Yang Liu

Rainfall event separation is mainly based on the selection of the minimum inter-event time (MIET). The traditional approach to determining a suitable MIET for estimating the probability density functions is often using the frequency histograms. However, this approach cannot avoid arbitrariness and subjectivity in selecting the histogram parameters. To overcome the above limitations, this study proposes a kernel density estimation (KDE) approach for rainfall event separation and characterization at any specific site where the exponential distributions are suitable for characterizing the rainfall event statistics. Using the standardized procedure provided taking into account the Poisson and Kolmogorov–Smirnov (K-S) statistical tests, the optimal pair of the MIET and rainfall event volume threshold can be determined. Two climatically different cities, Hangzhou and Jinan of China, applying the proposed approach are selected for demonstration purposes. The results show that the optimal MIETs determined are 12 h for Hangzhou and 10 h for Jinan while the optimal event volume threshold values are 3 mm for both Hangzhou and Jinan. The KDE-based approach can facilitate the rainfall statistical representation of the analytical probabilistic models of urban drainage/stormwater control facilities.

The length of historical records is important for analyzing trends and multidecadal variabilities in precipitation. Conventional studies usually used historical precipitation data less than 60 years, which may cause inaccurate precipitation predictions. To better understand the effects of the study period on precipitation trends and cycles, the Mann–Kendall test and Sen's slope test were applied to analyze the trend and wavelet, while the multi-temporal analysis was used to study the cycles of long historical precipitation data at four rain gauge stations in Shandong Province, China. The analysis results using long-term records show an insignificant upward trend and a longer cycle in the annual precipitation, whereas a downward trend is found when using short-term records. Furthermore, it is found that selecting the length of the representative cycle derived from the precipitation data series as the time scale for the study proved to be more reasonable. A thorough consideration of the impact of cycles on trends should, therefore, be taken to facilitate a more accurate precipitation trend analysis.

Conflict in cost sharing is normal in complex water distribution system projects, such as the inter-basin water diversion project (IWDP). China’s South to North Water Diversion Project (SNWDP) is the largest IWDP in the world, with a complex relationship between upstream and downstream users of the water supply. Therefore, it is necessary to propose an applicable and unsophisticated cost-sharing method to deal with the complex relationship between upstream and downstream users. This paper proposes an improved cost-sharing method based on the continuity equation of water quantity and the balance equation of the project cost between upstream and downstream users. The fairness of sharing the joint cost between parties involved in the eastern route of SNWDP (ER-SNWDP) obtained using the proposed improved cost-sharing method is investigated by comparing its results with the existing cost-sharing method. The results demonstrate that the proposed method can overcome the non-convergence issue of the existing sharing formula and reduce the differences between upstream and downstream users’ sharing costs. The improved method provides a cost-sharing strategy that is more easily accepted by both the upstream and downstream users than the existing estimation approach. Therefore, the proposed pricing approach can provide technical guidance for decision makers in the effective operation of large-scale IWDPs in areas with quasi water markets.