## 3 Results and Discussion
### Future Climate Projections
#### 3.2.2 Heat Waves  
HW are identified for HIST, MED, and LONG for WRF and CORDEX models. This HW analysis is performed only for extended summer. Figure 10 presents the annual average of NWAVE (a) and NDAYS (b) for WRF HIST, MED, and LONG; and the CORDEX average, maximum, and minimum for MED and LONG. Figure 9: Annual average Tmax difference (**a**) MED-HIST and (**b**) LONG-HIST, for WRF and average, maximum, and minimum CORDEX models. NWAVES trends are positive with values increasing from 2 per year in HIST to 7 and 10 per year in MED and LONG, respectively. More relevant is the increase in NDAYS by a factor of 3-4 and more than 6 in MED and LONG, respectively, representing an average of 30-40 and 60 NDAYS in the future climates. In line with these results, [PERSON] et al. [32] refer to an increase in the number of extended summer (MJJAS) days with Tmax above the 90 th percentile from 15 days in the recent climate to 80 days by the end of the century. The remaining HW measures are shown in Figure 11, namely, DUR, INT, RF, Tmax_ave, and Tmax_sum (annual average and HW average). Figure 10: Annual average of (**a**) NWAVES and (**b**) NDAYS for WRF HIST, MED and LONG and CORDEX average, maximum and minimum for MED and LONG. NWAVES: Number of HW. Figure 11: _Cont_. All these quantities are projected to increase in the future, more in LONG than in MED, except for the RF (Figure 11c), which reduces by about 0.5 \({}^{\circ}\)C. This represents, for the future, reduced relief during the night of HW days when daytime temperatures are expected to be even higher than in HIST (see Tmax_ave in Figure 11d). Figure 11: (**a**) DUR, (**b**) INT, (**c**) RF, (**d**) Tmax_ave, (**e**) Tmax_sum annual average and (**f**) Tmax_sum HW average, for WRF HIST, MED and LONG and CORDEX average, maximum and minimum for MED and LONG. DUR: Duration (days) of a HW, INT: intensity, defined as Tmax minus Tmax_c, Tmax_c: Certain threshold value (Tmax) that when surpassed for a period of at least three consecutive days defines a HW, Tmax_ave: Tmax averaged over all days of a HW. [PERSON] et al. [1] studied the impact of extreme temperatures on mortality for Lisbon and identified a critical temperature of 33.4 \({}^{\circ}\)C above which there is an increase of 31.3% in mortality for each 1 \({}^{\circ}\)C above the threshold. Here, Tmax_ave for the extended summer is 33.7 \({}^{\circ}\)C for HIST and 34.1 \({}^{\circ}\)C and 34.9 \({}^{\circ}\)C for MED and LONG, respectively. The annual average Tmax_sum (Figure 11f), which combines the average duration and average Tmax_ave, increases from 358 \({}^{\circ}\)C-day to more than 1000 \({}^{\circ}\)C-day and 2000 \({}^{\circ}\)C-day in MED and LONG, respectively. Recent positive trends of HW duration, intensity, and frequency in Extremadura (Spain) reported by [PERSON] et al. [18] are consistent with the results shown in this study. Figure 12 shows annual total NWAVES, NDAYS, and Tmax_sum for (a) HIST, (b) MED, and (c) LONG. Figure 12: _Cont._  
For Figure 12, CORDEX models are not shown, since it is not useful and meaningful to show, for each CORDEX model, the respective annual values of NWAVES/NDAYS, as well as their ensemble average. These are yearly average values but, in particular years, values can reach 100 NDAYS in LONG, which represents much of the extended summer under HW conditions. In line with these results, [PERSON] et al. [32] refer to an increase in the number of extended summer (MJJAS) days with Tmax above the 90 th percentile from 15 days in the recent climate to 80 days by the end of the century. Some extreme values of these HW measures values are shown in the supplementary material (Figure S4). These, together with the inter-annual variability of NWAVES, NDAYS, and Tmax_sum shown in Figure 11, give a glimpse of what may happen in some years/HW in the future. Another aspect that may be relevant for impact and adaptation studies is the HW distribution in the seasonal cycle (here, only the extended summer is considered).