Global warming is affecting the Earth climate year by year, the biggest difference being observable in increasing temperatures in the World Ocean. Following the long- term global ocean warming trend, average sea surface temperatures across the global tropics and subtropics have increased by 0.4–1◦C in the last 40 years. These rates become even higher in semi-enclosed southern seas, such as the Red Sea, threaten- ing the survival of thermal-sensitive species. As average sea surface temperatures are projected to continue to rise, careful study of future developments of extreme temper- atures is paramount for the sustainability of marine ecosystem and biodiversity. In this thesis, we use Extreme-Value Theory to study sea surface temperature extremes from a gridded dataset comprising 16703 locations over the Red Sea. The data were provided by Operational SST and Sea Ice Analysis (OSTIA), a satellite-based data system designed for numerical weather prediction. After pre-processing the data to account for seasonality and global trends, we analyze the marginal distribution of ex- tremes, defined as observations exceeding a high spatially varying threshold, using the Generalized Pareto distribution. This model allows us to extrapolate beyond the ob- served data to compute the 100-year return levels over the entire Red Sea, confirming the increasing trend of extreme temperatures. To understand the dynamics govern- ing the dependence of extreme temperatures in the Red Sea, we propose a flexible local approach based on R-Pareto processes, which extend the univariate Generalized Pareto distribution to the spatial setting. Assuming that the sea surface temperature varies smoothly over space, we perform inference based on the gradient score method over small regional neighborhoods, in which the data are assumed to be stationary in space. This approach allows us to capture spatial non-stationarity, and to reduce the overall computational cost by taking advantage of distributed computing resources. Our results reveal an interesting extremal spatial dependence structure: in particular, from our estimated model, we conclude that significant extremal dependence prevails for distances up to about 2500 km, which roughly corresponds to the Red Sea length.

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Part I - Level crossings and other level functionals.<br />Part II - Some contributions in statistics of extremes and in statistical mechanics.