A Probabilistic Metocean Model for Mooring Response in Gulf of Mexico Hurricanes

2013 ◽  
Author(s):  
Jan Mathisen ◽  
Torfinn Hørte
Keyword(s):  
Wave Height ◽  
Time Variation ◽  
Significant Wave Height ◽  
Short Interval ◽  
Random Variables ◽  
Extreme Value Distribution ◽  
Line Tension ◽  
Extreme Value ◽  
Value Distribution ◽  
Significant Wave

Hindcast data for a specific location is utilised to develop a joint probability function for the metocean variables that are expected to have a significant effect on mooring line tensions for a floating platform moored at that location. The main random variables comprise: peak significant wave height, peak wind speed, peak surface current speed, peak wave direction, peak wind direction and peak current direction, where “peak” indicates the maximum intensity of the metocean effect during a random hurricane. The time lead of peak wind relative to peak waves and the time lag of peak current after peak wind are included as random variables. It is also necessary to describe the time variation around the peak events. Simple models are assumed based on inspection of the time variations during severe hurricanes. Only the part of the hurricane during which the significant wave height exceeds 80% of the peak value is taken into account. The duration of this interval is included. Linear variation is assumed for the directions, hence the rates of change of the 3 directions are included. A linear (triangular) plus parabolic model is assumed for the time variation of the intensities of the 3 metocean effects around their respective peaks. A single parameter is required to define the proportion of linear and parabolic models for each effect and the values of this parameter for each of the 3 metocean effects are also included as random variables. A random hurricane can be drawn from this metocean model, such that the time variation of the metocean actions is deterministic once the values of the random variables have been selected. The overall duration of the hurricane is split into short intervals, each of 15 minutes duration, such that stationary response may be assumed during each short interval. The extreme value distribution of line tension during each short interval is obtained. These distributions are combined to obtain the extreme distribution of line tension during the hurricane. Second order reliability methods are applied to integrate over the distribution of the metocean variables and obtain the distribution of extreme tension during a random hurricane. The annual frequency of hurricanes is used to derive the annual extreme value distribution of line tension. The model is intended for the reliability analysis of the ultimate limit state of mooring lines, but may also be applicable to other response variables. The present paper is primarily concerned with the metocean model, but it is intended to include sample results for the extreme line tension.

Prediction of Mooring Line Tensions for Hurricane Conditions in the Gulf of Mexico

2014 ◽  
Author(s):  
Jan Mathisen ◽  
Torfinn Hørte
Keyword(s):  
Short Interval ◽  
Extreme Value Distribution ◽  
Line Tension ◽  
Time Domain Analysis ◽  
Extreme Value ◽  
Value Distribution ◽  
Mooring Line ◽  
Response Analysis ◽  
Short Term ◽  
Tension Distribution

A probabilistic metocean model for hurricane conditions is briefly described. The model is based on site-specific, hindcast data and defines the time variation of the metocean conditions during the realisation of a hurricane at the site. The annual extreme value distribution of mooring line tension for a large, semi-submersible, mobile drilling unit is computed. Time domain analysis is applied to obtain the short-term, extreme value distribution of line tension, conditional on stationary metocean conditions. A large number of different conditions are considered. A response surface is used to interpolate on the short-term distribution parameters in order to describe the tension response during the varying conditions associated with the passage of a hurricane. The hurricane duration is split into a sequence of 15-minute intervals such that the conditions can be assumed stationary during each such short interval. The tension distribution, conditional on the realisation of a hurricane, is accumulated across the sequence of short intervals. The distribution of hurricanes is taken into account to obtain the tension distribution in a random hurricane. Finally, the frequency of hurricanes is taken into account to give the annual extreme distribution of line tension. The characteristic tension computed using 10-year return conditions and the ISO 19901-7 design standard is found to correspond to a return period of 29 years in the test case. The effects of various assumptions in the design analysis are investigated. Sensitivities to simplifications of the metocean model are considered. The effects of uncertainties in the response calculation and in the distribution of peak significant wave height during hurricanes are quantified and included in the response analysis.

