# Assessing the Influences of a Flood Diversion Project on Mitigating River Stage, Inundation Extent and Economic Loss

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## Abstract

**:**

## 1. Introduction

^{8}m

^{3}of water in 27 flood events from 2004 to 2013 [4], and during this period, flooding has not occurred in the Taipei metropolitan area. Undoubtedly, the Yuansantze Flood Diversion Project has a significant contribution to the mitigation of inundation disasters and economic losses.

## 2. Description of the Study Area

^{2}with a mainstream length of 86 km. The Keelung River is one of the three major tributaries of the Tamsui River in northern Taiwan, flowing through the Taipei metropolis. It is rather steep in the upstream and very flat in the lower downstream. This terrain is ideal for frequent flooding when heavy downpours occur in the river basin. Rapid urbanization resulted in the formation of highly developed and densely populated zones over the Keelung River basin. The hydraulic facilities that existed before the project was initiated were unable to provide secure flood protection. Based on its design, the YFDT can divert 1310 m

^{3}/s of water at the designed peak discharge from the upper Keelung River basin into the East China Sea (Figure 1), and the remaining design flood of 310 m

^{3}/s is discharged into downstream of river weir in the Keelung River [11]. The YFDT provides an assurance of flood-carrying capacity and significantly increases the safety of the Keelung River basin under 200-year return-period flood protection.

**Figure 1.**Map of the study area. (White, blue, and cyan represent land, ocean, and river, respectively).

## 3. Materials and Methods

#### 3.1. Data

**Figure 2.**(

**a**) Bathymetry and topography for the model domain; (

**b**) unstructured grids for the model domain; and (

**c**) high-resolution meshes at the Yuansantze flood diversion.

#### 3.2. Hydrodynamic Model

^{−3}; $P(x,y,t)$ is the pressure; $\mathrm{\nu}$ is the vertical eddy viscosity; and $\mathrm{\mu}$ is the horizontal eddy viscosity.

#### 3.3. Estimation of Economic Loss

_{dis}) or a continued approach (AAEB

_{con}) as follows:

#### 3.4. Model Implementation

#### 3.5. Indices of Model Performance

^{2}), and the optimal value of percent bias (PBIAS [19]). Positive values of PBIAS indicate overstimulation of model while negative values indicate underestimation of model [20]. The equations for these three criteria are as follows:

## 4. Model Validation

^{3}/s. These errors may be the reason that some uncertainties are introduced by rating curve (i.e., stage-discharge relation) which is expected to be higher under low flow condition [21]. Overall, the model results are in good agreement with the observations. Table 2 shows the statistical errors for the difference between the simulated and observed water levels for the model validation. The average MAE, RMSE, and R

^{2}values of three typhoon events are 0.117 m, 0.157 m, and 0.93 at the Yuansantze diversion weir, respectively.

Typhoon Event | Maximum Diversion Discharge from the Keelung River (m^{3}/s) | Total Diversion Water Volume from the Keelung River (m^{3}) |
---|---|---|

Typhoon Sinlaku (2008) | 247 | 1065 × 10^{3} |

Typhoon Megi (2010) | 455 | 1792 × 10^{3} |

Typhoon Saola (2012) | 773 | 1879 × 10^{3} |

**Figure 3.**Model-data comparison of the water level at the Yuansantze diversion weir for (

**a**) Typhoon Sinlaku (2008); (

**b**) Typhoon Megi (2010); and (

**c**) Typhoon Saola (2012).

**Table 2.**Model performance for predicting water levels using two-dimensional and three-dimensional models at the Yuansnatze diversion weir for different typhoon events.

Typhoon Event | Model | MAE (m) | RMSE (m) | R^{2} | PBIAS (%) |
---|---|---|---|---|---|

Typhoon Sinlaku (2008) | Two-dimensional model | 0.19 | 0.20 | 0.86 | 0.29 |

Three-dimensional model | 0.12 | 0.16 | 0.87 | 0.15 | |

Typhoon Megi (2010) | Two-dimensional model | 0.23 | 0.24 | 0.95 | 0.35 |

Three-dimensional model | 0.12 | 0.16 | 0.96 | 0.16 | |

Typhoon Saola (2012) | Two-dimensional model | 0.34 | 0.36 | 0.96 | 0.52 |

Three-dimensional model | 0.11 | 0.15 | 0.96 | −0.11 |

^{2}values of three typhoon events are 0.253 m, 0.267 m, and 0.92 at the Yuansantze diversion weir, respectively, when the two-dimensional model is used to predict water levels.

**Figure 4.**Comparison of performance for predicting water levels using two-dimensional and three-dimensional hydrodynamic models for (

**a**) Typhoon Sinlaku (2008); (

**b**) Typhoon Megi (2010); and (

**c**) Typhoon Saola (2012).

**Figure 5.**Model (green color)-data (white color) comparison of the inundation extent during Typhoon Nari (2001).

## 5. Model Application and Discussion

#### 5.1. Influence of the YFDT on River Level and Inundation Extent

^{3}/s [24], which are used to specify the inflows at the upstream open boundary (see Figure 2a). Figure 6 shows only the time-series river flows at the upstream open boundary for the 50-year, 100-year, and 200-year return periods.

