# Using Adjacent Buoy Information to Predict Wave Heights of Typhoons Offshore of Northeastern Taiwan

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data Source

## 3. Model Development

#### 3.1. Artificial Neural Network (ANN)

#### 3.2. Data Partitioning

#### Wave Heights in the Testing Set

#### 3.3. Case Modeling and Parameter Calibration

_{1}to A

_{4}; the attributes obtained by the land-based weather stations were represented in sequence from B

_{1,j}to B

_{4,j}, which refer to the ground air pressure, average wind speed, maximum 10-min mean wind speed, and maximum instantaneous wind speed, respectively; moreover, when j = 1, 2, 3, and 4, the numbers refer to Keelung, Pengjiayu, Suao, and Yilan, respectively. The wave heights observed at the buoys were represented by H

_{1}and H

_{2}, which refer to Longdong and Guishandao, respectively.

#### 3.3.1. Cases of the Length of Lag Times

_{1,t+1}= f{(A

_{i}

_{,t−k})

_{i}

_{=1,4;k=0,∆t}, (B

_{i}

_{,j,t−k})

_{i}

_{=1,4; j=1,4;k=0,∆t}, (H

_{i}

_{,t−k})

_{i}

_{=2;k=0,∆t}}

_{2,t+1}= f{(A

_{i}

_{,t−k})

_{i}

_{=1,4;k=0,∆t}, (B

_{i}

_{,j,t−k})

_{i}

_{=1,4; j=1,4;k=0,∆t}, (H

_{i}

_{,t−k})

_{i}

_{=1;k=0,∆t}}

#### 3.3.2. Definition of the Evaluation Indexes

#### 3.3.3. Modeling and Parameter Calibration

## 4. Analysis of Scenarios and Evaluations

#### 4.1. Designed Scenarios—Whether to Use Data from the Adjacent Buoy

_{1,t+1}= f{(A

_{i}

_{,t−k})

_{i}

_{=1,4;k=0,1}, (B

_{i}

_{,j,t−k})

_{i}

_{=1,4; j=1,4;k=0,1}, (H

_{i}

_{,t−k})

_{i}

_{=2;k=0,1}}

_{1,t+1}= f{(A

_{i}

_{,t−k})

_{i}

_{=1,4;k=0,1}, (B

_{i}

_{,j,t−k})

_{i}

_{=1,4; j=1,4;k=0,1}}

_{2,t+1}= f{(A

_{i}

_{,t−k})

_{i}

_{=1,4;k=0,1}, (B

_{i}

_{,j,t−k})

_{i}

_{=1,4; j=1,4;k=0,1}, (H

_{i}

_{,t−k})

_{i}

_{=1;k=0,1}}

_{2,t+1}= f{(A

_{i}

_{,t−k})

_{i}

_{=1,4;k=0,1}, (B

_{i}

_{,j,t−k})

_{i}

_{=1,4; j=1,4;k=0,1}}

#### 4.2. Prediction Outcomes

#### 4.3. Evaluation and Discussion

#### 4.3.1. Evaluation: According to Wave Classification

- Small waves resulted in similar outcomes in Scenarios 1 and 2 at the Longdong buoy, yielding results of 0.378 m and 0.380 m, respectively. However, at the Guishandao buoy, the value of absolute error for Scenario 1 was 0.653 m, which was higher than that for the Scenario 2 value of 0.509 m. Thus, Scenario 1 was not advantageous for predicting small waves.
- Results from both buoys for both moderate and high waves demonstrated that Scenario 1 had a lower value of absolute error than Scenario 2. Particularly, the results for high waves at Longdong yielded a major difference of 0.445 m (RMSE with Scenario 1 = 1.101 m; RMSE with Scenario 2 = 1.546 m).

