Motivated by the EVA 2025 Data Challenge, we address the problem of predicting extreme rainfall in the eastern United States using data from a large ensemble of climate model runs. The challenge focuses on three quantities of interest related to the spatial extent and/or temporal duration of extreme rainfall, each requiring extrapolation. To tackle these questions, we adopt the recently developed geometric framework for extreme-value analysis, offering substantial flexibility for capturing complex extremal dependence structures and enabling extrapolation across the entire multivariate tail. In this work, we focus on the spatial geometric framework for analysing the spatial extent and consider a sampling procedure that retains the temporal information in the data, thereby enabling estimation of the duration of extreme rainfall events. We also account for the non-stationary behaviour, arising from topographical and seasonal effects, that commonly characterises extreme weather events in both space and time. Using diagnostic metrics, we demonstrate that the proposed model is appropriate for inferring extreme events on this dataset and apply it to estimate target quantities of interest.

翻译：受EVA 2025数据挑战赛的启发，我们利用大规模气候模式运行集合数据，研究美国东部地区极端降雨的预测问题。该挑战聚焦于与极端降雨空间范围及/或时间持续性相关的三个目标量，每个目标量均需进行外推。为解答这些问题，我们采用近期发展的极值分析几何框架，该框架能够灵活捕捉复杂的极值相依结构，并实现多元尾部的全局外推。本研究重点运用空间几何框架分析降雨的空间范围，并设计了一种保留数据时间信息的采样策略，从而能够估计极端降雨事件的持续时间。同时，我们考虑了由地形与季节效应导致的非平稳特征——这一特征普遍存在于时空极端天气事件中。通过诊断性指标验证，所提模型适用于该数据集的极端事件推断，并将其应用于目标量的估计。