Distributions of extreme wave, crest and trough heights measured in the North Sea
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Keywords:
Crest
Trough (economics)
Rogue wave
Significant wave height
Wave height
Elevation (ballistics)
For design purpose extreme wave crests can be determined by direct extrapolation or by estimating an extreme sea state condition. In the latter procedure it is common to estimate a n-year Hs level as a fractile of a marginal long-term distribution of significant wave height, combined with adequately chosen characteristics values for the other sea-state parameters. In this approach a sea state duration needs to be assumed when extremes are calculated. In the present study sensitivity of extreme crest characteristics to an assumed sea state duration is investigated for wave records which include a freak event. The wave time series recorded at the Draupner platform, January 1, 1995, and the data registered at Ekofisk, October 25, 1998, are used in the analysis. Predictions of several models are compared with the prediction given by the 2nd order Forristall crest distribution. Implications of the results for the current design practice are discussed.
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Sea state
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Wave height
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Abstract The area of the Central North Sea is notorious for the occurrence of very high waves in certain wave trains. The short-term distribution of these wave trains includes waves which are far steeper than predicted by the Rayleigh distribution. Such waves are often termed “extreme waves” or “freak waves.” An analysis of the extreme statistical properties of these waves has been made. The analysis is based on more than 12 yr of wave records from the Mærsk Olie og Gas AS operated Gorm Field which is located in the Danish sector of the Central North Sea. From the wave recordings more than 400 freak wave candidates were found. The ratio between the extreme crest height and the significant wave height (20-min value) has been found to be about 1.8, and the ratio between extreme crest height and extreme wave height has been found to be 0.69. The latter ratio is clearly outside the range of Gaussian waves, and it is higher than the maximum value for steep nonlinear long-crested waves, thus indicating that freak waves are not of a permanent form, and probably of short-crested nature. The extreme statistical distribution is represented by a Weibull distribution with an upper bound, where the upper bound is the value for a depth-limited breaking wave. Based on the measured data, a procedure for determining the freak wave crest height with a given return period is proposed. A sensitivity analysis of the extreme value of the crest height is also made.
Rogue wave
Crest
Significant wave height
Wave height
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Crest
Trough (economics)
Rogue wave
Significant wave height
Wave height
Elevation (ballistics)
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Abstract Due to the random nature of extreme waves, wave impacts follow a highly stochastic pattern. To reduce the statistical uncertainties that are naturally arising in estimates of design loads related to extreme waves, sufficient data must be gathered. The first step in a design load analysis is the realization of a set of realistic (typically 3-hour) waves which is large enough to describe the randomness in the impact in sufficient detail, such that the probability of exceedance of the maximum 3-hour load levels can be predicted accurately. In this paper we will investigate if Computational Fluid Dynamics (CFD) is capable of predicting realistic random 3-hour extreme waves. Since the maximum 3-hour load is driven by the highest and steepest waves we will look into the distribution of the maximum 3-hour crest height and the corresponding wave steepness of these events. A comparison is made with wave flume measurements in which 100 random realizations of an extreme wave (Hs = 16.7m, Tp = 15.9s) with a 10,000-year return period were generated and measured.
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Significant wave height
Flume
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Return period
Wave flume
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Rogue waves are individual ocean surface waves with a height greater than 2.2 times the significant wave height.  They can pose a danger to marine operations, onshore and offshore structures, and beachgoers, especially when encountered in high sea states. The prediction of bulk sea state parameters like significant wave height, period, direction, and swell components is satisfactorily addressed in current operational wave models. Individual wave heights cannot be predicted by those spectral models, and the prediction of rogue wave occurrence has to be in a probabilistic sense.Previous attempts on such a prediction are based on the Benjamin Feir Index (BFI), which reflects the nonlinear process of modulation instability as the dominant generation mechanism for rogue waves. However, there is increasing evidence that BFI has limited predictive power in the real ocean. Recent studies established the average crest-trough correlation as the strongest single variable to correlate with rogue wave probability.We demonstrate that crest-trough correlation can be forecast by an operational WAVEWATCHIII wave model with moderate accuracy. Using multi-year wave buoy observations from the northeast Pacific we establish the functional relation between crest-trough correlation and rogue wave occurrence rate, thus calibrating predicted crest-trough correlations into probabilistic rogue wave predictions. Combined with the predicted significant wave heights we can identify regions of enhanced rogue wave risk. Results from a case study of a large storm off Canada’s west coast are presented to evaluate the regional wave model at high seas, and to present the rogue wave probability forecast based on crest-trough correlation.
Rogue wave
Swell
Crest
Significant wave height
Buoy
Sea state
Trough (economics)
Wave height
Wave model
Modulational Instability
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The paper describes the effect of sampling variability on the predicted extreme individual wave height and the predicted extreme individual crests height for long return periods, such as for the 100-year maximum wave height and 100-year maximum crest height. We show that the effect of sampling variability is different for individual crest or wave height as compared to for significant wave height. The short term wave statistics is modeled by the Forristall crest height distribution and the Forristall wave height distribution [3,4]. Samples from the 3-hour Weibull distribution are simulated for 100.000 years period, and the 100-year extreme values for wave heights and crest heights determined for respectively 20 minute and 3 hour sea states. The simulations are compared to results obtained by probabilistic analysis. The paper shows that state of the art analysis approaches using the Forristall distributions give about unbiased estimates for extreme individual crest or wave height if implemented appropriately. Direct application of the Forristall distributions for 3-hour sea state parameters give long term extremes that are biased low, and it is shown how the short term distributions can be modified such that consistent results for 20 minute and 3 hour sea states are obtained. These modified distributions are expected applicable for predictions based on hindcast sea state statistics and for the environmental contour approach.
Crest
Significant wave height
Wave height
Sea state
Hindcast
Rogue wave
Return period
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Trough (economics)
Crest
Significant wave height
Wave height
Return period
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The statistics of extreme wave crest elevation and wave height have been calculated for realistic, directionally spread sea and swell using a probabilistic method tested and described previously. The nonlinearity of steep waves is modeled to the second order using Sharma and Dean kinematics, and a response surface (reliability type) method is used to deduce the crest elevation or wave height corresponding to a given probability of exceedance. The effects of various combinations of sea and swell are evaluated. As expected, in all cases, nonlinearity makes extreme crests higher than the corresponding linear ones. The nonlinear effects on the wave height are relatively small.
Swell
Crest
Significant wave height
Wave height
Elevation (ballistics)
Rogue wave
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Return period
Crest
Significant wave height
Wave Power
Wave height
Wave model
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Abstract : A sequence of 11,000 waves that passed on ODGP platform during Hurricane Camille is studied as 55 successive samples of 200 waves each to determine whether or not the Rayleigh probability density function fits the crest to trough heights defined in the conventional manner and whether or not the highest wave in the sample, which was 72.2 feet from crest to trough, was highly improbable in terms of extreme value theory. Five reasons why a sample of wave heights can depart from the theoretical Rayleigh distribution are analysed. Two are theoretical; two have to do with sampling problems; and the last is concerned with spectral estimation procedures. It was not possible to isolate each of the five reasons. The results do however show that if the last three are taken into account, the Rayleigh distribution comes close to describing the samples adequately. The highest waves that occurred were not unusual when tested against extreme value theory.
Crest
Trough (economics)
Rayleigh distribution
Significant wave height
Rayleigh Wave
Wave height
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