# Modeling Urban Flood Inundation and Recession Impacted by Manholes

^{*}

## Abstract

**:**

## 1. Introduction

^{3}and a maximum possible depth of 0.8 m. Son et al. [44] coupled a one-dimensional storm water management model with a 2D overland flow model from a manhole overland flow with a maximum overland flow, ranging from 2–5 m

^{3}/s at different manhole locations, and estimated a 0.9 m flood depth and 2.5 m/s flood velocity. Jang et al. [46] used a coupled one-dimensional sewer flow with the two-dimensional overland flow and estimated manhole overflow depth up to 2 m. Seyoum et al. [47] coupled 1D sewer and 2D dimensional flood inundation models to simulate urban flooding and showed the combined flood depth variations from 0.3 to 0.8 m in their study area. Manhole overflow is a critical issue in urban areas, yet their contribution to flooding is not well understood. Most hydrodynamic models assume that excess water will pond around the manhole and return back or will be lost from the system after the flood recedes [49]. Major cities have aging infrastructures and drainage systems designed and built more than a decade years ago [50]. These systems are increasingly underperforming due to their design assumption of stationary storms and flood events [51,52]. This assumption often causes inadequacy to handle the rising flood risk caused by increased storms and impervious layers.

## 2. Methods

#### 2.1. Hydrodynamic Modeling Using SWMM

_{t}represents state variables (such as flow rate and depth in a drainage network link), Y

_{t}represents output variables (such as runoff flow rate at each sub-catchments and outlet), P represents the constant parameter, I

_{t}represents input variables (such as rainfall and temperature) at a given time.

#### 2.2. Manhole Overland Flow Inundation and Recession Modeling

#### 2.2.1. Manhole Overland Flow Inundation Modeling

#### 2.2.2. Recession Modeling Associated with Manholes

#### 2.3. Study Site: The Hall Creek Watershed

#### 2.3.1. Data

#### 2.3.2. SWMM Model

^{obs}is observed, Y

^{sim}is simulated, Y

^{mean}is the mean of the observed lake level change, r is correlation coefficient between the modeled and observed lake levels; γ is a ratio between the standard deviation of modeled and observed lake levels and β is a ratio between the standard deviation and mean of the modeled and observed lake levels (Table 1).

#### 2.4. Model Inundation Accuracy

## 3. Results and Discussion

#### 3.1. SWMM Model Calibration and Validation

^{2}) is 0.42 for the spin up period, 0.83 for the calibration period, and 0.77 for the validation model simulation period. The correlation coefficients for the calibration and validation period also confirm the model captured the observed lake level reasonably well. The simulation was also evaluated using the NSE, KGE, RSR, and PBIAS.

#### 3.2. Flood Inundation and Recession

^{2}, 0.6 m, and 710 m

^{3}, 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

^{3}, 426 m

^{2}, and 0.15 m, respectively.

^{3}, 89 m

^{2}, 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

^{3}, 85 m

^{2}, 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.

