*3.2. Flood Inundation and Recession*

The spatial extent and depth of the flood inundation were simulated for a pluvial flood event that happened on 19 September 2016 using FIRM. A detailed conveyance network system with sub-daily meteorological data, such as rainfall data, were used to capture the flood event using SWMM continuous simulation. The FIRM simulate the floods caused by overflow from two manholes, and its results were compared with the inferred flood boundary (Figure 10). Figure 10 represents the areal extent and depth of the flood inundation at two locations. The red dot-line represents the inferred flood boundary, and the black point represents manholes. The color represents flooding depth. The fine-resolution LiDAR data were able to identify detailed urban infrastructures, such as building food prints, and streets. The FIRM was able to identify elevated urban infrastructures and with low-lying streets. Overall, coupling both the 1D SWMM model with the 2D FIRM model was able to delineate the spatial extent and depth of the flood generated from manholes overflow in the study area.

**Figure 10.** Simulated flood depth and extent (color maps) and observed flood inundation boundaries (red dotted lines). The areal extent and depth of flood in Case 1 (**a**) and Case 2 (**b**).

The flood started from a given manhole and propagated spatially by filling any neighboring grid cells with lower elevations. As shown in Figure 10a, representing Case 1, the flood is concentrated across a highway going west to east. The topographic variations around the manhole are relatively small, with the mean slope of the flooded region being 1.2 degrees (Figure 11a). The flat slope, particularly along the street, enables the overland flow to inundate along the street perpendicular to the main highway. Based on the FIRM result, the areal extent, maximum flood depth and volume of the inundation region is 2129 m<sup>2</sup> , 0.6 m, and 710 m<sup>3</sup> , respectively. The depth of the flood is controlled by the local elevation and the amount of the excess overland flow. The low-lying part of the street generally has deeper flood depth compared to the peripheral part of the flood extent. Hence, the pavement is often elevated compared with the street elevation. Another manhole flooding in our study (Figure 10b, Case 2) was used to evaluate the flood inundation simulation. In this case, the manhole is located in the steeper part of the street, where the average slope of the street is 5.2 degrees from the west to east (Figure 11b). Consequently, the flood is mostly concentrated along with the highway in the north and south direction, and did not spread much laterally. The volume, areal extent, and maximum depth of the flooded region are 38 m<sup>3</sup> , 426 m<sup>2</sup> , and 0.15 m, respectively.

**Figure 11.** Slope map of the two-flooded regions considered in our study. Case 1 (**a**) and Case 2 (**b**).

Based on the two cases, we observe that the flood inundation model considers the spatial heterogeneity of the surface feature to inundate, for example, flood inundation algorithm was able to differentiate building with streets (Figure 10a) and intersections of streets with varying slope and elevation (Figure 10b). FIRM inundates the lowest level and cover wider area for a relatively gentle region. Conversely, for the manhole located in a steeper region, the algorithm follows the preferred flow direction and inundate relatively smaller area.

To determine the flood recession, we assumed that once the storm ceased and the pipe full capacity decreased, the water eventually drains back to the conveyance system unless it is isolated from the manhole because of depression storages. Accordingly, some of the inundated floodwaters may recess, while the remaining waters are left as ponding associated with local topographic barriers. The result for Case 1 shows that most of the floodwaters drain since the manhole is located at a lower elevation. There is some ponded water away from the manhole due to possible topographic barriers between the manhole and the flooded areas (Figure 12a). Since the manhole is located at a lower elevation, most of the flooded water drained to the manhole. The volume, areal extent, and maximum depth of the ponded region are 15 m<sup>3</sup> , 89 m<sup>2</sup> , and 0.17 m, respectively. For Case 2, the ponded water is generally concentrated near the manhole due to the local topographical depression around the manhole (Figure 12b). The flood volume, the areal and depth of the ponded water decreases to 3 m<sup>3</sup> , 85 m<sup>2</sup> , and 0.06 m, respectively. The results showed the FIRM abilities to determine the maximum flood extent and the extent aftermath of a given storm. Each information is important to assess the flooding risk and associated potential short-term (flood inundation) and long-term (flood recession) impacts.

**Figure 12.** Flood spatial extents aftermath of storm and flood recession into the manholes for Case 1 (**a**) and Case 2 (**b**).

#### *3.3. Model Inundation and Recession Accuracy*

In addition to the visual comparison of the observed and simulated flood areas, the model performance evaluation for the inundation was carried out using statistical measures that compare the simulated and observed gridded flood areas. This enables us to identify and assess the model performance based on how accurately the model predicted the observed flooded and dry regions. We adopted the TPR and PPV from [66] and used the modified version of the fitting (MF) and bias (MB) indicators from [44,70]. The model inundation extents are compared with the inferred observed flood boundaries that were extracted from photos of the flood boundaries.

