本研究根據Carrier（2003）等人所提出的CWY方法模擬海嘯初始波形並可快速計算傳遞至近岸時的溯上高度，理論基礎為一維完全非線性淺水方程且在等坡度地形上，以不同的初始波形條件求得所有可能的波形並找出影響最嚴重的波形，此法所得到的格林函數水位則稱解析格林函數（AGF），可用來建立臺灣沿海近岸區域之解析格林函數合併現有之海嘯波高資料庫以利提升預報效率。
不同振幅比值（A1/A2）所建置出的任意波形的結果顯示，以A2為負所得到的PG wave（A1/A2 =0）及M1 wave（A1/A2 =1.2）相較於其他波形有較高的溯上高度及溢淹距離。再以PG wave做連續波形變化得到的結果大致相同，故以一PG wave即可得到最嚴重的結果。而將PG wave與M1 wave做類波數參數（k）變化即週期改變的結果則以M1 wave有較嚴重的結果於k1 = 33，k2 = 1.69，k1 /k2 =19.5266的波形，其可能為兩波的溯上疊合而造成嚴重結果。k的變化所得到的M1 wave結果是在固定兩波的時間及空間間距下，縮短兩波的間距x01 與x02 差值為1的情況下則會得到最嚴重的結果。另採用海嘯數值模式COMCOT代入等坡度地形及實際地形模擬並證明與CWY方法有一致的結果。

According to the CWY approach derived by Carrier et al. (2003) based on 1-D fully nonlinear shallow water equations over a uniform constant slope, it can have all possible waveforms for the conditions of various initial waveforms, then determine the highest runup height. The arbitrary water elevation is called analytical Green’s function (AGF) by CWY. It can be developed a fast forecast system for the tsunami elevation beside the inshore coasts of Taiwan based on the analytical Green’s function.
The different amplitude ratios (A1/A2) can generate the arbitrary waveforms, it is shown that the PG wave (A1/A2 =0) and the M1 wave (A1/A2 =1.2) has the highest runup height and the farest inundation distance comparing with other possible waveforms as A2 is negative. Additionally, the continuous PG wave result is coincident with the single PG wave. Then change the parameter k that mean period of the two waveforms, it is shown that the M1 wave (k1=33, k2=1.69, k1 /k2=19.5266) has the higher runup height then the PG wave. It may be resulted from the overlap of the runup of the two wave. The temporal interval t01 and t02 are fixed at the before mentioned, Then to shortened the temporal interval x01 and x02 , as it equal to 1, has the worsest result. To verify the CWY approach, simulations on Cornell Multigrid Coupled Tsunami (COMCOT) model is also executed and the results agrees well with the CWY results.

摘要 ........................................................................................................................................ i
Abstract .................................................................................................................................. ii
目錄 ...................................................................................................................................... iii
圖目錄 ................................................................................................................................... v
表目錄 ................................................................................................................................ viii
第一章 緒論 .......................................................................................................................... 1
1.1 前言 ..................................................................................................................... 1
1.2 研究動機與目的 ................................................................................................. 2
1.3 本文內容 ............................................................................................................. 4
第二章 文獻回顧 .................................................................................................................. 5
2.1 海嘯的模擬 ......................................................................................................... 5
2.2 格林函數 ............................................................................................................. 7
第三章 研究方法 .................................................................................................................. 8
3.1 CWY方法 ............................................................................................................ 8
3.1.1 初始波形 ................................................................................................. 13
3.2 COMCOT模式 .................................................................................................. 18
第四章 模擬結果 ................................................................................................................ 19
4.1 CWY方法模擬結果 .......................................................................................... 19
4.1.1 不同振幅比（A1/A2）的波形比較 ........................................................ 21
4.1.2 嚴重結果的波形之變化比較 ................................................................. 27
4.1.3 不同類波數參數k的波形比較 ............................................................. 32
IV
4.1.4 不同初始波形空間差（x02-x01）之變化比較 ....................................... 39
4.1.5 不同坡度的綜合比較 ............................................................................. 43
4.2 CWY方法與COMCOT的驗證及比較結果 ................................................... 48
4.2.1 在等斜坡地形下之CWY方法與COMCOT結果比較 ...................... 48
4.2.2 在實際地形下之CWY方法與COMCOT結果比較 .......................... 52
第五章 結論 ........................................................................................................................ 56
參考文獻 .............................................................................................................................. 57
附錄一 CWY方法-二階偏微分解ψ及格林函數G之演算 ........................................ 60
附錄二 COMCOT模式 .................................................................................................... 62

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