#### 3.3. Model Inundation and Recession Accuracy

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Wallemacq, P.; Herden, C.; House, R. The Human Cost of Natural Disasters 2015: A Global Perspective; Technical report; Centre for Research on the Epidemiology of Disasters: Brussels, Belgium, 2015. [Google Scholar]
- Stocker, T.F.; Qin, D.; Plattner, G.-K.; Tignor, M.; Allen, S.K.; Boschung, J.; Nauels, A.; Xia, Y.; Bex, V.; Midgley, P.M. Climate change 2013: The physical science basis. In Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change; Cambridge University Press: Cambridge, UK, 2013; Volume 1535. [Google Scholar]
- Technical Mapping Advisory Council (TMAC). Technical Mapping Advisory Council (TMAC) 2015 Annual Report Summary. Available online: https://www.fema.gov/media-library-data/1454954186441-34ff688ee1abc00873df80c4d323a4df/TMAC_2015_Annual_Report_Summary.pdf (accessed on 13 March 2020).
- Federal Emergency Management Agency (FEMA). Loss Dollars Paid by Calendar Year. Available online: https://www.fema.gov/loss-dollars-paid-calendar-year (accessed on 13 March 2020).
- European Environmental Agency (EEA). Mapping the impacts of natural hazards and technological accidents in Europe – an overview of the last decade. EEA Technical Report No13/2010. Available online: https://www.eea.europa.eu/publications/mapping-the-impacts-of-natural (accessed on 13 March 2020).
- Wang, W.; Li, H.Y.; Leung, L.R.; Yigzaw, W.; Zhao, J.; Lu, H.; Deng, Z.; Demisie, Y.; Blöschl, G. Nonlinear filtering effects of reservoirs on flood frequency curves at the regional scale. Water Resour. Res.
**2017**, 53, 8277–8292. [Google Scholar] [CrossRef] - Ye, S.; Li, H.-Y.; Leung, L.R.; Guo, J.; Ran, Q.; Demissie, Y.; Sivapalan, M. Understanding flood seasonality and its temporal shifts within the contiguous United States. J. Hydrometeorol.
**2017**, 18, 1997–2009. [Google Scholar] [CrossRef] - Milner, A.M.; Picken, J.L.; Klaar, M.J.; Robertson, A.L.; Clitherow, L.R.; Eagle, L.; Brown, L.E. River ecosystem resilience to extreme flood events. Ecol. Evol.
**2018**, 8, 8354–8363. [Google Scholar] [CrossRef] [PubMed][Green Version] - Scanlon, B.R.; Keese, K.E.; Flint, A.L.; Flint, L.E.; Gaye, C.B.; Edmunds, W.M.; Simmers, I. Global synthesis of groundwater recharge in semiarid and arid regions. Hydrol. Processes
**2006**, 20, 3335–3370. [Google Scholar] [CrossRef] - Wang, X.; Zhang, G.; Xu, Y.J. Impacts of the 2013 extreme flood in Northeast China on regional groundwater depth and quality. Water
**2015**, 7, 4575–4592. [Google Scholar] [CrossRef][Green Version] - Jasechko, S.; Birks, S.J.; Gleeson, T.; Wada, Y.; Fawcett, P.J.; Sharp, Z.D.; McDonnell, J.J.; Welker, J.M. The pronounced seasonality of global groundwater recharge. Water Resour. Res.
**2014**, 50, 8845–8867. [Google Scholar] [CrossRef][Green Version] - Cuthbert, M.O.; Taylor, R.G.; Favreau, G.; Todd, M.C.; Shamsudduha, M.; Villholth, K.G.; MacDonald, A.M.; Scanlon, B.R.; Kotchoni, D.V.; Vouillamoz, J.-M. Observed controls on resilience of groundwater to climate variability in sub-Saharan Africa. Nature
**2019**, 572, 230–234. [Google Scholar] [CrossRef] - Dahlke, H.; Brown, A.; Orloff, S.; Putnam, D.; O’Geen, T. Managed winter flooding of alfalfa recharges groundwater with minimal crop damage. Calif. Agr.
**2018**, 72, 65–75. [Google Scholar] [CrossRef][Green Version] - GebreEgziabher, M. An Integrated Hydrogeological Study to Understand the Groundwater Flow Dynamics in Raya Valley Basin, Northern Ethiopia: Hydrochemistry, Isotope Hydrology and Flow Modeling Approaches. Master’s Thesis, Addis Ababa University, Addis Ababa, Ethiopia, 2011. [Google Scholar]
- Changnon, S.A., Jr. Recent studies of urban effects on precipitation in the United States. Bull. Am. Meteorol. Soc.
