# A Support Vector Machine Forecasting Model for Typhoon Flood Inundation Mapping and Early Flood Warning Systems

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## Abstract

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## 1. Introduction

## 2. Study Area and Hydrological Data

^{2}. Several irrigation and drainage systems have been built in the Yilan River basin. The Meifu drainage system, located on the southern side of the Yilan River, is one of the major drainage systems. Typhoons usually hit this region in the summer and fall, from August to October. During typhoons, severe flood inundations may quickly form in low-lying areas between the Meifu drainage system and the Yilan River, causing serious property loss and damage.

^{2}) and $B$ is the local slope (degree).

## 3. Methodology Development

#### 3.1. Hydrodynamic Simulation

^{3}/s), g is the acceleration due to gravity (m/s

^{2}), t is the time (s), h is the water level (m), R is the hydraulic radius (m), ${q}_{lat}$ presents the lateral discharge per unit length (m

^{2}/s), ${A}_{f}$ is the cross sectional flow area (m

^{2}), C is the Chezy coefficient, ${W}_{f}$ is the cross sectional width at the corresponding water level (m

^{2}), ${\tau}_{wi}$ is the wind shear stress ($\frac{\mathrm{kg}}{\mathrm{m}\times {\mathrm{s}}^{2}}$), and ${\rho}_{w}$ is the water density (kg/m

^{3}).

#### 3.2. k-means Clustering Algorithm

_{j}is the input vector, c

_{i}is the ith cluster center and w

_{ji}is a l × k data matrix. For more details on the k-means clustering algorithm, refer to [37].

#### 3.3. Support Vector Machine

_{i}and output data y

_{i}. The objective of the SVM is to find a nonlinear regression function $\widehat{y}=f(x)={\mathbf{w}}^{\mathrm{T}}\varphi (x)+b$ and produce the output $\widehat{y}$, which is the optimal approximate of the observed data with an error tolerance of $\epsilon $, where $\varphi (x)$ is a nonlinear function, $\mathbf{w}$ is weight, and b is the bias of the regression function, respectively. According to the structural risk minimization (SRM) induction principle, $\mathbf{w}$ and b are calculated by minimizing the structural risk function:

_{p}represents the tradeoff between model complexity and empirical error.

_{i}is the support vector, and K(x

_{i},x) is a kernel function, used for mapping the SVM input vector into a higher-dimensional feature space. The radial basis function (RBF) is used herein and expressed as follows:

_{p}and the error tolerance ε are also crucial SVM parameters. In this study, the grid-search method is employed for determining the optimal combination of the kernel function, γ, C

_{p}and ε. In this study, the SVM is applied to develop the point forecasting module to forecast the flood inundation depth for each flood gauging station. Then, the SVM is used to develop the spatial expansion module to expand the flood inundation depth from points to areas for each cluster.

#### 3.4. Methodology Construction

#### 3.4.1. Hydrodynamic simulation step

#### 3.4.2. Classification Step

#### 3.4.3. Point Forecasting Step

#### 3.4.4. Spatial Expansion Step

#### 3.5. Model Evaluation and Cross Validation

_{Tp}), error of peak water level (E

_{Wp}), capture rate (CR) and coefficient of efficiency (CE). Smaller RMSE, MAE, E

_{Tp}and E

_{Wp}values indicate less significant errors between the observed and forecasted values, whereas higher CR value means better agreement of flood inundation extents between observed and forecasted values. The CE value is used to evaluate forecasting ability, with a CE value close to 1 representing high performance. In particular, RMSE and CE are selected as performance measures for the point forecasting module.

## 4. Results and Discussion

#### 4.1. Calibration and Validation of SOBEK

_{Tp}and RMSE values at upstream water level stations (i.e., Yixing and Ximen) are worse than those at downstream water level stations. E

_{Tp}values below 2 h are acceptable, as are E

_{Wp}values below 10%. Meanwhile, CE values above 0.7 are acceptable [49]. Though the E

_{Wp}value at Dongjin is greater than 10%, the difference between observed and simulated peak water levels is only 0.5 m; therefore, we accept the errors of the simulated water levels as reasonable. Moreover, the simulated and observed flood inundation extents are in a good agreement (see Figure 6). The CR value of 78% indicates that the SOBEK model can accurately simulate the flood inundation extents. We accept the SOBEK model as an accurate and efficient way to simulate flood inundation in the Yilan River basin.

#### 4.2. Identification of Clusters

#### 4.3. Performance of the Point Forecasting Module

#### 4.4. Performance of the Spatial Expansion Module

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The Yilan River basin and the locations of rainfall, water level and flood gauging stations.

**Figure 5.**Comparison of observed water levels with simulated ones by SOBEK model for Typhoon Dujuan (from 27 September 2015 9:00 am to 28 September 2015 9:00 am) at (

**a**) Gamalan, (

**b**) Sijie, (

**c**) Dongjin, (

**d**) Zhuangwei, (

**e**) Yixing, and (

**f**) Ximen.

**Figure 7.**Data clustering results from the k-means clustering algorithm, along with locations of flood gauging stations.

