydrometeors, viz., liquid cloud droplets and rain for liquid particles ; pristine, snow, hail, graupel, and aggregates for ice particles [START_REF] Meyers | New RAMS cloud microphysics parameterization. Part II : The two-moment scheme[END_REF].

This new microphysical parameterization scheme incorporates the application of the generalized gamma distribution as the basis function for all type of hydrometeors. Furthermore, it takes the advantage of using a heat budget equation for different category of hydrometeors that allows the heat storage and mixed phase hydrometeors by introducing additional classifications of graupel and hail hydrometeors. Therefore, they lead to their number concentration and mass mixing ratio as prognostic variables in the BRAMS simulation.

The bi-directional stream radiation scheme uses the two-stream equation method of [START_REF] Louis | A parametric model of vertical eddy fluxes in the atmosphere[END_REF] in the compact matrix forms, and can be expressed as,

dF dτ = AF(τ) + S(τ), (2.16
)

dF s dτ = F s μ • , (2.17)
where the matrices can be given as,

F =   F + F -   , A =   γ 1 -γ 2 γ 2 -γ 1   , S =   S + S -   , (2.18)
where τ is the optical depth, F + and F -are the direct upward and downward diffused fluxes, respectively, S + and S -are the upward and downward source contributors to diffuse the fluxes, respectively, γ 1 and γ 2 are the coefficients related to the reflection and transmission functions, respectively, and μ • is the cosine of solar zenith angle. It is consistent with the single-moment bulk microphysical scheme of Walko et al.

[1995a], an explicit liquid microphysical model of [START_REF] Feingold | The relationship between drop in-cloud residence time and drizzle production in numerically simulated stratocumulus clouds[END_REF], and a mixed phase microphysical model of [START_REF] Reisin | Rain production in convective clouds as simulated in an axisymmetric model with detailed microphysics. part i : Description of the model[END_REF]. Thus, cloud optical properties are determined for each form of the cloud condensate, i.e., for the aforementioned seven classes of hydrometeors.

This radiative transfer model adopts the FESFT (fast exponential sum-fitting) method of [START_REF] Ritter | A comprehensive radiation scheme for numerical weather prediction models with potential applications in climate simulations[END_REF] to determine the absorption due to CO 2 , H 2 O and O 3 molecules. The ice hydrometeors' extinction coefficients and absorption coefficients are determined using the method of [START_REF] Mitchell | A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. part ii : Dependence of absorption and extinction on ice crystal morphology[END_REF]. Similarly, for the H 2 O molecule in liquid form, the respective coefficients are computed following a modified ADT (anomalous diffraction theory) method as described in [START_REF] Mitchell | Parameterization of the mie extinction and absorption coefficients for water clouds[END_REF], while the optical properties are determined using the method of [START_REF] Slingo | On the shortwave radiative properties of stratiform water clouds[END_REF]. And in case of liquid bin microphysical model for a given hydrometeor at a given bin, the optical properties are determined by its distribution functions.

Module for Microphysics

The microphysics parameterization scheme represents the ability of a model to emulate the cloud and rainfall accumulation processes, which remove excess moisture from the ambient atmosphere directly as a result of the dynamically driven wind circulation pattern, temperature and moisture fields. In the BRAMS mesoscale model, the microphysical scheme corresponds to the work developed in [START_REF] Cotton | RAMS 2001 : Current status and future directions[END_REF] and is known as 'bulk' microphysical scheme. Routinely, two microphysical schemes are used, where the first one assumes the size-spectra determined by the analytical gamma distribution functions with fixed shape parameter, while the second one is an explicit bin representation of the size-spectra distribution functions of ice-liquid hydrometeors without any prescribed distribution of shape dependency. In our case, this version of microphysics adapt the first condition, and is termed 'bulk', because it assumes the fact that all hydrometeors' distribution follows a gamma function form [START_REF] Flatau | The csu-rams cloud microphysics module : General theory and code documentation[END_REF], Walko et al., 1995a],

which can be expressed as below,

n(D) = N t Γ(ν) D D n ν-1 I e -D Dn D n II , (2.19)
where n(D) is the number density, D is the diameter of hydrometeor ∈ [0, ∞], ν is the shape parametermust be a real number (≥ 1) that controls the relative amount of smaller vs. larger hydrometeors in the distribution, N t is the total concentration of a given microphysical species, D n is the characteristic diameter of the distribution of various moments (mass of the hydrometeors), and Γ(ν) is the gamma function. In As mentioned earlier, this bulk microphysics deals with seven different hydrometeors classes, viz., cloud water, rain, pristine ice, snow, hail, graupel, and aggregates, both diagnostically and prognostically according to the settings. The simplest version of the model assumes an immediate conversion of the supersaturated vapor to liquid water. This water is termed as cloud water. Rain starts forming as the size of the cloud droplets become bigger enough to initiate the collision-coalescence process, which is based on the work of [START_REF] Berry | An analysis of cloud drop growth by collection : Part i. double distributions[END_REF]. Pristine ice forms by the vapor deposition, leading it to attain a small amount of rime. Snow is produced by the vapor-grown pristine ice, i.e., larger pristine ice converts into the snow. The collection of snow and ice produces aggregates, which may also attain rime in small quantity. The rest of the significant rimed ice is treated as either hail or graupel. A detailed description about these hydrometeors can be found in Walko et al. [1995a].

The cloud concentration nuclei (CCN) and the nuclei for these ice hydrometeors can be given as an input to the simulation or can be prognosed. The shape parameter (ν) of gamma function Γ(ν) of all types of hydrometeors must be specified, and higher values of it generally narrow the distribution spectra of hydrometeors. A schematic diagram is given in Figure 2.3 representing the variability of ν and its impact on the number density distribution (n(D)) and the hydrometeor diameter (D).

In Figure 2.3 as ν increases, the concentration is weighted more to the hydrometeors having larger sizes, as well as larger masses. Consequently, in order to account for this significant concentration loss, the mass-loss ratio increases [START_REF] Harrington | Parameterization of ice crystal conversion processes due to vapor deposition for mesoscale models using double-moment basis functions. part i : Basic formulation and parcel model results[END_REF]. Hence, this scheme incorporates the physical processes accounting for ice nucleation, sedimentation, precipitation, condensation, sublimation, evaporation, collisions, and shedding. [START_REF] Cotton | RAMS 2001 : Current status and future directions[END_REF] microphysical set up is such that it can have the flexibility to change the formulation of the parameterization scheme in order to adapt for different applications.

Module for Surface Flux

Within the coupling scheme of the land surface model to atmospheric model [e.g., [START_REF] Chan | On the co2 exchange between the atmosphere and the biosphere : the role of synoptic and mesoscale processes[END_REF][START_REF] Denning | Simulated variations in atmospheric co2 over a wisconsin forest using a coupled ecosystem-atmosphere model[END_REF], i.e., the land-atmosphere (here, SiB vs. BRAMS) interaction, the exchange of the energy, momentum, and tracer between them play a major role. Considering the varieties of land (controlled by temperature and wind speed) are parameterized by the SiB model [Sellers et al., 1996a,b].

Prescribing a partition between sensible heat and latent heat fluxes can control the surface temperature fields, which is mostly driven by the land surface type. While the momentum flux parameterization imple-mented in the BRAMS model can be expressed as,

w u = -(a 2 F m )u 2 , (2.20) a 2 = Κ ln( z z• ) 2 , (2.21)
where w u denotes the time averaged vertical momentum of the horizontal wind (u), 'a' refers to the drag coefficient under neutral conditions, 'Κ' is the von Kármán constant, 'z' is the corresponding vertical level, z • is the roughness length, and F m can be defined for two conditions, i.e., for stable condition [START_REF] Louis | A parametric model of vertical eddy fluxes in the atmosphere[END_REF] :

F m = 1 1 + 10R iB √ 1+5R iB , (2.22)
and for the unstable and neutral condition [START_REF] Holtslag | Local versus nonlocal boundary-layer diffusion in a global climate model[END_REF] :

F m = 1 - 10R iB 1 + 75a 2 z z• |R iB | , ( 2

Experimental Design

All the simulations presented in the frame of this dissertation are mostly performed using a single grid Before going into further details of different types of simulations carried out, a table below (Table 2.1) highlights the name list configuration prescribed in a file called 'RAMSIN' -the input file for the simulation with all the variables and varieties of settings. RAMSIN carries the various constituents of the input data preparation codes that are provided to the model to initiate the simulation, similarly for the output data, procedures are also mentioned inside RAMSIN.

Description of RAMSIN file

A brief version of the RAMSIN is tabulated in Table 2.1 with short descriptions regarding the model setups. This is compiled for all types of simulations carried out during our study.

Table 2.1 -Name list of the RAMSIN file and their description.

MODEL_GRIDS

-set up for the simulation real-time run, space domain with a number of grid-points and other grid parameters MODEL_FILE_INFO -generally comprised of the variables who control the input and output data of the simulation : refers to the frequency of writing the analysis and history files MODEL_OPTIONS -consists of majority of choices for model parameterization (microphysics scheme) -hydrometeors category and their mean diameters -number concentration per unit volume of air (CCN) -shape parameter (ν) of the gamma distribution -lateral and top boundary conditions -surface roughness length for computing the surface vertical fluxes of momentum, sensible heat, and latent heat MODEL_SOUND -specifications of the sounding to be used for the initialization of the simulation ISAN -flag to switch on or off the ISAN stage run, and directs towards the observational data to be used for the simulation MODEL_PRINT -specifications for writing selected data as outputs of the simulation into the standard output files

Physics of the Mesoscale Simulation

The modules corresponding to various physical parameterization schemes, which are incorporated within the BRAMS simulations, are tabulated in Table 2.2.

Technical Aspects

The Table 2.3 shows some typical computing parameters and corresponding values required to accomplish the scale of simulations we present in this dissertation. These values can be optimized according to the requirements (e.g., simulation run time, stable spin-up of the simulation).

Overview

The TRO-Pico campaign [e.g., [START_REF] Carminati | Impact of tropical land convection on the water vapour budget in the tropical tropopause layer[END_REF], Ghysels et al., 2016] The main objective of this project is to investigate the impact of deep convection, and especially overshooting convection on the TTL and the lower stratosphere water vapor budget on the local scale.

Furthermore, it provides the variability of water vapor budget in the TTL during a full convective season.

This becomes a great asset for numerical simulations to upscale the impact of overshooting convection at a large-scale (the main objective of this dissertation). As a complement to the satellite-borne observations also, this field campaign provides key meteorological parameters for large-scale studies of the overshooting convection [e.g., [START_REF] Khaykin | Evidence of horizontal and vertical transport of water in the southern hemisphere tropical tropopause layer (TTL) from high-resolution balloon observations[END_REF]. Moreover, this project is formulated as such to answer the dilemma of electric fields akin to thunderstorms, and its consequences on the life cycle and composition of cirrus clouds.

The water vapor measurements of this project are supposed to be incorporated as a validation tool, required for both the infrared atmospheric sounding interferometer (IASI) instrument onboard the European space platform MetOps satellites, and the sounder for probing vertical profiles of humidity (SAPHIR) onboard the French-Indian space platform Megha-Tropiques. To accomplish these objectives, this field campaign includes a combination of balloon-borne, ground-based, and satellite-borne observations. Additionally, the application of cloud-resolving models (CRM) helps to characterize the local-scale processes. Satelliteborne observations that are useful for a chemistry-transport model are used as complements to upscale these processes at large-scales. instrument of ∼9 kg, which emits at 2.63 µm, and the optical path length of the instrument in ambient conditions is 1 m, thus particularly very sensitive to the pollution by ambient water vapor [START_REF] Durry | Laser diode spectroscopy of H 2 O at 2.63 μm for atmospheric applications[END_REF]. It uses the Beer-Lambert law to retrieve the mixing ratio from the absorbed signal by ambient water vapor molecules [START_REF] Ghysels | Intercomparison of in situ water vapor balloon-borne measurements from Pico-SDLA H2O and FLASH-B in the tropical utls[END_REF]. Thermal design of this laser module was development very carefully due to the drastic change in its the ambient temperature (in the TRO-Pico campaign, it varied from 40 • C à -90 • C). The estimation of uncertainties in the retrieved mixing ratio of a single spectrum in the TTL ranges from 3.5% to 7.5%, note that the estimation of uncertainty in mixing ratio was 4.4% during a most severe condition of CPT -85 • C. Here, the precision of vapor mixing ratio can be enhanced by the data average technique using N spectra, then the signal to noise ratio would be improved by a factor of √ N.

See Chapter 3.3 for more details of the measurements done using Pico-SDLA in the TRO-Pico campaign.

FLASH-B

FLASH-B (Fluorescent Advanced Stratospheric Hygrometer for Balloon) is a balloon version of Lymanα hygrometer, a light-weight (∼2 kg) compact sonde developed at the Central Aerology Observatory, Russia, and can be easily integrated with Vaisala radiosonde [START_REF] Yushkov | Optical balloon hygrometer for upper troposphere and stratosphere water vapor measurements[END_REF]]. Its purpose is the same as Pico-SDLA, just the mixing ratio retrieval technique is slightly different as it is dedicated to night-time water vapor measurements only. This instrument's working principle is the fluorescent method based in [START_REF] Bertaux | Premières measures stratosphériques par un hygromètre à fluorescence ultraviolette[END_REF], [START_REF] Kley | Measurement of water vapor in the stratosphere by photodissociation with Ly α (1216 å) light[END_REF]. As every hygrometer has to be calibrated in the laboratory before the flight, it is not an absolute instrument for water vapor measurements. It uses the fluorescence at λ ∼310 nm of excited OH -radicals produced in the photodissociation of H 2 O molecules (at λ <137 nm using a Hamamatsu R647-P photomultiplier in photon-counting mode) by UV radiation with hydrogen glow-discharge lamp, viz., Lyman-α radiation with λ =121.6 nm. The fluorescent light intensity is directly proportional to the vapor mixing ratio within 150 hPa à 30 hPa, with a little O 2 absorption of 3% at 50 hPa [START_REF] Ghysels | Intercomparison of in situ water vapor balloon-borne measurements from Pico-SDLA H2O and FLASH-B in the tropical utls[END_REF], Vömel et al., 2007]. See Chapter 3.3 for the FLASH-B water vapor measurements used during the TRO-Pico campaign.

RS92

The Vaisala radiosonde, manufactured by Vaisala -a Finnish company, RS92-SGP PTU gives excellent accuracy in relative humidity (RH), pressure, temperature and wind measurements using a silicon pressure sensor, heated twin humidity sensor, a small, fast temperature sensor, featuring a GPS receiver for wind finding. The transmitter in RS92-SGP working principle is synthesizer-based, stable, and uses a narrow bandwidth. In addition, it can measure ozone as well using an interface unit of ozone sensor. A detail evaluation of this radiosonde can be found in [START_REF] Kobayashi | Comparison of meisei rs2-91 rawinsondes and vaisala rs92-sgp radiosondes at tateno for the data continuity for climatic data analysis[END_REF]. [START_REF] Milankovitch | Development and validation of a time-lag correction for vaisala radiosonde humidity measurements[END_REF] propose a correction method to account for the time-lag error in the measurement calibrations due to the slow response of the sensors at very low temperatures ; while [START_REF] Miloshevich | Accuracy assessment and correction of vaisala rs92 radiosonde water vapor measurements[END_REF] prescribe a correction to the RH measurements retrieved from RS92 radiosonde, where the bias correction was reported to be influenced by the clear-sky or the near-clear conditions corresponding to the complicated solar radiation reflection mechanisms in the presence of clouds. However, the temperature uncertainty in RS92-SGP is about 0.5 • C, while the pressure uncertainties could vary differently within difference pressure levels, as such the uncertainty in the pressure measurement is 1.5 hPa for 1080 hPa à 100 hPa, and 0.6 hPa for 100 hPa à 3 hPa range of pressure levels, respectively. During the TRO-Pico campaign, the RS92-SGP were launched from January 23 to February 12, 2013, with a frequency of 1 to 4 measurements per day. Concurrently, zonal wind (u) and meridional wind (v) are collected for inertia-gravity wave analysis. Furthermore, the temperature and pressure measurements from the RS92 onboard the FLASH-B payload are also taken into account in the temperature climatology. In this dissertation, we utilize this series of radio soundings during the IOP2. drawback could be its little sensitivity towards detecting ice hydrometeors. Thus, the cloud top altitude retrieved from the echo top akin to an overshooting turret could be underestimated, as the turrets are mostly comprised of ice hydrometeors. We comment further on this while the analysis in Chapter 4. The detailed radar technology can be found in [START_REF] Meischner | Weather radar : principles and advanced applications[END_REF].

S-Band Radar

Other Observational Data

MHS

Microwave Humidity Sounder (MHS) [START_REF] Bonsignori | The microwave humidity sounder (mhs) : in-orbit performance assessment[END_REF] [2005], Rysman et al. [2017]. There is a wide application of this climatology in detecting the overshooting convection to study its impact on the TTL and lower stratosphere [START_REF] Funatsu | Convective activity in Mato Grosso state (Brazil) from microwave satellite observations : Comparisons between AMSU and TRMM data sets[END_REF][START_REF] Hong | Interannual to diurnal variations in tropical and subtropical deep convective clouds and convective overshooting from seven years of AMSU-B measurements[END_REF][START_REF] Rysman | Severe convection in the mediterranean from microwave observations and a convection-permitting model[END_REF].

Using the measurements received from the three channels, viz., 183.3 ± 1 GHz, 183.3 ± 3 GHz, and 183.3 ± 7 GHz of a microwave radiometer called Advanced Microwave Sounding Unit-B (AMSU-B), [START_REF] Hong | Detection of tropical deep convective clouds from AMSU-B water vapor channels measurements[END_REF] develop a method to separate out the deep convective clouds from the overshooting clouds penetrating into the TTL. They develop this method based on some numerical simulation and observational studies to probe the impact of deep convective clouds on the brightness temperature (T B ) at the water vapor channels of radiometers [START_REF] Burns | Effects of precipitation and cloud ice on brightness temperatures in AMSU moisture channels[END_REF][START_REF] Heymsfield | Structure of florida thunderstorms using high-altitude aircraft radiometer and radar observations[END_REF][START_REF] Weng | Retrieval of ice cloud parameters using a microwave imaging radiometer[END_REF]. This further leads to the understanding of the effects of precipitation and clouds on the T B . Based on the analogy between T B and the water vapor channels of 183.3 ± 1 GHz, 183.3 ± 3 GHz, and 183.3 ± 7 GHz developed while investigating the impact of storms on the microwave radiances [START_REF] Wang | Storm-associated microwave radiometric signatures in the frequency range of 90-220 ghz[END_REF], [START_REF] Hong | Detection of tropical deep convective clouds from AMSU-B water vapor channels measurements[END_REF] put to the fore the analysis of the effects of deep convection on the T B of AMSU-B channels. A criterion is deduced then to detect convective overshooting (COV) from the AMSU satellite radiometers using the difference of brightness temperature (ΔT B ) between the three aforementioned water vapor channels.

For the our study, we use a similar type climatology developed by [START_REF] Rysman | Monitoring deep convection and convective overshooting from 60 • S to 60 • N using MHS : A Cloudsat/CALIPSO-based assessment[END_REF] using MHS, which is a very similar radiometer like AMSU-B, but the third water vapor channel of MHS is 190.

GOES-12

As a part of Megha-Tropiques (MT) mission, very high spatial and temporal resolution visible (VIS)

and infrared (IR) radiance data of cloud masking and cloud type classifications are retrieved from the Geostationary Operational Environmental Satellite (GOES) employing an algorithm developed by Satellite Application Facility for supporting NoWCasting and very short range forecasting (SAFNWC) [START_REF] Derrien | MSG/SEVIRI cloud mask and type from SAFNWC[END_REF][START_REF] Derrien | Improvement of cloud detection near sunrise and sunset by temporaldifferencing and region-growing techniques with real-time seviri[END_REF][START_REF] Sèze | Evaluation against CALIPSO lidar observations of the multi-geostationary cloud cover and type dataset assembled in the framework of the Megha-Tropiques mission[END_REF]. For this dissertation work, we take advantage of the IR radiometers onboard GOES-12 (centered on South America) satellite (projection longitude :

60 • W).
Following the modus operandi as in [START_REF] Inoue | On the temperature and effective emissivity determination of semi-transparent cirrus clouds by bi-spectral measurements in the 10μm window region[END_REF], [START_REF] Saunders | An automated scheme for the removal of cloud contamination from AVHRR radiances over western europe[END_REF], [START_REF] Wylie | Two years of cloud cover statistics using VAS[END_REF] that the additional data retrieved from VIS and/or IR channels and/or water vapor and/or CO 2 sounding channels can improve the cloud detection, and can alleviate the differentiation between multi-layered clouds and mid-level clouds [START_REF] Ackerman | Cloud detection with MODIS. part II : validation[END_REF][START_REF] Dessler | A reexamination of the "stratospheric fountain" hypothesis[END_REF], Frey et al., 2008], the SAFNWC algorithm is tailored to adapt the spectral bands from multiple channels available. For GOES-12, SAFNWC algorithm works on one VIS channel or near-IR channel, two IR channels, viz., 3.9 µm and 10.8 µm, and one H 2 O or CO 2 sounding channel (mandatory requirements for the algorithm), missing out the 12 µm channel which can separate out the small low level clouds or cloud edges from very thin cirrus [START_REF] Schmetz | Monitoring deep convection and convective overshooting with meteosat[END_REF][START_REF] Sèze | Evaluation against CALIPSO lidar observations of the multi-geostationary cloud cover and type dataset assembled in the framework of the Megha-Tropiques mission[END_REF]. Therefore, overlooking the twilight time measurements, this algorithm readily evaluates the cloud radiative height only from the optically thick high clouds using the radiance measurements, i.e., the brightness temperature (T B ), ancillary temperature and humidity profiles from the channel 10.8 µm, thus by segregating the cirrus clouds using a multi-spectral threshold tests, and the height of the cloud is given by placing the radiative altitude of the cloud at 0.4 km à 1.4 km below the physical boundaries of the cloud depending on the opacity of cloud top [START_REF] Garnier | Retrieval of cloud properties using CALIPSO imaging infrared radiometer. part i : Effective emissivity and optical depth[END_REF][START_REF] Minnis | Estimating the top altitude of optically thick ice clouds from thermal infrared satellite observations using CALIPSO data[END_REF]. Additionally, this algorithm incorporates a correction for semi-transparency produced by high-level thin clouds using two IR channels, a window channel and a sounding channel [START_REF] Menzel | Improved cloud motion wind vector and altitude assignment using VAS[END_REF][START_REF] Schmetz | Operational cloud-motion winds from meteosat infrared images[END_REF]. We use the temperature measurements from these stations during the aforementioned days as in Table borne observations. In addition, the ability of the model to produce high clouds is evaluated using the measurements of satellite-borne MHS radiometers, who detects overshoots (not necessarily stratospheric).

MLS

Upper-air data

On one hand, it is shown that the variation of temperature and WV is well reproduced by the model during the wet season, and particularly during the intensive period when a short cold and dry period was observed. However, the modeled TTL is wetter by a margin of 0.4 ppmv, and less cold by 2 • C during the most extreme case of convection. This is explained partially by the nudging of ECMWF operational analyses at the model grid boundaries, where ECMWF analyses are themselves less dry and less cold in comparison to observations. On the other hand, the fact that the convection is set, but does not allow overshoots, also partly explains a less cold modeled TTL. We depict that temperature difference between model and observation is thermodynamically compatible with the difference between model and observation for WV. There is also a fairly good correlation between the model and observation for cloud top altitude as well as position, with an average correlation of 0.3 over the entire wet season. It is also shown that in the vicinity of the MHS detected overshooting positions, the BRAMS model is able to calculate high clouds, typically around 15 km à 16 km altitude. Finally, the analysis of the series of radio soundings made it possible to highlight the presence of inertia-gravity wave in the region of Bauru. The BRAMS model during the same period, also simulates two inertia-gravity waves comparable in period, wavelength and direction of propagation, as per the observation during the field campaign. It is deduced that this model does a very good job for these key parameters, and validates the use of this model for the study of the TTL processes related to WV at the continental scale. In addition, BRAMS's good performance in reproducing the reality of TTL without taking into account overshoots confirms for this season that overshoots play a significantly lower role than those of larger-scale processes in the stratospheric WV abundance.

Initial Simulation

At first to become familiar with the BRAMS model, and to observe a typical modeled TTL during a convective season over a continent (a large part of South America) where overshooting convection is known to be very frequent, we start working on the evaluation of a simulation already done by V. Marécal, hereafter denoted by REF 0 simulation. The model configuration is tabulated in Table 3.1. Table 3.1 represents the overall set up of all the simulations performed in our study, both for the long duration simulations (Chapter 3) and for the case study simulations (Chapter 4).

Evaluation of REF 0

In order to advance in the study of upscaling the impact of the overshooting convection on the water vapor budget in the TTL and the lower stratosphere using the REF 0 simulation, we investigate certain modeled parameters to build a platform for the next (most important one and hereafter denoted by Therefore, it is evident that higher vertical grid-point resolution at the TTL would account well the colder regions, though not as cold as per the observations retrieved from upper-air radiosoundings. The warmer conditions observed in the BRAMS simulations are commented with more explanations in Chapter 3.3.

Water Vapor Variability

We investigate the H 2 O mixing ratio distribution within the limited range of altitude around the TTL,

Rainfall Accumulation

After investigating the possible impacts due to the changes in the vertical grid-point resolution akin to the TTL, we make several sensitivity tests on a few parameters prescribed in the bulk microphysics of the BRAMS model. This time, we make tests using the simulation with vertical grid-point resolution of ∼100 m at 14.5 km à 18.2 km altitude -105 vertical levels. Cloud condensation nuclei (CCN) and the shape parameter (ν) of the gamma distribution are probed in the modeled outputs corresponding to rainfall accumulation, a proxy to the deep convection as well as to CCN and ν. To examine the variations brought in by modulating the aforementioned parameters in the modeled rainfall accumulation, we take advantage of the TRMM satellite observations (recall Chapter 2.3.1). So, the three hourly available TRMM rainfall data are used to calculate weekly rainfall accumulation, i.e., the sum up for all the three hourly measured rainfall accumulation during a full week within the full domain of the simulation. Similarly, we calculate the total rainfall accumulation during the corresponding week using the modeled parameters having the same temporal resolution of sampling as the TRMM measurements. A figure below is given for the sensitivity tests performed before we could proceed with the simulation for the FMOP.

In Figure 3.4, the total rainfall accumulation is calculated from December 15 00 :00 UTC to December 21 23 :00 UTC, 2012. First thing in this figure is to note that the color-scale represents the precipitation amount in mm, but several of them don't have the same upper limit of the color-scale. The main reason is the overestimation of rainfall accumulation by the model. Sometimes, it is almost more than 200% of the satellite-borne observations. Thus, representing the modeled precipitation with the same color-scale upper limit as the TRMM could diminish the pattern/distribution of rainfall within the domain of the simulation due to the exaggeration of color contrast due to the overestimation. Hence, sometimes to observe the minute details of the rainfall spatial distribution produced by the model, color-scale is compromised with respect to the TRMM measurement in order to keep the same color-ratio aspect. Another point to note on Figure 3.4c is that it is represented with a slightly different way -red star marks, because starting from 3.4c-h, zlev = 105, except Figure 3.4b having zlev = 68 (REF 0 simulation). Similarly, Figure 3.4f-h, the representation is also slightly different, as all of them have ν = 2.1, but with varying CCN values. The red star marks therein are several well-known cities in South America. The inferences are discussed below.

From Figure 3.4, several vital conclusions are deduced before proceeding in completing the simulation for the FMOP at a continental scale. The remarks concluded can be depicted as follows :

-Figure 3.4a vs. 3.4b vs. 3.4c : by varying the number of vertical levels of the simulation (zlev), i.e., due to the finer vertical grid-points within the TTL, and keeping the bulk microphysics intact, i.e., Figure 3.4b (zlev=68) vs. 3.4c (zlev=105), we improve the modeled rainfall accumulation significantly, mainly from the point of view of the total amount of rainfall accumulation and up to some extent, the spatial distribution/pattern of rainfall. 3.4a has the color-scale from 0 mm à 200 mm, while 3.4b has 0 mm à 400 mm and 3.4c has 0 mm à 300 mm. One could make statement that the reduction of rainfall accumulation is due to finer vertical grid-point resolution in the TTL ;

-Figure 3.4c (ν = 2.0) vs. 3.4d (ν = 2.1) vs. 3.4e (ν = 1.9), we probe the ν value and its corresponding impact on the total rainfall accumulation by keeping constant CCN value, i.e., 0.5 × 10 9 for these three cases. We observe again the enhancement of rainfall accumulation by slightly varying the ν value. To keep the same color contrast in the Figure 3.4d and 3.4e with 3.4c, the color-scale upper limit is set to 400 mm, similar to 3.4b. We don't observe any enhancement in the rainfall distribution over the domain. Thus following the experimental data given in [START_REF] Harrington | Parameterization of ice crystal conversion processes due to vapor deposition for mesoscale models using double-moment basis functions. part i : Basic formulation and parcel model results[END_REF], we continue further with ν = 2.1 (higher value), and carry out further tests with varying CCN values ;

-Figure 3.4f-h, the CCN value is tuned to get the optimal result in comparison to the satelliteborne observations, having ν = 2.1 and zlev = 105 for all the simulations. 3.4f-h have the CCN values of 20 × 10 9 , 20 × 10 10 and 20 × 10 11 , respectively. 3.4g-h have the color-scale upper limit of 250 mm, which is very close to the TRMM observation, i.e., 3.4a -200 mm, while 3.4f has color-scale upper limit of 300 mm. Here, one could conclude that the increasing CCN values would reduce the overestimation of the rainfall accumulation by the model, given that ν and zlev are kept constant.

Furthermore, we infer from 3.4g that it is the best-fit so far in comparison to 3.4a by making crosscorrelation tests (values are not shown), both from the point of view of spatial distribution and total amount of rainfall accumulation.

At this point, we could briefly summarize the concluding remarks on the sensitivity tests carried out.

Firstly on the increment in the vertical grid-point resolution around the tropopause, which allows the BRAMS model to account well the coldest and driest regions within the TTL. It resolves better the CPT variability. Secondly on the bulk microphysics of the BRAMS model, it is evident that by modulating the CCN and ν values, one could achieve an improved version of modeled rainfall accumulation -the settings of CCN = 20 × 10 10 , and ν = 2.1 provides an enhancement of 50% on the total overestimation of the precipitation with respect to the satellite-borne observations. It could be difficult to conclude on the overestimation of rainfall accumulation in the model. The absence of SOC and the corresponding slight warmer and wetter conditions of the modeled TTL could be a factor. We comment on details on it in subsequent sections. We continue therefore forward to make the simulation for the full wet season on a continental scale. with GOES-12. Furthermore, the overshooting cells detected by MHS are observed at the locations, where 75% of the modeled cloud tops are higher than 11 km. Finally, the modeled inertia-gravity wave periodicity and wavelength are comparable with those deduced from the radio sounding measurements during TRO-Pico campaign. The good behavior of BRAMS confirms the SOC contribution in the WV abundance and variability is of lesser importance than the large-scale processes. This simulation can be used as a reference run for upscaling the impact of SOC at a continental scale for future studies.

Towards

Article

Introduction

The presence of water vapor (WV) in the stratosphere is now recognized to play a role in the surface climate [START_REF] Avery | Large anomalies in lower stratospheric water vapour and ice during the 2015-2016 El Nino[END_REF][START_REF] Dessler | Stratospheric water vapor feedback[END_REF][START_REF] Forster | Stratospheric water vapour changes as a possible contributor to observed stratospheric cooling[END_REF], Solomon et al., 2010]. H 2 O is also a key species for stratospheric chemistry, especially for the ozone layer [START_REF] Graf | Changing lower stratospheric circulation : The role of ozone and greenhouse gases[END_REF][START_REF] Solomon | The mystery of the antarctic ozone "hole[END_REF].

Not only it enhances the abundance of OH -radical which controls the life-time of many other chemical species in the stratosphere, but also it modifies the processes linked with O 3 depletion [START_REF] Shindell | Climate and ozone response to increased stratospheric water vapor[END_REF][START_REF] Solomon | Stratospheric ozone depletion : A review of concepts and history[END_REF]. The radiative and microphysical feedbacks of H 2 O abundance in the stratosphere may also govern the formation of polar stratospheric clouds over the Arctic or the Antarctic, as the stratosphere cools down [START_REF] Ramaswamy | Fingerprint of ozone depletion in the spatial and temporal pattern of recent lower-stratospheric cooling[END_REF], Toon et al., 1989b].

The seminal work of [START_REF] Brewer | Evidence for a world circulation provided by the measurements of helium and water vapour distribution in the stratosphere[END_REF] puts to the fore the mechanisms linked with the abundance of stratospheric WV. It is mainly modulated by the intrusions through the tropical tropopause layer (TTL) [START_REF] Highwood | The tropical tropopause[END_REF]]. This layer extends from the mean convective outflow (∼14 km or 150 hPa)

to the highest altitude reached by severe deep convection (∼19 km or 70 hPa) above which the mass flux is constant [START_REF] Fueglistaler | Tropical tropopause layer[END_REF]. That depicts a smooth transition from a convectively modulated troposphere to a radiatively modulated stratosphere at the tropics [Gettelman andForster, 2002, Seidel et al., 2001]. Many field campaign measurements [e.g., [START_REF] Jensen | Physical processes controlling the spatial distributions of relative humidity in the tropical tropopause layer over the pacific[END_REF] and modeling studies [e.g., [START_REF] Smalley | Contribution of different processes to changes in tropical lower-stratospheric water vapor in chemistry-climate models[END_REF] report that it is the region of complex dynamical interactions at different scales and speeds, where most of them have a potential role in the stratospheric WV budget. These complex dynamical activities can be resolved into processes such as, the slow ascent due to the positive net radiative heating above 14 km à 15 km [e.g., [START_REF] Gettelman | Radiation balance of the tropical tropopause layer[END_REF][START_REF] Küpper | Mass and water transport into the tropical stratosphere : A cloud-resolving simulation[END_REF], the deep convection penetrating through the lapse-rate tropopause [e.g., [START_REF] Corti | Unprecedented evidence for deep convection hydrating the tropical stratosphere[END_REF][START_REF] Danielsen | A dehydration mechanism for the stratosphere[END_REF][START_REF] Khaykin | Hydration of the lower stratosphere by ice crystal geysers over land convective systems[END_REF][START_REF] Romps | Overshooting convection in tropical cyclones[END_REF], and the atmospheric waves generated by deep convection [e.g., [START_REF] Dinh | Effect of gravity wave temperature fluctuations on homogeneous ice nucleation in the tropical tropopause layer[END_REF], Schoeberl et al., 2015]. Understanding all these processes and their interactions is of prime importance, given the potential role of the TTL's WV abundance in the climate evolution [Dessler et al., 2016, Randel andJensen, 2013].

Several trajectory studies driven by meteorological analyses succeed at least qualitatively in reproducing the WV abundance and its variability rather well in the TTL [e.g., [START_REF] Dessler | Variations of stratospheric water vapor over the past three decades[END_REF][START_REF] Schoeberl | Simulation of stratospheric water vapor and trends using three reanalyses[END_REF] without considering the severe overshooting convection exceeding the level of neutral-buoyancy, hereafter referred to as convective overshooting (COV). Thus, it is deduced that most of the WV entry to the stratosphere is due to an advection-condensation mechanism during the slow ascent towards the very cold tropopause, followed by the sedimentation of ice particles [START_REF] Holton | The influence of gravity wave breaking on the general circulation of the middle atmosphere[END_REF]Gettelman, 2001, Liu et al., 2010b]. This freezing-drying or cold-trap mechanism leads to the dehydration of air mass entering into the stratosphere at the tropics, and particularly very efficient in the Pacific Ocean where the cold-point tropopause (CPT) is the coldest [Hasebe et al., 2007, Schoeberl and[START_REF] Schoeberl | Dehydration of the stratosphere[END_REF]. As such, the tropical CPT, a stratospheric feature having dependency on the chemistry of O 3 , CO et al., 1999] and deep convection [START_REF] Kuang | Convective influence on the heat balance of the tropical tropopause layer : A cloud-resolving model study[END_REF], regulates H 2 O abundance in the lower stratosphere [START_REF] Randel | Decreases in stratospheric water vapor after 2001 : Links to changes in the tropical tropopause and the Brewer-Dobson circulation[END_REF], Wang et al., 2015].

Gravity waves play a key role in the stratosphere-troposphere exchange [START_REF] Fritts | Gravity wave dynamics and effects in the middle atmosphere[END_REF]Alexander, 2003, Holton et al., 1995]. They have a well observed influence on the net radiative heating and WV exchange that occurs in the upper troposphere-lower stratosphere (UTLS) [START_REF] Holton | The influence of gravity wave breaking on the general circulation of the middle atmosphere[END_REF], and are also known for its energy dissipation that can cool down the ambient atmosphere -increasing the favorable conditions for the formation of ice clouds in the TTL [START_REF] Kim | Ubiquitous influence of waves on tropical high cirrus clouds[END_REF]. Admittedly, the deep convection in the tropics is a major driving force in producing inertia-gravity waves [START_REF] Alexander | The gravity wave response above deep convection in a squall line simulation[END_REF][START_REF] Jewtoukoff | Gravity waves generated by deep tropical convection : Estimates from balloon observations and mesoscale simulations[END_REF].

