En prévision numérique du temps, les modèles de prévision d'ensemble sont devenus un outil incontournable pour quantifier l'incertitude des prévisions et fournir des prévisions probabilistes. Malheureusement, ces modèles ne sont pas parfaits et une correction simultanée de leur biais et de leur dispersion est nécessaire.Cette thèse présente de nouvelles méthodes de post-traitement statistique des prévisions d'ensemble. Celles-ci ont pour particularité d'être basées sur les forêts aléatoires.Contrairement à la plupart des techniques usuelles, ces méthodes non-paramétriques permettent de prendre en compte la dynamique non-linéaire de l'atmosphère.Elles permettent aussi d'ajouter des covariables (autres variables météorologiques, variables temporelles, géographiques...) facilement et sélectionnent elles-mêmes les prédicteurs les plus utiles dans la régression. De plus, nous ne faisons aucune hypothèse sur la distribution de la variable à traiter. Cette nouvelle approche surpasse les méthodes existantes pour des variables telles que la température et la vitesse du vent.Pour des variables reconnues comme difficiles à calibrer, telles que les précipitations sexti-horaires, des versions hybrides de nos techniques ont été créées. Nous montrons que ces versions hybrides (ainsi que nos versions originales) sont meilleures que les méthodes existantes. Elles amènent notamment une véritable valeur ajoutée pour les pluies extrêmes.La dernière partie de cette thèse concerne l'évaluation des prévisions d'ensemble pour les événements extrêmes. Nous avons montré quelques propriétés concernant le Continuous Ranked Probability Score (CRPS) pour les valeurs extrêmes. Nous avons aussi défini une nouvelle mesure combinant le CRPS et la théorie des valeurs extrêmes, dont nous examinons la cohérence sur une simulation ainsi que dans un cadre opérationnel.Les résultats de ce travail sont destinés à être insérés au sein de la chaîne de prévision et de vérification à Météo-France. / In numerical weather prediction, ensemble forecasts systems have become an essential tool to quantifyforecast uncertainty and to provide probabilistic forecasts. Unfortunately, these models are not perfect and a simultaneouscorrection of their bias and their dispersion is needed.This thesis presents new statistical post-processing methods for ensemble forecasting. These are based onrandom forests algorithms, which are non-parametric.Contrary to state of the art procedures, random forests can take into account non-linear features of atmospheric states. They easily allowthe addition of covariables (such as other weather variables, seasonal or geographic predictors) by a self-selection of the mostuseful predictors for the regression. Moreover, we do not make assumptions on the distribution of the variable of interest. This new approachoutperforms the existing methods for variables such as surface temperature and wind speed.For variables well-known to be tricky to calibrate, such as six-hours accumulated rainfall, hybrid versions of our techniqueshave been created. We show that these versions (and our original methods) are better than existing ones. Especially, they provideadded value for extreme precipitations.The last part of this thesis deals with the verification of ensemble forecasts for extreme events. We have shown several properties ofthe Continuous Ranked Probability Score (CRPS) for extreme values. We have also defined a new index combining the CRPS and the extremevalue theory, whose consistency is investigated on both simulations and real cases.The contributions of this work are intended to be inserted into the forecasting and verification chain at Météo-France.