**1969**, 50, 411–421. [Google Scholar] [CrossRef] - Arnbjerg-Nielsen, K.; Willems, P.; Olsson, J.; Beecham, S.; Pathirana, A.; Bülow Gregersen, I.; Madsen, H.; Nguyen, V.-T.-V. Impacts of climate change on rainfall extremes and urban drainage systems: A review. Water Sci. Technol.
**2013**, 68, 16–28. [Google Scholar] [CrossRef] - Boyd, E.; Juhola, S. Adaptive climate change governance for urban resilience. Urban Stud.
**2015**, 52, 1234–1264. [Google Scholar] [CrossRef] - Ford, A.; Barr, S.; Dawson, R.; Virgo, J.; Batty, M.; Hall, J. A multi-scale urban integrated assessment framework for climate change studies: A flooding application. Comput. Environ. Urban
**2019**, 75, 229–243. [Google Scholar] [CrossRef] - Chen, J.; Hill, A.A.; Urbano, L.D. A GIS-based model for urban flood inundation. J. Hydrol.
**2009**, 373, 184–192. [Google Scholar] [CrossRef] - Wang, R.-Q.; Mao, H.; Wang, Y.; Rae, C.; Shaw, W. Hyper-resolution monitoring of urban flooding with social media and crowdsourcing data. Comput. Geosci.
**2018**, 111, 139–147. [Google Scholar] [CrossRef][Green Version] - National Academies of Sciences, Engineering, and Medicine. Framing the Challenge of Urban Flooding in the United States; National Academies Press: Washington, DC, USA, 2019. [Google Scholar]
- Jacobson, C.R. Identification and quantification of the hydrological impacts of imperviousness in urban catchments: A review. J. Environ. Manage.
**2011**, 92, 1438–1448. [Google Scholar] [CrossRef] [PubMed] - Zhang, W.; Villarini, G.; Vecchi, G.A.; Smith, J.A. Urbanization exacerbated the rainfall and flooding caused by hurricane Harvey in Houston. Nature
**2018**, 563, 384–388. [Google Scholar] [CrossRef] [PubMed] - Shuster, W.D.; Bonta, J.; Thurston, H.; Warnemuende, E.; Smith, D. Impacts of impervious surface on watershed hydrology: A review. Urban Water J.
**2005**, 2, 263–275. [Google Scholar] [CrossRef] - Diakakis, M.; Deligiannakis, G.; Pallikarakis, A.; Skordoulis, M. Identifying elements that affect the probability of buildings to suffer flooding in urban areas using Google Street View. A case study from Athens metropolitan area in Greece. Int. J. Disaster Risk Reduct.
**2017**, 22, 1–9. [Google Scholar] [CrossRef] - Golz, S.; Schinke, R.; Naumann, T. Assessing the effects of flood resilience technologies on building scale. Urban Water J.
**2015**, 12, 3043. [Google Scholar] [CrossRef] - Hu, M.; Sayama, T.; Zhang, X.; Tanaka, K.; Takara, K.; Yang, H. Evaluation of low impact development approach for mitigating flood inundation at a watershed scale in China. J. Environ. Manage.
**2017**, 193, 430–438. [Google Scholar] [CrossRef] - Brody, S.; Sebastian, A.; Blessing, R.; Bedient, P. Case study results from southeast Houston, Texas: Identifying the impacts of residential location on flood risk and loss. J. Flood Risk Manage.
**2018**, 11, S110–S120. [Google Scholar] [CrossRef] - Teng, J.; Jakeman, A.J.; Vaze, J.; Croke, B.F.; Dutta, D.; Kim, S. Flood inundation modelling: A review of methods, recent advances and uncertainty analysis. Environ. Modell. Softw.
**2017**, 90, 201–216. [Google Scholar] [CrossRef] - Yu, D.; Coulthard, T.J. Evaluating the importance of catchment hydrological parameters for urban surface water flood modelling using a simple hydro-inundation model. J. Hydrol.
**2015**, 524, 385–400. [Google Scholar] [CrossRef][Green Version] - Courty, L.G.; Pedrozo-Acuña, A.; Bates, P.D. Itzï (version 17.1): An open-source, distributed GIS model for dynamic flood simulation. Geosci. Model. Dev.
**2017**, 10, 1835. [Google Scholar] [CrossRef][Green Version] - Rosenberg, E.A.; Keys, P.W.; Booth, D.B.; Hartley, D.; Burkey, J.; Steinemann, A.C.; Lettenmaier, D.P. Precipitation extremes and the impacts of climate change on stormwater infrastructure in Washington State. Clim. Change
**2010**, 102, 319–349. [Google Scholar] [CrossRef][Green Version] - Mishra, V.; Ganguly, A.R.; Nijssen, B.; Lettenmaier, D.P. Changes in observed climate extremes in global urban areas. Environ. Res. Lett.
**2015**, 10, 024005. [Google Scholar] [CrossRef] - Muis, S.; Güneralp, B.; Jongman, B.; Aerts, J.C.; Ward, P.J. Flood risk and adaptation strategies under climate change and urban expansion: A probabilistic analysis using global data. Sci. Total Environ.
