T年重现期波高的最大熵估计  

Maximum entropy estimation of T-year extreme waveheights

作　　者：张军[1] 葛勇[1] 陈航宇[1] 周喜武[1] 

机构地区：[1]国家海洋局第三海洋研究所,福建厦门361005

出　　处：《台湾海峡》2006年第2期153-159,共7页Journal of Oceanography In Taiwan Strait

基　　金：国家海洋局第三海洋研究所科技体制改革资助项目(HF05004)

摘　　要：本文在最大熵原则的基础上,通过解一条件变分问题,导出一种由观测数据估计T年（常用的有50a或100a）重现期波高的新方法.本文导出的概率密度函数为f4（H）=αH^γe^-βH4,式中参量α、β、γ可以由年极值波高H的1～4阶分布矩（Hm^-,m=1,2,3,4）显式地表示出来.其具有如下的优越性：（1）参量中包含了H的3阶和4阶分布矩,适用于描述不确定性很大的海浪的重现期波高;（2）符合最大熵原则,即其信息熵最大,从而特别适用于重现期波高的估计;（3）形式简单且其参量容易由已知观测数据确定,便于理论和实际应用.作者对两个水文观测站的实测数据,分别使用该方法,及一些现有常用的方法计算其50、100a重现期波高.比较计算结果表明该方法非常接近于皮尔逊-Ⅲ方法和龚贝尔方法的结果.A new method of estimating the T （50 or 100） -year return-period waveheight, namely, the extreme waveheight expected to occur in T years from a set of observed data is presented on the basis of the maximum entropy principle. A maximum entropy probability density function （PDF） of the the extreme waveheight H of f4 （H） = αH^γe^ -βH4 is derived through solving a conditional variation problem based on the maximum entropy principle, and its parameters α, β,γ are expressed explicitly in terms of the distribution moments of H （Hm^- = 1,2,3,4）. This PDF has the following advantages ： （ 1 ） Its parameters involve the 3rd and 4th moments,H3^- and H^4, which play the roles analogous to the skewness λ3 and kurtosis λ4 in the PDFs for surface elevation of nonlinear sea waves, such as the Gram-Charlier series PDF and beta PDF, so this PDF is suitable to estimate the T-year return-period wave height; （2） it maximizes the information entropy of H and accords with the maximum entropy principle, so it is competent for estimating the T-year return-period waveheight; and （3） it is simple and the parameters are easy to be determined from known data, so it is convenient to theoretical and practical applications. Example of estimating the 50- and 100-year return period waveheights by the present method and some currently used method from observed data acquired from two hydrographic stations are given. Comparison of these estimated results show that the present method is very approximately to the Pearson-Ⅲ and the Gumbel method.

关 键 词：重现期波高 最大熵原则 概率密度函数 分布矩 

分 类 号：Q958.885.3[生物学—动物学]