Future high-temperature extremes and stationarity

Abstract

Designing some long-lasting industrial assets necessitates an estimation of far future extremes. Extreme value estimation is commonly based on an application of the statistical extreme value theory (EVT), which requires that the studied variable is independent and identically distributed, or, at least, stationary. Climate variables exhibit different behaviors which potentially violate this assumption: Seasonality is generally the easiest to handle, and interannual variability is more complicated. Now, as far as temperature is concerned, an additional source of non-stationarity appears: the warming trend, whose interactions with interannual variability add another range of complexity. The approach proposed here is based on the construction of a standardized variable, whose extremes can be considered as stationary. This allows an application of EVT in better accordance with its assumptions. Recent works (Parey et al. in J Geophys Res Atmos 118:8285–8296, 2013. https://doi.org/10.1002/jgrd.50629) have shown that if optimized smooth trends in mean and standard deviation are removed from the temperature time series, then the extremes of the residuals can be considered as stationary. A statistical test has been designed to check this assumption. Here, the inference of high-temperature extremes from the extremes of this standardized variable and future mean and standard deviation projected at the desired time horizon, and given by climate model simulations, is further analyzed and justified.