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Numerical climate models are complex and combine a large number of physicalprocesses. They are key tools in quantifying the relative contribution ofpotential anthropogenic causes (e.g., the current increase in greenhouse gases)on high impact atmospheric variables like heavy rainfall. These so-calledclimate extreme event attribution problems are particularly challenging in amultivariate context, that is, when the atmospheric variables are measured on apossibly high-dimensional grid.  In this paper, we leverage two statistical theories to assess causality inthe context of multivariate extreme event attribution. As we consider an eventto be extreme when at least one of the components of the vector of interest islarge, extreme-value theory justifies, in an asymptotical sense, a multivariategeneralized Pareto distribution to model joint extremes. Under this class ofdistributions, we derive and study probabilities of necessary and sufficientcausation as defined by the counterfactual theory of Pearl. To increase causalevidence, we propose a dimension reduction strategy based on the optimal linearprojection that maximizes such causation probabilities. Our approach is testedon simulated examples and applied to weekly winter maxima precipitation outputsof the French CNRM from the recent CMIP6 experiment.

Climate extreme event attribution using multivariate peaks-over-thresholds modeling and counterfactual theory