Au cours des dernières années, des changements importants dans le domaine des assurances et des finances attirent de plus en plus l’attention sur la nécessité d’élaborer un cadre normalisé pour la mesure des risques. Récemment, il y a eu un intérêt croissant de la part des experts en assurance sur l’utilisation de l’espérance conditionnelle des pertes (CTE) parce qu’elle partage des propriétés considérées comme souhaitables et applicables dans diverses situations. En particulier, il répond aux exigences d’une mesure de risque “cohérente”, selon Artzner [2]. Cette thèse représente des contributions à l’inférence statistique en développant des outils, basés sur la convergence des intégrales fonctionnelles, pour l’estimation de la CTE qui présentent un intérêt considérable pour la science actuarielle. Tout d’abord, nous développons un outil permettant l’estimation de la moyenne conditionnelle E[X|X > x], ensuite nous construisons des estimateurs de la CTE, développons la théorie asymptotique nécessaire pour ces estimateurs, puis utilisons la théorie pour construire des intervalles de confiance. Pour la première fois, l’approche de bootstrap non paramétrique est explorée dans cette thèse en développant des nouveaux résultats applicables à la valeur à risque (VaR) et à la CTE. Des études de simulation illustrent la performance de la technique de bootstrap.

Fundação de Amparo a Pesquisa no Estado do Rio Grande do Sul / Extreme climatic events have been occurring with greater intensity and/or frequency over South America. Indicatives for these alterations encompass natural climate variability, land use (deforestation and urbanization), global warming, and increase of greenhouse gases and aerosols in the atmosphere. South America receives a great input of moisture from the Amazon rainforest, as well as a 37% contribution from the Atlantic Ocean. Considering the whole planet, some atmospheric events need to be analyzed when regarding moisture input towards a continent. Ocean circulation can interfere for example in sea surface temperature (SST), either influencing or not the input of moisture to the continent. The objective of the present study was to analyze the variability of atmospheric moisture in South America and its extreme values, as well as the relationships with the sea surface temperature of the adjacent oceans. The present study made use of ECMWF data, ERA-INTERIM reanalysis (pressure at sea level and surface pressure, evaporation, air and dew point temperatures at 2 meters, and zonal and meridional wind at 10 meters) and also sea surface temperature data from the MetOffice Hadley Centre (HADISST). The analysis period of the present study was between 1980 and 2009, encompassing a period of 30 years of data. First, climatology, trends and extremes of moisture and evaporation (frequency, intensity and reoccurrence of events) were calculated. These were followed by lagged compositions to assess the role of sea surface temperature anomalies during extreme moisture and evaporation events. The main results found were regarding an increase of the pressure at sea level gradient and SST in the southwestern Atlantic, increase evaporation in the eastern and northern coasts of South America, and its decrease in the center-southern region of the continent. Moreover, the center-southern region also demonstrated a decrease of dew point temperature and specific moisture, and an increase in the difference between air temperature and dew point temperature. Decrease in the moisture flow magnitude and intensification of dry events over the center-southern region of South America were also observed. Finally, results showed that an SST anomaly cycle during an extreme event in the continent lasted approximately five months and, at least one month prior to the event, signs of this SST anomaly were already observable. In summary, the most significant moisture alterations in South America were found in the center-southern sector of the continent and over the southwestern Atlantic Ocean, near the Brazil-Malvinas Confluence (BMC). Nevertheless, more studies are needed to understand the relationships between SST at the BMC and moisture extremes, particularly in the center-southern portion of South America. / Atualmente os eventos climáticos extremos têm ocorrido com maior intensidade e/ou frequência sobre a América do Sul. Os indicativos para essas alterações circundam a variabilidade natural do clima, uso da terra (desmatamento e urbanização), aquecimento global, aumento da concentração de gases do efeito estufa e aerossóis na atmosfera. A América do Sul recebe um grande aporte de umidade pela existência da floresta Amazônica em seu território e também cerca de 37% de contribuição oriunda do Oceano Atlântico. Considerando todo o globo terrestre, alguns dos eventos atmosféricos precisam ser analisados com relação ao aporte de umidade sobre o continente. Com relação ao oceano, a circulação dos oceanos podem interferir, por exemplo, na