## 4 Discussions
### Evaluations of Uncertainty in Flood Hazard Assessments According to Safety Indices  
To ensure the safe evacuation of citizens in the event of underground station flooding, it is essential to conduct a comprehensive flood risk assessment across the entire facility. The flood risk assessment results lie in their applicability to subway flooding disasters, and their potential to aid in determining pedestrian evacuation routes. [PERSON] and [PERSON] [38] demonstrated that while information supporting evacuation choices can improve evacuation efficiency, inefficient or incorrect information may have a more substantial negative impact on effectiveness. Additionally, they found that simple and actionable instructions can further enhance evacuation efficiency [39]. These findings suggest that providing a single, accurate indicator is more advantageous for making evacuation route decisions than relying on multiple safety indices, which could cause confusion for evacuees or subway platform managers. In this study, flood hazard indices based on the empirical or semi-quantitative formulas (\(M_{0}\), \(FD\), and \(FIF\)) were utilized for flood risk assessment within the subway platform (Figure 8). Additionally, areas exceeding the toppling and sliding velocities (\(U_{cp}\) and \(U_{cl}\)) were calculated to classify risky regions for flooding (Figure 10). Figures 8 and 10 demonstrate that the flood risk assessment results vary depending on the chosen assessment index. \(FIF\) tends to underestimate the flood hazard area compared to other indices, while  
Figure 14: Comparison with critical velocity near human models with simulated data. \(M_{0}\) tends to overestimate it. Consequently, in case Q1, the flood hazard area determined by the \(M_{0}\) criterion was estimated to be 8.9% to 29.7% over time, whereas the results from the \(FIF\) assessment indicated that the entire area was safe. The use of momentum is influenced predominantly by flow velocity when water depth is low [12]. Therefore, there is a risk of overestimating or underestimating flood hazards depending on the assessment indices used, underscoring the importance of considering multiple indices to arrive at a comprehensive conclusion. Figure 15 presents the flood risk assessment results based on considering all possible weighting scenarios for the five flood hazard assessment indices used in this study (\(M_{0}\), \(FD\), \(FIF\), \(U_{\text{ct}}\), and \(U_{\text{cs}}\)) according to the following formula:  
\[FR_{wj}=\sum_{i=1}^{5}w_{ij}FR_{i}, \tag{9}\]  
where \(FR_{i}\) is the flood risk value for the \(i\) flood risk analysis index; \(w_{ij}\) is the weighting value for the \(j^{\text{th}}\) weighting scenario; \(FR_{wj}\) is the weighted flood risk value. Since a reliable objective criterion for determining the appropriate weights for these indices was insufficient, 45 weighting scenarios were generated to address potential bias in the assignment of \(w_{ij}\)[40]. These scenarios were created by combining weighting values ranging from 0.1 to 0.6 for each index, ensuring that the summation of \(w_{ij}\) in each scenario equals one. In Figure 15, the upper and lower limit lines are the maximum and minimum values of the weighted average flood hazard risk (\(FR_{wj}\)), and the dashed line is the averaged values of \(FR_{wj}\) for 45 weighting scenarios. The maximum values of \(FR_{wj}\) were 6.6%, 22.8%, and 30.8% in Cases Q1, Q2, and Q3, respectively. The standard deviation of weighted average values in Case Q1 ranged from 0.9 percentage points to 3.34 percentage points over time. This range broadened in Cases Q2 and Q3, with standard deviations of 3.7 to 5.7 percentage points and 4.2 to 5.8 percentage points, respectively, indicating increased uncertainty in the flood risk assessment results. The upper limit was obtained when \(M_{0}\) had the maximum weighting value of 0.6, while the lower limit appeared when \(FIF\) had the maximum weighting.