## 3 Results and Discussion
### Impact of Agricultural Droughts on Grain Yield
In NS, the average yield reduction was 5% for wheat and 10% for barley, reaching 11% and 16%, respectively, with the 3M approach. The NW region showed smaller values than NS, with an average yield reduction of 2% for wheat and 3% for barley. Yield increases in years of agricultural drought identified in BY can be explained by drought periods also being characterized by increased energy availability [96]. In this way, the main limiting variable for crops in this area increases, favoring the conditions for crop development and, therefore, yield. Furthermore, in the same context, this result can also be explained by consequences resulting from climate change, which have already been seen to influence crop yields in Europe, affecting them differently according to region and a variety of other factors [132]. Thus, due to global warming, energy factors such as the average annual temperature in Europe in the period 2006-2015 increased by approximately 1.52 \({}^{\circ}\)C [133] and were found to cause crop yields to increase, except in southern Europe [134]. This is consistent with the slight increase in crop yield obtained in dry years in BY, where the yield increase implied by an increase in energy variables probably outweighs the yield reduction caused by agricultural drought. However, some regions with little or small positive impacts of climate change could reverse this circumstance, leading to more severe drought situations [135; 136]. This idea is further reinforced as climate change is projected to worsen in the near future [137]. In northern Germany, there are other factors that could explain the results obtained for NS and NW. In those regions, the soils are mostly sandy [138] and therefore have a low water-holding capacity. The sand fraction has an inverse relationship with important soil water properties such as water-holding capacity [139]. This circumstance increases the susceptibility to soil drought in the regions of NS and NW, located in northwestern Germany, where decreases in wheat and barley yields have been reported. Therefore, this finding warns of the deleterious consequences already occurring for the yield of the two main exported cereals from Europe [140] in areas where SM was not previously a limiting factor for crop development. Ref. [141] found several years ago that those agricultural regions of northern Germany could lose productivity if they are subjected to more frequent and long-lasting droughts without irrigation. Evidence of all this was observed in 2011, a year of particularly intense agricultural drought in the German regions (Figure 4), causing an average yield reduction of more than 9% in cereals (Table 4). This result is consistent with that of [142], which classified the 2011 drought in the EU as having the largest spatial extent on record. In the same context, [115] studied droughts using meteorological indices for southwestern Germany and classified 2011 as one of the most extreme years with precipitation shortages accompanied by high temperatures. Thus, 2011 was identified as a dry year in Germany due to a precipitation deficit in early April, ending the month with a soil moisture deficit and leading to vegetation stress in mid-May and consequent reductions in crop yields, especially for cereals [40]. Consistent with the aforementioned research, the present study finds that in 2011, identified as an agricultural drought year in Germany, both cereals showed a marked reduction in yield for all regions and approaches (Table 4). Barley showed an average yield reduction of 13%, which was much larger than that of wheat, with an average reduction of 5% (Table 4). Therefore, this shows that in areas where, until now, soil water content was not a limiting factor, a soil moisture deficit in April is promoting a reduction in cereal yields, with barley being more vulnerable than wheat. Several studies have shown that in recent decades, there has been a general trend of change toward drier conditions, mainly in central and eastern Europe [41; 102].