Natural Hazards

, Volume 97, Issue 3, pp 1231–1251 | Cite as

Uncertainties of the 50-year wave height estimation using generalized extreme value and generalized Pareto distributions in the Indian Shelf seas

  • T. Muhammed Naseef
  • V. Sanil KumarEmail author
  • Jossia Joseph
  • B. K. Jena
Original Paper


Information about waves with specific return period in a region is essential for the safe design of marine facilities. In this study, significant wave height for 50-year return period is estimated using generalized extreme value (GEV) distribution and generalized Pareto distribution (GPD) based on the 15-year wave hindcast data. In order to realize the dependency of nature of the time series data on return value estimation, three types of data series: daily maxima (DM), monthly maxima (MM) and annual maxima (AM) are considered for GEV, whereas for GPD, threshold values are estimated from the parent data set at 6 h and the DM series. The GEV distribution shows that AM predicts higher significant wave height followed by MM and then DM. The large number (~ 50%) of smaller wave height value (< 1 m) in the DM leads to smaller estimate in wave height for 50-year return period for DM series compared to other data series. Among the locations studied, the maximum value of the significant wave height with 50-year return period by GEV with AM data series is 7.15 m in the western shelf seas and is 7.36 m for the eastern shelf seas, whereas the values based on GPD with peak over threshold are 6.94 and 7.42 m, respectively. Case studies are also done to know the influence of tropical cyclone on the estimated 50-year return value.


Extreme value distribution Surface waves Design wave height Return period Indian Ocean 



Wave model data was generated under the research project ‘Technical Criteria Atlas (TCA)’ sponsored by the Ministry of Earth Sciences (MoES), Govt. of India. We thank the two reviewers and the Editor for the suggestions which improved the scientific content of this paper. This manuscript is a part of the Doctoral thesis of the first author registered with Bharathidasan University, Tiruchirappalli and is NIO contribution 6433.


