A Comparative Study of Different Ways to Estimate Extreme Temperatures and Associated Uncertainties in a Non-Stationary Context

Estimating the extreme temperatures and associated uncertainties under non-stationary

conditions is a key research question in the nuclear safety field. The analysis of the risk

associated to extreme temperatures has already been intensively studied in the literature.

Nevertheless, methods for estimating temperature return levels and constructing confidence

intervals were often used separately, without detailed comparison and in a stationary context.

The extreme value theory is often used to assess risks in a context of climate change. It provides

an accurate indication on marginal laws describing the frequency of occurrence of extreme

phenomena such as heat waves. However, in a non-stationary context, the notions of duration

and return periods are not easily interpretable. For example to evaluate the 100-year return level

in a future year, time-varying frequency models with different ways to compute the extreme

temperatures and different methods to evaluate associated uncertainties must be used and

compared.

This study examines the performance of three different ways to compute high temperature

return levels in a non-stationary context and three methods for constructing the associated

confidence intervals. To address this issue, we have used three explanatory variables (max daily

temperatures, anomalies and residuals) and we have used and compared the delta, the profile

likelihood and the bootstrap methods for computing confidence intervals. The analyses were

conducted assuming the General Extreme Value (GEV) distribution. The daily maximum

temperatures observed at the station of Orange in France are used as a case study.