temperatura da superfície do mar (TSM), influenciando ou não no aporte de umidade para o continente. O objetivo do presente trabalho foi analisar a variabilidade da umidade atmosférica na América do Sul e de seus valores extremos e as relações com a temperatura da superfície do mar nos oceanos adjacentes. O presente trabalho utilizou dados do ECMWF, da reanálise do ERA-INTERIM (pressão ao nível do mar e pressão em superfície, evaporação, temperatura do ar e temperatura do ponto de orvalho a 2 metros e vento zonal e meridional a 10 metros) e também dados de temperatura da superfície do mar do MetOffice Hadley Centre (HADISST). O período de análise do presente trabalho foi de 1980 a 2009, compreendendo um período de 30 anos de dados. Primeiramente foram calculadas as climatologias, as tendências e os extremos de umidade e evaporação (frequência, intensidade e recorrência dos eventos). Posteriormente, foram realizadas as composições defasadas para verificar o papel das anomalias da temperatura da superfície do mar durante os eventos extremos de umidade e evaporação. Os principais resultados encontrados foram em relação a um aumento da pressão ao nível do mar e da TSM no Atlântico sudoeste, aumento também da evaporação na costa leste e norte da América do Sul, e sua diminuição na região centro-sul do continente. Além disso, a região centro-sul também demonstrou uma diminuição da temperatura do ponto de orvalho e da umidade específica, e um aumento na diferença entre a temperatura do ar e a temperatura do ponto de orvalho. Diminuição da magnitude do fluxo de umidade e intensificação de eventos extremos secos sobre a região centro-sul da América do Sul também foram observados. E por fim, os resultados mostraram que um ciclo de anomalia de TSM durante um evento extremo no continente durou aproximadamente cinco meses e, pelo menos um mês antes do evento, sinais da anomalia de TSM já era observada. Em suma, as alterações mais significativas na umidade sobre a América do Sul foram encontradas no setor centro-sul do continente e sobre o Oceano Atlântico sudoeste, próximo a Confluência Brasil-Malvinas (CBM).

A partir des équations gouvernant le champ de vitesse, on peut non seulement s'attendre à un vent (fortement) non-gaussien, mais aussi à un vent présentant un comportement scalant. Par ‘scalant' ou invariant d'échelle, nous faisons référence à un comportement statistique auto-similaire particulier; les cascades de tourbillons. Les multifractales stochastiques (avec des singularités et des co-dimensions multiples) reproduisent facilement le comportement scalant et les distributions de probabilités à queues épaisses omniprésentes dans le vent et dont la quantification est essentielle pour la communauté. Les quelques paramètres qui définissent ces modèles peuvent être déduits soit de considérations théoriques, soit de l'analyse statistique de données. Nous avons constaté que les approximations de flux basées sur le module du cisaillement du vent donnent des moments statistiques non-scalants et donc des estimations faussées des paramètres multifractals. La méthode DSF n'exige pas cette approximation et garantit un comportement scalant sur une certaine gamme d'échelles. Nous n'avons trouvé aucune estimation véritablement stable d'alpha en utilisant des méthodes standards. Ceci n'arrive plus quand nous optimisons localement (par la différenciation fractionnaire) le comportement scalant du DTM. Nous obtenons alors des estimations très stables de l'indice de multifractalité qui sont en outre en accord (alpha ≤ 2) avec des résultats publiés. Au contraire, les deux autres paramètres (C1 et H) deviennent des fonctions non-linéaires de l'ordre q des moments statistiques. Ces résultats suggèrent que le modèle UM isotrope ne peut être utilisé pour reproduire le cisaillement de vent dans la couche de surface atmosphérique. Lesdites hypothèses sont examinées en utilisant un repère tournant pour analyser l'anisotropie de la vitesse horizontale dans la couche de surface atmosphérique. Cela permet de quantifier la dépendance angulaire de l'exposant de Hurst. Les valeurs de cet exposant restent tout de même conformes aux résultats précédemment publiés. Pour des échelles de temps supérieures à quelques secondes, les deux jeux de données présentent une anisotropie scalante forte, qui décroît avec l'altitude. Nous mettons en évidence une expression analytique de la variation angulaire de l'exposant de Hurst, reposant sur les corrélations entre les composantes horizontales. Ceci pilote la formation des extrêmes du cisaillement, y compris dans le sillage d'une éolienne. Les cisaillements turbulents du vent sont si extrêmes que leur loi de probabilité est une loi de puissance. L'exposant correspondant (qD) est similaire pour les deux sites à une hauteur de 50m (4 ≤ qD ≤ 5), malgré des conditions orographiques très différentes. Nous discutons aussi de ses conséquences en analysant la stabilité de la couche limite atmosphérique et proposons une nouvelle