Recent works of Kim andAlexander [2013, 2015], [START_REF] Schoeberl | The impact of gravity waves and cloud nucleation threshold on stratospheric water and tropical tropospheric cloud fraction[END_REF][START_REF] Schoeberl | Gravity waves amplify upper tropospheric dehydration by clouds[END_REF] put to the fore its significance in the modulation of ice particle formation and WV abundance in the TTL.

In contrast to these large-scale processes, COV may penetrate into the stratosphere, hereafter denoted as stratospheric overshooting convection (SOC), injecting ice particles into an environment that is often sub-saturated, leading to the sublimation of ice in the stratosphere and an increase of WV. This is concluded both by in situ observations [e.g., [START_REF] Khaykin | Hydration of the lower stratosphere by ice crystal geysers over land convective systems[END_REF], 2016, Schiller et al., 2009] and modeling studies at the convective system scale [e.g., [START_REF] Chaboureau | A numerical study of tropical cross-tropopause transport by convective overshoots[END_REF][START_REF] Chemel | Quantifying the imprint of a severe hector thunderstorm during ACTIVE/SCOUT-O3 onto the water content in the upper troposphere/lower stratosphere[END_REF], Liu et al., 2010a]. The signature of individual overshooting turrets cannot be identified through the satellite-borne WV measurements at global scale, because either of the coarse vertical resolution (e.g., MLS) or the poor precision (e.g., AIRS) to detect local WV enhancement within a narrow range of altitude in the TTL. Consequently, the quantitative role of SOC on the stratospheric WV with respect to the large-scale dehydration has not been estimated directly so far. However, the stratospheric WV enhancement due to a single event has been estimated to range between 100 t [START_REF] Hassim | A model study on the influence of overshooting convection on TTL water vapour[END_REF], 300 t à 500 t [Liu et al., 2010a] and 2776 t [START_REF] Dauhut | Large-eddy simulations of hector the convector making the stratosphere wetter[END_REF] with a frequency estimation of 13 overshooting events per minute in the tropical belt [START_REF] Iwasaki | Characteristics of deep convection measured by using the A-train constellation[END_REF]. [START_REF] Lelieveld | Stratospheric dryness : model simulations and satellite observations[END_REF] estimate the annual mean of upward One method to advance our knowledge in this topic is the 3D modeling approach. Because overshooting turrets are known to be of very limited area (typically of a few km 2 horizontally), the cloud resolving model resolution must be of 1 km or less horizontally and of a few hectometres vertically to properly resolve this process. This makes it difficult to compute a global impact of the SOC on the stratospheric WV abundance.

The current work proposes a possible strategy to upscale its effect in a global model, or, as a first step, in a regional model at a continental scale by the use of a sub-grid scale nudging of hydration (or dehydration).

A priori, a detailed evaluation of a model should be performed disclosing the key parameters linked to WV abundance in the TTL, i.e., height and position of deep convection, thermal structure of the TTL and inertia-gravity waves generated by convection. This is the aim of the present paper. To set up this platform, we use the Brazilian Regional Atmospheric Modeling System (BRAMS), a 3D mesoscale model to simulate the TTL over a large part of Brazil during a particular wet season from November 2012 to March 2013.

Furthermore, we also take advantage of the balloon-borne measurements from the TRO-Pico campaign at Bauru (22.31 • S, 49.05 • W) during the same five months of observation period (FMOP), radio soundings (RS) at different locations in Brazil, and space-borne measurements like the Geostationary Operational Environmental Satellite (GOES-12), Microwave Limb Sounder (MLS) and Microwave Humidity Sounder (MHS), in order to evaluate our proposal.

The paper is organized as follows : section 3.3.2 describes the mesoscale model, as well as the strategy of its evaluation. Subsequently, section 3.3.3 provides the details of the validation tools used, section 3.3.4

evaluates the modeled thermal structure and WV variability against the TRO-Pico measurements, section 3.3.5 evaluates the simulated deep convection against GOES-12 and MHS, and section 3.3.6 discusses the ability of BRAMS in reproducing the inertia-gravity wave. A summary, including further objectives, is given in section 3.3.7.

Methodology

Model description and setup

The Brazilian version of the Regional Atmospheric Modeling System (BRAMS : version 4.2 with meteorology tailored to tropics [START_REF] Freitas | The Coupled Aerosol and Tracer Transport model to the Brazilian developments on the Regional Atmospheric Modeling System (CATT-BRAMS) -Part 1 : Model description and evaluation[END_REF]) is a limited area weather model developed at CPTEC/INPE (Centro de Previsão de Tempo e Estudos Climáticos), which is derived from the RAMS : version 5.04 [START_REF] Cotton | RAMS 2001 : Current status and future directions[END_REF][START_REF] Pielke | A comprehensive meteorological modeling system-RAMS[END_REF] of the University of Colorado/ATMET. It incorporates a double moment microphysical scheme having 7 hydrometeors (liquid cloud droplets and rain for liquid particles ; pristine, snow, hail, graupel and aggregates for ice particles) [START_REF] Meyers | New RAMS cloud microphysics parameterization. Part II : The two-moment scheme[END_REF]. Here, the number concentrations and mass mixing ratios of hydrometeors are prognostic variables of BRAMS, assuming that each hydrometeor size follows a gamma function Γ(ν) distribution, ν being the shape parameter. The main differences between BRAMS and RAMS are the parameterization of sub-grid scale cumulus convection, the surface scheme and the soil moisture initialization. BRAMS incorporates the Grell parameterization of deep convection [START_REF] Grell | A generalized approach to parameterizing convection combining ensemble and data assimilation techniques[END_REF].

On the research and application side, [START_REF] Marécal | Mesoscale modelling of water vapour in the tropical UTLS : two case studies from the HIBISCUS campaign[END_REF] show that the BRAMS model is able to simulate the WV distribution in the TTL, but on a relatively shorter time scale using a coarser vertical grid-point resolution. Our approach is almost the same, as such a horizontal grid-point resolution of 20 km × 20 km is used, keeping in mind the spatial and temporal scale of simulation and computing cost.

This resolution is too coarse to produce SOC, which should occur typically on a 1 km × 1 km grid-point resolution given a convective parameterization scheme in the model. For initialization and the six-hourly nudging at the grid-boundary of the simulation, the ECMWF (European Centre for Medium-Range Weather Forecasts) operational analyses in pressure levels are incorporated, with no nudging inside the domain.

The simulation is carried out for the FMOP having 105 vertical levels starting from surface to 30 km altitude with a resolution of ∼100 m between 14.5 km à 18.3 km. The domain of simulation covers the latitude from 7.28 • S to 28.41 • S and longitude from 38.42 • W to 61.48 • W, which encompasses a large part of the tropical region of Brazil (the domain of simulation is shown in Figure 3.9). Note that an evaluation of another mesoscale model WRF (Weather Research and Forecasting) in the TTL has been performed already by [START_REF] Evan | The representation of the TTL in a tropical channel version of the WRF model[END_REF], but with a coarser horizontal and vertical grid-point resolution on a larger domain. While BRAMS and WRF have a similar origin [START_REF] Skamarock | A description of the advanced research WRF version 2[END_REF], the version 4.2 offers a lower number of options due to its optimized aspects for the tropical meteorology. However, a comparison between BRAMS and WRF would be a subjective paper itself, but the following features are highlighted below :

-Data assimilation : in case of BRAMS only nudging prevails, while WRF includes a more sophisti-cated var-assimilation system ;

-Dynamical core : non-hydrostatic model with possibility of hydrostatic model ;

-Boundary condition : a sponge layer at the top of the domain, possibly cyclic conditions at the lateral boundaries with boundary conditions from meteorological operational analysis ; -Double moment microphysical scheme : 7 types of hydrometeors (5 for ice) in BRAMS [START_REF] Meyers | New RAMS cloud microphysics parameterization. Part II : The two-moment scheme[END_REF], while 5 types of hydrometeors (3 for ice) in WRF [START_REF] Morrison | Impact of cloud microphysics on the development of trailing stratiform precipitation in a simulated squall line : Comparison of one-and two-moment schemes[END_REF].

For our study, the sub-grid scale parameterization for deep convection with the ensemble closure type is chosen. This closure is shown to be the best for tracer transport by deep convection over the Maritime continent [START_REF] Arteta | Regional modelling of tracer transport by tropical convection -part 1 : Sensitivity to convection parameterization[END_REF]. The CO 2 vertical profiles in the SiB sub-model [Sellers et al., 1996a,b] initialization and in the radiative parameterization scheme [START_REF] Harrington | The effects of radiative and microphysical processes on simulated warm and transition season Arctic stratus[END_REF] are updated to 395 ppmv from the values of Pico-SDLA CO 2 spectrometer of the TRO-Pico campaign. For the bulk microphysics, the shape parameter ν is set to 2.1 for each category of hydrometeor after performing sensitivity tests in order to get the optimal results based on the comparisons with satellite observations (tests are made using ν = 1.9, 2.0 et 2.1). A 5 km deep sponge layer is used to damp the gravity waves at the top of the domain.

The typical time step of integration is ∼10 s à 30 s to maintain the simulation stability.

Strategy of model evaluation

We utilize the TRO-Pico campaign measurements to validate the modeled parameters, i.e., tempera- open balloons or 1.2 kg meteorological rubber balloons) as close as possible to convective events. The measured parameters were H 2 O, CH 4 , CO 2 mixing ratios and particles/aerosols concentration or backscattering ratio. In this study, we make use of the H 2 O mixing ratio from the Pico-SDLA and the FLASH-B stratospheric hygrometers during the IOP2, from the Pico-SDLA during the FMOP (see Figure 3.7a for the list of the profiles) and from the MLS : version 4.2 measurements (see section 3.3.4). We also make use of temperature (see section 3.3.4) and wind (see section 3.3.6) measurements from RS92 SGP radiosondes of the TRO-Pico campaign, and some more temperature measurements from the RS over Brazil during the FMOP. A detailed description of TRO-Pico can be found in [START_REF] Ghysels | Intercomparison of in situ water vapor balloon-borne measurements from Pico-SDLA H2O and FLASH-B in the tropical utls[END_REF]. Thereafter, the performance of the model in producing convective clouds, both in spatial and temporal precision is investigated, using GOES-12 and MHS measurements (see section 3.3.5).

Validation tools

RS92

Within the TRO-Pico campaign, radio soundings (RS) with Vaisala RS92-SGP PTU are used. The temperature uncertainty in RS92 is 0.5 • C, while the pressure uncertainties provided by the manufacturer for two different pressure ranges are 1.5 hPa for 1080 hPa à 100 hPa, and 0.6 hPa for 100 hPa à 3 hPa. The RS92 were launched from January 23 to February 12, 2013, with a frequency of 1 to 4 measurements per day. Concurrently, zonal wind (u) and meridional wind (v) are collected for inertia-gravity wave analysis.

Furthermore, temperature and pressure measurements from the RS92 onboard the FLASH-B payload are also taken into account in the temperature climatology (see section 3.3.4).

Upper-air soundings

During the FMOP, regular balloon-borne RS measurements of temperature are retrieved from the upper-air sounding database of Wyoming University for six stations in Brazil (see Figure 3

Pico-SDLA

Pico-SDLA hygrometer is a compact, light-weight, direct absorption infrared spectrometer. The hygrometer allows probing WV at 2.63 µm over a 1 m optical path length in ambient air. The measurement principle is simple : H 2 O mixing ratio is extracted from the absorbed signal applying the Beer-Lambert law, knowing temperature and pressure. A full description of the instrument, including its uncertainties, is provided by [START_REF] Ghysels | Intercomparison of in situ water vapor balloon-borne measurements from Pico-SDLA H2O and FLASH-B in the tropical utls[END_REF]. In the TRO-Pico flight conditions, the measurement uncertainty for a unitary spectrum (10 ms acquisition time, not averaged) in the TTL ranges from 3.5% to 7.5%. In extreme conditions at the CPT (measured to be -85.0 • C), the uncertainty was estimated to be 4.4%. The precision can be improved by averaging over N unitary spectra, enhancing the signal-to-noise ratio by a factor of √ N. The time schedule of the different measurements used in this study can be found in Ghysels et al.

[2016] (see also Figure 3.7a). Most of the observations were made during the IOP2, while 8 other profiles were taken from the FMOP.

FLASH-B

FLASH is a Lyman-alpha hygrometer. The balloon version of FLASH (FLASH-B) is a compact lightweight sonde developed at the Central Aerology Observatory Russia for balloon-borne WV measurements in the upper troposphere and the stratosphere [START_REF] Yushkov | Optical balloon hygrometer for upper troposphere and stratosphere water vapor measurements[END_REF]]. The instrument is based on the fluorescent method [START_REF] Bertaux | Premières measures stratosphériques par un hygromètre à fluorescence ultraviolette[END_REF], which uses the photodissociation of H 2 O molecules exposed to ultraviolet radiation (λ <137 nm) in vacuum followed by the measurement of fluorescence of excited OH -radicals using a photomultiplier in photon-counting mode. The intensity of the fluorescent light sensed by the photomultiplier is directly proportional to the H 2 O mixing ratio under stratospheric conditions (150 hPa à 10 hPa). Each FLASH-B instrument is calibrated in the laboratory against a reference dew-point hygrometer MBW 373L [START_REF] Vömel | Intercomparisons of stratospheric water vapor sensors : FLASH-B and NOAA/CMDL frost-point hygrometer[END_REF]. The detection limit for a 4 s integration time at stratospheric conditions is approximately 0.1 ppmv, while accuracy is limited by the calibration error amounting to a relative uncertainty of 4%. The typical measurement precision in the stratosphere is 5% to 6%, whereas the combined relative uncertainty in WV concentration is less than 10% throughout the stratosphere.

Here, we apply a composite dataset of WV profiles from both Pico-SDLA and FLASH-B hygrometers to evaluate the modeled TTL. [START_REF] Ghysels | Intercomparison of in situ water vapor balloon-borne measurements from Pico-SDLA H2O and FLASH-B in the tropical utls[END_REF]

GOES-12

In order to assess the simulated convective cloud cells in intensity, temporal and spatial precision over Brazil during the FMOP, cloud products [Derrien andGléau, 2005, Sèze et al., 2015] obtained from the radiance data of visible and infrared radiometer onboard GOES-12 provided by the SAFNWC (Satellite Application Facility for supporting NoWCasting and very short range forecasting) are used. In this dataset, the cloud top height is available every 15 min with a spatial resolution of 4 km × 4 km. In the SAFNWC scheme, after separating the cirrus clouds from the high opaque clouds using a multi-spectral threshold test, the cloud radiative altitude of optically thick high cloud is obtained from the 10.8 µm brightness temperature (T B ), ancillary temperature and humidity profiles. This radiative cloud altitude is placed at 0.4 km à 1.6 km below the physical boundaries of the cloud depending on the opacity of cloud top [START_REF] Garnier | Retrieval of cloud properties using CALIPSO imaging infrared radiometer. part i : Effective emissivity and optical depth[END_REF][START_REF] Minnis | Estimating the top altitude of optically thick ice clouds from thermal infrared satellite observations using CALIPSO data[END_REF]. For high-level thin clouds, a correction for semi-transparency is applied using two infrared channels, a window channel and a sounding one [START_REF] Menzel | Improved cloud motion wind vector and altitude assignment using VAS[END_REF][START_REF] Schmetz | Operational cloud-motion winds from meteosat infrared images[END_REF].

MHS

The locations of COV, i.e., the convective turrets penetrating to the TTL, which may also enter into the stratosphere (SOC), within the domain of simulation for the FMOP are collected from the Microwave Humidity Sounder (MHS) on board the National Oceanic and Atmospheric Administration (NOAA) and Meteorological Operational polar orbiting (Metop) satellites. We probe the modeled cloud tops to investigate whether the BRAMS is able to produce very high clouds at the locations where overshooting cells (>14 km) were detected. This examination is important for further application of BRAMS to study the impact of SOC on the TTL at a large-scale.

This verification is made by using a climatology based on a satellite-borne microwave radiometer, following a method developed by and assessed in [START_REF] Hong | Detection of tropical deep convective clouds from AMSU-B water vapor channels measurements[END_REF] and [START_REF] Rysman | Monitoring deep convection and convective overshooting from 60 • S to 60 • N using MHS : A Cloudsat/CALIPSO-based assessment[END_REF]. Specifically, they take advantage of the sensitivity of WV channels to frozen hydrometeors for detecting atmospheric convection, and to discriminate COV from the deep convection. This method has been previously used in the tropics by [START_REF] Hong | Interannual to diurnal variations in tropical and subtropical deep convective clouds and convective overshooting from seven years of AMSU-B measurements[END_REF], in Brazil by [START_REF] Funatsu | Convective activity in Mato Grosso state (Brazil) from microwave satellite observations : Comparisons between AMSU and TRMM data sets[END_REF], and in the Mediterranean by [START_REF] Rysman | Severe convection in the mediterranean from microwave observations and a convection-permitting model[END_REF]. Using a microwave radiometer and an X-band radar onboard a scientific aircraft, [START_REF] Hong | Detection of tropical deep convective clouds from AMSU-B water vapor channels measurements[END_REF] state that for clear sky conditions, the T B measured by the three WV channels is always higher for channels with frequencies further away from the central frequency, but within convective clouds this relationship is observed to be reversed. Based on these properties, a criterion is deduced for detecting COV using the difference of T B between the WV channels. The present study uses the climatology of COV derived from MHS by [START_REF] Rysman | Monitoring deep convection and convective overshooting from 60 • S to 60 • N using MHS : A Cloudsat/CALIPSO-based assessment[END_REF].

Evaluation of the TTL temperature and water vapor

Temperature evolution

Bauru -TRO-Pico campaign : It can be noted that the coldest periods correspond to the CPT having the highest altitudes which are typically above 80 hPa. Conversely, the warmer periods are associated with CPT below 100 hPa. Figure 3.5b shows the corresponding simulated version of temperature series. It follows the same structure of the observed time evolution, with a strong cooling of the TTL at the end of January/beginning of February, followed by a warming around February 6 -8, and a slight cooling at the end of the IOP2. The CPT series is very similar to the measured one of RS92. The coldest CPT is observed on January 29, 2013 (-84.8 • C marked with the white box), the same coldest period as per RS92 measurement (February 2, 2013), but a bit warmer and appearing few days earlier to the observation. The difference between the observation and the modeled temperature is higher than the RS92 precision of 0.5 • C. It can also be noticed that the magnitude of the cooling in the model is not as high as the observations.

In order to examine whether the cooling and warming tendencies, apparent both in the model and in the RS92 measurements, are due to large-scale advection of cold air in the TTL or not, the temperature series from the ECMWF operational analyses used for the boundary conditions of the BRAMS simulation are also displayed in Figure 3.5c at a position (22.00 • S, 49.00 • W) near to Bauru, recalling that the ECMWF analyses are nudged just at the boundaries, not at the centre of the domain of simulation. It shows that the temperature field follows a similar time evolution, as observed in the RS92 and the simulation (Figure 3.5a and 3.5b), respectively. Furthermore, the coldest CPT falls in the same period (-83.7 • C marked with the white box) -end of January/beginning of February, and is a bit warmer and higher in comparison to RS92. Since we are using the pressure levels to extract the ECWMF operational analyses (in the UTLS, they correspond to 150 hPa, 100 hPa, 70 hPa, 50 hPa et 30 hPa), the CPT is poorly resolved compared to the ones in BRAMS or in RS92, yet they do display the warming of CPT at the end of January/beginning of February 2013. It can be deduced that most of the time evolution shown here is the consequence of a large-scale process rather than due to the severe convection, which cannot be resolved in the ECMWF

analyses. An anomalously cold UTLS is confirmed to be related with the stratospheric sudden warming (SSW) in the Arctic with a consequently large-scale cooling in the tropical belt observed during January and February 2013 in the ATTREX campaign [START_REF] Evan | TTL cooling and drying during the January 2013 stratospheric sudden warming[END_REF], also concluded in section S1 in the "Supporting Information". Further comments on this event can be found in section 3.3.4.

Other locations in South America : Probing into CPT : 3.2) are expressed in two ways. Firstly, they are calculated as the standard deviation (σ) of the differences (δ) for each individual data point between RS vs. BRAMS. Secondly, they are given by XBRAMS -XRS , where X denotes the mean value of the CPT during the observation period. Table 3.2 quantifies the findings from Figure 3.6, where the results from BRAMS are always warmer than the observations. This warm bias is higher than the 0.5 • C precision of the RS92.

This can be explained by two facts : firstly, the vertical grid-point resolution of ∼100 m near the TTL is typically coarser by a factor of about three than the RS vertical resolution (∼35 m). Secondly, the ECMWF operational analyses data used for nudging the initial and boundary conditions of BRAMS grid-points are already coarser and warmer. Therefore, BRAMS should be qualitatively warmer and lower in representing the CPT. A third hypothesis could be proposed here, i.e., the 20 km horizontal grid-point resolution implies that COV and SOC cannot be resolved explicitly by the model, thus the associated cooling of the TTL is absent. more mature stage of deep convection, the model is performing better, as would be expected. and CTTH_Effect from the SAFNWC products, where CTTH_Height accounts mostly for all types of optically thick clouds, but the addition of a condition CTTH_Effect =100 to the former parameter allows to discriminate only optically thick convective clouds [START_REF] Derrien | Algorithm theoretical basis document for cloud products (cma-pge01 v3. 2[END_REF]. Note that in the CC calculation (Figure 3.8a), only the CTTH_Height parameter is considered. Thus, it can be deduced that percentage wise, modeled high clouds are comparable with GOES-12 (blue vs. red lines). In addition, the temporal trend of BRAMS (blue line) is typically coherent with GOES-12 (dotted black line), while considering only thick convective clouds in GOES-12. Therefore, the modeled and observed cloud tops are consistent. The main difference between Figure 3.10a vs. 3.10b is the bell shape distribution of the altitude of cloud tops below the overshooting cells. The bell shape in Figure 3.10a starts at a lower altitude of 10 km than in the case of Figure 3.10b, which is 11 km. Furthermore, the maximum of high cloud distribution, i.e., 19% for cloud tops from 13 km à 14 km, is lower for a low range of altitude than the maximum value obtained in the bell shape of Figure 3.10b, i.e., 23% for a higher range of 14 km à 15 km. This implies that the highest modeled cloud tops around a COV location are spread in a limited range of high altitudes.

Water vapor mixing ratio (WV) -TRO-Pico campaign

MHS vs. BRAMS

In case of Figure 3.10b, the occurrence of high clouds (14 km à 17 km) is higher with respect to the case Figure 3.10a. The number of COV occurrence within the bell in Figure 3.10a, typically for cloud tops higher than 11 km accounts for 63% ; whereas in Figure 3.10b, it accounts for 75%. It can be concluded that accounting for a possible small error in the computed high cloud positions, the agreement improves significantly in the modeled high clouds vs. MHS detected overshooting cells. This analysis highlights the ability of BRAMS in positioning the highest cloud cells correctly.

Gravity wave

Since it has been shown that gravity waves can influence the presence of cirrus ice particles in the TTL through the temperature field [e.g., [START_REF] Dinh | Effect of gravity wave temperature fluctuations on homogeneous ice nucleation in the tropical tropopause layer[END_REF], Schoeberl et al., 2016], it is worth investigating the Horizontal wind perturbation profiles [START_REF] Tsuda | Rocketsonde observations of the middle atmosphere dynamics at Uchinoura (31. DEG. N, 131. DEG. E) during the DYANA campaign. part ii : Characteristics of gravity waves[END_REF][START_REF] Tsuda | Radiosonde observations of equatorial atmosphere dynamics over Indonesia : 2. characteristics of gravity waves[END_REF] depict the detection of the inertia-gravity waves from the RS92 PTU radio soundings. In this paper, the RS92 radio soundings of the TRO-Pico campaign at Bauru are used to investigate the inertia-gravity waves during the IOP2. The zonal wind perturbation profile (u ) is calculated by subtracting the 3 rd order polynomial function fit of the u profile from itself [START_REF] Hankinson | Gravity waves generated by convection during TWP-ICE : I. inertia-gravity waves[END_REF], Tsuda et al., 1994a] ; simultaneously the same parameters are calculated from the simulation at Bauru.

The polynomial function fit of the zonal wind profile is the mean wind profile (ū). Therefore, the wind profile can be expressed as u(x, y, z, t) = ū(z, t) + u (x, y, z, t). Similarly, the calculations are performed on the meridional wind (v).

Figure 3.11depicts the vertical and temporal trends of the perturbed horizontal velocity from both the RS92 measurements and BRAMS simulations, respectively. In the velocity perturbations, the pattern of oscillations highlights the influence of inertia-gravity waves with a constant phase dispersing downward with time, typical of a negative vertical wave number and a positive horizontal wave number, respectively.

The modeled profiles show about the same order of magnitude and patterns of oscillation, as in the measurements during January 24 -28, February 2 -3 and 7 -9, 2013, and are reasonably comparable with respect to the observed wavelength and periodicity of the inertia-gravity waves (Table 3.3). It is noticeable that, especially from u (less from v , more noisy) around January 28, 2013, there is a wave period of about one day (more comments in section 3.3.6) with a vertical wavelength of ∼3 km. In the BRAMS around January 28 12 :00 UTC, we obtain the same order of magnitude of periodicity with a vertical wavelength of ∼2.4 km. It is more visible on the modeled v profiles than the corresponding u profiles. Thus, it can be concluded that BRAMS is able to represent the typical behavior of the inertia-gravity waves in the TTL.

Hodograph analysis

A hodograph analysis of the u and v can highlight a monochromatic behavior of the wave, if it exhibits an elliptical shape [Alexander andVincent, 2000, Fovell et al., 1992]. From the ratio of major axis to minor axis of the ellipse in the hodograph, information about the wave field with the rotation direction varying with altitude, and many intrinsic wave properties can be deduced [Alexander andHolton, 1997, Tsuda et al., 1990]. Specific cases obtained from the RS92 measurements during IOP2 of the TRO-Pico campaign and from the BRAMS are shown in Figure S3 in the "Supporting Information", where at least a partially elliptical feature can be identified, indicating monochromaticity of the wave. The intrinsic frequency ω, observed in a frame of reference moving with the ambient wind (ū, v), can be calculated from the ratio of major to minor axes of the ellipse, which is equal to the ratio of ω to the Coriolis parameter (f). When this ratio is of the order 1, the dispersion relationship is ω2 -

f 2 = N 2 B K 2 h m 2
, where N B is the Brunt-Väisälä frequency, K h is the horizontal wave number and m = 2π λz [START_REF] Fritts | Gravity wave dynamics and effects in the middle atmosphere[END_REF]]. Table 3.3 summarizes the periodicities (T) obtained from the hodograph analysis -calculations are given in section S3 in the "Supporting Information". The few hours of time-lag between the measurements and the simulation producing gravity wave patterns can be affiliated with the sporadic distribution of their sources, i.e., the deep convection.

Influence of ECMWF on BRAMS

In section 3.3.4, it is shown that the nudging of ECMWF operational analyses at the boundary conditions could play a role in the temperature and WV variability in the BRAMS results. Therefore, it is important to evaluate its role in the modeled wave activity as well, especially for long waves that can propagate horizontally far from its source. It is found that in the ECMWF operational analyses used for nudging the simulation grid-boundary condition and initialization, a similar oscillation is present in the u and v profiles, respectively, corresponding to the BRAMS ones. However, due to the poor vertical resolution of the ECMWF analyses, the vertical wavelength (λ z ) for the cases discussed in section 3.3.6 cannot be determined precisely. It could be roughly 6 km, but half of it ( λz 2 , as observed) could also be possible. The periodicity of the wave pattern in the South of the domain is ∼1 day. Thus, these numbers are compatible with the results from the simulation during the IOP2. Nevertheless, inside the domain, where the ECMWF analyses are not nudged, BRAMS is able to compute a wave pattern with higher harmonics corresponding to the observations, showing that either the source of the wave is inside the domain, or that the physics inside BRAMS are able to better resolve this type of wave pattern.

Discussion of the results and future objectives

The main objective of this paper is to evaluate the ability of the BRAMS model to capture correctly the key patterns of the tropical UTLS, which can have an impact on the stratospheric WV budget. In the current BRAMS set up, the deep and shallow convection is parameterized, and no SOC can be simulated.

Having only deep convective activity, the model can simulate the temperature evolution with a relatively precise CPT variation throughout the FMOP at the Brazilian scale, albeit the modeled temperature near the TTL is warmer than the RS measurements. For the same reasons, the H 2 O mixing ratio in BRAMS is observed to be slightly wetter than the measurements obtained from the TRO-Pico campaign. This can be partly attributed to BRAMS vertical resolution in the TTL, and also to the nudging with ECMWF operational analyses having a poor vertical resolution in the UTLS. The fact that no SOC can be simulated in the model may also play a role, as deep penetrating convection should cool down the TTL. Nevertheless, BRAMS follows a correct evolution of the thermal structure and WV abundance in the TTL. An important result also found is that the convective parameterization is exhibiting well the wide variability of convection in the TTL recorded in the observations, with a possible feedback of deep convection on the TTL's WV budget. Albeit the relatively coarser grid-point resolution and larger-scale simulation, the model is able to reproduce relatively high cloud tops of 14 km à 17 km altitude near the location of overshooting cells detected by MHS. Besides that, the spatial and temporal variability of modeled cloud cells are in good correlation with GOES-12. The BRAMS zonal and meridional winds show the presence of inertia-gravity waves, identified by the TRO-Pico radiosondes ; this is also confirmed by the hodograph analysis of similar parameters (wavelength and periodicity).

In conclusion, the BRAMS mesoscale model appears to simulate adequately the main features of the tropical UTLS, emphasizing the notable role of temperature-driven processes in the tropopause to control the ingress of H 2 O into the stratosphere. It can also be confirmed that SOC is of a smaller importance, yet possibly not negligible on a global scale, for the stratospheric WV budget. It is especially true for this particular wet season when the dramatic cooling and dehydration were observed above the Pacific, as well as in South America, as a response to a SSW in the Arctic.

A future objective will be the implementation of a sub-grid scale nudging for overshooting hydration (or dehydration) in the stratosphere with the same grid-point resolution incorporating the MHS measurements, to explore the climatology of SOC on a continental scale. Figure 3.12 shows that the tropical region of the western Pacific Ocean is drier in comparison to the South American continent at the 82.5 hPa pressure level, which is almost in the lower stratosphere. In both the cases, the minimum H 2 O mixing ratio is observed around January 31, 2013. Nonetheless, this dry lower stratosphere appears in the tropical region of the western Pacific Ocean approximately two days earlier than in South America, and is slightly drier by ∼0.5 ppmv. During the TRO-Pico campaign, we also observe a very dry hygropause (∼2 ppmv) at Bauru around the same period, viz., January 31, 2013.

Supporting

All these observations could be attributed to the impact of SSW reported by [START_REF] Evan | TTL cooling and drying during the January 2013 stratospheric sudden warming[END_REF], which was initiated on January 6, 2013 in the Arctic, as observed during the 2013 ATTREX campaign [Jensen et al., 2013b]. Thus, it is noteworthy that all these features occur in both hemispheres at about the same time : the TRO-Pico driest period at Bauru representing a tropical region in the Southern hemisphere, and at Guam representing the tropical region of the western Pacific Ocean in the northern hemisphere, respectively.

1 J a n 1 1 J a n 2 1 J a n 3 1 J a n 1 1 F e b 2

S2. Saturation temperature (T sat ) calculation : Case study at Bauru

In order to explain further the slightly less colder and drier conditions, respectively, in the modeled tropical tropopause layer (TTL) with respect to the TRO-Pico field campaign measurements, we determine the saturation temperature (T sat ) during the IOP2, which was the driest period of the FMOP. The T sat can be expressed as in [START_REF] Dessler | Mechanisms controlling water vapor in the lower stratosphere : "A tale of two stratospheres[END_REF],

T sat (WV) = 252.7 + 10.4 ln(WV) + 0.407 [ln(WV)] 2 + 0.0102 [ln(WV)] 3 , (3.2)
where WV is the partial pressure of water vapor in hPa, and T sat is in K.

We calculate the T sat using the partial vapor pressures from the balloon-borne stratospheric hygrome- The most important feature that can be observed in Figure 3.13 is that the driest air mass measured (Pico-SDLA and FLASH-B) or simulated at the hygropause, is always in the sub-saturated condition, as the ambient temperature (× symbol) is found to be warmer in comparison to its corresponding T sat (* symbol). Furthermore, the coldest point reached by an air mass during the slow ascent to the stratosphere can be situated somewhere else near the hygropause. Another inference drawn on the slightly less drier condition of the modeled hygropause could be its warmer condition. Figure 3.13 also reveals that a minor adjustment in the saturation temperature (* symbol) of an air mass at the hygropause can dehydrate it further. As the modeled TTL is already warmer, it underestimates the dehydration process (freezing-drying mechanism [START_REF] Holton | Horizontal transport and the dehydration of the stratosphere[END_REF]), and resulting in the H 2 O mixing ratio to be slightly less drier in comparison to the hygrometer measurements during the TRO-Pico campaign. m)) is 0.0189 s -1 between 13 km à 16 km altitude. From the u profile, λ z is found to be ∼2400 m, and the corresponding mean meridional wind speed (v) is 2.87 m s -1 . The major axis of this particular profile coincides with the vertical axis. It can be assumed that k ≈ 0, leading to the following relation : ω = ω -K h v [START_REF] Fritts | Gravity wave dynamics and effects in the middle atmosphere[END_REF], where ω is the ground frame pulsation and obtained to be 7.6741 × 10 -5 rad s -1 . Hence, the periodicity is ∼23 h (Figure 3.14c), while the corresponding RS92 estimation is ∼26 h (Figure 3.14a). A similar method to calculate the periodicity of the inertia-gravity waves is applied to Figure 3.14b and 3.14d. The results are summarized in Table 3.3.

S3. Hodograph analysis : Determination of gravity wave periodicity at Bauru

Further Supplementary Materials to the Article

This section describes all the supplementary work which was carried out in the frame of evaluating the BRAMS model but was too long to fit in the publication. It contains the methods adapted for the measurements/observational data obtained from the satellite-borne sensors, viz., MHS, MLS, and GOES-12, to make them comparable with the BRAMS mesoscale simulation. Some more inferences are also added here regarding the driest period (IOP2) observed during the TRO-Pico campaign.

Overshooting Cells

Recalling the main objective of this dissertation, which is to study the impacts of SOC on the water vapor budget in the TTL and in the lower stratosphere, respectively, at large-scale during a complete wet season, satellite-borne MHS measurements turn out to be a very important asset to validate the modeled parameters akin to overshooting convection (recall Chapter 2.3.2). Though in the REF 1 simulation, there is no SOC at all (see Chapter 3.3), it is important to investigate the altitude as well as spatial distribution of convective clouds at the locations where the satellite-borne MHS radiometer detected overshooting cells within the domain of the simulation corresponding to our study period (FMOP).

We discuss in details about the data extraction criteria adopted for the passive microwave radiometer observations so that the measurements would be comparable with the modeled parameters. For the FMOP, information (both spatial and temporal : latitude, longitude and UTC time of the overshooting events on daily basis) regarding overshooting cells, definitively higher than 14 km altitude [START_REF] Hong | Detection of tropical deep convective clouds from AMSU-B water vapor channels measurements[END_REF], are retrieved from the data files obtained from ICARE/Climserv/Aeris. They are in HDF file format configuration storing information regarding overshooting events in binary format, i.e., 0 for no overshooting event and 1 for the contrary, providing the latitude and longitude of the overshooting cell, not the altitude.

Here, the horizontal resolution of the MHS measurement is 0.04 • × 0.04 • . The overshooting cells' positions are available on daily basis, which is used in the REF 1 simulation. The first thing to note here is that before comparing the MHS measurements against BRAMS, bilinear interpolation is incorporated in order to make its horizontal grid-point resolution the same as the model, i.e., 20 km × 20 km. As such, the modeled highest cloud tops on daily basis are calculated for each grid-point during the FMOP at the position of overshooting cell. For example, Figure 3.15 provides a flavor of the methodology adopted for the validation of the REF 1 simulation. Figure 3.15 depicts the highest cloud tops obtained from numerical simulation on November 16, 2012, i.e., each grid-points show the altitude of highest modeled cloud tops. The highest cloud tops are chosen within the available 24 data points (hourly data corresponding to a day) for each grid-points. The «+» signs therein represent the positions of the overshooting cells detected by the MHS, i.e., the microwave radiometer onboard satellite corresponding to the same day within the domain of simulation. The color of «+» signs varies with the frequency of overshooting events within a particular satellite grid-point. For instance, white color refers to one overshooting event detected by MHS. Similarly, magenta colored cross marks represent two events of overshooting at the corresponding grid-point (very few events in this case), and more than equal to three overshooting events are represented by the black colored cross marks (for this case, there are none).

The histogram shown in Figure 3.10 is the altitude of modeled cloud tops just at (at the exact location of detected overshooting cells -the «+» marks) and around (within ∼50 km radius around the overshooting cells -the «+» marks) the position of overshooting cells detected by MHS during the FMOP for the full domain of simulation. Albeit this is a particular case (Figure 3.15) from the FMOP, a good point to note here that the overshooting cells and the pattern of cloud formation in the model are fairly compatible.

Except for very few locations of overshooting cells, most of them fall below the modeled cloud top.

