Abstract
Environmental contours are often applied in structural reliability assessment and design of ships and other marine structures. Such contours are a practical tool for identifying joint extreme values of environmental variables to determine critical design conditions for the environmental loads. This may be used in the analysis of extreme structural responses and is particularly useful for structures with complicated response behaviour where full long-term analyses are not feasible. Environmental contours are typically calculated based on a joint probability distribution function established for the relevant input parameters, for example significant wave height and wave period, and stationary conditions are often assumed when fitting such models. However, non-stationarities due to, e.g., seasonality or directionality will often be important and this paper presents a simple approach for accounting for such non-stationary ocean environments in the construction of environmental contours. The usefulness of this simple approach is demonstrated by an example, where seasonally varying environmental contours are constructed. Different environmental contours are estimated for every week of the year and it is shown that these contours vary considerably between weeks. Contours corresponding to some average annual condition can also be made and compared to contours established without regard to seasonal variation.
Similar content being viewed by others
References
O.J. Aarnes, M. Reistad, Ø. Breivik, E. Bitner-Gregersen, L.I. Eide, O. Gramstad, A.K. Magnusson, B. Natvig, E. Vanem, Projected changes in significant wave height towards the end of the 21st century—Northeast Atlantic. J. Geophys. Res. Oceans 122, 3394–3403 (2017)
C. Armstrong, C. Chin, I. Penesis,, Y. Drobyshevski, Sensitivity of vessel responses 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) (2015)
G.S. Baarholm, S. Haver, Application of environmental contour lines—a summary of a number of case studies. In: Proceedings of International Conference on Floating Structures for Deepwater Operations. ASRANet (2009)
G.S. Baarholm, S. Haver, O.D. Økland, Combining contours of significant wave height and peak period with platform response distributions for predicting design response. Mar. Struct. 23, 147–163 (2010)
G.S. Baarholm, T. Moan, Application of contour line method to estimate extreme ship hull loads considering operational restrictions. J. Ship Res. 45, 228–240 (2001)
G.S. Baarholm, H. Sverre, C.M. Larsen, Wave sector dependent contour lines. In: Proceedings of 26th International Conference on Offshore Mechanics and Arctic Engineering (OMAE 2007). American Society of Mechanical Engineers (ASME) (2007)
E.M. Bitner-Gregersen, Joint met-ocean description for design and operation of marine structures. Appl. Ocean Res. 51, 279–292 (2015)
DNV: Environmental Conditions and Environmental Loads. Det Norske Veritas (2014). DNV-RP-C205
K. Ewans, P. Jonathan, Evaluating environmental joint extremes for the offshore industry using the conditional extremes model. J. Mar. Syst. 130, 124–130 (2014)
A.F. Haselsteiner, J.H. Ohlendorf, W. Wosniok, K.D. Thoben, Deriving environmental contours from highest density regions. Coast. Eng. 123, 42–51 (2017)
S. Haver, Analysis of uncertainties related to the stochastic modelling of ocean waves. Tech. Rep. UR-80-09, Norges tekniske høgskole (1980)
S. Haver, On the joint distribution of heights and periods of sea waves. Ocean Eng. 14, 359–376 (1987)
S. Haver, K. Bruserud, Environmental contour method: An approximate method for obtaining characteristic response extremes for design purposes. In: Proceedings of 13th International Workshop on Wave Hindcasting and Forecasting and 4th Coastal Hazard Symposium (2013)
S. Haver, S. Winterstein, Environmental contour lines: a method for estimating long term extremes by a short term analysis. Trans. Soc. Naval Archit. Mar. Eng. 116, 116–127 (2009)
J.E. Heffernan, J.A. Tawn, A conditional approach for multivariate extreme values. J. R. Stat. Soc. B 66, 497–546 (2004)
A.B. Huseby, E. Vanem, K. Eskeland, Evaluating properties of environmental contours. In: Proceedings of ESREL 2017. European Safety and Reliability Association(ESRA) (2017)
A.B. Huseby, E. Vanem, B. Natvig, A new approach to environmental contours for ocean engineering applications based on direct Monte Carlo simulations. Ocean Eng. 60, 124–135 (2013)
A.B. Huseby, E. Vanem, B. Natvig, A new Monte Carlo method for environmental contour estimation. In: Proceedings of ESREL 2014. European Safety and Reliability Association(ESRA) (2014)
A.B. Huseby, E. Vanem, B. Natvig, Alternative environmental contours for structural reliability analysis. Struct. Saf. 54, 32–45 (2015)
P. Jonathan, K. Ewans, Statistical modelling of extreme ocean environments for marine design: a review. Ocean Eng. 62, 91–109 (2013)
P. Jonathan, K. Ewans, J. Flynn, On the estimation of ocean engineering design contours. In: Proceedings of 30th International Conference on Ocean, Offshore and Arctic Engineering (OMAE 2011). American Society of Mechanical Engineers (ASME) (2011)
B.J. Leira, A comparison of stochastic process models for definition of design contours. Struct. Saf. 30, 493–505 (2008)
Q. Li, Z. Gao, T. Moan, Modified environmental contour method for predicting long-term extreme responses of bottom-fixed offshore wind turbines. Mar. Struct. 48, 15–32 (2016)
L.D. