The sensitivity of results to the threshold chosen for fitting the generalized Pareto distribution
In this section we present analyses that show the results of our paper are not sensitive to choosing a 
different (higher) threshold than that specified to fit the GPD. When performing a peak over threshold 
extreme value analysis the data chosen must be far enough into the extreme tail of the distribution to 
ensure the near-asymptotic behaviour of the exceedences. There are several diagnostic (and parametric) 
methods to estimate a suitable threshold. Essentially, these diagnostics indicate at which threshold the 
shape and modified scale parameter of the GPD distribution are invariant with the threshold (Coles, 2001). 
Figure S4 (a-c) shows three such plots of the shape parameter as a function of threshold chosen to fit 
the GPD to VOR in Boxes 1-3 for the A1B scenario for the period 2060-2100. All sub-figures provide 
evidence that the shape parameter at each of the chosen thresholds (97.5, 95, 95% quantiles respectively) 
and for each Box are located far enough into the tail of the distribution to justify fitting a GPD. 
Although there is some tendency for the shape parameter in Fig. S4a to become less negative around a 
threshold of 4 hPa/(deg.lat^2), the errors associated with these values are well within the error bars 
for the shape parameter estimated at the 97.5% quantile (vertical solid black line, Fig S4a). Likewise, 
there is some tendency for the shape parameter to change from threshold to threshold for the other boxes. 
Nevertheless, all values are with the range of error estimates. From these plots we conclude that the 
chosen thresholds are suitable for the analysis perform in the main paper. We performed additional 
tests to verify if the changes in RP shown in Tab. 1 are sensitive to alterations in the GPD threshold. 
For this analysis we calculated the change in RP using each of the 95, 96, 97, 97.5, 98, 98.5, and the 
99% quantile thresholds. Results indicate that all conclusions in this study are insensitive to the 
choice of the above listed thresholds. For instance RP changes shown in Tab. 1 differ by less than 10% 
across the full range of thresholds tested (95-99% quantiles). 

