Environmental contours for describing extreme ocean wave conditions based on combined datasets

  • Erik VanemEmail author
Original Paper


Environmental contours are often applied in structural reliability assessment and design of ships and other marine structures in order to describe joint extreme values of environmental variables such as significant wave height and wave period. Environmental contours are typically calculated based on a joint probability distribution function established for the relevant input parameters by fitting a parametric model to available data. However, in some situations there might be several datasets available with different probability content, and it may be desirable to make environmental contours that take the combined dataset into account. This paper explores different ways the information contained in such combined datasets can be utilized in order to establish environmental contours. Two different approaches are investigated. The first weights data points according to their probability content when calculating environmental contours directly on the data to obtain weighted contours. The second approach uses the combined dataset for fitting a parametric distribution to the data, where different censoring effects are taken into account, in order to get more accurate estimates of extreme conditions. Both approaches may work well, depending on the type of datasets that are available and can be combined. However, the first approach assumes that the direct sampling method for environmental contours are used, and this method has been used in all examples in this paper. Some examples illustrate the usefulness and drawbacks of the different methods.


Environmental contours Extreme ocean environments Safety and reliability Multivariate extreme values analysis Combined data 



The work presented in this paper has been carried out within the research project ECSADES, with support from the Research Council of Norway (RCN) under the MARTEC II ERA-NET initiative (Grant No. 249261).


