A lightweight framework for characterising extreme precipitation events in climate ensembles

Abstract

This article summarises the methods used by the team ``Ca' Foscari" for the EVA 2025 Data Challenge. The questions of the challenge concern the estimation of exceedance probabilities across several locations. Rather than modelling the spatial dependence structure, we reduce the problems to univariate ones by considering relevant spatial order statistics across the sites. Within a Peaks over Threshold framework, we model the marginal distributions of exceedances using generalised Pareto distributions. Generalised additive models are employed to allow the parameters to vary as functions of external predictors, which for all questions are reduced to the month. For questions 1 and 2, the required estimates and confidence intervals are obtained by generating samples from our fitted models. Question 3 involves the dependence between two consecutive observed statistics. To account for this temporal dependence, we fit a conditional extreme value model and derive empirical estimates of persistent extreme events by simulating from this model.

Figures (4)

• Figure 1: Illustration of the declustering procedure on a toy dataset. The red dashed line indicates a fixed threshold $u$ and clusters are defined using a run length of $l=3$. $C_1,C_2,C_3$ and $C_4$ denote the four clusters and $X_1^*,X_2^*,X_3^*$ and $X_4^*$ are the maxima of each cluster, which together form the declustered time series.
• Figure 2: Visual illustration of the simulation setup for target quantity 1. The top row displays a subset of simulated extreme events for each run; the solid black line represents the monthly thresholds per run, while the dashed line marks the target quantity of 1.7 Leadbetters. The bottom row presents the simulated extreme events for one individual simulated time series.
• Figure 3: (Left) Plot of $X_{i+1}$ against $X_i$, which represent the third largest precipitation (Leadbetters) on day $i+1$ and $i$ respectively. Data is plotted for only one of the four provided climate model runs. (Right) The equivalent data as in the left-hand panel after being transformed to have Laplacian margins. Threshold $q$ (marked as a vertical dashed red line) above which we fit the conditional extreme value model (shown as a solid green line) with 95% predictive interval shown in the shaded region.
• Figure 4: QQ plot on standard exponential margins for GP distribution with a separate shape parameter, $\xi$, for each month, used to estimate target quantity 1 (left), and constant shape parameter estimate used to estimate target quantity 2 (right).