Modelling the Seasonality of Extreme Waves in the Gulf of Mexico

2008 ◽  
Author(s):  
Philip Jonathan ◽  
Kevin Ewans
Keyword(s):  
Gulf Of Mexico ◽  
Wave Height ◽  
Significant Wave Height ◽  
Poisson Model ◽  
Extreme Value ◽  
Extreme Waves ◽  
Significant Wave ◽  
Seasonal Model ◽  
Pareto Model ◽  
Optimal Value

Statistics of storm peaks over threshold depend typically on a number of covariates including location, season and storm direction. Here, a non-homogeneous Poisson model is adopted to characterise storm peak events with respect to season for two Gulf of Mexico locations. The behaviour of storm peak significant wave height over threshold is characterised using a generalised Pareto model, the parameters of which vary smoothly with season using a Fourier form. The rate of occurrence of storm peaks is also modelled using a Poisson model with rate varying with season. A seasonally-varying extreme value threshold is estimated independently. The degree of smoothness of extreme value shape and scale, and the Poisson rate, with season, is regulated by roughness-penalised maximum likelihood; the optimal value of roughness selected by cross-validation. Despite the fact that only the peak significant wave height event for each storm is used for modelling, the influence of the whole period of a storm on design extremes for any seasonal interval is modelled using the concept of storm dissipation, providing a consistent means to estimate design criteria for arbitrary seasonal intervals. Characteristics of the 100-year storm peak significant wave height, estimated using the seasonal model, are examined and compared to those estimated ignoring seasonality.

scholarly journals Tail Properties and Asymptotic Expansions for the Maximum of the Logarithmic Skew-Normal Distribution

2013 ◽  
Vol 50 (3) ◽  
pp. 900-907 ◽  
Author(s):  
Xin Liao ◽  
Zuoxiang Peng ◽  
Saralees Nadarajah
Keyword(s):  
Asymptotic Expansion ◽  
Convergence Rate ◽  
Normal Distribution ◽  
Asymptotic Expansions ◽  
Random Variables ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Skew Normal Distribution ◽  
Skew Normal

We discuss tail behaviors, subexponentiality, and the extreme value distribution of logarithmic skew-normal random variables. With optimal normalized constants, the asymptotic expansion of the distribution of the normalized maximum of logarithmic skew-normal random variables is derived. We show that the convergence rate of the distribution of the normalized maximum to the Gumbel extreme value distribution is proportional to 1/(log n)1/2.

Limit laws for maxima of a sequence of random variables defined on a Markov chain

1970 ◽  
Vol 2 (2) ◽  
pp. 323-343 ◽  
Author(s):  
Sidney I. Resnick ◽  
Marcel F. Neuts
Keyword(s):  
Markov Chain ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Extreme Value Distributions ◽  
Limit Laws ◽  
Limiting Behavior ◽  
Normalizing Constants

Consider the bivariate sequence of r.v.'s {(Jn, Xn), n ≧ 0} with X0 = - ∞ a.s. The marginal sequence {Jn} is an irreducible, aperiodic, m-state M.C., m < ∞, and the r.v.'s Xn are conditionally independent given {Jn}. Furthermore P{Jn = j, Xn ≦ x | Jn − 1 = i} = pijHi(x) = Qij(x), where H1(·), · · ·, Hm(·) are c.d.f.'s. Setting Mn = max {X1, · · ·, Xn}, we obtain P{Jn = j, Mn ≦ x | J0 = i} = [Qn(x)]i, j, where Q(x) = {Qij(x)}. The limiting behavior of this probability and the possible limit laws for Mn are characterized.Theorem. Let ρ(x) be the Perron-Frobenius eigenvalue of Q(x) for real x; then:(a)ρ(x) is a c.d.f.;(b) if for a suitable normalization {Qijn(aijnx + bijn)} converges completely to a matrix {Uij(x)} whose entries are non-degenerate distributions then Uij(x) = πjρU(x), where πj = limn → ∞pijn and ρU(x) is an extreme value distribution;(c) the normalizing constants need not depend on i, j;(d) ρn(anx + bn) converges completely to ρU(x);(e) the maximum Mn has a non-trivial limit law ρU(x) iff Qn(x) has a non-trivial limit matrix U(x) = {Uij(x)} = {πjρU(x)} or equivalently iff ρ(x) or the c.d.f. πi = 1mHiπi(x) is in the domain of attraction of one of the extreme value distributions. Hence the only possible limit laws for {Mn} are the extreme value distributions which generalize the results of Gnedenko for the i.i.d. case.

