The important role of the evolution of mean temperature in the changes of extremes has been recently documented in the literature, and variability is known to play a role in the occurrence of extremes, too. This paper aims at further investigating the role of their evolutions in the observed changes of temperature extremes. Analyses are based on temperature time series for Eurasia and the United States and concern absolute minima in winter and absolute maxima in summer of daily minimum and maximum temperatures. A test is designed to check whether the extremes of the residuals after accounting for a time-varying mean and standard deviation can be considered stationary. This hypothesis is generally true for all extremes, seasons, and locations. Then, the comparison between the directly fitted parameters and the retrieved ones from those of the residuals compares favorably. Finally, a method is proposed to compute future return levels from the stationary return levels of the residuals and the projected mean and variance at the desired time horizon. Comparisons with return levels obtained through the extrapolation of significant linear trends identified in the parameters of the generalized extreme value (GEV) distribution show that the proposed method gives relevant results. It allows taking mean and/or variance trends into account in the estimation of extremes even though no significant trends in the GEV parameters can be identified. Moreover, the role of trends in variance cannot be neglected. Lastly, first results based on two CMIP5 climate models show that the identified link between mean and variance trends and trends in extremes is correctly reproduced by the models and is maintained in the future.
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