Températures maximales au 21ème siècle

As global warming alters the distribution of extreme temperatures, classical stationary risk indices such as return levels that can be interpreted in a stationary framework become inadequate, calling for new probabilistic tools that integrate both future projected trajectories, varied sources of information, and increased uncertainty.This thesis addresses the challenge of characterizing risks associated with extreme hot temperatures in a non-stationary climate context. In the first part of this thesis, we present a methodology for producing distributions of extreme temperatures in a non-stationary context. Building on the generalized extreme value distribution of the block maxima approach, we introduce a covariate to represent global warming trajectories and future emission scenarios. Distribution parameters are estimated using a Bayesian framework similar to Robin et Ribes (2020), which synthesizes climate model projections from General Circulation Models into an a priori distribution and then updates it based on observations, to propose projections of annual maxima. Particular attention is devoted to computational aspects, with a systematic evaluation of various posterior sampling algorithms. The adoption of the STAN implementation of the No-U-Turn Sampler (NUTS) substantially reduces computation time while improving the reliability of posterior estimates, thereby enabling analyses at both higher resolution and over larger domains.In the second part of this thesis, we introduce the Predictive Equivalent Reliability level (PER), a synthetic risk index to summarize distributions of hot extremes. The PER extends the concept of return levels to the non-stationary setting by considering cumulative exceedance probabilities over the design period. It ensures both consistency with established practice and robustness under climate change conditions. The predictive formulation further integrates stochastic and parameter uncertainty into this single, probabilistic index. To illustrate its practical meaning, we carry out life-level analyses that show how PER levels depend strongly on design choices, including the design period, exceedance probability, and emission scenario. These results underscore that defining a risk index is not merely a technical exercise but is inherently tied to decision-making contexts. In the third part of this thesis, we apply this methodology across global, national, and local scales. Efforts are being made to assess the representativity of input data, whether observational or simulated. At the global level, for the design period 2050-2100 with a 5% probability of exceedance, we obtained PER levels of 55.5 °C under SSP1-1.9, 57.4 °C under SSP2-4.5, and 61.5 °C under SSP5-8.5. At the national scale, analyses reveal that observational datasets strongly condition projected PER levels, even though over France, differences between ERA5 and a national observational database prove less influential than the choice of emission scenario itself. At the local scale, we focus on a coastal site where GCMs failed to capture important local phenomenas. Here, we propose correcting the prior distribution using higher-resolution regional climate models to account for local specificities. Overall, this thesis provides both methodological advances and practical insights for assessing risk due to extremes of hot temperatures under climate change. By conciliating climate model projections and observations based on Bayesian inference, predictive and cumulative risk metrics, and multi-scale applications, it contributes to the development of tools to describe future extremes and to inform adaptation strategies in sectors where extreme heat poses critical challenges, such as public health and nuclear safety.