Until recent times, weather forecasts were deterministic in nature. For example, a forecast might state ``The temperature tomorrow will be $20^\circ$C.'' More recently, however, increasing interest has been paid to the uncertainty associated with such predictions. By quantifying the uncertainty of a forecast, for example with a probability distribution, users can make risk-based decisions. The uncertainty in weather forecasts is typically based upon `ensemble forecasts'. Rather than issuing a single forecast from a numerical weather prediction (NWP) model, ensemble forecasts comprise multiple model runs that differ in either the model physics or initial conditions. Ideally, ensemble forecasts would provide a representative sample of the possible outcomes of the verifying observations. However, due to model biases and inadequate specification of initial conditions, ensemble forecasts are often biased and underdispersed. As a result, estimates of the most likely values of the verifying observations, and the associated forecast uncertainty, are often inaccurate. It is therefore necessary to correct, or post-process ensemble forecasts, using statistical models known as `ensemble post-processing methods'. To this end, this thesis is concerned with the application of statistical methodology in the field of probabilistic weather forecasting, and in particular ensemble post-processing. Using various datasets, we extend existing work and propose the novel use of statistical methodology to tackle several aspects of ensemble post-processing. Our novel contributions to the field are the following. In chapter~3 we present a comparison study for several post-processing methods, with a focus on probabilistic forecasts for extreme events. We find that the benefits of ensemble post-processing are larger for forecasts of extreme events, compared with forecasts of common events. We show that allowing flexible corrections to the biases in ensemble location is important for the forecasting of extreme events. In chapter~4 we tackle the complicated problem of post-processing ensemble forecasts without making distributional assumptions, to produce recalibrated ensemble forecasts without the intermediate step of specifying a probability forecast distribution. We propose a latent variable model, and make a novel application of measurement error models. We show in three case studies that our distribution-free method is competitive with a popular alternative that makes distributional assumptions. We suggest that our distribution-free method could serve as a useful baseline on which forecasters should seek to improve. In chapter~5 we address the subject of parameter uncertainty in ensemble post-processing. As in all parametric statistical models, the parameter estimates are subject to uncertainty. We approximate the distribution of model parameters by bootstrap resampling, and demonstrate improvements in forecast skill by incorporating this additional source of uncertainty in to out-of-sample probability forecasts. In chapter~6 we use model diagnostic tools to determine how specific post-processing models may be improved. We subsequently introduce bias correction schemes that move beyond the standard linear schemes employed in the literature and in practice, particularly in the case of correcting ensemble underdispersion. Finally, we illustrate the complicated problem of assessing the skill of ensemble forecasts whose members are dependent, or correlated. We show that dependent ensemble members can result in surprising conclusions when employing standard measures of forecast skill.

Cette étude s'inscrit dans le cadre de la documentation de la variabilité intrasaisonnière atmosphérique et l'analyse de la prévisibilité sur les régions Afrique Centrale et Golfe de Guinée. Elle porte sur les saisons de l'année pour lesquelles la ZCIT est au dessus de l'équateur. Des travaux menés distinctement sur les mois de Mars à Juin et de Septembre à Novembre, il ressort que les activités convective et pluvieuse au cours de ces saisons sont régies par trois modes principaux de variabilité assez proches. Au cours de ces deux saisons, les systèmes individuels générateurs de pluie se déplacent d'est en ouest, et leur activité est régulée par des enveloppes convectives se déplaçant vers l'est. Des analyses spécifiques ont mis en lumière la forte empreinte de signaux équatoriaux de type onde de Kelvin se propageant vers l'est et dont les phases régulent l'organisation des systèmes convectifs. L'impact relatif d'ondes équatoriales se propageant vers l'ouest (Rossby en particulier) et celui d'advections de masses d'air méditerranéennes n'est pas à négliger, d'autant plus qu'elles sont susceptibles d'interagir avec les ondes de Kelvin, et donc de moduler les phases de l'activité convective. Les forçages externes ainsi identités constituent des sources potentielles de prévisibilité pour les modes