In statistics, extreme events are often defined as excesses above a given large threshold. This definition allows hydrologists and flood planners to apply Extreme-Value Theory (EVT) to their time series of interest. Even in the stationary univariate context, this approach has at least two main drawbacks. First, working with excesses implies that a lot of observations (those below the chosen threshold) are completely disregarded. The range of precipitation is artificially shopped down into two pieces, namely large intensities and the rest, which necessarily imposes different statistical models for each piece. Second, this strategy raises a nontrivial and very practical difficultly: how to choose the optimal threshold which correctly discriminates between low and heavy rainfall intensities. To address these issues, we propose a statistical model in which EVT results apply not only to heavy, but also to low precipitation amounts (zeros excluded). Our model is in compliance with EVT on both ends of the spectrum and allows a smooth transition between the two tails, while keeping a low number of parameters. In terms of inference, we have implemented and tested two classical methods of estimation: likelihood maximization and probability weighed moments. Last but not least, there is no need to choose a threshold to define low and high excesses. The performance and flexibility of this approach are illustrated on simulated and hourly precipitation recorded in Lyon, France.

This study focuses on two main rivers of Bohemia (Czech Republic): the Vltava and the Elbe. Flows are determined for the Elbe at Děčín (discharges) and Litoměřice (water stages), and for the Vltava at Prague (discharges). Extreme flows have an important socio-economic impact; hence modelling their occurrence accurately is crucial. We identify the meteorological causes for floods: (a) the winter type due to snowmelt, ice damming, and usually rain, and (b) the summer type due to continuous heavy rains. The amplitude and frequency of floods are analysed using extreme value theory, in a non-stationary context. This allows the determination of the trends of flood features during the instrumental period and their dependence on atmospheric circulation patterns.Key words Bohemia; floods; generalized extreme value theory; peak over threshold; return level; Elbe River; Vltava River Analyse statistique des crues en Bohême (République Tchèque) depuis 1825Résumé Cette étude traite des deux rivières principales de Bohême (République Tchèque): la Rivière Vltava et la Rivière Elbe. Les mesures sont effectuées à Děčín (débits) et à Litoměřice (niveaux d'eau) pour la Rivière Elbe, et à Prague (débits) pour la Vltava. Les débits extrêmes ont un important impact socio-économique, et la prévision de leurs occurrences et ordres de grandeur est donc cruciale. Nous identifions deux causes météorologiques pour les crues: (a) celles d'hiver sont causées par la fonte des neiges, les embâcles de glace et les pluies, et (b) celles d'été sont dues à des pluies intenses et continues. L'amplitude et la fréquence de ces crues sont analysées dans le cadre de la théorie statistique des valeurs extrêmes non-stationnaire. Ceci nous a permis de détecter les tendances des caractéristiques des crues depuis le début de la période instrumentale et leur dépendance aux types de circulation atmosphérique.