Im folgenden wird ein Verfahren dargestellt welches die Möglichkeit bietet komplexe räumliche Zusammenhänge zwischen Niederschlagsereignissen quantitativ in Klimanetzwerke zu fassen und diese auf vielfältige Arten und Weisen zu analysieren. In dem Maße wie synchronisiert Niederschlagsereignisse zwischen Raumpunkten auftreten, in dem Maße sind diese Raumpunkte in Event Synchronization Klimanetzwerken verbunden. Zum einen wird das bestehende Ähnlichkeitsmaß der Ereignissynchronisation verbessert und erweitert, und zum anderen werden verschiedene, zum Teil neue, statistische Methoden zur Netzwerkanalyse vorgestellt und erläutert. Klimanetzwerke sind räumlich eingebettete Netzwerke und die statistisch zu zeigende Abhängigkeit der Ähnlichkeit vom räumlichen Abstand führt zu einer vom Raum nicht unabängigen Netzwerkstruktur. Dies ist in einer Vielzahl von Fällen ein ungewünschter Effekt und es wird eine Methodik entwickelt wie dieser statistisch quantifiziert werden kann. Des weiteren werden zwei weitere neue Netzwerkstatistiken vorgestellt. Einerseits das neue Netzwerkmaß Directionality und andererseits eine Netzwerkreduktion welche Klimanetzwerke auf Klimanetzwerke mit weitreichenden Verbindungen reduziert. Dieser neue Ansatz steht gewissermaßen im Gegensatz zur klassischen Klimanetzwerkkonstruktion die vor allem zu kurzreichweitigen Verbindungen führt. Das neue Netzwerkmaß Directionality gibt für jeden Raumpunkt des Netzwerks eine dominante Raumrichtung der Netzwerkverbindungen an und kann dadurch z.B. für bestimmte Event Synchronization Klimanetzwerke Isochronen abbilden. / In the following an approach to the analysis of spatial structures of precipitation event synchronizations is presented. By estimating the synchronicity of precipitation events between points in space, a spatial similarity network is constructed. These Climate Networks can be analyzed statistically in various ways. However, the similarity measure Event Synchronization that will be presented, as well as the concept of Climate Networks, is more general. Climate Network precipitation analyses are done in the applications part in order to present improvements to existing methodologies, as well as novel ones. On one hand, the existing similarity measure Event Synchronization will be refined and extended to a weighted and continuous version, and on the other hand, new methods for statistical analyses of Climate Networks will be presented. Climate Networks are spatially embedded networks and the probability of a link between two nodes decreases with the distance between these nodes. In other words, Climate Network topologies depend on the spatial embedding. Often this effect is distracting and should be considered as a bias in Climate Network statistics. This thesis provides a methodology to estimate this bias and to correct network measures for it. Furthermore, two novel graph statistics are introduced. First, the novel network measure Directionality, and second, a network coarse-graining approach that reduces Climate Networks to Climate Networks of teleconnections, i.e., long-ranged interrelations. This new approach is in contrast to existing Climate Network construction schemes, since commonly most links are short. The novel network measure Directionality provides a dominant direction of links in the embedding space. For undirected Event Synchronization networks this measure is applied for the estimation of Isochrones, i.e., lines of synchronous event occurrences.

Das Ziel dieser Arbeit ist es Geheimnisse des Indischen Monsuns aufzudecken-ein groß-skaliges Klimaphänomen,das mehr als 1,7 Milliarden Menschen stark beeinflußt.Folglich ist das Verständnis der Mechanismen des Indischen Monsuns und seine erfolgreiche Prognose nicht nur eine Frage von größtem Interesse,sondern auch eine bedeutende wissenschaftliche Herausforderung.Der erste Teil dieser Arbeit ist den extremen Niederschlagsereignissen über dem Indischen Subkontinent gewidmet.In dieser Arbeit wurde gezeigt,dass eine Synchronizität zwischen extremen Niederschlagsereignissen in den Eastern Ghats und Nord Pakistan Regionen durch das Zusammenspiel zwischen dem indischen Monsun und einem nicht-Monsun-Niederschlagsmuster verursacht wird.Dieses Ergebnis unterstreicht die Bedeutung der Region Nord-Pakistan zur Ableitung der Wechselwirkung zwischen dem indischen Monsun-System und den West-Störungen,und verbessert daher das Verständnis der Kopplung des indischen Monsuns mit den Extratropen.Der zweite Teil der Arbeit befasst sich mit dem Problem der räumlichen und zeitlichen Organisation des abrupten Übergangs auf den indischen Monsun.Hier wird ein