méthode pour sa classification. Enfin, nous démontrons analytiquement que l'anisotropie augmente la probabilité des extrêmes. Ce résultat met en lumière un des nombreux mécanismes de turbulence possibles dans la couche de surface qui peut apparemment surproduire les cisaillements extrêmes du vent, s'ils sont étudiés dans le cadre des UM isotropes. Nous en analysons théoriquement les conséquences sur les estimations des paramètres multifractales par la méthode DTM. Les résultats analytiques obtenus sont en parfait accord avec les observations empiriques. Nous discutons alors de la prise en compte de toutes ces considérations pour faire des simulations multifractales des champs du vent dans la couche limite atmosphérique / From the governing equations of the velocity field, one can not only expect a (highly) non-Gaussian wind but also one that is scaling. By ‘scaling' we mean a given statistical self-similarity; a turbulent cascade of eddies. Stochastic multifractals (with multiple singularities and co-dimensions) easily reproduce the scaling, heavy-tailed probabilities ubiquitous with the wind and essential to quantify for the wind energy community. The few parameters that define these models can be derived either from theoretical considerations or from statistical data analysis. It is sometimes possible to determine the statistics of the velocity shears with the universal multifractal (UM) parameters: alpha - the index of multifractality (0 ≤ alpha ≤ 2), C1 - the co-dimension of the mean intermittency (C1 ≥ 0) and H - the degree of non-conservation - the linear part of the scaling exponents. The latter of the three parameters is often called the Hurst exponent. We inter-compare the results from the rather standard method of empirical estimation of the UM parameters, the Double Trace Moment (DTM) method, with that of the Double Structure Function (DSF), a newly developed method. We found that flux proxies based on the modulus of the wind velocity shears yield non-scaling statistical moments and therefore spurious multifractal parameter estimates. DSF does not require this proxy approximation thus providing the scaling of the structure-function to an extent. We found no truly stable estimate of alpha using standard methods. This no longer occurs when we locally optimise (by fractionally differentiating) the DTM scaling behaviour. We then obtain very stable estimates of the multifractality index that are furthermore consistent (alpha ≤ 2) with other literature. On the contrary, the two other parameters (C1 and H) become non-linear functions of the order q of the statistical moments. These results suggest that the isotropic UM model cannot be used to reproduce the velocity shears in the atmospheric surface-layer. To investigate the above hypothesis we use a rotated frame of reference to analyse the anisotropy of the horizontal velocity in the atmospheric surface-layer. This enables us to quantify the angular dependency of a Hurst exponent. Despite being anisotropic the Hurst exponent is consistent with other surface-layer literature. For time-scales above a few seconds, both data exhibit a strong, scaling anisotropy that decreases with height. We put forward an analytical expression for the angular variation of the Hurst exponent based on the correlation of the horizontal components. It determines the generation of wind shear extremes, including those in the wake of a turbine. We find that the turbulent wind shears are so extreme that their probability distributions follow a power law. The corresponding exponent (qD) is rather the same in both sites at 50m heights (4 ≤ qD ≤ 5), in spite of very different orographic conditions. We also discuss its consequences when analysing the stability of the atmospheric boundary-layer and propose a new method for its classification. Finally, we analytically demonstrate that anisotropy increases the extremes probability. This finding reveals one of the many possible turbulence mechanisms in the atmospheric surface-layer that may seemingly over-generate wind shear extremes if they are studied in an isotropic UM framework. We theoretically analyse the consequences of this on the UM estimates for the DTM method. The obtained analytical results fully support empirical findings. We then discuss how to take into account all of these considerations when simulating multifractal fields of the wind in the atmospheric boundary-layer. The overall results of this dissertation go beyond wind energy, they open up new perspectives for the theoretical predictions of extremes in the general case of strongly correlated data