Convective Cloud Tops

This section provides the working principles adopted for making the SAFNWC products comparable with the modeled cloud tops. The GOES-12 satellite-borne observations of cloud top altitude are derived using the algorithm of SAFNWC. This algorithm incorporates two CTTH parameters, i.e., CTTH_Height and CTTH_Effect (recall Chapter 2.3.3), where these parameters provide the altitude of mostly the optically thick cloud tops, and also optically thin cirrus clouds during twilight times. The Figure 3.16 represents an instantaneous satellite-borne observation obtained from the ICARE/AERIS data service center to discuss in detail the steps incorporated for data extraction. to detect the grid-points corresponding to optically very thick clouds higher than 10 km.

Cloud Tops in Mesoscale Simulations

As discussed in the earlier section about the retrieval of GOES-12 observations by the SAFNWC algorithm involving the two aforementioned CTTH parameters, the SAFNWC algorithm is completely based on the brightness temperature (T B ) measured by the radiometers onboard GOES-12 [START_REF] Derrien | Algorithm theoretical basis document for cloud products (cma-pge01 v3. 2[END_REF]. Now in mesoscale models, it is quite difficult to derive an equivalent parameter to the T B measured by the sensors onboard GOES-12. This makes difficult to make the so-called 'apple to apple' comparison.

Parametrization of cloud tops and spatial variability in large-scale numerical simulations are still limited to several constraints. One main constraint could be to define an equivalent parameter of T B for the numerical models [e.g., [START_REF] Savijärvi | Fast radiation parameterization schemes for mesoscale and short-range forecast models[END_REF]. [START_REF] Albers | The local analysis and prediction system (laps) : Analyses of clouds, precipitation, and temperature[END_REF], [START_REF] Dudhia | Numerical study of convection observed during the winter monsoon experiment using a mesoscale two-dimensional model[END_REF] propose certain criteria to represent the cloud tops within 2D or 3D mesoscale models, and Doutriaux-Boucher and Quaas [2004], [START_REF] Yu | A methodology study of the validation of clouds in GCMs using ISCCP satellite observations[END_REF] in general circulation models (GCM) stating that cloud tops prescribed within are sensitive towards the model horizontal and vertical grid-point resolution, and therefore towards convection, cloud condensation nuclei, precipitation and long-wave emissivity. All these features require a good representation of largeor small-scale boundary layer activities within the numerical simulations, which is limited so far due to several reasons. However, there is no as such a definitive methodology or an algorithm for regional models to construct cloud tops as the SAFNWC algorithm does by treating clouds as black bodies and using the radiance data measured by the sensors onboard satellite. Here, our attempt is to prescribe certain criteria that would possibly be relevant enough to be compared with the GOES-12 observations. We show our results in the publication (recall Chapter 3.3). But before concluding to the specified methodology to obtained cloud tops in this mesoscale simulation, we made several tests. For instance, we checked on each grid-point for its vertical continuity in ice+cloud mixing ratio. Each grid-point must fulfill certain conditions before investigating its vertical distribution. The use of the first derivative is therefore taken into account to decide the height of the cloud top -see Figure 3.17. Figure 3.17a shows the ice+cloud mixing ratio vertical profile at a certain grid-point on January 12 09 :00 UTC, 2013, for the REF 1 simulation. Now considering the cloud top altitude to be the point/altitude, where the mixing ratio would possibly tend to zero (or negligible), we need to investigate the first derivative, or maybe the second derivative of the mixing ratio profile for its continuity. The first derivative will provide an indication of the continuity and monotonicity of the profile, and discontinuous profiles could be rejected therefore before considering them to represent the cloud tops. Thus in Figure 3.17b, we observe that the first derivative (f = df dz ) is changing its sign sharply when the mixing ratio profile itself tends to zero, which is very significant from the second derivative (f = d 2 f dz 2 ) in Figure 3.17c that is the altitude is the end-point or the top layer of cloud, and for this case, it is ∼16 km. It can also be observed that when the mixing ratio tends to zero -decreasing function, the first derivative becomes negative. For a decreasing function, the first derivative changes its sign from positive to negative. And, we choose the vertical point corresponding to the highest altitude to assign the cloud top to that grid-point. The second derivative suffices the criterion.

Based on this method, the following Figure 3.18 demonstrates the cloud tops calculated by the BRAMS model (REF 1 simulation), along with the GOES-12 measurements for the evaluation of modeled cloud tops. The mixing ratio values used in the calculation of the modeled cloud tops are comparable with measurements [e.g., [START_REF] Ware | A multichannel radiometric profiler of temperature, humidity, and cloud liquid[END_REF] and modelings [e.g., [START_REF] Hong | A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation[END_REF]. Here, we recall that it would possibly be the representative of a CTTH_Height parameter in SAFNWC products. 3.18e and 3.18f can be considered, where the horizontal grid-points are considered only when the maximum value of the ice+cloud mixing ratio profile is >0.3 g kg -1 within the corresponding cloudy column -case of 3.18c ; similarly, >0.1 g kg -1 -case of 3.18e, and in case of 3.18f, all horizontal gridpoints are considered irrespective of any maximum or minimum mixing ratio present in the corresponding cloudy column. It is well observed that in Figure 3.18c, BRAMS is underestimating the cloud tops, and is not a good comparison with 3.18a or 3.18d of GOES-12 measurements. On the other hand, putting little fewer constraints to the upper limit or lower limit of the mixing ratio as in Figures 3.18e and 3.18f, BRAMS is overestimating the cloud tops in comparison to 3.18a and 3.18d, respectively. But, it is a good indication to see in Figures 3.18f vs. 3.18a, or 3.18d that the numerical simulation is capable of reproducing the cloud cells exactly at the same position at the same time as per the observation, albeit it overestimates the altitude of the cloud tops. Therefore, it could be assessed finally that deciding a criterion in a mesoscale model to compute the cloud tops is still a challenge for atmospheric scientists, and it demands further extensive analysis to develop a concrete algorithm.

As such, in order to put to the fore the criteria of determining cloud tops as mentioned in Chapter 3.3, we estimate the high cloud (>10.0 km) occurrence averaged over the eight UTC hours, viz., 00 :00, 03 :00, 06 :00, 09 :00, 12 :00, 15 :00, 18 :00 and 21 :00 UTC, respectively, for the FMOP, both in BRAMS and GOES-12 -see Figure 3.19.

The main feature to note in Figure 3.19 is that percentage wise BRAMS is performing well (black vs. dotted red) in simulating high clouds (>10.0 km), albeit the large-scale of simulation during a full season.

Another feature is the variability of high cloud occurrence in BRAMS (black) and GOES-12 (blue) are typically the same when we consider only convective clouds in the GOES-12 measurements. However, the high clouds occurrence, both in BRAMS and GOES-12, are comparable when we consider all kinds of optically thick clouds, occasionally optically thin cirrus clouds as well, in GOES-12. In the dotted red line representing GOES-12 observation using only CTTH_Height parameter, the discrepancy is due to Figure 3.18 -Cloud tops retrieved from satellite-borne observations and concurrent modeled cloud tops calculated using different criteria for January 12 09 :00 UTC, 2013. (a) is the SAFNWC product using only the CTTH_Height parameter ; (b) is the modeled cloud top using the aforementioned three step criteria for ice+liquid mixing ratiorecall Chapter 3.3 ; (c) is the modeled cloud tops, where they are determined using the vertical continuity of the ice+cloud mixing ratio given that the corresponding grid-point must possess a mixing ratio >0.3 g kg -1 within its cloudy column ; (d) is the SAFNWC product representing both the CTTH_Effect and CTTH_Height values, where the CTTH_Effect=100 ; (e) is the modeled cloud top, determined using the vertical continuity of mixing ratio as (c), but each horizontal grid-point must have a mixing ratio >0.1 g kg -1 at certain altitude corresponding to its cloudy column ; (f) is the modeled cloud top chosen as (c) or (e), but in this case all horizontal grid-points are considered irrespective of the maximum or minimum mixing ratio value within the cloudy column. the unavailability of 12 µm channel causing a problem during the twilight time in detecting the optically thin clouds. Then, we investigate the variability in the occurrence of high clouds while considering only the convective clouds in GOES-12 observations. For the same, we incorporate the additional parameter of CTTH_Effect=100 to take into account only optically very thick clouds (blue). By comparing the trend of BRAMS cloud top evolution (black) with GOES-12 (blue) throughout the FMOP, we could state that BRAMS with the defined cloud top criteria (recall Chapter 3.3) is doing a good job as expected. To promote the previous statement, we also look into the scatter plot (Figure 3.20) of high clouds occurrence. .20 -A scatter plot of the percentage of high clouds detected by GOES-12 against the modeled high clouds within the domain of the simulation during the FMOP. X is a random variable corresponding to the percentage of occurrence of high clouds (>10.0 km). Abscissa depicts X from the numerical simulation of REF 1 , while the ordinate represents X from three different sources, i.e., from the REF 1 simulation (black line), and from GOES-12 observations, but using CTTH_Height+CTTH_Effect (red) and CTTH_Height (blue), respectively.

GOES-12 Data Extraction

GOES-12 geostationary satellite-borne observations are extracted for eight UTC hours every day, viz., 00 :00, 03 :00, 06 :00, 09 :00, 12 :00, 15 :00, 18 :00 and 21 :00 UTC during the FMOP, and in case of missing measurements, 15 min before and after measurements are taken into consideration. In some cases, if the measurements are not available within 30 min before or after the aforementioned UTC hours, we don't consider that data point for the analyses.

Probing into the resolution of GOES-12 measurements (use of GeoMapping Toolbox -MATLAB R ), we make a test on different grid-point resolution of data extraction, i.e., transformation of satellite grid (geolocation points in latitude and longitude retrieved from ICARE/Aeris) to a regular raster grid-point format for a smaller time period of data sets, viz., first two weeks of November 2012, before making the measurements ready to be compared with the modeled cloud tops for the full season of study. The main point to highlight here is on the impact of grid-point resolution change brought into the satellite observations because satellite observations don't have the same grid-point resolution as the modeled world.

And, before transforming such a big data set during the FMOP having 3 h time resolution into our required criteria, it is necessary to make such sensitivity tests, and observing its impact on the measurements.

We apply two grid-point resolutions of data extraction from the GOES-12 measurements, viz., 0.18 • × 0.18 • ∼ REF 1 simulation grid-point resolution and 0.5 • × 0.5 • , the second one being quicker in terms of computation as it has to deal with less number of pixels in raster format. Here, the computing time is quite important, as we deal with about << 2 × 8 × 151 >> data files (8 UTC hours, 151 days corresponding Figure 3.21 -A schematic diagram of extracting vector format satellite gridded data to raster gridded format using a particular cell size, i.e., size of each individual pixel. As such, for our case, the cell size of 0.04 • is transformed into 0.18 • and 0.5 • , respectively. Courtesy : http://www.cursosgis.com to the FMOP, both for GOES and BRAMS). In the first case, the satellite grid-points of 0.04 • × 0.04 • resolution is spread over 0.18 • cell size by using sampling method using ∼ 4 × 4 pixels -each of 0.04 • ; similarly for the later case, the satellite grid-point of 0.04 • is spread over 0.5 • cell size using ∼ 12 × 12 pixels. Figure 3.21 gives an overview of this method.

In case of the first choice of 0.18 • cell size, the extracted data is exactly with the same grid resolution as the modeled cloud tops in the REF 1 simulation. So, the inter-comparison is done directly after that. However, in case of second choice (favorable choice for this large set of data, as it is faster and computing time-saving), the gridded data is further incorporated with bilinear interpolation, so that it would be the same as the REF 1 simulation grid-point resolution, i.e., from 0.5 • cell size to 0.18 • cell size (once the data is in raster format, it is quick to interpolate it into another cell size). Then the cross-correlation is calculated for the first two weeks during November 2012, on daily basis for the aforementioned UTC hours -see Figure 3.22. Figure 3.22 depicts that there is not a significant impact of different cell size data extraction on the calculated cross-correlation coefficients between GOES-12 and BRAMS cloud tops. The maximum correlation is observed to appear at 09 :00 UTC and 12 :00 UTC, which correspond to the very early hours of the day in local time (LT), viz., ∼ 06 :00 LT and 09 :00 LT, respectively. It signifies the importance of the development of cumulus convection, which is one of the major processes controlling the dynamics and energetics of the atmospheric circulation, and playing a role in the correlation coefficients obtained. Since at this stage of simulation, viz., REF 1 can not simulate SOC, the model shows good compatibility with the GOES-12 measurements during the early local hours of the day, when it is quite plausible that there are fewer possibilities of occurrence of deep convective clouds.

H 2 O Mixing Ratio : Application of Aura MLS

Aura MLS (version -4.2) measurements (recall Chapter 2) are used as supporting materials to the water vapor measurements carried out in the frame of TRO-Pico field campaign at Bauru, Brazil during 2012 and 2013. In our article (Chapter 3.3), we discuss a very cold and dry TTL observed during the end of January/beginning of February 2013, in the frame of TRO-Pico campaign. In the "Supporting Information", we discuss briefly this dry air mass which would have traveled from the tropical region of western Pacific Ocean to the continent of South America, where the measurements were carried out at Guam (13.44 • N, 144.79 • E) and Bauru (22.31 • S, 49.05 • W), respectively. Now, in order to observe the , 00 :00, 03 :00, 06 :00, 09 :00, 12 :00, 15 :00, 18 :00 and 21 :00 UTC of a day, respectively. Missing columns highlights the absence of GOES measurements.

advent of this large-scale driest period around the tropical belt of the full globe, we further investigate the mid-January and end-January, 2013, H 2 O mixing ratio at 82.5 hPa pressure level for the full globe between the latitudes of ±30 • to the equator. Figure 3.23 gives the global water vapor distribution during these two periods in the lower stratosphere.

Figure 3.23 depicts the global presentation of water vapor variability at 82.5 hPa pressure level retrieved from the Aura MLS measurements, which is a more detailed representation of Figure 3.12 during the driest periods corresponding to mid-January and end-January, 2013. In Figures 3.23a vs. 3.23b, the noticeable feature is the aridity observed in the lower stratosphere (82.5 hPa altitude) in the tropical belt.

As mentioned earlier, on January 06, 2013, there was already a SSW triggered in the Arctic. Supposedly as a consequence of which, the lower stratosphere in the tropical belt started getting colder and drier.

During the mid-January, 2013, the tropical region of Pacific Ocean was observed to be drier in comparison to other longitudes within the tropical belt. However, the period corresponding to January 31 to February 02, 2013, is observed to be the driest period for the full globe in the tropical belt, where the H 2 O mixing ratio was measured to be around 2.0 ppmv at 82.5 hPa pressure level. This feature comes along with the TRO-Pico campaign measurements, which was observed during the balloon-borne measurements in the IOP2 phase at Bauru and could be affiliated with the impact of SSW and faster Brewer-Dobson circulation.

The ATTREX 2013 field campaign and the TRO-Pico second phase field campaign (IOP2) were carried out during the same time period very close to the SSW event in the Arctic. This supports our results from the simulation REF 1 , and already commented in the article (see Chapter 3.3).

Gravity waves -Application of Fourier analysis

Fast Fourier transform (FFT) analysis is an ample tool to analyze the frequency domain of any typical time series with mostly a constant sampling time [START_REF] Wei | Time series analysis[END_REF][START_REF] Zavadil | Two dimensional Fourier transform using MATLAB[END_REF]. The definition is as follows :

F(u, v) = ∞ -∞ ∞ -∞ f(x, y) exp(-i2π(ux + vy))dxdy, (3.3) f(x, y) = ∞ -∞ ∞ -∞ F(u, v) exp(i2π(ux + vy))dudv, (3.4)
where i is the iota, u and v are the spatial frequencies, F(u, v) is the Fourier transform of f(x, y) -the FT pairs f(x, y) ⇐⇒ F(u, v). F(u, v) is generally complex function, can be expressed as

F(u, v) = F R (u, v) + iF I (u, v). |F(u, v)
| represents the magnitude or power of the spectrum. arctan u,v) is the phase angle of the spectrum. Now recalling Table 3.3, in order to check the periodicities present in the perturbed zonal and meridional wind profiles calculated from the REF 1 simulation, fast Fourier transform is employed on each component of the perturbed wind, respectively, i.e., u and v profiles at Bauru within an altitude range of 12 km à 23 km during the IOP2 phase. We don't apply FFT on the RS92 measurements of the TRO-Pico campaign due to the fact that they are not constant in terms of sampling time, i.e., the discontinuity in the measurements.

F I (u,v) F R (
The Fourier coefficients are shown in a frequency-altitude 2D plot, as shown in Figure 3.24. Thick bands of high power representing varying periodicities are observed, confirming the periodic behavior of inertiagravity waves [START_REF] Chane-Ming | Gravity wave characteristics over tromelin island during the passage of cyclone hudah[END_REF][START_REF] Tsuda | Radiosonde observations of equatorial atmosphere dynamics over Indonesia : 1. equatorial waves and diurnal tides[END_REF]. Figure 3.24 depicts the results from the Dans la base de l'overshoot, les agrégats jouent également un rôle important dans la composition en glace.

On montre également qu'environ 70% de la masse totale de glace dans l'overshoot stratosphérique est concentrée dans la couche basse du dôme comprise entre les niveaux isentropes 380 K à 385 K. De manière très intéressante, cette tranche où la masse est essentiellement concentrée, à la base de l'overshoot, une surface typique de 450 km 2 , ce qui est comparable à la taille de la maille de la simulation REF 1 du chapitre 3 (400 km 2 ), dans laquelle nous voulons forcer les overshoots stratosphériques. L'analyse des simulations a également permis de déduire une estimation de la quantité totale de glace injectée dans la stratosphère par une cellule d'overshoot. Elle varie typiquement entre 4 kt à 6 kt, selon le réglage microphysique. Une fois qu'une partie de la glace a sédimentée et/ou a sublimé, on peut estimer la quantité de vapeur d'eau qui reste dans la stratosphère. Elle varie entre 330 t et 1400 t pour la simulation REF et entre 750 t et 2000 t pour la simulation NU21. Ainsi les estimations varient d'environ 30% selon les réglages du modèle, mais elles sont quoiqu'il arrive supérieures à d'autres estimations pour des cas d'overshoots en Afrique de l'ouest avec le même modèle. La présente analyse montre cependant un bilan d'eau comparable, quoi qu'un peu inférieur, aux dernières estimations du rôle du système convectif Hector au Nord de l'Australie, avec un autre modèle méso-échelle.

In this chapter, we analyze several fine-scale BRAMS simulations corresponding to a series of overshooting events observed during the IOP1 phase of the TRO-Pico campaign. The goal is to extract the essential details embedded within the overshooting turrets in order to force the impact of stratospheric overshooting convections (SOCs) on the stratospheric water vapor budget, using the BRAMS model as a tool for a type of simulation similar to the one we present in Chapter 3. In order to obtain vital information corresponding to an overshooting turret (e.g., ice flow, the majority of types hydrometeors, average particle size, distribution of mass), three different nested-grid simulations akin to the case of overshoots observed on March 13, 2012, at Bauru are proposed and analyzed. Mostly, they are examined for certain variabilities recorded in the frame of TRO-Pico field campaign. The three simulations differ from each other by the bulk microphysical settings of the model and the vertical grid-point resolution, mostly corresponding to the tropical tropopause layer (TTL). The case study of overshoots on March 13, 2012, at Bauru is presented from the meteorological point of view, and also from the point of view of balloon-borne field campaign carried out in the frame of TRO-Pico project, which was realized on that same day. The simulation settings are elaborated, and then validated by comparing them with the echo-top measurements (the highest signal of the hydrometeors detected by the radar corresponding to a low-estimate of cloud peak) of the S-Band radar of the IPMet, and water vapor measurements by the stratospheric hygrometers, viz., Pico-SDLA and FLASH-B, used in the TRO-Pico campaign. The hygrometer measurements were carried out after five to six and half hours after the overshooting event.

It is shown paradoxically that the simulation with better vertical resolution near the TTL is less in agreement with the observations (e.g., convection too violent in the model) than the other two simulations.

These two simulations have 300 m of vertical resolutions around the TTL, and depict a fair temporal agreement in the development and dissipation of the overshooting cells, entirely compatible with the observations. However, the modeled overshooting cells are slightly ahead of the time with respect to reality, and also possessing a spatial shift of about 50 km to the north of the exact overshooting location.

We also show a number of stratospheric overshoots slightly higher than the radar observations. The analyses demonstrate the following results : pristine ice and snow are the only two dominant modeled hydrometeors among the five, viz., pristine ice, snow, graupel, hail, and aggregates, to play a role in the composition of the overshooting turret. Furthermore, we compute the ice mass distribution in the stratospheric part (above the isentropic level of 380 kelvin), which is of mainly distributed (∼70% of the total mass of the ice injected during the overshooting events) between 380 K à 385 K isentropic surfaces. Very interestingly, this slice where the mass is essentially concentrated, is obtained to be a typical surface area of 24 km × 24 km at the base of the overshoot, which is comparable to the grid-mesh size of the REF 1 simulation of the Chapter 3, in which we make absent the overshoots.

Introduction

Upscaling the impact of stratospheric overshooting convection (SOC) on the water vapor (WV) budget belonging to the TTL and the lower stratosphere is the main motivation of this dissertation. In Chapter 3, we put to the fore the ability of the BRAMS model to emulate the key features of the TTL in the absence of SOC, depicting, therefore, the BRAMS model as an equitable tool to upscale the impact of SOC on the WV budget. A priori, to advance further in the attempt of upscaling, a typical impact of overshooting convection in the stratospheric WV budget must be established at a local-scale, so that it can be extrapolated further. Recalling Chapter 1, several studies have already simulated some SOC cases, and sometimes estimated its impact on the stratospheric WV [e.g., [START_REF] Chaboureau | A numerical study of tropical cross-tropopause transport by convective overshoots[END_REF][START_REF] Chemel | Quantifying the imprint of a severe hector thunderstorm during ACTIVE/SCOUT-O3 onto the water content in the upper troposphere/lower stratosphere[END_REF][START_REF] Dauhut | Large-eddy simulations of hector the convector making the stratosphere wetter[END_REF], Grosvenor et al., 2007[START_REF] Hassim | A model study on the influence of overshooting convection on TTL water vapour[END_REF], Liu et al., 2010a]. However, the quantity of WV akin to overshoot, which will remain in the stratosphere, depends on the ambient condition of sub-saturation or supersaturation, and cannot be upscaled and nudged directly in the model (see for example [START_REF] Chemel | Sensitivity of tropical deep convection in global models : effects of horizontal resolution, surface constraints, and 3d atmospheric nudging[END_REF], [START_REF] Hassim | A model study on the influence of overshooting convection on TTL water vapour[END_REF]). Nonetheless, the ice injected by SOC cells could be nudged instead by incorporating its nature, quantity and vertical mass distribution. In the ensuing chapter, we take advantage of the TRO-Pico campaign field measurements corresponding to the SOC events (IOP1), during which several overshooting cells above 17 km were observed. It provides precious data that would help to validate any overshoot simulation. Here, we make three simulations of the TTL at fine-scale corresponding to the observational case of March 13, 2012, of the TRO-Pico campaign.

After validating the simulations, proving that our results are realistic and applicable for retrieving those quantities which are not directly accessible by the measurements, our main aim is to retrieve and calculate key information that will help to prescribe a nudging scheme of SOC hydration (or dehydration) in the stratosphere. The fine-scale simulations presented here are led by E. D. Rivière at GSMA. My contribution in this work comprises the analyses of the simulations. A particular focus is drawn towards the time-scale of hydrometeors injected in the stratosphere, the vertical as well as horizontal size of the overshooting dome, and the ice mass flux and the ice mass budget.

Presentation of the Case

The modeled overshoots investigated here refer to the observational case of March 13, 2012, in the region of Bauru, Brazil, during the IOP1 phase (March 2012) of the TRO-Pico field campaign. This case is chosen, because it is one of the most documented cases of the whole campaign, and the measurements are used as resources to validate the simulation of such a case. During the campaign, it was observed that several overshooting cells reached the stratosphere southeast and east of Bauru in the early local afternoon.

In the late local afternoon, the flight train of stratospheric hygrometer Pico-SDLA and the optical particle counter LOAC were launched under a 500 m 3 open balloon. Later, just after the sunset, the flight train comprised of the FLASH-B hygrometer and the COBALD backscatter sonde was launched under a rubber balloon. Another impacting fact to study this case could also be the comparison of water vapor profiles between FLASH-B and Pico-SDLA hygrometers, which is already reported by [START_REF] Ghysels | Intercomparison of in situ water vapor balloon-borne measurements from Pico-SDLA H2O and FLASH-B in the tropical utls[END_REF] to have very similar mixing ratios in the TTL with local H 2 O enhancement linked to the SOCs [START_REF] Khaykin | Evidence of horizontal and vertical transport of water in the southern hemisphere tropical tropopause layer (TTL) from high-resolution balloon observations[END_REF]. Further details on this observational case are given below. Only a few convective clouds (8 km à 10 km height) were triggering then around 100 km south/southeast to Bauru. Afterward, these clouds were intensified in time and in size in this area with some convective

Radar Observations

Balloon-borne Observations

Description of the Simulations

General Setup

The common features of the aforementioned three simulations are as follows. They comprise of three nested-grid simulations with the same grid positions, and with the same telescopic horizontal grid-point resolutions. It starts from 20 000 m -parent grid, 4000 m -grid 2, and 800 m -grid 3. Grid 1 (parent grid) embeds a large part of Brazil in the southern hemisphere (though smaller than the domain used in the layers. Whatever the vertical resolution is, the top of the domain is up to 30 km altitude with a sponge layer of 5 km to absorb the gravity wave at the top.

Specific Setup

The three simulations, viz., REF, NU21, and HVR differ from each other in the following points.

The only difference between the REF and the NU21 is the shape parameter (ν) of the gamma function distribution of the hydrometeors. For the REF, it is set to 2.0 for all hydrometeors ; whereas, it is set to 2.1 in the NU21. Please note that ν = 2.1 would imply that the size of particles is shared among a narrower range of size distribution than for the ν = 2.0 size distribution. The ν = 2.1 setting is activated from the activation of grid 3, that is 10 :00 UTC on March 13, 2012. In other terms, both simulations are exactly the same until this point in time. This is chosen in such a way to investigate the impact of this

Validation of Simulations

In this section, we validate the aforementioned simulations against observations from the S-Band radar of IPMet, State of São Paulo, Brazil, and balloon-borne measurements carried out in the frame of TRO-Pico field campaign, respectively. The radar measurements are available from 12 :01 LT (15 :01 UTC) onwards on March 13, 2012, since before this time, there was no major deep convective activity in the region around Bauru. The balloon-borne measurements are part of IOP1 phase of the field campaign.

Validation against Bauru Radar Echo Top

In order to compare the modeled parameters against the radar observation, the simulation outputs are expressed in cloud top layers of 1 km each varying from 9 km à 20 km range of altitude, similar to the echo top products. Basically, if the modeled condensed water (ice+liquid) concentration is above a prescribed threshold of mixing ratio within a given layer, then the modeled cloud top is determined for this range of altitude. As this criterion is applied in a vertical loop starting from the bottom, the cloud top altitude assignment for a given (x, y) grid mesh is definitive, once all the vertical levels have been scanned through. To account for the decrease in the concentration of hydrometeors with altitude within the TTL akin to a deep convective cloud, the threshold of concentration belongs to a layer of cloud top depending on its range of altitudes. It is 1 g kg -1 for the layers starting from 9 km à 10 km up to 15 km à 16 km.

Then, it is 0.45 g kg -1 for 16 km à 17 km, and 0.2 g kg -1 for 17 km à 18 km layer. It is 0.008 g kg -1 for the higher layers above 18 km. These thresholds are chosen as a function of typically modeled concentrations of hydrometeors inside vertical cross-sections of deep overshooting cells.

The complete time series of comparison between the radar observation of cloud tops and the three simulations starting from 14 :00 UTC to 18 :52 UTC on March 13, 2012, is provided in Appendix C.

The key features corresponding to the overshooting case are reproduced here and commented accordingly.

Firstly, Figure 4.6 provides the initial cloud tops at 14 :00 UTC and 15 :00 UTC for the three simulations.

Note that the radar image is not available at 14 :00 UTC since no high cloud was detected at that time. (c) NU21 simulation@14 :00 UTC. (d) NU21 simulation@15 :00 UTC.

(e) HVR simulation@14 :00 UTC. (f) HVR simulation@15 :00 UTC. The complete time evolution of the NU21 simulation highlights a similar progression of the cloud cluster to the north/north-west as in the REF simulation, following the bank of river Tiete. However, the NU21 simulation appears to be less realistic than the REF simulation in terms of the severity of deep convection after 18 :30 UTC, when the decay period is not clear for NU21. Moreover, before 15 :00 UTC when the radar is cloud free, the NU21 simulation has already produced 16 km à 17 km high convective cells.

Furthermore, counting the total number of SOC cells above 17 km for NU21, the simulation leads to a lower number of cells than for the radar observation and for the REF simulation (see Table 4.1). The detailed examination of these cells shows that they have a longer lifetime in the case of NU21. From this conclusion, we cannot state that the overshooting activity is lower in the NU21 with respect to the REF and to the radar observations. to 49 • W. Thus, this is more severe than the radar observations during that period. After these earliest SOC cells, the HVR simulation appears to be unrealistic from the point of view of the severity of deep convection and above all, in the surface areas of cloud covers above 16 km.

A remark on the increment of the vertical grid-point resolution around the tropopause and its impact in resolving the tropopause (recall Chapter 3) could lead to an interpretation of the higher deep convection in the HVR simulation, in comparison to the REF or the NU21, respectively. Here one important fact is that the tropopause and the level of neutral buoyancy (LNB) are better resolved. Nonetheless, a point to note is that the criteria used for the modeled cloud top assignment do not account for a discontinuity in the vertical cloud column. If there is a stratospheric plume from a SOC turret disconnected from the convective cloud just below, this criterion will assign the altitude to the cloud top, which corresponds to the plume, not to the detached cloud cover above it. Furthermore, the S-Band Radar is mostly sensitive to liquid hydrometeors, rather than the ice hydrometeors. As a consequence of which, the echo top products are likely to underestimate the altitude of the cloud tops, in a range of altitude where most of the water content is in the solid phase. In the subsequent sections, the HVR simulation will not be commented in detail, though some of the outputs will be analyzed in comparison with the two other simulations.

Validation against TRO-Pico Balloon-borne Measurements

Now, we take advantage of the TRO-Pico H 2 O and particle measurements in the vicinity of overshooting turrets to validate the aforementioned three simulations. As the measurements were performed several hours after the overshooting event (we denote the time interval between the time of the overshooting event and the time of the balloon-borne measurement as Δt om ), the strategy for the validation is therefore as follows : the overshooting plume is followed after at those altitudes where the local enhancements of H UTC most of the original turret is observed eastward to 49.1 • W and is advected northward, as described in the trajectory analysis of the same case by [START_REF] Khaykin | Evidence of horizontal and vertical transport of water in the southern hemisphere tropical tropopause layer (TTL) from high-resolution balloon observations[END_REF]. In Figure 4.13, vertical profiles of total water content (ice+liquid+vapor), at different locations akin to the same turret are shown. At some locations (corresponding to the maxima of H 2 O mixing ratio within the overshooting turret at 17.2 km), the local enhancement is typically 2 ppmv of total water. When the profile is extracted in the border of the turret, the local enhancement is reduced. The green and red profiles show typically a local enhancement of about 0.5 ppmv. In these profiles, it is checked that no ice was remaining, which means that in this part of the plume, all the ice has sublimated or sedimented. This is in line with the TRO-Pico measurements of the LOAC and COBALD under the Pico-SDLA and FLASH-B, respectively, that measured no ice in the stratosphere. The 0.5 ppmv enhancement here in the modeled profile is also comparable with the one measured by FLASH-B in this range of altitude.

The same analysis is then carried out for the turret corresponding to the same SOC cell at 17.8 km.

This is the altitude of the second water enhancement in both the Pico-SDLA and the FLASH-B H 2 O profiles, respectively. [START_REF] Khaykin | Evidence of horizontal and vertical transport of water in the southern hemisphere tropical tropopause layer (TTL) from high-resolution balloon observations[END_REF] report that this H 2 O enhancement is due to another SOC than the one explaining the 17.2 km enhancement. However, we check if a realistic overshooting turret in the model can lead to a similar water vapor enhancement after the same Δt om . For the water enhancement in Figure 4.17. Figure 4.17 shows that for certain locations, the enhancement of total H 2 O is of several ppmv, particularly when located at the center of the turret (black line). Such large enhancements from overshoots have already been reported from measurement by the FISH hygrometer onboard the Russian M55 Geophysica high-altitude aircraft during SCOUT-AMMA field campaign in West Africa [START_REF] Schiller | Hydration and dehydration at the tropical tropopause[END_REF]. However, when located at the border of the turret, the enhancement of water in the model is typical of half a ppmv (red profile). This is fully compatible with the local enhancement measured by FLASH at 17.2 km. Furthermore, it is important to highlight that there is no ice remaining in the profile of total H 2 O, and the total H 2 O is only in the form of vapor. This is also what was observed during the TRO-Pico campaign when neither the LOAC particle counter nor the COBALD backscatter sonde measured any ice particle.

A similar work is then performed for the overshooting turret at 17.8 km altitude. Here, we only show the vertical profile of total H 2 O content within the plume at 20 :52 UTC, that is Δt om = 4 h40 min after the 1615 UTC overshoot (see Figure 4.18). This Δt om is the same as the time interval between the Pico-SDLA measurements and the overshooting event captured by Pico-SDLA. The conclusion reached here is that when located at the border of the SOC cell (magenta profile), a 0.7 ppmv H 2 O enhancement is computed at 17.8 km, without any remaining ice. This fully promotes the validation in term of water vapor enhancement.

Conclusion of the Validation

In S-Band radar observation, though the overshooting cells in the model are located slightly northwest to the real case. The severity of the overshooting cells in the model are similar to the radar, though seemingly higher in altitude in the model. This could be a fact that the S-Band radar is little sensitive towards the ice hydrometeors. The number of overshooting cells above 17 km are similar in the model and the radar observation until 18 :30 UTC, after which the model behaves unrealistically in terms of the severity of the convection. Tracking the overshooting turret using the total H 2 O content, we also depict that the modeled H 2 O profiles extracted from the plume of the modeled overshoot after about 4.5 h and 7 h, respectively, are compatible with the balloon-borne measurement of H 2 O enhancement by Pico-SDLA and FLASH, respectively, ∼4.5 h and 7 h after the observed overshooting event. These extracted profiles must be at the edge of the overshooting turrets. It is also shown that no ice is remaining in the vertical profiles of total H 2 O content within the turrets. This is fairly compatible with the observational case of overshoot.

Above analyses depict the pragmatic behavior of these two simulations (REF and NU21) and make them a precious material to be analyzed further for documenting our quantitative knowledge about SOCs at the local-scale. Unfortunately, the HVR simulation with a higher vertical resolution seems to behave too severe in terms of producing convection, making it incompatible for such studies. In the following, this simulation will only be analyzed in terms of comparison with the REF and the NU21 simulation. The subsequent sections are dedicated to the quantitative analysis of the SOC cells.

Analysis

We make several analyses for getting into the details of the structure of the SOC cells. Here, the main aim is to give important values akin to SOC that could be used in the forcing scheme of overshooting turrets. Firstly, this analysis comprises of the distribution of the five types of ice hydrometeors within the overshooting turret. Then, it is followed by the impacting area of SOC at 380 K isentropic surface.

Secondly, we make the calculation of the instantaneous mass flux of individual hydrometeors at 380 K isentropic surface, further proceed with making their mass budget calculation within the belt of 380 K à 430 K isentropic surfaces. Finally, we conclude in giving typical features/values, which would be a pragmatic representation of SOC within the numerical models.

Structure and Composition of SOC

We use modern mathematical toolboxes to analyze precisely the overshooting turrets and conclude on their typical features which can't be measured directly so far. The estimation of the ratio of each hydrometeor with respect to the total five hydrometeors within the overshooting turret is made here. For example, the series of figures below (pristine ice, aggregates, snow, graupel, and hail) starting from Figure teor as a proportion within the overshooting turrets. The horizontal cross-section shows the typical mass ratio of pristine ice, aggregates, snow, graupel, and hail, respectively, with respect to the total ice mass.

Therein, the leftmost column refers to the REF, the middle one to the NU21, and the rightmost one to the HVR simulation, respectively. The important concluding remark from this analysis is that within the overshooting turret, pristine ice and snow are the predominant ice hydrometeors above the tropopause (see Appendix D for the full-time evolution). This is compatible with the work of [START_REF] Chemel | Quantifying the imprint of a severe hector thunderstorm during ACTIVE/SCOUT-O3 onto the water content in the upper troposphere/lower stratosphere[END_REF],

where they analyze the Hector simulation using WRF model. They put to the fore the (pristine) ice and snow as the dominant ice hydrometeors within the SOCs. However, our work takes the advantage of the BRAMS model, where it incorporates five types of ice hydrometers, instead of three in the WRF model. Now, observing the Figure 4.20, the proportion of aggregates within the SOC is not negligible, but just at the base of the turret, it is not significant as we go further up towards the tropopause. It is also important

to note that at the base of the turret (15.4 km à 16.6 km altitude) near the deepest core (the center of the turret), pristine ice is completely absent, only aggregates is prevailing as a dominant ice hydrometeor (∼60%) within a very narrow range of radius ∼5 km. However, this feature is significant at a lower altitude (∼16 km) below the tropopause. Only pristine ice and snow are traveling further up into the stratosphere, and observed to reach ∼17.8 km altitude, which is almost the lower stratosphere at this range of latitudes.