neuartiger Mechanismus des räumlich-zeitlichen Übergangs zur Regenperiode vorgeschlagen.Er hat mehrere Vorteile gegenüber bestehenden Erklärungen der Natur des indischen Monsuns:Es beschreibt den abrupten Übergang in einer gewählten Region des indischen Subkontinents sowie die räumliche Ausbreitung und Variabilität des indischen Monsuns beim Einsetzen entlang der Achse des Monsuns.Der dritte Teil dieser Arbeit konzentriert sich auf das Problem der Vorhersagbarkeit des indischen Monsuns.Das vorgeschlagene Verfahren ermöglicht die Vorhersage des Einsetzens und Endens über einen mehr als zwei Wochen bzw.einen Monat früheren Zeitraum im Vergleich zu bisher bekannten Methoden.Schließlich kann die vorgeschlagene Instrumentarium direkt in das bestehende lang-reichweitige Vorhersagesystem für den Monsuns implementiert werden. / The aim of this thesis is to uncover some of the mysteries surrounding the Indian Monsoon - a large-scale climatic phenomenon affecting more than 1.7 billion people. Consequently, understanding the mechanisms of the Indian monsoon and its successful forecasting is not only a question of great interest, but also a significant scientific challenge. The first part of this thesis is devoted to extreme rainfall events over the Indian subcontinent. In this thesis, I have shown that a synchronicity between extreme rainfall events in the Eastern Ghats and North Pakistan regions is caused by the interplay between the Indian Monsoon and a non-monsoonal precipitation pattern driven by the Westerlies - Western Disturbances. This result highlights the importance of the North Pakistan region for inferring the interaction between the Indian Monsoon system and Western Disturbances, and, therefore, improves the understanding of the Indian Monsoon coupling with the extratropics. The second part of this dissertation is concerned with the problem of the spatial and temporal organization of the abrupt transition to the Indian monsoon. Here, I have proposed a novel mechanism of a spatio-temporal transition to monsoon. It has several advantages in comparison to existing explanations of the Indian Monsoon nature: it describes the abrupt transition to monsoon in a chosen region of the Indian subcontinent, as well as the spatial propagation and variability of the Indian Monsoon onset along the axis of advance of monsoon. The third part of this thesis focuses on the problem of predictability of the Indian Monsoon. I have developed a novel method that predicts the onset and withdrawal dates more than two weeks and a month earlier than existing methods, respectively. Finally, the proposed scheme can be directly implemented into the existing long-range forecasting system of the monsoon''s timing.

In den vergangenen Jahrzehnten wurden extreme Ereignisse, die nicht durch Gauß-Verteilungen beschrieben werden können, in einer Vielzahl an physikalischen Systemen beobachtet. Während statistische Methoden eine zuverlässige Identifikation von extremen Ereignissen ermöglichen, ist deren Entstehungsmechanismus nicht vollständig geklärt. Das Auftreten von extremen Ereignissen ist nicht vollkommen verstanden, da sie nur selten beobachtet werden können und häufig unter schwer reproduzierbaren Bedingungen auftreten. Deshalb ist es erstrebenswert Experimente zu entwickeln, die eine einfache Beobachtung von extremen Ereignissen erlauben. In dieser Dissertation werden extreme Ereignisse untersucht, die bei Multi-Filamentation von Femtosekundenlaserimpulsen entstehen. In den Experimenten, die in dieser Dissertation vorgestellt werden, werden Multi-Filamente durch Hochgeschwindigkeitskameras analysiert. Die Untersuchung der raum-zeitlichen Dynamik der Multi-Filamente zeigt eine L-förmige Wahrscheinlichkeitsverteilung, Diese Beobachtung impliziert das Auftreten von extremen Ereignissen. Lineare Analyse liefert Hinweise auf die physikalischen Prozesse, die zur Entstehung der extremen Ereignisse führen und nicht-lineare Zeitreihen-Analyse charakterisiert die Dynamik des Systems. Die Analyse der Multi-Filamente wird außerdem auf extreme Ereignisse in Wellen-Messungen und optische Superkontinua angewandt. Die durchgeführten Analysen zeigen Unterschiede in den physikalischen Prozessen, die zur Entstehung von extremen Ereignissen führen. Extreme Ereignisse in optischen Fasern werden durch stochastische Fluktuationen von verstärktem Quantenrauschen dominiert. In Multi-Filamenten und Ozeanwellen resultieren extreme Ereignisse dagegen aus klassischer mechanischer Turbulenz, was deren Vorhersagbarkeit impliziert. In dieser Arbeit wird anhand der von Multi-Filament-Zeitreihen die Vorhersagbarkeit in einem kurzen