Design storm for mixed level-1 and level-2 urban drainage standards based on the secondary return period

In this paper, we estimated the design storm for mixed level-1 and level-2 urban drain standards according to data of the combination of 1-hour rainstorm and 6-hour rainstorm (R_1h-R_6h), the combination of 1-hour rainstorm and 12-hour rainstorm(R_1h-R_12h), and the combination of 1-hour rainstorm and 24-hour rainstorm(R_1h-R_24h) in Zhuhai city between 1984 and 2015. First, the models of joint probability distribution about different combinations were built using the Archimedean extreme value Copula and the Kendall distribution function. Then, the occurrence probability, "OR" return period, "AND" return period and the secondary return period for each combination were analyzed, and the design storms for each combination were estimated by the method with the maximum occurrence probability. The results are as follows: the cumulative frequency corresponding the secondary return period more accurately represents the risk probabilities of rainstorms of different combinations with specific design frequency; the estimated design storm quantiles of the secondary return period based on return periods with 2-year, 3-year, 5-year, 10-year, 20-year, 50-year and 100-year are between the design storm quantiles of the "OR" return period and these of the "AND" return period, and less than these of the marginal distribution return period, respectively. Compared with the case of design storm quantiles of the marginal distribution return period, the relative error of the R_1h-R_6h is between 3.1% and 7.1%; that of the combination of R_1h-R_12h is between 3.3% and 9.3%; that of R_1h-R_24h is between 3.95% and 12.0%. These provide optimization criterion and guide for the risk management of waterlogging project and the design of drainage pipe, respectively.