The simultaneous occurrences of several extreme events, known as compound extremes, are often associated with greater impact than univariate extremes. Flooding and windstorms are widespread hazards in Europe which can lead to severe property damage and fatalities. During winter, extreme wind and precipitation often co-occur, since they are associated with a common driver, namely extratropical cyclones. In this project, the occurrences of compound wind and precipitation events in Europe are investigated using the ERA5 reanalysis dataset. The analysis covers the years 1979-2019 with a focus on boreal winter. Areas that experience the highest occurrence of compound wet-windy extremes are the west coast of Norway, the Iberian peninsula, parts of central Europe, and southeast of the Black Sea. A few case studies are discussed with the purpose to give an idea of the magnitude of possible impacts. Further, the relationship between extreme wind and precipitation events and the North Atlantic Oscillation (NAO) is presented. During days with positive NAO, extreme precipitation and wind events occur in the central and northern parts of Europe while the negative phase brings extreme wind and precipitation to the southern parts of Europe. Lastly, a short analysis to discover changes in the occurrences of compound precipitation and wind events for the two periods 1979-1999 and 2000-2019 is performed. The result showed no clear changes. The number of compound extremes does not seem to vary for the two periods. / Olika extrema väderhändelser som sammanfaller orsakar ofta större skada än enskilda extrema händelser på många håll i samhället. Översvämningar och vindstormar är vanligt förekommande i Europa och kan leda till kostsamma skador och dödsfall. Extrema vind-och nederbördshändelser sammanfaller vanligen under vintern eftersom de båda ofta orsakas av Nordatlantiska cykloner, som är vanligast under den årstiden. I detta projekt kartläggs sammanfallande vind- och nederbördshändelser i Europa under vintermånaderna december-februari, med hjälp av ERA5 reanalysdata för åren 1979-2019. Områden med relativt hög förekomst av sammanfallande vind- och nederbördshändelser är Norges västkust, Iberiska halvön, delar av Centraleuropa och östra Turkiet. Några fallstudier kopplade till dessa områden är diskuterade för att ge en uppfattning om konsekvenserna av dessa sammanfallande händelser. Eventuella kopplingar mellan sammanfallande vind- och nederbördshändelser och den Nordatlantiska Oscillationen (NAO) är också undersökt. Under den positiva fasen av NAO sker extrema nederbörd- och vindhändelser i norra och centrala delar av Europa medan den negativa fasen ger extrem vind och nederbörd i de södra delarna av Europa.En kort analys för undersöka om förekomsten av extrema sammanfallande händelser har ändrats genomfördes genom att jämföra andelen sammanfallande händelser under de två perioderna 1979-1999 och 2000-2019. Ingen betydande förändring i andelen sammanfallande händelser mellan dessa perioder hittades.

La partie principale de cette thèse s'intéresse à développer les aspects théoriques et algorithmiques pour trois procédures statistiques distinctes. Le premier problème abordé est la complétion de matrices binaires. Nous proposons un estimateur basé sur une approximation variationnelle pseudo-bayésienne en utilisant une fonction de perte différente de celles utilisées auparavant. Nous pouvons calculer des bornes non asymptotiques sur le risque intégré. L'estimateur proposé est beaucoup plus rapide à calculer qu'une estimation de type MCMC et nous montrons sur des exemples qu'il est efficace en pratique. Le deuxième problème abordé est l'étude des propriétés théoriques du minimiseur du risque empirique pénalisé pour des fonctions de perte lipschitziennes. Nous pouvons ensuite appliquer les résultats principaux sur la régression logistique avec la pénalisation SLOPE ainsi que sur la complétion de matrice. Le troisième chapitre développe une approximation de type Expectation-Propagation quand la vraisemblance n'est pas explicite. On utilise alors l'approximation ABC dans un second temps. Cette procédure peut s'appliquer à beaucoup de modèles et est beaucoup plus précise et rapide. Elle est appliquée à titre d'exemple sur un modèle d'extrêmes spatiaux. / The main part of this thesis aims at studying the theoretical and algorithmic aspects of three distinct statistical procedures. The first problem is the binary matrix completion. We propose an estimator based on a variational approximation of a pseudo-Bayesian estimator. We use a different loss function of the ones used in the literature. We are able to compute non asymptotic risk bounds. It is much faster to compute the estimator than a MCMC method and we show on examples that it is efficient in practice. In a second part we study the theoretical properties of the regularized empirical risk minimizer for Lipschitz loss functions. We are therefore able to apply it on the logistic regression with the SLOPE regularization and on the matrix completion as well. The third chapter develops an Expectation-Propagation approximation when the likelihood is not explicit. We then use an ABC approximation in a second stage. This procedure may be applied to many models and is more precise and faster than the classic ABC approximation. It is used in a spatial extremes model.

