[Paper Review] Analysing Extreme Rainfall via a Geometric Framework

Ryan Campbell, Kristina Grolmusova+2 more|arXiv (Cornell University)|Mar 18, 2026

Climate variability and models0 citations

TL;DR

The paper adopts a geometric extreme-value framework to model and extrapolate spatial-temporal extremes for eastern US rainfall, accounting for non-stationarity and deforming the spatial domain to enable tail extrapolation and estimation of multiple target extreme-event quantities.

ABSTRACT

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.

Motivation & Objective

• Motivate and address extreme rainfall prediction in the EVA 2025 Data Challenge context.
• Develop a geometric, tail-dependence based framework capable of extrapolating multivariate extremes across space and time.
• Incorporate non-stationarity in margins and dependence through temporal non-stationarity modelling and spatial deformation.
• Assess model fit with diagnostic tools and apply the framework to estimate target extreme quantities.
• Provide extrapolated estimates for competition target quantities (CTQs) relevant to distributional extremes of rainfall across a grid.

Proposed method

• Adopt a spatial geometric framework with standard exponential margins and a gauge function to describe tail sets and extrapolate in the multivariate tail.
• Model temporal non-stationarity in margins via a location-scale GAM for Y_t and non-stationary GPD for exceedances with covariate-dependent shape/scale.
• Apply spatial deformation to map sampling locations to a latent plane where stationarity is assumed, using a thin-plate spline and a Brown-Resnick process for tail dependence.
• Fit a truncated gamma model for the radial component R given angular component W in the deformed space, with a generalised Gaussian gauge g_Z(w;θ) and isotropic spatial correlation with powered-exponential form.
• Approximate high-thresholds using r_tau(w) = C_tau / g(w;φ,κ) and perform likelihood-based inference for the truncated gamma, followed by extrapolation of Z using angular-radial sampling in the extreme region.

Figure 1 : Left: Original grid coordinates (G-plane) of the eastern U.S. rainfall data. Right: Deformed grid coordinates (D-plane) obtained using data from run 1 of the climate model.

Experimental results

Research questions

• RQ1 How can a geometric extremes framework capture complex extremal dependence and enable extrapolation in the multivariate tail for rainfall data?
• RQ2 Can temporal and spatial non-stationarity be effectively accommodated to improve inference on extreme rainfall and its duration?
• RQ3 How well does the framework reproduce tail dependence and enable estimation of target extreme quantities (CTQs) under non-stationarity?
• RQ4 What are the practical gains of deforming the spatial grid to a latent plane for achieving stationarity in the tail analysis?
• RQ5 How can one reliably extrapolate tail probabilities and quantify their uncertainties for multi-site extreme rainfall metrics?

Key findings

• The geometric framework with non-stationarity handling shows good agreement with empirical tail dependence estimates across climate model runs in the D-plane.
• Diagnostic plots (PP, QQ) indicate overall satisfactory fit of the truncated gamma model for exceedances, with some tail deviation as expected since temporal non-stationarity was not fully modelled in the tail fit.
• Tail dependence estimates from model-based simulations align with empirical estimates across runs, supporting the ability to characterise joint tails in the climate data.
• CTQ estimates show reasonable performance across runs 2–4, with some overestimation for CTQ1 in run 1, highlighting areas for methodological refinement (notably temporal non-stationarity in tails).
• Incorporating spatial deformation reduced anisotropy and non-stationarity in tail dependence, improving stationarity in the D-plane and enabling robust extrapolation.
• The paper provides concrete estimates for three competition target quantities (CTQs) using simulated extremal samples and bootstrap uncertainty quantification.