This turns out to be a very important feature for nudging the impact of SOC. The forcing scheme would possess pristine ice and snow, as rest of the ice hydrometeors are almost negligible above the tropopause (∼17 km). For example, in this case, as we reach about 17.8 km altitude, the only remaining in the turret are the pristine ice (∼70%) and snow (∼30%). This feature is quite similar to all the cases given as the full-time evolution of SOCs in appendix D. Furthermore, another feature could be added here that at the bottom of turret (around the tropopause) in a range of altitude 15.4 km à 16.6 km, the turret comprises almost 100% of pristine ice, as we go further away horizontally towards the boundary from the center of the turret. In subsequent sections, we calculate their mass budget within the certain range of isentropic layers.

Then before proceeding further into the details of the mass budget calculation for each type of hydrometeor, it is important to get an overview of the impacting area of overshooting turret at 380 K isentrope.

It would be very valuable for numerical simulations before prescribing a nudging scheme of overshoot with the comparable size of horizontal grid-point resolution. In 4.1, which gives information about the number of SOC events and their top altitude for each individual simulations, as well as for the S-Band radar measurements. Keen observations on the sizes of impacting areas among these four cases would lead to the conclusion that the typical variability of the impacting area of overshooting plume is about 24 km × 24 km at the 380 K isentropic layer. In . The solid arrows depict the typical size of the SOCs. 1 4 0 0 1 4 3 0 1 5 0 0 1 5 3 0 1 6 0 0 1 6 3 0 1 7 0 0 1 7 3 0 1 8 0 0 1 8 3 0 1 8 5 2 1 4 0 0 1 4 3 0 1 5 0 0 1 5 3 0 1 6 0 0 1 6 3 0 1 7 0 0 1 7 3 0 1 8 0 0 1 8 3 0 1 8 5 2 1 4 0 0 1 4 3 0 1 5 0 0 1 5 3 0 1 6 0 0 1 6 3 0 1 7 0 0 1 7 3 0 1 8 0 0 1 8 3 0 1 8 5 2 incorporating a coarser grid-point resolution. Now, the impact area of SOC turns out to be very comparable with the size of grid-point we use in REF 1 . This would be a key factor while forcing the impact of SOC in a model similar to REF 1 .

Budget

We calculate the amount of the instantaneous mass flux at 380 K isentropic layer, and total mass corresponding to individual ice hydrometeors within the slice of 380 K à 430 K isentropic layers, again thanks to the modern mathematical toolboxes (MATLAB R ). The transformation of simulated grid-points from Cartesian coordinate system to isentropic coordinate is an important step before evaluating the SOC features within this aforementioned band of isentropic layers. surface. These values would be used for prescribing the nudging of SOC above 380 K isentrope, providing a general idea to take care of the proportion of different hydrometeors and the vertical velocity of injection.

However, it would be difficult here to comment on the differences between the REF and the NU21 simulation based on Table 4.2, as the values are also dependent on the vertical wind values (w), and of course, the cases presented here correspond to different SOCs. We also check the total volume of grid-points present between the slice of isentropic layers from 380 K à 430 K and its deformation due to the impact of SOC. Following the time series of total (absolute) volume and the starting time of the deformation can be related to the Table 4.1. The maxima of the volume depict the calm period, no deep convective activities. At the time of overshoots, the total volume starts decreasing, and minima in both the profiles put to the fore the severity of the convection. This is due to the fact that the higher isentropic levels are less deformed than the 380 K (please also refer to the vertical cross-sections of condensed water content, for example Figure In Figure 4.27, the mass budget is calculated with respect to the volume at the unperturbed state for each simulation that is at 15 :00 UTC for REF simulation and 14 :00 UTC for NU21 simulation, respectively. This is why for the REF simulation, the time of study begins from 15 :00 UTC, while it is 14 :00 UTC in case of NU21 simulation. It clearly depicts the total H 2 O (ice+water vapor) enhancement within the layer of 380 K à 430 K isentrope. It is clear that there is an increment of 8 kt of total H 2 O content in both the simulations, while only the water vapor enhancement is 2 kt in REF, and 3 kt in NU21 simulation, respectively, within this range of isentropic layers due to SOCs. In the meanwhile, the ice is supposedly partly sublimating to the troposphere. Among the important features in Figure 4.27, for the REF simulation, there is a plateau in total H 2 O mass starting from 15 :37 UTC until 16 :07 UTC. This can be associated with the SOC event of 15 :37 UTC as discussed earlier (see also Table 4.1). Then, the peak corresponds to 16 :22 UTC, but before that the SOC at 16 :15 could be the predominant one to inject a bulk amount of total H 2 O content that remains in the lower stratosphere until the next SOC of 16 :22 UTC, where the total H 2 O content reaches its peak. Two SOC are already tabulated in Table 4.1 corresponding to 16 :15 UTC. Afterward, Table 4.1 show two SOC events at 16 :37 UTC, which are clear in the plot. Then, the total mass of H 2 O content approximately attains a plateau, however, there is a SOC event measured at 16 :52 UTC. This last SOC gives a little enhancement to the total mass. Now, in case of NU21 simulation, the scenario is a bit different. The first reason could be that it instigates SOC very early in comparison to the REF simulation. We see several peaks in the total mass budget during 15 :00 UTC to 16 :37 UTC. Recalling Table 4.1, NU21 does not produce that many SOCs during the aforementioned hours. This could be associated with the cloud top determination criteria, already discussed in section 4.3.2. Nonetheless, by the end of this observation period starting from 16 :52 UTC, we observe an approximate plateau in both the simulation until 17 :30 UTC, attaining a value of about 8 kt of H 2 O enhancement due to several SOCs occurred during then. Here also, we recall the Figure 4.25 to promote the concluding remarks on the total mass budget. During the period of 16 :52 UTC to 17 :30 UTC, the mass flux profiles of each ice hydrometeor is observed to remain almost zero. This depicts a calm period, therefore the plateau observed in the mass profiles are reasonable. This plateau is the sign of a SOC free period. Concurrently, this is also the period of transformation of ice into water vapor, so that the total mass remains approximately constant, which is the indication of a net hydration in the lower stratosphere. Now from Table 4.1, we know the number of SOC events in each simulation during the period of observation. We can calculate the typical amount of hydration for each overshooting turret, providing both upper limit and lower limit by considering total H 2 O content and water vapor, respectively. In case of REF simulation, the upper limit is about 8 kt 6 = ∼1.34 kt ; whereas in case of NU21 simulation, it is about 8 kt 4 = 2 kt. Similarly, the lower limit of hydration can be calculated as : for REF simulation, it is

2 kt 6 = ∼333 t ; whereas in case of NU21 simulation, it is 3 kt 4 = ∼750 t.
Here, the denominator denotes the total number of SOC events during the period of study, while the numerator gives the amount of total hydration caused by SOC -see Figure 4.27. Furthermore, Figure 4.27 can also provide the total amount of ice injected by a single overshooting turret. For the REF simulation, at 16 :15 UTC, the enhancement in the total ice is about 12 kt, and referring to Table 4.1, during then REF has 2 SOCs. Thus, in REF simulation, one SOC contributes 12 kt 2 = 6 kt of only ice. Similarly, for NU21 simulation, at 15 :07 UTC, the only ice enhancement due to single SOC is 8 kt 2 = 4 kt. This type of total H 2 O enhancement due to overshooting convection in the lower stratosphere is already reported using mesoscale models [e.g., [START_REF] Chaboureau | A numerical study of tropical cross-tropopause transport by convective overshoots[END_REF][START_REF] Chemel | Quantifying the imprint of a severe hector thunderstorm during ACTIVE/SCOUT-O3 onto the water content in the upper troposphere/lower stratosphere[END_REF], Liu et al., 2010a], and also using satellite-borne observations [e.g., [START_REF] Iwasaki | Characteristics of deep convection measured by using the A-train constellation[END_REF][START_REF] Lelieveld | Stratospheric dryness : model simulations and satellite observations[END_REF]. [START_REF] Dauhut | Large-eddy simulations of hector the convector making the stratosphere wetter[END_REF] estimate about 2776 t of water vapor enhancement, which is of the same order, albeit higher to our calculation. However, our calculation is significantly higher than the estimation of Liu et al. [2010a] (about 500 t at maximum), where they use the same BRAMS model to study SOCs in West Africa. Thus, this total H 2 O enhancement is realistic and can be fed to numerical models while forcing its impact corresponding to upscale studies. Furthermore, as seen from Figure 4.19, it is evident that most of the mass of the injected hydrometeors due to SOC are at the base (380 K) of the turret. We calculate the mass budget for individual ice hydrometeors within the layers of 380 K à 385 K isentropic levels (see Table 4.3). Here also, we pick up some particular cases of severe convection following the Table 4.1 in order to estimate the typical values of the ice hydrometeors present within the base of the turret. They are expressed in terms of percentage of the mass, but in two-ways : firstly, the mass of a particular ice hydrometeor lying between 380 K à 385 K isentropic levels with respect to the total mass of that hydrometeor between 380 K à 430 K isentropic levels, namely, h H × 100 (say, ρ 1 ) : where h corresponds to the mass of a particular hydrometeors within 380 K à 385 K isentropic levels, and H refers to the mass of the same hydrometeor but within 380 K à 430 K isentropic levels ; secondly, they are expressed in terms of percentage of mass with respect to the total mass corresponding to all five ice hydrometeors, namely, 4.2, hail turns out to be completely negligible within the SOCs, and graupel also. Thus the information from Table 4.3 will be playing an important role in assigning the proportion of ice hydrometeors (the vertical distribution) within the overshooting turret in order to prescribe the nudging scheme. The difference in the mass budget for these two simulations is due to the microphysics adopted to investigate the impact of shape parameter (ν) on the SOC. As we choose a higher value in NU21 simulation, the particle size distribution followed by the gamma function would be narrower in comparison to the REF simulation (see Chapter 2). This is then plausible to comment that in NU21 simulation hydrometers size distribution is more limited than the REF simulation, therefore leads to a lesser variability in the size distribution of each particle. Then, the bigger ice hydrometeors are expected to fall back more efficiently in the troposphere for the REF simulation, which explains the values of ρ 1 . Similarly, the small particles will then manage to go further upwards (recall Figure 4.27 for the total mass difference in both simulations). This justifies the percentage difference in both the simulations. These numbers stand out to be very valuable for the prescription of a forcing scheme of overshoots in the stratospheric H 2 O budget. In the following section, we conclude on the nudging scheme of SOC in the TTL and lower stratosphere, which would be used for upscaling studies using the type of simulation we prescribe in Chapter 3, the REF 1 simulation.

h 5 i=1 H i × 100 (say, ρ 2 ).

Sub-grid Scale Nudging

In this chapter, we carry out several fine-scale BRAMS simulations corresponding to the observations overshooting case of March 13, 2012, in the frame of TRO-Pico field campaign. During this event, several overshoots reached the stratosphere. After comparing and validating the simulations using the field campaign measurements (radar and balloon-borne measurements), the overshooting turrets from the BRAMS simulations are analyzed to quantify the typical features embedded within the turrets. With the analyses carried out so far, we advance in quantifying certain key features of the overshooting turrets. They can be summarized as follows :

-the dominant ice hydrometeors are pristine ice (about 100% at the base of the turret, mostly outside the core of the turret) and snow (almost 90% at the core as we move further higher within the turret), and to some extent aggregates (about 60% at the base of the turret, but only around the core) -base of the turret denotes the 380 K isentrope ;

-the impact area of SOC at 380 K isentropic surface is about 24 km × 24 km, typically comparable with the 20 km × 20 km grid mesh size in the continental simulation ;

-in general, about 70% of the total ice injected above 380 K isentrope remains in a thin layer of 380 K à 385 K, that means rest of the 30% of the total H 2 O content go further up to the stratosphere ;

-net amount of only ice hydrometers injected by a single overshooting turret is ∼5 kt ;

-the total enhancement of H 2 O content akin to an overshooting plume ranges between 1.34 kt à 2 kt as the upper limit and 333 t à 750 t as the lower limit, within 380 K à 430 K isentropic levels.

Based on these conclusions, we can possibly advance in prescribing the nudging scheme of SOC in the lower stratosphere using the REF 1 simulation of Chapter 3, or similar simulation at a continental scale.

This work is currently in progress for publication.

151

Chapitre 5

Conclusions and Future work

Perspectives

Ce travail ne nous a pas encore permis d'arrêter les choix de paramètres à forcer dans le modèle pour une autre simulation continentale avec, cette fois-ci, la prise en compte les overshoots stratosphériques.

Research Summary

The main subject of this dissertation is the exchange of water between the troposphere and the stratosphere in tropical regions. Water vapor has a significant radiative impact in this region of the atmosphere, and also plays an important role in the chemical budget of the ozone layer. Among all the processes that play a role in the entry of water into the tropical stratosphere, we focus on overshoots, and in particular, on stratospheric overshooting convection (SOC), that is the convective protrusion reaching up to the lower stratosphere. They are relatively rare with respect to the total convective activity in the tropics, but their total number is not negligible. However, if we consider that the amount of water in the tropical tropopause is mainly constrained due to the coldest temperatures encountered by the air masses during their slow ascent to the stratosphere (drying by condensation followed by sedimentation), the stratospheric overshoots could partially limit this drying up in the total balance. So far, we do not know how to quantify the role of these SOCs at the global scale, mainly because their large-scale signature cannot be detected by satellites. The goal is, therefore, to advance in quantifying the role of overshoots at a large-scale. The approach we want to develop is the upscaling of their known-role at the cloud-scale. To do this, we perform several numerical simulations at two different spatial scales with the BRAMS mesoscale model, they can be summarized as follows.

-At a continental scale, which is the main canvas of this work, we carry out a complete simulation of a wet season with a horizontal grid-point resolution that requires deep convection to be parameterized, thus preventing any possibility of simulating SOCs which occur at smaller scales. The aim is to show that the BRAMS model is a relevant tool for simulating TTL realistically throughout a wet season, and thus to show that BRAMS can be used for the purpose of upscaling studies. The small balloonborne measurement campaign of the TRO-Pico project during a wet season, and during two purely convective seasons is the instrumental framework of this thesis, which validates the model's results during this period. We are particularly interested in the thermal structure of TTL and its temporal evolution, the variability of water vapor, deep convection through the study of cloud tops, and gravity waves. Indeed, all these parameters/processes can influence the abundance of stratospheric water vapor.

-At the local scale, the goal is to simulate several stratospheric overshoots to deduce a typical impact of overshoots. Then, this typical impact could be forced into a larger scale simulation whenever a satellite (including MHS) detects an overshoot in the region of study, and during the continental simulation period. Therefore, we need to extract from these fine-scale simulations, the typical quantities (especially ice mass budget above 380 K) that will help us determine how to force the impact of stratospheric overshoots in the continental simulation. The measurements of the TRO-Pico campaign are also used to validate these fine-scale simulations.

Conclusion

We can summarize the main results of the thesis as follows.

At the continental scale, the simulation of the 2012-2013 wet season of a large part of the southern hemisphere (Brazilian scale) without taking into account the SOCs, first we show a fairly good ability of the model to reproduce the variability of the thermal structure of the TTL observed by several series of radio soundings during the wet season (please recall Chapter 3). This is as true in the Bauru region as in other

Brazilian sites where the radiosoundings are launched regularly. The end of January/beginning of February 2013, is marked by an extremely cold period. It is linked to an episode of sudden stratospheric warming in the Arctic inducing cooling a little bit later in tropical regions. This trend is also highlighted by the simulation. These variabilities in the model, which are fairly comparable with the observations, are largely explained by the ECMWF operational analyses. The fact that these operational analyses, used for forcing the model at the boundaries of the simulation domain, correctly take into account these variabilities, with, however, a warm bias is observed for this period in the case of the BRAMS simulation. Another possible reason why BRAMS is warmer than observations is the absence of overshoots in the model due to the relatively coarse resolution. These could be a source of pseudo-adiabatic cooling.

The modeled water vapor variability in Bauru, the location of the TRO-Pico campaign, is also compared to the Pico-SDLA and FLASH-B hygrometer measurements throughout the series of measurements. An entirely comparable variability between observation and model is shown, with, however, less dry mixing ratios for the model than the observations. It is interesting to note that the coldest period corresponds to the driest period, both for BRAMS and observations, respectively. It is shown that the warm and wet bias of the model quantitatively follows the evolution of the vapor pressure with temperature. Thus, the driest and coldest period of the wet season would be largely driven by the dehydration of the air masses traveling through the coldest temperatures encountered during the ascent to the stratosphere.

Furthermore, the fact that the simulation without SOCs reproduces quite well the temporal variability of water vapor in the TTL confirms that overshoots are not the major cause of this variability, and is rather related to large-scale processes. Here again, the ECMWF operational analyses correctly follow the temporal variability of water vapor, even though ECMWF is also wetter than the observations at the pressure levels that we use to nudge the BRAMS model at the boundaries of the grid-points of simulation. We are also interested in the ability of the model to reproduce cloud tops with the correct position at the correct time. The results are compared to the products from the GOES-12 geostationary satellite measurements. It varies between 330 t à 1400 t for the REF simulation (please recall Chapter 4), and between 600 t à 2000 t for the NU21 simulation. Thus, the estimations vary by about 30% depending on the settings of the model. These are larger than other estimations for overshoot cases in West Africa with the same model.

Cross-correlation coefficients (∈

The present study, however, benefits from a measurement campaign to better assess the realism of the simulations compared to the African cases.

Outlooks

So far during this dissertation, we have not yet fixed the parameters to be used for nudging the hydration due to SOCs at a continental scale simulation, as the one discussed in Chapter 3. Nonetheless, this work allows defining a framework and a precious material for future studies of the upscaling. We benefit from a climatology of overshooting convection by MHS measurements during the wet season. It is known that about 51% of the overshoots of this climatology enter the stratosphere (SOC). We established that for one overshoot, 4 kt à 6 kt of ice is injected above the 380 K level across a surface area whose size is comparable to the size of the 20 km grid mesh we are using for the continental scale simulations. It remains to be determined how to inject this ice flux and this amount of ice into the BRAMS model. Our future studies at GSMA/CNRS will proceed further in this direction. As soon as the forcing scheme is developed and established, a simulation by nudging the SOCs will be implemented. The stratospheric water vapor balance will be performed for both simulations during the wet season -one without SOC, already done and one with SOC, to be accomplished. By this difference, we can then estimate the role of the SOCs at the continental scale on the stratospheric water budget.

Publications

This is a list of academic published or submitted or arising paper works.

-Behera, A. K., Rivière, E. D., Marécal, V., Rysman, J.-F., Chantal, C., Sèze, G., et al. (2018).

Modeling the TTL at continental scale for a wet season : An evaluation of the BRAMS mesoscale 100., 220., 364., 537., 744., 993., 1292., 1650., 2080., 2580., 3080., 3580., 4080., 4580., 5080., 5580., 6080., 6480., 6880., 7280., 7680., 8080., 8480., 8880., 9280., 9680., 10080., 10480., 10880., 11080., 11380., 11680., 11980., 12280., 12580., 12880., 13080., 13280., 13480., 13630., 13780., 13930., 14080., 14230., 14380., 14530., 14680., 14830., 14980., 15130., 15280., 15430., 15580., 15730., 15880., 16030., 16130., 16230., 16330., 16430., 16530., 16630., 16730., 16830., 16930., 17030., 17130., 17230., 17330., 17430., 17580., 17730., 17880., 18030., 18180., 18330., 18480., 18630., 18780., 18930., 19080., 19330., 19580., 19830., 20330., 20830., 21330., 21830., 22530., 23230., 23930., 24630., 25330., 26000., 27000., 28000., 29000., 30000., ! this one with 99 levels !100., 170., 240., 310., 380., 450., 520., 590., 660., 730., 800., !870., 950., 1026., 1108., 1196., 1292., 1395., 1507., 1628., 1758., !1899., 2050., 2215., 2392., 2583., 2790., 3013., 3254., 3515., !3796., 4099., 4427., 4782., 5164., 5577., 6024., 6506., 7026., !7588., 8195., 8851., 9301., 9851., 10401., 10951., 11501., 12051., !12601., 13151., 13701., 14251., 14401., 14497., 14595., 14692., !14791., 14890., 14990., 15090., 15191., 15293., 15395., 15499., !15602., 15707., 15812., 15918., 16025., 16132., 16240., 16349., !16459., 16569., 16680., 16792., 16904., 17017., 17131., 17246., !17362., 17478., 17595., 17713., 17832., 17951., 18101., 18303., !18644., 19204., 19780., 20373., 20984., 21614., 22262., 22930., !23618., 24327., 25057., 25808., 26583., 27380., 28201., 29048., !29919., ! this one with 105 levels !100., 220., 364., 537., 744., 993., 1292., 1650., 2080., 2580., !3080., 3580., 4080., 4580., 5080., 5580., 6080., 6480., 6880., !7280., 7680., 8080., 8480., 8880., 9280., 9680., 10080., 10480., !10780., 11080., 11380., 11680., 11980., 12280., 12580., 12880., !13180., 13480., 13780., 14080., 14263., 14448., 14636., 14826., !15019., 15412., 15612., 15815., 16021., 16229., 16440., 16654., !16870., 17090., 17312., 17537., 17765., 17996., 18230., 18600., !19195., 19809., 20443., 21097., 21772., 22469., 23188., 23930., !24696., 25486., 26302., 27143., 28012., 28908., 29833., 2,3,4,5,6,7,8,9,10,10,10,10, RODA_SFCE = 50000.,100.,100.,100., RODA_SFC0 = 100000.,100000.,100000.,100000., RODA_UPAE = 100000.,200.,200.,200., RODA_UPA0 = 200000.,2000.,2000.,2000., RODA_HGT = 3000.,3000.,3000.,3000., = 395., 395., 395., 390., 390., 390., 385., 385., 380 , 1000., 2000., 3000., 4000., 6000., 8000., 11000., 15000., 20000., 25000., TS = 25., 18.5, 12., 4.5, -11., -24., -37., -56.5, -56.5, -56.5, -56.5, RTS = 70.,70.,70.,70.,20.,20.,20.,20.,10.,10.,10., ! US = 2.5,2.5,2.5,2.5,2.5,2.5,2.5,2.5,2.5,2.5,2.5, US = 10.,10.,10.,10.,10.,10.,10.,10.,10.,10.,10., ! US = 0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0., ! US = 3.,3.,3.,3.,3.,3.,3.,3.,3.,3.,3., ! VS = 3.,3.,3.,3.,3.,3.,3.,3.,3.,3.,3., ! VS = 2.5,2.5,2.5,2.5,2.5,2.5,2.5,2.5,2.5,2.5,2.5, VS = 0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0 = 270, 272, 274, 276, 278, 280, 282, 284, 286, 288, 290, 292, 294, 296, 298, 300, 303, 306, 309, 312, 315, 318, 321, 324, 327, 330, 335, 340, 345, 350, 355, 360, 380, 400, 420, 440, 460, 480, 500, 520, 540, 570, 600, 630, 670, 700, 750, ! Wavelength in km to be retained to the ! RESPON % from the data to the upper air grids. SWVLNTH = 750.,300.,750., ! Wavelength for surface objective analysis RESPON = .90,.9,.9, ! Percentage of amplitude to be retained.

!
!

  list of the RAMSIN file and their description. . . . . . . . . . . . . . . . . . . . . . . 2.2 Options for the Bulk (micro) physics used in the simulations. . . . . . . . . . . . . . . . . . 2.3 Technical specifications used for the simulations. . . . . . . . . . . . . . . . . . . . . . . . . 2.4Table representing the list of apparatuses flew (center column) and the corresponding dates (left column) and tracers measured (right column), respectively, during the TRO-Pico campaign. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 List of radio sounding stations : upper-air radio soundings data with corresponding locations and the duration of measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Options used in the simulations (highlights of RAMSIN). . . . . . . . . . . . . . . . . . . . 3.2 Biases in CPT altitude (z) and temperature (T). . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Comparison of the wave parameters derived from hodograph analysis of the RS92 measurements and the simulation for January 28 and February 08, 2013. . . . . . . . . . . . . . . .4.1 Time of the SOC events and their altitudes range for the radar observations, the REF, and the NU21 simulation, respectively. Results are given in UTC time and altitudes in km. The altitude corresponds to the minimum altitude within a 1 km thick layer. . . . . . . . . . . . 4.2 Mean mass flux (g m -2 s -1 ) over the domain of grid3 for different types of hydrometeors corresponding to an overshooting turret at 380 K à 430 K layer. Results are shown from the REF and the NU21 simulation, respectively, and the corresponding UTC times are chosen from Table 4.1 at the peak time of overshoots. . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Percentage (%) of mass of individual ice hydrometeors within 380 K à 385 K isentropic levels, firstly with respect to the corresponding total mass (ρ 1 ), and secondly with respect to the total ice mass (ρ 2 ), within 380 K à 430 K isentropic levels. Results are given for total four different cases corresponding to the REF and the NU21 simulation, two cases from each simulation, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix xx

  . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 The Earth's energy budget -it accounts the balance between the incoming solar energy and the outgoing energy radiated back into the outer space. The energy budget shown is the 10 years averaged values in W m -2 measured by satellites. Courtesty : www.nasa.gov. . . . . . 1.3 Various constituents of atmospheric circulations : (a) the global view of the Earth's atmospheric circulation of convective air masses, highlighting the Hadley cell (30 • N -30 • S), mid-latitude (Ferrel) cell (30 • -60 • N-S), polar cell (>60 • N-S), intertropical convergence zone (ITCZ) at the equatorial belt (<15 • N-S), and trade winds and westerlies in an idealized conditions (e.g., the equinox). (b) the vertical cross-section of these circulations starting from the equator to the north-pole. Courtesy : https://www.seas.harvard.edu/climate/eli/ research/equable/hadley.html . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 A schematic diagram of ICTZ : the trade wind ITCZ (left-most column) and the monsoon ITCZ (two right columns). The monsoon regimes are divided into those types of the Australian/southeast Indian Ocean ITCZ during January (middle column) and the northwest Pacific Ocean during August (right-most column). The vertical wind shears between the low-and upper-level flow, respectively, are indicated in the lower panels. Courtesy : https://www.meteo.physik.uni-muenchen.de. . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 A schematic representation of the global Walker circulation in the southern hemisphere during the summer. Courtesy : http://www.elnino.noaa.gov/. . . . . . . . . . . . . . . . . .

  The largescale circulations are shown by broad arrows. The curly arrows indicate the meridional transport by eddy motions. (b) The zoomed version of (a), corresponds to the smaller range of altitude from about 13 km à 18 km, which came into light after two-decades of research work [Jensen et al., 2017a]. It mostly depicts the typical high-frequency atmospheric wave induced processes, freezing-drying mechanism, cirrus clouds formation and overshooting convection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.10 Vertical cross-section of an overshooting turret, where the turret top reaching up to 60 hPa -exctracted from Danielsen [1982]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 This is a schematic diagram of the horizontal cross-section of Arakawa-C gridding system denoting the distribution of different meteorological parameters (e.g., u, v, ρ) within the grid-points of a simulation. Courtesy : Patrick Marchesiello IRD [2005]. . . . . . . . . . . . 2.2 A schematic diagram of the framework of the Grell's convection scheme is shown for the updraft and downdraft motions depicting a typical convective system. Courtesy : https: //www.meted.ucar.edu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 A set of gamma distribution curves is shown for different integer values of shape parameter (ν) ∈ [1, 10] -extracted from Walko et al. [1995a]. The abscissa denotes the hydrometeor diameter (D), and ordinate denotes the number density (n(D)) following from the equation 2.19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Temperature evolution at Bauru during IOP2 phase of the field campaign. (a) denotes the radio sounding (RS92) measurements, (b) denotes the REF 0 simulation temperature profile with the CPT altitude (black line), and the white box highlights the coldest temperature obtained during IOP2. In (a), the cross-marks depict the availability of the measurements, missing data are linearly interpolated. There are 1 to 4 measurements per day are shown, while for the simulation, 24 data points corresponding to each hour of the day are shown. The coldest period obtained during the campaign corresponds to February 2, while in REF 0 it corresponds to January 26. More discussion can be found in Chapter 3.3 regarding the temperature trends. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Histogram of the temperatures within 12 km à 23 km altitude for the 3 rd week of November, 2012 at Bauru. (a) corresponds to the REF 0 simulation with 68 vertical levels having ∼300 m resolution at the TTL, (b) refers to a simulation with 76 vertical levels having ∼200 m resolution at the TTL, and (c) refers to a simulation with 105 vertical levels having ∼100 m resolution at the TTL. The bin-width is 0.25 • C. . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Histogram of the H 2 O mixing ratios within 12 km à 23 km altitude for the 3 rd week of November, 2012 at Bauru. (a) corresponds to the REF 0 simulation with 68 vertical levels having ∼300 m resolution at the TTL, (b) refers to a simulation with 76 vertical levels having ∼200 m resolution at the TTL, and (c) refers to a simulation with 105 vertical levels having ∼100 m resolution at the TTL. The bin-width is 0.01 ppmv. . . . . . . . . . . . . . . 3.4 Total rainfall accumulation (mm) during the 3 rd week of December 2012, for the domain of simulation. (a) corresponds to the TRMM observation, while (b) to (h) refer to the modeled precipitation corresponding to the week of observation. (b) has ν = 2.0, CCN = 0.5 × 10 9 and zlev = 68 (settings of REF 0 simulation), (c) has ν = 2.0, CCN = 0.5 × 10 9 and zlev = 105, (d) has ν = 2.1, CCN = 0.5 × 10 9 and zlev = 105, (e) has ν = 1.9, CCN=0.5 × 10 9 and zlev = 105, (f) has ν = 2.1, CCN = 20 × 10 9 and zlev = 105, (g) has ν = 2.1, CCN = 20 × 10 10 and zlev = 105 (settings of REF 1 simulation), and (h) has ν = 2.1, CCN = 20 × 10 11 and zlev = 105. 'zlev' denotes the total number of vertical grid-points of the simulation starting from surface to 30 km altitude. . . . . . . . . . . . . . . . . . . . . . . . xxii 3.5 (a) Temperature profile from radio soundings (RS92 SGP), obtained at Bauru (22.31 • S, 49.05 • W) during the IOP2 of the TRO-Pico campaign. The time of each sounding is indicated by '+'. The black line represents the CPT altitude. The white box shows the coldest CPT, viz., ∼ -88 • C observed at ∼70 hPa on February 2, 2013. (b) Concurrent temperature profile from the BRAMS analyses at the same location, based on hourly data. The white box corresponds to the coldest CPT, viz., ∼ -85 • C observed at ∼85 hPa on January 29, 2013. (c) Concurrent temperature profile near Bauru from the ECMWF analyses, based on four data points per day. The white box corresponds to the coldest CPT, viz., ∼ -84 • C observed at ∼70 hPa on February 1, 2013. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Cold-point tropopause (CPT) depicting its altitude (solid lines ; left y-axis) and temperature (dotted lines ; right y-axis) as a function of time (different periods) from radiosonde measurements (blue) and the concurrent CPT evolution generated by BRAMS (red) at different stations over Brazil : (a) SBAT during Nov 2012, (b) SBFI during Dec 2012, (c) SBCY during Nov-Dec 2012, (d) SBGL during Mar 2013, (e) SBBR during Jan-Mar 2013, and (f) SBCT during Jan-Mar 2013. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 (a) Water vapor (WV) mixing ratio, measured by the Pico-SDLA (solid lines) and FLASH-B (dotted lines) H 2 O spectrometers during the TRO-Pico campaign at Bauru. The minimum and maximum H 2 O mixing ratios of corresponding pressure levels during the FMOP in the Bauru region are also shown (dots) from MLS : version 4.2 measurements for a domain of 24.00 • S to 19.00 • S and 55.50 • W to 43.50 • W ; (b) WV profiles from the BRAMS simulation at Bauru. Profiles for 12 :00 UTC to 23 :59 UTC, are shown starting from November 20, 2012 to March 30, 2013 to be better comparable with the broad variability of WV profiles akin to deep convection from the hygrometer measurements. . . . . . . . . . . . . . . . . . . 3.8 (a) Cross-correlation coefficients between the cloud tops measured by the GOES-12 satellite and calculated by the BRAMS model for the full domain of simulation during the FMOP. The coefficients are calculated every three hours starting from November 01 00 :00 UTC, 2012 to March 31 21 :00 UTC, 2013. (b) Mean value of the percentage of cloud tops >10 km, calculated on a daily basis, for BRAMS (blue line) and GOES-12. The red line represents the high clouds in GOES-12 (including all types of optically thick clouds), while the black dotted line corresponds to only very thick convective clouds. . . . . . . . . . . . . . . . . . . 3.9 Cloud tops : (a) and (c) measured by the GOES-12 satellite on January 12 09 :15 UTC, 2013 and March 4 15 :15 UTC, 2013, respectively. (b) and (d) from the BRAMS model during the same time period, as in (a) and (c), respectively. The locations of RS stations from the upper-air database (red dots) and Bauru (green dot) are only shown in (d). . . . . . . . . . 3.10 Histograms of the cloud top altitudes from BRAMS at the locations of overshooting cells (>14 km) detected by MHS from November 1, 2012 to March 31, 2013 (FMOP). (a) cloud top altitude distribution exactly at the positions of overshooting cells ; (b) distribution of the highest cloud tops present within the ∼50 km radius of overshooting cells. . . . . . . . . 3.11 Perturbed wind profiles at Bauru from the RS92 measurements during the TRO-Pico campaign and from the BRAMS model are shown for the period January 23 to February 12, 2013. (a) RS92 u profile, (b) BRAMS u profile, (c) RS92 v profile, and (d) BRAMS v profile. The blanks in the RS92 measurements correspond to the absence of data. Clearly visible gravity wave patterns are highlighted with dotted lines in (a) and (d). . . . . . . . . 3.12 S1 : Mean H 2 O mixing ratio at 82.5 hPa pressure level retrieved from Aura MLS : version 4.2. The two time series denote the lower stratospheric water vapor variability in the neighborhood of Bauru (blue) and Guam (red), respectively. . . . . . . . . . . . . . . . . . . 3.13 S2 : Vertical profiles (solid lines) of saturation temperatures (T sat ) corresponding to five different WV mixing ratios -calculated from equation 3.2. The colors indicate the different concentration of WV. The * symbols depict T sat s in • C and corresponding pressure levels in hPa, obtained from the H 2 O mixing ratio at the hygropause measured by Pico-SDLA (blue), FLASH-B (red), and simulated by the BRAMS model (green), respectively. The × symbols represent the corresponding ambient temperatures of the hygropause. . . . . . . . . 3.14 S3 : Hodographs of wind perturbations (u , v ) due to inertia-gravity waves deduced from RS92 soundings (upper panel) during the TRO-Pico campaign and the BRAMS simulations (lower panel) on January 28 and February 08, 2013, respectively, at Bauru. Note that there is a time difference of few hours between the RS91 and the BRAMS hodographs due to the sporadic distribution of the deep convection over the continent, which provides well known sources for these wave patterns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii 3.15 A schematic diagram representing the highest cloud tops obtained from the numerical simulation on a particular day, including the positions of the overshooting cells («+» signs) detected by satellite-borne MHS radiometer. The results are shown for November 16, 2012, covering the full domain of the simulation. The red «*» are some prominent cities in South America, while the black «*» denotes the location of Bauru (22.31 • S, 49.05 • W). . . . . . . 3.16 GOES-12 observation of cloud tops on November 1 00 :15 UTC, 2012. (a) is the quick viewer of the satellite-borne observation, color scale is in hPa ; (b) refers to the presentation of CTTH_Height product which considers mostly high level clouds (optically thick, also optically thin cirrus during the twilight times), color scale ranges from 0 km à 18 km ; (c) represents the same cloud top as in (b), but transformed to show only our domain of interest, color scale ranges from 0 km à 18 km ; (d) shows the CTTH_Effect product corresponding to (c), where the effective emissivity of cloud top is in a scale of 0 -100. . . . . . . . . . . . 3.17 The vertical profile of ice+cloud mixing ratio profile on January 12 09 :00 UTC, 2013, at a particular grid-point of the REF 1 simulation. (a) is the mixing ratio (g kg -1 ) profile, (b) is its first derivative, and (c) is its second derivative. . . . . . . . . . . . . . . . . . . . . . . . 3.18 Cloud tops retrieved from satellite-borne observations and concurrent modeled cloud tops calculated using different criteria for January 12 09 :00 UTC, 2013. (a) is the SAFNWC product using only the CTTH_Height parameter ; (b) is the modeled cloud top using the aforementioned three step criteria for ice+liquid mixing ratio -recall Chapter 3.3 ; (c) is the modeled cloud tops, where they are determined using the vertical continuity of the ice+cloud mixing ratio given that the corresponding grid-point must possess a mixing ratio >0.3 g kg -1 within its cloudy column ; (d) is the SAFNWC product representing both the CTTH_Effect and CTTH_Height values, where the CTTH_Effect=100 ; (e) is the modeled cloud top, determined using the vertical continuity of mixing ratio as (c), but each horizontal gridpoint must have a mixing ratio >0.1 g kg -1 at certain altitude corresponding to its cloudy column ; (f) is the modeled cloud top chosen as (c) or (e), but in this case all horizontal gridpoints are considered irrespective of the maximum or minimum mixing ratio value within the cloudy column. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.19 The seasonal average of the high clouds (>10.0 km) occurrence in BRAMS (black) -cloud tops determined using the criteria as in Chapter 3.3, in SAFNWC products for CTTH_Height (dotted red) -any kind of optically thick cloud with optically thin cirrus clouds mostly during the twilight times, and for CTTH_Height+CTTH_Effect (blue) -mostly the optically thick convective clouds, as well as optically thick cirrus clouds. They are averaged upon the eight UTC hours considered on daily basis during the FMOP. . . . . . . . . . . . . . . . . . 3.20 A scatter plot of the percentage of high clouds detected by GOES-12 against the modeled

