Metocean Design Criteria Considerations in South China Sea by Adopting Multivariate Extreme Value Theory

2017 ◽  
Author(s):  
Ping Li ◽  
Qi Zhu ◽  
Chunqi Zhou ◽  
Linbin Li ◽  
Hongtao Li
Keyword(s):  
Probability Distribution ◽  
South China Sea ◽  
Joint Probability ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Design Criteria ◽  
Joint Probability Distribution ◽  
Wind Speeds ◽  
Wave Heights ◽  
Significant Wave Heights

The proper determination of metocean design criteria is critical for offshore structures. We study in this paper the univariate and multivariate compound extreme value theories and their applications to metocean data. Firstly, we adopt Compound Extreme Value Distribution (CEVD) method to derive the marginal distributions of wind speeds and significant wave heights respectively. Modelling uncertainties are considered with different distribution models. Secondly, the basic theory of Bivariate Compound Extreme Value Distribution (BCEVD), especially Poisson Bivariate Gumbel Logistic Distribution (PBGLD) is reviewed and utilized to analyze the joint probability distribution of significant wave heights and the concomitant wind speeds. Thirdly, Extreme Water Level (EWL) which is defined as the combination of wave crest, surge height and tidal elevation, is analyzed. We treat astronomical tide as a deterministic phenomenon and estimate the joint probability distribution of crest heights and storm surges. Case studies are given for picked position points in Northern South China Sea with 40 years hindcasted data. The results of this paper could give some knowledge for the determination and refinement of metocean design parameters.

Statistics of Extreme Wind Speeds and Wave Heights by the Bivariate ACER Method

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Arvid Naess ◽  
Oleh Karpa
Keyword(s):  
Time Series ◽  
Extreme Value Distribution ◽  
Offshore Structures ◽  
Accurate Estimate ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Extreme Value Statistics ◽  
Wind Speeds ◽  
Wave Heights

In the reliability engineering and design of offshore structures, probabilistic approaches are frequently adopted. They require the estimation of extreme quantiles of oceanographic data based on the statistical information. Due to strong correlation between such random variables as, e.g., wave heights and wind speeds (WS), application of the multivariate, or bivariate in the simplest case, extreme value theory is sometimes necessary. The paper focuses on the extension of the average conditional exceedance rate (ACER) method for prediction of extreme value statistics to the case of bivariate time series. Using the ACER method, it is possible to provide an accurate estimate of the extreme value distribution of a univariate time series. This is obtained by introducing a cascade of conditioning approximations to the true extreme value distribution. When it has been ascertained that this cascade has converged, an estimate of the extreme value distribution has been obtained. In this paper, it will be shown how the univariate ACER method can be extended in a natural way to also cover the case of bivariate data. Application of the bivariate ACER method will be demonstrated for measured coupled WS and wave height data.

Statistical Analysis of Ocean Environmental Conditions With PTGEVD

2004 ◽  
Author(s):  
Sheng Dong ◽  
Xiaoli Hao
Keyword(s):  
Environmental Conditions ◽  
Oil And Gas ◽  
Design Method ◽  
Discrete Distribution ◽  
Extreme Value Distribution ◽  
Offshore Structures ◽  
Extreme Value ◽  
Value Distribution ◽  
Design Criteria ◽  
Wind Speeds

Poisson Trivariate Gumbel Extreme Value Distribution (PTGEVD), a multivariate from of the Compound Extreme Value Distribution, is presented to solve for the ocean environmental design criteria in this paper. The proposed model is combined with a discrete distribution of storm frequency and a continuous trivariate extreme value distribution of environmental conditions simultaneously occurred in storm processes. Different from traditional univariate design method, the proposed design method with PTGEVD can reflect the combined effect of multi-loads on offshore structures and result in reasonable reduction of the design criteria. Validated with the synchronically measured significant wave heights, wind speeds and current velocities of 20 typhoon processes, PTGEVD model shows that it is easy to be applied and has considerable economic potential in the exploitation of ocean oil and gas, especially for marginal field.

scholarly journals Idealized models of the joint probability distribution of wind speeds

