Journal of Marine Science and Application

, Volume 18, Issue 3, pp 247–259 | Cite as

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

  • Duanfeng Han
  • Ting Cui
  • Yingfei ZanEmail author
  • Lihao Yuan
  • Song Ding
  • Zhigang Li
Research Article


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.


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


  1. Aberg S (2007) Application of Rice’s formula in oceanographic and environmental problems. PhD thesis, Mathematic Statistical, Center for Mathematics Science, Lund Univiversity, SwedenGoogle Scholar
  2. Azas J-M, Déjean S, León JR, Zwolska F (2011) Transformed Gaussian stationary models for ocean waves. Probab Eng Mech 26:342–349. CrossRefGoogle Scholar
  3. Baxevani A (2004) Modelling sea surface dynamics using crossing distributions. PhD thesis, Mathematic Statics, Center for Mathematics Science, Lund Univiversity, SwedenGoogle Scholar
  4. Baxevani A, Rychlik I (2006) Maxima for Gaussian seas. Ocean Eng 33:895–911. CrossRefGoogle Scholar
  5. Brodtkorb P, Myrhaug D, Rue H (2001) Joint distribution of wave height and wave crest velocity from reconstructed data with application to ringing. Int J Offshore Polar Eng 11(1):23–32Google Scholar
  6. Buows E, Gunther H, Rosenthal W, Vincent C (1985) Similarity of the wind wave spectrum in finite depth water 1. Spectral form. J Geophys Res 90(C1):975–986. CrossRefGoogle Scholar
  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, 354–360Google Scholar
  8. Coles S (2001) An introduction to statistical modeling of extreme values. Springer-Verlag, LondonCrossRefzbMATHGoogle Scholar
  9. Lindgren G (1972) Wave-length and amplitude in Gaussian noise. Adv Appl Probab 4:81–108. MathSciNetCrossRefzbMATHGoogle Scholar
  10. Lindgren G, Rychlik I (1982) Wave characteristic distributions for Gaussian waves--wave-length, amplitude, and steepness. Ocean Eng 9:411–432. CrossRefGoogle Scholar
  11. Lindgren G, Rychlik I (1991) Slepian models and regression approximations in crossing and extreme value theory. Int Stat Rev 59(2):195–225. CrossRefzbMATHGoogle Scholar
  12. Lindgren G, Rychlik I (1993) CROSSING – a technique for first passage and wave density analysis. Probab Eng Inf Sci 7:125–148. CrossRefGoogle Scholar
  13. Lindgren G, Rychlik I, Prevosto M (1998) The relation between wave length and wave period distributions in random Gaussian waves. Int J Offshore Polar Eng 8(4):258–264Google Scholar
  14. Longuet-Higgins (1975) On the joint distribution wave periods and amplitudes of sea waves. J Geophys Res 80:2688–2694.
  15. Longuet-Higgins (1983) On the joint distribution of wave periods and amplitudes in random wave field. Proc R Soc A 389:241–258.
  16. Marthinsen T, Winterstein S (1992) On the skewness of random surface waves. Int J Offshore Polar Eng. Conerence, ISOPE, San Francisco, USA, III, 472–478Google Scholar
  17. Ochi M, Ahn K (1994) Probability distribution application to non-Gaussian random process. Probab Eng Mech 9:255–264. CrossRefGoogle Scholar
  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 UniversityGoogle Scholar
  19. Rychlik I, Lindgren G, Lin YK (1995) Markov based correlations of damages in Gaussian and non-Gaussian loads. Probab Eng Mech 10:103–115. CrossRefGoogle Scholar
  20. Rychlik I, Johannesson P, Leadbetter MR (1997) Modelling and statistical analysis of ocean-wave data using transformed Gaussian process. Mar Struct 10:13–47. CrossRefGoogle Scholar
  21. Schuster A (1898) On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena. Terr Magn Atmos Electr 3:13–41CrossRefGoogle Scholar
  22. Srokosz MA, Challenor PG (1987) Joint distributions of wave height and period, a critical comparison. Ocean Eng 14:295–311. CrossRefGoogle Scholar
  23. Winterstein S (1988) Nonlinear vibration models for extremes and fatigue. J Eng Mech 114(10):1772–1790. CrossRefGoogle Scholar
  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 (2015) Toward a mesoscale hydrological and marine meteorological observation network in the South China Sea. Bull Am Meteorol 96(7):1117–1135. CrossRefGoogle Scholar
  25. Zeng L, Wang Q, Chen R, Wang D (2015) Hydrographic field investigations in the Northern South China Sea by open cruises during 2004-2013. Sci Bull 60(6):607–615. CrossRefGoogle Scholar
  26. Zheng CW, Zhou L, Jia BK, Pan J, Li X (2014) Wave characteristic analysis and wave energy resource evaluation in the China Sea. J Renew Sust Energ 6:043101. CrossRefGoogle Scholar

Copyright information

© Harbin Engineering University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Duanfeng Han
    • 1
  • Ting Cui
    • 1
  • Yingfei Zan
    • 1
    Email author
  • Lihao Yuan
    • 1
  • Song Ding
    • 2
  • Zhigang Li
    • 3
  1. 1.College of Shipbuilding EngineeringHarbin Engineering UniversityHarbinChina
  2. 2.China Ship Research and Development AcademyBeijingChina
  3. 3.Offshore Oil Engineering Co., Ltd.TianjinChina

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