## 4 Discussion and Conclusions  
The results show that heatwaves can have a very strong impact on grapevine yields. These impacts strongly depend on the onset dates and duration of the heatwaves. The highest negative impacts may result in a decrease in the yield by up to \(-35\%\) in some regions (Figure 5, left panel). The descending-order ranking of the frequency of occurrence of the heatwave peak dates is 15 July, 1 July and 1 August (Figure 4). The results have shown that regions that have their peak date on 1 August will be more  
Figure 5: Left panel: highest and lowest yield decrease due to heatwaves for each winemaking region at the peak date. Right panel: geographical representation of the highest and lowest decrease in yields over Europe at the peak date. Figure 6: Average relative yield differences (%) for all the regions at each peak date. negatively impacted than other regions (Figure 6). The impacts of heatwaves before and after these dates resulted in much less yield reduction (Figure 3). Heatwaves in September show a very low impact in many regions. While being true that heatwaves at this specific period may not be very common, this pattern may be modified by climate change. This reduction in yields is explained by the detrimental effects of extremely high temperatures on grapevine physiology. Several studies have documented these effects [23; 48; 49; 50; 51]. As an example, [PERSON] and [PERSON] [52] showed for the Luxembourgish Moselle region that post-bloom maximum temperatures (especially over the first three weeks after bloom) are negatively correlated with annual yield. This might be explained by the fact that cell division and cell expansion are reduced under heat conditions and, as a result, berries remain smaller [52]. [PERSON] [53] demonstrated that temperatures above 32.5 \({}^{\circ}\)C between bloom and 12 to 18 days thereafter reduced berry size compared to 25 \({}^{\circ}\)C.  
The geographical representation of yield reduction hints at a latitudinal gradient in the heatwave impact (Figure 5, right panel). In fact, regions at lower latitudes seem to show slightly lower negative impacts than regions at higher latitudes. This may be partially explained by the fact that vineyards in Southern Europe are most adapted to higher temperatures than regions in Central Europe. Furthermore, productivity in Southern European countries, such as Spain and Portugal, is already typically low [54], when compared to Central Europe, and this productivity difference could partially explain the lower decrease. Under Southern European conditions, the highest yield reductions were observed when a heatwave occurs in July, while this was verified in early August for the northern cooler regions. This might be explained by the later annual phenological cycle under cooler conditions, i.e., it is assumed that the temporal shift in phenology might be the reason for the temporal shift of maximum yield reduction. Some limitations of the present study can be mentioned. In effect, there are uncertainties inherent to this kind of modelling assessment. The first limitation is tied to the crop model. Although STICS has previously shown a high agreement with observed conditions, the model may not satisfactorily incorporate critical plant processes to assess the full impact of heatwaves. As an example, the model does not include a module to address berry and leaf sunburn, which is a common consequence of heatwaves. Another limitation of the current study is that it does not take into account multiple heatwaves in a single year, i.e., only one heatwave per year was considered. The uncertainty related to the future scenarios should also be mentioned. Increased atmospheric CO\({}_{2}\) concentration partially offsets the dryness effects, promoting yield and leaf area index increases in Central/Northern Europe.