本文分析台灣海域颱風期間暴潮與波浪的歷史觀測資料，透過常態分布、雷禮分布、伽瑪分布、韋伯分布及一般型極端值分布與適合度檢定，推導出適合於波浪與暴潮分佈的機率密度函數，獲得波高與暴潮之最佳統計分佈。分析結果顯示台灣東岸明顯受颱風環流影響，使波高的分佈情形隨著颱風接近逐漸成長，隨著颱風的遠離，波高逐漸的下降，波高分佈均為一般形極端值分佈；而台灣西岸當發佈警報時，因中央山脈阻擋，波高的成長不似東部明顯，各海域分別為新竹伽瑪分佈，大鵬灣一般形極端值分佈分佈，澎湖 伽瑪分佈，料羅灣一般形極端值分佈分佈；而暴潮主要受氣壓影響台灣環島暴潮分佈較為一致，台灣本島均為韋伯分佈，離島的澎湖及料羅灣為一般形極端值分佈分佈，但韋伯分佈亦通過Kolmogorov Smirnov檢定。
波高與暴潮之相關性分析的結果，發現當颱風行進路徑與研究海域之岸線角度呈近直角時其波高與暴潮的相關係數最高，尤以台灣東岸的花蓮與龍洞在颱風路徑2相關係數最高，分別為花蓮的0.6583及龍洞的0.7922。而台灣西部的新竹、大鵬灣及離島澎湖、料羅灣在颱風警報期間波高與暴潮相關係數最高路徑分別為路徑1、3、4、8，在相關係數最高的颱風路徑表示大浪與暴潮同時發生的機率相對提高，在未來的海事工程結構的設計應加入考量。
由聯合機率分佈圖分析結果可知台灣東西海岸及離島地區，波高與暴潮聯合分佈的方式，因地形的影響及颱風侵襲的機率不同呈現不同的態樣，分析的結果顯示，台灣海峽離島金門與澎湖的波高暴潮聯合機率分佈範圍最廣，這代表著這些海域的波高與暴潮發生事件較為散佈，且不會集中於某一量值。
本文利用蒙地卡羅法產生亂數，來模擬波高與暴潮資料，進行不同復現期水位的推估，準確度在於實測資料的所選用之統計分佈函數是否能準確的描述出組體分佈。若統計分佈函數無法精準描述波高以及暴潮的組體分佈，將直接影響到蒙地卡羅法模擬波高與暴潮資料的準確度，並進而影響到後續復現期之分析。

It is the aim of present study to identify the best fit probability distribution and associate parameters from the historical records that could describe the occurrence probability of the typhoon waves and surges around Taiwan Waters. The probability density functions of Normal distribution, Rayleigh distribution, Gamma distribution, Weibull distribution and the Extreme Value distribution Type I are chosen as statistic models for comparative study and the tests of goodness of fitting are carried out respectively. It could be seen from the observed data that the typhoons dominated the wave field along the eastern coast of Taiwan. The significant wave heights increase with approaching typhoons and vice versa. The typhoon wave heights distribution in the eastern coast can be expressed using r effect of central mountain ridge, the wave growth rate during typhoon passage along the General form of Extreme Value Distribution function. On the other hand, due to the shelte western coasts featured much different than the eastern coast. In Hsinchu Dapeng Bay, Penghu and Kinmen areas the typhoon waves are better fit using Gamma, EVI, Gamma, EVI distribution, respectively. The typhoon surges around Taiwan Island are better fit by Weibull distribution function while in the remote islands, the EVI is better.
The results of the correlation analysis between the typhoon wave heights and surges show that the coefficient of correlation reaches to the maxima (0.6583 ~ 0.7922) when the typhoon trajectories are more perpendicular to the tangent of the coastline. This is obvious when the typhoons of the path category 2 made landfalls on the coastline section between Hualien and Longdon at the eastern coast. The typhoons of path category 1, 3, 4 and 8 brought greater impacts to Hsinchu, Dapeng Bay, Penghu and Kinmen and may causing joint high wave and surges.
The results of joint probability distribution of wave heights and surges demonstrate significant differences in the eastern and western coasts as well as the remote islands. Broad and widely distributed joint probability can be found in Kinmen and Penghu, indicating the diversity of sea state in these areas.
In order to estimate the water elevation with respect to the design return period, the Monte Carlo method is performed to simulate the wave heights and surges. It is also found that the accurate estimation of the parameters of the distribution functions play key role to the quality of Monte Carlo simulations the determination of design water level.

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