Abstract: With the flood peak and flood volume of Gangnan reservoir as a case study, the “OR” return periods, “AND” return periods, Kendall return periods (hereinafter referred to as KRP) and survival Kendall return periods (SKRP) of bivariate joint distribution were computed by using the optimally fitted Gumbel copula. The joint design quantiles in a bivariate environment was calculated based on the maximum likelihood method, conditional most likely combination, and bivariate equivalent frequency combination. The main conclusions of this study are summarized as follows: (1) The traditional “AND” and “OR” approach in multivariate return periods definition is limited in identifying safe and dangerous regions, while the KRP based approach would be more rational, but the safe region of KRP is unbounded, which is inconsistent with reality. As specific features, the proposed approach of SKRP yields a bounded safe region (a natural request in applications), where all the variables of interest are finite and limited. Consequently, the SKRP is logically the most reasonable. (2) The design values calculated using these three methods see no considerable difference, but from the point of view of simplicity and practicality, the bivariate equivalent frequency combination is recommended. (3) The design values based on the return period definitions differ obviously, among which OR return period yields the maximum design value, followed by SKRP, KRP, and AND in sequence. (4) SKRP is recommended for bivariate flood design because of its rigorous theoretical basis, and its design results give consideration to both safety and economy. (5) The difference between bivariate joint design value and univariate design value is greatly affected by the correlation between variables. The weaker the correlation between variables, the greater the difference. In summary, KRP based bivariate equivalent frequency combination is currently the more scientific and rational approach to the joint design of flood peak and volume.

Key words: flood, flood volume, Kendall function, Copula, return period