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

Abstract

The effective precipitation (Pe) and crop water requirements (ETc) can reflect the agricultural water supply and demand situations under natural precipitation conditions, and the encounter risk analysis of Pe 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 Pe, and analyzed the natural agriculture water shortages risk of different encounter situations. The results indicated ETc and Pe presented a negative relativity, and the Gaussian copula was found to be more suitable to estimate the joint distribution of ETc and Pe. The asynchronous encounter probability was higher two times than the synchronous encounter probability, and the pairs (rich Pe-poor ETc, poor Pe-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 Pe without exceeding a certain value for different ETc states increased with increased Pe, and the conditional probability of ETc with exceeding a certain value for different Pe states decreased with increased ETc. The conditional probability of Pe without exceeding Pe 37.5%, Pe 62.5%, Pe average (ETc exceeding ETc 37.5%, ETc 62.5%, ETc average) for different ETc (Pe) 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 Pe) with given low Pe (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.