intrasaisonniers mis en évidence. Utilisant les données de la base multi-modèle TIGGE, l'analyse de la prévisibilité de chacun des modes principaux de variabilité est réalisée. Se focalisant sur les phases spécifiques de ces modes, les scores obtenus augurent une prévisibilité au delà de 10 jours surtout pour des prévisions initialisées lorsque les principales sources sont actives. / In this study we document the intraseasonal variability of the tropical convection and its predictability during the rainy season over the Central Africa and the Gulf of Guinea. Here, our study mainly focuses on seasons of the year for which the ITCZ is north of the equator. Based separate studies carried out on March to June and September to November seasons, we are able to identify three main modes of variability that modulate tropical convection and rainfall in West and Central Africa. During these two seasons, while individual rain-producing systems move westward, their activity is highly modulated by eastward propagating subregional and regional scale systems. Results of detailed analysis indicate the coupling between tropical convection and equatorial Kelvin wave in the region. The phases of these eastward propagating signals play an important role by regulating the organization of convective systems. Moreover, the role played by westward propagating signals (Rossby wave in particular) and Mediterranean air intrusion needs to be taken into account. These systems by interacting with Kelvin wave, may modulate the phases of convective activity in the region. Therefore, external forcing associated with these systems can be useful to the predictability of the intraseasonal modes the region. A multi model diagnostic study is performed using data available from the TIGGE project in order to evaluate the predictability of each of the main modes of variability. For a typical phase of these modes, there seems to be a statistically significant skill associated with predictability of beyond 10 days, especially for predictions initiated from active main sources.

Les erreurs des modèles de prévision numérique du temps (PNT) peuvent être réduites par des méthodes de post-traitement (dites d'adaptation statistique ou AS) construisant une relation statistique entre les observations et les prévisions. L'objectif de cette thèse est de construire des AS de prévisions de vent pour la France sur la grille de plusieurs modèles de PNT, pour les applications opérationnelles de Météo-France en traitant deux problèmes principaux. Construire des AS sur la grille de modèles de PNT, soit plusieurs milliers de points de grille sur la France, demande de développer des méthodes rapides pour un traitement en conditions opérationnelles. Deuxièmement, les modifications fréquentes des modèles de PNT nécessitent de mettre à jour les AS, mais l'apprentissage des AS requiert un modèle de PNT inchangé sur plusieurs années, ce qui n'est pas possible dans la majorité des cas.Une nouvelle analyse du vent moyen à 10 m a été construite sur la grille du modèle local de haute résolution (2,5 km) de Météo-France, AROME. Cette analyse se compose de deux termes: une spline fonction de la prévision la plus récente d'AROME plus une correction par une spline fonction des coordonnées du point considéré. La nouvelle analyse obtient de meilleurs scores que l'analyse existante, et présente des structures spatio-temporelles réalistes. Cette nouvelle analyse, disponible au pas horaire sur 4 ans, sert ensuite d'observation en points de grille pour construire des AS.Des AS de vent sur la France ont été construites pour ARPEGE, le modèle global de Météo-France. Un banc d'essai comparatif désigne les forêts aléatoires comme meilleure méthode. Cette AS requiert un long temps de chargement en mémoire de l'information nécessaire pour effectuer une prévision. Ce temps de chargement est divisé par 10 en entraînant les AS sur des points de grille contigü et en les élaguant au maximum. Cette optimisation ne déteriore pas les performances de prévision. Cette approche d'AS par blocs est en cours de mise en opérationnel.Une étude préalable de l'estimation du « continuous ranked probability score » (CRPS) conduit à des recommandations pour son estimation et généralise des résultats théoriques existants. Ensuite, 6 AS de 4 modèles d'ensemble de PNT de la base TIGGE sont combinées avec les modèles bruts selon plusieurs méthodes statistiques. La meilleure combinaison s'appuie sur la théorie de la prévision avec avis d'experts, qui assure de bonnes performances par rapport à une prévision de référence. Elle ajuste rapidement les poids de la combinaison, un avantage lors du changement de performance des prévisions combinées. Cette étude a soulevé des contradictions entre deux critères de choix de la meilleure méthode de combinaison : la minimisation du CRPS et la platitude des histogrammes de rang selon les tests de Jolliffe-Primo. Il