Consideration of Epistemic Uncertainty in Extreme Wave Height Estimation

2014 ◽  
Author(s):  
Ryota Wada ◽  
Takuji Waseda
Keyword(s):  
Gulf Of Mexico ◽  
Observational Data ◽  
Wave Height ◽  
Extreme Values ◽  
Epistemic Uncertainty ◽  
Extreme Value Distribution ◽  
Predictive Distribution ◽  
Extreme Value ◽  
Posterior Predictive Distribution ◽  
Value Estimation

Extreme value estimation of significant wave height is essential for designing robust and economically efficient ocean structures. But in most cases, the duration of observational wave data is not efficient to make a precise estimation of the extreme value for the desired period. When we focus on hurricane dominated oceans, the situation gets worse. The uncertainty of the extreme value estimation is the main topic of this paper. We use Likelihood-Weighted Method (LWM), a method that can quantify the uncertainty of extreme value estimation in terms of aleatory and epistemic uncertainty. We considered the extreme values of hurricane-dominated regions such as Japan and Gulf of Mexico. Though observational data is available for more than 30 years in Gulf of Mexico, the epistemic uncertainty for 100-year return period value is notably large. Extreme value estimation from 10-year duration of observational data, which is a typical case in Japan, gave a Coefficient of Variance of 43%. This may have impact on the design rules of ocean structures. Also, the consideration of epistemic uncertainty gives rational explanation for the past extreme events, which were considered as abnormal. Expected Extreme Value distribution (EEV), which is the posterior predictive distribution, defined better extreme values considering the epistemic uncertainty.

DETERMINATION OF EXTREME VALUES OF WAVES, WINDS CURRENTS, AND TIDES FOR THE DESIGN OF OFFSHORE INSTALLATIONS

1974 ◽  
Vol 14 (1) ◽  
pp. 166
Author(s):  
P. M. Aagaard
Keyword(s):  
Wave Height ◽  
Extreme Values ◽  
Meteorological Data ◽  
Extreme Value Distribution ◽  
Relevant Information ◽  
Extreme Value ◽  
Distribution Functions ◽  
Design Parameters ◽  
Final Design ◽  
Wave Heights

Frequently the only relevant information available to a designer about a propective offshore platform site is its location, the water depth, and whatever can be gleaned from oceanographic atlases. In spite of this lack of data the platform designer is faced with the problem of selecting design parameters such that the proposed platform will not fail during its exposed life. He therefore needs to know what are the greatest wave height, current speed, etc., the platform will experience, and must specify studies that can provide the needed information on extreme values. This paper discusses methods used in such studies and their associated uncertainties.The method for acquiring extreme value data should be chosen on the basis of available oceanographic and meteorological data for the site, reliability requirements, time available before final design, and cost. Wave height is usually the most critical design parameter. Data over a long time span (e.g. greater than ten years) are needed to achieve reliable extreme values. Measured wave data covering such time spans are almost never available for a site of interest, and schedules seldom permit lengthy data-collection periods. Frequently the most reliable extreme wave heights can be obtained by calculating wave heights (i.e. hindcasting) from windfields derived from historical weather charts and fitting certain extreme-value distribution functions to the hindcast results. This preferred approach should include calibration of the wave height calculation method with local measured data. Alternative approaches, usually involving greater uncertainties in predicted extremes, are also appropriate for particular cases. Methods for determining extreme winds, currents, and tides are similar to those used for extreme waves, but some differences result from the nature of the phenomena and the type of data typically available.

Tree-dependent extreme values: the exponential case

1990 ◽  
Vol 27 (01) ◽  
pp. 124-133 ◽  
Author(s):  
Vijay K. Gupta ◽  
Oscar J. Mesa ◽  
E. Waymire
Keyword(s):  
Branching Process ◽  
Extreme Values ◽  
Rooted Tree ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Extinction Time ◽  
Brownian Excursion ◽  
Weighted Trees

The length of the main channel in a river network is viewed as an extreme value statistic L on a randomly weighted binary rooted tree having M sources. Questions of concern for hydrologic applications are formulated as the construction of an extreme value theory for a dependence which poses an interesting contrast to the classical independent theory. Equivalently, the distribution of the extinction time for a binary branching process given a large number of progeny is sought. Our main result is that in the case of exponentially weighted trees, the conditional distribution of n–1/2 L given M = n is asymptotically distributed as the maximum of a Brownian excursion. When taken with an earlier result of Kolchin (1978), this makes the maximum of the Brownian excursion a tree-dependent extreme value distribution whose domain of attraction includes both the exponentially distributed and almost surely constant weights. Moment computations are given for the Brownian excursion which are of independent interest.

