## 3 Results
### Heavy Rain Disaster Risk Assessment  
#### 3.2.1 Risk Assessment System  
Heavy rain disasters refer to natural disasters directly or indirectly triggered by regional heavy rain events, often resulting in agricultural, transportation, or other property losses and casualties [39]. They can also lead to secondary disasters such as flash floods, urban waterlogging, and landslides. The risk of heavy rain disasters is the uncertainty of potential losses or adverse impacts on society, the economy, the environment, and human life safety caused by heavy rain events. The formation of heavy rain disaster risk is influenced by multiple factors, including meteorological conditions, topographical features, land use types, and regional disaster mitigation and emergency response capabilities. Based on disaster system theory, this paper integrates regional disaster mitigation capacity with disaster-inducing factors, disaster-prone environments, and disaster-bearing bodies [40] to construct a four-dimensional assessment framework for heavy rain disaster risk. This framework systematically analyzes the characteristics of disaster risk within the region. According to relevant studies [41; 42], we have selected 10 risk factors to establish a heavy rain disaster risk assessment system, with specific indicators and selection criteria as follows:  
1. Heavy Rain Disaster-Inducing Factors: This study selects the number of heavy rain days, rainfall amount, and rainfall contribution rate as the disaster-inducing factors. The principles for their selection and the analysis of their spatiotemporal variation characteristics are detailed in Section 3.1 above.
2. Disaster-Prone Environment for Heavy Rain: This refers to the natural and socio-cultural environments that play a role in disasters under the influence of heavy rain. The slope of the land affects the direction and speed of surface runoff, influencing the degree of water accumulation. The steeper the slope, the shorter the time for floodwaters to gather in low-lying areas, increasing disaster risk. The extent of the impervious surface area directly affects the infiltration of surface runoff and the drainage pressure on the sewer system. Therefore, slope and impervious surface ratio are considered as risk factors for the disaster-prone environment.
3. Disaster-Bearing Bodies for Heavy Rain: These are the objects affected by disaster-inducing factors, primarily the population, buildings, and socio-economic aspects within a region. Thus, this paper uses population density, GDP per unit area, and land use type to describe the disaster-bearing bodies [30]. The greater the population density, GDP density, and utilization level in a region, the greater the potential loss in the event of a disaster.
4. Disaster Mitigation Capacity for Heavy Rain: This refers to a city's ability to prevent and respond to disasters. The greater the density of drainage pipes, the greater the drainage capacity, and the lower the risk of heavy rain disasters. Additionally, since heavy rain disasters often accompany road collapses, leading to urban road system failures or partial paralysis, road network density is also considered an indicator of disaster mitigation capacity.  
The specific heavy rain disaster risk assessment system and the data sources for risk factors are presented in Table 2.  
The calculation formula for the heavy rain disaster risk index (HDRI) is as follows:  
\[HDRI=\sum_{i=1}^{n}W_{i}*X_{i} \tag{6}\]  
where _HDRI_ represents the heavy rain disaster risk index, categorized into four levels: low, medium, relatively high, and high. The variable \(n\) denotes the number of risk factors, which is set at 10. \(W_{i}\) is the weight of the \(i\)-th indicator, and \(X_{i}\) is the risk level of the \(i\)-th indicator.