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.

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.

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

A Spatiodirectional Model for Extreme Waves in the Gulf of Mexico

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Philip Jonathan ◽  
Kevin Ewans
Keyword(s):  
Gulf Of Mexico ◽  
Thin Plate ◽  
Poisson Model ◽  
Thin Plate Spline ◽  
Design Criteria ◽  
Extreme Waves ◽  
Generalized Pareto ◽  
Pareto Model ◽  
Fitting Algorithm ◽  
Spatial Dimensions

The characteristics of extreme waves in hurricane dominated regions vary systematically with a number of covariates, including location and storm direction. Reliable estimation of design criteria requires incorporation of covariate effects within extreme value models. We present a spatiodirectional model for extreme waves in the Gulf of Mexico motivated by the nonhomogeneous Poisson model for peaks over threshold. The model is applied to storm peak significant wave height HS for arbitrary geographic areas from the proprietary Gulf of Mexico Oceanographic Study (GOMOS) hindcast for the US region of the Gulf of Mexico for the period of 1900–2005. At each location, directional variability is modeled using a nonparametric directional location and scale; data are standardized (or “whitened”) with respect to local directional location and scale to remove directional effects. For a suitable choice of threshold, the rate of occurrence of threshold exceedences of whitened storm peak HS with direction per location is modeled as a Poisson process. The size of threshold exceedences is modeled using a generalized Pareto form, the parameters of which vary smoothly in space, and are estimated within a roughness-penalized likelihood framework using natural thin plate spline forms in two spatial dimensions. By reparameterizing the generalized Pareto model in terms of asymptotically independent parameters, an efficient back-fitting algorithm to estimate the natural thin plate spline model is achieved. The algorithm is motivated in an appendix. Design criteria, estimated by simulation, are illustrated for a typical neighborhood of 17×17 grid locations. Applications to large areas consisting of more than 2500 grid locations are outlined.

Uncertainties in Extreme Value Analysis of Wave Climate Data and Wave Climate Projections

2015 ◽  
Author(s):  
Erik Vanem
Keyword(s):  
Wave Height ◽  
Significant Wave Height ◽  
Wave Climate ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Climate Projections ◽  
Data Sets ◽  
Climate Data ◽  
Value Analysis ◽  
Significant Wave

The extreme values of climate data are of interest in design of marine structures and the return values of certain met-ocean parameters such as significant wave height is of particular importance. However, there are various ways of analyzing the extremes and estimating the required return values, which introduce additional uncertainties. These are investigated in this paper by applying different methods to particular data sets of significant wave height, corresponding to the historic climate and two future projections of the climate assuming different forcing scenarios. In this way, the uncertainty due to the extreme value analysis can also be compared to the uncertainty due to a changing climate. The different approaches that will be considered is the initial distribution approach, the block maxima approach, the peak over threshold (POT) approach and the average conditional exceedance rate method (ACER). Furthermore, the effect of different modelling choices within each of the approaches will be explored. Thus, a range of different return value estimates for the different data sets is obtained. This exercise reveals that the uncertainty due to the extreme value analysis method is notable and, as expected, the variability of the estimates increases for higher return periods. Moreover, even though the variability due to the extreme value analysis is greater than the climate variability, a shift towards higher extremes in a future wave climate can clearly be discerned in the particular datasets that have been analysed.

Observations of Surface Wave–Current Interaction

2017 ◽  
Vol 47 (3) ◽  
pp. 615-632 ◽  
Author(s):  
Leonel Romero ◽  
Luc Lenain ◽  
W. Kendall Melville
Keyword(s):  
Surface Wave ◽  
Gulf Of Mexico ◽  
Wave Height ◽  
Significant Wave Height ◽  
Second Order ◽  
Wave Crest ◽  
Significant Wave ◽  
Wave Statistics ◽  
Whitecap Coverage ◽  
Current Interaction

AbstractWave–current interaction can result in significant inhomogeneities of the ocean surface wave field, including modulation of the spectrum, wave breaking rates, and wave statistics. This study presents novel airborne observations from two experiments: 1) the High-Resolution Air–Sea Interaction (HiRes) experiment, with measurements across an upwelling jet off the coast of Northern California, and 2) an experiment in the Gulf of Mexico with measurements of waves interacting with the Loop Current and associated eddies. The significant wave height and slope varies by up to 30% because of these interactions at both sites, whereas whitecap coverage varies by more than an order of magnitude. Whitecap coverage is well correlated with spectral moments, negatively correlated with the directional spreading, and positively correlated with the saturation. Surface wave statistics measured in the Gulf of Mexico, including wave crest heights and lengths of crests per unit surface area, show good agreement with second-order nonlinear approximations, except over a focal area. Similarly, distributions of wave heights are generally bounded by the generalized Boccotti distribution, except at focal regions where the wave height distribution reaches the Rayleigh distribution with a maximum wave height of 2.55 times the significant wave height, which is much larger than the standard classification for extreme waves. However, theoretical distributions of spatial statistics that account for second-order nonlinearities approximately bound the observed statistics of extreme wave elevations. The results are discussed in the context of improved models of breaking and related air–sea fluxes.

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.

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