  • and 0.5 • , respectively. Courtesy : http:// www.cursosgis.com . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.22 The histogram of cross-correlation coefficients calculated every 3 h, starting from November 1 00 :00 UTC, 2012 to November 14 21 :00 UTC, 2012, for the two types of grid-point resolution or the cell size used in data extraction from GOES-12 satellite observations. (a) corresponds to the first step of data extraction having 0.18 • cell size. (b) corresponds to the second step with data extraction of 0.5 • cell size. The 8 types of color bars represent different hours of the day, viz., 00 :00, 03 :00, 06 :00, 09 :00, 12 :00, 15 :00, 18 :00 and 21 :00 UTC of a day, respectively. Missing columns highlights the absence of GOES measurements. 3.23 Water vapor measurements at 82.5 hPa for the full globe in the tropical belt retrieved from the Aura MLS : version 4.2 : (a) January 13 to 15, 2013 and (b) January 31 to February 02, 2013. The belt chosen here ranges from 30 • N -30 • S, while the color bar represents the H 2 O mixing ratio on a scale of 1 -5 ppmv. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.24 FFT of the perturbed wind profiles from BRAMS (the REF 1 simulation) corresponding to the IOP2 (location -Bauru ; latitude : 22.31 • S, longitude : 49.05 • W, January 23 to February 12, 2013). (a) shows the FFT of u profiles, and (b) shows the same for v profiles from the BRAMS simulation. The color bar corresponds to the power of the obtained Fourier spectrum.112 xxiv 4.1 Time sequence of the observational case of overshooting events occurred on March 13, 2012, seen by the S-Band radar at IPMet, Bauru. The echo top (in km) products are shown at 1201 LT (a), 12 :53 LT (b), 13 :46 LT (c), 14 :08 LT (d), 14 :38 LT (e), 16 :31 LT (f). . . . 4.2 Extracted from Figure 4 of Khaykin et al. [2016]. Left panel refers to the descent H 2 O mixing ratio profile from Pico-SDLA (a), and right panel corresponds to the same but retrieved from FLASH-B (c). The corresponding backscattering ratio profile at 532 nm obtained from COBALD is also given in the right panel. Here, the ordinate is chosen to be the potential temperature, while the corresponding altitude in km is also given on the right-hand side. Horizontal dotted lines highlight the potential temperature level corresponding to 386 K and 404 K, respectively, where a local maximum of H 2 O are observed. In the right panel, the relative humidity with respect to ice, computed from the FLASH-B H 2 O profile and temperature profile, is also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 (Figure 7 of Khaykin et al. [2016]) : Echo top maps (same color scale as in Figure 4.1) recorded by S-Band radar at IPMet, Bauru on March 13, 2012. The overshooting cells linked by trajectories with hydrated layers at 386 K and 404 K potential temperatures are highlighted by rectangles in (a, b). Solid lines indicate the trajectories of balloons carrying FLASH-B and Pico-SDLA stratospheric hygrometers with indication of time (UTC) when 386 K and 404 K levels were sampled. Dots depict the ensembles of forward trajectories initialized within the rectangle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Three different grids of the BRAMS simulations for the case of March 13, 2012. Grid 1 (PG) is shown in contour, representing the topography in the meter. Grid 2 is shown in shaded colors, while the third grid (the smallest) refers to the red rectangle, the red color being independent of the orography to better identify the grid position. . . . . . . . . . . . . . . . 4.5 Levels of vertical grid-points (left panel) and resolution (right panel) for the REF (and NU21) and HVR simulation. respectively. The red color stands for the HVR, while the black color refers to the REF/NU21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 BRAMS model cloud tops for the simulation REF (a, b), NU21 (c, d) , and HVR (e, f) at 14 :00 UTC (a, c, e) and 15 :00 UTC (b, d, f), respectively. Corresponding S-Band radar echo top at 15 :00 UTC is already shown in Figure 4.1a. . . . . . . . . . . . . . . . . . . . . 4.7 REF simulation results. Cloud top at 16 :15 UTC (a), and vertical cross-sections of condensed water within grid 3 at 22.2 • S at 16 :07 UTC (b), 16 :15 UTC (c) and 16 :22 UTC(d). Ice+liquid concentration color contour varies from 0 g kg -1 à 4 g kg -1 . . . . . . . . . . . . . . 4.8 REF simulation results. Cloud top at 16 :52 UTC (a), and vertical cross-sections of condensed water within grid 3 at 22.1 • S at 16 :45 UTC (b), 16 :52 UTC (c) and 17 :00 UTC (d). Ice+liquid concentration color contour varies from 0 g kg -1 à 4 g kg -1 . . . . . . . . . . . . . . 4.9 NU21 simulation results. Cloud top at 16 :15 UTC (a), and vertical cross-sections of condensed water within grid 3 at 22.3 • S at 16 :07 UTC (b), 16 :15 UTC (c) and 16 :22 UT(d). Ice+liquid concentration color contour varies from 0 g kg -1 à 4 g kg -1 . . . . . . . . . . . . . . 4.10 NU21 simulation results. Cloud top at 18 :00 UTC (a), and vertical cross-sections of condensed water within grid 3 at 22.3 • S at 1752 UTC (b), 18 :00 UTC (c) and 18 :07 UT(d). Ice+liquid concentration color contour varies from 0 g kg -1 à 4 g kg -1 . . . . . . . . . . . . . . 4.11 HVR simulation results. Cloud top at 15 :52 UTC (a), and vertical cross section of condensed water within grid 3 at 22.3 • S at 15 :45 UTC (b), 15 :52 UTC (c) and 16 :00 UTC (d).

Figure 1

 1 Figure1.1 -A schematic diagram of the generalized distribution of the temperature and pressure, representing different layers present within the Earth's atmosphere. The layers are defined according to the change in their ambient thermodynamical composition which varies with altitude. The lowermost layer is known as the troposphere, which determines mostly the weather conditions, then the upper layer is stratosphere. The composition of this (ozone) layer is very important to sustain life on the Earth. Then further high in altitude, there exist mesosphere, thermosphere, and exosphere. There are three relatively warmer layers, i.e., near the surface, at 50 km à 60 km, and at ∼120 km altitude. They are separated by relatively two colder layers, i.e., at 10 km à 30 km, and at 80 km à 100 km altitude. These altitudes can differ slightly from the equator to the poles. Courtesy : https://www.britannica.com/science/atmosphere.

Figure 1 . 2 -

 12 Figure 1.2 -The Earth's energy budget -it accounts the balance between the incoming solar energy and the outgoing energy radiated back into the outer space. The energy budget shown is the 10 years averaged values in W m -2 measured by satellites. Courtesty : www.nasa.gov.

Figure 1

 1 Figure 1.3 -Various constituents of atmospheric circulations : (a) the global view of the Earth's atmospheric circulation of convective air masses, highlighting the Hadley cell (30 • N -30 • S), mid-latitude (Ferrel) cell (30 • -60 • N-S), polar cell (>60 • N-S), intertropical convergence zone (ITCZ) at the equatorial belt (<15 • N-S), and trade winds and westerlies in an idealized conditions (e.g., the equinox). (b) the vertical cross-section of these circulations starting from the equator to the north-pole. Courtesy : https://www.seas.harvard.edu/climate/eli/research/equable/hadley.html

Figure 1

 1 Figure 1.4 -A schematic diagram of ICTZ : the trade wind ITCZ (left-most column) and the monsoon ITCZ (two right columns). The monsoon regimes are divided into those types of the Australian/southeast Indian Ocean ITCZ during January (middle column) and the northwest Pacific Ocean during August (right-most column). The vertical wind shears between the low-and upper-level flow, respectively, are indicated in the lower panels. Courtesy : https://www.meteo.physik.uni-muenchen.de.

Figure 1

 1 Figure 1.5 -A schematic representation of the global Walker circulation in the southern hemisphere during the summer. Courtesy : http://www.elnino.noaa.gov/.

Figure 1 .

 1 Figure 1.5 represents the global Walker circulation, which is one of the dominant circulations in the tropics after the Hadley cell. The Walker circulation results from the zonal gradient in the surface temperature corresponding to the differential thermal structure of the Oceans and land surface due to the differential radiative heating [McGregor et al., 2014]. The Walker circulation highlights the air mass aloft

Figure 1

 1 Figure 1.6 -The ozone hole time evolution over 30 years of satellite observations. The color scale is in Dobson units, varies from navy-blue to red at a scale of 0 -500. The histogram below indicates the number of contributions to the ozone measurements for each satellite with time starting from 1980s to 2010s. Courtesty : https://www.nasa.gov.

( 2 .

 2 8 • N -January 1964 to August 1967), Gan/Maldive island (0.7 • S, September 1967 to December 1975), and Singapore (1.4 • N, January 1976 to February 1990), where the u profiles are below 31 km altitude. For higher altitude, rocketsonde data retrieved from Kwajalein (8.7 • N) and Ascension Island (8.0 • S) are

Figure 1 .

 1 Figure 1.7b, the typical dynamics of the northern hemispheric QBO is shown. Furthermore, mesospheric QBO (MQBO) is also shown for >80 km altitude. The planetary-scale waves are shown in the red arrows, where the tropical waves are shown with orange arrows. Below the tropopause, convective activities are shown producing large-scale atmospheric waves, e.g., inertia-gravity waves, Kelvin waves and Rossby waves. The easterly anomalies are shown in light-blue color, whereas the westerly anomalies are shown with lightorange color.

Figure 1 . 7 -

 17 Figure 1.7 -The structure of the QBO -extracted from Baldwin et al. [2001]. (a) The time evolution of the vertical cross-section of the monthly-mean zonal (u) wind (m s -1 ) corresponding to years of 1964 -1990, after the removal of the seasonal cycle. The red color represents the positive westerly winds, and the counterpart is shown with blue color. (b) The dynamical overview of the QBO during the winter in the northern hemisphere. The orange arrows depict the propagation of various atmospheric waves at the tropics, driving the QBO upward. The contour (black) lines refer the difference in the zonal winds between easterly and westerly phases of the QBO. Here, the QBO phase is defined at 40 hPa equatorial wind.

Figure 1

 1 Figure 1.8 -(a)The meridional supply of air mass between the troposphere and the stratosphere -the Brewer-Dobson circulation (BDC). The dotted lines refer to the isotherms over the globe, and the solid lines corresponds to the circulation towards the summer and winter poles, respectively, from the equatorial belt, envisaged by keeping track of H 2 O budget[START_REF] Brewer | Evidence for a world circulation provided by the measurements of helium and water vapour distribution in the stratosphere[END_REF] and by keeping track of O 3 budget by[START_REF] Dobson | Origin and distribution of the polyatomic molecules in the atmosphere[END_REF]. Courtesy : http://birner.atmos.colostate.edu/bdc.html. (b) The recent depiction of the BDC playing role in sending H 2 O, H 2 and CH 4 , i.e., the greenhouse gases to the lower stratosphereextracted from[START_REF] Ravishankara | Water vapor in the lower stratosphere[END_REF]. The left inlet shows the H 2 O mixing ratio variation with altitude at midlatitude, which reveals the enhancement up to 7 ppmv in the lower stratosphere (∼70 hPa).

Figure 1

 1 Figure 1.9 -(a) A version of TTL envisaged by Holton et al. [1995], with the dynamics controlling the transport mechanism occurring between 1000 hPa à 10 hPa pressure levels. The TTL is denoted by the thick line, other lines correspond to the isentropic surfaces. The large-scale circulations are shown by broad arrows. The curly arrows indicate the meridional transport by eddy motions. (b)The zoomed version of (a), corresponds to the smaller range of altitude from about 13 km à 18 km, which came into light after twodecades of research work[Jensen et al., 2017a]. It mostly depicts the typical high-frequency atmospheric wave induced processes, freezing-drying mechanism, cirrus clouds formation and overshooting convection.

Figure 1 .

 1 Figure1.10 -Vertical cross-section of an overshooting turret, where the turret top reaching up to 60 hPa -exctracted from[START_REF] Danielsen | A dehydration mechanism for the stratosphere[END_REF].

  field campaigns are quite resourceful providing large meteorological datasets during a long period of time. The TRO-Pico (see Chapter 2.2 for more details) field campaign project was carried out in the context of upscaling the impact of overshooting convection on the water vapor budget of the TTL -a seasonal study of the tropopause from CNRS. The main objective was to address the uncertainties in the TTL composition, stratospheric ozone, as well as water vapor concentration. All the measurements were short duration balloon-borne measurements, carried out in the State of São Paulo, Brazil during a convective season corresponding to March 2012 and November to March 2013. Future objectives of this campaign are to upscale the impact of deep convection in the water vapor budget of the TTL using these meteorological datasets by the incorporation of numerical simulations -main frame of this dissertation. With a similar aim like the TRO-Pico campaign, the ATTREX field campaign took place in the tropical western Pacific Ocean starting from 2012-2017, which was mostly a 5-year long aircraft-borne science program from NASA. The measurements were carried out by the long-range NASA Global Hawk (GH) unmanned aircraft system (UAS) in order to provide the meteorological datasets corresponding to the physical processes occurring within the TTL.

  validation toolsCe chapitre passe en revue les outils essentiels utilisés pendant cette thèse. En particulier, je décris le modèle méso-échelle BRAMS (Brazilian Regional Atmospheric Modeling System), la version dédiée aux régions tropicales du modèle américain RAMS. Je décris en particulier les réglages et les paramétrisations en lien à ce travail (convection, microphysique, module radiatif). Dans ce chapitre sont décrites également les principales mesures utilisées pour valider le modèle. Dans un premier temps, la campagne du projet TRO-Pico est décrite. Il s'agit d'une campagne sous petit ballons stratosphériques ouverts (500 m 3 à 1500 m 3 ) ou ballons légers dilatables (1.2 kg) pendant toute une saison humide, comprenant une période d'observation intensive au maximum de la saison concevtive. TRO-Pico vise à mieux comprendre et quantifier le rôle des overshoots stratosphériques sur la vapeur d'eau stratosphérique, à petite échelle, pour en déduire un impact à plus grande échelle. Les instruments de la campagne que nous décrivons en priorités sont l'hygromètre laser Pico-SDLA et l'hygromètre Lyman-α FLASH-B. Nous décrivons également la série de radiosondages RS92 pendant la période intensive de TRO-Pico. Nous utilisons également le radar Bande S de Bauru permettant de déduire les sommets de nuages convectifs. Il est brièvement décrit. Enfin, nous décrivons les mesures satellitales qui sont utilisées pour valider nos simulations : les produits de sommets de nuage issus du satellite géostationnaire GOES-12, les mesures de précipitations par TRMM, la climatologie des overshoots (pas nécessairement stratosphériques) par l'instrument MHS, et les mesures de vapeur d'eau par MLS/AURA. La précision des instruments y est aussi rappelée.

Figure 2 .

 2 Figure 2.1 -This is a schematic diagram of the horizontal cross-section of Arakawa-C gridding system denoting the distribution of different meteorological parameters (e.g., u, v, ρ) within the grid-points of a simulation. Courtesy : Patrick Marchesiello IRD [2005].

Figure 2 . 2 -

 22 Figure 2.2 -A schematic diagram of the framework of the Grell's convection scheme is shown for the updraft and downdraft motions depicting a typical convective system. Courtesy : https://www.meted.ucar. edu

  .15) where A (λ) and A (λ) are the cloud-work function representative based on the calculation of thermodynamic fields, but modified by a forcing term and by a cloud with arbitrary mass unit (m b (λ)dt), respectively.

equation 2 .

 2 19, first two variables (I) must be specified as an input, and the third one (II) is diagnosed from the equation of mass-moment. A high level of variables embedded within the parameterization are prognostic variables. Varieties of microphysical set ups can be incorporated as per the objective of a numerical experiment.

Figure 2 .

 2 Figure 2.3 -A set of gamma distribution curves is shown for different integer values of shape parameter (ν) ∈ [1, 10] -extracted from Walko et al. [1995a]. The abscissa denotes the hydrometeor diameter (D), and ordinate denotes the number density (n(D)) following from the equation 2.19.

  surface types (e.g., the surface of vegetation, deep green forest, or urbanization -no cultivation land), the availability or unavailability of adequate soil water content, canopy temperature fields and moisture fields with the transpiration process of plants can influence the lowest level of the atmospheric model. This lowest level works as the reference level, where the atmospheric boundary layer values of temperature, H 2 O vapor pressure, wind velocity and CO 2 partial pressure are fed into the atmospheric model, serving as the upper boundary conditions to the surface model. The surface layer, which is between the surface and the reference level to the atmospheric model, is incorporated as part of the SiB model. The surface latent heat flux (controlled by moisture availability and wind speed) and sensible heat flux

  .23)where R iB is bulk Richardson number and is determined by the vertical wind shear and the local lapse rate of temperature. Along with several other parameterizations, viz., soil water movement, plant water consumption, solar radiation reflection, and absorption, etc., this land surface scheme can simulate in a more realistic way.For our study as an input parameter to the SiB 2.5 sub-model soil map, 1 km vegetation map (LEAF data, Land Ecosystem-Atmosphere Feedback model[START_REF] Walko | Coupled atmosphere-biophysics-hydrology models for environmental modeling[END_REF]) for South American biomes, and NDVI (Normalized Difference Vegetation Index) map retrieved from MODIS/TERRA satellite images as surface characteristics are used. This can be parameterized for latent heat flux, sensible resultant (heat, moisture, momentum) fluxes, surface albedo, outgoing long-wave radiation (OLR), and photosynthesis together within CO 2 flux. The inclusion of vegetation parameterization in the model enhances the quality of the modeled air temperatures, the representation of the vertical structure of boundary-layer interaction and the calculation of the surface fluxes. The vegetation fraction is calculated by NDVI data, and LEAF calculates the turbulent fluxes due to the vegetation fractions.

(

  PG) of the BRAMS mesoscale model (version -4.2) having a horizontal resolution of 20 km × 20 km, but with a different number of vertical levels akin to the vertical resolution near the TTL. The simulations corresponding to Chapter 3 are carried out for the wet season of November 1, 2012 to March 31, 2013(FMOP) for South America (∼ Brazilian scale) using single grid (PG), while the simulations in Chapter 4 only cover several other nested-grid simulations, up to 3 rd -grid with a horizontal grid-point resolution down to 20 000 m à 800 m out of the FMOP duration. These simulations in Chapter 4 refer to a particular case study of overshooting convection observed on March 13, 2012, in the frame of the TRO-Pico campaign -inside the IOP1 duration. The nested-grid simulations therein are cloud-resolving simulations, so that they could represent the typical features of the overshooting turrets properly. The simulations include all these aforementioned modules in previous sections. The time resolution of the long duration simulations are of 1 h (analysis files), while for the case study of March 13, 2012, the simulation outputs have a time resolution of 7.5 min.

  consists of a series of balloonborne measurements, carried out during the convective/wet season of the years 2012 and 2013 in the state of São Paulo, Brazil. The TRO-pico field campaign is a five-year science project funded by the French-ANR (L'Agence Nationale de la Recherche) to study the composition and variability of the TTL during a wet season and mostly focused on the water vapor variability in the lower stratosphere. The concerned scientific team consists of four French institutes, namely, the Groupe de Spectrométrie Moléculaire et Atmosphérique (GSMA) in Reims, the Laboratoire Atmosphères, Milieux et Observations Saptiales (LATMOS) in Guyancourt, the Division Technique de l'Institut National des Sciences de l'Univers (DT-INSU) in Meudon, and the Laboratoire d'Aérologie (LA) in Toulouse. This field campaign groups are supported by other three French partners, viz., the Laboratoire de Météorologie Dynamique (LMD) at the École Polytechnique in Palaiseau, the Laboratoire de Physique et Chimie de l'Environnement et de l'Espace (LPC2E) in Orleans, and the Centre National de Recherches Météorologiques -Groupe d'Etudes de l'Atmosphère Météorologique (CNRM-GAME) in Toulouse. Importantly, the whole campaign was accompanied and supported by one Brazilian partner, i.e., the Instituto de Pesquisas Meteorológicas (IPMet) of the State University of São Paulo (UNESP), providing very necessary manpower to carry out the measurements.

A

  Radar's (RAdio Detection And Ranging) working principle is based on a two-way communication using electromagnetic signal transmission, where it emits the electromagnetic radiation and detects the echo signal returned from the reflecting objects. The nature of echo signal provides the information about the target objects. For our study, we retrieve radar measurements of cloud echo tops from a Doppler S-Band Radars, situated at Instituto de Pesquisas Meteorológicas (IPMet)/Universidad e Estadual Paulista (UNESP), Bauru. The IPMet radar has a spatial range of 450 km surveillance with a 2 • beam width. It is aligned in the east-west direction. Its spatial resolution is 250 m radially and 1 • in azimuth, while temporal resolution to perform volume-scan is 7.5 min[START_REF] Held | The structure of severe storms and associated lightning in the state of sao paulo, brazil[END_REF]. When operated in a volume-scan mode, its spatial range is limited to 240 km. The S-Band operates within the frequency band of 2 GHz à 4 GHz, which is an accurate range of frequency for long-range weather radars to make a precise estimation of rainfall rate, depicting its sensitivity towards liquid hydrometeors. The IPMet radar records reflectivity, spectral width and radial velocity at 16 different elevations varying within 0.3 • à 45 • . For our study, one

  Measuring Mission (TRMM) satellite provides the measurement of rainfall and energy (latent heat of condensation) exchange at the tropics and sub-tropics for the full globe having a circular orbit at altitude of 403 km (from 1997 -2001, it was 350 km) with a 35 • angle of inclination to the equator (non-sun-synchronous). This satellite mission was launched to study the rainfall for weather and climate research [e.g.,[START_REF] Alcala | Observations of deep convection in the tropics using the tropical rainfall measuring mission (TRMM) precipitation radar[END_REF][START_REF] Houze | From hot towers to TRMM : Joanne simpson and advances in tropical convection research[END_REF][START_REF] Zipser | Where are the most intense thunderstorms on earth[END_REF], as a joint project between the National Aeronautics and Space Administration (NASA) of the United States and the National Space Development Agency (NASDA) of Japan, which was operational during 1997 -2015 (more information can be found about TRMM at https://pmm.nasa.gov/trmm). This satellite used five instruments, viz., TRMM Microwave Imager (TMI), the precipitation radar (PR), the Visible and Infrared Radiometer System (VIRS), Clouds and Earth's Radiant Energy System (CERES), and the Lightning Imaging System (LIS)[START_REF] Kummerow | The tropical rainfall measuring mission (TRMM) sensor package[END_REF] during the 17 years of mission period. The data product contains a horizontal resolution of 0.04 • . For our study, global rainfall accumulation data are collected for the FMOP over a large part of South America from the TRMM-based real-time Multi-satellite Precipitation Analysis (TMPA-RT/3B42) having a time resolution of 3 h.

  is a high-frequency across-track scanning microwave radiometer onboard 16, 17, 18, 19 and EUMETSAT MetOp-A, B, C satellites, providing a solid platform to study the deep convection with a horizontal resolution of 0.04 • . This instrument is the core of atmospheric vertical sounder suit used by Initial Joint Polar System (IJPS), and operates in five channels in the 89 GHz à 190 GHz spectral range having the unique ability to penetrate clouds.We take advantage of the sensitivity of these water vapor channels towards frozen hydrometeors to detect atmospheric convection, and to discriminate overshooting convection penetrating into the TTL (COVconvective overshooting) or sometimes to the stratosphere (SOC -stratospheric overshooting convection) from deep convection (DC) using a climatology developed and assessed by[START_REF] Funatsu | Potential of advanced microwave sounding unit to identify precipitating systems and associated upper-level features in the mediterranean region : Case studies[END_REF],Hong et al.

3

 3 GHzin comparison to 183.3 ± 7 GHz of AMSU. Near to the convective cores, ΔT B of the water vapor channels tends to be close to zero, albeit the T B from the channels with frequencies farther than the center, i.e., 183.3 ± δ GHz (δ > 0), remains lower than those closer to 183.3 GHz. Henceforth, the criterion to detect the COV breaks down into as follows : T B1 -T B3 > T B1 -T B2 > T B2 -T B3 > T 1 , where the subscripts 1, 2 et 3 refer to 183.3 ± 1 GHz , 183.3 ± 3 GHz, 190.3 GHz, respectively. T 1 is a threshold in K depending on the view angle θ of MHS : For θ ≤ 30 • , T 1 = 0 K, and for θ > 30 • , T 1 = 7 K. It is also important to recall that ∼50% of the MHS detected COVs are SOCs[START_REF] Rysman | Monitoring deep convection and convective overshooting from 60 • S to 60 • N using MHS : A Cloudsat/CALIPSO-based assessment[END_REF]. Additional comments are given in Chapter 3.5.1.

  The cloud top products, i.e, a cloud mask, cloud type classification and cloud top pressure products, gathered for the FMOP duration from the ICARE data and services center (see http://www.icare.univ-lille1. fr). The data retrieved has a spatial resolution of 4 km × 4 km and time resolution of 15 min. We make use of the CTTH parameters from the GEOCLD-SAFNWC (version -1.3) products, viz., CTTH_Height gives the altitude of optically thick cloud tops, and also optically thin cirrus clouds during twilight time in meters, and CTTH_Effect gives the emissivity of the cloud tops (CTTH_Effect = 100 gives the optically thick convective clouds only)[START_REF] Derrien | Algorithm theoretical basis document for cloud products (cma-pge01 v3. 2[END_REF]. Additional comments on these parameters are in Chapter 3.5.2.

  Aura microwave limb sounder (MLS) water vapor measurements are collected from earth observing system (EOS), NASA Goddard space flight center data and information services center (GSFC-DISC) (find https://mls.jpl.nasa.gov) on daily basis during the FMOP. The data used here corresponds to the Version : 4.2× Level 2, after incorporating all the quality flags, viz., quality threshold, convergence threshold, precision, and status. This version water measurement is derived from 190 GHz CorePlusR2 retrieval with a vertical resolution of 12 levels per decade change in pressure (LPD) for 1000 hPa à 1 hPa, and horizontal resolution of 1.5 • along the orbit track[START_REF] Livesey | Version 4.2x level 2 data quality and description document[END_REF]. They are used for supporting the water vapor measurements from the TRO-Pico campaign. Thus, the wide range variability of water vapor around Bauru (24.0 • S to 19.0 • S, 55.5 • W to 42.5 • W) for the FMOP is studied, and shown in Chapter 3.2.

2. 5 .

 5 The time series of altitude and temperature values of the CPT are compared with the modeled CPT to evaluate the BRAMS mesoscale model. Further comments are in Chapter 3.3.59On montre aussi une assez bonne corrélation entre le modèle et les observations pour l'altitude des sommets de nuages, avec une corrélation moyenne de 0.3 sur toute la saison humide. On montre également qu'au voisinage des pixels d'overshoots détectés par MSH, le modèle BRAMS calcule généralement des nuages hauts, typiquement autour de 15 -16 km d'altitude. Enfin, l'analyse de la série de radiosondage a permis de mettre en évidence la présence d'onde d'inertie-gravité dans la région de Bauru. Le modèle BRAMS pendant la même période, simule également à deux reprises des ondes d'inertie-gravité comparables en période, en longueur d'onde et en direction de propagation. On en déduit que ce modèle réalise un travail tout à fait correct pour ces paramètres clé, et valide l'utilisation de ce modèle pour l'étude des processus de la TTL en lien avec la vapeur d'eau à l'échelle continentale. De plus les bonnes performances de BRAMS à reproduire le réalisme de la TTL sans tenir compte des overshoots confirme pour cette saison le fait que les overshoots jouent un rôle significativement inférieur à ceux des processus de plus grande échelles dans le bilan de l'eau stratosphérique.This chapter develops the base of this dissertation aiming at the upscaling the impact of stratospheric overshooting convection (SOC) on the water vapor (WV) budget in the TTL and the lower stratosphere at large-scale. First of all, it is necessary to demonstrate the ability of the BRAMS mesoscale model, when it does not take into account the SOCs, to simulate the essential processes or parameters (e.g., temperature, humidity, cold-point, convective clouds, and gravity waves) that may play a role in the abundance of the WV in the TTL. To evaluate the model, a whole wet season is simulated in a large part of Brazil in the Southern hemisphere with a single-grid having a horizontal resolution of 20 km × 20 km. This resolution does not allow the mesoscale model to reproduce SOC, which requires the grid-point resolution typically of size 1 km 2 à 4 km 2 . This modeled TTL corresponds to five months of the observation period (FMOP) akin to the TRO-Pico field campaign which took place at Bauru, State of São Paulo, Brazil, from November 2012 to March 2013. During this campaign, a series of balloon-borne stratospheric hygrometers were used for WV measurements, and a series of radio soundings were also carried out. The latter one made it possible to study the thermal structure of the TTL, as well as the gravity waves. The convective clouds of the model during the FMOP are validated by products retrieved from the GOES-12 geostationary satellite-

  REF 1 )simulation before we could possibly prescribe the hydration (or dehydration) caused by the overshooting turrets in the TTL. Chapter 4 illustrates this hydration (or dehydration) forcing scheme developed using cloud-scale simulations. Therefore, we make tests on the bulk-microphysics of the BRAMS model by evaluating key parameters linked to a typical TTL during a wet season at a continental scale against the observations retrieved from various sources (e.g., TRO-Pico campaign balloon-borne measurements, upper-air radio soundings, TRMM satellite measurements). Particularly, we study the TTL's temperature evolution, cold-point temperature (CPT) time series, H 2 O mixing ratio and total rainfall accumulation, which are the prototypical features of deep convection.

Figure 3 . 1 -

 31 Figure 3.1 -Temperature evolution at Bauru during IOP2 phase of the field campaign. (a) denotes the radio sounding (RS92) measurements, (b) denotes the REF 0 simulation temperature profile with the CPT altitude (black line), and the white box highlights the coldest temperature obtained during IOP2. In (a), the cross-marks depict the availability of the measurements, missing data are linearly interpolated. There are 1 to 4 measurements per day are shown, while for the simulation, 24 data points corresponding to each hour of the day are shown. The coldest period obtained during the campaign corresponds to February 2, while in REF 0 it corresponds to January 26. More discussion can be found in Chapter 3.3 regarding the temperature trends.

Figure 3 . 2 -

 32 Figure 3.2 -Histogram of the temperatures within 12 km à 23 km altitude for the 3 rd week of November, 2012 at Bauru. (a) corresponds to the REF 0 simulation with 68 vertical levels having ∼300 m resolution at the TTL, (b) refers to a simulation with 76 vertical levels having ∼200 m resolution at the TTL, and (c) refers to a simulation with 105 vertical levels having ∼100 m resolution at the TTL. The bin-width is 0.25 • C.

  and its variability corresponding to a different vertical grid-point resolution around the TTL. During November 15 00 :00 UTC to November 21 23 :00 UTC, 2012, we make the statistics of WV distribution within 12 km à 23 km altitude at Bauru for the aforementioned three different simulations, where they differ by a number of vertical levels. The histogram in Figure3.3 shows the H 2 O mixing ratio at Bauru for the full 3 rd week of November 2012.In Figure3.3, the PDF of the distribution of WV around the TTL makes it evident that within 12 km à 23 km range of altitude, the H 2 O mixing ratio varies around ∼4 ppmv at the tropics. Now, the inference from Figure3.3a vs. 3.3b vs. 3.3c is that the higher vertical resolution can resolve well the driest region of the TTL. In Figure3.3c, we observe several bins having H 2 O mixing ratio less than 3.0 ppmv. This is very important to emphasize here that the simulation with higher vertical resolution within the TTL can account for the very dry concentrations. Now recalling both Figure3.2c and 3.3c, the simulation with 105 vertical levels is colder and drier, thus resolving better the TTL features. Note that the number of bins/grid-points considered in Figure3.2 and in Figure3.3 are the same. This analysis turns out to be very crucial for the simulation of the full wet season of the years 2012 and 2013, over South America, particularly with a very dry and cold TTL, which was observed in the frame of TRO-Pico field campaign.

Figure 3

 3 Figure 3.3 -Histogram of the H 2 O mixing ratios within 12 km à 23 km altitude for the 3 rd week of November, 2012 at Bauru. (a) corresponds to the REF 0 simulation with 68 vertical levels having ∼300 m resolution at the TTL, (b) refers to a simulation with 76 vertical levels having ∼200 m resolution at the TTL, and (c) refers to a simulation with 105 vertical levels having ∼100 m resolution at the TTL. The bin-width is 0.01 ppmv.

Figure 3 . 4 -

 34 Figure 3.4 -Total rainfall accumulation (mm) during the 3 rd week of December 2012, for the domain of simulation. (a) corresponds to the TRMM observation, while (b) to (h) refer to the modeled precipitation corresponding to the week of observation. (b) has ν = 2.0, CCN = 0.5 × 10 9 and zlev = 68 (settings of REF 0 simulation),

  sensitivity tests carried out on the REF 0 simulation, we complete the REF 1 simulation for the FMOP. This time, we increase the domain slightly in comparison to the REF 0 simulation, which encompasses the latitudes from 28.41 • S to 7.28 • S and longitudes from 61.48 • W to 38.42 • W, covering a large tropical region of South America. We follow the same horizontal grid-point resolution of 20 km × 20 km, whereas its vertical grid-points comprise of 105 levels starting from surface to 30 km altitude with ∼100 m resolution at 14.5 km à 18.2 km altitude. Due to its horizontal grid-point resolution, the simulation cannot take into account the stratospheric protrusion of deep convection -stratospheric overshooting convection (SOC). Most of the bulk microphysics parameters are chosen to be the same as REF 0 simulation, while the main advancements have done in REF 1 can be listed as below :-GNU = 2.1 (before it was 2.0) -CCN = 20 × 10 10 (before it was 0.5 × 10 9 ) -CO 2 = 395 ppm (before it was 300 ppm)During the evaluation process of REF 1 simulation, we submit one article, currently under revision, based on the performance of the BRAMS model depicting the typical variability of the TTL at a continental scale during a wet season. The evaluation is done mostly using the TRO-Pico field campaign balloonborne measurements, and other observations retrieved from the satellite-borne observations and upper-air radiosoundings. The submitted version of the article can be found in the following section.

-

  The model depicts the typical variability of temperature and water vapor in the tropical tropopause layer, and the gravity wave properties -Observation of high modeled cloud tops at the overshooting locations detected by MHS with modeled cloud tops similar to GOES-12 measurements -Detection of the impact of stratospheric sudden warming occurring in the Arctic in the tropical tropopause layer over South America Abstract : In order to better understand the water vapor (WV) intrusion into the tropical stratosphere, a mesoscale simulation of the tropical tropopause layer (TTL) using the BRAMS (Brazilian version of RAMS) model is evaluated for a wet season. This simulation with a horizontal grid-point resolution of 20 km × 20 km cannot resolve the stratospheric overshooting convection (SOC). Its ability to reproduce other key parameters playing a role in the stratospheric WV abundance is investigated using the balloonborne TRO-Pico campaign measurements, the upper-air soundings over Brazil, and the satellite observations by Aura MLS (Microwave Limb Sounder), MHS (Microwave Humidity Sounder) and GOES-12. The BRAMS exhibits a good ability in simulating temperature, cold-point, WV variability around the tropopause. However, the simulation is typically observed to be warmer by ∼2.0 • C and wetter by ∼0.4 ppmv at the hygropause, which can be partly affiliated with the grid-boundary nudging of the model by ECMWF operational analyses. The modeled cloud tops show a good correlation (maximum cross-correlation of ∼0.7)

  2 and H 2 O [Kirk-Davidoff

  H 2 O flux ∼600 t min -1across 75 hPa on the tropical belt from the general circulation model ECHAM5/MESSy1 during the halogen occultation experiment (HALOE).[START_REF] Ueyama | Dynamical, convective, and microphysical control on wintertime distributions of water vapor and clouds in the tropical tropopause layer[END_REF] estimate an enhancement of ∼0.3 ppmv of H 2 O across 100 hPa at a large-scale in the Southern hemisphere from the trajectory study initiated from convective cloud tops. An indirect signature of the SOC at global scale can be obtained by studying the diurnal cycle of MLS H 2 O mixing ratio due to deep convection reaching higher than 100 hPa[START_REF] Carminati | Impact of tropical land convection on the water vapour budget in the tropical tropopause layer[END_REF], highlighting the regions where convection is most active, and confirming former results of[START_REF] Liu | Global distribution of convection penetrating the tropical tropopause[END_REF]. But none of these aforementioned studies are able to quantify the impact of SOC in the global abundance of stratospheric WV.

ture, H 2 O

 2 mixing ratio and inertia-gravity waves. TRO-Pico is a French funded project which aims at studying the TTL's WV budget at a local scale, but on two different time scales : the full wet season corresponding roughly to a five months observation period (FMOP) from November 2012 to March 2013, and the most active convective periods (IOP, intensive observation period) during the FMOP. The most active convective periods of sampling (IOP) correspond to March 2012 (IOP1) and January-February 2013 (IOP2). During the IOPs, a set of light instruments were launched under small balloons (500 m 3 à 1500 m 3

Figure 3 .

