Statistical Analysis of Rainfall Intensity Frequency Considering Rainfall Time in the Diurnal Cycle

Rainfall intensity at a specific time is an important factor affecting the occurrence of combined sewer overflow (CSO). In this study, a statistical analysis of rainfall intensity frequency considering rainfall time (or cross-section) in the diurnal cycle were conducted based on the original 10-year rainfall intensity time series (the temporal resolution is 5 min). First, the stationarity of two different types of time series was evaluated by Augmented Dickey-Fuller (ADF) test and Phillips-Perron (PP) test, including the original rainfall time series and the diurnal cycle time series of five statistical characteristics (mean value (Mean), standard deviation (Std), coefficient of variation (Cv), skewness coefficient (Cs) and kurtosis coefficient (Kurt)). Moreover, the cumulative distribution function (CDF) of rainfall intensity at different cross-sections was analyzed. Finally, the best-fitting CDF of cross-section was used to quantify the CSO overflow frequency in the diurnal cycle under different thresholds. Results revealed that: (1) The original 10-year rainfall time series was second-order stationary time series. (2) The diurnal cycle time series of rainfall intensity statistics (Mean and Std) were non-stationary while those of rainfall intensity statistics (Cv, Cs and Kurt) were second-order stationary. (3) CDF of rainfall intensity at different cross-sections can be elaborated by the Generalized exponential distribution (Genexpon) and Generalized Pareto distribution (GPD) (R² > 0.914). (4) CSO overflow has a high probability of occurring in three time intervals: (4:0–5:25), (15:35 − 16:40), and (20:30 − 22:55).