2018 ◽  
Vol 25 (2) ◽  
pp. 335-353 ◽  
Author(s):  
Adam H. Monahan
Keyword(s):  
Probability Distribution ◽  
Weibull Distribution ◽  
Joint Probability ◽  
Maximum Likelihood Estimates ◽  
Horizontal Wind ◽  
Dependence Structure ◽  
Joint Probability Distribution ◽  
Rice Distribution ◽  
Wind Speeds ◽  
Bivariate Weibull Distribution

Abstract. The joint probability distribution of wind speeds at two separate locations in space or points in time completely characterizes the statistical dependence of these two quantities, providing more information than linear measures such as correlation. In this study, we consider two models of the joint distribution of wind speeds obtained from idealized models of the dependence structure of the horizontal wind velocity components. The bivariate Rice distribution follows from assuming that the wind components have Gaussian and isotropic fluctuations. The bivariate Weibull distribution arises from power law transformations of wind speeds corresponding to vector components with Gaussian, isotropic, mean-zero variability. Maximum likelihood estimates of these distributions are compared using wind speed data from the mid-troposphere, from different altitudes at the Cabauw tower in the Netherlands, and from scatterometer observations over the sea surface. While the bivariate Rice distribution is more flexible and can represent a broader class of dependence structures, the bivariate Weibull distribution is mathematically simpler and may be more convenient in many applications. The complexity of the mathematical expressions obtained for the joint distributions suggests that the development of explicit functional forms for multivariate speed distributions from distributions of the components will not be practical for more complicated dependence structure or more than two speed variables.

Statistics of Extreme Wind Speeds and Wave Heights by the Bivariate ACER Method

2013 ◽  
Author(s):  
Arvid Naess ◽  
Oleh Karpa
Keyword(s):  
Time Series ◽  
Extreme Value Distribution ◽  
Offshore Structures ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Extreme Value Statistics ◽  
Wind Speeds ◽  
Wave Heights ◽  
Extreme Wind Speeds

In the reliability engineering and design of offshore structures probabilistic approaches are frequently adopted. They require the estimation of extreme quantiles of oceanographic data based on the statistical information. Due to strong correlation between such random variables as e.g. wave heights and wind speeds, application of the multivariate, or bivariate in the simplest case, extreme value theory is sometimes necessary. The paper focuses on the extension of the ACER method for prediction of extreme value statistics to the case of bivariate time series. Using the ACER method it is possible to provide an estimate of the exact extreme value distribution of a univariate time series. This is obtained by introducing a cascade of conditioning approximations to the exact extreme value distribution. When this cascade has converged, an estimate of the exact distribution has been obtained. In this paper it will be shown how the univariate ACER method can be extended in a natural way to also cover the case of bivariate data. Application of the bivariate ACER method will also be demonstrated at the measured coupled wind speed and wave height data.

scholarly journals Idealized Models of the Joint Probability Distribution of Wind Speeds

2017 ◽  
Author(s):  
Adam H. Monahan
Keyword(s):  
Probability Distribution ◽  
Weibull Distribution ◽  
Joint Probability ◽  
Maximum Likelihood Estimates ◽  
Horizontal Wind ◽  
Dependence Structure ◽  
Joint Probability Distribution ◽  
Rice Distribution ◽  
Wind Speeds ◽  
Bivariate Weibull Distribution

Abstract. The joint probability distribution of wind speeds at two separate locations in space or points in time completely characterizes the statistical dependence of these two quantities, providing more information than linear measures such as correlation. In this study, we consider two models of the joint distribution of wind speeds obtained from idealized models of the dependence structure of the horizontal wind velocity components. The bivariate Rice distribution follows from assuming that the wind components have Gaussian and isotropic fluctuations. The bivariate Weibull distribution arises from power law transformations of wind speeds corresponding to vector components with Gaussian, isotropic, mean-zero variability. Maximum likelihood estimates of these distributions are compared using wind speed data from the mid-troposphere, from different altitudes at the Cabauw tower in the Netherlands, and from scatterometer observations over the sea surface. While the bivariate Rice distribution is more flexible and can represent a broader class of dependence structures, the bivariate Weibull distribution is mathematically simpler and may be more convenient in many applications. The complexity of the mathematical expressions obtained for the joint distributions suggests that the development of explicit functional forms for multivariate speed distributions from distributions of the components will not be practical for more complicated dependence structure or more than two speed variables.

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