**2015**, 538, 445–457. [Google Scholar] [CrossRef] - Zhao, G.; Xu, Z.; Pang, B.; Tu, T.; Xu, L.; Du, L. An enhanced inundation method for urban flood hazard mapping at the large catchment scale. J. Hydrol.
**2019**, 571, 873–882. [Google Scholar] [CrossRef] - Zhao, T.; Shao, Q.; Zhang, Y. Deriving flood-mediated connectivity between river channels and floodplains: Data-driven approaches. Sci. Rep.
**2017**, 7, 43239. [Google Scholar] [CrossRef][Green Version] - Wang, X.; Kinsland, G.; Poudel, D.; Fenech, A. Urban flood prediction under heavy precipitation. J. Hydrol.
**2019**, 577, 123984. [Google Scholar] [CrossRef] - Jamali, B.; Bach, P.M.; Cunningham, L.; Deletic, A. A Cellular Automata Fast Flood Evaluation (CA-ffé) Model. Water Resour. Res.
**2019**, 55, 4936–4953. [Google Scholar] [CrossRef][Green Version] - Zheng, X.; Maidment, D.R.; Tarboton, D.G.; Liu, Y.Y.; Passalacqua, P. GeoFlood: Large-Scale Flood Inundation Mapping Based on High-Resolution Terrain Analysis. Water Resour. Res.
**2018**, 54, 10013–10033. [Google Scholar] [CrossRef] - Yang, T.-H.; Chen, Y.-C.; Chang, Y.-C.; Yang, S.-C.; Ho, J.-Y. Comparison of different grid cell ordering approaches in a simplified inundation model. Water
**2015**, 7, 438–454. [Google Scholar] [CrossRef][Green Version] - Meng, X.; Zhang, M.; Wen, J.; Du, S.; Xu, H.; Wang, L.; Yang, Y. A Simple GIS-Based Model for Urban Rainstorm Inundation Simulation. Sustainability
**2019**, 11, 2830. [Google Scholar] [CrossRef][Green Version] - Sörensen, J.; Mobini, S. Pluvial, urban flood mechanisms and characteristics–assessment based on insurance claims. J. Hydrol.
**2017**, 555, 51–67. [Google Scholar] [CrossRef] - Leandro, J.; Martins, R. A methodology for linking 2D overland flow models with the sewer network model SWMM 5.1 based on dynamic link libraries. Water Sci. Technol.
**2016**, 73, 3017–3026. [Google Scholar] [CrossRef] - Son, A.-L.; Kim, B.; Han, K.-Y. A simple and robust method for simultaneous consideration of overland and underground space in urban flood modeling. Water
**2016**, 8, 494. [Google Scholar] [CrossRef][Green Version] - Chang, T.-J.; Wang, C.-H.; Chen, A.S.; Djordjević, S. The effect of inclusion of inlets in dual drainage modelling. J. Hydrol.
**2018**, 559, 541–555. [Google Scholar] [CrossRef] - Jang, J.-H.; Chang, T.-H.; Chen, W.-B. Effect of inlet modelling on surface drainage in coupled urban flood simulation. J. Hydrol.
**2018**, 562, 168–180. [Google Scholar] [CrossRef] - Seyoum, S.D.; Vojinovic, Z.; Price, R.K.; Weesakul, S. Coupled 1D and noninertia 2D flood inundation model for simulation of urban flooding. J. Hydraul. Eng.
**2012**, 138, 23–34. [Google Scholar] [CrossRef] - Chen, A.S.; Leandro, J.; Djordjević, S. Modelling sewer discharge via displacement of manhole covers during flood events using 1D/2D SIPSON/P-DWave dual drainage simulations. Urban Water J.
**2016**, 13, 830–840. [Google Scholar] [CrossRef][Green Version] - Rossman, L.A.; Huber, W. Storm water management model reference manual volume II–hydraulics. US Environ. Prot. Agency II (Mayo)
**2017**, 190. Available online: https://nepis.epa.gov/Exe/ZyPDF.cgi?Dockey=P100S9AS.pdf (accessed on 17 April 2020). - Kessler, R. Stormwater strategies: Cities prepare aging infrastructure for climate change. Environ. Health Perspect.
**2011**, 119, 514–519. [Google Scholar] [CrossRef] [PubMed] - Milly, P.C.; Betancourt, J.; Falkenmark, M.; Hirsch, R.M.; Kundzewicz, Z.W.; Lettenmaier, D.P.; Stouffer, R.J. Stationarity is dead: Whither water management? Science
**2008**, 319, 573–574. [Google Scholar] [CrossRef] [PubMed] - Yan, H.; Sun, N.; Wigmosta, M.; Skaggs, R.; Hou, Z.; Leung, L.R. Next-generation intensity–duration–frequency curves to reduce errors in peak flood design. J. Hydrol. Eng.
**2019**, 24, 04019020. [Google Scholar] [CrossRef] - Mullen, K.; Ardia, D.; Gil, D.L.; Windover, D.; Cline, J. DEoptim: An R package for global optimization by differential evolution. J. Stat. Softw.