 3 Figure 3.5 shows the time evolution of the vertical structure of the TTL temperature profile from January 23 to February 12, 2013 radio sonde ascents with RS92, BRAMS and ECMWF operational analyses, respectively, at Bauru. Data availability of RS92 is shown using the (black) cross marks, and missing points are linearly interpolated. It should be noted that RS92 provides only 1 to 4 measurements per day, whereas BRAMS has 24 (hourly) data points per day, and ECMWF operational analyses has 4 regular data points throughout the observation period (IOP2). In Figure 3.5a, the RS92 measurements show a succession of mild and very cold periods in the first part of IOP2 in the TTL. The cold periods are characterized by temperatures below -85.0 • C around the cold-point (January 27 & 29 and 'February 2' -the coldest one being -87.7 • C, marked with a white box in the plot). The second part of the IOP2 is significantly warmer, especially around February 6 -8, 2013.

Figure 3

 3 Figure 3.5 -(a) Temperature profile from radio soundings (RS92 SGP), obtained at Bauru (22.31 • S, 49.05 • W) during the IOP2 of the TRO-Pico campaign. The time of each sounding is indicated by '+'. The black line represents the CPT altitude. The white box shows the coldest CPT, viz., ∼ -88 • C observed at ∼70 hPa on February 2, 2013. (b) Concurrent temperature profile from the BRAMS analyses at the same location, based on hourly data. The white box corresponds to the coldest CPT, viz., ∼ -85 • C observed at ∼85 hPa on January 29, 2013. (c) Concurrent temperature profile near Bauru from the ECMWF analyses, based on four data points per day. The white box corresponds to the coldest CPT, viz., ∼ -84 • C observed at ∼70 hPa on February 1, 2013.

Figure 3 .

 3 Figure 3.6 calls attention to the variability of the altitude and temperature series of CPT retrieved from the upper-air database with the concurrent modeled CPT. The altitude time series of the CPT simulated by the BRAMS show a similar pattern of time evolution as observed in RS measurements, although they seem to be warmer and lower in altitude. A summary of biases among them (Table3.2) are expressed in

Figure 3 .

 3 Figure 3.7 shows a comparison of the balloon-borne WV measurements performed during the TRO-Pico campaign at Bauru with the WV profiles from the BRAMS. Most of the profiles shown in Figure 3.7 belong to the IOP2 (blue and red lines), but also include a few WV measurements obtained during November and December 2012 (black lines) and March 2013 (green lines), i.e., part of the FMOP. Here, the measurements are obtained from both the balloon-borne Pico-SLDA (solid lines) and FLASH-B (dotted

Figure 3 . 7 -

 37 Figure 3.7 -(a) Water vapor (WV) mixing ratio, measured by the Pico-SDLA (solid lines) and FLASH-B (dotted lines) H 2 O spectrometers during the TRO-Pico campaign at Bauru. The minimum and maximum H 2 O mixing ratios of corresponding pressure levels during the FMOP in the Bauru region are also shown (dots) from MLS : version 4.2 measurements for a domain of 24.00 • S to 19.00 • S and 55.50 • W to 43.50 • W ; (b) WV profiles from the BRAMS simulation at Bauru. Profiles for 12 :00 UTC to 23 :59 UTC, are shown starting from November 20, 2012 to March 30, 2013 to be better comparable with the broad variability of WV profiles akin to deep convection from the hygrometer measurements.

Figure 3

 3 Figure 3.8 -(a) Cross-correlation coefficients between the cloud tops measured by the GOES-12 satellite and calculated by the BRAMS model for the full domain of simulation during the FMOP. The coefficients are calculated every three hours starting from November 01 00 :00 UTC, 2012 to March 31 21 :00 UTC, 2013. (b) Mean value of the percentage of cloud tops >10 km, calculated on a daily basis, for BRAMS (blue line) and GOES-12. The red line represents the high clouds in GOES-12 (including all types of optically thick clouds), while the black dotted line corresponds to only very thick convective clouds.

Figure 3

 3 Figure 3.9 -Cloud tops : (a) and (c) measured by the GOES-12 satellite on January 12 09 :15 UTC, 2013 and March 4 15 :15 UTC, 2013, respectively. (b) and (d) from the BRAMS model during the same time period, as in (a) and (c), respectively. The locations of RS stations from the upper-air database (red dots) and Bauru (green dot) are only shown in (d).

Figure 3 .

 3 Figure 3.8b highlights BRAMS ability in simulating high clouds during the FMOP. It represents three time series illustrating the average value of the percentage of occurrence of high clouds (>10 km) calculated on a daily basis. Since we extract all types of optically thick clouds from GOES-12 (red line), the introduction of another parameter to observe only the deep convective cloud (dotted black line) makes it more specific in terms of the temporal trend to evaluate BRAMS. The chosen parameters are CTTH_Height

Figures 3 .

 3 Figures 3.10a and 3.10b depict the distribution of the modeled cloud altitude at and nearby the COV locations, respectively, detected by the satellite-borne MHS. Figure 3.10a shows an overall good ability of BRAMS to produce high cloud tops exactly at the position of overshooting cells detected by MHS. In order to account for possible errors in the modeled location of the high clouds, namely if (x, y) denotes the COV location from MHS, then (x + δx, y + δy) corresponds to the highest cloud top in the BRAMS model output, where δx + δy are <50 km, Figure 3.10b should be considered. It confirms that the highest altitude of the cloud tops generated by BRAMS around a COV detected by MHS is usually very high (sometimes up to 16 km à 17 km for the maximum of the distribution, just below the 380 K isentrope in the simulation).

Figure 3 .

 3 Figure 3.10 -Histograms of the cloud top altitudes from BRAMS at the locations of overshooting cells (>14 km) detected by MHS from November 1, 2012 to March 31, 2013 (FMOP). (a) cloud top altitude distribution exactly at the positions of overshooting cells ; (b) distribution of the highest cloud tops present within the ∼50 km radius of overshooting cells.

Figure 3 .

 3 Figure 3.11 -Perturbed wind profiles at Bauru from the RS92 measurements during the TRO-Pico campaign and from the BRAMS model are shown for the period January 23 to February 12, 2013. (a) RS92 u profile, (b) BRAMS u profile, (c) RS92 v profile, and (d) BRAMS v profile. The blanks in the RS92 measurements correspond to the absence of data. Clearly visible gravity wave patterns are highlighted with dotted lines in (a) and (d).

  Aura microwave limb sounder (MLS : version -4.2[START_REF] Livesey | Version 4.2x level 2 data quality and description document[END_REF]) measurements are used to demonstrate the large-scale cooling of the TTL observed during January -February 2013 due to SSW in the Arctic, both in the frame of the TRO-Pico campaign at Bauru (22.31 • S, 49.05 • W) and the 2013 ATTREX campaign at Guam (13.44 • N, 144.79 • E), respectively. In section 4, a very cold and dry TTL, which was observed during the end of January/beginning of February 2013, is discussed, and one could suppose that the dry air mass would have traveled from the tropical region of the western Pacific Ocean to the continent of South America. In the simulation, we also observe a similar dry and a cold period, although not as a drier or colder TTL with respect to the TRO-Pico field campaign measurements. Being a limited area simulation, it cannot reproduce directly the global-scale features like the advection of a very dry air parcel from the tropical region of the western Pacific Ocean towards the continent of South America. However, recalling that the numerical simulation is nudged by the ECMWF operational analyses every 6 h of real time simulation for the grid-boundary conditions and grid-point initialization, this analysis could demonstrate the good ability of the BRAMS mesoscale model in adapting to the state of art of the physical conditions within the ECMWF analyses. Another fact could be the increased acceleration of the Brewer-Dobson circulation in response to the sudden stratospheric warming (SSW) in the Arctic. This would explain the faster cooling of the TTL everywhere, and therefore the efficient dehydration in the lower stratosphere. Figure3.12 represents the mean H 2 O mixing ratio (ppmv) profiles at 82.5 hPa pressure level, where the averaging is done within the following domains : the domain chosen around Bauru extends from 10 • S to 23 • S latitude and from 39 • W to 59 • W longitude ; the tropical region of the western Pacific Ocean ranges from 20 • N to 10 • S latitude and from 145 • E to 165 • E longitude.

Figure 3

 3 Figure3.12 -S1 : Mean H 2 O mixing ratio at 82.5 hPa pressure level retrieved from Aura MLS : version 4.2. The two time series denote the lower stratospheric water vapor variability in the neighborhood of Bauru (blue) and Guam (red), respectively.

  ters of the TRO-Pico field campaign at Bauru and from the BRAMS model, corresponding to the driest (hygropause) profiles for each case. The driest WV profiles at hygropause correspond to January 31 for Pico-SDLA (2.0 ppmv), February 2 for both FLASH-B (2.2 ppmv) and BRAMS(2.4 ppmv), respectively.In Figure3.13, we show the T sat variability with altitude corresponding to five different partial vapor pressures, which is expressed in terms of H 2 O mixing ratio varying from 2.0 ppmv to 2.4 ppmv. The different colors of solid lines, indicating different WV concentration, depict that an air mass falling in these lines would possess only the corresponding WV concentration in its saturation condition.

Figure 3

 3 Figure 3.13 -S2 : Vertical profiles (solid lines) of saturation temperatures (T sat ) corresponding to five different WV mixing ratioscalculated from equation 3.2. The colors indicate the different concentration of WV. The * symbols depict T sat s in • C and corresponding pressure levels in hPa, obtained from the H 2 O mixing ratio at the hygropause measured by Pico-SDLA (blue), FLASH-B (red), and simulated by the BRAMS model (green), respectively. The × symbols represent the corresponding ambient temperatures of the hygropause.

Figure 3 .

 3 Figure 3.14 shows the hodographs for four cases, two each from RS92 (upper panel) and BRAMS (lower panel), respectively. The comparison between Figure 3.14a vs. 3.14c and 3.14b vs. 3.14d shows very similar hodographs. Considering the particular case of January 28, 2013 in the simulation at Bauru (22.31 • S, 49.05 • W), shown in Figure 3.14c, the ratio a b is obtained to be 1.16. The mean value of Brunt-Väisälä frequency (N B = g θ dθ dz , g : local acceleration of gravity, θ : potential temperature (K) and z : geometric height (m)) is 0.0189 s -1 between 13 km à 16 km altitude. From the u profile, λ z is found to

Figure 3 .

 3 Figure 3.14 -S3 : Hodographs of wind perturbations (u , v ) due to inertia-gravity waves deduced from RS92 soundings (upper panel) during the TRO-Pico campaign and the BRAMS simulations (lower panel) on January 28 and February 08, 2013, respectively, at Bauru. Note that there is a time difference of few hours between the RS91 and the BRAMS hodographs due to the sporadic distribution of the deep convection over the continent, which provides well known sources for these wave patterns.

Figure 3 .

 3 Figure 3.15 -A schematic diagram representing the highest cloud tops obtained from the numerical simulation on a particular day, including the positions of the overshooting cells («+» signs) detected by satellite-borne MHS radiometer. The results are shown for November 16, 2012, covering the full domain of the simulation. The red «*» are some prominent cities in South America, while the black «*» denotes the location of Bauru (22.31 • S, 49.05 • W).

Figure 3 .

 3 Figure 3.16(a) shows the pressure levels of cloud tops measured by GOES-12 on November 1 00 :15 UTC, 2012, while 3.16(b) corresponds to the same case, but the cloud top altitude is given in km, retrieved using the CTTH_Height product of SAFNWC. The resolution of each satellite grid-point is kept intact, which is 0.04 • × 0.04 • , no re-gridding is done. However in case of 3.16(c), the satellite grid-points are transformed to the REF 1 simulation grid-point resolution using bilinear interpolation, i.e., the grid-point resolution is changed from 0.04 • × 0.04 • to 20 km × 20 km. This is the reason behind such coarse representation of the cloud top measurements in 3.16(c).Figure 3.16(d) represents the effective cloudiness corresponding to

  Figure 3.16(d) represents the effective cloudiness corresponding to 3.16(c). Now here each grid-point with CTTH_Effect = 100 represents an optically very thick cloud top, possibly corresponding to a convective cloud top or optically thick cirrus cloud top. We use this parameter

Figure 3 .

 3 Figure 3.16 -GOES-12 observation of cloud tops on November 1 00 :15 UTC, 2012. (a) is the quick viewer of the satellite-borne observation, color scale is in hPa ; (b) refers to the presentation of CTTH_Height product which considers mostly high level clouds (optically thick, also optically thin cirrus during the twilight times), color scale ranges from 0 km à 18 km ; (c) represents the same cloud top as in (b), but transformed to show only our domain of interest, color scale ranges from 0 km à 18 km ; (d) shows the CTTH_Effect product corresponding to (c), where the effective emissivity of cloud top is in a scale of 0 -100.

Figure 3 .

 3 Figure 3.17 -The vertical profile of ice+cloud mixing ratio profile on January 12 09 :00 UTC, 2013, at a particular grid-point of the REF 1 simulation. (a) is the mixing ratio (g kg -1 ) profile, (b) is its first derivative, and (c) is its second derivative.

Figure 3 .

 3 Figure 3.18 represents a case study of January 12 09 :00 UTC, 2013, where the maximum correlation obtained between GOES-12 and BRAMS during the FMOP, i.e., Figures 3.18a vs. 3.18b -recall Figure 3.8. Now, we put to the fore other sensitivity tests carried out (not shown in Chapter 3.3) before making a decision about the criteria to calculate modeled cloud tops for the FMOP. Figure 3.18d gives a perspective of considering only convective clouds by considering the CTTH_Effect=100, i.e., optically very thick clouds possibly corresponding to the convective clouds only. Now to bring in this prospective in the modeled cloud tops, Figures 3.18c, 3.18e and 3.18f can be considered, where the horizontal grid-points are considered only

  ,

Figure 3

 3 Figure3.19 -The seasonal average of the high clouds (>10.0 km) occurrence in BRAMS (black) -cloud tops determined using the criteria as in Chapter 3.3, in SAFNWC products for CTTH_Height (dotted red) -any kind of optically thick cloud with optically thin cirrus clouds mostly during the twilight times, and for CTTH_Height+CTTH_Effect (blue) -mostly the optically thick convective clouds, as well as optically thick cirrus clouds. They are averaged upon the eight UTC hours considered on daily basis during the FMOP.

Figure 3 .

 3 Figure 3.20 depicts the scatter plot of Figure 3.8b to put the results in a different perspective. One important feature of this plot is to put to the fore the dispersion of the high cloud occurrences retrieved from GOES-12 observations (blue and red) around the modeled high clouds (black). It can be concluded that the dispersion of the SAFNWC product is evenly biased around the X = Y line, the straight line representing the REF 1 modeled cloud tops, when we consider only CTTH_Height (blue dots) ; whereas the consideration of CTTH_Effect in addition to CTTH_Height in SAFNWC leads to negative biases most of the time. This could invoke the overestimation of cloud tops in the REF 1 simulation. The general interpretation of this result would be the fact that in the real world there are less convective clouds >10.0 km. Furthermore, consideration of only the CTTH_Height parameter in the SAFNWC product while making the cross-correlation analysis against the modeled (REF 1 simulation) cloud tops seems to be consistent numerically due to their comparable magnitudes, rather than considering both the CTTH parameters of GOES-12 against the REF 1 simulation. Nevertheless, it requires further investigation in this domain in order to establish one conclusive criterion to calculate the cloud tops in any kind of mesoscale numerical modeling.

  Figure3.20 -A scatter plot of the percentage of high clouds detected by GOES-12 against the modeled high clouds within the domain of the simulation during the FMOP. X is a random variable corresponding to the percentage of occurrence of high clouds (>10.0 km). Abscissa depicts X from the numerical simulation of REF 1 , while the ordinate represents X from three different sources, i.e., from the REF 1 simulation (black line), and from GOES-12 observations, but using CTTH_Height+CTTH_Effect (red) and CTTH_Height (blue), respectively.

Figure 3 .

 3 Figure 3.22 -The histogram of cross-correlation coefficients calculated every 3 h, starting from November 1 00 :00 UTC, 2012 to November 14 21 :00 UTC, 2012, for the two types of grid-point resolution or the cell size used in data extraction from GOES-12 satellite observations. (a) corresponds to the first step of data extraction having 0.18 • cell size. (b) corresponds to the second step with data extraction of 0.5 • cell size. The 8 types of color bars represent different hours of the day, viz., 00 :00, 03 :00, 06 :00, 09 :00, 12 :00, 15 :00, 18 :00 and 21 :00 UTC of a day, respectively. Missing columns highlights the absence of GOES measurements.

Figure 3 .

 3 Figure 3.23 -Water vapor measurements at 82.5 hPa for the full globe in the tropical belt retrieved from the Aura MLS : version 4.2 : (a) January 13 to 15, 2013 and (b) January 31 to February 02, 2013. The belt chosen here ranges from 30 • N -30 • S, while the color bar represents the H 2 O mixing ratio on a scale of 1 -5 ppmv.

Figure 3 .

 3 Figure 3.24 -FFT of the perturbed wind profiles from BRAMS (the REF 1 simulation) corresponding to the IOP2 (location -Bauru ; latitude : 22.31 • S, longitude : 49.05 • W, January 23 to February 12, 2013). (a) shows the FFT of u profiles, and (b) shows the same for v profiles from the BRAMS simulation. The color bar corresponds to the power of the obtained Fourier spectrum.

Figure 4 .

 4 Figure 4.1 shows a time evolution of radar cloud tops from the S-Band radar at IPMet, Bauru. It shows that around local noon, almost no clouds were detected in the radar range (about 240 km around Bauru).

  (a) Radar observation@15 :00 UTC (12 :01 LT). (b) Radar observation@15 :53 UTC (12 :53 LT) (c) Radar observation@16 :46 UTC (13 :46 LT) (d) Radar observation@17 :08 UTC (14 :08 LT) (e) Radar observation@17 :38 UTC (14 :38 LT) (f) Radar observation@19 :31 UTC (16 :31 LT)

Figure 4 . 1 -

 41 Figure 4.1 -Time sequence of the observational case of overshooting events occurred on March 13, 2012, seen by the S-Band radar at IPMet, Bauru. The echo top (in km) products are shown at 1201 LT (a), 12 :53 LT (b), 13 :46 LT (c), 14 :08 LT (d), 14 :38 LT (e), 16 :31 LT (f).

Figure 4 . 2 -

 42 Figure 4.2 -Extracted from Figure4of[START_REF] Khaykin | Evidence of horizontal and vertical transport of water in the southern hemisphere tropical tropopause layer (TTL) from high-resolution balloon observations[END_REF]. Left panel refers to the descent H 2 O mixing ratio profile from Pico-SDLA (a), and right panel corresponds to the same but retrieved from FLASH-B (c). The corresponding backscattering ratio profile at 532 nm obtained from COBALD is also given in the right panel. Here, the ordinate is chosen to be the potential temperature, while the corresponding altitude in km is also given on the right-hand side. Horizontal dotted lines highlight the potential temperature level corresponding to 386 K and 404 K, respectively, where a local maximum of H 2 O are observed. In the right panel, the relative humidity with respect to ice, computed from the FLASH-B H 2 O profile and temperature profile, is also shown.

At 20 :

 20 20 UTC, a flight train comprised of Pico-SDLA and LOAC apparatuses were launched under a 500 m 3 Aerostar open balloon. The flight train was in the upper TTL at about 21 :54 UTC and the descent (under parachute) started around 22 :00 UTC. The H 2 O mixing ratio retrieved from Pico-SDLA is shown in Figure 4.2a -extracted from[START_REF] Khaykin | Evidence of horizontal and vertical transport of water in the southern hemisphere tropical tropopause layer (TTL) from high-resolution balloon observations[END_REF], where they report about two specific local enhancements at 18.5 km and 17.8 km altitude. The third one of much smaller amplitude is measured at 17.2 km. The analysis of the LOAC particle counter shows that no ice particles were recorded then within this range of altitude.

Figure 4 .

 4 Figure 4.3 -(Figure 7 of Khaykin et al. [2016]) : Echo top maps (same color scale as in Figure 4.1) recorded by S-Band radar at IPMet, Bauru on March 13, 2012. The overshooting cells linked by trajectories with hydrated layers at 386 K and 404 K potential temperatures are highlighted by rectangles in (a, b). Solid lines indicate the trajectories of balloons carrying FLASH-B and Pico-SDLA stratospheric hygrometers with indication of time (UTC) when 386 K and 404 K levels were sampled. Dots depict the ensembles of forward trajectories initialized within the rectangle.

REF 1

 1 Figure 4.4 for the nested-grids and the parent grid (PG) of the simulation.The simulations start at 12 :00 UTC on March 12, 2012, and stop 48 h later. To save computing time, grid 3 is only activated from March 13 10 :00 UTC. The analyses files -model outputs are stored every 7.5 min. This frequency matches with the S-Band radar measurements of IPMet, Bauru. We use them to validate our simulation cloud tops. The time step of integration can vary during the simulation to ensure the numerical stability of the model. It is typically about 2 s à 10 s for grid 1, and 5 times smaller for grid 2 and 25 times smaller for grid 3. The time resolution of calling the radiation module varies between 300 s à 500 s.As for the simulation presented in Chapter 3, these fine-scale simulations are also initialized by the ECMWF operational analyses, and during the simulation, the boundary conditions of grid 1 are nudged from the ECMWF analyses for winds, temperature, and specific humidity. The nudging parameters are the same as in the REF 1 simulation of Chapter 3, recalling that only the boundary of grid 1 is nudged, and there is no nudging at the center of the domain. This latter option is chosen from the setting ofLiu et al. [2010a] because this leads to more realistic results. The simulation includes 7 different types of soil

Figure 4 . 4 -

 44 Figure 4.4 -Three different grids of the BRAMS simulations for the case of March 13, 2012. Grid 1 (PG) is shown in contour, representing the topography in the meter. Grid 2 is shown in shaded colors, while the third grid (the smallest) refers to the red rectangle, the red color being independent of the orography to better identify the grid position.

  microphysical parameter at the most active time of deep convection and to avoid any earlier divergence in both the simulations. The HVR simulation setup is exactly the same as of the REF simulation, except for the vertical resolution. The REF simulation has 68 vertical levels with typically 300 m of resolution in the TTL. The HVR simulation has 99 vertical levels with typically 150 m vertical resolution in the TTL, except at the tropopause where it is 100 m.

Figure 4 .

 4 5 summarizes the distribution of vertical levels and resolution for each simulation. Please note that in contrary to the NU21 simulation and the REF simulation, the HVR simulation is carried out entirely with this vertical resolution since March 12 12 :00 UTC, 2012. This is not possible in BRAMS to change the vertical grid structure during a simulation unless each level of the REF would correspond to a level of the HVR, which is not the case here.

Figure 4 . 5 -

 45 Figure 4.5 -Levels of vertical grid-points (left panel) and resolution (right panel) for the REF (and NU21) and HVR simulation. respectively. The red color stands for the HVR, while the black color refers to the REF/NU21.

Figure 4 .

 4 Figure 4.6 illustrates that for each simulation, no very deep convective clouds exist in the surrounding of Bauru. One hour later at 15 :00 UTC, a few small in size but severe in height convective cell are developing in the three simulation, in Bauru area (more west/southwest for the HVR simulation), while the radar is almost cloud-free (see Figure4.1a), except 100 km south to Bauru where deep convection is observed to be triggering. It can be deduced that the simulations are slightly earlier in time with respect to the beginning of the convective activity, though not unrealistic than the observations.

Figure 4 .

 4 9a shows the modeled cloud top at 16 :15 UTC and the corresponding vertical cross-section at 22.3 • S from NU21 simulation. The high 123 (a) REF simulation@14 :00 UTC. (b) REF simulation@15 :00 UTC.

Figure 4 .

 4 Figure 4.6 -BRAMS model cloud tops for the simulation REF (a, b), NU21 (c, d) , and HVR (e, f) at 14 :00 UTC (a, c, e) and 15 :00 UTC (b, d, f), respectively. Corresponding S-Band radar echo top at 15 :00 UTC is already shown in Figure 4.1a. 124

Figure 4 . 7 -

 47 Figure 4.7 -REF simulation results. Cloud top at 16 :15 UTC (a), and vertical cross-sections of condensed water within grid 3 at 22.2 • S at 16 :07 UTC (b), 16 :15 UTC (c) and 16 :22 UTC(d). Ice+liquid concentration color contour varies from 0 g kg -1 à 4 g kg -1 .

Figure 4 .

 4 Figure 4.8 -REF simulation results. Cloud top at 16 :52 UTC (a), and vertical cross-sections of condensed water within grid 3 at 22.1 • S at 16 :45 UTC (b), 16 :52 UTC (c) and 17 :00 UTC (d). Ice+liquid concentration color contour varies from 0 g kg -1 à 4 g kg -1 .

Figure 4 .Figure 4 .

 44 Figure 4.9 -NU21 simulation results. Cloud top at 16 :15 UTC (a), and vertical cross-sections of condensed water within grid 3 at 22.3 • S at 16 :07 UTC (b), 16 :15 UTC (c) and 16 :22 UT(d). Ice+liquid concentration color contour varies from 0 g kg -1 à 4 g kg -1 .

Figure 4 .

 4 Figure 4.11, highlighting a continuous cloud top above 16 km within the longitudes ranging from 49.8 • W

  Vertical cross-section@ 15 :45 UTC.(c) Vertical cross-section@ 15 :52 UTC.(d) Vertical cross-section@ 16 :00 UTC.

Figure 4 .

 4 Figure 4.11 -HVR simulation results. Cloud top at 15 :52 UTC (a), and vertical cross section of condensed water within grid 3 at 22.3 • S at 15 :45 UTC (b), 15 :52 UTC (c) and 16 :00 UTC (d). Ice+liquid concentration color contour varies from 0 g kg -1 à 4 g kg -1 .

Figure 4 .

 4 Figure 4.12 shows the horizontal cross-section of total water content at 17.2 km altitude at 16 :15 UTC, 19 :45 UTC and 23 :15 UTC, respectively. It also depicts the horizontal wind streamlines to follow the direction of the moving plume at this altitude. This kind of plots are made every 7.5 min to track precisely the moving overshot plume ; however, we show three of them here to highlight the analysis.In Figure4.12a, the overshooting turret penetrating the stratosphere at 16 :15 UTC is located at 22.2 • S, 49.15 • W. About 3.5 h later, this turret is observed to spread wide horizontally, mostly east to 49.4 • W. Some other SOC cells are appeared in between but don't interact with the eastern part of the turret. At 23 :15

Figure 4 .

 4 Figure 4.12 -BRAMS total water (ice, liquid and vapor) content in g kg -1 at 17.2 km altitude at 16 :15 UTC (a), 19 :45 UTC (b) and 23 :15 UTC (c). Streamlines of the horizontal wind are also shown. The domain is a composite of grid 2 and grid 3.

Figure 4 .

 4 Figure 4.13 -REF simulation : Vertical profiles of total water content at different locations of the overshooting turret at 17.2 km from the SOC cell at 16 :15 UTC. The location are : 48.5 • W, 21.75 • S (black) ; 48.4 • W, 22.9 • S (green) ; 48.4 • W, 21.5 • S (yellow) ; 48.3 • W, 22.0 • S (magenta).

17. 8

 8 km altitude detected by Pico-SDLA at 22 :04 UTC, the associated SOC explaining this enhancement corresponds 17 :38 UTC. This means the Δt om = 4 h26 min. The tracking of the SOC cell in the REF

Figure 4 .

 4 Figure 4.14 -Same as Figure4.12, but here the plume is at 17.8 km, and followed at 16 :15 UTC, 18 :30 UTC and 20 :52 UTC, respectively.

Figure 4 .

 4 Figure 4.15 -Same as Figure 4.13, but for the plume of the same SOC cell at 17.8 km altitude. The location of the profiles are : 48.8 • W, 22.05 • S (black) ; 49.0 • W, 22.15 • S (green) ; 48.9 • W, 21.1 • S (yellow), 49.0 • W, 21.1 • S (red) ; 48.9 • W, 22.0 • S (magenta).

  section 4.3, we demonstrate that the simulations REF and NU21 of the same overshooting case are realistic. In both cases, the time evolution of the cloud clusters until 18 :30 UTC is compatible with the 135 (a) Horizontal cross-section@ 16 :15 UTC. (b) Horizontal cross-section@ 19 :45 UTC. (c) Horizontal cross-section@ 23 :15 UTC.

Figure 4 .

 4 Figure 4.16 -Same as Figure 4.12, but for the NU21 simulation.

Figure 4 .

 4 Figure 4.17 -Vertical profiles of total H 2 O from the NU21 simulation. The profiles are extracted at different locations within the plume at 17.2 km altitude at 23 :15 UTC, from an overshooting turret penetrating the tropopause at 16 :15 UTC. The locations of the different profiles are as follows : 48.5 • W, 21.75 • N (black line), 48.3 • W, 21.95 • N (green) ; 48.3 • W, 21.75 • S (yellow) ; 48.3 • W, 21.6 • S (red) ; 48.33 • W, 21.67 • S (magenta).

Figure 4 .

 4 Figure 4.18 -Vertical profiles of total H 2 O content from the NU21 simulation. The profiles are extracted at different locations within the plume at 17.8 km altitude at 20 :52 UTC, from an overshoot turret penetrating the tropopause at 16 :15 UTC. The location of the profiles are : 48.7 • W, 22.3 • S (black), 48.5 • W, 22.25 • S (green) ; 49.6 • W, 22.6 • S (yellow) ; 48.45 • W, 22.35 • S (red) ; 49.1 • W, 22.4 • S (magenta).

4 .Figure 4 .

 44 Figure 4.19 -Horizontal cross-sections (within 15.4 km à 18.8 km altitude) representing the ratio of pristine ice within the domain at 16 :15 UTC.

Figure 4 .

 4 Figure 4.20 -Horizontal cross-sections (within 15.4 km à 18.8 km altitude) representing the ratio of aggregates within the domain at 16 :15 UTC.

Figure 4 .

 4 Figure 4.21 -Horizontal cross-sections (within 15.4 km à 18.8 km altitude) representing the ratio of snow within the domain at 16 :15 UTC.

Figure 4 .

 4 Figure 4.22 -Horizontal cross-sections (within 15.4 km à 18.8 km altitude) representing the ratio of graupel within the domain at 16 :15 UTC.

Figure 4 .

 4 Figure 4.23 -Horizontal cross-sections (within 15.4 km à 18.8 km altitude) representing the ratio of hail within the domain at 16 :15 UTC.

Figure 4 .

 4 24, we demonstrate the area of impact for each individual overshooting turret at 380 K isentropic surface, for two different simulations, viz., REF and NU21.

Figure 4 .

 4 Figure 4.24 gives vital information regarding the size of the impacting area of the overshooting plume at 380 K isentropic surface, which corresponds roughly to the lapse rate tropopause. The cases are chosen by following the Table4.1, which gives information about the number of SOC events and their top altitude

Figure 4 .

 4 Figure 4.24a, the impact area is about 14 km × 14 km ; for 4.24b, it is about 22 km × 22 km ; for 4.24c, it is about 30 km × 30 km ; and for 4.24d, it is about 33 km × 33 km. A circle of 24 km diameter would have an area of ∼450 km 2 , that is roughly the area of 20 km × 20 km grid mesh, which is used in the continental scale simulation (REF 1 ) in Chapter 3. In the REF 1 simulation, SOC is thieved from the simulated TTL by

Figure 4 .

 4 Figure 4.24 -A schematic diagram for the impacting area of overshoots at 380 K isentropic layer, shown for REF simulation (a : 15 :37 UTC & b : 16 :37 UTC), and for NU21 simulation (c : 15 :30 UTC & d : 15 :52 UTC). UTC times are followed from the Table 4.1. Color contours are the representative of total ice mixing ratio, shown for only few layers starting from 0 g kg -1 à 0.1 g kg -1. The solid arrows depict the typical size of the SOCs.

Figure 4 .

 4 Figure 4.25 -Mean mass flux (g m -2 s -1 ) over the domain of grid3 for REF (green) and NU21 (blue) simulation, calculated at 380 K isentropic surface for aggregates, graupel, hail, pristine ice, snow and water vapor, respectively.

Figure 4 .Figure 4 .

 44 Figure 4.26 -Volume of available grid-points (km 3 ) within the belt of 380 K à 430 K isentropic levels corresponding to the grid 3 of domain of simulation, shown for the REF (red) and the NU21 (blue) simulation. Ordinate represents the absolute volume, no normalization is done.

Figure 4 .

 4 Figure 4.26 gives an indication of the impact of SOC above the 380 K isentrope. The extent of deformation caused by SOC could be an indirect quantity to measure the severity of overshooting convection.

4. 7 )

 7 . Now recalling Table4.1, REF simulation has number of SOCs than NU21 before 18 :30 UTC. This would explain the difference of magnitude in the total volume of the slice between 380 K à 430 K for the

Figure 4 .

 4 Figure 4.27 -Mass budget (kt) of total five ice hydrometeors and water vapor within 380 K à 430 K isentropic surface, shown for the REF and NU21 simulation. Blue is for total ice, red is for water vapor, black is for sum of both ice and vapor.

Figure 4 .Figure 5

 45 Figure 4.28: A schematic diagram of the cross-section of a grid-p corresponds to the location of SOC detected by MHS. The RHI% of determined by the sub-grid scale vertical column of ice injection ab

  [-1, 1]) are calculated for the entire wet season on the cloud top fields. An average correlation of +0.3 is calculated, with better agreements for the most and least convective hours of the day (no convection, and mature phase of convection). It is also shown that, to a large extent, the model is capable of forming the highest clouds where the microwave satellite MHS sounder detects overshoots (not necessarily stratospheric). Finally, the inertia-gravity waves that have been highlighted by the Bauru radiosonde series during the TRO-Pico campaign are studied. The parameters from two different waves at different dates are shown to be similar for the BRAMS and for the observations. These waves have long horizontal wavelengths and are partially resolved by the ECMWF operational analyses. The model is nevertheless able to reconstruct the good harmonics unresolved by ECMWF. A Fourier transform analysis in BRAMS shows wave frequencies typical of waves that have already been observed in the literature. In conclusion, the BRAMS model describes the TTL adequately and can serve as a tool for future studies of upscaling the role of overshoots.At the local scale, the case of March 13, 2012 (during the first intensive period of the TRO-Pico campaign) is simulated. This case presents several cells of stratospheric overshoots, of different intensity.It, therefore, allows, through modeling, to quantify the typical impact of these different cells, and therefore to quantify the average impact of an isolated SOC. Three fine-scale simulations of the same case are performed by varying either the microphysical settings or the vertical grid-point resolution of the model with respect to a reference simulation. The simulations are of 3 nested-grids with horizontal resolutions of 20 000 m, 4000 m, and 800 m. The simulations are validated using the observations from the IPMet S-Band radar at Bauru, and by Pico-SDLA and FLASH-B water vapor measurements on the same day. Although the modeled overshoot cells do not form exactly at the same place and time, as the observations, they are nevertheless realistic in the temporal evolution of the cloudy packets, along the Tiete River. Paradoxically, the high vertical resolution (HVR : please recall Chapter 4) simulation is the least realistic, because it is too violent in terms of deep convection, and therefore not be examined in detail. We show that by following the plume of the overshoot for a time corresponding to the actual time of the overshoot and the time of the measurement, we can reproduce local enhancement of water vapor of the order of 0.5 ppmv to 0.7 ppmv, as measured by Pico-SDLA and FLASH-B. These enhancements are simulated on the edge of the plume. For both realistic simulations (excluding the high vertical resolution), it is shown that the vertical structure of the overshooting turret is as follows : it consists only of pristine ice, snow, for the upper part of the turret, and also aggregates for the lower part. Thus, the other two types of ice hydrometeors in the model (graupel and hail) are not present within the overshooting turret, and will not need to be forced into an upscaling work. We also show that about 60% to 70% of the mass of total ice present in the stratospheric part of the turret (above the 380 K isentropic level) is concentrated in the layers comprised of the 380 K à 385 K isentropic levels. It is also shown that the cross-section of the overshooting turret at the 380 K isentropic level has a typical surface contained within a circle of 24 km in diameter, i.e. approximately 450 km 2 . This surface almost corresponds to the horizontal grid-point size of the continental scale simulation (400 km 2 ). The analysis of the simulations also makes it possible to estimate the total amount of ice injected into the stratosphere by an overshooting cell. It typically varies between 4 kt à 6 kt, depending on the microphysical setting of the model. Once a portion of the ice has sedimented and/or has sublimated, the amount of water vapor left in the stratosphere can be estimated.

  Figure 5.1 summarizes the main results of this dissertation at different scales, and what it allows for future studies. The outlooks are also outlined in the following paragraph.

