*3.2. Perform of Optimum Inundation Map by FLO-2D Model*

The overflow calculated by considering the simulated results for accumulated overflow from 342 manholes was used as the input data for the 2D hydraulic analysis program (FLO-2D model) based on the finite-difference method, as well as generated optimum inundation maps that can reflect maximum flood depth. According to the simulated total overflow results, most of the simulated maximum values of total overflow in the same year exist in different quartiles. Thus, the minimum and maximum flood occurrence maps were generated for different quantiles in the same year (Figures 7–9), using the simulated results of a 1-h minimum, and maximum total overflow for the 100 years from the 1st to the 4th quartile of the Huff method. Figure 7 shows the minimum flood occurrence map results; over the 100 years, the largest flood scale can be seen in the map of the 3rd quartile. Similarly, Figure 8 shows that over 100 years, the largest flood scale can be found in the map of the 4th quartile. Figure 9 shows the simulated results of 100-year 1-h rainfall events with different exceedance probabilities (10%, 30%, 60%, 90%) of the Huff 4th quartile. The results showed that different exceedance probabilities for Huff events also produce different flood inundation responses. This means that the temporal concentration level of storms has a strong influence on the inundation behaviors, even when they occur in the same temporal peak location.

(**c**) (**d**)

**Figure 7.** Sample minimum inundation maps applying 100-year, 1-h rainfall events with different Huff quartile distributions ((**a**–**d**): 1st, 2nd, 3rd, and 4th quartile).

**Figure 8.** Sample maximum inundation maps applying 100-year, 1-h rainfall events with different Huff quartile distributions ((**a**–**d**): 1st, 2nd, 3rd, and 4th quartile).

The results demonstrated that the same quantity of rainfall events showed considerable differences in overflow quantities with different time distribution characteristics. The difference between overflow amount and temporal distribution showed the different inundation behaviors. The rainfall event of the 4th quartile, with a 90% exceedance probability according to the Huff distribution, showed the maximum manhole overflow and widest range of inundation. The results showed that the temporal characteristics of storms, such as the temporal location of the storm peak and concentration level should be considered in order to generate the optimal inundation map to establish inundation prevention measures and conduct preliminary analysis and identification of the flood risk areas in urban drainage basins.

#### *3.3. Discussion*

Boxplots of the simulated total manhole overflow provide a visual summary of the results of 432 different rainfall scenarios reflecting the temporal characteristics of rainfall events such as the temporal concentration level and the temporal location of the storm peak. The rainfall scenarios consisted of nine different exceedance probabilities (10–90%), four different quartiles (1–4th quartile) of the Huff method, three different storm durations (1–3 h) and four different return periods (10, 50, 80, and 100-year) (Figure 10). The difference between the maximum and minimum total overflow with different temporal concentration levels of the 1, 2, and 3 h 10-year return period was 28.4 to 340.4 m3 (the maximum total overflow was 1.4 to 10.5 times larger than the minimum total overflow), the difference

between maximum total overflow and minimum with different temporal concentration levels of the 1, 2 and 3 h 100-year return period was 101 to 1323.8 m<sup>3</sup> (the maximum total overflow was 1.5 to 4.7 times the minimum total overflow), shown according to the growth in the return period and duration, has the larger difference in overflow quantity with the same rainfall amount, and is related to temporal concentration levels. In addition, the difference between maximum total overflow and minimum in the 1st quartile of the 1, 2, and 3 h 10 to 100-year return period was 87.4 to 928.8 m3 (the maximum total overflow was 2.8 to 10.5 times larger than the minimum total overflow), whereas the difference between maximum total overflow and minimum in the 2nd quartile of the 1, 2, and 3 h 10 to 100-year return period was 28.4 to 485.9 m3 (the maximum total overflow was 1.4 to 2.6 times larger than the minimum total overflow). Furthermore, the difference between maximum total overflow and minimum in the 3rd quartile of the 1, 2, and 3 h 10 to 100-year return period was 44 to 323.6 m<sup>3</sup> (the maximum total overflow was 1.4 to 1.7 times larger than the minimum total overflow). The difference between maximum total overflow and minimum in the 4th quartile of the 1, 2, and 3 h 10 to 100-year return period was 89.8 to 1323.8 m3 (the maximum total overflow was 3.1 to 4.9 times larger than the minimum total overflow). The simulated total overflow results for the different quartiles in the same period showed that most of the simulated maximum values of total overflow in the same year exist in different quartiles. The simulated total overflow results also showed considerable differences.

