Pareto archived dynamically dimensioned search (PA-DDS) is one of the meta-heuristic methods available to solve multiobjective reservoir operation problems. This study uses this method to optimize reservoir operation rules with the objectives of maximizing the power generation and water supply. The performance of PA-DDS is compared with the nondominated sorting genetic algorithm–II (NSGA-II) in terms of a hypervolume indicator and the distribution of optimized nondominated solutions (NDSs) in a case study of Hanjiang cascade reservoirs in China. The results indicate that PA-DDS can increase the amount of power generation and water supply, respectively. Moreover, the uncertainty in reservoir operation optimized by both methods is analyzed in terms of the NDS distribution and the trade-off relationship between water supply and power generation. The results demonstrate that PA-DDS outperforms NSGA-II not only in the Pareto front approximation (NDS), but also with an increase in water supply by about $300\mathrm{million}{\mathrm{m}}^3/\mathrm{year}$ for Hanjiang cascade reservoir operation.

Reservoirs operation alters the natural flow regime at downstream site and thus has a great impact on the design flood values. The general framework of flood regional composition and Equivalent Frequency Regional Composition (EFRC) method are currently used to calculate design floods at downstream site while considering the impact of the upstream reservoirs. However, this EFRC method deems perfect correlation between peak floods that occurred at one sub-basin and downstream site, which implicitly assumes that the rainfall and the land surface process are uniformly distributed for various sub-basins. In this study, the Conditional Expectation Regional Composition (CERC) method and Most Likely Regional Composition (MLRC) method based on copula function are proposed and developed under the flood regional composition framework. The proposed methods (i.e., CERC and MLRC) are tested and compared with the EFRC method in the Shuibuya-Geheyan-Gaobazhou cascade reservoirs located at Qingjiang River basin, a tributary of Yangtze River in China. Design flood values of the Gaobazhou reservoir site are estimated under the impact of upstream cascade reservoirs, respectively. Results show that design peak discharges at the Gaobazhou dam site have been significantly reduced due to the impact of upstream reservoir regulation. The EFRC method, not taking the actual dependence of floods occurred at various sub-basins into account; as a consequence, it yields an under-or overestimation of the risk that is associated with a given event in hydrological design. The proposed methods with stronger statistical basis can better capture the actual spatial correlation of flood events occurred at various sub-basins, and the estimated design flood values are more reasonable than the currently used EFRC method. The MLRC method is recommended for design flood estimation in the cascade reservoirs since its composition is unique and easy to implement.

Seasonal design floods reflecting seasonal variation information are very important for reservoir operation and management. The seasonal design flood estimation method currently used in China is based on univariate frequency analysis and assumes that the seasonal and annual design frequencies are equal, which neither satisfies flood prevention standards nor considers the interdependence between different seasonal floods. The Danjiangkou reservoir located in the Han River basin, the first pilot basin of most regulated water resources management policy in China, was selected as a case study. After dividing the entire flood season into subseasons, a dependent structure of summer and autumn floods was established by copula functions. Three bivariate flood quantile selection methods, namely the equivalent frequency combination (EFC) method, conditional expectation combination (CEC) method, and conditional most likely combination (CMLC) method, were performed to estimate unique seasonal design floods to meet the needs in engineering and compared with the univariate design values. The evaluation criteria and a boundary identification method were used to assess the rationality of these combination methods. Compared with the CEC and EFC methods, the CMLC method has smaller root-mean square error (RMSE) and bias values by 12.9–34.8% and 22.6–36.4%, respectively. The CMLC and EFC methods are within the feasible regions, whereas the CEC estimators are beyond the feasible range. The results of economic analysis show that the CMLC method can enhance the floodwater use rate from 79.7 to 82.8% for the wet year and from 91.8 to 93.7% for the dry year in comparison with the EFC method. The CMLC method is more rational in physical realism and recommended for estimating seasonal design floods in the Danjiangkou reservoir, which would provide rich information as references for flood risk assessment, reservoir scheduling, and management.