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

Abstract

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).

A Non-Stationary Heat Spell Frequency, Intensity, and Duration Model for France, Integrating Teleconnection Patterns and Climate Change

“…There were no shifts or changes in the trend detected in the annual variables computed from the heat spells identified in the last section. Such a result is coherent with the one obtained by Hamdi et al [33] for Orange using the same data. The authors showed that the AIC and BIC gave an advantage to a NS model, covering the full period with a linear trend on the location parameter of the GP.…”

“…However, in the context of climate warming and under the influence of large-scale oscillation patterns, the time series of temperature extremes and heat spells are not stationary. One approach to address non-stationarity is to use the so-called conditional distribution (e.g., [32][33][34]). These distributions are termed conditional because their parameters vary as a function of time-dependent covariates, which could incorporate trends, cycles, or physical variables that can represent atmosphere-ocean patterns [16,35,36].…”

Active Probability Backpropagation Neural Network Model for Monthly Prediction of Probabilistic Seismic Hazard Analysis in Taiwan

“…It is a statistical measurement typically based on average recurrence interval over an extended period of time. However, recently some researchers have pointed out that return period was nonstationary and unsuitable to be used for risk analysis ( [10], [61], [57], [19]). Reference [10] mentioned that current infrastructure design based on precipitation Intensity-Duration-Frequency (IDF) curves and assuming a stationary return period is unsuitable for extreme climatic events e.g.…”

“…The concept of probability of exceedance for risk assessment and communication were failed by a given design life period that provided more coherent, and well devised tools. Reference [19] estimated temperature extremes with uncertainties of return period under the nonstationary research question for several domains, including the nuclear safety field. The methods stipulated in researches for estimating and associated confidence intervals have often been used but in a stationary context, separately and without detailed comparison.…”

“…Looking for the suitable PDF for an event is not easy because the return period must be known. Using different PDFs results in exceedance probabilities, and when an incorrect return period is used, estimated exceedance probabilities are unreliable due to uncertainty and the nonstationary nature of the return period [2], [19]. Therefore, two unreliable factors exist in the estimation of exceedance probability: unreliable PDF and unreliable return period.…”