PREDICTION OF TYPHOON SWELLS USING NEURAL ETWORKS 蕭松山 1 丁肇隆 2 林銘崇 2 蘇昭安 3  國立台灣海洋大學河海工程學系副教授  國立台灣大學工程科學及海洋工程學系教授  國立台灣大學工程科學及海洋工程學系碩士 指導老師 : 陳榮昌 老師 工業工程與管理系 碩一 A 學生 : 林巧玲 、 白彩綾

Outline 1.Introduction 2.Back-Propagation Neural network (BPN) 3.Forming the BPN framework 4.Results and discussion 5.Conclusions 2

1.Introduction 3

Motivation The track of Typhoon Fred in 1994 did not hit Taiwan, however, the maximum significant wave height reached 7.59 m. The potential for such large waves cannot be ignored. The establishment of a swell warning system is now urgent. A precise warning system must yield good wave-height predictions. Accurately predicting swell motion is therefore extremely important. 4

Reference 5 World War Ⅱ Predictive models of wind waves have developed since World War II. These models predict the characteristics of waves from wind data. Sverdrup and Munk (1947) developed a model to predict significant wave heights generated by winds. Bretschneider (1952) used empirical data to present the well-known SMB method, which forecasts significant wind waves under steady-fetch conditions.

Reference 6 World War Ⅱ Wilson (1955) developed a graphical SMB method to overcome this weakness. Ijima et al. (1968) extended Wilson’s method to predict the heights of wind waves in hallow water. Based on Bretschneider’s method, Breschneider and Tamaye (1976) developed a method to forecast the heights of waves generated by hurricanes.

Objective Their numerical results did not agree closely with field measurements. The mechanism of swell generation by typhoons is extremely complicated, so no physical model is currently available to describe swell motion. A neural network method is used herein to improve predictions of typhoon swell. 7

Objective Neural networks are data-oriented, meaning that the relationship between the input and the output parameters is not necessarily assumed to be fixed. An ANN can tolerate errors in input data and still yield solutions. They can also adjust themselves effectively to new input data. 8

2.Back-propagation neural network BPN is a supervised learning model that mimics a human being’s nerve system. Learning from past records (experiences), BPN can optimally predict a target’s future behaviors. 9

2.Back-propagation neural network 10

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3.Forming the BPN framework Fifteen sets of typhoon-related meteorological data and the corresponding time series of significant wave height data near Hualien and Suau Harbors. It provided by Central Weather Bureau in Taiwan, were used to establish the BPN framework and to confirm the ability of the network to forecast accurately. 13

3.Forming the BPN framework Define six parameters W max ： the maximum speed of the wind storms. V ： the speed of the typhoon. d ： the distance from the center of typhoon to the observing station. R 7 ： the radius of force 7 wind. θ 1 ： the azimuthal angle. θ 2 ： the angle between the direction of motion of the typhoon and the line that connects the center of the typhoon to the observing station. 14

3.Forming the BPN framework 15 root-mean-squared values (rms) of E.

3.Forming the BPN framework 16

3.Forming the BPN framework H p(t+1) is significant wave height predicted for the next hour at the observation station. 17

3.Forming the BPN framework 18 when η = 5 → 0.01 and α = 0.2

3.Forming the BPN framework 19

The mathematical expression of the BPN is 20 3.Forming the BPN framework

4. Results and discussion 21

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5. Conclusions The back-propagation neural network (BPN), an artificial neural network, mimics the nerve system of a human being. Learning from the past records (history), BPN can predict the future behavior of an object. Several data (12 sets) concerning typhoons and the associated measured wave heights at Hualien were fed into BPN to determine the optimal relationship among elements in the BPN. An optimal framework of BPN was thus developed by trial and error. 29

5. Conclusions The developed BPN was tested by predicting several examples. The BPN was found to predict the measured data very accurately. However, as the predictions are made further into the future (such as over two hours or three hours), the forecast of the BPN becomes worse perhaps because the unexpected path of the typhoons cause inaccuracies. This problem can be solved by improving the forecasts of the characteristics of typhoons and training the BPN often with new typhoon swell data. The BPN method is generally suitable for forecasting swells. 30