*2.2. Hydraulic Modeling (EPA-SWMM and FLO-2D Model)*

To construct the flood prediction model and calculate the runoff or overflow at each manhole in the urban watershed, the EPA-SWMM model was used to simulate 432 different extreme rainfall event data (1 to 3-h, in 10 min intervals) considering the high-intensity rainfall conditions. This was obtained from the United States Environmental Protection Agency and was useful for checking the amount of urban overflow [26]. The EPA-SWMM can calculate the total accumulative overflow in the study area. The flood volume for each rainfall scenario was calculated and the flows in the drainage pipe network in urban basins with drainage systems were analyzed [27]. The EPA-SWMM model performed the initial calculations of the flow rate and depth of the drainage pipe system, which allowed analysis of the backflow and overflow amount in the pipe based on the various rainfall events in the study area [28]. The Saint–Venant equations (Equations (1) and (2)) were used in this calculation.

$$Q = W \times \frac{1}{n}(d - d\_p)^{\frac{5}{5}} \times S^{\frac{1}{7}} \tag{1}$$

$$\frac{\partial \mathcal{Q}}{\partial t} + g A S\_f - 2V \frac{\partial A}{\partial t} - V^2 \frac{\partial A}{\partial x} + g A \frac{\partial H}{\partial x} = 0 \tag{2}$$

where *Q* is runoff (m3/s), *W* is the sub-watershed width (m), *n* is the Manning's roughness coefficient, *d* is the depth (m), *dp* is the ground reservoir lost depth (m), *S* is the subwatershed slope, *A* is the surface flow cross-sectional area of sub-watershed (m2), and *V* is the surface flow velocity (m/s). The EPA-SWMM model was used for the one-dimensional simulation of urban flood overflow analysis. To determine the adequacy of the onedimensional urban runoff analysis results, the total accumulative overflow at each manhole point underwent a two-dimensional inundation analysis using a two-dimensional flood analysis program, the FLO-2D model [29]. The results were compared with those for actual flood areas because only the actual flood map can be used to verify the EPA-SWMMsimulated results at present, and data on the water level and discharge in the conduit were absent. Figure 3 shows the verification of the two-dimensional flood analysis results used for rainfall data and the flood mask map from 21 September 2010 in Samsung-dong. The total rainfall was 278 mm over 6 h in 10 min intervals.

FLO-2D is a grid-based, two-dimensional hydraulic model approved by the Federal Emergency Management Agency (FEMA), and developed by O'Brien in 2003. It is a two-dimensional, finite-difference model used to simulate flood hazards and urban floodplains [30]. In the whole digital elevation model simulated domain, the construction of two-dimensional grids needs to be completed; the exact location of a manhole in the two-dimensional 5 m<sup>2</sup> grid system was found by using the spatial join tool of the ArcGIS model and flood routing and two-dimensional inundation analysis were performed using the FLO-2D model. Interactive flood routing between channel, street, and floodplain flow was performed using a 5 m2 grid system to properly reflect the influence of buildings and roads on the flood waves, and to describe the complex floodplain topography. The overflows of each manhole were calculated from EPA-SWMM, and these were entered into the input file of FLO-2D, which helped construct the two-dimensional grids. After completing the two-dimensional grids, the model-governing equations included the continuity equation and the two-dimensional equations of motion. The one continuity equation (Equation (3)) and two momentum equations were applied in the *x* and *y* directions (Equations (4) and (5), respectively) to carry out a two-dimensional analysis of urban flood inundation changes [31,32]. According to the results compared with those for actual flood areas, the synthetic roughness coefficient calibrated was 0.15.

$$\frac{\partial d}{\partial t} + \frac{\partial q\_x}{\partial x} + \frac{\partial q\_y}{\partial y} = e \tag{3}$$

$$
\rho \frac{\partial \mu}{\partial t} + \mu \frac{\partial \mu}{\partial x} + v \frac{\partial \mu}{\partial y} = \mathbf{g} \left( S\_{ox} - S\_{fx} - \frac{\partial d}{\partial x} \right) \tag{4}
$$

$$\frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} = \mathbf{g} \left( S\_{oy} - S\_{fy} - \frac{\partial d}{\partial y} \right) \tag{5}$$

where *d* is depth at a surface; *qx* and *qy* are the flows per unit width in the *x* and *y* directions, respectively; *u* and *v* indicate average velocities in the *x* and *y* directions, respectively; *Sox* and *Soy* are the bed slope *x* and *y* directions, respectively; *Sfx* and *Sfy* are the friction slopes in the *x* and *y* directions, respectively. The variable *e* is the generation or extinction section per unit area.

Figure 4 illustrates the summarized procedure of the EPA-SWMM and FLO-2D simulation. To effectively calculate and analyze total overflows that accumulated in urban manholes with different temporal distribution characteristics, heavy rainfall scenarios were designed using the Huff rainfall distribution method and the 10 min intervals rainfall data from the Seoul site of the Automated Synoptic Observation System (ASOS) of the Korea Meteorological Administration. These rainfall scenario data were used as the input for the EPA-SWMM to calculate the total overflow amount of each manhole in the target drainage basin of Samsung-dong, Seoul, Korea. The EPA-SWMM model was suitable for the one-dimensional simulation of urban flood overflow analysis. The adequacy of the one-dimensional urban runoff analysis results was validated for the actual urban flood observation by using a two-dimensional flood analysis program, the FLO-2D model. To do the two-dimensional flood simulation, a digital elevation model (DEM) (Figure 5) with a 5-m cell size was composed of the target area, which was produced by using the add building tool in the ArcGIS model.

**Figure 4.** Flowchart of study methodology.

**Figure 5.** Digital elevation model (DEM) for the target area.

In addition, the exact location of each manhole was found by using the spatial join tool in the ArcGIS model in the whole 5-m cell size digital elevation model simulated domain, which was needed to complete the construction of two-dimensional grids (Figure 6). After completing the two-dimensional grids, the total overflows of each manhole data and the exact location of each manhole were used as the input data for the FLO-2D model. Flood routing and two-dimensional inundation analysis were performed by interactive flood routing between channel, street, and floodplain flow to properly reflect the influence of buildings, and describe the complex floodplain topography. Also, the mapper pro. 2009 tool in the FLO-2D model was used to generate maximum flow depth in the cell map and to generate the optimal inundation map. The optimal inundation maps were generated according to the total overflows, reflecting different temporal rainfall distribution characteristics.

**Figure 6.** The exact location of each manhole was adjusted by the ArcGIS model.