Zeitfenster vor Auftreten des extremen Ereignisses bewiesen. / In the last decades, extreme events, i.e., high-magnitude phenomena that cannot be described within the realm of Gaussian probability distributions have been observed in a multitude of physical systems. While statistical methods allow for a reliable identification of extreme event systems, the underlying mechanism behind extreme events is not understood. Extreme events are not well understood due to their rare occurrence and their onset under conditions that are difficult to reproduce. Thus, it is desirable to identify extreme event scenarios that can serve as a test bed. Optical systems exhibiting extreme events have been discovered to be ideal for such tests, and it is now desired to find more different examples to improve the understanding of extreme events. In this thesis, multifilamentation formed by femtosecond laser pulses is analyzed. Observation of the spatio-temporal dynamics of multifilamentation shows a heavy-tailed fluence probability distribution. This finding implies the onset of extreme events during multifilamentation. Linear analysis gives hints on the processes that drive the formation of extreme events. The multifilaments are also analyzed by nonlinear time series analysis, which provides information on determinism and chaos in the system. The analysis of the multifilament s is compared to an analysis of extreme event time series from ocean wave measurements and the supercontinuum output of an optical fiber. The analysis performed in this work shows fundamental differences in the extreme event mechnaism. While the extreme events in the optical fiber system are ruled by the stochastic changes of amplified quantum noise, in the multifilament and the ocean system extreme events appear as a result of the classical mechanical process of turbulence. This implies the predictability of extreme events. In this work, the predictability of extreme events is proven to be possible in a brief time window before the onset of the extreme event.

Made available in DSpace on 2017-07-10T19:24:49Z (GMT). No. of bitstreams: 1 Agnaldo Passolongo Preti.pdf: 3515934 bytes, checksum: 02a0cd639e522e2412af47a054476fc1 (MD5) Previous issue date: 2005-12-12 / There is a clear conflict between the reservoir utilization for control and use multiple of the water mainly for electric power generation. In order to control the floods, it is necessary to predict the availability of empty reservoir volumes, capable of absorbing some inflow parcels, to avoid or reduce the damage caused to the downstream area. From an energy standpoint, it is desirable to allocate the smallest possible protection volume, while from a flood control standpoint, it is desirable to have a reliable estimate of the possibility of the reservoir failing to control a flood when a given protection volume is allocated. The objective of this work was to obtain the Curve Volume x Duration using maximum inflow with different duration fitted by GEV distribution and LH moments used to estimate the protection volume in reservoir. It was used maximum affluent volumes of the Paraná River recorded in Guaira gauge. All the fit of the maximum affluent volumes was agree by the approximate goodness-of-fit test of fitted generalized extreme value distribution using LH moments by WANG (1998) with 5% significance level. The Curve Volume x Duration was build appropriately for ten different affluent volumes durations. / Existe conflito na utilização de reservatórios para o controle de cheias e usos múltiplos da água, principalmente para a geração de energia elétrica. Para controlar cheias é necessário um volume vazio no reservatório capaz de absorver uma eventual cheia sem causar danos nas áreas à jusante. Por outro lado, para gerar energia é desejável alocar o menor volume de proteção possível, ao passo que para controlar cheias é desejável ter uma estimativa confiável da possibilidade do reservatório falhar quando um dado volume de proteção é alocado. O objetivo deste trabalho foi construir a curva volume x duração, empregada para estimar volume de espera, por meio do ajuste das séries de volumes máximos afluentes, utilizando a distribuição GEV e momentos LH. Foram trabalhados volumes afluentes observados em várias estações de rio do Paraná. Todos os ajustes dos volumes máximos afluentes foram aceitos através dos testes de qualidade de ajuste propostos por WANG (1998) e Kolmogorov-Smirnov com 5 % de significância e critério de Kite. As curvas volume x duração foram adequadamente construídas usando valores de volumes máximos afluentes para diferentes durações e estações.

