## 3 Results
### Agro-Climatic Model Results in 2000 and 2050
#### 3.2.2 National Analysis  
In this first approach, we analyzed the frequency of extreme droughts with an intensity equal or superior to 2003 and 2011 at the national scale. In the current climate distribution, 29 drought events were identified. A quick estimation of the return period of these extreme droughts in current climate was 13 years. This first result is consistent with the 30 years of available historical data (1989-2018), with two extreme droughts (2003 and 2011), giving an empirical return period of 15 years. In the 2050 scenario, 57 extreme drought events were identified with a return period of seven years.  
On average, these droughts affected 81.7% of utilized agricultural land (UAL) in 2000 and 86.1% in 2050. All these events were systemic, with a minimum of 61.8% (2000 climate) and 52.7% (2050 climate) of UAL affected by drought.  
The annual DOWKI value at the national scale decreased by 40% (DOWKI was equal to \(-\)78 mm for the climate in 2000 and \(-\)110 mm for the climate in 2050) when comparing the 2000 and 2050 distributions.  
At the national scale, the effect of climate change on the frequency of extreme droughts, considering 2003 as the reference, will increase significantly (+100%) between 2020 and 2050, according to the ARPEGE-Climat simulations. These events will remain systemic in the climate in 2050, with at least 50% of the UAL affected by drought.  
Beyond the average, Figure 5 illustrates the yield losses (%) at the national scale for soft winter wheat (a), winter barley (b), and grassland (c) with respect to their return period in the current climate and in 2050.  
A lot of information can be extracted from Figure 5. When integrating the model uncertainties (percentile 10-90), the empirical cumulative distribution functions (ECDF curves) between the 2000 climate and the 2050 climate did not overlap over 10 years, showing a significant increase in yield losses between 2000 and 2050 for all return periods.  
First, the annual average loss will increase in 2050 by:  
- 40% for grasslands;  
- 47% for winter barley;  
- 45% for soft winter wheat.  
The yield losses due to 10-year droughts will increase by:  
- 35% for grassland;  
- 75% for soft winter wheat;  
- 79% for winter barley (Table 3).  
The results show a more important yield loss increase for cereals than grassland (Table 3) due to 10-year droughts. The whole of France would be impacted by a significant increase in risk in 2050, but the evolution would be even more significant in the northern half of France, where straw cereals are cultivated. Indeed, we analyzed the DOWKI values of 10-year droughts between the 2000 climate and the 2050 climate: A critical increase in the water balance anomaly (30-50%) was registered in the North of France, particularly where cereals are cultivated [46]. In the South of France, for 10-year droughts an increase in the water balance anomaly of 10-30% was recorded [46].  
The return period of the highest losses (50-year return period at current climate) will become every 19.6 years for grasslands and winter barley and every 26.1 years for soft winter wheat.  
In terms of output and income losses, these droughts will affect the agricultural economy with a loss of:  
* 4.5 million metric tons and a deficit of EUR 745 million (with an average price of EUR 168/T) for soft winter wheat;
* 1 million metric tons and a deficit of EUR 163 million (with an average price of EUR 164/T) for winter barley;
* 8.8 million metric tons of dry matter and an indirect deficit of EUR 1.3 billion (with an average price estimated at EUR 150/T of dry matter).