## 3 Results
### Heavy Rain Disaster Risk Assessment
#### 3.2.6 Risk Assessment and Validation
The rainfall contribution rate of these four cities increased to 0.67 during this heavy rain event, leading to a slower infiltration rate of rainwater and a substantial increase in surface runoff, thereby aggravating the degree of heavy rain disaster losses in these areas. In Figure 8d, the high-risk zones cover 25.08% of the region, showing a clustered zoning characteristic. The high-risk areas are concentrated in Shijiazhuang City, Cangzhou City, Chengde City, and Tangshan City in Hebei Province. Affected by continuous heavy rain weather, the maximum daily precipitation in Shijiazhuang City reached 218.3 mm, and that in Cangzhou City reached 181.4 mm. These two places are located in the southern part of the North China Plain, with relatively flat terrain. The drainage pipe density is the lowest in the whole region. At the same time, the impervious surface ratio has increased by 29.49% compared with that in Figure 8c, affecting the urban runoff infiltration capacity, thus leading to an increase in heavy rain disaster risk. However, in Tangshan City during this period, factors such as the impervious surface ratio, drainage pipe density, and ecological land remained relatively stable. The main reason for the increase in disaster risk in this area is the growth of population density and GDP density, with respective average annual growth rates of 0.6% and 4.4%. Under the influence of continuous extreme rainstorm weather, the disaster risk level in this area has significantly increased. The distribution of high-risk areas fluctuates in different years, which is mainly influenced by external factors such as the occurrence of rainstorms, regional terrain, and drainage conditions. The medium-risk areas are scattered in the central and northeastern areas, while low-risk zones persisted in the west and south, but their proportion decreased to 22.71%. Examining the changes in urban risk, in 2012, the high-risk area in Beijing reaches its peak among the four typical years, but decreases by 2016. In Tianjin, the area around the Haihe River estuary consistently remains a high-risk zone for heavy rain disasters across all four years, with high-risk areas comprising 35.2% of the city's total area. The combined area of relatively high-risk and high-risk zones in Tangshan, Hebei Province, accounted for more than half of the city's total area, primarily near the estuary of the Luan River (Laoting County section). According to the risk assessment results, the southern coastal areas of Qinhuangdao City continue to face a high risk of heavy rain disasters, with the total area of relatively high-risk and high-risk zones, mainly concentrates in the low-lying southern coastal regions. The spatial distribution of disaster risk in Cangzhou, Hengshui, Xingtai, and Langfang in southern Hebei Province shows that, on average, 88.62% of the high-risk zones for heavy rain disasters were located within floodplains during typical years (see Figure 1 for floodplain distribution). Notably, risk aggregation was particularly significant in areas such as the Xian County floodplain in Cangzhou and the Dongdian flood detention area in Langfang. In Chengde, northern Hebei Province, the risk of heavy rain disasters was predominantly medium to relatively high-risk, with the total area of medium and relatively high-risk zones accounting for 30-40% of the city's total area during the four typical years. In Zhangjiakou, located in northwestern Hebei Province, low-risk zones for heavy rain disasters covered more than 80% of the city's total area. Overall, the spatiotemporal distribution of heavy rain disaster risk in the region has exhibited significant changes. The spatial heterogeneity of disaster risk is the result of coupling of multiple factors, including rain intensity, underlying surface conditions, disaster-bearing bodies, and regional disaster reduction capabilities. Between 2003 and 2016, the area of high-risk for heavy rain disasters within the study region increases, with the proportion of high-risk areas rising by 14.29% of the total area.