Made available in DSpace on 2017-05-12T14:48:13Z (GMT). No. of bitstreams: 1 Agnaldo Passolongo Preti.pdf: 3515934 bytes, checksum: 02a0cd639e522e2412af47a054476fc1 (MD5) Previous issue date: 2005-12-12 / There is a clear conflict between the reservoir utilization for control and use multiple of the water mainly for electric power generation. In order to control the floods, it is necessary to predict the availability of empty reservoir volumes, capable of absorbing some inflow parcels, to avoid or reduce the damage caused to the downstream area. From an energy standpoint, it is desirable to allocate the smallest possible protection volume, while from a flood control standpoint, it is desirable to have a reliable estimate of the possibility of the reservoir failing to control a flood when a given protection volume is allocated. The objective of this work was to obtain the Curve Volume x Duration using maximum inflow with different duration fitted by GEV distribution and LH moments used to estimate the protection volume in reservoir. It was used maximum affluent volumes of the Paraná River recorded in Guaira gauge. All the fit of the maximum affluent volumes was agree by the approximate goodness-of-fit test of fitted generalized extreme value distribution using LH moments by WANG (1998) with 5% significance level. The Curve Volume x Duration was build appropriately for ten different affluent volumes durations. / Existe conflito na utilização de reservatórios para o controle de cheias e usos múltiplos da água, principalmente para a geração de energia elétrica. Para controlar cheias é necessário um volume vazio no reservatório capaz de absorver uma eventual cheia sem causar danos nas áreas à jusante. Por outro lado, para gerar energia é desejável alocar o menor volume de proteção possível, ao passo que para controlar cheias é desejável ter uma estimativa confiável da possibilidade do reservatório falhar quando um dado volume de proteção é alocado. O objetivo deste trabalho foi construir a curva volume x duração, empregada para estimar volume de espera, por meio do ajuste das séries de volumes máximos afluentes, utilizando a distribuição GEV e momentos LH. Foram trabalhados volumes afluentes observados em várias estações de rio do Paraná. Todos os ajustes dos volumes máximos afluentes foram aceitos através dos testes de qualidade de ajuste propostos por WANG (1998) e Kolmogorov-Smirnov com 5 % de significância e critério de Kite. As curvas volume x duração foram adequadamente construídas usando valores de volumes máximos afluentes para diferentes durações e estações.

Cette thèse porte sur l'étude numérique des fluctuations extrêmes de la force de traînée exercée par un écoulement turbulent sur un corps immergé.Ce type d'évènement, très rare, est difficile à caractériser par le biais d'un échantillonnage direct, puisqu'il est alors nécessaire de simuler l'écoulement sur des durées extrêmement longues. Cette thèse propose une approche différente, basée sur l'application d'algorithmes d'échantillonnage d'événements rares. L'objectif de ces algorithmes, issus de la physique statistique, est de modifier la statistique d'échantillonnage des trajectoires d'un système dynamique, de manière à favoriser l'occurrence d'événements rares. Si ces techniques ont été appliquées avec succès dans le cas de dynamiques relativement simples, l'intérêt de ces algorithmes n'est à ce jour pas clair pour des dynamiques déterministes extrêmement complexes, comme c'est le cas pour les écoulement turbulents.Cette thèse présente tout d'abord une étude de la dynamique et de la statistique associée aux fluctuations extrêmes de la force de traînée sur un obstacle carré fixe immergé dans un écoulement turbulent à deux dimensions. Ce cadre simplifié permet de simuler la dynamique sur des durées très longues, permettant d'échantillonner un grand nombre de fluctuations dont l'amplitude est assez élevée pour être qualifiée d'extrême.Dans un second temps, l'application de deux algorithmes d’échantillonnage est présentée et discutée.Dans un premier cas, il est illustré qu'une réduction significative du temps de calcul d'extrêmes peut être obtenue. En outre, des difficultés liées à la dynamique de l'écoulement sont mises en lumière, ouvrant la voie au développement de nouveaux algorithmes spécifiques aux écoulements turbulents. / This thesis discusses the numerical simulation of extreme fluctuations of the drag force acting on an object immersed in a turbulent medium.Because such fluctuations are rare events, they are particularly difficult to investigate by means of direct sampling. Indeed, such approach requires to simulate the dynamics over extremely long durations.In this work an alternative route is introduced, based on rare events algorithms.The underlying idea of such algorithms is to modify the sampling statistics so as to favour rare trajectories of the dynamical system of interest.These techniques recently led to impressive results for relatively simple dynamics. However, it is not clear yet if such algorithms are useful for complex deterministic dynamics, such as turbulent flows.This thesis focuses on the study of both the dynamics and statistics of extreme fluctuations of the drag experienced by a square cylinder mounted in a two-dimensional channel flow.This simple framework allows for very long simulations of the dynamics, thus leading to the sampling of a large number of events with an amplitude large enough so as they can be considered extreme.Subsequently, the application of two different rare events algorithms is presented and discussed.In the first case, a drastic reduction of the computational cost required to sample configurations resulting in extreme fluctuations is achieved.Furthermore, several difficulties related to the flow dynamics are highlighted, paving the way to novel approaches specifically designed to turbulent flows.