LOAD_BAL

  model using TRO-Pico campaign, and measurements from airborne and spaceborne sensors. Journal of Geophysical Research : Atmospheres, 123. https ://doi.org/10.1002/2017JD027969. -Abhinna K. Behera, and Emmanuel D. Rivière, untitled : in progress based on the work of Chapter 4 version of RAMSIN, i.e., the input file with all the defined variable for the model to start simulation, we use for REF 1 simulation, and other simulations performed during our studies, which are not very different from this RAMSIN prescription. h', ! 'h','m','s' -Time units of TIMMAX, TIMSTR TIMMAX = 24., !3906., ---> 06hrs of 20th Oct to 31st Mar 2013

NINEST! 0 !

 0 , ! Contort coarser grids if negative NSTRATZ2 = 1,1,2,1, POLELAT = -18.0, ! Latitude of pole point POLELON = -50.0, ! Longitude of pole point CENTLAT = -18.0,-22.4,-22.35, CENTLON = -50.0,-49.0,-47.75, ! Grid point on the next coarser nest where the lower southwest !corner of this nest will start. ! If NINEST or NJNEST = 0, use CENTLAT/LON !!! ATTENTION FOR THE POSITION of GRID3 goes the top or bottom of the ! coarsest nest. GRIDU = 0.,0.,0.,0., ! u-component for moving grids GRIDV = 0.,0.,0.,0., ! v-component for moving grids / !-------------------------------------------------------------Analysis nudging parameters--------------------------NUD_TYPE = 2, ! =1 -nudge from history files(1-way nest) ! =2 -nudge from varfiles ! =0 -no analysis nudging VARFPFX = '/scratch/cnt0022/pce2227/behera/BRAMS_out/new_isan/a', !'$SCRATCHDIR/BRAMS4.2/BRAMS_output/isan/a', VWAIT1 = 0.,! wait between each VFILE check (s) VWAITTOT = 0.,! total wait before giving up on a VFILE (s) NUD_HFILE = '/scratch/cnt0022/pce2227/behera/BRAMS_out/ hist/1g/a-H-2012-11-01-000000-head.txt', ! '$SCRATCHDIR/BRAMS4.2/BRAMS_output/hist/ a-H-2012-03-12-120000-head.txt', ! Header file name for history nudging files ! (only prefix is used) NUDLAT = 5,! Number of points in lateral bnd region TNUDLAT = 900.,! Nudging time scale(s) at lateral boundary TNUDCENT = 0.,! Nudging time scale(s) in center of domain TNUDTOP = 900.,! Nudging time scale (s) at top of domain ZNUDTOP = 22000.,! Nudging at top of domain above height(m) , ! Anal nudging weight for u and v WT_NUDGE_TH = 1., ! Anal nudging weight for theta WT_NUDGE_PI = 1., ! Anal nudging weight for pi WT_NUDGE_RT = 1., ! Anal nudging weight for r_tot !------------------------------------------------------------!-------------Condensate nudging ---------------------------NUD_COND = 0,! Only nudge total water where condensate ! exists (from previous history files, HFILIN) COND_HFILE = '/scratch/cnt0022/pce2227/behera/BRAMS_out/hist/ 1g/a-H-2012-11-01-000000-head.txt', ! Header file name for cond nudging history files ! (only prefix is used) TCOND_BEG=0., TCOND_END=21600., ! Model time start and end of cond nudging (sec) Relative nudging weights for active grids ! =0., turns off nudging for that grid WT_ODA_UV = 1., ! ODA nudging weight for u and v WT_ODA_TH = 1., ! ODA nudging weight for theta WT_ODA_PI = 1., ! ODA nudging weight for pi WT_ODA_RT = 1., ! ODA nudging weight for r_tot ! Following are radii that affect the "smoothness" of ! the analyzed fields. The SFCE and UPAE are the radii ! where the affect falls off to e**(-2). The SFC0 and ! UPA0 are the radii where the affect falls off to Values are grid dependent.

0 -

 0 Height at which transition from SFC radii to UPA ! radii occursRODA_ZFACT = 100.,100.,100.,100., ! Vertical factor related to dx/dz ! -Time interpolate limit (TIL)-if the future-past ! obs time is > this limit, do not use to interpolate ! -Time extrapolate limit (TEL)-if past/future obs ! is greater than TIL, but less than TEL, use the obs ----------------------------------------------------------!------------------History file input------------------------TIMSTR = 3894., ! Time of history start (see TIMEUNIT) HFILIN = '/scratch/cnt0022/pce2227/behera/BRAMS_out/hist/1g/ a-H-2013-03-31-120000-head.txt', files, 1-save ASCII, 2-save binary HFILOUT = '/scratch/cnt0022/pce2227/behera/BRAMS_out/hist/1g/a', AFILOUT = '/scratch/cnt0022/pce2227/behera/BRAMS_out/anal/1g/ar', !'$SCRATCHDIR/BRAMS4.2/BRAMS_output/anal/ar', ICLOBBER = 1, ! 0=stop if files exist, 1=overwite files IHISTDEL = 0,! 0=keep all hist files, 1=delete previous FRQHIS = 10800.,! History file frequency FRQANL = 3600., ! Analysis file frequency !--------------LITE FILES OUTPUT ---------------------------FRQLITE = 0., ! Analysis freq. for "lite" variables ! = 0 : no lite files XLITE = '/0:0/', ! nums>0 are absolute grid indexes YLITE = '/0:0/', ! nums<0 count in from the domain edges ZLITE = '/0:0/', ! nums=0 are domain edges NLITE_VARS=22, LITE_VARS='PI0','TOPTA','GLAT','GLON','TOPT','THETA', 'RV','RPP','RSP','RAP','RGP','RHP','RCP','RRP','CPP', 'CSP','CGP','CAP','CHP','CCP','CRP','WP',!---------------------------------------------------------no averaged files FRQMEAN = 0.,! Analysis freq. for "averaged" variables FRQBOTH = 0.,! Analysis freq. for Both "averaged" /scratch/cnt0022/pce2227/behera/BRAMS_out/new_sfc/top', SFCFILES = '/scratch/cnt0022/pce2227/behera/BRAMS_out/new_sfc/sfc', SSTFPFX = '/scratch/cnt0022/pce2227/behera/BRAMS_out/new_sfc/sst', NDVIFPFX = '/scratch/cnt0022/pce2227/behera/BRAMS_out/new_sfc/ndv', ITOPTFLG = 1,1,1,1, ! 2 -Fill data in "leaf3_init" No update of NDVI values during run IUPDSST = 1, ! 0 -No update of SST values during run ! 1 -Update values during run ! The following only apply for IxxxxFLG=1 ITOPTFN = '/scratch/cnt0022

DISTIM

  2/BRAMS_input/mar/NDVI_mar_',!----------------------Topography scheme--------------------table: 0 = no, 1 = yes COLTABFN = '/scratch/cnt0022/pce2227/behera/BRAMS_out/new_tables/ct2.0_M', ! Filename to read or write ! '$SCRATCHDIR/BRAMS4.2/BRAMS_output/tables/ct2.0_M', ! Filename to read or write gradient inflow and outflow ! 1 = zero gradient inflow, radiative b.c. outflow ! 2 = constant inflow, radiative b.c. outflow ! 3 = constant inflow and outflow NFPT = 0.,! Rayleigh friction: number of points from the top like Fritsch Chappel or Kain Fritsch ! AS: Arakawa-Schubert(exclusive to BRAMS) NNSHCU = 1,0,0,1,! Shallow Cumulus Param. (0-off, 1-on) CONFRQ = 900., ! Frequency of conv param. updates (s) SHCUFRQ= 900., ! Frequency of Shallow param. updates (s) WCLDBS = .0005, ! Vertical motion needed at cloud base for ! to trigger convection ! Surface layer and soil parameterization NPATCH = 2, ! Number of patches per grid cell (min=2) NVEGPAT= 1, ! Number of patches per grid cell to be filled ! from vegetation files (min of 1, max of NPATCH-1) N_CO2 = 1,! Number of CO2 tracers for use with SiB submodel CO2_INIT

!

  ,! Constant land % if for all domain(used if IVEGTFLG=2) NSLCON = 6,! Constant soil type if for all domain(used if ISOILFLG=2) 05, ! Constant roughness if for all domain ALBEDO = .2, ! Constant albedo if not running soil model SEATMP = 298.,! Constant water surface temperature (if ! ISSTFLG=2) DTHCON = 0., ! Constant sfc layer temp grad for no soil !(is ISFCL=O) DRTCON = 0., ! Constant sfc layer moist grad for no soil ! (is ISFCL=O) SOIL_MOIST = 'a', ! n => Homogeneous (standard) ! i,h,a => Heterogenous Soil Moist.Init.with file. of Heterogenous Soil Moist. file was not found, what to do? ! s => STOP the program ! h => Initialize with Homogenous Soil Moist. ! l => Looking for 5 days old files, and if ! not found again then stop. USDATA_IN = '/scratch/cnt0022/pce2227/behera/BRAMS_input/soilmoist/ GL_SM.GPNR.', ! Soil Moisture File prefix ! '$SCRATCHDIR/BRAMS4.2/BRAMS_input/soilmoist/ GPNR/2012/GL_SM.GPNR.',! Soil Moisture File prefix USMODEL_IN = '/scratch/cnt0022/pce2227/behera/BRAMS_input/soilmoist/ GL_SM.GPNR.',! File prefix with pre-calculated data by BRAMS SLZ = -2.0, -1.75, -1.50, -1.25, -1.00, -0.75, -0.50, -0temperature offset from lowest atmospheric level !------------------------------------------------------------!------Urban canopy parameterization -----------------------IF_URBAN_CANOPY =0, !------------------------------------------------------------!---------Eddy diffusion coefficient parameters --------horizontal gradient. Non-conserving, but allows small DZ CSX = .32,.32,.32,.2, ! Deformation horiz. K's coefficient (for IDIFFK=1 or 2) CSZ = .32,.32,.32,.2, ! Deformation vert. K's coefficient (for IDIFFK=1 or 2) XKHKM = 3.,3.,3.,3., ! Ratio of horiz K_h to K_m for deformation (for IDIFFK=1 or 2) ZKHKM = 3.,3.,3.,3., ! Ratio of vert K_h to K_m for deformation (for IDIFFK=2 or 3) AKMIN = 0.5,1.,1.,2., ! Ratio of minimum horizontal eddy (for IDIFF=1 or 2) ! viscosity coefficientto typical value from deformation K !------------------------------------------------------------!----------Microphysics----------------------------------one of those (except IPRIS and ICLOUD) IHAIL = 5, ! is set to 5 then the others will be set to ! 5 automatically) !------------Microphysics parameters -----------------------! Characteristic diameter, # concentration or y-intercept CPARM = 2.0e11, ! cloud (CCN concentration #/kg of air) RPARM = 0.6e-3, ! rain (if IRAIN=2 => mean diameter (m) ! ;=3 => y-intercept ;=4 => #/kg) Flags for how sounding is specified IPSFLG = 1, ! Specifies what is in PS array ! 0-pressure(mb) 1-heights(m) ! PS(1)=sfc press(mb)

  fields to be printed during the simulation !-----------------------------------NPLT = 0, ! Number of fields printed at each time ! for various cross-sections (limit of 50) IPLFLD = 'WP', ! Field names -see table below

  point slab value for third direction ! The following variables can also be set in the namelist: ! IAA, IAB, JOA, JOB, NAAVG, NOAVG, PLTIT, PLCONLO, PLCONHI, -USTARL(M/S) 'USTARW'-USTARW(M/S) 'TSTARL'-TSTARL (PRESS',! Type of first guess input-'PRESS', 'RAMS' I1ST_FLG = 1, ! What to do if first guess file should be ! used but does not exist. ! 1=I know it may not be there, skip this data time ! 2=I screwed up, stop the run ! 3=interpolate first guess file from nearest surrounding ! times, stop if unable (not yet available) do if other data files should be used, but does not exist. ! 1 = I know it may not be there, skip this data time ! 2 = I screwed up, stop the run ! 3 = Try to continue processing anyway ! Input data file prefixes IAPR = '/scratch/cnt0022/pce2227/behera/BRAMS_input/DP/dp-p/scratch/cnt0022/pce2227/behera/BRAMS_out/new_isan/a', ! check point ** ! '$SCRATCHDIR/BRAMS4.2/BRAMS_output/isan/a', IOFLGISZ = 0, ! Isen-sigz file flag: 0 = no write, 1 = write IOFLGVAR = 1, ! Var file flag: 0 = no write, 1

  of RAMS grids to analyze TOPSIGZ = 20000.,! Sigma-z coordinates to about this height HYBBOT = 4000.,! Bottom (m) of blended sigma-z/isentropic ! layer in varfiles HYBTOP = 6000.,! Top (m) of blended sigma-z/isentropic layr SFCINF = 1000.,! Vert influence of sfc observation analysis SIGZWT = 1.,! Weight for sigma-z data in varfile: ! 0.= no sigz data, ! 1.=full weight from surface to HYBBOT NFEEDVAR = 1, ! 1=feed back nested grid varfile, 0=don't !--------------------------------', ! Station ID's to be excluded ! Prefix with 'r' for rawindsonde, 's' for surface IOBSWIN = 1800, STASEP = .1, ! Minimum sfc station separation in degrees. ! Any surface observations within this distance of another observation ! will be thrown out unless it has less missing data, in which case ! the other observations will be thrown out. IGRIDFL = 3, ! Grid flag=0 if no grid point, only obs ! 1 if all grid point data and obs ! 2 if partial grid point and obs ! 3 if only grid data ! 4 all data... fast GRIDWT = .01,.001, ! Relative weight for the gridded press data ! compared to the observational data in the objective analysis GOBSEP = 2., ! Grid-observation separation (degrees) GOBRAD = 2., ! Grid-obs proximity radius (degrees) WVLNTH = 1600.,1000.,600., ! Used in S. Barnes objective analysis.

/Figure

  Figure C.1 -Cloud top Validation : 14 :00 UTC

  -1 at 17.2 km altitude at 16 :15 UTC (a), 19 :45 UTC (b) and 23 :15 UTC (c). Streamlines of the horizontal wind are also shown. The domain is a composite of grid 2 and grid 3. . . . . . . . . . . . . . . . . . . . . 4.13 REF simulation : Vertical profiles of total water content at different locations of the overshooting turret at 17.2 km from the SOC cell at 16 :15 UTC. The location are : 48.5 • W, 21.75 • S (black) ; 48.4 • W, 22.9 • S (green) ; 48.4 • W, 21.5 • S (yellow) ; 48.3 • W, 22.0 • S (magenta).133 4.14 Same as Figure 4.12, but here the plume is at 17.8 km, and followed at 16 :15 UTC, 18 :30 UTC and 20 :52 UTC, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.15 Same as Figure 4.13, but for the plume of the same SOC cell at 17.8 km altitude. The location of the profiles are : 48.8 • W, 22.05 • S (black) ; 49.0 • W, 22.15

• S (green) ; 48.9 • W, 21.1 • S (yellow), 49.

  Vertical profiles of total H 2 O content from the NU21 simulation. The profiles are extracted at different locations within the plume at 17.8 km altitude at 20 :52 UTC, from an overshoot turret penetrating the tropopause at 16 :15 UTC. The location of the profiles are : 48.7 • W, 22.3 • S (black), 48.5 • W, 22.25 • S (green) ; 49.6 • W, 22.6 • S (yellow) ; 48.45 • W, 22.35 • S (red) ; 49.1 • W, 22.4 • S (magenta). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.19 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) representing the ratio of pristine ice within the domain at 16 :15 UTC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.20 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) representing the ratio of aggregates within the domain at 16 :15 UTC. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.21 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) representing the ratio of snow within the domain at 16 :15 UTC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.22 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) representing the ratio of graupel within the domain at 16 :15 UTC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.23 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) representing the ratio of hail within the domain at 16 :15 UTC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.24 A schematic diagram for the impacting area of overshoots at 380 K isentropic layer, shown for REF simulation (a : 15 :37 UTC & b : 16 :37 UTC), and for NU21 simulation (c : 15 :30 UTC & d : 15 :52 UTC). UTC times are followed from the Table 4.1. Color contours are the representative of total ice mixing ratio, shown for only few layers starting from 0 g kg -1 à 0.1 g kg -1 . The solid arrows depict the typical size of the SOCs. . . . . . . . . . . . . . . .4.25 Mean mass flux (g m -2 s -1 ) over the domain of grid3 for REF (green) and NU21 (blue) Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @15 :00 UTC . D.2 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @15 :07 UTC . D.3 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @15 :15 UTC . D.4 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @15 :22 UTC . D.5 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @15 :30 UTC . Elle est le lieu d'interactions entre des processus complexes à différentes échelles : la convection profonde, l'ascension lente des masses d'air par chauffage radiatif au-dessus d'environ 15 km, la formation de particules de glace et les ondes atmosphériques. C'est cette ascension lente qui va en grande partie déterminer la quantité d'eau qui rentre dans la stratosphère puisque le point le plus froid rencontré par la masse d'air lors de sa montée détermine de taux de déshydratation qu'elle va subir via la formation de cristaux de glace qui sédimentent. La convection profonde peut être vue comme un ascenseur vers la TTL.C'est aussi la source principale des ondes de gravité dans ces régions. Or, vis-à-vis de la vapeur d'eau, au coeur de cette thèse, la convection profonde la plus intense peut atteindre la basse stratosphère. On parle d'overshoot stratosphérique. C'est alors a priori un processus qui mène à une hydratation de la stratosphère puisqu'il injecte de la glace dans une région souvent sous-saturée, permettant la sublimation des particules de glace donc l'augmentation de sa concentration locale. Ce rôle est montré par certaines observations locales, mais elles sont rares à l'échelle globale. Les mesures dans la stratosphère tropicales sont, de fait,

	Chapitre 1
	Advent of meteorology, climatology
	and concerns raised over
	stratospheric water vapor
	xxvii xxviii

• S (magenta). . . . . . . . . . . . . . . 4.16 Same as Figure 4.12, but for the NU21 simulation. . . . . . . . . . . . . . . . . . . . . . . . 4.17 Vertical profiles of total H 2 O from the NU21 simulation. The profiles are extracted at different locations within the plume at 17.2 km altitude at 23 :15 UTC, from an overshooting turret penetrating the tropopause at 16 :15 UTC. The locations of the different profiles are as follows : 48.5 • W, 21.75 • N (black line), 48.3 • W, 21.95 • N (green) ; 48.3 • W, 21.75 • S (yellow) ; 48.3 • W, 21.6 • S (red) ; 48.33 • W, 21.67 • S (magenta). . . . . . . . . . . . . . . . . . . . . . . xxv 4.18 simulation, calculated at 380 K isentropic surface for aggregates, graupel, hail, pristine ice, snow and water vapor, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.26 Volume of available grid-points (km 3 ) within the belt of 380 K à 430 K isentropic levels corresponding to the grid 3 of domain of simulation, shown for the REF (red) and the NU21 (blue) simulation. Ordinate represents the absolute volume, no normalization is done. . . . 4.27 Mass budget (kt) of total five ice hydrometeors and water vapor within 380 K à 430 K isentropic surface, shown for the REF and NU21 simulation. Blue is for total ice, red is for water vapor, black is for sum of both ice and vapor. . . . . . . . . . . . . . . . . . . . . . . 5.1 Résumé des principaux résultats de la thèse et ses perspectives à différentes échelles. Les caractères en italique font référence aux travaux futurs. Summary of the main results of the thesis and its outlooks at different scales. The italic characters refer to the future work. . . D.1 D.6 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @15 :37 UTC . D.7 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @15 :45 UTC . D.8 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @15 :52 UTC . D.9 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @16 :00 UTC . D.10 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @16 :07 UTC . D.11 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @16 :15 UTC . D.12 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @16 :22 UTC . D.13 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @16 :30 UTC . D.14 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @16 :37 UTC . D.15 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @16 :45 UTC . D.16 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @16 :52 UTC . D.17 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @17 :00 UTC . D.18 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @17 :07 UTC . D.19 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @17 :15 UTC . D.20 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @17 :22 UTC . D.21 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @17 :30 UTC . D.22 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @17 :37 UTC . D.23 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @17 :45 UTC . D.24 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @17 :52 UTC . D.25 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @18 :00 UTC . D.26 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @18 :07 UTC . D.27 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @18 :15 UTC . D.28 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @18 :22 UTC . D.29 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @18 :30 UTC . D.30 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @18 :37 UTC . D.31 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @18 :45 UTC . D.32 Horizontal cross-sections (within 15.4 km à 18.8 km altitude) of the domain @18 :52 UTC . Dans ce chapitre, nous reprenons plus en détail les concepts présentés dans l'introduction générale. Des éléments fondateurs de la météorologie sont d'abord rappelés. Nous nous focalisons ensuite sur la météorologie tropicale, avec notamment, le rôle des cellules de Hadley, et des jets subtropicaux. Nous décrivons également d'autres éléments de la météorologie tropicale tels que la zone de convergence intertropicale (ITCZ) et la circulation zonale de Walker permettant d'expliquer le lien entre des conditions climatiques particulières de régions pourtant éloignées l'une de l'autre. Nous nous focalisons ensuite sur l'historique des recherches stratosphériques, depuis la découverte de la couche d'ozone, son rôle, puis la découverte de sa destruction aux milieux des années 1980. Nous décrivons très brièvement les raisons de cette destruction liée notamment à l'entrée dans la stratosphère de composés chlorés et bromés, et à l'existence de réactions chimiques hétérogènes à la surface des nuages stratosphériques qui ne peuvent se former que dans les conditions très froides de la stratosphère arctique ou antarctique. Principal ingrédient des nuages stratosphériques polaires et de radicaux OH, la vapeur d'eau stratosphérique est présentée pour son rôle chimique et radiatif. Alors que peu à peu, après l'interdiction des sources halogénées stratosphériques, la destruction de la couche d'ozone se réduit, la priorité des recherches stratosphériques est désormais l'étude des régions tropicales. S'il est admis que les régions intertropicales sont la zone d'entrée des masses d'air vers la stratosphère, toute espèce rentrant dans la stratosphère par ces régions peut alors éventuellement jouer un rôle sur l'équilibre chimique de la couche d'ozone. Nous décrivons alors certains processus dynamiques de la stratosphère tropicale tels que la circulation de Brewer-Dobson permettant une ascension lente jusque dans la haute stratosphère puis un export vers les plus hautes latitudes où l'air subside. Nous commentons également l'oscillation quasi-biennale (QBO), c'est-à-dire un changement de direction du vent zonal stratosphérique près de l'équateur avec une période d'environ 27 -29 mois. La QBO est une source de grande variabilité d'espèces stratosphériques dans cette région. Nous discutons également du rôle radiatif de la vapeur d'eau, particulièrement important dans la basse stratosphère tropicale. Nous présentons enfin une région clé autour de la tropopause tropicale appelée TTL entre typiquement 14 km et 19 km d'altitude. C'est une région de transition entre la haute troposphère et la basse stratosphère tropicale. limitées par les faibles possibilités de plateforme (principalement avion et ballon) permettant d'y accéder in situ. Nous présentons quelques campagnes passées ayant permis de mieux connaître la composition de la basse stratosphère tropicale et les processus qui s'y déroulent. A l'échelle globale, les observations satellitales vont permettre d'obtenir une vision d'ensemble de l'état de la stratosphère tropicale. Cependant, elles ne permettent pas de renseigner sur le rôle de certains processus se déroulant à petite échelle, limitant la connaissance de leur rôle à grande échelle. C'est le cas notamment des overshoots stratosphériques au coeur de cette thèse. Alors qu'ils sont détectables par satellites (observation par sondeurs micro-onde ou par radars/lidars embarqués), leur impact sur la vapeur d'eau n'est pas identifiable au cas par cas, à cause de la trop faible résolution (ou précision) des sondeurs de vapeur d'eau. Ainsi l'approche de modélisation

  atmosphere, viz., N 2 , O 2 , CO 2 , water vapor and other trace gases (comprise ∼0.1% of the atmosphere), and their composition in the atmosphere. The primeval Earth's atmosphere was supposedly a mixture of CO 2 , N 2 , H 2 O, trace amount of H 2 and a composition of gases released by present-day volcanos

  that originates from the ATMET (ATmospheric, Meteorological, and Environmental Technologies) and Colorado State University (CSU). There is a recent release of a new version of BRAMS model (latest version -5.2) [Freitas et al., 2017] from CPTEC/INPE. Since we have started working with the version -4.2 BRAMS model, our work in this dissertation doesn't incorporate the version -5.2. One can find other extensive applications of the BRAMS mesoscale model in http:

(

  European Centre for Medium-Range Weather Forecasts) operational analyses data are used for model grid-point initialization and grid-boundary conditions, and are nudged every 6 h of the real-time simulation. Here, we incorporate the ECMWF data in its pressure levels, having only 5 levels within the UTLS, viz., 150 hPa, 100 hPa, 70 hPa, 50 hPa et 30 hPa. Then, the incorporation of GDAS (Global Data Assimilation System) analysis available in GRIB (Gridded Binary data files) format containing the state of the atmosphere on a Gaussian grid assists further the model for the initial and boundary conditions. It

requires the 'GeraDP' software (grib2dp application) for converting them into BRAMS DP format (see http://brams.cptec.inpe.br/input-data/). Furthermore, ISAN (ISentropic ANalysis package)

Table 2 .

 2 2 -Options for the Bulk (micro) physics used in the simulations.

	Microphysical scheme	Meyers et al. [1997] -Double moment
	Meteorological fields initialization	ECMWF operational analysis
	Deep convection parameterization	Grell and Dévényi [2002]
	Shallow convection parameterization	Souza et al. [2000]
	Closure type	ENSEMBLE
	Land surface model	Sellers et al. [1996b,b]
	Lateral boundary condition (normal velocity)	Klemp and Wilhelmson [1978]
	Short/long wave parameterization	Harrington [1997]
	Boundary condition	Zero-gradient inflow/outflow

Table 2 .

 2 3 -Technical specifications used for the simulations.

	Number of nodes required for simulation	2 -3
	Total number of processors	48 -72
	Memory (RAM) required per processor (single core) 3000 -5000 MB
	Number of thread(s) per processor	1
	Number of task(s) per processor	1
	Number of thread(s) per node	24
	2.2

TRO-Pico Campaign and Instrumental Payloads

Table 2 .

 2 The TRO-Pico campaign built a contemporary sets of observational data on meteorology, but on two different time scales, viz., full wet season of November, 2012 to March, 2013, hereafter denoted as five months of observation period (FMOP), and the intensive observation periods (IOP) for most active convective sessions, i.e.,March, 2012 (IOP1) and January toFebruary, 2013 (IOP2).The crux of this campaign is the water vapor measurements by balloon-borne Pico-SDLA and FLASH-B hygrometers, and temperature and wind velocity measurements by RS92 radiosondes.The first phase campaign took place during the convective period of March 2012 (IOP1), and the second phase was during November 2012 to March 2013 (FMOP) at Bauru (22.31 • S, 49.05 • W), respectively, which is situated about 330 km west of São Paulo, Brazil. Being located near the South Atlantic convergence zone, Bauru is one of the most severe convective places in Southern hemisphere during the wet season[Kent et al., 1995, Liu and[START_REF] Liu | Global distribution of convection penetrating the tropical tropopause[END_REF]. This field campaign project consists of small balloon campaigns of 500 m 3 à 1500 m 3 open balloons, or 1.2 kg rubber balloons, and were launched with light-weight apparatuses as close as possible to the severe convective events. During the FMOP, regular H 2 O mixing ratio and temperature measurements were carried out, which are not specifically related to the deep convective events. This campaign also provides the meteorological data sets of tracers of horizontal and vertical transport, viz., aerosols and particles, CO 2 , NO 2 , CH 4 and O 3 . During the IOPs, apparatuses were flown for the measurements of the CO 2 , NO 2 , CH 4 , O 3 , and aerosols, and concurrently, PTU radiosondes were also launched. During the whole campaign, total 37 balloons were launched, while 34 of them measured the water vapor in the TTL and the lower stratosphere. The field project is tabulated briefly in Table2.4 representing the apparatuses flew and the corresponding tracers measured. All the measurements were conducted then with the collaboration of the Institute of Meteorological Research (IPMet) of the state of São Paulo, Brazil. It is noteworthy that the presence of S-band radar to monitor thunderstorms at Bauru makes it a very suitable location for balloon launching. Below we present the main apparatuses used in the field campaign.In Table2.4, we represent all the instruments flew during the TRO-Pico campaign at two different phases. Our work comprises of only H 2 O mixing ratio retrieved from the stratospheric hygrometers, i.e., Pico-SDLA and FLASH-B laser spectrometers. Among other important apparatuses flew in the TRO-Pico project, the mini systèm d'analyse par observations zenithales (SAOZ) provides the measurements of O 3 , H 2 O, and NO 2 mixing ratios. This spectrometer is developed at the service d'aéronomie (SA, now it is LATMOS), CNRS. Its working principle is based on the solar occultation 3 . The spectrometer covers the near-IR spectral region to provide the measurements of O 3 , H 2 O, and aerosols. Similarly, 4 -Table representing the list of apparatuses flew (center column) and the corresponding dates (left column) and tracers measured (right column), respectively, during the TRO-Pico campaign.

the compact optical backscatter aerosol detector (COBALD), developed at the Swiss federal institute of technology in Zurich (ETHZ), is a backscattering sonde. It incorporates two wavelengths, viz., 455 nm and 870 nm, for detecting the backscattered light from aerosols and cloud droplets. The aerosol particle size

Table 2 .

 2 Radio sounding measurements from the database of Wyoming University (see http://weather.uwyo.edu/ upperair/sounding.html) are gathered on daily basis for the FMOP (two measurements a day corresponding to 00 :00 UTC and 12 :00 UTC), mostly for six stations in South America falling in our domain of interest (please see Chapter 3.2). The stations are chosen depending on the regular availability of data during the FMOP and are evenly distributed nearby Bauru (22.31 • S, 49.05 • W). They are tabulated in Table2.5. 5 -List of radio sounding stations : upper-air radio soundings data with corresponding locations and the duration of measurements.

	Station Name Latitude Longitude	Duration
	SBAT	9.86 • S	56.10 • W	November, 2012
	SBFI	25.51 • S	54.58 • W	December, 2012
	SBCY	15.65 • S	56.10 • W	November to December, 2012
	SBGL	22.81 • S	43.25 • W	March, 2013
	SBBR	15.86 • S	47.93 • W	January to March, 2013
	SBCT	25.51 • S	49.16 • W	January to March, 2013

Table 3 .

 3 1 -Options used in the simulations (highlights of RAMSIN).

	Nudging points in lateral boundary region	4
	Nudging time scale(s) at lateral boundary	900 s
	Nudging time scale(s) at center of domain	0 s -no nudging
	Nudging time scale(s) at top boundary	900 s
	Nudging at top of domain above height	22 000 m
	Phase speed of internal gravity waves	20 m s -1
	Time step of integration	2 s à 30 s
	Frequency of radiation tendency update(s)	900 s à 1200 s
	Frequency of convective parameters updates(s)	900 s
	Frequency of shallow parameters updates(s)	900 s
	Number of soil layers	7
	Number of snow layers	1
	Microphysics	5 (prognostic concentration)

The REF 0 simulation covers the convective season of November 1, 2012, to March 31, 2013 (Five Months of Observation Period : FMOP) of South America. The domain of the simulation encompasses the latitudes from 15 • S -30 • S and longitudes from 40 • W -59 • W. Here, the horizontal grid-point resolution is 20 km × 20 km, and the vertical grid-points constitute of 68 levels from surface to 30 km altitude having ∼300 m of resolution at 14.0 km à 18.5 km range of altitude. For the grid-boundary condition and initialization, the ECMWF operational analyses data are used to nudge the model every 6 h of the realtime simulation during the FMOP. The ECMWF data are incorporated into pressure levels. Here, a 5 km sponge layer at the top of the domain is chosen to damp the gravity waves (recall Chapter 2.1). The model output (analyses) files have a time resolution of 1 h during the FMOP. The bulk microphysics and other modules, settings incorporated in the simulation can be found in

Table 2.2 and Table 3.1. In case of any different settings adapted for certain parameters in REF 0 simulation, they are commented in the subsequent sections.

Modeling the TTL at Continental Scale for a Wet Season : An Evaluation of the BRAMS Mesoscale Model Using TRO-Pico Campaign, and Measurements From Airborne and Spaceborne Sensors Abhinna

  K. Behera 1 , Emmanuel D. Rivière 1 , Virginie Marécal 2 , Jean-François Rysman 3 , Chantal Claud 3 , Geneviève Sèze 4 , Nadir Amarouche 5 , Mélanie Ghysels 1 , Sergey M. Khaykin 6 , Jean-Pierre Pommereau 6 , Gerhard Held 7 , Jérémie Burgalat 1 , and Georges Durry 1

	Journal of Geophysical Research -Atmosphere (2018)

  .9d), viz., Alta Floresta (SBAT : 9.86 • S, 56.10 • W), Curitiba (SBCT : 25.51 • S, 49.16 • W), Foz do Iguaçu (SBFI : 25.51 • S, 54.58 • W), Brasilia (SBBR : 15.85 • S, 47.93 • W), Couiabá (SBCY : 15.65 • S, 56.10 • W) and Galeão/Rio de Janeiro (SBGL : 22.81 • S, 43.25 • W).

  have shown a relative difference of H 2 O mixing ratio <1.9% between Pico-SDLA and FLASH-B in the TTL, based on a couple of coincident flights during the TRO-Pico campaign. This constitutes one of the best inter-comparison results of WV sensors, making it a fully consistent dataset. S to 19.00 • S and 55.50 • W to 43.50 • W. As Aura is a sunsynchronous satellite, depending on the local time and pressure level, MLS H 2 O measurement precision can vary in the UTLS, and is more reliable at monthly and seasonal time scales. Version 4.2 of H 2 O measurement tends to possess dry biases of >20% at the tropopause level. A full technical description of the MLS : version 4.2 can be found in Livesey et al. [2015] and Yan et al. [2016].

	MLS
	Satellite-borne aura Microwave Limb Sounder (MLS : version 4.2) WV measurements are used for the
	FMOP around Bauru, i.e., a domain of 24.00 •

Table 3 .

 3

	SBAT	0.705	1.68	-0.319	3.445
	SBCT	0.855	1.31	-0.600	2.407
	SBFI	0.700	2.09	-0.589	2.188
	SBBR	0.958	1.57	-0.803	2.068
	SBCY	0.877	1.85	-0.441	1.828
	SBGL	0.877	1.34	-0.216	2.613

2 -Biases in CPT altitude (z) and temperature (T).

Stations σ(δz) (km) σ(δT) ( • C) Xz (km) XT ( • C)

Table 3 .

 3 3 -Comparison of the wave parameters derived from hodograph analysis of the RS92 measurements and the simulation for January 28 and February 08, 2013.

	Cases/profiles	a b	N B (s -1 ) λ z (m) v (m s -1 ) λ h (km) T (h)
	21 :00 UTC 28/01/13 -RS92	1.2800	0.0200	2800	0.63	1264	25.8
	12 :00 UTC 28/01/13 -BRAMS 1.1624	0.0189	2400	2.87	1389	23.2
	20 :00 UTC 08/02/13 -RS92	2.3709	0.0200	2520	-11.05	398	40.8
	09 :00 UTC 08/02/13 -BRAMS 1.9872	0.0192	2440	-3.61	457	30.4

Table 4 .

 4 1 summarizes the number of SOCs cells above 17 km in the period from 14 :00 UTC to 18 :30 UTC on March 13, 2012. It shows that the REF simulation has a comparable number of SOC cells as the observation, albeit slightly higher. However, deep convection in the model remains active after 18 :30 UTC, while the radar observations show a decay in deep convection from that point of time. Investigating the time evolution of the cloud clusters (see Appendix C for the full-time evolution of the case study), we note first that the location of the main convective activity is located further north in the model (typically 50 km à 60 km north/northwest). Secondly, the time evolution of the convective clusters shows that they are moving north/northwest in both cases, and most of the convective activity remains west of the Tiete river in both cases. All these aforementioned elements make this REF simulation realistic with respect to the radar observation.NU21 Simulation A similar approach of comparison is made here to evaluate the NU21 simulation.As shown in the full-time evolution of cloud tops against radar images (see Appendix C), it is noted that deep convection is triggered earlier in the REF simulation.

Table 4 .

 4 1 -Time of the SOC events and their altitudes range for the radar observations, the REF, and the NU21 simulation, respectively. Results are given in UTC time and altitudes in km. The altitude corresponds to the minimum altitude within a 1 km thick layer.

	RADAR (in UTC and km) REF (in UTC and km) NU21 (in UTC and km)
	16 :08 ->19	15 :37 ->17	15 :07 ->18
	16 :23 ->17	16 :15 ->17	15 :07 ->18
	16 :46 ->19	16 :15 ->18	15 :30 ->19
	16 :53 ->18	16 :37 ->18	15 :52 ->19
	16 :53 ->19	16 :37 ->18	18 :37 ->17
	17 :08 ->18	16 :52 ->17
	17 :08 ->18	17 :37 ->17
	17 :38 ->19	17 :45 ->17
		18 :07 ->19
		18 :30 ->17
	HVR Simulation The HVR simulation is different from both the REF and the NU21 simulations,

  2 O were measured by FLASH-B and Pico-SDLA (17.2 km and 17.8 km -see Figure 4.2). At the same Δt om after the modeled overshoot appears, the modeled vertical profiles of water vapor are extracted at a different location of the plumes. REF Simulation In order to validate the local H 2 O enhancement at 17.2 km altitude, measured by FLASH-B at 23 :45 UTC due to a SOC cell at 16 :46 UTC (Δt om = 7 h), the time evolution of the plume from the BRAMS SOC cell at 16 :15 UTC is followed at 17.2 km until 16 :15 UTC + Δt om , which is 23 :15 UTC.