Modeling the Seasonality of Extreme Waves in the Gulf of Mexico

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
Philip Jonathan ◽  
Kevin Ewans
Keyword(s):  
Gulf Of Mexico ◽  
Wave Height ◽  
Significant Wave Height ◽  
Poisson Model ◽  
Extreme Value ◽  
Significant Wave ◽  
Generalized Pareto ◽  
Seasonal Model ◽  
Pareto Model ◽  
Optimal Value

Statistics of storm peaks over threshold depend typically on a number of covariates including location, season, and storm direction. Here, a nonhomogeneous Poisson model is adopted to characterize storm peak events with respect to season for two Gulf of Mexico locations. The behavior of storm peak significant wave height over threshold is characterized using a generalized Pareto model, the parameters of which vary smoothly with season using a Fourier form. The rate of occurrence of storm peaks is also modeled using a Poisson model with rate varying with season. A seasonally varying extreme value threshold is estimated independently. The degree of smoothness of extreme value shape and scale and the Poisson rate with season are regulated by roughness-penalized maximum likelihood; the optimal value of roughness is selected by cross validation. Despite the fact that only the peak significant wave height event for each storm is used for modeling, the influence of the whole period of a storm on design extremes for any seasonal interval is modeled using the concept of storm dissipation, providing a consistent means to estimate design criteria for arbitrary seasonal intervals. The characteristics of the 100 year storm peak significant wave height, estimated using the seasonal model, are examined and compared with those estimated ignoring seasonality.

Omnidirectional Return Values for Storm Severity From Directional Extreme Value Models: The Effect of Physical Environment and Sample Size

2014 ◽  
Author(s):  
David Randell ◽  
Elena Zanini ◽  
Michael Vogel ◽  
Kevin Ewans ◽  
Philip Jonathan
Keyword(s):  
Sample Size ◽  
Wave Height ◽  
Significant Wave Height ◽  
Extreme Value ◽  
Dependence Structure ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Directional Model ◽  
Significant Wave ◽  
Extreme Storm

Ewans and Jonathan [2008] shows that characteristics of extreme storm severity in the northern North Sea vary with storm direction. Jonathan et al. [2008] demonstrates, when directional effects are present, that omnidirectional return values should be estimated using a directional extreme value model. Omnidirectional return values so calculated are different in general to those estimated using a model which incorrectly assumes stationarity with respect to direction. The extent of directional variability of extreme storm severity depends on a number of physical factors, including fetch variability. Our ability to assess directional variability of extreme value parameters and return values also improves with increasing sample size in general. In this work, we estimate directional extreme value models for samples of hindcast storm peak significant wave height from locations in ocean basins worldwide, for a range of physical environments, sample sizes and periods of observation. At each location, we compare distributions of omnidirectional 100-year return values estimated using a directional model, to those (incorrectly) estimated assuming stationarity. The directional model for peaks over threshold of storm peak significant wave height is estimated using a non-homogeneous point process model as outlined in Randell et al. [2013]. Directional models for extreme value threshold (using quantile regression), rate of occurrence of threshold exceedances (using a Poisson model), and size of exceedances (using a generalised Pareto model) are estimated. Model parameters are described as smooth functions of direction using periodic B-splines. Parameter estimation is performed using maximum likelihood estimation penalised for parameter roughness. A bootstrap re-sampling procedure, encompassing all inference steps, quantifies uncertainties in, and dependence structure of, parameter estimates and omnidirectional return values.

Seasonality and duration in extreme value distributions of significant wave height

2008 ◽  
Vol 35 (1) ◽  
pp. 131-138 ◽  
Author(s):  
Fernando J. Méndez ◽  
Melisa Menéndez ◽  
Alberto Luceño ◽  
Raúl Medina ◽  
Nicholas E. Graham
Keyword(s):  
Wave Height ◽  
Significant Wave Height ◽  
Extreme Value ◽  
Extreme Value Distributions ◽  
Significant Wave

Non-homogeneously paced random records and associated extremal processes

1978 ◽  
Vol 15 (3) ◽  
pp. 552-559 ◽  
Author(s):  
Donald P. Gaver ◽  
Patricia A. Jacobs
Keyword(s):  
Poisson Process ◽  
Random Variables ◽  
Extreme Value Distribution ◽  
Rate Function ◽  
Extreme Value ◽  
Value Distribution ◽  
Homogeneous Poisson Process ◽  
Extremal Process ◽  
Extremal Processes ◽  
Non Homogeneous Poisson Process

A study is made of the extremal process generated by i.i.d. random variables appearing at the events of a non-homogeneous Poisson process, 𝒫. If 𝒫 has an exponentially increasing rate function, then records eventually occur in a homogeneous Poisson process. The size of the latest record has a classical extreme value distribution.

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