## 4 Results and Discussion
### Mapping Vulnerable Areas in Other Flood Events  
To evaluate the performance of the logistic regression model developed in this study, inundation trace maps and the maximum 1-h rainfall data were collected for floods that occurred in September 2010 and July 2011. Of the rainfall observatories, the Bukaksan (422) and Namhyeon (425) observatories were excluded because they had not yet opened in 2010, and the Bukhansan (420) observatories, which were closed in 2011, were also excluded. The rainfall of the observatories was interpolated using the IDW method as shown in Figure 9. In 2010, very high-intensity rainfall of around 100 mm/h occurred in the west of the study area, while relatively low-intensity rainfall of around 60 mm/h was recorded in the north. Overall, in 2011, it rained less than in 2010, except in the south with 100 mm/h of rainfall.  
In addition, the year-end statistical data for 2009 and 2010 [51; 52] were used to consider drainage pumping stations that were newly built or increased in capacity after flooding in 2001. In 2009 and 2010, the number of pumping stations was increased from 91 in 2000 to 111, and the capacity also was increased to 155,313 m\({}^{3}\)/min (2009) and 161,279 m\({}^{3}\)/min (2010). The changed pump capacity per drainage area is shown in Figure 10.  
In the logistic regression model developed above with data for 2001, the same values as those in 2001 were used for surface and locational factors, and values for 2010 and 2011 were entered for resistant and inducing factors, respectively. The flood vulnerability that was recalculated by inputting pumping capacity and rainfall to this model is shown in Figure 11. Interestingly, as low rainfall was input compared to that used in the development  
Figure 8: Proportion of flood occurrence in vulnerable areas.  
Figure 9: Rainfall interpolation results by year: (**a**) September 2010; (**b**) July 2011.  
of the model, the vulnerability in 2010 and 2011 was decreased significantly compared to in 2001. In addition, in 2010, the high-intensity rainfall in the west increased the vulnerability, and the low-intensity rainfall in the north decreased the vulnerability. In 2011, most areas were calculated to have low vulnerability, except for the increase in vulnerability in some areas due to high-intensity rainfall in the south.  
An ROC analysis was conducted to quantitatively analyze the extent to which calculated flood vulnerability in 2010 and 2011 actually detects floods. The ROC curves for 2010 and 2011 are shown in Figure 12. In both cases, it was found that the measure of flood vulnerability (AUC = 0.861, 0.815) that considered the hydrological factors together detected flood occurrence better than that (AUC = 0.841, 0.766), which considered only the topographic factors. The detection rate was calculated as shown in Figure 13. In 2010, among vulnerable areas considering rainfall, flooding occurred at a rate of 66% (\(\Gamma\), 57%) in the very high class; 54% (\(\Gamma\), 31%) in the high; 47% (\(\Gamma\), 18%) in the medium; 33% (\(\Gamma\), 12%) in the low; and 11% (\(\Gamma\), 7%) in the very low. In 2011, floods occurred at a rate of 36% (\(\Gamma\), 17%) in the very high class; 41% (\(\Gamma\), 12%) in the high; 31% (\(\Gamma\), 9%) in the medium; 28% (\(\Gamma\), 6%) in the low; and 9% (\(\Gamma\), 4%) in very low. Through ROC analysis and precision, it was found that the model for calculating flood vulnerability that only considers topographic  
Figure 11: Results of the selection for flood vulnerable areas: (**a**) September 2010; (**b**) July 2011.  
Figure 10: Density of drainage pump capacity by year: (**a**) September 2010; (**b**) July 2011.  
factors has a disadvantage of overestimating vulnerable areas, but that the detection rate could be improved by up to over four times (in the low class in 2011) when the rainfall was also considered.