## 3 Urban Inundation Simulation Using the Rainfall Simulator
### Analysis of Flood Vulnerabilities  
The inundation depth was compared at three points, which were depicted in Figure 6a. The measured depth and the runoff velocity at the same points was plotted in Figure 8. As can be seen in the inundation depth distributions, the depth shows a small increment in range of 80-130 mm/h. When the rainfall intensity was above 160 mm/h, the inundation depth significantly increased, and the depth slowly increased again. These flooding patterns affect the runoff velocity, and there were small increments in the velocity in the range of 160-200 mm/h. From these results, the threshold rainfall intensity increased flood damage due to a rapid increase of inundation depth and runoff velocity. Especially, the inundated properties of point C in the crossroad were more sensitive to changes of rainfall intensity than other points. Thus, the inundation depth at each the subway station entrance located in the crossroad was compared in Figure 9 according to the rainfall intensity. The results show that the inundation depth at entrance No. 1 shows the largest variations and the deepest depth caused by the increase of the rainfall intensity. Entrance No. 14, located in the eastern part of the crossroad, also shows large increments in the inundation depth when the rainfall intensity  
Figure 7: Inundation depth changes according to rainfall intensity: (a) 80 mm/h; (b) 130 mm/h; (c) 160 mm/h; (d) 185 mm/h. was 160 mm/h. The eastern part of the crossroad has a relatively low bed elevation, and the region was severely flooded by the flow runoff from the mountain hill. Figure 8: Velocity and inundation depth against rainfall intensity: (**a**) point A; (**b**) point B; (**c**) point C.  
The vulnerability from the flood events was evaluated using the moment instability (\(hvc_{c}\)) and the friction instability (\(hvc_{c}^{2}\)) as follows [13]. \[hvc_{c}\ =\ \sqrt{\frac{2 mg\cos\alpha L}{C_{D}B\rho}}\ =\ C_{M}\sqrt{m} \tag{3}\]  
\[hvc_{c}^{2}\ =\ \frac{2\mu g}{C_{D}B\rho}m\ =\ C_{F}m \tag{4}\]  
where \(m\) and \(L\) is the mass and height of standard adult male, respectively; \(\alpha\) is the person's angle to flowing direction; \(C_{D}\) is the drag coefficient; \(B\) is the body width exposed normal to the flow; \(\rho\) is the density of water; \(C_{M}\) is the moment coefficient; \(\mu\) is the friction coefficient; \(C_{F}\) is the friction coefficient. From Equations (3) and (4), threshold values of runoff velocity (\(v_{c}\)) and inundation depth (\(h_{c}\)) for human safety can be achieved when \(hvc_{c}\) equals to \(hvc_{c}^{2}\) as follow. \[h_{c}\ =\ \frac{C_{M}^{2}}{C_{F}} \tag{5}\]  
\[v_{c}\ =\ \frac{C_{F}m^{0.5}}{C_{M}} \tag{6}\]  
The threshold values (\(h_{c}\), \(v_{c}\)) in conditions of standard adult male in South Korea who has \(L\) = 174 cm, \(m\) = 76 kg, \(C_{D}\) = 1.1 and \(B\) = 0.4 m and on a concrete covered road (\(\mu\) = 0.5 [14]) were calculated by changing \(\alpha\) (0-90\({}^{\circ}\)) and plotted in Figure 10. In Figure 10, the measurement points shown in Figures 8 and 9 were also plotted to evaluate the human instability from floods in the study area. A symbol marked over the instability boundary indicates that a person at the point is in danger to be toppled or sliding due to runoff. As can see in the figure, point 1 on Road B was the most vulnerable because the data was plotted in the unstable area when the rainfall intensity exceeded 160 mm/h that is relatively lower than other areas. In other cases, points 2 and 3 were included in the unstable condition when the rainfall intensity is over than 185 mm/h and 200 mm/h, respectively. Among the subway station entrances, only entrance No. 1 was marked above the boundary when the rainfall intensity was 200 mm/h. From these results, it can be said that instabilities for human activities during flood events would mainly occur on Road B. Furthermore, Road B is a densely populated area, which is occupied by parking lots and business buildings.