Analysis on the joint distribution of low flows between Xijiang River and Beijiang River under a changing environment

The risk analysis approach based on Clayton copula and Kendall distribution function is used to analyze the joint distribution of low flows between Xijiang River in Makou and Beijiang River in Sanshui, which are connected through the Sixianjiao waterway in Guangdong, China. Using samples with seven consecutive average minimum flows of Makou gauge and the corresponding low flows of Sanshui gauge during the hydrological years 1959-2010, the "OR," "AND," and secondary return period of the joint distributions of low flows between 1959 and 1985 (referred to as sample A) and between 1986 and 2010 (referred to as sample B) of the two rivers were calculated using the Clayton copula and Kendall distribution function, respectively. The main conclusions of this study can be summarized as follows: ① The design quantiles of the low flows of Makou in sample B are less than the design quantiles for the corresponding return periods of sample A, while the design quantiles of low flows significantly increased in Sanshui; ② The encounter probabilities of low flows between Xijiang River and Beijiang River were significantly reduced, with the same frequencies of samples A and B since 1985; ③ The cumulative frequencies calculated using the secondary return period represent the risk possibilities between Xijiang River and Beijiang River low flows with specific design frequencies; ④ The Q_7d,T=20a, Q_7d,T=10a, and Q_7d,T=2a of the most likely design quantiles calculated using the secondary return period for the Makou and Sanshui gauges may be more suitably used as the design reference for water supply planning of the West River Delta during the low water season.