花蓮海域波浪之波高分佈及其統計特性研究

Abstract

本研究利用交通部港灣技術研究中心運輸研究所提供之花蓮2004年波浪資料，分別以Gamma、Rayleigh、Normal及Weibull分佈等四種機率分佈函數與其波高直方圖套配(fitted)，再根據均方根誤(MSE)及相關性(R2)以判斷何種分佈模式較近似花蓮港實際波高分佈情形，而為進一步探討波高直方圖分組組數與分佈函數密合程度之關係，分 別以多峰直方圖與離島型直方圖來評估其波高直方圖之較佳分組數。

根據分析結果，驗證出花蓮港之波高分佈較近似於Weibull佈，其波高直方圖適合分組組數大概介於5至8組，依其分佈特性，並以最大概似法估其參數，可由參數計算出相關理論波高統計值，如示性波高、波高均方根值、最大波高與波高平均值，經與實際波高統計值比較分析後，以Weibull分佈所計算而得之理論示性波高，與實際示性波高甚為接近。因此本文進一步建立其它相關波高統計值與示性波高之關係，其關係一旦建立，即可藉示性波高以推得其它波高統計值，而本研究同時比較其理論與實際值之差異，以了解花蓮海域之波高統計特性及以Weibull分佈理論計算的可行性，此結果對於往後分析花蓮港之波浪現象，與工程設計上可作為參考之依據。

Four distributions, that are Gamma, Normal, Rayleigh and Weibull distribution, are used to approximate the histogram of the significant wave heights of each measured data during 20 min at the Hua-lien waters for 2004. The best fitting distribution is the Weibull distribution among these four distributions. The expressions for significant wave height、average wave height、maxium wave height and wave height root-mean square are derived in terms of the parameters in the Weibull distribution. According to these expressions, the estimated significant wave height has close agreement with the observed significant wave height. It is found that the histogram of the values of the significant waves from 20-min records of every month, quarter-year, and one year also shows that the Weibull distribution is also the best one among all examined distributions.