Climate change adaptation has received limited attention compared to mitigation across all spatial levels. This is besides the documented adverse impacts of climate change in different sectors of societies including mining in general and coal mining specifically. Against this background, the study set three objectives. The first objective was to identify current and possible future climate change impacts that may affect selected coal mines in South Africa. The second objective was to establish the nature and extent to which these mines were ready to address and implement adaptation measures. The last objective was to determine and document existing climate change adaptation practices in selected mines. Employing the mixed methods approach, the research engaged five coal mines located in Mpumalanga, Free State and Kwa Zulu-Natal, gathering both the qualitative and quantitative data. This data was analysed thematically. The research made three major findings. The first finding was that the climatic conditions in the research areas have been changing over the observed period. In general, rainfall has been declining and temperatures have been increasing, leading to increased cases of extreme fog, mist and heatwaves. The second finding was that there has been an increase in frequency and intensity of extreme weather events, most notably, floods and droughts. These changes in the climate and associated weather events have frequently affected mine operations particularly at the production sub-chain of the coal mining value chain. The third major finding was that despite this evidence of adverse impact of climate change on the production sub-chain of the South African coal mining value chain, adaption responses in all the studied mines showed reactive adaptation to extreme events instead of proactive adaptation planning and implementation. South Africa depends on coal-derived energy, electricity in particular and the coal mines are implicitly exposed and vulnerable to the adverse impacts of climate change. Reducing this exposure and vulnerability dictates the urgent need to implement anticipatory adaptation measures in all the sub-chains of the coal mining value chain. / Environmental Sciences / D. Litt. et Phil (Environmental management)

Ces travaux de thèse présentent l’étude des différentes classes d’effets linéaires et non-linéaires en optiquequi génèrent des événements extrêmes dont les propriétés sont analogues à celles des « vagues scélérates » destructrices qui apparaissent à la surface des océans. La thèse commence avec un bref aperçu de l’analogie physique entre la localisation d’onde dans les systèmes hydrodynamique et les systèmes optique, pour lesquels nous décrivons les mécanismes de génération de vagues scélérates linéaire et non-linéaire. Nous présentons ensuite quelques résultats numérique et expérimentaux de la génération de vagues scélérates dans un système optique linéaire dans le cas d’une propagation spatiale d’un champ optique qui présenteune phase aléatoire, où nous interprétons les résultats obtenus en terme de caustiques optiques localisées.Nous considérons ensuite les vagues scélérates obtenues dans des systèmes non-linéaires qui présentent une instabilité de modulation décrite par l’équation de Schrödinger non-linéaire (ESNL). Nous présentons une étude numérique détaillée comparant les caractéristiques spatio-temporelles des structures localisées obtenues dans les simulation numérique avec les différentes solutions analytiques obtenues à partir de l’ESNL.Deux études expérimentales d’instabilités de modulation sont ensuite effectuées. Dans la première, nous présentons des résultats expérimentaux qui étudient les propriétés d’instabilité de modulation en utilisant un système d’agrandissement temporel par lentille temporelle; dans la deuxième, nous rapportons des résultats expérimentaux sur les propriétés des instabilités de modulation dans le domaine fréquentiel en utilisant une technique de mesure spectrale en temps-réel. Cette dernière étude examine l’effet sur la bande spectrale et surla stabilité d’un faible champ perturbateur. Tous les résultats expérimentaux sont comparés avec la simulation d’ESNL et abordés en termes des propriétés qualitatives d’instabilité de modulation. Dans toutes ces études,différentes propriétés statistiques sont analysées en rapport