Stepped spillways, as highly effective energy dissipation facilities, have been widely applied in hydraulic engineering. By introducing an inclination angle to the horizontal step surface, either energy dissipation efficiency or sediment transport capacity can be enhanced. The manner and size of vortices within the steps vary with changes in the inclination angle and spillway slope, enhancing energy dissipation through momentum exchange between the main flow and these vortices. This study, drawing upon data in the literature and numerical simulations, investigates the influence of a spillway slope and step inclination angle on the energy dissipation characteristics of inclined stepped spillways. Results indicate that the energy dissipation rate decreases with an increasing spillway slope while increasing with a greater upward inclination of the step’s horizontal surface. However, changes in both parameters show a limiting effect on vortex development. As the spillway slope decreases and the step inclination angle increases, the rate of vortex size expansion diminishes. Finally, an inclination/slope ratio is proposed to characterize the energy dissipation effect of inclined steps, and an empirical formula relating the energy dissipation rate to the relative critical depth, relative spillway height, and inclination/slope ratio is established, with errors controlled within 10%.

This study utilizes historical monitoring data from the Xu Fan small watershed spanning 1962 to 2021 and employs the K-means clustering algorithm to classify extreme rainfall events into three distinct categories: short-duration high-intensity rainfall, sustained moderate-intensity rainfall, and long-duration heavy rainfall. Through the application of the Random Forest model, key factors influencing flood characteristics are identified, including total rainfall, maximum rainfall intensity, the timing of maximum intensity, and rainfall duration. The comparative analysis of data before and after 1990 highlights that climate change has led to increased maximum rainfall intensity, reduced rainfall duration, and shifts in the temporal distribution of rainfall, thereby exerting a significant influence on the flood generation process.

Climate change increases the intensity and frequency of extreme rainfall. Heavy rain is one of the main input sources for the complex water resources system in the watershed. Understanding its regional spatial correlation is of vital importance for promoting sustainable disaster management in the watershed. The Qiantang River Basin is a significant ecological and economic area in the Yangtze River Delta, yet systematic research on its multi-regional rainstorm-dependent structure remains insufficient. In this study, hourly rainfall data of the basin from 1950 to 2024 were used to construct marginal functions by using the peaks-over-threshold and the generalized Pareto distribution, and a mixed Copula model was established to describe the dependence structure of multi-regional extreme rainfall events. The model has been tested by RMSE and Cramér–von Mises statistics and shows reliable performance. The study reveals that the basin has a “double cluster” spatial pattern: the internal conditions of northern clusters (Hangzhou–Shaoxing) and southern clusters (Jinhua–Lishui–Quzhou) showed a strong dependence. On the contrary, under cluster conditions with low inter-regional dependence, all high-probability combinations occurred within the clusters, not outside them. This finding provides quantitative support for optimizing trans-regional emergency response, improving flood control resilience, and realizing precise allocation of resources, and is of great significance for promoting sustainable watershed governance.