Encounter risk analysis of crop water requirements and effective precipitation based on the copula method in the Hilly Area of Southwest China

The effective precipitation (P-e) and crop water requirements (ETc) can reflect the agricultural water supply and demand situations under natural precipitation conditions, and the encounter risk analysis of P-e and ETc is a prerequisite for regional water resources allocation and irrigation planning. Considering an entire growing season of rape-maize in the Hilly Area of Southwest China during 1961-2017, this study employed the popular copula functions to fit two-dimensional joint distribution of annual ETc and P-e, and analyzed the natural agriculture water shortages risk of different encounter situations. The results indicated ETc and P-e presented a negative relativity, and the Gaussian copula was found to be more suitable to estimate the joint distribution of ETc and P-e. The asynchronous encounter probability was higher two times than the synchronous encounter probability, and the pairs (rich P-e-poor ETc, poor P-e-rich ETc) had the greatest probability with value of 16.59%, indicating the natural water supply and demand usually was unmatched. The conditional probability of P-e without exceeding a certain value for different ETc states increased with increased P-e, and the conditional probability of ETc with exceeding a certain value for different P-e states decreased with increased ETc. The conditional probability of P-e without exceeding P-e (37.5%), P-e (62.5%), P-e (average )(ETc exceeding ETc (37.5%), ETc (62.5%), ETc average) for different ETc (P-e) states was 44.97-69.12% (the corresponding return period was 1.45-2.22 years), showing natural agriculture water shortages risk was high under general situations. However, the conditional probabilities of extremely high ETc (low P-e) with given low P-e (high ETc) were less than 3%, so extreme water shortages rarely occurred in the Sichuan Hilly Area. This study successfully applied the copula method to regional agricultural water shortages risk analysis and could provide a theoretical basis for regional water resources management and planning.& nbsp;