• climate change;
  • extreme value theory;
  • trends;
  • extrapolation;
  • return level


The climate change context has raised new problems in the computation of temperature return levels (RLs) in using the statistical extreme value theory. This arises since it is not yet possible to accept the hypothesis that the series of maxima or of high level values are stationary, without at least verifying the assumption. Thus, in this paper, different approaches are tested and compared to derive high order RLs in the nonstationary context. These RLs are computed by extrapolating identified trends, and a bootstrap method is used to estimate confidence intervals. The identification of trends can be made either in the parameters of the extreme value distributions or in the mean and variance of the whole series. Then, a methodology is proposed to test if the trends in extremes can be explained by the trends in mean and variance of the whole dataset. If this is the case, the future extremes can be derived from the stationary extremes of the centered and normalized variable and the changes in mean and variance of the whole dataset. The RL can then be estimated as nonstationary or as stationary for fixed future periods. The work is done for both extreme value methods: block maxima and peak over threshold, and will be illustrated with the example of a long observation time series for daily maximum temperature in France. Copyright © 2010 John Wiley & Sons, Ltd.