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

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## Abstract

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## 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

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**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