Table 5 shows the model performance indicators used to evaluate the flood inundation model based on the inferred flood regions. The TPR for Case 1 (89%) indicates the model's ability to capture the flooded grid cells, while for Case 2, the TRP is 71%, indicating the model predicted a relatively more flooded region as dry land. Thus, the model under predict the flood hazard in Case 2. The PPV for Case 1 and Case 2 are found to be 95.4% and 97.25%, respectively. These indicate the model's ability to capture the observed none flooded cells. The MF of 85% for Case 1 indicates that the model has better agreements with the observed flood boundary compared to that of Case 2, which has MF of 69.90%, indicating the existence of relatively large variation between the predicted and observed flooded regions. The negative values of the MB for both cases indicates that the flooded regions in both cases were underestimated. Overall, the relative errors are relatively higher for Case 2 compared to Case 1. This is due to underestimating the flood hazard in Case 2 compare with the observed boundary, and possibly due lack of the FIRM to simulate the impact of direct rainfall during the flood events or lack to represent flood water loses into the buildings.

**Table 5.** Statistical evaluations of the flood inundation model based on inferred flood area at the two manhole locations (Case 1 and Case 2).


The low TPR values compared to the PPV values suggest that the flood inundation model underestimated the total flooded regions for both cases; but predicted well the flooded region within the observed flood boundaries (Figure 10). The underestimation of the flood areas might be due to the model inundation algorithm not incorporating the additional flooding resulted from direct precipitation or generated surface runoff. The relatively poor performance of the model for Case 2 might also be due to the inundation algorithm limitation to incorporate direct additional flood flux from upstream overland flow into the flooded regions. In addition, the relatively higher slopes in the area, which facilities rapid overland flow from the manhole toward the low elevated regions, may have impacted the model performance. Moreover, the relatively better model performance for Case 1 might be because of the relatively homogenous topography in the area, which is well represented by the 1-m LiDAR data.

Coupling the FIRM model and hydrodynamic model with projected future storm scenarios may help to identify areas that may experience future manhole flooding. This modeling capability can help to better assess flooding risk, and improve designs of storm water drainage systems in flood-prone urban areas. To further improve the work, it is important to consider direct rainfall during storm events and other sources or losses of floodwaters (e.g., possible loses of floodwater by draining into the building or addition of excess runoff from rooftops), as well as the land cover and slopes.

#### **4. Conclusions**

We have presented effective flood inundation and recession methodologies that use overflow from given manholes and topography of an urban region. We used the SWWM model to estimate the volume of overflow from manholes. In order to determine the associated flood depth and extent during and after storm events, we developed a flood inundation and recession model (FIRM) that uses high-resolution LIDAR elevation data. SWMM was developed on the basis of watershed characteristics and the drainage conveyance network in the area. SWMM was calibrated using a differential evolution optimization method and validated based on observed lake level data at the outlet of the watershed. The manhole overflows were extracted and used in FIRM to delineate the spatial extent and flood depths.

The spatial extent of the simulated flood area was compared with the observed flood boundary, which was derived from social media pictures and reports from the cities. Two case studies, based on flood events in Edmonds, WA, were considered to evaluate the flood inundation and recession model. In these case studies, the flood occurred across and along a main highway under different topographical characteristics. The results showed that the spatial extent of the flood regions is highly influenced by local topography and the position of the manholes. Particularly, the spatial arrangement of the manhole and the slope of nearby areas are crucial for determining the spatial extent, spatial heterogeneity of the flood depth, and selecting preferential flow paths to inundate low-lying areas. The model is able to capture the flood extent for manhole overland flow in fluvial flood events. Incorporating the direct impact of rainfall on the fluvial flood event can improve the representation of the physical process and the accuracy of the model. As the flood recession observation data are scarce, the performance of the flood recession model result was difficult to quantify. Finally, proper understanding and representation of the study area, the boundary condition, and engineering structures are important for the flood inundation and recession modeling associated with manhole overland flow.

Regional authorities can utilize the presented model (FIRM) by coupling with existing hydrodynamic modeling (e.g., SWMM) to quantify flood hazard based on pluvial generated overland flooding and manholes induced flooding in urban areas, where flood mechanism is complex and modified by local infrastructures. FIRM can be used to estimate the areal extent and depth of flood caused by manholes overland flow during a flood event (flood inundation) and after the event is over (flood recession). Because of the relative simplicity of the model and its uses of readily available data, the model can be used for a real-time assessment of flood progression and to identify potential impact areas. The model's ability to simulate flood recession will also allow identifying areas where the flooded water will remain ponded for days after the floodwater subsides. The ponded water, or the floodwater not drained, can impact human health and properties. In addition to the real-time forecast of flood inundation and estimation of the aftermath ponding condition for the existing drainage system, the model can be used to design better a new or retrofit the current drainage system to minimize the overflow and ponding after the flood events. The model can be used to assess the flood condition under multiple storms, watershed conditions, and drainage scenarios. It can contribute to our understanding of climate change and appropriate engineering designs for mitigation.

**Author Contributions:** Conceptualization, M.G. and Y.D.; methodology, M.G. and Y.D.; validation, M.G. and Y.D.; writing—original draft preparation, M.G.; writing—review and editing, M.G. and Y.D.; supervision, Y.D.; funding acquisition, Y.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** Department of Defense's Strategic Environmental Research and Development Program (SERDP) under contract W912HQ-15-C-0023.

**Acknowledgments:** We are thankful for the city of Edmonds and Mountlake Terrace for providing sewer network dataset and observation data. The first author is grateful for the research input from Joan Wu, Akram Hossain, Jennifer Adam, Mark Wigmosta, Debra Perrone, and Scott Jasechko. We are thankful for the anonymous reviewers for helpful comments on the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
