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

## TL;DR

This paper develops a statistical framework combining multivariate peaks-over-thresholds modeling and counterfactual causality theory to attribute climate extreme events, like heavy rainfall, to anthropogenic causes, especially in high-dimensional atmospheric data.

## Contribution

It introduces a novel approach that integrates extreme-value theory with counterfactual causality for multivariate climate event attribution, including a dimension reduction strategy for high-dimensional data.

## Key findings

- Effective modeling of joint extremes using multivariate generalized Pareto distribution.
- Successful application to French winter precipitation data from CMIP6.
- Enhanced causal attribution evidence through optimal linear projection.

## Abstract

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