Using spatial extreme-value theory with machine learning to model and understand spatially compounding extremes

When extreme weather events affect large areas, their regional to sub-continental spatial scale is important for their impacts. We propose a novel methodology that combines spatial extreme-value theory with a machine learning (ML) algorithm to model weather extremes and quantify probabilities associated with the occurrence, intensity and spatial extent of these events. The model is here applied to Western European summertime heat extremes. Using new loss functions adapted to extreme values, we fit a theoretically-motivated spatial model to extreme positive temperature anomaly fields from 1959-2022, using the daily 500-hpa geopotential height fields across the Euro-Atlantic region and the local soil moisture as predictors. Our generative model reveals the importance of individual circulation features in determining different facets of heat extremes, thereby enriching our process understanding of them from a data-driven perspective. The occurrence, intensity, and spatial extent of heat extremes are sensitive to the relative position of individual ridges and troughs that are part of a large-scale wave pattern. Heat extremes in Europe are thus the result of a complex interplay between local and remote physical processes. Our approach is able to extrapolate beyond the range of the data to make risk-related probabilistic statements, and applies more generally to other weather extremes. It also offers an attractive alternative to physical model-based techniques, or to ML approaches that optimise scores focusing on predicting well the bulk instead of the tail of the data distribution.