Seit der industriellen Revolution haben Menschen durch Verbrennung von fossilen Energieträgern die Treibhausgaskonzentration in der Atmosphäre erhöht. Die daraus folgende Erderwärmung hat weitreichende Folgen für das Klima, unter anderem häufigere und intensivere Wetterextreme. Wegen ihrer gravierenden Auswirkungen auf die Gesellschaft, ist es von allgemeinem Interesse zu verstehen, wie der menschengemachte Klimawandel diese Wetterextreme beeinflusst. In dieser kumulativen Dissertation analysiere ich erst zwei komplexe Wettereignisse, die die Nahrungsmittelproduktion in Europa beeinträchtigen: Frosttage nach dem Beginn der Apfelblüte und Feuchte Frühsommerperioden nach warmen Wintern. In einer dritten Studie untersuche ich wie dynamische Klimaveränderungen in den mittleren Breiten der Nordhalbkugel zu beständigerem Sommerwetter beitragen. Schließlich beschäftige ich mich mit tropischen Stürmen im Nordatlantik und damit, wie sie von der globalen Erwärmung beeinflusst werden. Eine zentrale methodische Herausforderung in diesem Forschungsfeld ist, dass Wetterextreme per Definition selten sind und dass es aufgrund der starken internen Klimavariabilität schwierig ist, die Veränderungen zu quantifizieren, die auf den menschgemachten Klimawandel zurück zu führen sind. In dieser Arbeit verfolge ich zweigegenläufige Ansätze um mit dieser Herausforderung um zu gehen: 1) Ich verwende große Klimasimulationsensembles um den Effekt der internen Klimavariabilität aus zu glätten und dadurch die erzwungenen Veränderungen beim Apfelfrost und in der Persistenz zu ergründen. 2) Mit Methoden, die auf Beobachtungsdaten beruhen, quantifiziere ich den Einfluss der internen Klimavariabilität auf tropische Zyklone um dann einschätzen zu können, in welchem Maß der beobachtete Anstieg der tropischen Zyklonaktivität im Atlantik der internen Klimavariabilität oder erzwungenen Veränderungen zugeschrieben werden kann. / Since the industrial revolution, humans have increased the greenhouse gas concentration of the atmosphere by burning fossil fuels. The resulting global warming has far reaching impacts on the climate system including increasingly frequent and intense weather extremes. Due to the severe impacts these weather extremes cause to societies, there is a strong interest in understanding how anthropogenic climate change affects weather extremes. In this cumulative thesis I first study two compound weather extremes that affect food production in Europe: frost days after apple blossom and wet early summers after warm winters. In a third study I quantify how dynamic changes in the climate system contribute to more persistent summer weather extremes in the northern hemispheric mid-latitudes. Finally, I analyze tropical cyclones in the Atlantic basin and changes in tropical cyclone activity as a result of global warming. One central methodological challenge in the research field is that weather extremes are rare by definition and that due to the strong internal climate variability it is difficult to quantify changes that are forced by anthropogenic climate change. In this thesis I explore two divergent approaches to this challenge: 1) Using large ensemble climate simulations I smooth out the effect of internal variability thereby exposing the forced change in apple frost and weather persistence. 2) Using observation based approaches, I quantify the contributions of internal climate variability on tropical cyclones in order to subsequently estimate to which extent the observed increase in tropical cyclone activity in the Atlantic can be attributed to internal climate variability or forced changes.