(**a**) (**b**)

(**c**) (**d**)

**Figure 9.** Sample inundation maps applying 100-year, 1-h rainfall events with different exceedance probabilities ((**a–d**): 10%, 30%, 60%, 90%) of Huff 4th quartile distribution.

**Figure 10.** Boxplots of the EPA-SWMM-model-simulated total overflow from 1 to 3 h for a period from 10 to 100 years ((**a**) total overflow of 1-h rainfall, (**b**) total overflow of 2-h rainfall, (**c**) total overflow of 3-h rainfall).

(**c**)

Overall, the results demonstrated that the average total overflow increases with the increase in the quartile of the storm peak location. The maximum total overflow generally occurred when the storm peak was located in the 4th quartile. The minimum total overflow generally occurred when the storm peak was located in the 1st quartile. Nevertheless, the difference between the maximum and minimum total overflow in the 1st and 4th quartile was greater than that of the 2nd and 3rd quartile. The storm concentration level effect on the total overflow is larger than that of the storm peak location. This means that accurate time distribution characteristics of rainfall events are essential for a correct understanding and response to unban flood management. Even though the results showed that the total overflow is highly related to the storm concentration level and the temporal location of the storm peak, there are limitations to generalizing the results since the results are generated by a case study of an urban drainage basin. To overcome the locality issues and to enhance the applicability, extensive further research is necessary to generalize the relationships between the characteristics of time distribution of heavy storms and manhole overflow.

#### **4. Conclusions**

The urban flood inundation impacts associated with the temporal characteristics of heavy storms were analyzed for a target drainage basin in Seoul, Korea. The total manhole overflow and the inundation behavior were simulated using the EPA-SWMM and the FLO-2D model, respectively. Rainfall scenarios reflecting the temporal characteristics of rainfall events, such as the temporal concentration level and the temporal location of the storm peak were created using the Huff method for nine different exceedance probabilities (10–90%), for four different quartiles (1–4th quartile), for three different storm durations (1–3 h) and four different return periods (10, 50, 80, and 100-years).

The simulated manhole overflow and inundation area were highly related to the temporal characteristics of storms, not only the temporal location of the storm peak but also the concentration level. The manhole overflow with different temporal concentration levels of 1, 2, and 3 h 10-year return period events showed a 4.8, 7.2 and 10.5 times difference, respectively. This means that the longer rainfall duration has the larger difference in overflow quantity with the same rainfall amount. The overflow amount with different temporal concentration levels of 1, 2, and 3 h 100-year return period events showed a 3.7, 3.8 and 2.8 times difference, respectively.

The manhole overflow with different temporal locations of the storm peak of 1, 2, and 3 h 10-year return period events showed a 29.7, 98.5 and 79.1%, difference, respectively. The manhole overflow with different temporal locations of the storm peak of 1, 2, and 3 h 100-year return period events showed a 2.17, 1.92 and 1.65 times difference, respectively. The rainfall event in the 4th quartile, with 90% exceedance in terms of Huff distribution probability, showed the maximum manhole overflow and widest inundation range. The results also illustrated that the temporal concentration level is more effective in determining the manhole overflow amount than the temporal location of the storm peak.

The results illustrate that despite the same rainfall quantity, there is a huge difference in the manhole overflow amount and the inundation area according to the difference in the time distribution characteristics. Therefore, a consideration of the temporal distribution characteristics of extreme rainfall events is essential for an accurate understanding of the rainfall–runoff response and the inundation behavior in urban areas. The results also show the possibility of establishing appropriate inundation prevention measures in urban drainage basins when rainfall forecasts including not only quantity but also time distribution characteristics are available.

**Author Contributions:** T.L., G.L. and G.K. conceived and designed the experiments; T.L. performed the experiments; G.K. provided the Huff rainfall data; T.L. ran the EPA-SWMM and FLO-2D model; T.L. analyzed the data; G.K. and G.L. supervision experiments; T.L. wrote the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Korea Environmental Industry & Technology Institute (KEITI) of the Korea Ministry of Environment (MOE) as part of the "Advanced Water Management Research Program". (79615).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Authors have the raw data readily available for presentation to the referees and the editors of the journal, if requested. Authors ensure appropriate analysis are taken so that raw data is retained in full for a reasonable time after publication.

**Acknowledgments:** This work was supported by the Korea Environmental Industry & Technology Institute (KEITI) of the Korea Ministry of Environment (MOE) as part of the "Advanced Water Management Research Program". (79615).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

