臺灣海域之波高分佈及其週期分佈之比較

Abstract

本研究利用交通部運輸研究所港灣技術研究中心提供之2006 年 安平港與臺北港的波浪資料，探討其波高分佈、週期分佈與波高週期 聯合分佈。在波高方面分別以Gamma、Rayleigh、Normal 及Weibull 分佈等四種機率分佈函數(probability density function)，週期方面則以Gamma、Erlang、Rayleigh 及Longuet-Hinggins 等四種機率分佈函數，利用直方圖套配(fitted)，根據均方根誤差(MSE)、相關性(R2)、多峰型直方圖與離島型直方圖等四種指標，判斷何種分佈模式較近似實際波高與週期分佈情形。在波高方面最適分佈為Weibull 分佈，週期是Erlang 分佈為最適分佈。波高與週期聯合分佈則是Cavani□ (1976)所提出的聯合機率分佈會比Longuet-Higgins (1983)的聯合機率分佈更為適當。 另外，本文以頻譜矩之分析，比較安平港、臺北港與花蓮港之理 論值與統計值示性波高間的差異性，並根據Erlang 的理論參數，推 估其理論示性週期與平均週期，並提出經驗公式，可迅速推估其理論 週期的參數。在各港的月、季與年之示性波高(Hs)與示性週期(Ts)的 最適分佈，本研究發現均為Gamma 分佈，由此之統計特性，於工程 設計上可作為參考之依據。

The wave data at Taipei harbor and An-ping harbor collected by research center of marine and harbor technology for year 2006 are used to investigate the characteristics of wave height distribution, period distribution and their joint distribution. The best distribution of wave height is examined to be Weibull distribution for both harbors comparing among four possible distributions based on four criteria, that are correlation coefficient, mean square error, percentage of zero and two peak histogram. The best fitting for the distribution of wave period is Erlang for both harbors following the procedure of fitting significant wave height. The joint distribution of wave height and period proposed by Cavani□ (1976) describes for the distribution of observed data much better than that of Longuet-Higgins (1983). When the best fitting distributions are observed, the corresponding statistical properties, such are mean wave height, significant wave height and maximum wave heights, are also investigated. The results show that the average of is higher than the observed one by about 15-20 % for both harbor. The maximum wave height is hardly expressed by the Weibull distribution. The distributions of monthly, seasonally and yearly significant wave heights and period for both harbors are studied and the best fitting distribution is Gamma function. The proposed results of monthly and yearly distributions of significant wave height and period are useful for engineering practice.