**2011**, 40, 1–26. [Google Scholar] [CrossRef][Green Version] - Means, J.E.; Acker, S.A.; Harding, D.J.; Blair, J.B.; Lefsky, M.A.; Cohen, W.B.; Harmon, M.E.; McKee, W.A. Use of large-footprint scanning airborne lidar to estimate forest stand characteristics in the Western Cascades of Oregon. Remote Sens. Environ.
**1999**, 67, 298–308. [Google Scholar] [CrossRef] - Leutnant, D.; Döring, A.; Uhl, M. swmmr-an R package to interface SWMM. Urban Water J.
**2019**, 16, 68–76. [Google Scholar] [CrossRef][Green Version] - Niazi, M.; Nietch, C.; Maghrebi, M.; Jackson, N.; Bennett, B.R.; Tryby, M.; Massoudieh, A. Storm water management model: Performance review and gap analysis. J. Sustain. Water Built Env.
**2017**, 3, 04017002. [Google Scholar] [CrossRef][Green Version] - Gray, J.E.; Pribil, M.J.; Van Metre, P.C.; Borrok, D.M.; Thapalia, A. Identification of contamination in a lake sediment core using Hg and Pb isotopic compositions, Lake Ballinger, Washington, WA, USA. J. Appl. Geochem.
**2013**, 29, 1–12. [Google Scholar] [CrossRef] - Thapalia, A.; Borrok, D.M.; Van Metre, P.C.; Musgrove, M.; Landa, E.R. Zn and Cu isotopes as tracers of anthropogenic contamination in a sediment core from an urban lake. Environ. Sci. Technol.
**2010**, 44, 1544–1550. [Google Scholar] [CrossRef] - Boyle, D.P.; Gupta, H.V.; Sorooshian, S. Toward improved calibration of hydrologic models: Combining the strengths of manual and automatic methods. Water Resour. Res.
**2000**, 36, 3663–3674. [Google Scholar] [CrossRef] - Price, K.; Storn, R.M.; Lampinen, J.A. Differential Evolution: A Practical Approach to Global Optimization; Springer Science & Business Media: Berlin, Germany, 2006. [Google Scholar]
- Ardia, D.; Mullen, K.; Peterson, B.; Ulrich, J. DEoptim’: Differential Evolution in ‘R’. Version 2.2-3. 2015. Available online: https://cran.r-project.org/web/packages/DEoptim/DEoptim.pdf (accessed on 4 April 2020).
- Nash, J.E.; Sutcliffe, J.V. River flow forecasting through conceptual models part I—A discussion of principles. J. Hydrol.
**1970**, 10(3), 282–290. [Google Scholar] [CrossRef] - Gupta, H.V.; Kling, H.; Yilmaz, K.K.; Martinez, G.F. Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. J. Hydrol.
**2009**, 377, 80–91. [Google Scholar] [CrossRef][Green Version] - Legates, D.R.; McCabe, G.J., Jr. Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour. Res.
**1999**, 35, 233–241. [Google Scholar] [CrossRef] - Kling, H.; Fuchs, M.; Paulin, M. Runoff conditions in the upper Danube basin under an ensemble of climate change scenarios. J. Hydrol.
**2012**, 424, 264–277. [Google Scholar] [CrossRef] - Wang, Y.; Chen, A.S.; Fu, G.; Djordjević, S.; Zhang, C.; Savić, D.A. An integrated framework for high-resolution urban flood modelling considering multiple information sources and urban features. Environ. Modell Softw.
**2018**, 107, 85–95. [Google Scholar] [CrossRef] - Wing, O.E.; Bates, P.D.; Sampson, C.C.; Smith, A.M.; Johnson, K.A.; Erickson, T.A. Validation of a 30 m resolution flood hazard model of the conterminous United States. Water Resour. Res.
**2017**, 53, 7968–7986. [Google Scholar] [CrossRef] - Bates, P.D.; De Roo, A. A simple raster-based model for flood inundation simulation. J. Hydrol.
**2000**, 236, 54–77. [Google Scholar] [CrossRef] - Bernini, A.; Franchini, M. A rapid model for delimiting flooded areas. Water Resour Manag.
**2013**, 27, 3825–3846. [Google Scholar] [CrossRef] - Lhomme, J.; Sayers, P.; Gouldby, B.; Samuels, P.; Wills, M.; Mulet-Marti, J. Recent development and application of a rapid flood spreading method. In Proceedings of the FloodRisk 2008 Conference, Oxford, UK, 30 September–2 October 2008; Taylor and Francis Group: London, UK, 2008. [Google Scholar]
- Moriasi, D.N.; Arnold, J.G.; Van Liew, M.W.; Bingner, R.L.; Harmel, R.D.; Veith, T.L. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE
**2007**, 50, 885–900. [Google Scholar] [CrossRef]