avec l’apparition des vagues scélérates. / This thesis describes the study of several different classes of linear and nonlinear effects in optics that generatelarge amplitude extreme events with properties analogous to the destructive “rogue waves” on the surface of theocean. The thesis begins with a brief overview of the analogous physics of wave localisation in hydrodynamicand optical systems, where we describe linear and nonlinear rogue wave generating mechanisms in bothcases. We then present numerical and experimental results for rogue wave generation in a linear opticalsystem consisting of free space propagation of a spatial optical field with random phase. Computed statisticsbetween experiment and modelling are in good agreement, and we interpret the results obtained in termsof the properties of localised optical caustics. We then consider rogue waves in the nonlinear system ofmodulation instability described by the Nonlinear Schrodinger Equation (NLSE), and a detailed numericalstudy is presented comparing the spatio-temporal characteristics of localised structures seen from numericalsimulations with different known analytic solutions to the NLSE. Two experimental studies of modulationinstability are then reported. In the first, we present experimental results studying the properties of modulationinstability using a time-lens magnifier system; in the second, we report experimental results studying thefrequency-domain properties of modulation instability using real-time spectral measurements. The latter studyexamines the effect of a weak seed field on spectral bandwidth and stability. All experimental results arecompared with the NLSE simulations and discussed in terms of the qualitative properties of modulationinstability, in order to gain new insights into the complex dynamics associated with nonlinear pulse propagation.In all of these studies, different statistical properties are analised in relation to the emergence of rogue waves.

This thesis aims to develop a new model for stress-testing financial portfolios using Extreme Value Theory (EVT) and General Adversarial Networks (GANs). The current practice of risk management relies on mathematical or historical models, such as Value-at-Risk and expected shortfall. The problem with historical models is that the data which is available for very extreme events is limited, and therefore we need a method to interpolate and extrapolate beyond the available range. EVT is a statistical framework that analyzes extreme events in a distribution and allows such interpolation and extrapolation, and GANs are machine-learning techniques that generate synthetic data. The combination of these two areas can generate more realistic stress-testing scenarios to help financial institutions manage potential risks better. The goal of this thesis is to develop a new model that can handle complex dependencies and high-dimensional inputs with different kinds of assets such as stocks, indices, currencies, and commodities and can be used in parallel with traditional risk measurements. The evtGAN algorithm shows promising results and is able to mimic actual distributions, and is also able to extrapolate data outside the available data range. / Detta examensarbete handlar om att utveckla en ny modell för stresstestning av finansiella portföljer med hjälp av extremvärdesteori (EVT) och Generative Adversarial Networks (GAN). Dom modeller för riskhantering som används idag bygger på matematiska eller historiska modeller, som till exempel Value-at-Risk och Expected Shortfall. Problemet med historiska modeller är att det finns begränsat med data för mycket extrema händelser. EVT är däremot en del inom statistisk som analyserar extrema händelser i en fördelning, och GAN är maskininlärningsteknik som genererar syntetisk data. Genom att kombinera dessa två områden kan mer realistiska stresstestscenarier skapas för att hjälpa finansiella institutioner att bättre hantera potentiella risker. Målet med detta examensarbete är att utveckla en ny modell som kan hantera komplexa beroenden i högdimensionell data med olika typer av tillgångar, såsom aktier, index, valutor och råvaror, och som kan användas parallellt med traditionella riskmått. Algoritmen evtGAN visar lovande resultat och kan imitera verkliga fördelningar samt extrapolera data utanför tillgänglig datamängd.