General formula derivation of most likely regional composition method for design flood estimation of cascade reservoirs system

In this study the joint probability distributions of floods at all sub-basins of cascade reservoirs were established using Copula function and based on the principle of maximizing joint probability density function the general formula of the most likely regional composition (MLRC) method was derived for design flood estimation of downstream reservoirs. The developed procedure was tested and compared with equivalent frequency regional composition (EFRC) method for determination of design flood of the Shuibuya-Geheyan-Gaobazhou cascade reservoirs system located at the Qingjiang River, a tributary of the Yangtze River in China. The results show that the design flood values of the MLRC method are within the range of peak discharges estimated by different EFRC schemes. The design flood reduction rates of the Yidu site are found to be evident due to the regulation of upstream cascade reservoirs, and the 100-year design flood reduction rate estimated by the MLRC method is 30.2%. The findings of the study reveal that the proposed method not only has strong statistical basis, but also has rational results with unique composition scheme, which will provide a new approach for design flood estimation of complex cascade reservoirs system.