# Modeling Flood Inundation Induced by River Flow and Storm Surges over a River Basin

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

**Figure 1.**Map of study area shown with dashed line: the land, the coastal sea, and the Tsengwen River are included in the model domain. Cyan color and white color represent the ocean and land, respectively.

## 2. Description of Study Area

^{2}, which includes part of the southwestern rugged foothills and fertile coastal plains. In the past, the Tsengwen River continuously carried abundant sediments that were deposited onto its floodplain. The annual sediment load is estimated at 31 million metric tons. The M

_{2}tide is the primary tidal constituent at the river mouth and has a mean tidal range below 1 m. Based on the tidal classification [22], the Tsengwen River mouth can be classified as a microtidal estuary. The estuarine zone is approximately 10 km to 25 km from the river mouth, depending on the river discharge. Therefore, the estuarine area ranges from 2 km

^{2}in the flood season to 3 km

^{2}in the wet season and 4 km

^{2}in the dry season. The average annual rainfall for the drainage basin is 2643 mm, with a contrasting rainfall pattern between dry and wet seasons. The dry and wet seasons are October–April and May–September, respectively. Thus, the river discharge varies seasonally with a high discharge of 411 × 10

^{3}m/day in the wet season and a low discharge of 14 × 10

^{3}m/day in the dry season. In the wet season, episodic flooding from heavy monsoon rains and typhoons are not unusual and critically affect the water discharge and the suspended load [23].

## 3. Model Descriptions

#### 3.1. Governing Equations

_{0}is reference density of water; P

_{A}(x, y, t) is the atmospheric pressure at the free surface; v is the vertical eddy viscosity; and μ is the horizontal eddy viscosity.

_{s}is the wind stress, which can be expressed as

_{a}and V

_{a}are the x and y components, respectively, at a 10-m height wind speed, W, which is generated from the prototypical typhoon model; ρ

_{a}is the air density; and C

_{s}is the wind drag coefficient that depends on the wind speed. The wind drag coefficient, C

_{s}, is given by Large and Pond [25] and Powell et al. [26].

_{b}is the bottom stress. The bottom friction stress is given by a quadratic drag law:

_{b}is the drag coefficient.

#### 3.2. Prototypical Typhoon Model

_{n}and P

_{c}are the ambient pressure and the central air pressure of the typhoon, respectively; R

_{max}is the maximum wind radius; r is the radial distance from the typhoon center; W is wind speed; W

_{x}, W

_{y}are wind speed in x, y components, respectively; θ is the azimuthal angle with respect to the typhoon’s eye; and B is a parameter that characterizes the scale of the typhoon. We adopted the formula of Hubbert et al. [28], i.e., B = 1.5 + (980 − P

_{c})/120.

#### 3.3. Model Implementation

**Figure 3.**Unstructured grids for entire modeling domain including the Taiwan Strait, the Tsengwen River channel, and the land of the Tsengwen River basin.

#### 3.4. Indices of Simulation Performance

_{m}is the predicted water level; and Y

_{o}is the observational water level.

## 4. Model Validation

**Figure 4.**Typhoon tracks for model validation (Typhoon Krosa, Typhoon Kalmagei, and Morakot) and model application (Typhoon Chebi). The value in the typhoon track represents center pressure (mb). Cyan color and white color represent the ocean and land, respectively.

**Figure 5.**Comparison of model predictions of water level with observation results at the Jianjung Fish Port for (

**a**) Typhoon Krosa (2007); (

**b**) Typhoon Kalmaegi (2008); and (

**c**) Typhoon Morakot (2009). The blue interval represents the period of storm surge.

**Figure 6.**Comparison of model predictions of water level with observation results at the Tsengwen Bridge for (

**a**) Typhoon Krosa (2007); (

**b**) Typhoon Kalmaegi (2008); and (

**c**) Typhoon Morakot (2009). The flow represents the measured freshwater discharge at the upstream boundary (Erxi Bridge).