  Figure 4.15 shows the vertical profiles of total H 2 O content for the REF simulation at different locations of the plume about 4 h 22 min after the overshoot of 16 :15 UTC. For most of the profiles, the H 2 O enhancement relative to an unperturbed profile (the red one) at 17.8 km altitude is due to a large enhancement below 17.8 km. However, at 48.9 • W, 22.0 • S, a local maximum of H 2 O is seen by the model (magenta profile). Again, no ice is computed in this part of the plume, which is in agreement with the COBALD and LOAC measurements. The 0.7 ppmv local enhancement at 17.8 km is thus fully compatible with the H 2 O enhancement measured at the same altitude by Pico-SDLA (0.65 ppmv) and FLASH (0.55 ppmv), respectively. NU21 Simulation We incorporate the same method, as applied for the REF simulation SOC cell tracking, on the NU21 simulation. The modeled SOC at 16 :15 UTC is also chosen for this study. Firstly, we consider the overshooting turret at 17.2 km, and we follow the SOC cell until 16 :15 UTC + Δt om , that is 23 :15 UTC (Δt om = 7 h from the observed overshoot to the FLASH measurement). The plume time evolution is shown in Figure 4.16. The plume spread horizontally, slightly southeastward and finally northward, where most of the original plume is north to 22.4 • S and east to 48.8 • W at 23 :15 UTC. The vertical profiles of total H 2 O are extracted at different locations within the plume and are shown

	simulation starting from 16 :15 UTC until 20 :52 UTC makes a comparable Δt om while extracting the
	modeled H 2 O profiles. Figure 4.14 shows the overshoot plume (total water) at 16 :15 UTC, 18 :30 UTC
	and 20 :52 UTC, respectively, corresponding to 17.8 km altitude.

Table 4 .

 4 3 -Percentage (%) of mass of individual ice hydrometeors within 380 K à 385 K isentropic levels, firstly with respect to the corresponding total mass (ρ 1 ), and secondly with respect to the total ice mass (ρ 2 ), within 380 K à 430 K isentropic levels. Results are given for total four different cases corresponding to the REF and the NU21 simulation, two cases from each simulation, respectively.The first inference drawn by observing the values of ρ 1 from Table4.3 could be the fact that most of the mass injected by overshooting turrets lie within a very thin layer of 380 K à 385 K isentropic levelsabout 72% of total ice in REF simulation and 65% in NU21 simulation, respectively. Secondly, the values corresponding ρ 2 put to the fore the conclusion of section 4.4.1 that is the overshooting turret is mostly comprised of pristine ice, snow, and little amount of aggregates, aggregates being present at the base of the turret. Putting together the values of ρ 2 with the results shown in Table

	Cases	Aggregates Graupel ρ 1 , ρ 2 ρ 1 , ρ 2	Hail ρ 1 , ρ 2	Pristine ρ 1 , ρ 2	Snow ρ 1 , ρ 2
	15 :37 UTC -REF	70 (34.6)	74 (3.9)	81 (0.2)	69 (22.0) 68 (9.25)
	16 :37 UTC -REF	71 (2.64)	78 (0.11) 83 (2 × 10 -5 ) 61 (49.2) 56 (12.5)
	15 :30 UTC -NU21	60 (13.5)	63 (2.62)	71 (0.31)	60 (33.80) 56 (8.84)
	15 :52 UTC -NU21	64 (6.58)	69 (0.52) 83 (6 × 10 -5 ) 62 (45.07) 56 (9.08)

  Ce travail de thèse a pour thème principale les échanges d'eau entre la troposphère et la stratosphère en régions tropicales. La vapeur d'eau a en effet un impact radiatif important dans cette région de l'atmosphère, et elle joue également un rôle important dans l'équilibre chimique de la couche d'ozone. Parmi A l'échelle locale, le but est de simuler plusieurs overshoots stratosphériques pour déduire un impact typique des overshoots. Cet impact typique pourrait être forcé à dans la simulation de grande échelle à chaque fois qu'un satellite (notamment MHS) détecte un overshoot dans la région et la période de simulation continentale. Il nous faut donc extraire de ces simulations à fine échelle, les grandeurs typiques (en particulier les bilans de masse de glace) qui pourrons nous aider à déterminer la façon de forcer l'impact des overshoots stratosphériques dans la simulation continentale. Les mesures de la campagne TRO-Pico ont également servi à valider nos simulations.Nous pouvons résumer les principaux résultats de la thèse comme suit : A l'échelle continentale, la simulation de la saison humide 2012-2013 d'une grande partie de l'hémisphère sud brésilien sans prendre en compte les overshoots, a tout d'abord montré une assez bonne faculté du modèle à reproduire la variabilité de la structure thermique de la TTL observée par plusieurs séries de radiosondage pendant la saison humide. C'est aussi vrai dans la région de Bauru que dans d'autres sites brésiliens où des radiosondages sont effectués régulièrement. La fin janvier début février 2013 est marquée par une période extrêmement froide. On fait le lien avec un épisode de réchauffement stratosphérique soudain en arctique induisant un refroidissement un peu plus tard en régions tropicales. Cette tendance est également mise en évidence par la simulation. Ces bonnes tendances du modèle sont en grande partie expliquées par le fait que les analyses Il est intéressant de noter que la période la plus froide correspond à la période la plus sèche, à la fois pour BRAMS et pour les observations. On montre que le biais chaud et humide du modèle suit quantitativement l'évolution de la pression de vapeur saturante avec la température. Ainsi, la période la plus sèche et froide de la saison humide serait en très grande partie gérée par la déshydratation des masses d'air lors du passage à travers les températures les plus froides rencontrées lors de l'ascension vers la stratosphère. D'autre part, le fait que la simulation sans overshoot stratosphérique reproduise assez bien la variabilité temporelle de la vapeur d'eau dans la TTL confirme que les overshoots ne sont pas la cause majeure de cette variabilité, plutôt liée à des processus de grande échelle. Là encore, les analyses ECMWF suivent correctement la variabilité temporelle de la vapeur eau, même si celles-ci sont également plus humide que les observations sur les niveaux de pression qui nous servent à forcer le modèle BRAMS. Nous nous sommes également intéressés à la faculté du modèle à reproduire l'altitude des nuages avec la bonne sondeur satellitale micro-onde MHS détecte des overshoots (non nécessairement stratosphériques).Enfin les ondes d'inertie-gravité qui avait été mises en évidence par la série de radiosondage de Bauru pendant la campagne TRO-pico ont été étudiées. On montre pour deux dates différentes des paramètres d'ondes très similaires pour BRAMS et pour les observations. Ces ondes sont de grandes longueurs d'onde horizontales, et sont partiellement résolues par les analyses ECMWF. Le modèle est néanmoins capable de reconstruire les bonnes harmoniques non résolues par ECMWF. Une analyse de Fourrier des ondes dans BRAMS montre des fréquences d'onde typiques de ce qui a déjà été observé dans la littérature. En conclusion, le modèle BRAMS décrit très correctement la TTL et pourra servir d'outil pour des études futures d'upscaling du rôle des overshoots.Au niveau de l'échelle locale, le cas du 13 mars 2012 (première période intensive de la campagne TRO-Pico) a été modélisé. Ce cas présente plusieurs cellules d'overshoots stratosphériques, d'intensité variable.Il permet donc, par la modélisation, de quantifier l'impact typique de ces différentes cellules, et donc de l'impact moyen d'un overshoot stratosphérique isolé. Trois simulations à fine échelle du même cas ont été réalisées en faisant varier soit les réglages microphysiques, soit la résolution verticale du modèle par rapport à une simulation de référence. Il s'agissait de simulation à 3 grilles imbriquées dont les résolutions horizontales étaient de 20 km, 4 km, et 800 m. Les simulations ont été validées par les observations du radar Bande-S de l'IPMET à Bauru, et par les mesures de vapeur d'eau par Pico-SDLA et FLASH le pas besoin d'être forcé dans une optique d'upscaling. Je montre également que 60% à 70% de la masse de glace présente dans la partie stratosphérique du dôme (au-dessus du niveau isentrope 380 K) est concentrée dans la couche entre les niveaux isentropes 380 K à 385 K. On montre également que la section du dôme d'overshoot au niveau isentrope 380 K a une surface typique contenue dans un domaine de 24 km de diamètre, soit environ 450 km 2 , c'est-à-dire une surface correspondant pratiquement à la maille de la simulation à l'échelle continentale (400 km 2 ). L'analyse des simulations a également permis de déduire une estimation de la quantité totale de glace injectée dans la stratosphère par une cellule d'overshoot. Elle varie typiquement entre 4 kt et 6 kt, selon le réglage microphysique. Une fois qu'une partie de la glace a par rapport aux cas africains. La Figure5.1 résume les principaux résultats de cette thèse à différentes échelles et ce qu'elle permet pour des études futures. Elle présente également les perspectives exposées dans le paragraphe suivant.

	5.1 Conclusion
	connaissons à l'échelle du nuage. Pour ce faire, j'ai conduit des simulations numériques à deux échelles
	différentes avec le modèle méso-échelle BRAMS.
	-A l'échelle continentale, ce qui constitue le canevas principal de ce travail, j'ai mis en oeuvre une si-
	mulation complète d'une saison humide, avec une résolution horizontale qui impose que la convection
	profonde soit paramétrée, empêchant ainsi toute possibilité de simuler des overshoots stratosphé-
	riques qui se déroulent à des échelles inférieures. Le but était de montrer que le modèle BRAMS
	était un outil pertinent pour simuler la TTL de manière réaliste pendant toute une saison humide
	et ainsi, de montrer que BRAMS pourrait être utilisé pour des études d'upscaling. La campagne

l'ensemble des processus jouant un rôle sur l'entrée d'eau dans la stratosphère tropicale, nous nous focalisons sur les overshoots, et en particulier, les overshoots stratosphériques, c'est-à-dire les pénétrations convectives qui atteignent la basse stratosphère. Ils sont relativement rares au regard de l'ensemble de l'activité convective tropicale, mais leur nombre total n'est pourtant pas négligeable. Or, si l'on pense que la quantité d'eau à la tropopause tropicale est essentiellement due aux températures les plus froides rencontrées par les masses d'air lors de leur ascension lente vers la stratosphère (assèchement par condensation solide puis sédimentation), les overshoots stratosphériques pourraient partiellement limiter cet assèchement dans le bilan total. Cependant, nous ne savons pas encore bien quantifier le rôle de ces overshoots à l'échelle globale, essentiellement parce que leur signature à grande échelle est indétectable par les satellites. Le but de ma thèse est d'avancer dans la quantification du rôle des overshoots à grande échelle. L'approche que nous voulons développer est l'extrapolation à grande échelle (upscaling en anglais) du rôle que nous leur de mesure sous petits ballons du projet TRO-Pico pendant toute une saison humide, et pendant deux saisons purement convectives a été le cadre instrumental de cette thèse, permettant de valider les résultats du modèle pendant cette période. Nous nous sommes particulièrement intéressés à la structure thermique de la TTL et son évolution temporelle, la variabilité de la vapeur d'eau, la convection profonde à travers l'étude des sommets de nuage, et les ondes de gravité, tous ces paramètres/processus pouvant influencer l'abondance de vapeur d'eau stratosphérique.

opérationnelles d'ECMWF servant à forcer le modèle aux limites du domaine de simulation, prennent correctement en compte ces variabilités, avec cependant, pour cette période, un biais chaud, comme dans le cas de la simulation BRAMS. Une autre raison possible pour laquelle BRAMS est plus chaud que les observations est l'absence de prise en compte des overshoots dans le modèle. Ces derniers pourraient être une source de refroidissement pseudo-adiabatique.

La variation de vapeur à Bauru, lieu de la campagne TRO-pico, est également comparée à la série de profils des hygromètres Pico-SDLA et FLASH. On montre une variabilité tout à fait comparable entre observation et modèles, avec néanmoins, des minimums de rapport de mélange plus humide pour le modèle que pour les observations. position. Les résultats ont été comparés à un produit issu des mesures du satellite géostationnaire GOES-12. Des coefficients de corrélation (de -1 à 1) ont été calculés pour toute la saison humide sur les champs de sommet de nuage. Une corrélation moyenne de +0.3 est calculée, avec des meilleurs accords pour les heures les plus et les moins convectives de la journée (absence de convection, et phase mure de la convection).

On montre également qu'en grande partie, le modèle est capable de former les nuages les plus hauts là où le même jour. Si les cellules d'overshoots modélisées ne se forment pas exactement au même endroit et à la même heure que les observations, elles sont néanmoins réalistes dans la séquence temporelle, et dans l'évolution temporelle des paquets nuageux, le long de la rivière Tiete. Paradoxalement, la simulation à haute résolution verticale est la moins réaliste, car trop violente en termes de convection profonde et ne sera pas examinée en détail. On montre qu'en suivant le panache de l'overshoot pendant une durée qui correspond entre l'heure réelle de l'overshoot et l'heure de la mesure, on arrive à reproduire des augmentations locales de vapeur de l'ordre de 0.5 ppmv à 0.7 ppmv, comme l'ont mesuré Pico-SDLA et FLASH. Ces augmentations sont modélisées sur le bord du panache. Pour les deux simulations réalistes, on montre que la structure verticale du dôme d'overshoot est la suivante : il est composé uniquement de glace primaire, de neige, pour la partie haute, et d'agrégats également pour la partie basse. Ainsi les deux autres types hydrométéore de glace du modèle (grésil et grêle) ne sont pas présents dans le dôme et n'auront sédimentée et/ou a sublimé, on peut estimer la quantité de vapeur d'eau qui reste dans la stratosphère. Elle varie entre 330 t et 1400 t pour la simulation REF et entre 750 t et 2000 t pour la simulation NU21. Ainsi les estimations varient d'environ 30% selon les réglages du modèle, mais elles sont quoiqu'il arrive supérieures à d'autres estimations pour des cas d'overshoot en Afrique de l'ouest avec le même modèle. La présente étude bénéfice cependant d'une campagne de mesure permettant de mieux évaluer le réalisme des simulations

  Cette thèse a néanmoins permis de définir un canevas et un matériel précieux pour des études futures d'upscaling. Nous bénéficions d'une climatologie d'overshoots par MHS pendant la saison humide d'étude dont on sait que typiquement 50% des overshoots pénètrent dans la stratosphère. Nous savons que 4 kt à 6 kt de glace sont injectées au-dessus du niveau 380 K à travers des surfaces de taille comparable à la taille de la maille de 20 km que nous utilisons pour les simulations continentales. Reste à déterminer la façon d'injecter ce flux et cette quantité de glace dans le modèle BRAMS. Nos études futures au GSMA iront dans ce sens. Dès que le schéma de forçage sera réalisé et testé, la simulation en forçant les overshoots stratosphérique sera mise en oeuvre. Le bilan de vapeur d'eau stratosphériques sera réalisé pour les deux simulations pendant la saison humide. On pourra alors estimer par cette différence le rôle des overshoots à l'échelle continentale sur le bilan de l'eau stratosphérique.

  '$SCRATCHDIR/BRAMS4.2/BRAMS_input/topo10km/H', ISSTFN = '/scratch/cnt0022/pce2227/behera/BRAMS_input/sst/W', '/scratch/cnt0022/pce2227/behera/BRAMS_input/sst/W', '/scratch/cnt0022/pce2227/behera/BRAMS_input/sst/W', !'$SCRATCHDIR/BRAMS4.2/BRAMS_input/sst/2012/W',

	IVEGTFN = '/scratch/cnt0022/pce2227/behera/BRAMS_input/GL_OGE_INPE/OGE',
	'/scratch/cnt0022/pce2227/behera/BRAMS_input/GL_OGE_INPE/OGE',
	'/scratch/cnt0022/pce2227/behera/BRAMS_input/GL_OGE_INPE/OGE',
	ISOILFN = '/scratch/cnt0022/pce2227/behera/BRAMS_input/GL_FAO_INPE/FAO',
	'/scratch/cnt0022/pce2227/behera/BRAMS_input/GL_FAO_INPE/FAO',
	'/scratch/cnt0022/pce2227/behera/BRAMS_input/GL_FAO_INPE/FAO',
	!'$SCRATCHDIR/BRAMS4.2/BRAMS_input/GL_FAO_INPE/FAO',
	NDVIFN = '/scratch/cnt0022/pce2227/behera/BRAMS_input/mar/NDVI_',
	'/scratch/cnt0022/pce2227/behera/BRAMS_input/mar/NDVI_',
	'/scratch/cnt0022/pce2227/behera/BRAMS_input/mar/NDVI_',
	!'$SCRATCHDIR/BRAMS4.

/pce2227/behera/BRAMS_input/topo10km/H', '/scratch/cnt0022/pce2227/behera/BRAMS_input/topo10km/H', '/scratch/cnt0022/pce2227/behera/BRAMS_input/topo10km/H', !

In meteorology, 'isohyets' depicts a line on a map connecting points having the same amount of rainfall in a given period.

Rudolf Oskar Robert Williams Geiger, a German meteorologist, was the first to coin this term 'micro-climatology'the study of the climatic conditions within a few metres of the ground surface.

The term 'prognostic' is given to those variables that can be directly calculated by the model, such as temperature, different types of hydrometeors, i.e., the variables which can be obtained as a direct model outcome. While there are some other variables that need to be calculated separately as derived variables, such as relative humidity, which may be a 'diagnostic' variable obtained from the calculated 'prognostic' variables, viz., temperature and water vapor.

The Brunt-Väisälä frequency or buoyancy frequency is the angular frequency at which a vertically displaced air mass will vibrate inside a static and stable environment. It is named after David Brunt and Vilho Väisälä.

A method developed for measuring the vertical profiles of atmospheric optical depth from the Earth's orbit using the Sunlight as a source.

H 2 O December 05, 2012 December 15, 2012 December 20, 2012

sur l'abondance de la vapeur d'eau dans la TTL (ici, la température, la vapeur d'eau, les nuages convectifs, et les ondes de gravité). Pour évaluer le modèle, on simule toute une saison humide dans une grande partie de hémisphère sud du Brésil dans avec un domaine monogrille à 20 km de résolution horizontale. Cette résolution ne permet pas la modélisation des overshoots stratosphériques, dont la taille est typiquement de 1 km 2 à 4 km 2 . La période simulée correspond à la période FMOP (Five Month Observation Period) de la campagne TRO-Pico qui a eu lieu à Bauru, Etat de São Paulo, au Brésil, du mois de novembre 2012 au mois de mars 2013, durant laquelle des mesures de vapeur d'eau sous ballons stratosphérique et une série de radiosondage ont été réalisées. Ces derniers ont permis d'étudier la structure thermique de la TTL, ainsi que les ondes de gravité. Les nuages convectifs du modèle pendant la saison humide sont validés par des produits issus d'observations du satellite géostationnaire GOES-12. De plus, on évalue la faculté du modèle à produire des nuages hauts là où l'instrument satellital MHS détecte des overshoots (non nécessairement stratosphériques). On montre d'une part que la variation de température et de vapeur d'eau est bien reproduite par le modèle pendant la saison humide, et particulièrement pendant la période intensive où une courte période particulièrement froide et sèche est observée. Toutefois, le modèle est plus humide (0.4 ppmv) et moins froid de 2 degrés dans le cas le plus extrême. Ceci est expliqué en partie par un forçage aux limites du modèle par les analyses opérationnelles d'ECMWF, elles-mêmes moins sèches et moins froides que les observations. D'autre part, le fait que la convection soit paramétrée et ne permette pas d'overshoots explique également en partie un modèle moins froid. Je montre que la différence de température entre modèle et observations est compatible thermodynamiquement avec la différence entre modèle et observation pour la vapeur d'eau.

(a) Horizontal cross-section@ 16 :15 UTC. (b) Horizontal cross-section@ 19 :45 UTC.(c) Horizontal cross-section@ 23 :15 UTC.

(a) Horizontal cross-section@ 16 :15 UTC.(b) Horizontal cross-section@ 18 :30 UTC.(c) Horizontal cross-section@ 20 :52 UTC.

(a) Radar image@1745 UTC

Remerciements

Chapitre 3

Evaluation of the BRAMS mesoscale model in the TTL during a wet season at a continental scale Le travail de ce chapitre constitue le socle de ce travail de thèse en préparation d'une extrapolation du rôle des overshoots stratosphériques sur le bilan à grande échelle de la vapeur d'eau. Il s'agit en premier lieu d'estimer la capacité du modèle méso-échelle BRAMS, quand il ne prend pas en compte les overshoots stratosphériques, à bien simuler les processus ou les paramètres essentiels pouvant jouer un rôle

Results and Discussions

Temperature Variability

Using the radiosoundings of TRO-Pico campaign (recall Chapter 2.2) and upper-air database of Wyoming University, we evaluate the temperature evolution in the TTL, i.e., the REF 0 simulation during the FMOP at different locations within the domain of simulation. Here, we show the temperature evolution at Bauru (22.31 • S, 49.05 • W) only. The other radio sounding data are used to evaluate the CPT time series apart from Bauru. The results are shown below.

In Figure 3.1, it is observed that the simulated temperature evolution is coherent with the RS92 radio sounding measurements carried out during the TRO-Pico campaign. The duration chosen here corresponds to IOP2 phase, viz., January 23 to February 12, 2013. It is well noticed that the modeled TTL is less cold in comparison to the RS92 measurements. Furthermore, the modeled CPT altitude is also lower in comparison to the measurements. In the REF 0 simulation, the coldest CPT (white box in Figure 3.1) appears a few days earlier, warmer as well as lower than that of the observation. More comments are there in Chapter 3.3 on this particular case in comparison with the REF 1 simulation, i.e., the simulation with an improved version of REF 0 , mostly with respect to the vertical grid-point resolution and a few more other parameters, as discussed in subsequent sections.

The main idea behind this analysis is to see how important is the vertical resolution in resolving the TTL temperature and CPT variability. Additionally, we probe into the CPT variability at different places in Brazil (see Table 2.5) using the upper-air soundings against the REF 0 simulation. The results are not shown here, nevertheless, the conclusion is that the model (REF 0 simulation) behaves warmer and lower in terms of reproducing the typical CPT features, i.e., temperature and altitude, respectively, in comparison to the upper-air radiosoundings. However, the time evolution of the modeled CPT is compatible with the radiosoundings. Note that Chapter 3.3 provides the detailed explanation of this warming conditions of the model.

Then, we perform few more simulations, not completely for the FMOP, rather just for few weeks during the beginning of the FMOP with increased vertical resolutions at the TTL to observe the impact of higher vertical grid-point resolution in resolving the TTL. We start probing with the temperature distribution within 12 km à 23 km altitude at Bauru for the 3 rd week of November 2012, viz., November 15 00 :00 UTC to November 21 23 :00 UTC. It consists of three different simulations, where they differ from each other by the vertical grid-point resolution near the TTL : the first one with 68 levels, the second one with 76 levels and the third one with 105 levels. The vertical resolution near the TTL vary as follows : 300 m, 200 m and 100 m, respectively. The histogram of corresponding temperature profiles is shown in Figure 3.2.

From Figure 3.2, it is seemingly visible that the vertical resolution at the TTL plays an important role in resolving the typical temperature variability within it. In Figure 3 .2a vs. 3.2b vs. 3.2c, the total number of grid-points sampling are not same for an obvious reason that the vertical grid-point resolution is increasing from 3.2a to 3.2c, therefore the number of grid-points corresponding to 12 km à 23 km range of altitude. The PDFs of their distributions make them comparable. It is important to observe the changes brought in the pattern of the histogram due to finer vertical resolution. For the simulation with 105 vertical levels, the temperature distribution within the coldest region of the TTL seems symmetrical in comparison to lower vertical resolution simulations. Furthermore, it is getting colder, where the peak is about -75 • C. Figure 3.7a clearly highlights that the WV profiles are usually wetter at the beginning of the wet season (black lines) and drier at the end (green lines). The IOP2 measurements at the peak of the convective activity (blue and red profiles) depict a variability in between the beginning and the end of the wet season.

However, the period at the end of January/beginning of February 2013 is observed to be very dry (red lines) with H 2 O mixing ratio as low as ∼2.0 ppmv in the hygropause. Referring to Figure 3.5 and 3.7, it can be concluded that the driest period in the TTL corresponds to the coldest period during the IOP2, suggesting dehydration associated with the cold temperature. This striking feature is in line with the observations reported by [START_REF] Evan | TTL cooling and drying during the January 2013 stratospheric sudden warming[END_REF] in the context of the 2013 ATTREX campaign [Jensen et al., 2017a[Jensen et al., , 2013b]]. They report very dry measurements of WV from the Global Hawk Aircraft as low as 1.2 ppmv in the stratospheric part of the TTL over the Pacific Ocean on February 26, 2013. This noticeable feature happens later than the dry period during the IOP2 over Brazil. However, [START_REF] Evan | TTL cooling and drying during the January 2013 stratospheric sudden warming[END_REF] make the link between these dry and cold measurements with a SSW in the Arctic which started at the end of December 2012, and lasted until January 23, 2013. The consecutive TTL cooling was at a maximum around January 23, but was still cold until February 1, 2013 within the latitudes ranging from 15.0 • N to 15.0 • S at the CPT, and is compatible with the coldest period observed in Brazil around February 1, 2013 during TRO-Pico (Figure 3.5) -additional comments are also given in section S1 in the "Supporting Information". More WV profiles are shown for the BRAMS in Figure 3.7b in order to have a broader view of the modeled WV variability during the FMOP.

In Figure 3.7, the time evolution of the wettest (black lines) and driest (red lines) periods, both in the measurements and in the simulation, is similar. It is also important to note that the driest (hygropause) profiles in the modeled TTL also correspond to the end of January/beginning of February 2013 with the mixing ratios decreasing to ∼2.4 ppmv in the hygropause, which is close to the hygrometers measurements from the TRO-Pico, though not as dry ; it is note worthy that on January 31, 2013, Pico-SDLA measurement is 2.0 ± 0.1 ppmv at this pressure level. It can be concluded that the WV variability in the region of Bauru, at least during the IOP2, was likely driven by large-scale processes rather than just local deep convection. This is consistent with the conclusion reached from the analysis in section 3.3.4. Maximum and minimum H 2 O mixing ratios available for each pressure level during the FMOP for the MLS : version 4.2 measurements suggest such large-scale dehydration processes. BRAMS cannot fully succeed in computing quantitatively a TTL with very dry conditions in comparison to the observations. Several reasons can be suggested. Firstly, the warmer conditions in the model lead to an underestimation of dehydration, which is concluded by using T sat calculation as in [START_REF] Dessler | Mechanisms controlling water vapor in the lower stratosphere : "A tale of two stratospheres[END_REF] -see section S2 in "Supporting Information", and shows that a colder condition by ∼2 • C in the model could lead to a drier hygropause by ∼0.4 ppmv, as obtained during the TRO-Pico campaign. Secondly, the ECMWF operational analyses used for nudging the grid-points of the simulation for initial and boundary conditions are themselves wetter than the observations, noting that the minimum value of H 2 O mixing ratio in ECMWF at the hygropause at a location (22.00 • S, 49.00 • W) near Bauru is ∼2.3 ppmv during the driest period of IOP2.

Cloud tops in BRAMS

A set of different criteria are applied in BRAMS to assign cloud tops for thick deep convective clouds, shallow cumulus clouds and cirrus clouds, so that the obtained cloudy column can be representative of SAFNWC products (space constraint restricts to show the sensitivity tests carried out to decide the cloud column using the ice+liquid mixing ratio). The condensed water content (ice+liquid, g kg -1 ) is calculated for each level in the BRAMS model using three conditions following the decrease of condensed water with altitude in the different stages of development of convective clouds [START_REF] Hong | A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation[END_REF]. Firstly, if there is any vertical profile having a layer of the condensed water content concentration >0.3 g kg -1 , we choose the cloud top of the corresponding grid-point to be the highest level having a concentration >0.15 g kg -1 .

Otherwise, for profiles reaching a water content concentration >0.15 g kg -1 , we choose the cloud top to be the highest level having a water content concentration of >0.12 g kg -1 . Finally, if both conditions are not fulfilled, the altitude of the cloud top is chosen to be always the layer for which the water content of the corresponding grid-point is >0.1 g kg -1 with the highest altitude.

GOES-12 vs. BRAMS

The estimated cloud tops in BRAMS, calculated every three hours during the FMOP, viz., 00 :00, 03 :00, 06 :00, 09 :00, 12 :00, 15 :00, 18 :00 and 21 :00 UTC are used for the 2-D cross-correlation (CC) analysis (two parameters : position and altitude of cloud tops) with the corresponding SAFNWC products (see Figure 3.8 for the whole FMOP and Figure 3.9 for example of direct cloud top comparisons). The satellite data is re-gridded to 20 km × 20 km resolution before comparing with the modeled cloud top. The CC formula is explained in Appendix A.

In Figure 3.8a, black areas indicate the absence of SAFNWC products, while white areas represent a null relation. This also corresponds to the situation where most of the grid-points within the domain of simulation have no clouds at all, both in BRAMS and GOES-12, respectively. Most of the patterns show positive correlation (blue). The maximum agreement between GOES-12 and BRAMS is found to be 0.67, as can be seen from Figure 3.9a vs. 3.9b, where the modeled cloud cells are at comparable position and altitude as observed by GOES-12, leading to a positive and high correlation coefficient. Concurrently, only very short periods during the FMOP depict negative correlation (brown), with the lowest value being -0.14. This is demonstrated in Figure 3.9c vs. 3.9d, where the modeled cloud tops are found where there are no clouds in GOES-12. Thus, most of the time such cases explain the negative or low correlations obtained.

The best correlations are obtained for the period between 18 :00 UTC (15 :00 LT) and 06 :00 UTC (03 :00 LT). This corresponds to the period of most mature convection after 15 :00 LT, or the less active phase before 03 :00 LT. During the period 21 : 00 -23 : 59 UTC, a large cloud cover is commonly observed, while during the rest of the night a lesser cloud coverage is retrieved from BRAMS, as well as from GOES-12, yielding a good correlation. Similarly, the agreement is less good at the times when convection is starting to be trigged, but has not yet reached its mature phase (early afternoon or later, viz., 09 : 00 -15 : 00 UTC or 06 : 00 -12 : 00 LT), which confirms the well known diurnal cycle of continental deep convection [START_REF] Carminati | Impact of tropical land convection on the water vapour budget in the tropical tropopause layer[END_REF][START_REF] Khaykin | Impact of land convection on temperature diurnal variation in the tropical lower stratosphere inferred from COSMIC GPS radio occultations[END_REF][START_REF] Liu | Global distribution of convection penetrating the tropical tropopause[END_REF]. The model may not be able to trigger this deep convection exactly at a given location at a correct time. But later in the afternoon during the Appendix : A -Cross-correlation (CC) : The CC coefficients vary between -1 and 1, which quantifies the relationship (co-variation) between two different sets of similar variables, and here the CC coefficients are obtained by the 2-D matrix multiplication method as employed by [START_REF] Kishtawal | Estimation of Atmospheric Motion Vectors from Kalpana-1 Imagers[END_REF] for wider application, depicting the quality of modeled cloud cells with both intensity, spatial and temporal precision.

Here, CC is given by From the FFT analysis, as shown in Figure 3.24, the red color signifies the dominant periodicities present in the spectrum. The thick band of high power corresponds to a group of periodicities present in the perturbed zonal and meridional wind profiles, respectively. One could observe that in the REF 1

simulation, the dominant frequency band corresponds to 0.038 h -1 , which represents the well known ∼26 h periodicity [START_REF] Sato | Low-frequency inertia-gravity waves in the stratosphere revealed by three-week continuous observation with the mu radar[END_REF]. This comes in line with the results shown in Chapter 3.3 using the hodograph analysis corresponding to the RS92 measurements during January 28 -29, 2013. Furthermore, a thick band of high power is observed in the Fourier power spectrum representing the periodicities of 7 -42 days (corresponding to the frequency range of 0.001 h -1 à 0.005 h -1 in Figure 3.24a and 3.24b). This range of periodicities within this range of altitude is known to be triggered by the deep convection in the tropics [START_REF] Tsuda | Radiosonde observations of equatorial atmosphere dynamics over Indonesia : 2. characteristics of gravity waves[END_REF]. Hence, FFT puts to the fore the ability of the BRAMS mesoscale model in resolving the inertia-gravity waves.

Three In a trajectory analysis, [START_REF] Khaykin | Evidence of horizontal and vertical transport of water in the southern hemisphere tropical tropopause layer (TTL) from high-resolution balloon observations[END_REF] make the links between overshooting convection and some of the above-mentioned water vapor enhancement (see SOCs. Even if the Pico-SDLA measurements were carried out earlier, the trajectory of the balloon carrying Pico-SDLA was further downwind of the overshooting cells, while FLASH-B was later, but nearer from the cells (see also Figure 4.3). Concurrently, the local maximum at 18.5 km is reported to be caused by the horizontal advection of midlatitude air mass : at this altitude in mid-latitude regions, we are already higher in the stratosphere, resulting in higher H 2 O mixing ratios, and higher load of aerosols seen by COBALD (Figure 4.2 -right panel) and LOAC (not shown).

March 13, 2012 : Simulation Setups and Validation

To infer the key parameters playing role in the overshooting plumes and stratospheric water vapor at the local scale, which will later promote the concept of forcing the impact of SOC on the WV budget in the lowermost stratosphere, several cloud-scale simulations using the BRAMS model are proposed. The strategy is to evaluate the sensitivity of the results to the setup of the model, and the range of variability of the hydration or ice injection computed in each case. This would possibly influence our conclusion regarding the key parameters and their setup in the nudging strategy of H 2 O akin to SOC. As such three simulations are analyzed : the first simulation is used as a reference run (hereafter denoted as «REF»)

with 800 m × 800 m horizontal grid-point resolution in grid3 of the nested-gridding system ; the second one, keeping the same set up as the REF simulation, but changing a parameter in the bulk microphysics (hereafter denoted as «NU21»), that is the shape parameter (ν) of the hydrometeors. A third one, similar to the REF, but finer vertical resolution at the TTL (hereafter denoted as «HVR»).

(b) Vertical cross-section@ 17 :52 UTC.

(c) Vertical cross-section@ 18 :00 UTC.

(d) Vertical cross-section@ 18 :07 UTC.

Appendices Annexe B

Modifications in the BRAMS model

B.1 Upgrading the CO 2 value

Being a green house gas like H 2 O vapor, CO 2 has also significant influence on the fluctuation of global surface temperature, and is known well for the land surface warming. It absorbs the long wave radiation emitted from the surface, and releases it back to the surface, resulting with more surface warming than would occur otherwise. Thus, it is an integral part of any atmospheric circulation model to keep it up to date while making diagnostic tests on certain events observed.

The [START_REF] Harrington | The effects of radiative and microphysical processes on simulated warm and transition season Arctic stratus[END_REF] radiative parameterization scheme uses a constant value of CO 2 mixing ratio, primarily because RAMS doesn't prognose the CO 2 value. Initially, the long wave parameterization was using a value of ∼300 ppm (can be found in subroutine 'path_lengths' of the file 'rad_driv.f90'), which is far from the current value of 400 ppm. We update this value before performing the simulations using the observational data of CO 2 mixing ratio from the TRO-Pico campaign at Bauru during 2012 -2013.

B.1.1 Calculation

The factor to be tuned in the BRAMS model described in the subroutine called 'path_lengths' of the file 'rad_driv.f90' is given by, say ζ :

where M CO 2 = 44.001 g mol -1 , M air = 28.966 g mol -1 , and amount of CO 2 used in the model is 395 ppm.

Thus, ζ = 0.600 16 × 10 -3 .

Source Code

The ζ value is changed from 0.455 75 × 10 -3 to 0.600 16 × 10 -3 .

SUBROUTINE path_lengths (nrad,u,rl,dzl,dl,o3l,vp,pl,eps) ! Get the path lengths for the various gases... Toward the upscaling of the impact of overshoots on the stratospheric water budget at a continental scale Abstract: This dissertation aims at laying a foundation on upscaling work of the impact of stratospheric overshooting convection (SOC) on the water vapor budget in the tropical tropopause layer (TTL) and lower stratosphere at a continental scale. To do so, we take advantage of the TRO-Pico field campaign measurements held at Bauru, Brazil, during two wet/convective seasons in 2012 and 2013, and perform accordingly several numerical simulations of the TTL which encompass through a large part of South America using the BRAMS mesoscale model. Firstly, we adopt a strategy of simulating a full wet season without considering SOC. This simulation is then evaluated for other typical key features (e.g., TTL temperature, convective clouds, gravity wave) of the TTL. In the absence of SOC and before upscaling its impact, we demonstrate that the model has a fair enough ability to reproduce a typical TTL. The importance of large-scale upwelling in comparison to the finite-scale deep convective processes is then discussed. Secondly, from fine-scale BRAMS simulations of an observational case of SOC during TRO-Pico, we deduce physical parameters (mass flux, ice mass budget, SOC size) that will be used to set a nudging of the SOC impact in large-scale simulations. A typical maximum impact of about 2 kt of water vapor, and 6 kt of ice per SOC cell is computed. This estimation is 30% lower for another microphysical setup of the model. We also show that the stratospheric hydration by SOC is mainly due to three types of hydrometeors in the model.