Abstract. Coupled general circulation models are of paramount importance to quantitatively assessing the magnitude of future climate change. Usual methods for validating climate models include the evaluation of mean values and covariances, but less attention is directed to the evaluation of extremal behaviour. This is a problem because many severe consequences of climate change are due to climate extremes. We present a method for model validation in terms of extreme values based on classical extreme value theory. We further discuss a clustering algorithm to detect spatial dependencies and tendencies for concurrent extremes. To illustrate these methods, we analyse precipitation extremes of the Alfred Wegener Institute Earth System Model (AWI-ESM) global climate model and from other models that take part in the Coupled Model Intercomparison Project CMIP6 and compare them to the reanalysis data set CRU TS4.04. The clustering algorithm presented here can be used to determine regions of the climate system that are then subjected to a further in-depth analysis, and there may also be applications in palaeoclimatology.

We present a new approach to modeling the future development of extreme temperatures globally and on the time-scale of several centuries by using non-stationary generalized extreme value distributions in combination with logistic functions. The statistical models we propose are applied to annual maxima of daily temperature data from fully coupled climate models spanning the years 1850 through 2300. They enable 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 find that in general, changes in extremes are stronger and more rapid over land masses than over oceans. In addition, our statistical models allow for changes in the different parameters of the fitted generalized extreme value distributions (a location, a scale and a shape parameter) to take place independently and at varying time periods. Different statistical 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 is predicted to increase rather quickly in the second half of the twenty-first century, probably due to the melting of ice, whereas changes in the mean values take longer and come into effect later.

Abstract. Coupled general circulation models are of paramount importance to assess quantitatively the magnitude of future climate change. Usual methods for validating climate models include the evaluation of mean values and covariances, but less attention is directed to the evaluation of extremal behaviour. This is a problem because many severe consequences of climate changes are due to climate extremes. We present a method for model validation in terms of extreme values based on classical extreme value theory. We further discuss a clustering algorithm to detect spacial dependencies and tendencies for concurrent extremes. To illustrate these methods, we analyse precipitation extremes of the AWI-ESM global climate model compared to the reanalysis data set CRU TS4.04. The methods presented here can also be used for the comparison of model ensembles, and there may be further applications in palaeoclimatology.