Integrating non-stationarity and uncertainty in design life levels based on climatological time series

This work focuses on inferring design life levels for extreme events under non-stationary conditions. Its objectives are twofold. The first one is to provide a single indicator that summarizes relevant and interpretable information about large values in time series, even when stationarity cannot be assumed. Classical risk indicators such as the 100-year return level become difficult to interpret in a non-stationary framework. To address this, we leverage the existing concept of the equivalent reliability (ER) level. Under stationarity, the ER level coincides with the classical return level, but it differs otherwise. More precisely, the ER level ensures that the probability of having all observations below the ER level during a specified design period is controlled. This definition ensures interpretability in terms of safety or failure risk. A second objective is to capture stochastic and estimation uncertainty, a key aspect in any risk analysis, as uncertainties due to inference schemes can grow with extreme intensities. We incorporate both by using the Bayesian predictive distribution. Although well known in Bayesian statistics, the predictive distribution has rarely been applied to climatological time series risk analysis.

Our approach is demonstrated on simulated data and on a case study of annual maxima of temperatures at a site in Southern France. To do so, a non-stationary Bayesian hierarchical extreme value model is used to combine data from 26 CMIP6 general circulation model simulations (SSP2-4.5, 1850-2100) with observations. The resulting predictive ER levels clearly indicate that non-stationarity over a design period of interest, as well as sampling and estimation uncertainty, have to be taken into account for risk assessment. For example, the 1000-year posterior predictive ER level for 2050-2100 is higher than any non-stationary 1000-year return level median estimate over the same period, reflecting the increasing risk due to the non-stationarity of the SSP 2-4.5 pathway.