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.

Flood frequency analysis (FFA) is needed for the design of water engineering and hydraulic structures. The choice of an appropriate frequency distribution is one of the most important issues in FFA. A key problem in FFA is that no single distribution has been accepted as a global standard. The common practice is to try some candidate distributions and select the one best fitting the data, based on a goodness of fit criterion. However, this practice entails much calculation. Sometimes generalized distributions, which can specialize into several simpler distributions, are fitted, for they may provide a better fit to data. Therefore, the generalized gamma (GG) distribution was employed for FFA in this study. The principle of maximum entropy (POME) was used to estimate GG parameters. Monte Carlo simulation was carried out to evaluate the performance of the GG distribution and to compare with widely used distributions. Finally, the T-year design flood was calculated using the GG and compared with that with other distributions. Results show that the GG distribution is either superior or comparable to other distributions.

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.

Design flood estimation is very important for hydraulic structure design, reservoir operation, and water resources management. During the last few decades, severe flash floods have caused substantial human, agricultural, and economic damages in Pakistan during the Monsoon seasons. However, despite phenomenal losses, the flood characteristics are rarely investigated. In this paper, flood frequency analysis (FFA) on four major rivers over Pakistan is performed to probe probability distributions (PDs)at the right-tail flood events. For this purpose, (i) we employed ten different probability distributions associating with an L-moments method for constructing FFA models across Pakistan; (ii) we evaluated the best-fit distribution by using goodness-of-fit test and statistical criteria; and finally; (iii) we devised a Monte Carlo simulation to systematically evaluate the robustness of a selected distribution’s fitting performance by using a synthetic data series of different sizes. Our results indicated that generalized Pareto and Weibull emerged as the most viable options for quantifying hydrological quantiles for most of the river basins in Pakistan. Our main findings would provide rich information as references for flood risk assessment and water resource management in Pakistan.

Flood frequency analysis (FFA) provides an important basis for determining the construction size of hydraulic facilities. The selection of a suitable distribution and parameter estimation method (D/E procedure) is of vital importance in FFA. In this study, the method of Halphen (HP) distribution, coupled with the principle of maximum entropy (ME), was proposed for FFA. First, the relations among Lagrange multipliers, constraints, and parameters were derived firstly. Annual maximum flood data series at 12 gauging stations and Monte Carlo simulation were used to evaluate the descriptive and predictive abilities of the proposed HP/ME procedure. The proposed HP/ME procedure was compared with the commonly used procedures. It is shown that the HP/ME procedure has the smallest root-mean-square error (RMSE) values for 10 of the 12 sites and the smallest Akaike information criterion (AIC) values for 7 of the 12 sites. The descriptive ability of the HP/ME procedure is good because of its flexible shapes and excellent tail properties. The Monte Carlo simulation results demonstrate that the HP/ME procedure performs well, which gives a narrower 90% confidence interval and produces higher efficiency than other compared procedures in several simulated cases. The proposed HP/ME procedure performs well to estimate design floods at two selected sites and might be suggested as an alternative candidate for hydrologic frequency analysis.

Flood events are characterized by flood peaks and volumes that can be mutually constructed using a copula function. The Indus basin system of Pakistan is periodically threatened by floods during monsoon seasons and thus causes huge losses to infrastructure as well as the community and economy. The design flood hydrograph (DFH) of suitable magnitude and degree is imperative for sheltering dams against the flood risk. The hydrological pair of flood peak and volume is required to be defined using a multivariate analysis method. In this paper, the joint probability function of the hydrological pair is employed to derive the DFH in the Indus basin system of Pakistan. Firstly, we compared the fitting performance of different probability distributions (PDs) as a marginal distribution. Next, we compared the Archimedean family of copulas to construct the bivariate joint distribution of flood peak and volume. Later, the equal frequency combination (EFC) method and most likely combination (MLC) method using “OR” joint return period (JRP_or), was involved to derive the design flood quantiles. Finally, we derived the DFH using the two combination methods based on Gumbel–Hougaard copula for different return periods. We presented the combination methods for updating the shape of the DFH in Pakistan. Our study will contribute towards the improvement of design standards of dams and environmental recovery in Pakistan.