## 2 Materials and Methods
### Methodology
#### 2.3.3 Flood Risk Assessment Baseline Model  
We constructed the risk assessment model based on the disaster system theory by [PERSON] et al. [72], a Chinese disaster management approach that has been widely used for years [73], which is defined as a composite product of hazardous (i.e., hazard intensity), the sensitivity of the geographical environment and the vulnerability of the exposed socioeconomic entities.  
\[R=H\cap S\cap V=\sum w_{i}f_{i} \tag{2}\]  
where \(R\) is the flood risk; \(H,S,V\) are the hazardous, sensitivity and vulnerability, respectively; \(f_{i}\) is the normalized assessment factor \(i\) (\(i=1,\ldots,9\)) based on the Min-Max normalization method; and \(w_{i}\) is the weight of factor \(i\).  
Hazardousness refers to the intensity or probability of natural events (causal factors) that contributes to flood impact. In this study, we chose precipitation (climatic indicator) and inundation frequency (historical evidence) to characterize this parameter. Maximum 3-day rainfall (RMAX3) rather than annual rainfall amount (RA) and rainstorm frequency (RF), was used as the climatic indicator, as explained in Section 3.1.1. The codes for extracting daily rainfall on GEE and then calculating RMAX3 are reported in Part B of Appendix A. The historical frequency of inundation based on multilayer scenarios is an important hazard factor that reflects the probability of occurrence. Incorporating objective real-world inundation data reduces the MCDA model's subjectivity and uncertainty. Higher RMAX3 and inundation frequency indicate more severe hazard intensity. Sensitivity represents the susceptibility of the topographic, hydrologic, vegetation and other geographic environmental conditions to flooding; it characterizes the natural environment's favorability for inducing flooding at a given intensity. Here, we adopted elevation, TWI, NDVI and distance from the river system to characterize the sensitivity. Areas with low elevation, high TWI, low NDVI and close proximity to rivers are generally more prone to flooding. Vulnerability measures the exposure of socioeconomic entities to floods and their resistance ability. Population density and GDP reflect the potential losses of population and assets. Land-use type can indicate the adaptive capacity of a unit. For example, cropland is more vulnerable than built-up land, and forest and unused land less vulnerable to flooding [74; 75].  
Another crucial aspect of the MCDA approach is the determination of the indicator weights. In this study, we employed the FAHP-Entropy method, which integrates the fuzzy analytic hierarchy process (FAHP) and Entropy methods. The former reduces sub jectivity in the weighting assignment by considering the inherent fuzziness of manual decision making through fuzzy set theory [31], while the latter allows for a completely objective weighting driven by the data variability [76]. In previous research, it has been proven that FAHP-Entropy yields more scientific weight results than FAHP, Entropy and AHP-Entropy [77]. We share the illustrative calculation process of weights in Part C of Appendix A. The following linear distance function determines the weight assignment of FAHP and Entropy [74].  
\[w_{i}=\alpha w_{i}^{\prime}+\beta w_{i}^{\prime\prime} \tag{3}\]  
\[d\big{(}w_{i}^{\prime},w_{i}^{\prime}\big{)}=\left[\frac{1}{2}\sum_{i=1}^{m} \big{(}w_{i}^{\prime}-w_{i}^{\prime\prime}\big{)}^{2}\right]^{\frac{1}{2}} \tag{4}\]  
\[\left\{\begin{aligned} d\big{(}w_{i}^{\prime},w_{i}^{\prime\prime} \big{)}^{2}&=(\alpha-\beta)^{2}\\ \alpha+\beta&=1\end{aligned}\right. \tag{5}\]  
where \(w_{i}\) is the FAHP-Entropy weight of factor \(i\); \(w_{i}^{\prime}\) is the subjective weight of FAHP; \(w_{i}^{\prime\prime}\) is the objective weight of the Entropy method; \(\alpha\), \(\beta\) are the assignment coefficients of the weights; and \(d\big{(}w_{i}^{\prime},w_{i}^{\prime\prime}\big{)}\) is the linear distance between FAHP and Entropy methods.