**Figure 1.**Schematic representation of the flood inundation modeling from one-manhole (the circle with cross) for different amounts of manhole overflow: (

**a**) 1 unit, (

**b**) 11 units, (

**c**) 17 units, and (

**d**) 46 units. The numbers inside the unshaded and unshaded grids represent surface elevation and flood levels, respectively. Dashed line represents the profile line.

**Figure 2.**Schematic diagram showing flood inundation from two manholes (the circles with cross) for different amounts of manhole overflow: (

**a**) 22 units from the left manhole and 19 units from the right manhole, (

**b**) 110 units from the left manhole and 111 units from the right manhole. The numbers inside the unshaded and unshaded grids represent surface elevation and flood levels, respectively. Dash line represents the profile line.

**Figure 3.**Schematic representation of flood recession processes from a single and multiple manhole. (

**a**) Represent the areal extent and profile section of the flooded regions, (

**b**) represents the areal extent and profile of flood recession for a single manhole, and (

**c**) show a recession surface and profile after drained by two manholes.

**Figure 4.**Hall Creek watershed showing (

**a**) buildings, drainage network, and the surface elevation as a background, and (

**b**) land cover map.

**Figure 6.**The location of the two manholes, which cause flood along a street (Case 2) and across a street (Case 1).

**Figure 9.**Scatter plots of observed and simulated lakes level during the spin up (

**a**), calibration (

**b**), and validation (

**c**) periods. The lines are the linear regression fit with 95% confidence intervals.

**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**).

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

**a**) and Case 2 (

**b**).

Statistics | Ranges | Optimal Value |
---|---|---|

$\mathrm{NSE}=1-\left[\frac{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{Y}}_{\mathrm{i}}^{\mathrm{obs}}-{\text{}\mathrm{Y}}_{\mathrm{i}}^{\mathrm{sim}}\right)}^{2}}{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{Y}}_{\mathrm{i}}^{\mathrm{obs}}-{\text{}\mathrm{Y}}^{\mathrm{mean}}\right)}^{2}}\right]$ | −∞ to 1 | 1 |

$\mathrm{PBIAS}=\left[\frac{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{Y}}_{\mathrm{i}}^{\mathrm{obs}}-{\text{}\mathrm{Y}}_{\mathrm{i}}^{\mathrm{sim}}\right)\times 100}{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{Y}}_{\mathrm{i}}^{\mathrm{obs}}\right)}\right]$ | 0 to 100 | 0 |

