The Frequency Distribution Estimation Method of Excess Rainfall Intensity of Double Thresholds (ERId) for Combined Sewer Overflow

Nowadays, many cities in China are facing the challenge of returning black and odorous waters during the rainy seasons. Combined sewer overflow (CSO) was one of the critical triggers. In this study, a new method for estimating frequency distribution of the excess rainfall intensity considering double thresholds (ERId in short) was proposed, which is helpful for estimating severity of CSO. For the specific interceptor well, the upper threshold is the design areal unit discharge (the equivalent rainfall intensity) of its upstream combined sewer and the lower one is the design areal unit discharge of its downstream interceptor sewers minus dry weather flow rate. First, rainfall events were divided and the minimum inter-event time (MIET) was set based on the time of concentration of the combined sewer catchment. Second, double-threshold method was used for ERId calculation and sampling for scenario of 30- minute CSO duration. Finally, the empirical frequency of the sampled ERId(30) was calculated by the mathematical expectation formula (Weibull formula) and five functions (doubly censored exponential distribution, exponential function, Gumbel distribution, Weibull distribution and lognormal distribution) were used for comparison to obtain the best theoretical frequency distribution. Results revealed that: (1) The excess rainfall intensity of double thresholds (ERId) is suitable for characterizing CSO. (2) The frequency distribution of ERId was right (positively) skewed. (3) The kurtosis of the ERId samples is not greater than 3 for all the thresholds studied, which indicates that the distribution is thin-tailed. (4) The optimal frequency distribution function for ERId is doubly censored exponential distribution.