Basierend auf der Theorie von Netzwerken wird ein allgemeines Rahmenwerk entwickelt, um kollektive Synchronisationsphänome von Extremereignissen in komplexen Systemen zu studieren. Die Methode vergleicht die Variabilität der einzelnen Teile des Systems auf Grundlage von Beobachtungszeitreihen mit dem Ziel, emergente Synchronisationsmuster von Extremereignissen auf makroskopischer Ebene aufzudecken. Zu diesem Zweck werden die einzelnen Zeitreihen eines interaktiven Systems mit den Knoten eines Netzwerks identifiziert und die Abhängigkeiten zwischen diesen durch die Kanten des Netzwerks dargestellt. Die komplexe interne Synchronisationsstruktur des Systems wird so in Form der Netzwerktopologie mathematisch zugänglich gemacht und kann durch die Einführung geeigneter Netzwerkmaße analysiert werden. Die Methode wird im Folgenden auf räumlich und zeitlich hochaufgelöste Regendaten aus Satellitenmessungen angewendet, um die kollektive Dynamik extremer Regenereignisse in Südamerika zu untersuchen. Diese Anwendung verfolgt drei Ziele: Erstens wird gezeigt, wie die hier entwickelte Methode zur klimatologischen Analyse verwendet werden kann. Zweitens können Quellen und Senken von Extremereignissen durch die Einführung des Konzeptes der Netzwerkdivergenz identifiziert werden. Dies erlaubt es, die gerichteten Netzwerkpfade, entlang derer Extremereignisse synchronisieren, nachzuverfolgen. Auf dieser Grundlage wird eine statistische Regel gewonnen, die beträchtliche Anteile der extremen Regenereignisse in den Zentralanden vorhersagt. Drittens werden die bis dahin entwickelten Methoden und gewonnenen Einsichten dazu verwendet, die Darstellung extre- mer Regenereignisse in verschiedenen Datensätzen zu vergleichen. Insbesondere wird in diesem Kontext die Implementierung solcher Ereignisse in drei gängigen Klimamodellen evaluiert. / Based on the theory of networks, a general framework is developed to study collective synchronization phenomena of extreme events in complex systems. The method relies on observational time series encoding the variability of the single parts of the system, and is intended to reveal emerging patterns of extreme event synchronization on the macroscopic level. For this purpose, the time series obtained from an interactive system under consideration are identified with network nodes, and the possibly delayed and non-linear interdependence of extreme events in different time series is represented by network links connecting the nodes. In this way, the complex internal synchronization structure of the system becomes accessible in terms of the topology of the network, which can be analyzed by introducing suitable network measures. The methodology is applied to satellite-derived rainfall time series of high spatiotemporal resolution in order to investigate the collective dynamics of extreme rainfall events in South America. The purpose of this application is threefold: First, it is shown how the methodology can be used for climatic analysis by revealing climatological mechanism from the spatial patterns exhibited by different network measures. Second, by introducing the concept of network divergence, sink and source regions of extreme events can be identified, allowing to track their directed synchronization pathways through the network. A simple statistical forecast rule is derived on this basis, predicting substantial fractions of extreme rainfall events in the Central Andes. Third, the methodology and the insights developed in the first two steps are used to evaluate the dynamical representation of extreme events in different datasets, and in particular their dynamical implementation in three state of the art climate models.

This dissertation analyzes the impact of climate, and atmospheric carbon dioxide (CO2) on crop yields and grain transportation. The analysis of crop yields endeavors to advance the literature by statistically estimating the effects of atmospheric carbon dioxide (CO2) on observed crop yields. This is done using an econometric model estimated over pooled historical data for 1950-2009 and data from the free air CO2 enrichment experiments. The main findings are: 1) yields of soybeans, cotton, and wheat directly respond to the elevated CO2, while yields of corn and sorghum do not; 2) the effect of crop technological progress on mean yields is non-linear; 3) ignoring atmospheric CO2 in an econometric model of crop yield likely leads to overestimates of the pure effects of climate change and technological progress on crop yields; and 4) average climate conditions and climate variability contribute in a statistically significant way to average crop yields and their variability. To examine climate change impacts on grain transportation flows, this study employs two modeling systems, a U.S. agricultural sector model and an international grain transportation model, with linked inputs/outputs. The main findings are that under climate change: 1) the excess supply of corn and soybeans generally increases in Northern U.S. regions, while it declines in Central and Southern regions; 2) the Corn Belt, the largest producer of corn in the U.S., is anticipated to ship less corn; 3) the importance of lower Mississippi River ports, the largest current destination for U.S. grain exports, diminishes under the climate change cases, whereas the role of Pacific Northwest ports, Great Lakes ports, and Atlantic ports is projected to increase; 4) the demand for grain shipment via rail and truck rises, while demand for barge transport drops.

Ces travaux de thèse rapportent l’étude des instabilités non-linéaires et des évènements extrêmesse développant lors de la propagation guidée d’un champ électromagnétique au sein de fibresoptiques. Après un succinct rappel des divers processus linéaires et non-linéaires menant à lagénération de super continuum optique, nous montrons que le spectre de celui-ci peut présenterde larges fluctuations, incluant la formation d’événements extrêmes, dont les propriétés statistiqueset l’analogie avec les vagues scélérates hydrodynamiques sont abordées en détail. Nous présentonsune preuve de principe de l’application de ces fluctuations spectrales à la génération de nombres etde marches aléatoires et identifions le phénomène d’instabilité de modulation, ayant lieu lors de laphase initiale d’expansion spectrale du super continuum, comme principale contribution à la formationd’événements extrêmes. Ce mécanisme est étudié numériquement et analytiquement, en considérantune catégorie de solutions exactes de l’équation de Schrödinger non-linéaire présentant descaractéristiques de localisations singulières. Les résultats obtenus sont vérifiés expérimentalement,notamment grâce à un système de caractérisation spectrale en temps réel et à l’utilisation conjointede métriques statistiques innovantes (ex : cartographie de corrélations spectrales). L’excellent accordentre simulations et expériences a permis de valider les prédictions théoriques et d’accéder àune meilleure compréhension des dynamiques complexes inhérentes à la propagation non-linéaired’impulsions optiques. / This thesis reports the study of nonlinear instabilities and extreme events occurring during the guidedpropagation of an electromagnetic field into optical fibers. After a short overview of the various linearand nonlinear processes leading to optical supercontinuum generation, we show that its spectrumcan exhibit large fluctuations, including the formation of extreme events, whose statistical propertiesas well as hydrodynamic rogue waves analogy are studied in detail. We provide a proof of principle ofusing these spectral fluctuations for random number and random walk generation and identify modulationinstability, associated with the onset phase of supercontinuum spectral broadening, as themain phenomenon leading to extreme event formation. This mechanism is studied both numericallyand analytically, considering a class of exact solutions of nonlinear Schrödinger equation which exhibitsingular localization characteristics. The results are experimentally verified, especially througha real-time spectral characterization system along with the use of innovative statistical metrics (e.g.spectral correlation maps). The excellent agreement between simulations and experiments allowedus to validate the theoretical predictions and get further insight into the complex dynamics associatedto nonlinear optical pulse propagation.