過去數十年，許多學者利用數值模式進行風暴潮研究與速算系統之發展，但大部分模式仍有諸多限制，例如受限小區域之計算域，無法完整涵蓋颱風生命週期之風暴潮模擬，或者僅限於卡氏座標系統。因此，本研究以康乃爾大學所之開放原始碼（Open Source）多重網格海嘯模式COMCOT（Cornel Multi-grid Coupled of Tsunami Model）為基礎進行風暴潮模式之開發，並於理想條件下進行解析解之驗證。在氣象力導入部分，本研究耦合理想颱風模式Holland Model（1980）、CWB Model和大氣模式TWRF（Typhoon Weather Research and Forecasting），並且以2011年南瑪都颱風（Tyhpoon Nanmadol）和2013年蘇力颱風（Typhoon Soulik）為實際案例進行模式校驗，模擬結果和實測資料有良好之比對結果。
西元1845年（清道光25年）農曆六月初七，雲林縣口湖鄉沿海村莊因颱風暴潮影響俱為大水吞沒，超過三千人喪生，為台灣歷史上最嚴重之水災，罹難民眾就地掩埋為萬人塚，並由道光皇帝賜名萬善同歸弔祭此事件（曾，1978；金，2002）。本研究以數值模式為主，輔以野外調查，還原1845年雲林口湖歷史風暴潮事件。由近代歷史風暴潮紀錄，1986年韋恩颱風為第一個由臺灣西部直接登陸之颱風，登陸時雖僅為中度颱風，卻造成中部地區嚴重之海水倒灌，因此選定韋恩颱風為1845年雲林口湖事件之參考案例。模擬結果顯示，颱風直接由臺灣西部登陸之路徑於雲林口湖地區之暴潮偏差有高度敏感性。
本研究討論氣候變遷下與韋恩颱風相同路徑之強烈颱風事件，同時以2013年海燕颱風（Typhoon Haiyan）參數代入情境模擬，模擬結果顯示於雲林口湖地區最高有4.45公尺之暴潮偏差，若未來發生類似路徑之強烈颱風，於麥寮和梧棲等中部地區應嚴防海水倒灌之災害。

Several storm surge models had been developed in the last decades for the purposes of research and early warning. However, some deficiencies limit the model application. For example, small computational domain makes simulating the complete life cycle impossible, not to mention adopting the Cartesian coordinate system.
In this study, the open-source code, COMOCOT (Cornel Multi-grid Coupled of Tsunami Model), was chosen for developing the storm surge model, and validated with analytic solutions for the meteorological forcing terms. Parametric model, such as Holland model (1980) and CWB model, and TWRF Model (Typhoon Weather Research and Forecasting) were coupled into the code. The 2011 Typhoon Nanmadol and 2013 Typhoon Soulik events were chosen for model validation. The result comparison with the observation data was in the good agreement.
After the model development and validation, we further applied this model to the case of 1845 Kouhu storm surge event. In that event, nine villages were destroyed by a disastrous flood, and more than 3,000 inhabitants were killed. It was the most serious storm surge event in Taiwan. In this study, efforts were made for reconstructing this storm surge. According to the modern historical records, the 1986 Typhoon Wayne was the only one case that effected Kouhu significantly and chosen as the reference case. The simulation results showed that the surge deviation in Yunlin Kouhu was highly sensitive to the typhoon route if the typhoon lands at the western coast of Taiwan.
Considering the global climate change, the meteorological parameters of the 2013 Typhoon Haiyan and the route of 1986 Typhoon Wayne were adopted. The simulation results showed that the 4.45 m surge deviation was observed in Yunlin Kouhu. Some places in middle Taiwan, such as Wuchi and Mailiao, were under the threat of inland flooding.

一、 緒論..............................................................................................................1
1.1 研究背景與動機.....................................................................................1
1.2 文獻回顧.................................................................................................4
1.2.1 風暴潮研究之文獻回顧..............................................................4
1.2.2 風暴潮速算系統與作業化模式之文獻回顧..............................9
1.2.3 COMCOT 風暴潮模式開發之文獻回顧 ..................................13
1.2.4 歷史風暴潮事件之文獻回顧....................................................15
1.3 研究方法...............................................................................................18
二、 數值模式介紹............................................................................................19
2.1 數值模式簡介.......................................................................................19
2.2 統御方程式...........................................................................................20
2.2.1 線性淺水波方程式....................................................................21
2.2.2 線性淺水波方程式之有限差分離散........................................22
2.2.3 非線性淺水波方程式................................................................24
2.2.4 非線性淺水波方程式之中央差分離散....................................27
2.3 移動邊界法...........................................................................................32
2.4 巢狀網格系統.......................................................................................34
2.5 大氣模式耦合.......................................................................................37
2.5.1 Holland Model ............................................................................37
2.5.2 CWB Model................................................................................38
2.5.3 TWRF Model..............................................................................41
2.5.4 風剪力和風場向量....................................................................43
2.6 風暴潮速算系統介紹...........................................................................45
三、 模式校驗....................................................................................................48
3.1 邊界條件測試.......................................................................................48
3.2 解析解驗證...........................................................................................54
3.2.1 壓力梯度之解析解驗證............................................................54
3.2.2 風剪力之解析解驗證................................................................62
3.3 歷史個案分析.......................................................................................69
3.3.1 地形與網格設置........................................................................69
3.3.2 數值潮位計設置........................................................................70
3.3.3 南瑪都颱風................................................................................73
3.3.4 蘇力颱風..................................................................................130
四、 1845 年雲林口湖風暴潮事件還原.........................................................198
4.1 雲林口湖風暴潮事件介紹.................................................................198
4.2 韋恩颱風.............................................................................................201
4.2.1 韋恩颱風介紹..................................................................201
4.2.2 1986 年韋恩颱風之數值模擬..................................................203
4.2.3 模擬結果之序列資料比較......................................................219
4.2.4 韋恩颱風模擬之結果與討論..................................................233
4.3 雲林口湖事件之還原.........................................................................234
4.3.1 雲林口湖事件情境還原之數值模擬......................................234
4.3.2 雲林口湖事件還原之暴潮偏差時序列資料比較..................250
4.3.3 雲林口湖事件還原之結果與討論..........................................263
五、 結論與建議..............................................................................................264
5.1 結論.....................................................................................................264
5.2 建議.....................................................................................................265
六、 參考文獻..................................................................................................266

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