**Table 1.**Model performance for predicting water levels during three typhoon events at different stations.

Typhoon | Jianjun Fish Port | Tsengwen Bridge | ||||
---|---|---|---|---|---|---|

MAE (m) | RMSE (m) | SRE (%) | MAE (m) | RMSE (m) | SRE (%) | |

Typhoon Krosa (2007) | 0.06 | 0.08 | 1.41 | 0.71 | 0.87 | 8.72 |

Typhoon Kalmaegi (2008) | 0.07 | 0.09 | 1.55 | 0.47 | 0.63 | 4.14 |

Typhoon Morakot (2009) | 0.07 | 0.09 | 1.26 | 0.91 | 1.10 | 9.90 |

## 5. Model Applications and Discussion

#### 5.1. Effect of Storm Surge

^{3}/s was used as the upstream boundary condition. Figure 8 shows the predicted time series water levels at the Jiangjun Fish Port and the Tsengwen River mouth. We found that the maximum storm surges at the Jiangjun Fish Port and the Tsengwen River mouth were 2.1 m and 3.26 m, respectively. This extremely high water level at the Tsengwen River mouth would have resulted in inundation. Figure 9 shows the predicted inundation depth and extent induced by a storm surge only. Figure 9a shows the instantaneous inundation pattern when the storm surge height reached its maximum value. This pattern indicates that the seawater rushed into the Tsengwen River estuary, thereby increasing the water depth up to 10 m in height. Figure 9b presents the inundation depth and extent at a simulation time of 168 h. The inundation area was 60 km

^{2}, and the maximum inundation depth was 1.98 m (see Table 2). Thus, the artificial super typhoon would have resulted in an extreme storm surge and produced severe inundation in the coastal region.

#### 5.2. Effect of Freshwater Discharge

^{3}/s, respectively [31]. The observed hourly discharge at the upstream boundary in the Tsengwen River during Typhoon Krosa (2007) was used to calculate the discharge hydrograph for the different return periods that were used in the model simulation.

^{2}and 1.58 m, respectively. The inundation area and the maximum inundation depth for 200-year return period flow only are smaller than those for the effect of storm surge (Table 2).

**Figure 7.**Distribution of air pressure and wind speed generated from the prototypical typhoon model used in a numerical experiment (using tracks of Typhoon Chebi in 2001 and intensity of Typhoon Haiyan in 2013). The center pressure and time of typhoon track show in the small frame.

**Figure 8.**Time series for water level induced by a typhoon of similar intensity as Typhoon Haiyan in 2013 at (

**a**) Jiangjun Fish Port and (

**b**) Tsengwen River mouth.

**Figure 9.**Inundation extent and depth induced by a storm surge at simulation times of (

**a**) 99 h and (

**b**) 168 h.

**Figure 10.**Inundation extent and depth induced by a freshwater discharge only during peak flows for (

**a**) 50 year; (

**b**) 100 year; and (

**c**) 200 year return periods.

Inundation Condition | Effect of Storm Surge | Effect of Freshwater Discharge | ||
---|---|---|---|---|

Return Period | ||||

50 Year | 100 Year | 200 Year | ||

Inundation area (km^{2}) | 60 | 21 | 25 | 30 |

Maximum inundation depth (m) | 1.98 | 1.53 | 1.56 | 1.58 |

#### 5.3. Effect of Storm Surge Combined with Freshwater Discharge

^{2}and 1.97 m, respectively. Thus, the extreme storm surge combined with high freshwater discharge increased the severity of the flooding.

