## 5 Conclusions  
This paper analyzed the intensity and frequency of extreme agricultural droughts in 2050. For this purpose, the analysis focused on three crops: soft winter wheat, winter barley, and grassland. A new meteorological index was developed, which represents a cumulative water anomaly and is correlated to the yield losses. The model created simulated the crop yield losses at the departmental scale from the index values. Then, the index was projected in 2050 using the ARPEGE-Climat model from Meteo-France. The results compared the intensity and frequency of extreme droughts between the climate in 2000 and the climate in 2050 and show that the yield losses due to 10-year drought increased by 35% for grassland and by more than 70% for cereals.  
Within the frameworks of both (1) the new CAP program (2023-2027) and (2) the French risk management scheme reform, these numbers are useful to alert and inform political stakeholders to the consequences of climate change, at the national and regional scale, on grassland and cereals. Our results show that to calibrate a risk management scheme and to be able to estimate the national farm exposure in the mid-term, the evolution of climatic extremes has to be taken into account. Insurers, reinsurers, public funds, and farmers (individually and globally) are exposed at different levels to the increase in climatic events in the next 30 years.  
Insurance and reinsurance solvability is linked to the capacity to face extreme losses and, by definition, to the capacity to model the frequency/intensity curve. Nevertheless, as shown in this paper, this frequency/intensity curve cannot be considered stationary over the next 30 years. Under this condition, pricing treaties to allow loss balance in the mid-term have to integrate a mix between current and future losses.  
The next step will be to integrate risk management scenarios in our model and to estimate the losses for the different stakeholders. A public-private partnership is a promising route to face systemic extreme events when insurance mutualization is to be reconsidered. Today, in France, the crop insurance diffusion rate is 30% for cereals and less than 2% for grasslands [73]. In this respect, after the occurrence of an extreme event at the national scale, the State must intervene to support farmers' resiliency. A significant increase in the diffusion rates is one way to achieve sustainable agriculture in the context of increasing risks.  
Agriculture has always been able to adapt to the changing climate. However, considering pessimistic scenarios like RCP 8.5 and the fast increase in extreme droughts, risk management policies must support national agricultural production during the adaptation period.  
Validation, J.C. and J.-M.S.; writing--original draft, D.K., D.M. and M.V. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data used for yield are available in [[https://agreste.agriculture.gouv.fr](https://agreste.agriculture.gouv.fr)]([https://agreste.agriculture.gouv.fr](https://agreste.agriculture.gouv.fr)) (accessed on 20 January 2022).  
**Acknowledgments:** The authors want to thank [PERSON] for helping with the revision of the manuscript and [PERSON] for the English corrections. We also want to thank our anonymous reviewers for their valued advice on the structure of the paper and the addition of complementary studies.  
**Conflicts of Interest:** The authors declare no conflict of interest.