There remain vast knowledge gaps in the global south as to how tourism will affect climate change and vice versa. Recent extreme weather events in southern Africa attributed to climate variability and change have led to speculation that, the Victoria Falls, is under threat from climate change. This research was aimed at examining the two-way linkage between tourism and climate change. The research adopted a pragmatism paradigm in a mixed-method case study. A number of research techniques were used to investigate the problem, namely: an online survey (n=427), secondary data analysis, field observation and interviews. Data analysis was done making use of Mann-Kendall Trend Analysis, QuestionPro analytics, Microsoft Excel Analysis Toolpak, Tools from ArcMap 10.3.1 and SPSS 24. Content analysis and thematic analysis was used to analyse secondary and interview data respectively. It emerged that the Victoria Falls is experiencing climate change, which resulted in statistically significant increase in temperature over the past 40 years of between 0.3°C and 0.75°C per decade. However, no significant changes in rainfall were noted, although there has been a seasonal shift in average rainfall onset. Weather extremes and annual rainfall point to increased occurrence and severity of extreme years of droughts and wetting which has in turn also affected waterflow regime at the waterfalls. The changes have a negative impact on wildlife, tourists, and tourism business in the area. The study also revealed that tourism is an equally significant driver of climate change through carbon emissions throughout its value chain. Carbon emissions from tourism value chain are set to increase in the foreseeable future despite efforts of going green by the industry owing to exponential growth of the industry. There is, therefore, a need for the industry to adapt, mitigate and intensify green tourism efforts to achieve sustainability. The study further suggests that there is a need for better communication and education to build resilience and capacity for the tourism industry to deal with climate change. Further research is suggested to ascertain the tourism threshold for the area, impact of climate change on wildlife and basin changes that led to water flow increase in the Zambezi River. / Environmental Sciences / Ph. D. (Environmental Management)

Cette thèse a pour but le développement de certains aspects de la modélisation de la dépendance dans la gestion des risques en dimension plus grande que un. Le premier chapitre est constitué d'une introduction générale. Le deuxième chapitre est constitué d'un article s'intitulant « Estimating Bivariate Tail : a copula based approach », soumis pour publication. Il concerne la construction d'un estimateur de la queue d'une distribution bivariée. La construction de cet estimateur se fonde sur une méthode de dépassement de seuil (Peaks Over Threshold method) et donc sur une version bivariée du Théorème de Pickands-Balkema-de Haan. La modélisation de la dépendance est obtenue via la Upper Tail Dependence Copula. Nous démontrons des propriétés de convergence pour l'estimateur ainsi construit. Le troisième chapitre repose sur un article: « A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation», soumis pour publication. Nous abordons le problème de l'extension de mesures de risque classiques, comme la Value-at-Risk et la Conditional-Tail-Expectation, dans un cadre multidimensionnel en utilisant la fonction de Kendall multivariée. Enfin, dans le quatrième chapitre de la thèse, nous proposons un estimateur des courbes de niveau d'une fonction de répartition bivariée avec une méthode plug-in. Nous démontrons des propriétés de convergence pour les estimateurs ainsi construits. Ce chapitre de la thèse est lui aussi constitué d'un article, s'intitulant « Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory», accepté pour publication dans la revue ESAIM:Probability and Statistics. / In this PhD thesis we consider different aspects of dependence modeling with applications in multivariate risk theory. The first chapter is constituted by a general introduction. The second chapter is essentially constituted by the article “Estimating Bivariate Tail: a copula based approach”, actually submitted for publication. It deals with the problem of estimating the tail of a bivariate distribution function. We develop a general extension of the POT (Peaks-Over-Threshold) method, mainly based on a two-dimensional version of the Pickands-Balkema-de Haan Theorem. The dependence structure between the marginals in the upper tails is described by the Upper Tail Dependence Copula. Then we construct a two-dimensional tail estimator and study its asymptotic properties. The third chapter of this thesis is based on the article “A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation” and submitted for publication. We propose a multivariate generalization of risk measures as Value-at-Risk and Conditional-Tail-Expectation and we analyze the behavior of these measures in terms of classical properties of risk measures. We study the behavior of these measures with respect to different risk scenarios and stochastic ordering of marginals risks. Finally in the fourth chapter we introduce a consistent procedure to estimate level sets of an unknown bivariate distribution function, using a plug-in approach in a non-compact setting. Also this chapter is constituted by the article “Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory”, accepted for publication in ESAIM: Probability and Statistics journal.

