Distribution of wave crests in a non-Gaussian sea

The sea elevation at a fixed point is modelled as a quadratic form of a vector valued Gaussian process with arbitrary mean. With this model, saddlepoint methods are used to approximate the mean upcrossing intensity with which the sea level crosses upwards at a certain height. This estimated intensity is further used to determine the probability distribution of wave crests. The use of saddlepoint technique is particularly important here because it can approximate the crest distribution without the need to perform simulations or use fitted distributions. Several numerical examples are given, including two with measured data. In the cases of real data, the results obtained with the saddlepoint technique are also compared with the results obtained with well known methods commonly used in the industry.

[1]  I. Rychlik,et al.  Wave Statistics in Non-Linear Random Sea , 2003 .

[2]  harald Cramer,et al.  Stationary And Related Stochastic Processes , 1967 .

[3]  Rayleigh Law and Stokes Correction for High Waves in Heavy Seas , 2002 .

[4]  T. Barnett,et al.  Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP) , 1973 .

[5]  K. Hasselmann.  On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory , 1962, Journal of Fluid Mechanics.

[6]  M. Prevosto,et al.  Probability distributions for maximum wave and crest heights , 2000 .

[7]  Billy L. Edge,et al.  Ocean Wave Measurement and Analysis , 1994 .

[8]  H. E. Daniels,et al.  Tail Probability Approximations , 1987 .

[9]  R. Langley.  A statistical analysis of non-linear random waves , 1987 .

[10]  Igor Rychlik,et al.  Analysis of Ocean Waves By Crossing And Oscillation Intensities , 1997 .

[11]  Igor Rychlik.  On Some Reliability Applications of Rice's Formula for the Intensity of Level Crossings , 2000 .

[12]  S. Rice.  Mathematical analysis of random noise , 1944 .

[13]  James Durbin,et al.  Approximations for densities of sufficient estimators , 1981 .

[14]  S. Winterstein,et al.  ON THE SKEWNESS OF RANDOM SURFACE WAVES , 1992 .

[15]  G. Forristall.  Wave Crest Distributions: Observations and Second-Order Theory , 2000 .

[16]  Igor Rychlik,et al.  WAFO - A Matlab Toolbox For Analysis of Random Waves And Loads , 2000 .

[17]  Ib M. Skovgaard,et al.  Saddlepoint expansions for conditional distributions , 1987, Journal of Applied Probability.

[18]  M. Asce,et al.  RESPONSE STATISTICS OF LARGE COMPLIANT OFFSHORE STRUCTURES , 2000 .

[19]  H. Daniels.  Saddlepoint Approximations in Statistics , 1954 .

[20]  U. Zähle.  A general rice formula, palm measures, and horizontal-window conditioning for random fields , 1984 .

[21]  J. Hüsler.  Extremes and related properties of random sequences and processes , 1984 .

[22]  W. Rosenthal,et al.  Similarity of the wind wave spectrum in finite depth water: 1. Spectral form , 1985 .

[23]  Igor Rychlik.  On the ‘narrow-band’ approximation for expected fatigue damage , 1994 .