Analysis of Ocean Wave Characteristic Distributions Modeled by Two Different Transformed Functions

Abstract

The probability distributions of wave characteristics from three groups of sampled ocean data with different significant wave heights have been analyzed using two transformation functions estimated by non-parametric and parametric methods. The marginal wave characteristic distribution and the joint density of wave properties have been calculated using the two transformations, with the results and accuracy of both transformations presented here. The two transformations deviate slightly between each other for the calculation of the crest and trough height marginal wave distributions, as well as the joint densities of wave amplitude with other wave properties. The transformation methods for the calculation of the wave crest and trough height distributions are shown to provide good agreement with real ocean data. Our work will help in the determination of the most appropriate transformation procedure for the prediction of extreme values.

Keywords

Wave characteristic distributions / Transformed Gaussian process / Transformed function / Parametric method / Non-parametric method / Crossing-density function

References

[1] Aberg S (2007) Application of Rice’s formula in oceanographic and environmental problems. PhD thesis, Mathematic Statistical, Center for Mathematics Science, Lund Univiversity, Sweden

[2] Azas J-M, Déjean S, León JR, Zwolska F. Transformed Gaussian stationary models for ocean waves. Probab Eng Mech, 2011, 26: 342-349

[3] Baxevani A (2004) Modelling sea surface dynamics using crossing distributions. PhD thesis, Mathematic Statics, Center for Mathematics Science, Lund Univiversity, Sweden

[4] Baxevani A, Rychlik I. Maxima for Gaussian seas. Ocean Eng, 2006, 33: 895-911

[5] Brodtkorb P, Myrhaug D, Rue H. Joint distribution of wave height and wave crest velocity from reconstructed data with application to ringing. Int J Offshore Polar Eng, 2001, 11(1): 23-32

[6] Buows E, Gunther H, Rosenthal W, Vincent C. Similarity of the wind wave spectrum in finite depth water 1. Spectral form. J Geophys Res, 1985, 90(C1): 975-986

[7] Cavanie A, Arhan M, Ezraty R (1976) A statistical relationship between individual heights and periods of storm waves. In: Proc. conf. on behavior of offshore structures, Trondheim. Norvegian Institute of Technology, Trondheim, 354–360

[8] Coles S. An introduction to statistical modeling of extreme values, 2001, London: Springer-Verlag

[9] Lindgren G. Wave-length and amplitude in Gaussian noise. Adv Appl Probab, 1972, 4: 81-108

[10] Lindgren G, Rychlik I. Wave characteristic distributions for Gaussian waves--wave-length, amplitude, and steepness. Ocean Eng, 1982, 9: 411-432

[11] Lindgren G, Rychlik I. Slepian models and regression approximations in crossing and extreme value theory. Int Stat Rev, 1991, 59(2): 195-225

[12] Lindgren G, Rychlik I. CROSSING – a technique for first passage and wave density analysis. Probab Eng Inf Sci, 1993, 7: 125-148

[13] Lindgren G, Rychlik I, Prevosto M. The relation between wave length and wave period distributions in random Gaussian waves. Int J Offshore Polar Eng, 1998, 8(4): 258-264

[14] Longuet-Higgins (1975) On the joint distribution wave periods and amplitudes of sea waves. J Geophys Res 80:2688–2694. https://doi.org/10.1029/JC080i018p02688

[15] Longuet-Higgins (1983) On the joint distribution of wave periods and amplitudes in random wave field. Proc R Soc A 389:241–258. https://doi.org/10.1098/rspa.1983.0107

[16] Marthinsen T, Winterstein S (1992) On the skewness of random surface waves. Int J Offshore Polar Eng. Conerence, ISOPE, San Francisco, USA, III, 472–478

[17] Ochi M, Ahn K. Probability distribution application to non-Gaussian random process. Probab Eng Mech, 1994, 9: 255-264

[18] Rychlik I, Lindgren G (2011) Matlab toolbox for analysis of random waves and loads--a tutorial. Statures Research Report, Department of Mathematic Statistical, Lund University

[19] Rychlik I, Lindgren G, Lin YK. Markov based correlations of damages in Gaussian and non-Gaussian loads. Probab Eng Mech, 1995, 10: 103-115

[20] Rychlik I, Johannesson P, Leadbetter MR. Modelling and statistical analysis of ocean-wave data using transformed Gaussian process. Mar Struct, 1997, 10: 13-47

[21] Schuster A. On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena. Terr Magn Atmos Electr, 1898, 3: 13-41

[22] Srokosz MA, Challenor PG. Joint distributions of wave height and period, a critical comparison. Ocean Eng, 1987, 14: 295-311

[23] Winterstein S. Nonlinear vibration models for extremes and fatigue. J Eng Mech, 1988, 114(10): 1772-1790

[24] Yang L, Wang D, Huang J, Wang X, Zeng L, Wang S, Chen R, Yuan J, Wang Q, Chen J, Zu T, Li J. Toward a mesoscale hydrological and marine meteorological observation network in the South China Sea. Bull Am Meteorol, 2015, 96(7): 1117-1135

[25] Zeng L, Wang Q, Chen R, Wang D. Hydrographic field investigations in the Northern South China Sea by open cruises during 2004-2013. Sci Bull, 2015, 60(6): 607-615

[26] Zheng CW, Zhou L, Jia BK, Pan J, Li X. Wave characteristic analysis and wave energy resource evaluation in the China Sea. J Renew Sust Energ, 2014, 6: 043101