$\mathrm{RSR}=\frac{\mathrm{RMSE}}{\mathrm{STDEVobs}}=\frac{\left[\sqrt{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{Y}}_{\mathrm{i}}^{\mathrm{Obs}}-{\text{}\mathrm{Y}}_{\mathrm{i}}^{\mathrm{sim}}\right)}^{2}}\right]}{\left[\sqrt{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{Y}}_{\mathrm{i}}^{\mathrm{Obs}}-{\text{}\mathrm{Y}}^{\mathrm{mean}}\right)}^{2}}\right]}$ | 0 to 1 | 0 |

$\mathrm{KGE}=1-\sqrt{{\left(\mathrm{r}-1\right)}^{2}+{\left(\mathsf{\gamma}-1\right)}^{2}+{\left(\mathsf{\beta}-1\right)}^{2}\text{}}$ $\mathsf{\beta}=\frac{{\mathsf{\mu}}_{\mathrm{s}}}{{\mathsf{\mu}}_{\mathrm{o}}}$ $\mathsf{\gamma}=\frac{{\mathrm{CV}}_{\mathrm{s}}}{{\mathrm{CV}}_{\mathrm{o}}}=\frac{{\mathsf{\sigma}}_{\mathrm{s}}/{\mathsf{\mu}}_{\mathrm{s}}}{{\mathsf{\sigma}}_{\mathrm{o}}/{\mathsf{\mu}}_{\mathrm{o}}\text{}}$ | 0 to 1 | 1 |

Flooded in Observed Boundary | Dry in Observed Boundary | |
---|---|---|

Flooded in FIRM | True flood (TP) | False flood (FP) |

Dry in FIRM | False dry (FN) | True dry (TN) |

Parameters | Lower–Upper Bound | Optimal Values |
---|---|---|

Impervious (%) | 25–90 | 70 |

Width (m) | 150–300 | 152 |

Roughness (−) | 0.01–0.03 | 0.012 |

Depression Storage (mm) | 1.2–5.2 | 1.78 |

Hydraulic Conductivity (mm/h) | 0.1–3 | 0.11 |

**Table 4.**Model performance statistics to evaluate the Storm Water Management Model (SWMM) daily and monthly lake water level simulations.

Simulation | KGE | NSE | RSR | PBIAS | Performance Rating [71] | |||||
---|---|---|---|---|---|---|---|---|---|---|

Daily | Mon | Daily | Mon | Daily | Mon | Daily | Mon | Daily | Mon | |

Spin Up | 0.64 | 0.61 | −0.31 | −1.15 | 1.14 | RSR | −0.10 | −0.10 | Unsat * | Unsat * |

Calibration | 0.91 | 0.96 | 0.82 | 0.94 | 0.43 | 1.39 | 0.00 | 0.00 | V. good ^ | V. good ^ |

Validation | 0.88 | 0.95 | 0.67 | 0.81 | 0.57 | 0.24 | 0.00 | 0.00 | Good | V. good ^ |

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

Inundation Model Performance | Case 1 | Case 2 |
---|---|---|

True positive rate, TPR (%) | 89.04 | 71.31 |

Positive predictive value, PPV (%) | 95.44 | 97.25 |

Modified fit, MF (%) | 85.04 | 69.90 |

Modified bias, MB (%) | −6.71 | −26.68 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

GebreEgziabher, M.; Demissie, Y. Modeling Urban Flood Inundation and Recession Impacted by Manholes. *Water* **2020**, *12*, 1160.
https://doi.org/10.3390/w12041160

**AMA Style**

GebreEgziabher M, Demissie Y. Modeling Urban Flood Inundation and Recession Impacted by Manholes. *Water*. 2020; 12(4):1160.
https://doi.org/10.3390/w12041160

**Chicago/Turabian Style**

GebreEgziabher, Merhawi, and Yonas Demissie. 2020. "Modeling Urban Flood Inundation and Recession Impacted by Manholes" *Water* 12, no. 4: 1160.
https://doi.org/10.3390/w12041160