  We present a new approach to modeling the future development of extreme
temperatures globally and on a long time-scale by using non-stationary
generalized extreme value distributions in combination with logistic functions.
This approach is applied to data from the fully coupled climate model AWI-ESM.
It enables us to investigate how extremes will change depending on the
geographic location not only in terms of the magnitude, but also in terms of
the timing of the changes. We observe that in general, changes in extremes are
stronger and more rapid over land masses than over oceans. In addition, our
models differentiate between changes in mean, in variability and in
distributional shape, allowing for developments in these statistics to take
place independently and at different times. Different models are presented and
the Bayesian Information Criterion is used for model selection. It turns out
that in most regions, changes in mean and variance take place simultaneously
while the shape parameter of the distribution is predicted to stay constant. In
the Arctic region, however, a different picture emerges: There, climate
variability drastically and abruptly increases around 2050 due to the melting
of ice, whereas changes in the mean values take longer and come into effect
later.