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.

Nonstationary Extreme-Value Predictions in the Gulf of Mexico

2007 ◽  
Author(s):  
Christos N. Stefanakos
Keyword(s):  
Time Series ◽  
Gulf Of Mexico ◽  
Wave Height ◽  
Missing Values ◽  
Extreme Value ◽  
Altimeter Data ◽  
Dependence Structure ◽  
Measured Time ◽  
Definition Of

In the present work, return periods of various level values of significant wave height in the Gulf of Mexico are given. The predictions are based on a new method for nonstationary extreme-value calculations that have recently been published. This enhanced method exploits efficiently the nonstationary modeling of wind or wave time series and a new definition of return period using the MEan Number of Upcrossings of the level value x* (MENU method). The whole procedure is applied to long-term measurements of wave height in the Gulf of Mexico. Two kinds of data have been used: long-term time series of buoy measurements, and satellite altimeter data. Measured time series are incomplete and a novel procedure for filling in of missing values is applied before proceeding with the extreme-value calculations. Results are compared with several variants of traditional methods, giving more realistic estimates than the traditional predictions. This is in accordance with the results of other methods that take also into account the dependence structure of the examined time series.

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.

Extreme values of phase-type and mixed random variables with parallel-processing examples

1999 ◽  
Vol 36 (01) ◽  
pp. 194-210 ◽  
Author(s):  
Sungyeol Kang ◽  
Richard F. Serfozo
Keyword(s):  
Parallel Processing ◽  
Asymptotic Distribution ◽  
Extreme Values ◽  
Random Variables ◽  
Extreme Value Distribution ◽  
Rates Of Convergence ◽  
Value Theory ◽  
Extreme Value ◽  
Independent Random Variables ◽  
Phase Type

A basic issue in extreme value theory is the characterization of the asymptotic distribution of the maximum of a number of random variables as the number tends to infinity. We address this issue in several settings. For independent identically distributed random variables where the distribution is a mixture, we show that the convergence of their maxima is determined by one of the distributions in the mixture that has a dominant tail. We use this result to characterize the asymptotic distribution of maxima associated with mixtures of convolutions of Erlang distributions and of normal distributions. Normalizing constants and bounds on the rates of convergence are also established. The next result is that the distribution of the maxima of independent random variables with phase type distributions converges to the Gumbel extreme-value distribution. These results are applied to describe completion times for jobs consisting of the parallel-processing of tasks represented by Markovian PERT networks or task-graphs. In these contexts, which arise in manufacturing and computer systems, the job completion time is the maximum of the task times and the number of tasks is fairly large. We also consider maxima of dependent random variables for which distributions are selected by an ergodic random environment process that may depend on the variables. We show under certain conditions that their distributions may converge to one of the three classical extreme-value distributions. This applies to parallel-processing where the subtasks are selected by a Markov chain.

scholarly journals Directional Extreme Value Models in Wave Energy Applications

Atmosphere ◽  
2020 ◽  
Vol 11 (3) ◽  
pp. 274
Author(s):  
Flora Karathanasi ◽  
Takvor Soukissian ◽  
Kostas Belibassakis
Keyword(s):  
Wave Height ◽  
Wave Energy ◽  
Extreme Values ◽  
Extreme Value ◽  
Fourier Series Expansion ◽  
Accurate Estimation ◽  
Wave Direction ◽  
Extreme Wave ◽  
Energy Applications ◽  
Wide Range

A wide range of wave energy applications relies on the accurate estimation of extreme wave conditions, while some of them are frequently affected by directionality. For example, attenuators and terminators are the most common types of wave energy converters whose performance is highly influenced by their orientation with respect to the prevailing wave direction. In this work, four locations in the eastern Mediterranean Sea are selected with relatively high wave energy flux values and extreme wave heights are examined with wave direction as a covariate. The Generalized Pareto distribution is used to model the extreme values of wave height over a pre-defined threshold, with its parameters being expressed as a function of wave direction through Fourier series expansion. In order to be consistent with the analysis obtained from the independent fits for directional sectors, the estimation of parameters is based on a penalized maximum likelihood criterion that ensures a good agreement between the two approaches. The obtained results validate the integration of directionality in extreme value models for the examined locations and design values of significant wave height are provided with respect to direction for the 50- and 100-year return period with bootstrap confidence intervals.