  1. Aarnes OJ, Reistad M, Breivik Ø, Bitner-Gregersen E, Eide LI, Gramstad O, Magnusson AK, Natvig B, Vanem E (2017) Projected changes in significant wave height towards the end of the 21st century—Northeast Atlantic. J Geophys Res Oceans 122:3394–3403CrossRefGoogle Scholar
  2. Armstrong C, Chin C, Penesis I, Drobyshevski Y (2015) Sensitivity of vessel response to environmental contours of extreme sea states. In: Proceedings of 34th international conference on ocean, offshore and arctic engineering (OMAE 2015). American Society of Mechanical Engineers (ASME)Google Scholar
  3. Balakrishnan N, Mitra D (2012) Left truncated and right censored Weibull data and likelihood inference with an illustration. Comput Stat Data Anal 56:4011–4025CrossRefGoogle Scholar
  4. Bitner-Gregersen EM (2015) Joint met-ocean description for design and operation of marine structures. Appl Ocean Res 51:279–292CrossRefGoogle Scholar
  5. Bitner-Gregersen EM, Vanem E, Gramstad O, Hørte T, Aarnes Oj, Reistad M, Breivik Ø, Magnussen AK, Natvig B (2018) climate change and safe design of ship structures. Ocean Eng 149:226–237CrossRefGoogle Scholar
  6. DNV GL (2017) Environmental conditions and environmental loads. DNV GL. DNVGL-RP-C205Google Scholar
  7. Fagbamigbe A, Adebowale A (2010) A model for measuring association between bivariate censored outcomes. J Mod Math Stat 4:127–136CrossRefGoogle Scholar
  8. Fagbamigbe A, Adebowale A, Bamgboye E (2017) A survival analysis model for measuring association between bivariate censored outcomes: validation using mathematical simulation. Am J Math Stat 7:7–14Google Scholar
  9. Gouldby B, Wyncoll D, Panzeri M, Franklin M, Hunt T, Hames D, Tozer N, Hawkes P, Dornbusch u, Pullen T (2017) Multivariate extreme value modelling of sea conditions around the coast of England. Proc Inst Civ Eng Marit Eng 170:3–20CrossRefGoogle Scholar
  10. Gramstad O, Vanem E, Bitner-Gregersen E (2018) Uncertainty of environmental contours due to sampling variability. In: Proceedings of the 37th international conference on ocean, offshore and arctic engineering (OMAE 2018). American Society of Mechanical Engineers (ASME)Google Scholar
  11. Groth Carolilne P, Banerjee S, Ramachandran G, Stenzel MR, Stewart PA (2018) Multivariate left-censored Bayesian modeling for predicting exposure using multiple chemical predictors. Environmetrics 29:e2505:1–e2505:16Google Scholar
  12. Haselsteiner AF, Ohlendorf JH, Wosniok W, Thoben KD (2017) Deriving environmental contours from highest density regions. Coast Eng 123:42–51CrossRefGoogle Scholar
  13. Haver S (1985) Wave climate off northern Norway. Appl Ocean Res 7:85–92CrossRefGoogle Scholar
  14. Haver S (1987) On the joint distribution of heights and periods of sea waves. Ocean Eng 14:359–376CrossRefGoogle Scholar
  15. Haver S, Winterstein S (2009) Environmental contour lines: a method for estimating long term extremes by a short term analysis. Trans Soc Nav Architd Mar Eng 116:116–127Google Scholar
  16. Hawkes PJ, Gouldby BP, Tawn JA, Owen MW (2002) The joint probability of waves and water levels in coastal engineering design. J Hydraul Res 40:241–251CrossRefGoogle Scholar
  17. Heffernan JE, Tawn JA (2004) A conditional approach for multivariate extreme values. J R Stat Soc Ser B 66:497–546CrossRefGoogle Scholar
  18. Heo JH, Salas J, Kim KD (2001) Estimation of confidence intervals of quantiles for the Weibull distribution. Stoch Environ Res Risk Assess 15:284–309CrossRefGoogle Scholar
  19. Hewett P, Ganser GH (2007) A comparison of several methods for analyzing censored data. Ann Work Expo Health 51:611–632Google Scholar
  20. Huseby AB, Vanem E, Natvig B (2013) A new approach to environmental contours for ocean engineering applications based on direct Monte Carlo simulations. Ocean Eng 60:124–135CrossRefGoogle Scholar
  21. Huseby AB, Vanem E, Natvig B (2014) A new Monte Carlo method for environmental contour estimation. In: Proceedings of the ESREL 2014. European Safety and Reliability Association (ESRA)Google Scholar
  22. Huseby AB, Vanem E, Natvig B (2015) Alternative environmental contours for structural reliability analysis. Struct Saf 54:32–45CrossRefGoogle Scholar
  23. Huseby AB, Vanem E, Eskeland K (2017) Evaluating properties of environmental contours. In: Proceedings of the ESREL 2017. European Safety and Reliability Association (ESRA)Google Scholar
  24. Huynh T, Ramachandran G, Banerjee S, Monteiro J, Stenzel M, Sandler DP, Engel LS, Kwok rK, Blair A, Stewart PA (2014) Comparison of methods for analyzing left-censored occupational exposure data. Ann Occup Hyg 58:1126–1142Google Scholar
  25. Jonathan P, Ewans K, Flynn J (2014) On the estimation of ocean engineering design contours. J Offshore Mech Arct Eng 136:041,101:1–041,101:8CrossRefGoogle Scholar
  26. Leira BJ (2008) A comparison of stochastic process models for definition of design contours. Struct Saf 30:493–505CrossRefGoogle Scholar
  27. Montes-Iturrizaga R, Heredia-Zavoni E (2017) Assessment of uncertainty in environmental contours due to parametric uncertainty in models of the dependence structure between metocean variables. Appl Ocean Res 64:86–104CrossRefGoogle Scholar
  28. NORSOK (2017) NORSOK standard N-003:2017. Action and action effects. Edition 3Google Scholar
  29. Serinaldi F (2015) Dismissing return periods!. Stoch Environ Res Risk Assess 29:1179–1189CrossRefGoogle Scholar
  30. Silva-González F, Vázques-Hernández Sagrilo, L, Cuamatzi R (2015) The effect of some uncertainties associated to the environmental contour lines definition on the extreme response of an FPSO under hurricane conditions. Appl Ocean Res 53:190–199CrossRefGoogle Scholar
  31. van der Laan MJ (1996) Efficient estimation in the bivariate censoring model and repairing NPMLE. Ann Stat 24:596–627CrossRefGoogle Scholar
  32. Vanem E (2015) Uncertainties in extreme value modeling of wave data in a climate change perspective. J Ocean Eng Mar Energy 1:339–359CrossRefGoogle Scholar
  33. Vanem E (2016) Joint statistical models for significant wave height and wave period in a changing climate. Mar Struct 49:180–205CrossRefGoogle Scholar
  34. Vanem E (2017) A comparison study on the estimation of extreme structural response from different environmental contour methods. Mar Struct 56:137–162CrossRefGoogle Scholar
  35. Vanem E (2018) 3-dimensional environmental contours based on a direct sampling method for structural reliability analysis of ships and offshore structures. Ships Offshore Struct 14:74–85CrossRefGoogle Scholar
  36. Vanem E, Bitner-Gregersen EM (2015) Alternative environmental contours for marine structural design—a comparison study. Journal of Offshore Mechanics and Arctic Engineering 137:051,601:1–051,601:8CrossRefGoogle Scholar
  37. Wells MT, Yeo KP (1996) Density estimation with bivariate censored data. J Am Stat Assoc 91:1566–1574CrossRefGoogle Scholar
  38. Winterstein S, Ude T, Cornell C, Bjerager P, Haver S (1993) Environmental parameters for extreme response: inverse FORM with omission factors. In: Proceedings of the 6th international conference on structural safety and reliabilityGoogle Scholar
  39. Yue S, Rasmussen P (2002) Bivariate frequency analysis: discussion of some useful concepts in hydrological application. Hydrol Process 16:2881–2898CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.DNV GL Group Technology and ResearchHøvikNorway

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