est proposé de choisir un modèle en imposant d'abord la platitude des histogrammes des rangs. / Errors of numerical weather prediction (NWP) models can be reduced thanks to post-processing methods (model output statistics, MOS) that build a statistical relationship between the observations and associated forecasts. The objective of the present thesis is to build MOS for windspeed forecasts over France on the grid of several NWP models, to be applied on operations at Météo-France, while addressing the two main issues. First, building MOS on the grid of some NWP model, with thousands of grid points over France, requires to develop methods fast enough for operational delays. Second, requent updates of NWP models require updating MOS, but training MOS requires an NWP model unchanged for years, which is usually not possible.A new windspeed analysis for the 10 m windspeed has been built over the grid of Météo-France's local area, high resolution (2,5km) NWP model, AROME. The new analysis is the sum of two terms: a spline with AROME most recent forecast as input plus a correction with a spline with the location coordinates as input. The new analysis outperforms the existing analysis, while displaying realistic spatio-temporal patterns. This new analysis, now available at an hourly rate over 4, is used as a gridded observation to build MOS in the remaining of this thesis.MOS for windspeed over France have been built for ARPEGE, Météo-France's global NWP model. A test-bed designs random forests as the most efficient MOS. The loading times is reduced by a factor 10 by training random forests over block of nearby grid points and pruning them as much as possible. This time optimisation goes without reducing the forecast performances. This block MOS approach is currently being made operational.A preliminary study about the estimation of the continuous ranked probability score (CRPS) leads to recommendations to efficiently estimate it and to generalizations of existing theoretical results. Then 4 ensemble NWP models from the TIGGE database are post-processed with 6 methods and combined with the corresponding raw ensembles thanks to several statistical methods. The best combination method is based on the theory of prediction with expert advice, which ensures good forecast performances relatively to some reference forecast. This method quickly adapts its combination weighs, which constitutes an asset in case of performances changes of the combined forecasts. This part of the work highlighted contradictions between two criteria to select the best combination methods: the minimization of the CRPS and the flatness of the rank histogram according to the Jolliffe-Primo tests. It is proposed to choose a model by first imposing the flatness of the rank histogram.

This thesis offers a new contextualisation of weather signs, naturally occurring terrestrial indicators of weather change (from, for example, animals, plants and atmospheric phenomena), in antiquity. It asks how the utility of this method of prediction was perceived and presented in ancient sources and studies the range of answers given across almost eight hundred years of Greek and Roman civilisation. The presentation of weather signs is compared throughout to that of another predictive method, astrometeorology, which uses the movement of the stars as markers of approaching weather. The first chapter deals with the presentation and discussion of weather signs in a range of Greek texts. It sees hesitant trust being placed in weather signs, lists of which were constructed so as to be underpinned by astronomical knowledge. The second chapter assesses how these Greek lists were received and assimilated into Roman intellectual discourse by looking to the strikingly similar practice of divining by portents. This lays the foundations for the final chapter, which describes and explains the Roman treatment of weather signs. Here, the perceived utility of weather signs can be seen to reduce rapidly as the cultural significance of astronomy reaches new heights. This thesis provides new readings and interpretations of a range of weather-based passages and texts, from the Pseudo-Theophrastan De Signis, to Lucan's Pharsalia, to Pliny's Natural History, many of which have previously been greatly understudied or oversimplified. It allows us to understand the social and scientific place of weather prediction in the ancient world and therefore how abstract and elaborate ideas and theories filtered in to the seemingly commonplace and everyday. I argue that between the 7th century BC and the end of the 1st century AD, the treatment of weather signs changes from being framed in fundamentally practical terms to one in which practical considerations were negligible or absent. As this occurred, astrometeorology comes to be seen as the only predictive method worthy of detailed attention. These two processes, I suggest, were linked.