  1. Abild J, Andersen EY, Rosbjerg D (1992) The climate of extreme winds at the Great Belt, Denmark. J Wind Eng Indus Aerodyn 41(1):521–532. CrossRefGoogle Scholar
  2. Amante C, Eakins BW (2009) ETOPO1 1 arc-minute global relief model: procedures, data sources and analysis. NOAA Technical Memorandum NESDIS, NGDC-24.
  3. Anoop TR, Kumar VS, Shanas PR, Johnson G (2015) Surface wave climatology and its variability in the North Indian Ocean based on ERA-Interim reanalysis. J Atmos Ocean Technol. Google Scholar
  4. Balkema AA, De Haan L (1974) Residual life time at great age. Ann Probab 2:792–804CrossRefGoogle Scholar
  5. Bernardara P, Mazas F, Kergadallan X, Hamm L (2014) A two-step framework for over-threshold modelling of environmental extremes. Nat Hazard Earth Syst Sci 14(3):635–647. CrossRefGoogle Scholar
  6. Coles S (2001) An introduction to statistical modeling of extreme values, vol 208. Springer, London, p 209. ISBN 978-1-4471-3675-0CrossRefGoogle Scholar
  7. Ferreira JA, Guedes Soares C (2000) Modelling distributions of significant wave height. Coast Eng 40 (4):361–374CrossRefGoogle Scholar
  8. Fisher RA, Tippett LHC (1928) Limiting forms of the frequency distribution of the largest or smallest member of a sample. Mathematical proceedings of the Cambridge, vol 24, no 02. Cambridge University Press, Cambridge, pp 180–190Google Scholar
  9. Goda Y (1992) Uncertainty of design parameters from viewpoint of extreme statistics. J Offshore Mech Arct Eng ASME 114(2):76–82. CrossRefGoogle Scholar
  10. Goda Y, Watanabe N (1991) A longshore current formula for random breaking waves. Coast Eng Jpn 34(2):159–175. CrossRefGoogle Scholar
  11. Goda Y, Kudaka M, Kawai H (2010) Incorporation of Weibull distribution in L-moments method for regional frequency analysis of peaks-over-threshold wave heights. Coast Eng Proc 1(32):62. CrossRefGoogle Scholar
  12. Gumbel EJ (1959) Statistics of extremes. Columbia University Press, New YorkGoogle Scholar
  13. Hosking JRM, Wallis JR, Wood EF (1985) Estimation of the generalized extreme-value distribution by the method of probability-weighted moments. Technometrics 27(3):251–261. CrossRefGoogle Scholar
  14. Regional Specialized Meteorological Centre-Tropical Cyclones, India Meteorological Department, RMSC (2013) Web (01 May 2016).
  15. Jenkinson AF (1955) The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Q J R Meteorol Soc 81(348):158–171CrossRefGoogle Scholar
  16. Komen GJ, Cavaleri L, Doneland M, Hasselmann K, Hasselmann S, Janssen PAEM (1994) Dynamics and modelling of ocean waves. Cambridge University Press, CambrideCrossRefGoogle Scholar
  17. Kumar VS, Johnson G, Dora GU, Chempalayil SP, Singh J, Pednekar P (2012a) Variations in nearshore waves along Karnataka, west coast of India. J Earth Syst Sci 121(2):393–403. CrossRefGoogle Scholar
  18. Kumar VS, Glejin J, Dora GU, Sajiv CP, Singh J, Pednekar P (2012b) Variations in nearshore waves along Karnataka, west coast of India. J Earth Syst Sci 121:393–403CrossRefGoogle Scholar
  19. Kumar VS, Shanas PR, Dubhashi KK (2014) Shallow water wave spectral characteristics along the eastern Arabian Sea. Nat Hazards 70:377–394CrossRefGoogle Scholar
  20. Li Y, Simmonds D, Reeve D (2008) Quantifying uncertainty in extreme values of design parameters with resampling techniques. Ocean Eng 35(10):1029–1038. CrossRefGoogle Scholar
  21. Goda Y, Hawkes P, Mansard E, Martin MJ, Mathiesen E, Peltier E, Thompson E, Van Vledder G (1993) Intercomparison of extremal wave analysis methods using numerically simulated data. In: Proceedings of 2nd international symposium on ocean wave measurement and analysis ASCE New Orleans, pp 963–977Google Scholar
  22. Méndez FJ, Menéndez M, Luceño A, Losada IJ (2006) Estimation of the long-term variability of extreme significant wave height using a time-dependent peak over threshold (POT) model. J Geophys Res Oceans (1978–2012) 111(C7):1. Google Scholar
  23. Méndez FJ, Menéndez M, Luceño A, Medina R, Graham NE (2008) Seasonality and duration in extreme value distributions of significant wave height. Ocean Eng 35(1):131–138. CrossRefGoogle Scholar
  24. Moritz HP, Moritz HR (2004) Regional analysis of extremal wave height variability Oregon Coast, USA. In: Proceedings 8th international workshop in wave hindcasting and forecasting, Oahu, Hawaii, USA 14–19 2004, pp 1–15Google Scholar
  25. Neelamani S, Al-Salem K, Rakha K (2007) Extreme waves for Kuwaiti territorial waters. Ocean Eng 34(10):1496–1504. CrossRefGoogle Scholar
  26. Palutikof JP, Brabson BB, Lister DH, Adcock ST (1999) A review of methods to calculate extreme wind speeds. Meteorol Appl 6(02):119–132CrossRefGoogle Scholar
  27. Panchang V, Jeong CK, Demirbilek Z (2013) Analyses of extreme wave heights in the gulf of Mexico for offshore engineering applications. J Offshore Mech Arctic Eng Trans ASME 135:031104–1–031104-15. Google Scholar
  28. Pickands J III (1975) Statistical inference using extreme order statistics. Ann Stat 3:119–131CrossRefGoogle Scholar
  29. Premkumar K, Ravichandran M, Kalsi SR, Sengupta D, Gadgil S (2000) First results from a new observational system over the Indian Seas. Curr Sci 78(3):323–330Google Scholar
  30. Sanil Kumar V, Anoop TR (2015) Spatial and temporal variations of wave height in shelf seas around India. Nat Hazards 78(3):1693–1706CrossRefGoogle Scholar
  31. Sanil Kumar V, Johnson G, Dubhashi KK, Balakrishnan Nair TM (2013) Waves off Puducherry, Bay of Bengal, during cyclone THANE. Nat Hazards 69(1):509–522CrossRefGoogle Scholar
  32. Singh OP, Khan TA, Rahman MS (2000) Changes in the frequency of tropical cyclones over the North Indian Ocean. Meteorol Atmos Phys 75(1–2):11–20CrossRefGoogle Scholar
  33. Sivakholundu KM, Jossia JK, Jena BK (2014) Wave atlas of the Indian Coast. National Institute of Ocean Technology, Chennai, ISBN-81901338-4-5Google Scholar
  34. Sørensen OR, Kofoed-Hansen H, Rugbjerg M, Sørensen LS (2004) A third-generation spectral wave model using an unstructured finite volume technique. In: Proceedings of the 29th international conference on coastal engineering, Lisbon, Portugal, ASCE, pp 894–906Google Scholar
  35. Teena NV, Kumar VS, Sudheesh K, Sajeev R (2012) Statistical analysis on extreme wave height. Nat Hazards 64(1):223–236. CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Ocean Engineering DivisionCSIR-National Institute of Oceanography (Council of Scientific and Industrial Research)Dona PaulaIndia
  2. 2.Coastal and Environmental Engineering DivisionNational Institute of Ocean TechnologyPallikaranai, ChennaiIndia

Personalised recommendations