**Figure 9.**Comparison of observed and forecasted water levels for 1–3 h lead time at (

**a**) ISR2, (

**b**) KXL1, (

**c**) ISR3, (

**d**) ISR7, (

**e**) GJL1, and (

**f**) ISR5.

**Figure 10.**Comparison of flood inundation data with forecasts obtained from the proposed model for Typhoon Dujuan.

Event | Date (yyyy/mm/dd) | Duration (h) | Cumulative Maximum within 36 h Rainfall (mm) | Inundation Extent (km^{2}) |
---|---|---|---|---|

Aere | 2004/08/23 | 80 | 350.4 | 0.82 |

Nanmadol | 2004/12/03 | 35 | 300.4 | 1.36 |

Sepat | 2007/08/16 | 77 | 186.6 | 1.75 |

Sinlaku | 2008/09/11 | 125 | 454.1 | 7.33 |

Jangmi | 2008/09/27 | 71 | 185.6 | 0.10 |

Parma | 2009/10/03 | 83 | 305.6 | 5.51 |

Megi | 2010/10/21 | 68 | 416.0 | 6.35 |

Saola | 2012/07/30 | 89 | 379.8 | 5.22 |

Soudelor | 2015/08/06 | 80 | 214.9 | 0.87 |

Dujuan | 2015/09/27 | 56 | 179.9 | 0.54 |

Water Level Station | E_{Tp} (h) | E_{Wp} (%) | CE | RMSE (m) |
---|---|---|---|---|

Gamalan | 0 | 0.34 | 0.98 | 0.09 |

Sijie | 0 | 4.92 | 0.97 | 0.16 |

Dongjin | 0 | 10.18 | 0.95 | 0.18 |

Zhuangwei | 0 | 8.16 | 0.96 | 0.30 |

Yixing | 2 | 5.07 | 0.90 | 0.76 |

Ximen | 2 | 5.10 | 0.74 | 1.09 |

Flood Gauging Station | Maximum Water Level (m) | Minimum Water Level (m) | Range of Water Levels (m) | Dominant Cluster |
---|---|---|---|---|

ISR2 | 5.18 | 2.37 | 2.81 | 3 |

KXL1 | 2.73 | 0.22 | 2.51 | 6 |

ISR3 | 6.57 | 4.33 | 2.24 | 1, 5 |

ISR7 | 1.81 | 0.07 | 1.74 | 10 |

GJL1 | 1.77 | 0.13 | 1.64 | 7, 8, 9 |

Lead Time (h) | ISR2 | KXL1 | ISR3 | ISR7 | GJL1 | ISR5 |
---|---|---|---|---|---|---|

RMSE (m) | ||||||

t + 1 | 0.19 | 0.12 | 0.09 | 0.03 | 0.07 | 0.01 |

t + 2 | 0.41 | 0.26 | 0.19 | 0.07 | 0.17 | 0.02 |

t + 3 | 0.55 | 0.36 | 0.27 | 0.10 | 0.24 | 0.02 |

CE | ||||||

t + 1 | 0.90 | 0.92 | 0.93 | 0.98 | 0.97 | 0.99 |

t + 2 | 0.57 | 0.69 | 0.67 | 0.91 | 0.81 | 0.94 |

t + 3 | 0.26 | 0.37 | 0.29 | 0.79 | 0.56 | 0.88 |

Lead Time (h) | Cluster | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |

RMSE (m) | ||||||||||

t + 1 | 0.07 | 0.09 | 0.08 | 0.13 | 0.14 | 0.20 | 0.20 | 0.13 | 0.35 | 0.11 |

t + 2 | 0.07 | 0.08 | 0.08 | 0.13 | 0.15 | 0.18 | 0.19 | 0.12 | 0.32 | 0.13 |

t + 3 | 0.07 | 0.08 | 0.08 | 0.13 | 0.14 | 0.18 | 0.20 | 0.12 | 0.31 | 0.16 |

MAE (m) | ||||||||||

t + 1 | 0.05 | 0.05 | 0.05 | 0.09 | 0.09 | 0.15 | 0.14 | 0.10 | 0.26 | 0.07 |

t + 2 | 0.05 | 0.05 | 0.05 | 0.08 | 0.10 | 0.13 | 0.13 | 0.09 | 0.24 | 0.09 |

t + 3 | 0.04 | 0.05 | 0.05 | 0.09 | 0.09 | 0.13 | 0.13 | 0.09 | 0.24 | 0.11 |

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## Share and Cite

**MDPI and ACS Style**

Chang, M.-J.; Chang, H.-K.; Chen, Y.-C.; Lin, G.-F.; Chen, P.-A.; Lai, J.-S.; Tan, Y.-C.
A Support Vector Machine Forecasting Model for Typhoon Flood Inundation Mapping and Early Flood Warning Systems. *Water* **2018**, *10*, 1734.
https://doi.org/10.3390/w10121734

**AMA Style**

Chang M-J, Chang H-K, Chen Y-C, Lin G-F, Chen P-A, Lai J-S, Tan Y-C.
A Support Vector Machine Forecasting Model for Typhoon Flood Inundation Mapping and Early Flood Warning Systems. *Water*. 2018; 10(12):1734.
https://doi.org/10.3390/w10121734

**Chicago/Turabian Style**

Chang, Ming-Jui, Hsiang-Kuan Chang, Yun-Chun Chen, Gwo-Fong Lin, Peng-An Chen, Jihn-Sung Lai, and Yih-Chi Tan.
2018. "A Support Vector Machine Forecasting Model for Typhoon Flood Inundation Mapping and Early Flood Warning Systems" *Water* 10, no. 12: 1734.
https://doi.org/10.3390/w10121734