#### 4.3.2. Evaluation: According to Each Typhoon

#### 4.3.3. Evaluation: According to Typhoon Path

#### 4.3.4. Evaluation: Prediction with Lead Time Varying from 1 to 6 H

_{1,t+L}= f{(A

_{i}

_{,t−k})

_{i}

_{=1,4;k=0,1}, (B

_{i}

_{,j,t−k})

_{i}

_{=1,4; j=1,4;k=0,1}, (H

_{i}

_{,t−k})

_{i}

_{=2;k=0,1}}

_{2,t+L}= f{(A

_{i}

_{,t−k})

_{i}

_{=1,4;k=0,1}, (B

_{i}

_{,j,t−k})

_{i}

_{=1,4; j=1,4;k=0,1}, (H

_{i}

_{,t−k})

_{i}

_{=1;k=0,1}}

## 5. Conclusions

- Scenario 1 achieved superior performance to Scenario 2 with respect to absolute errors (MAE and RMSE), relative errors (rMAE and rRMSE), and CE. Moreover, the CE of Longdong (0.802) was higher than that of Guish andao (0.565); moreover, the results concerning Longdong in Scenario 1 exhibited less underestimation of high wave heights than those for Guishandao.
- When the waves were classified as small, moderate, or high, the evaluation based on rRMSE yielded the following results. The values of rRMSE for each wave classification for Longdong in Scenario 1 progressively decreased in the order of small, moderate, and high waves; this phenomenon demonstrated that the Scenario 1 setting had the ability to reduce relative error when the wave height increased. The other finding demonstrated that the values of the relative error for small waves at Guishandao in Scenarios 1 and 2 were relatively higher at 0.610 and 0.476, respectively.
- An examination of each typhoon indicated that they took various types of paths; for example, typhoons passed the northeastern sea area from east to west, passed from south to north along the east coast, passed through the Central Mountain Range, or passed by the south end of Taiwan through the Bashi Channel. Various types of typhoon paths caused the periphery of the typhoon to become disrupted by the topography or the Central Mountain Range, which increased the complexity of making wind wave predictions and caused prediction accuracy to vary between the Longdong and Guishandao buoys.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Paths of the 11 typhoons in the testing set: (

**a**) Soulik in 2013; (

**b**) Trami in 2013; (

**c**) Kong-Rey in 2013; (

**d**) Usagi in 2013; (

**e**) Fitow in 2013; (

**f**) Hagibis in 2014; (

**g**) Matmo in 2014; (

**h**) Fung-Wong in 2014; (

**i**) Noul in 2015; (

**j**) Linfa in 2015; and (

**k**) Chan-Hom in 2015.

**Figure 4.**Observation record of (

**a**) maximum wave height (MWH) and (

**b**) mean value of wave height (AWH) of the 11 typhoons in the testing set.

**Figure 6.**Prediction outcomes for wave height at a lead time of 1 h: (

**a**) Longdong buoy, and (

**b**) Guishandao buoy.

**Figure 7.**X–Y distribution diagram of wave height at a lead time of 1: (

**a**,

**b**) Longdong buoy and (

**c**,

**d**) Guishandao buoy.

**Figure 8.**Performance levels of wave height predictions at a lead time of 1 h: (

**a**) Longdong buoy and (

**b**) Guishandao buoy.

**Figure 9.**Values of RMSE (

**a**,

**c**) and rRMSE (

**b**,

**d**) for Longdong and Guishandao according to the wave classification.

**Figure 11.**The values of RMSE (

**a**,

**c**) and rRMSE (

**b**,

**d**) for Longdong and Guishandao according to typhoon path.

**Figure 12.**Wave height prediction of lead time = 2 to 6 h at Longdong buoy: (

**a**) lead time = 2 h; (

**b**) 3 h; (

**c**) 4 h; (

**d**) 5 h; and (

**e**) 6 h.

**Figure 13.**Wave height prediction of lead time = 2 to 6 h at Guishandao buoy: (

**a**) lead time = 2 h; (

**b**) 3 h; (

**c**) 4 h; (

**d**) 5 h; and (

**e**) 6 h.

**Figure 14.**Evaluation indexes for wave height prediction of lead time = 1 to 6 h at Longdong and Guishandao buoys: (

**a**) MAE; (

**b**) rMAE; (

**c**) RMSE; (

**d**) rRMSE; (

**e**) CC; and (

**f**) CE.

Year | Typhoon and Date | Year | Typhoon and Date |
---|---|---|---|

2005 | Matsa (8/3–6), Sanvu (8/11–13), Damrey (9/21–23), Longwang (9/30–10/3) | 2011 | Aere (5/9–10), Songda (5/27–28), Meari (6/23–25), Muifa (8/4–6), Nanmadol (8/27–30) |

