[Paper Review] Estimating changes in extreme quantiles over time, applied to desert temperatures

Callum Leach, Kevin Ewans+1 more|arXiv (Cornell University)|Mar 7, 2026

Climate variability and models0 citations

TL;DR

The paper Develops a Bayesian non-stationary GEV regression framework to estimate changes in 100-year extreme temperature quantiles over a century using CMIP6 desert region data, and assesses model selection criteria for small-sample extreme value analysis.

ABSTRACT

We quantify changes DeltaQ in 100-year return values for regional annual maxima and minima of near-surface atmospheric temperature from output of five CMIP6 models, for five of the Earth's desert regions, over the interval (2025,2125). We use generalised extreme value (GEV) regression to characterise changes in extremes, considering a range of different parametric forms for the variation of GEV parameters with time, and coupling models for different scenarios so that they provide a common GEV tail in the first year of observation. Parameters are estimated using Bayesian inference. We perform a simulation study using ground truth models generating data qualitatively similar to the CMIP6 output, to assess the relative performance of different information criteria in selecting models from a set of candidates, to minimise error in predictions of DeltaQ. The Bayesian information criterion (BIC) provides best performance, out-performing the divergence and widely-applicable information criteria in particular. Using BIC-selected GEV regression models, we estimate joint posterior distributions of DeltaQ over three forcing scenarios, for different combinations of region, GCM and climate ensemble. Estimates show a consistent trend across regions, GCMs and climate ensembles, of DeltaQ increasing with climate scenario for both regional annual maxima and minima. Aggregating posterior distributions over climate ensembles and GCMs, we find evidence for significant increases in DeltaQ for regional annual maxima under more severe forcing scenarios for all desert regions. Similar but weaker and less significant trends are observed for regional annual minima.

Motivation & Objective

• Characterize non-stationarity in extreme temperature distributions over time using GEV regression.
• Assess which information criteria best select models for small-sample extreme value problems in climate data.
• Estimate changes in 100-year return values for regional annual maxima and minima under different forcing scenarios.
• Couple GEV models across three climate scenarios to obtain joint posterior distributions of return-value changes.
• Provide practical guidance on model averaging versus selection in extreme value regression for CMIP6 data.

Proposed method

• Use generalized extreme value (GEV) regression to model regional annual maxima and minima of near-surface temperature (tas) with time-varying parameters.
• Consider 11 parametric forms for time variation (constant, linear, quadratic, and asymptotic), applied to location, scale, and shape; enforce a common 2015 tail across SSP scenarios.
• Estimate parameters via Bayesian inference with MCMC to obtain full joint posterior distributions.
• Compute 100-year return values Qj(t) from the GEV parameters and the difference ΔQj = Qj(2125) − Qj(2025) for each scenario j.
• Evaluate multiple information criteria (AIC, BIC, DIC, WAIC) to select model complexity and validate via a simulation study that mimics CMIP6 data.
• Perform a simulation study generating data from 11 data-generating processes (CCC to QQQ) to compare RMSE of ΔQ predictions under different criteria, guiding the choice of BIC3 and AIC3 for CMIP6 analysis.

Figure 1 : World map showing desert regions considered. Details of longitude-latitude bounding boxes in Table 1 . Note that Mojave (MO) and Dasht-e Lut (DA) are small geographic regions consisting of small numbers of GCM grid locations.

Experimental results

Research questions

• RQ1 Can non-stationary GEV models accurately capture temporal evolution of extreme tas distributions in desert regions under climate forcing?
• RQ2 Which information criteria best predict out-of-sample changes in 100-year return values in small-sample extreme value analyses?
• RQ3 How do coupled GEV regression models perform across desert regions, GCMs, and forcing scenarios in estimating ΔQ over 2025–2125?
• RQ4 Does Bayesian model averaging offer advantages over single-model selection for predicting changes in extremes?
• RQ5 What are the regional patterns of projected changes in extreme tas return values under SSP126, SSP245, and SSP585 scenarios?

Key findings

• BIC-based model selection generally yields parsimonious models and robust ΔQ estimates, outperforming WAIC and DIC variants in the simulation study.
• Across CMIP6 desert regions and GCMs, there is evidence of significant increases in ΔQ for regional annual maxima under stronger forcing scenarios (SSP245 and SSP585).
• Regional annual minima show similar but weaker and less consistent increases in ΔQ across regions and scenarios.
• Coupled GEV regression with a common 2015 tail across scenarios provides unified estimates for ΔQ under multiple forcing paths.
• Aggregating posterior ΔQ estimates over climate ensembles and GCMs reveals consistent upward shifts in extreme maxima, with Antarctic showing the smallest changes.
• The analysis demonstrates the sensitivity of ΔQ estimates to the chosen non-stationary model form and supports using BIC-selected GEVs (and in some cases Bayesian model averaging) for robust inference.

Figure 2 : Regional annual maxima (left) and minima (right) time series of tas (K) for the UK “control” region from the UKESM1-0-LL GCM. Climate scenarios are distinguished by colour: SSP126 (green), SSP245 (orange), SSP585 (grey). Climate ensemble runs for each scenario, as listed in Table 2 , are