Temperature Extremes: Estimation of Non-Stationary Return Levels and Associated Uncertainties

Estimating temperature extremes (TEs) and associated uncertainties under the non-stationary (NS) assumption is a key research question in several domains, including the nuclear safety field. Methods for estimating TEs and associated confidence intervals (CIs) have often been used in the literature but in a stationary context, separately and without detailed comparison. The extreme value theory is often used to assess risks in a context of climate change. It provides an accurate indication of distributions describing the frequency of occurrence of TEs. However, in an NS context, the notion of the return period is not easily interpretable. For instance, to predict a high return level (RL) in a future year, time-varying distributions must be used and compared. This study examines the performance of a new concept to predict RLs in an NS context and compares three methods for constructing the associated CIs (delta, profile likelihood, and parametric bootstrap). The present work takes up the concept of integrated return periods that define the T-year RL as the level for which the expected number of events in a T-year period is one and proposes a new method based on conditional predictions that is useful for predicting high RLs of extreme events in the near future (the 100-year RL in the year 2030, for instance). The daily maximum temperature (DMT) observed at the Orange Station in France was used as a case study. Several trend models were compared and a new likelihood-based method to detect breaks in TEs is proposed. The analyses were conducted assuming the time-varying Generalized Extreme Value (GEV) distribution. The concepts have been implemented in a software package (Non-Stationary Generalized Extreme Value (NSGEV)). The application demonstrates that the RL estimates for NS situations can be quite different from those corresponding to stationary conditions. Overall, the results suggest that the NS analysis can be helpful in making a more appropriate assessment of the risk for periodic safety reviews during the life of a nuclear power plant (NPP).