*3.2. The 2003 and 2015 Heat Waves in the Context of Climate Change*

In the context of climate change, the number of heat waves is very likely to increase in the next decades [4]. In the following, we quantify the probability for heat waves comparable to the ones of 2003 and 2015 in the near and far future using RCM simulations.

RCM data is usually not available in a temporal resolution higher than daily means. Therefore, the analysis shown in Figure 3 was repeated using the daily mean HUMIDEX (Figure 4a). This approach led to very comparable results. The heat wave of 2003 was now characterized by 8 consecutive days above the 95th percentile, while for 2015, 5 consecutive days were found. To generalize these findings, we assessed the change in heat wave frequencies for all events where the daily mean HUMIDEX exceeds the 95th percentile for 3 to 10 consecutive days. Therefore, we calculated the 95th temperature percentile for each model separately to reduce the influence of model biases on the analysis [33]. The 95th temperature percentile was calculated using the reference period 1971–2000.

First, the RCM's capability to simulate these heat waves was assessed (Figure 4b). In the reference period the RCMs tend to overestimate the average number of heat waves per year for all durations. Heat waves with a duration of three days, for instance, occured on average every second summer in the observations (0.5 events/yr), while the multi model ensemble median suggest a frequency of about 0.6 events/yr. While for most durations at least a few models simulate frequencies comparable to the observations, the medium-length durations of 5 and 6 days are clearly overestimated by the models. This overestimation of the heat wave persistence in the CORDEX simulations has been discussed earlier [33] and may be attributed to a misrepresentation of land-atmosphere feedbacks (e.g, soil moisture, surface energy fluxes).

The projected changes are calculated separately for each model with respect to the model mean value of the reference period, to reduce some effect of the overestimated persistence. In the near future (2021–2050) and under RCP4.5, a clear increase in the frequency is found for all durations. Short term events (3 days) already increase by 0.9 events/yr (multi-model median). Furthermore, the very strong 10 day events increase by about one event per decade (0.1 events/yr) in comparison to less than one event in 30 yrs in the reference period (multi-model median 0.03 events/yr). No pronounced differences are found between RCP4.5 and RCP8.5 for the near future. Increases are in general slightly larger in RCP8.5, but much smaller than the differences between the models. On this time scale, differences in the emission scenarios have no systematic effect on the heat wave frequencies.

In the far future (2070–2099), however, the differences between the scenarios emerge. For RCP4.5 a further increase is found for all classes. However, at least for the shorter events, a weakening of the trend is found, i.e., the changes 1971–2000 to 2021–2050 are larger than the changes from 2021–2050 to 2070–2099. The three day heat waves, for instance, increase by 1.5 events/yr relative to the reference period (0.6 relative to 2021–2050). In case of the extreme long-lasting heat waves, changes are still small, but nevertheless pronounced. 10 day events may increase by 0.3 events/yr, suggesting one additional extreme heat wave every third summer.

**Figure 4.** (**a**) Similar to Figure 3 but for the daily mean HUMIDEX; (**b**) Boxplot statistics for number of heat waves per year in the RCM simulations. Heat waves are defined by 3 to 10 consecutive days with a daily mean HUMIDEX above the 95th percentile. Dots resemble the results from the individual simulations; colored squares denote the number of events per year derived from observations. The events of 2003 (8 consecutive days) and 2015 (5 consecutive days) are highlighted by the red and green color; (**c**) Boxplot statistics for the change of heat waves frequencies with a duration between 3 and 10 days in the near (2021–2050) and far (2070–2099) future for the RCP4.5 scenario relative to the model mean value for 1971–2000. Dots resemble the individual RCM simulations; (**d**) Same as (**c**), but for RCP8.5.

Still, in comparison to the RCP8.5 the changes found for RCP4.5 are moderate. For all duration the intensification is always larger than the changes from 1971–2000 to 2021–2050. 3 day heat waves increase by 3.5 events/yr, the 2015-like events with 5 day duration increase by 2.2 events/yr (two additional 2015-like heat waves in every summer), and a 2003-like event is also likely to take place once a summer (multi-model median increase by 1.2 events/yr). The strongest 10 day heat wave, finally, increases by 0.9 events/yr until the end of the 21th century.