**Figure 11.**(

**a**) Water level profile along Tsengwen River; and (

**b**) inundation extent and depth induced by storm surge and freshwater discharge for 200-year return period.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Flather, R.A. Storm surges. In Encyclopaedia of Ocean Science; Steele, J., Thorpe, S., Turekian, K., Eds.; Academia: San Diego, CA, USA, 2001; pp. 2882–2892. [Google Scholar]
- Bertin, X.; Bruneau, N.; Breilh, J.; Fortunato, A.B.; Karpytchev, M. Importance of wave age and resonance in storm surges: The case Xynthia, Bay of Biscay. Ocean Model.
**2012**, 42, 16–30. [Google Scholar] - Turner, A.B.; Colby, J.D.; Csontos, R.M.; Batten, M. Flood modeling using a synthesis of multi-platform LiDAR data. Water
**2013**, 5, 1533–1560. [Google Scholar] - Forunato, A.B.; Rodrigues, M.; Dias, J.M.; Lopes, C.; Olivera, A. Generating inundation maps for a coastal lagoon: A case study in the Ria de Aveiro (Portugal). Ocean Eng.
**2013**, 64, 60–71. [Google Scholar] [CrossRef] - Chen, W.B.; Liu, W.C.; Hsu, M.H. Predicting typhoon-induced storm surge tide with a two-dimensional hydrodynamic model and artificial neural network model. Nat. Hazards Earth Sys. Sci.
**2012**, 12, 3799–3809. [Google Scholar] [CrossRef] - Dietsche, D.; Hagen, S.C.; Bacopoulos, P. Storm surge simulation for Hurricane Hugo (1989): On the significance of inundation areas. J. Waterw. Port Coast. Ocean Eng.
**2007**, 133, 183–191. [Google Scholar] [CrossRef] - Jones, J.E.; Davis, A.M. Storm surge computations for the west coast of Britain using a finite element model (TELEMAC). Ocean Dynam.
**2008**, 58, 337–363. [Google Scholar] [CrossRef][Green Version] - Weisberg, R.H.; Zheng, L. Hurricane storm surge simulations comparing three-dimensional with two-dimensional formulaitons based on an Ivan-like storm over the Tampa Bay, Florida region. J. Geophs. Res.
**2008**, 113. [Google Scholar] [CrossRef] - Xia, M.; Xia, L.; Pietrafesa, L.J.; Peng, M. A numerical study of storm surge in the Cape Fear River Estuary and adjacent coast. J. Coast. Res.
**2008**, 24, 159–167. [Google Scholar] [CrossRef] - Rego, J.L.; Li, C. Storm surge propagation in Galveston Bay during Hurricane Ike. J. Mar. Syst.
**2010**, 82, 265–279. [Google Scholar] [CrossRef] - Xu, H.; Zhang, K.; Shen, J.; Li, Y. Storm surge simulation along U.S. Ease and Gulf Coasts using multi-scale numerical model approach. Ocean Dynam.
**2010**, 60, 1597–1619. [Google Scholar] [CrossRef] - You, S.H.; Lee, W.J.; Moon, K.S. Comparison of storm surge/tide predictions between a 2-D operational forecast system, the regional tide/storm surge model (RTSM), and the 3-D regional ocean modeling system (ROMS). Ocean Dynam.
**2010**, 60, 443–459. [Google Scholar] [CrossRef] - Krestenitis, Y.N.; Androulidakis, Y.S.; Kontos, Y.N.; Georgakopoulos, G. Coastal inundation in the north-eastern Mediterranean coastal zone due to storm surge events. J. Coast. Conserv.
**2011**, 15, 353–368. [Google Scholar] [CrossRef] - Orton, P.; Georgas, N.; Blumberg, A.; Pullen, J. Detailed modeling of recent severe storm tides in estuaries on the New York City region. J. Geophys. Res.
**2012**, 117. [Google Scholar] [CrossRef] - Sheng, Y.P.; Alymov, V.; Paramygin, V.A. Simulation of storm surge, wave, and inundation in the Outer Banks and Chesapeake Bay during Hurricane Isabel in 2003: The importance of waves. J. Geophy. Res.
**2010**, 115. [Google Scholar] [CrossRef] - Vested, H.J.; Jensen, H.R.; Petersen, H.M.; Jorgensen, A.; Machenhauer, B. An operational hydrographic warning system for the North Sea and Danish Belts. Cont. Shelf Res.
