Barbaux et al. (2025) Integrating non-stationarity and uncertainty in design life levels based on climatological time series

Identification

• Journal: Weather and Climate Extremes
• Year: 2025
• Date: 2025-09-27
• Authors: Occitane Barbaux, Philippe Naveau, Nathalie Bertrand, Aurélien Ribes
• DOI: 10.1016/j.wace.2025.100807

Research Groups

• Météo France, Toulouse, France
• Autorité de Radioprotection et de Sureté Nucléaire (ASN), Fontenay-aux-Roses, France
• Centre National de Recherches Météorologiques (CNRM), Toulouse, France
• Laboratoire des Sciences du Climat et de l’Environnement (LSCE), Saint-Aubin, France
• Centre national de la recherche scientifique (CNRS), Toulouse, France
• Université de Toulouse, Toulouse, France

Short Summary

This study develops a novel method to infer design life levels for extreme events under non-stationary climate conditions, integrating both non-stationarity and uncertainty. It introduces the Predictive Equivalent Reliability (PER) level, a single, interpretable indicator that accounts for stochastic and estimation uncertainties, demonstrating its utility for robust risk assessment in a changing climate.

Objective

• To provide a single, interpretable indicator (Equivalent Reliability level) that summarizes information about extreme values in time series, even under non-stationary conditions.
• To capture both stochastic and estimation uncertainty in risk analysis by leveraging the Bayesian predictive distribution.

Study Configuration

• Spatial Scale: Case study on annual maxima of temperatures at Pierrelatte (44.33°N 4.73°E), Southern France. Covariate data for annual mean temperature over continental Europe (35–70°N, 10°W–30°E).
• Temporal Scale:
  • Local observational data: 1985–2021.
  • Simulated GCM data: 1850–2100.
  • Observational covariate data (CRUTEM5): 1850–2020.
  • Design period for application: 2050–2100 (51 years).

Methodology and Data

• Models used:
  • Non-stationary Bayesian hierarchical Generalized Extreme Value (GEV) model (following Robin and Ribes, 2020).
  • Equivalent Reliability (ER) level concept.
  • Bayesian predictive distribution.
  • Markov chain Monte Carlo (MCMC) using the NUTS (No-U-Turn Sampler) algorithm for posterior sampling.
  • NSSEA and Pystan (Stan Development Team, 2024) Python packages.
• Data sources:
  • Local observational data: Annual maxima of daily maximum temperatures (TXx) from Pierrelatte meteorological station.
  • Simulated data: 26 CMIP6 General Circulation Models (GCMs) ensemble (SSP1-1.9, SSP2-4.5, and SSP5-8.5 scenarios).
  • Observational covariate data: CRUTEM5 dataset (annual mean temperature over Continental Europe).

Main Results

• For the SSP2-4.5 scenario and an annual exceedance probability of 𝑝=10⁻³, the Predictive Equivalent Reliability (PER) level for 2050–2100 is 47.4 °C. This is higher than the median time-dependent return level, which increases from 44.7 °C to 46.5 °C over the same period.
• For the SSP5-8.5 scenario, the PER level for 2050–2100 is 53.5 °C, exceeding the median time-dependent return level that increases from 45.5 °C to 51.6 °C.
• In all tested scenarios (SSP1-1.9, SSP2-4.5, SSP5-8.5), the PER level consistently exceeds the highest median time-dependent return level, highlighting the critical role of accounting for both parameter and stochastic uncertainty in design levels.
• The PER level provides a single, interpretable value for the total exceedance risk over a multi-year design period (e.g., 0.05 over 2050–2100), offering a clear advantage over annually varying time-dependent return levels in non-stationary contexts.
• Goodness-of-fit diagnostics (bootstrapped Kolmogorov–Smirnov tests with p-values of 0.82 for SSP5-8.5, 0.86 for SSP2-4.5, and 0.35 for SSP1-1.9) confirm the appropriateness of the non-stationary GEV model.

Contributions

• Introduces the Predictive Equivalent Reliability (PER) level, a novel single summary index that effectively integrates non-stationarity (through Equivalent Reliability levels) and both stochastic and estimation uncertainties (through Bayesian predictive distribution) for extreme event risk assessment.
• Addresses the interpretability challenges of classical return levels in non-stationary climates by providing a consistent probabilistic interpretation of risk over a specified design period.
• Demonstrates the practical application of the PER framework using real-world temperature maxima data and CMIP6 climate model projections, showcasing its utility for robust structural design and decision-making under climate change.
• Advocates for the use of predictive quantiles as robust point estimates for structural design, offering a compelling alternative to conventional interval-based summaries by inherently combining various sources of uncertainty.

Funding

• Autorité de sûreté nucléaire et de radioprotection (ASNR), France
• Météo-France, France
• Agence Nationale de la Recherche, France - France 2030 (PEPR TRACCS programme, grant number ANR-22-EXTR-0005)
• PEPR IRIMONT, France (France 2030 ANR-22-EXIR-0003)
• SHARE PEPR Maths-Vives, France (ANR-24-EXMA-0008)
• EXSTA, France
• Geolearning research chair, France (joint initiative of Mines Paris and the French National Institute for Agricultural Research (INRAE))

Citation

@article{Barbaux2025Integrating,
  author = {Barbaux, Occitane and Naveau, Philippe and Bertrand, Nathalie and Ribes, Aurélien},
  title = {Integrating non-stationarity and uncertainty in design life levels based on climatological time series},
  journal = {Weather and Climate Extremes},
  year = {2025},
  doi = {10.1016/j.wace.2025.100807},
  url = {https://doi.org/10.1016/j.wace.2025.100807}
}