Identification and Temporal Distribution of Typical Rainfall Types Based on K-Means++ Clustering and Probability Distribution Analysis

Characterizing rainfall events with recurrence periods of 1–5 years is crucial for urban flood risk assessment and water management system design. Traditional hydrological frequency analysis methods inadequately describe the temporal structure and intensity distribution of rainfall. In this study, we analyzed 1580 independent rainfall events in central Hangzhou (1950–2023) using PCA dimension reduction and K-means++ clustering to investigate typical rainfall types across different recurrence periods. The integrated approach effectively captures temporal characteristics while reducing dimensionality and improving clustering efficiency. Our results indicate that concentrated single-peak rainfall with short duration and a mid-to-late peak dominates the region, with longer recurrence periods exhibiting higher intensity, shorter duration, and greater temporal concentration. Furthermore, cumulative distribution function (CDF) and probability density function (PDF) analyses were conducted on these typical rainfall types, quantifying their distributional characteristics and yielding precise mathematical expressions. These standardized rainfall curves provide direct applications for engineering design and hydrological modeling, enabling more accurate flood prediction and mitigation strategies for Hangzhou’s urban infrastructure.