2006 | Chanchu (5/16–18), Ewiniar (7/7–9), Bilis (7/12–15), Kaemi (7/23–26), Saomai (8/9–10), Bopha (8/7–9), Shanshan (9/14–16) | 2012 | Talim (6/19–21), Doksuri (6/28–29), Saola (7/30–8/3), Haikui (8/6–7), Kai-Tak (8/14–15), Tembin (8/21–28), Jelawat (9/27–28) |

2007 | Pabuk (8/6–8), Wutip (8/8–9), Sepat (8/16–19), Mitag (11/26–27) | 2013 | Soulik (7/11–13), Trami (8/20–22), Kong-Rey (8/27–29), Usagi (9/19–22), Fitow (10/4–7) |

2008 | Kalmaegi (7/16–18), Fung-Wong (7/26–29), Nuri (8/19–21), Sinlaku (9/11–16), Hagupit (9/21–23), Jangmi (9/26–29) | 2014 | Hagibis (6/14–15), Matmo (7/21–23), Fung-Wong (9/19–22) |

2009 | Linfa (6/19–22), Molave (7/16–18), Morakot (8/5–10), Parma (10/3–6) | 2015 | Noul (5/10–11), Linfa (7/6–9), Chan-Hom (7/9–11) |

2010 | Lionrock (8/31–9/2), Namtheun (8/30–31), Meranti (9/9–10), Fanapi (9/17–20), Megi (10/21–23) |

Attribute (unit) | Min–Max, Mean | Attribute (unit) | Min–Max, Mean |
---|---|---|---|

Pressure at the typhoon center (hPa) | 910.0–998.0, 965.7 | Maximum instantaneous wind speed at Pengjiayu (m/s) | 2.0–65.8, 19.2 |

Iintensity of the typhoon (km/h) | 54.0–198.0, 121.9 | Ground air pressure at Suao (hPa) | 966.7–1011.9, 998.3 |

Latitude of the typhoon center (degree) | 15.9–29.1, 22.4 | Average wind speed at Suao (m/s) | 0–33.4, 4.7 |

Longitude of the typhoon center (degree) | 113.9–130.9, 122.1 | Maximum 10-min mean wind speed at Suao (m/s) | 0.3–37.2, 6.3 |

Ground air pressure at Keelung (hPa) | 934.6–1011.2, 997.2 | Maximum instantaneous wind speed at Suao (m/s) | 1.7–62.4, 12.1 |

Average wind speed at Keelung (m/s) | 0–24.0, 5.0 | Ground air pressure at Yilan (hPa) | 968.6–1013.6, 1000.4 |

Maximum 10-min mean wind speed at Keelung (m/s) | 0–25.1, 6.3 | Average wind speed at Yilan (m/s) | 0.1–25.2, 3.8 |

Maximum instantaneous wind speed at Keelung (m/s) | 0.1–39.6, 11.7 | Maximum 10-min mean wind speed at Yilan (m/s) | 0.1–29.6, 5.0 |

Ground air pressure at Pengjiayu (hPa) | 955.0–1003.8, 990.3 | Maximum instantaneous wind speed at Yilan (m/s) | 0.1–48.5, 8.8 |

Average wind speed at Pengjiayu (m/s) | 0–44.3, 11.3 | Wave height at Longdong (m) | 0.2–11.2, 2.2 |

Maximum 10-min mean wind speed at Pengjiayu (m/s) | 0.9–48.4, 12.7 | Wave height at Guishandao (m) | 0.2–16.4, 2.3 |

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## Share and Cite

**MDPI and ACS Style**

Wei, C.-C.; Hsieh, C.-J.
Using Adjacent Buoy Information to Predict Wave Heights of Typhoons Offshore of Northeastern Taiwan. *Water* **2018**, *10*, 1800.
https://doi.org/10.3390/w10121800

**AMA Style**

Wei C-C, Hsieh C-J.
Using Adjacent Buoy Information to Predict Wave Heights of Typhoons Offshore of Northeastern Taiwan. *Water*. 2018; 10(12):1800.
https://doi.org/10.3390/w10121800

**Chicago/Turabian Style**

Wei, Chih-Chiang, and Chia-Jung Hsieh.
2018. "Using Adjacent Buoy Information to Predict Wave Heights of Typhoons Offshore of Northeastern Taiwan" *Water* 10, no. 12: 1800.
https://doi.org/10.3390/w10121800