scholarly journals STATISTICAL INTERPRETATION OF HYDROMETEOROLOGICAL EXTREME VALUES

1972 ◽  
Vol 3 (4) ◽  
pp. 199-213 ◽  
Author(s):  
B. SAMUELSSON
Keyword(s):  
Stream Flow ◽  
Extreme Values ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Statistical Characteristics ◽  
Statistical Interpretation ◽  
Short Term ◽  
Frequency Distributions ◽  
Low Probability ◽  
Term Data

The application of Jenkinson's method to extremal distributions for low probability annual extremes of rainfall and stream flow is studied and discussed. A statistical method devised by Jenkinson has been examined and compared with other methods of fitting extreme value distributions to observed data. The Jenkinson method, being strictly objective, has the particular advantage of taking into account the extreme part of the extreme value distribution. The author shows, by applying the Jenkinson method to extreme values which significantly belong to several different kinds of frequency distributions, that this method could be applied as a standard one. Finally, the author indicates the possibility of using the Jenkinson method to extrapolate statistical characteristics from a series of statistically unstable short-term data.

scholarly journals Data Geometry and Extreme Value Distribution

2021 ◽  
Vol 2 (2) ◽  
pp. 06-15
Author(s):  
Mamadou Cisse ◽  
Aliou Diop ◽  
Souleymane Bognini ◽  
Nonvikan Karl-Augustt ALAHASSA
Keyword(s):  
Weibull Distribution ◽  
Extreme Values ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Data System ◽  
Peaks Over Threshold ◽  
Stochastic Graphs ◽  
Block Maxima ◽  
Extreme Values Theory

In extreme values theory, there exist two approaches about data treatment: block maxima and peaks-over-threshold (POT) methods, which take in account data over a fixed value. But, those approaches are limited. We show that if a certain geometry is modeled with stochastic graphs, probabilities computed with Generalized Extreme Value (GEV) Distribution can be deflated. In other words, taking data geometry in account change extremes distribution. Otherwise, it appears that if the density characterizing the states space of data system is uniform, and if the quantile studied is positive, then the Weibull distribution is insensitive to data geometry, when it is an area attraction, and the Fréchet distribution becomes the less inflationary.

Extreme values of phase-type and mixed random variables with parallel-processing examples

1999 ◽  
Vol 36 (1) ◽  
pp. 194-210 ◽  
Author(s):  
Sungyeol Kang ◽  
Richard F. Serfozo
Keyword(s):  
Parallel Processing ◽  
Asymptotic Distribution ◽  
Extreme Values ◽  
Random Variables ◽  
Extreme Value Distribution ◽  
Rates Of Convergence ◽  
Value Theory ◽  
Extreme Value ◽  
Independent Random Variables ◽  
Phase Type

A basic issue in extreme value theory is the characterization of the asymptotic distribution of the maximum of a number of random variables as the number tends to infinity. We address this issue in several settings. For independent identically distributed random variables where the distribution is a mixture, we show that the convergence of their maxima is determined by one of the distributions in the mixture that has a dominant tail. We use this result to characterize the asymptotic distribution of maxima associated with mixtures of convolutions of Erlang distributions and of normal distributions. Normalizing constants and bounds on the rates of convergence are also established. The next result is that the distribution of the maxima of independent random variables with phase type distributions converges to the Gumbel extreme-value distribution. These results are applied to describe completion times for jobs consisting of the parallel-processing of tasks represented by Markovian PERT networks or task-graphs. In these contexts, which arise in manufacturing and computer systems, the job completion time is the maximum of the task times and the number of tasks is fairly large. We also consider maxima of dependent random variables for which distributions are selected by an ergodic random environment process that may depend on the variables. We show under certain conditions that their distributions may converge to one of the three classical extreme-value distributions. This applies to parallel-processing where the subtasks are selected by a Markov chain.

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