## 2 Methodology
### Safety Index  
Safety indices were used to evaluate pedestrian stability during inundation flows. Most of these indices have been developed based on flood depth and flow velocity [36]. The indices from previous studies can be categorized into the following approaches [37]: (1) mechanical analysis-based formulas calibrated with experiments [8; 14; 15; 16; 17; 18]; (2) empirical or semi-quantitative formulas [10; 11; 12; 13; 19; 20]. The empirical or semi-quantitative formulas are also classified into flood intensity-based (\(hU\)) and momentum-based formulas (\(htL^{2}\)) [18]. Considering these classifications for flood risk assessment, the following indicators were adopted to analyze pedestrian safety: critical velocity derived from mechanical analysis [15], specific force indicating the boundary value for walking safety [19], and two categorical indicators [11; 12]. The risk of flooding can be assessed by evaluating the walking stability of the human body based on mechanical analysis. In a flood flow, friction, drag, gravity, buoyancy, and normal force act on the human body. The five forces caused by flood flow affect the walking stability of the human body and can be divided into a flood risk analysis method that considers sliding stability due to friction force and toppling stability due to moments [15]. Slip accidents occur when the drag generated by water flow is greater than the friction force between the feet of the human body and the ground surface and toppling accidents occurs when the moment generated by drag force by water is greater than the resisting moment due to the body weight [14]. [PERSON] et al. [15] developed a calculation formula for the critical flow velocity (\(U_{c}\)) at which sliding and toppling accidents can occur through  
Figure 2: Comparison results for the measured data and simulations [35]. experiments using a human body model. Equations (3) and (4) are the calculation formulas for the limit flow speeds for slipping and toppling accidents, respectively. \[U_{cs}=\alpha\left(\frac{h}{h_{p}}\right)^{\beta}\sqrt{\frac{m_{p}}{\rho h_{p}h}- \left(a_{1}\frac{h}{h_{p}}+b_{1}\right)\frac{\left(a_{2}m_{p}+b_{2}\right)}{h_{p }^{2}}} \tag{3}\]  
\[U_{ct}=\alpha\left(\frac{h}{h_{p}}\right)^{\beta}\sqrt{\frac{m_{p}}{\rho h^{2} }-\left(\frac{a_{1}}{h_{p}^{2}}+\frac{b_{1}}{hh_{p}}\right)\left(a_{2}m_{p}+b_ {2}\right)} \tag{4}\]  
where \(m_{p}\) and \(h_{p}\) are the target's height (m) and weight (kg), respectively, and \(\rho\) is the density of water. If the actual water velocity is higher than the calculated critical flow velocity, there is a high chance of slipping and toppling accidents occurring. The coefficients for the above equation are shown in Table 1.  
[PERSON] et al. [19] proposed specific force (\(M_{0}\)) per unit width as an index for evacuating evacuation safety and suggested boundary values for the safety based on experimental results. The marginal specific force is calculated as the following equation with the sum of dynamic and hydrostatic pressure:  
\[M_{0}=\frac{U^{2}h}{g}+\frac{h^{2}}{2}, \tag{5}\]  
where \(U\) is the depth-averaged velocity; \(h\) is the inundation depth; \(g\) is the gravitational acceleration. [PERSON] et al. [19] also proposed a specific force range in which safe evacuation is possible and suggested that safe evacuation is possible when \(M_{0}\) < 0.125 m\({}^{2}\) for adult men, \(M_{0}\) < 0.1 m\({}^{2}\) for elderly men, and \(M_{0}\) < 0.08 m\({}^{2}\) for elderly women. A categorical indicator based on flood intensity has been proposed to evaluate the risk of inundation flows using more detailed criteria. [PERSON] and EA [11] presented the following equation to calculate Flood Hazard Degree (\(FD\)) using flood depth and flow velocity:  
\[FD=h(U+0.5). \tag{6}\]  
The flood risk assessment method using \(FD\) is classified into 4 levels: \"Low\" for \(FD\)\(\leq\) 0.75, \"Moderate\" for 0.75 < \(FD\)\(\leq\) 1.25, \"Significant\" for 1.25 < \(FD\)\(\leq\) 2.0, and \"Extreme\" for 2.0 < \(FD\). [PERSON] et al.