基于独立样本的设计波高推算及其应用

doi:10.3969/j.issn.1001-909X.2023.03.007

摘要/Abstract

摘要：

极值样本的选取和分布模型的确定是设计波高推算中的两个关键环节。使用阈值法选取波高过阈样本作为极值样本时,常用标准风暴长度法对超出量序列进行“去聚类”处理,以使样本符合独立性标准。然而标准风暴长度法中的标准风暴长度需要人为选择,增加了取样结果的不确定性。本文提出了一种自动的标准风暴长度估计方法,并基于该方法选取了粤西海域的波高过阈样本。波高过阈样本具有尖峰、厚尾的统计特征,为了更准确地拟合该样本,本文基于组合模型原理构建了一种新的分布模型——Gumbel-Pareto分布模型,并用该模型进行了粤西海域的设计波高推算,结果表明Gumbel-Pareto分布对波高过阈样本的拟合优度比Gumbel分布和广义Pareto分布更高,可以为大型海洋工程设计波高的确定提供参考。

关键词: 独立样本, 标准风暴长度, Gumbel-Pareto分布, 设计波高推算

Abstract:

The selection of extreme value samples and the determination of distribution models are two crucial aspects when calculating the design wave height. When selecting extreme value samples using the peaks over threshold method, the standard storm length method is commonly used to “de-cluster” the exceedances in order to make the samples conform to independence standards. However, the crucial parameter in the standard storm length method needs to be manually selected which increases the uncertainty of samples. In this paper, an automatic standard storm length estimation method is proposed, then the wave height peaks over threshold sample in the western Guangdong sea area is selected based on this method. To accurately fit the sharp peak and heavy tail of the wave height peaks over threshold sample, the combined distribution method is used to construct a new model: Gumbel-Pareto distribution model. Based on this model, the design wave height calculation is carried out in the western Guangdong sea area. The result shows that the goodness of fit for the Gumbel-Pareto distribution model to the wave height peaks over threshold sample is higher than that of Gumbel distribution and Generalized Pareto distribution, which can offer a reasonable reference for the design of large offshore engineering.

Key words: independent samples, standard storm length, Gumbel-Pareto distribution, design wave height calculation

中图分类号:

P731.22

刘桂林, 房丹, 宋时春, 刘泊湖. 基于独立样本的设计波高推算及其应用[J]. 海洋学研究, 2023, 41(3): 73-82.

LIU Guilin, FANG Dan, SONG Shichun, LIU Bohu. Calculation of design wave height and its application base on independent sample[J]. Journal of Marine Sciences, 2023, 41(3): 73-82.

图/表 10

图1 自动的标准风暴长度估计方法

Fig.1 Procedures for automated standard storm length estimation

图2 Gumbel-Pareto分布的p.d.f.曲线

Fig.2 The p.d.f. curves of Gumbel-Pareto distribution

图3 日最大波高数据的平均剩余量图(a)和GPD参数图(b,c)

Fig.3 Mean excess plot (a) and GPD parameters’ stability plot (b,c) of wave height daily maxima data

图4 原始波高序列、波高超出量序列、波高过阈样本及阈值

Fig.4 Original wave height series, wave height exceedences, wave height peaks over threshold sample and the threshold

图5 原始波高序列(a)和波高过阈样本(b)的自相关图

Fig.5 Autocorrelation plot of original wave height series (a) and wave height peaks over threshold sample (b)

表1 样本的主要统计特征量

Tab.1 Main statistical characteristics of samples

样本	尾部指数	均值/m	方差/m²	偏度/m³	峰度/m³
波高过阈样本	3.059	4.351	1.798	1.092	3.124
波高年极值样本	9.958	4.610	2.611	0.437	2.354

表2 分布参数估计及K-S检验结果

Tab.2 Results of parameters’ estimation and K-S tests

样本	分布模型	参数	参数估计值	K-S检验的p值
波高过阈样本	Gumbel-Pareto 分布	β	2.839	0.807
		α	1.695
		σ	3.677
	Gumbel 分布	尺度	0.894	0.419
	Gumbel 分布	位置	3.772	0.419
	GPD	形状	0.076	0.322
		尺度	2.120
		位置	2.900
波高年极值样本	Gumbel-Pareto 分布	β	2.497	0.305
		α	0.970
		σ	3.584
	Gumbel 分布	尺度	1.362	0.689
	Gumbel 分布	位置	3.855	0.689
	GPD	形状	0.268	0.272
		尺度	3.110
		位置	1.500

图6 Gumbel-Pareto分布对波高过阈样本的拟合优度检验图

Fig.6 Goodness of fit test plot of Gumbel-Pareto distribution for wave height peaks over threshold sample

图7 波高过阈样本直方图及不同分布的p.d.f.曲线

Fig.7 Histogram of the wave height peaks over threshold sample and p.d.f. curves of different distributions

表3 不同分布模型计算的20年、50年、100年和500年一遇设计波高

Tab.3 20-, 50-,100-, 500-year return levels of design wave height calculated by different distribution models

重现期/年	设计波高/m
重现期/年	Gumbel-Pareto分布	Gumbel分布	GPD
20	6.037	5.904	7.646
50	7.346	6.748	10.060
100	8.500	7.376	11.990
500	11.890	8.821	16.910

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