Calculation of design wave height and its application base on independent sample

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

Abstract

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

CLC Number:

P731.22

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.

Figures/Tables 10

Fig.1 Procedures for automated standard storm length estimation

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

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

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

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

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

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

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

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

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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