La théorie statistique univariée des valeurs extrêmes se généralise au cas multivarié mais l'absence d'un cadre paramétrique naturel complique l'inférence de la loi jointe des extrêmes. Les marges d'erreur associée aux estimateurs non paramétriques de la structure de dépendance sont difficilement accessibles à partir de la dimension trois. Cependant, quantifier l'incertitude est d'autant plus important pour les applications que le problème de la rareté des données extrêmes est récurrent, en particulier en hydrologie. L'objet de cette thèse est de développer des modèles de dépendance entre extrêmes, dans un cadre bayésien permettant de représenter l'incertitude. Le chapitre 2 explore les propriétés des modèles obtenus en combinant des modèles paramétriques existants, par mélange bayésien (Bayesian Model Averaging BMA). Un modèle semi-paramétrique de mélange de Dirichlet est étudié au chapitre suivant : une nouvelle paramétrisation est introduite afin de s'affranchir d'une contrainte de moments caractéristique de la structure de dépendance et de faciliter l'échantillonnage de la loi à posteriori. Le chapitre 4 est motivé par une application hydrologique : il s'agit d'estimer la structure de dépendance spatiale des crues extrêmes dans la région cévenole des Gardons en utilisant des données historiques enregistrées en quatre points. Les données anciennes augmentent la taille de l'échantillon mais beaucoup de ces données sont censurées. Une méthode d'augmentation de données est introduite, dans le cadre du mélange de Dirichlet, palliant l'absence d'expression explicite de la vraisemblance censurée. Les conclusions et perspectives sont discutées au chapitre 5 / Uni-variate extreme value theory extends to the multivariate case but the absence of a natural parametric framework for the joint distribution of extremes complexifies inferential matters. Available non parametric estimators of the dependence structure do not come with tractable uncertainty intervals for problems of dimension greater than three. However, uncertainty estimation is all the more important for applied purposes that data scarcity is a recurrent issue, particularly in the field of hydrology. The purpose of this thesis is to develop modeling tools for the dependence structure between extremes, in a Bayesian framework that allows uncertainty assessment. Chapter 2 explores the properties of the model obtained by combining existing ones, in a Bayesian Model Averaging framework. A semi-parametric Dirichlet mixture model is studied next : a new parametrization is introduced, in order to relax a moments constraint which characterizes the dependence structure. The re-parametrization significantly improves convergence and mixing properties of the reversible-jump algorithm used to sample the posterior. The last chapter is motivated by an hydrological application, which consists in estimating the dependence structure of floods recorded at four neighboring stations, in the ‘Gardons’ region, southern France, using historical data. The latter increase the sample size but most of them are censored. The lack of explicit expression for the likelihood in the Dirichlet mixture model is handled by using a data augmentation framework

Large-scale atmospheric disturbances play important roles in determining the general circulation of the atmosphere during the North Pacific boreal winter. A number of scientific questions have been raised due to these disturbances’ spatial and temporal complexity as well as the hydrological implication associated with them. In this dissertation, the principal goal is to further improve our understanding of the atmospheric high frequency (HF) and intermediate frequency (IF) disturbances active over the North Pacific. The study focuses on their energetics, intraseasonal and interannual variability, and the resulting hydrological impact over the eastern North Pacific and Western U.S. including extreme events. To delineate the characteristics of HF and IF disturbances in the troposphere, we first derive a new set of equations governing the local eddy kinetic energy (EKE), and assess the critical processes maintaining local budgets of the HF and IF EKE. The diagnosis assesses the 3-D patterns of energy flux convergence (EFC), barotropic conversion (BT), baroclinic conversion (BC), and cross-frequency eddy-eddy interaction (CFEI). The local EKE budget analysis is followed by an investigation of the modulation of HF and IF eddy activity by different modes of low frequency climate variability. On interannual timescales, the response of various local energetic processes to El Niño-Southern Oscillation (ENSO) determines the HF and IF EKE anomalies and the role of CFEI process is important in producing these anomalies. Also on interannual timescales, winter precipitation deficits associated with suppressed cyclonic activity, i.e., negative HF EKE anomalies, are linked to severe droughts over the U.S. Southern Great Plain (SGP) region. The suppressed cyclonic activity is, in turn, tied to phase changes in the West Pacific (WP) teleconnection pattern. On intraseasonal timescales, variations in HF disturbances (a.k.a. storm tracks) over the North Pacific are closely coupled with tropical convection anomalies induced by the Madden-Julian Oscillation (MJO), and partly drive larger scale intraseasonal flow anomalies in this region through eddy-eddy interactions. Anomalous HF eddy activity induces subseasonal transitions between “wet” and “dry” regimes over the west coast of North America. Also on intraseasonal timescales, the East Asian cold surge (EACS) is found to provide a remote forcing of the winter precipitation anomalies in the western U.S. This modulation is achieved through “atmospheric rivers” (ARs), which are narrow channels of concentrated moisture transport in the atmosphere and are responsible for over 70% of the extreme precipitation events in the western U.S.. EACS effectively modulates the IF disturbance activity over the North Pacific, and the anomalous IF disturbances lead to the formation of an AR over the eastern North Pacific that ultimately induces precipitation anomalies in the western U.S. Analyses of the simulations from the NCAR Community Climate System Model version 4 (CCSM4) demonstrate that the connections among the EACS, AR and western U.S. precipitation are better captured by a model with higher spatial resolutions. The improved simulation of these connections is achieved mainly through a better representation of the IF disturbances, and the associated scale-interaction processes in the higher resolution model.