**1992**, 12, 65–81. [Google Scholar] [CrossRef] - Li, Y.S.; Zhang, M.Y. Dynamic coupling of wave and surge models by Eulerian-Lagrangian method. J. Waterw. Port Coast. Ocean Eng.
**1997**, 123, 1–7. [Google Scholar] [CrossRef] - Shen, J.; Zhang, K.; Xiao, C.; Gong, W. Improved prediction of storm surge inundation with a high-resolution unstructured grid model. J. Coast. Res.
**2006**, 22, 1309–1319. [Google Scholar] [CrossRef] - Peng, M.; Xie, L.; Pietrafesa, L.J. A numerical study of storm surge and inundation in the Croatan-Albemarle-Pamlico Estuary System. Estuar. Coast. Shelf Sci.
**2004**, 59, 121–137. [Google Scholar] [CrossRef] - Xie, L.; Kiu, H.; Liu, B.; Bao, S. A numerical study of the effect of hurricane wind asymmetry on storm surge and inundation. Ocean Model.
**2011**, 36, 71–79. [Google Scholar] [CrossRef] - Lewis, M.; Bates, P.; Horsburgh, K.; Neal, J.; Schumann, G. A storm surge inundation model of the northern Bay of Bengal using publicly available data. Quart. J. Roy. Meteor. Soc.
**2013**, 139, 358–369. [Google Scholar] [CrossRef] - Dyer, K.R. Estuaries: A Physical Introduction; Wiley: New York, NY, USA, 1997. [Google Scholar]
- Hong, E.; Huang, T.C.; Yu, H.S. Morphology and dynamic sedimentology in front or the retreating Tsengwen Delta, Southwestern Taiwan. Terre. Atmos. Ocean. Sci.
**2004**, 15, 565–587. [Google Scholar] - Zhang, Y.L.; Baptista, A.M. SELFE: A semi-implicit Eulerian-Lagrangian finite-element model for cross-scale ocean circulation. Ocean Model.
**2008**, 21, 71–96. [Google Scholar] [CrossRef] - Large, W.G.; Pond, S. Open ocean momentum flux measurements in moderate to strong winds. J. Phys. Oceanogr.
**1981**, 11, 324–336. [Google Scholar] [CrossRef] - Powell, M.D.; Vickery, P.J.; Reinhold, T.A. Reduced drag coefficient for high wind speeds in tropical cyclones. Nature
**2003**, 422, 279–283. [Google Scholar] [CrossRef] [PubMed] - Holland, G.J. An analytical model of the wind and pressure profiles in hurricanes. Mon. Weather Rev.
**1980**, 108, 1212–1218. [Google Scholar] [CrossRef] - Hubbert, G.D.; Holland, G.J.; Leslie, L.M.; Manton, M.J. A real-time system for forecasting tropical cyclone storm surges. Weather Forecast.
**1991**, 6, 86–97. [Google Scholar] [CrossRef] - Medeiros, S.C.; Hagen, S.C. Review of wetting and drying algorithms for numerical tidal flow models. Int. J. Numer. Method. Fluid.
**2012**, 71, 473–487. [Google Scholar] [CrossRef] - Zu, T.; Gana, J.; Erofeevac, S.Y. Numerical study of the tide and tidal dynamics in the South China Sea. Deep Sea Res. I Ocean. Res. Pap.
**2008**, 55, 137–154. [Google Scholar] [CrossRef] - Water Resources Agency. The Analysis of Storm Rainfall and River Discharge during the Typhoon Morakot in 2009; Technical Report; Water Resources Agency: Taipei, Taiwan, 2009. [Google Scholar]
- Condon, A.J.; Sheng, Y.P. Evaluation of coastal inundation hazard for present and future climates. Nat. Hazards
**2012**, 62, 345–373. [Google Scholar] [CrossRef]

© 2014 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 license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chen, W.-B.; Liu, W.-C.
Modeling Flood Inundation Induced by River Flow and Storm Surges over a River Basin. *Water* **2014**, *6*, 3182-3199.
https://doi.org/10.3390/w6103182

**AMA Style**

Chen W-B, Liu W-C.
Modeling Flood Inundation Induced by River Flow and Storm Surges over a River Basin. *Water*. 2014; 6(10):3182-3199.
https://doi.org/10.3390/w6103182

**Chicago/Turabian Style**

Chen, Wei-Bo, and Wen-Cheng Liu.
2014. "Modeling Flood Inundation Induced by River Flow and Storm Surges over a River Basin" *Water* 6, no. 10: 3182-3199.
https://doi.org/10.3390/w6103182