**Figure 6.**Designed river flow at the upstream boundary for the 50-year, 100-year, and 200-year return periods.

**Figure 7.**Comparison of the water levels along the Keelung River with (cyan color) and without (blue color) the Yuansantze flood diversion tunnel (YFDT) for the following return periods: (

**a**) 50-year; (

**b**) 100-year; and (

**c**) 200-year.

**Figure 8.**Comparison of time-series water levels at the Ruifang Bridge with and without the Yuansantze flood diversion tunnel (YFDT) for the following return periods: (

**a**) 50-year; (

**b**) 100-year; and (

**c**) 200-year.

**Figure 9.**Comparison of the maximum inundation extent with (cyan color) and without (blue color) the Yuansantze flood diversion tunnel (YFDT) for the following return period: (

**a**) 50-year; (

**b**) 100-year; and (

**c**) 200-year.

**Table 3.**Maximum inundation area and inundation depth for different return periods with and without YFDT conditions.

Return Period | With YFDT | Without YFDT | ||
---|---|---|---|---|

Inundation Area (km^{2}) | Inundation Depth (m) | Inundation Area (km^{2}) | Inundation Depth (m) | |

2-year | -- | -- | 0.71 | 3.16 |

5-year | -- | -- | 0.87 | 3.84 |

10-year | 0.28 | 0.56 | 0.99 | 4.15 |

20-year | 0.29 | 0.57 | 1.05 | 4.33 |

50-year | 0.39 | 1.23 | 1.13 | 4.52 |

100-year | 0.50 | 1.89 | 1.20 | 4.63 |

200-year | 0.52 | 1.96 | 1.23 | 4.82 |

#### 5.2. Influence of the YFDT on Economic Loss

_{dis}is a summation of column (e) in Table 4. Figure 11 plots the distribution of expected benefit (EB) vs. the probability of an event (Pr). The regression equation for EB and Pr is ${f}_{EB}=536.955\cdot {e}^{-1.599\mathrm{Pr}}$, and the R

^{2}value is 0.986. AAEB

_{con}is the area below the curve of ${f}_{EB}$ shown in Figure 11. It can be obtained through integrating equation ${f}_{EB}$. AAEB

_{dis}and AAEB

_{con}were 183.96 million NTD and 184.86 million NTD, respectively, as computed using Equations (9) and (10). The difference between these two approaches is only 0.49%. Hence, we conclude that the yearly benefit after the construction of the YFDT is approximately 184 million NTD in the Ruifang District. One should note that to avoid overestimating the average annual expected benefit (AAEB) with the YFDT, the average annual flood losses for events with a probability higher than 0.5 (i.e., 2-year return period) are neglected. In other words, a conservative estimation is adopted in the current study.

**Table 4.**Estimation of economic loss and benefit for different return periods with and without YFDT conditions.

Return Period | Pr (a) | Economic Loss (NTD, in Millions) | Pi (d) | Expected Benefits (EB) (NTD, in Millions) (e) = (c − b) × d | |
---|---|---|---|---|---|

With YFDT (b) | Without YFDT (c) | ||||

2-year | 0.5 | - | 246 | 0.150 | 36.90 |

5-year | 0.2 | - | 379 | 0.200 | 75.80 |

10-year | 0.1 | 13 | 456 | 0.075 | 33.23 |

20-year | 0.05 | 14 | 502 | 0.040 | 19.52 |

50-year | 0.02 | 45 | 558 | 0.020 | 10.26 |

100-year | 0.01 | 90 | 622 | 0.0075 | 3.99 |

200-year | 0.005 | 98 | 666 | 0.0075 | 4.26 |

Average annual expected benefit (AAEB_{dis}, summation of column (e)) | 183.61 |

#### 5.3. Discussion

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Chen, W.-B.; Liu, W.-C.; Fu, H.-S.; Jang, J.-H.
Assessing the Influences of a Flood Diversion Project on Mitigating River Stage, Inundation Extent and Economic Loss. *Water* **2015**, *7*, 1731-1750.
https://doi.org/10.3390/w7041731

**AMA Style**

Chen W-B, Liu W-C, Fu H-S, Jang J-H.
Assessing the Influences of a Flood Diversion Project on Mitigating River Stage, Inundation Extent and Economic Loss. *Water*. 2015; 7(4):1731-1750.
https://doi.org/10.3390/w7041731

**Chicago/Turabian Style**

Chen, Wei-Bo, Wen-Cheng Liu, Huei-Shuin Fu, and Jiun-Huei Jang.
2015. "Assessing the Influences of a Flood Diversion Project on Mitigating River Stage, Inundation Extent and Economic Loss" *Water* 7, no. 4: 1731-1750.
https://doi.org/10.3390/w7041731