基于马尔可夫链的极值波高预测

EXTREME WAVE PREDICTION IN MARKOV CHAIN CONDITION

本文研究了由日最大波高系列估算设计极值波高时，相邻日最大波高间的相关性对极值预测的影响。从日最大波高系列遵从马尔可夫链的假定出发，考虑到国内外经常采用对数─正态分布和韦布尔分布拟合波高长期分布的现实，本文用解析法求解了对数─正态分布情况下的极值预测。同时，对解折法难以求解的非正态随机变量情况（如韦布尔分布），用计算机随机模拟方法求解其极值预测。用上述两种方法对北大西洋和北海有关日最大波高系列的预测结果表明，考虑了马尔可夫概念的预测方法，比常用预测方法所得的百年一遇设计波高值低10％左右。

This paper discusses the effect of statistical dependence of the daily maximum significant wave heights assuming they are subjected to Markov chain condition. The formula of extreme wave prediction using daily maximum significant wave heights subjected to Markov chain condition is derived as a function of joint probability distribution of successive daily maxima , marginal distribution of daily maxima , correlation coefficient between successive daily maxima and sample size for which the extreme value distribution is studied.The extreme wave height is predicted for two cases: wave data fitted to Weibull distribution and fitted to log-normal distribution. Importance sampling procedure (ISP) is used for simulation of multivariate joint probability distribution. Analytical method is also used for bivariate log-normal distribution.Based on the observed wave data in Northern North Sea from 1975 to 1984 the 100 yrs. and 10 yrs. wave heights are predicted by proposed method with Markov concept and traditional method. Predicted results show that the 100 yrs. wave height with the Markov concept is about 10% less than those predicted by traditional method.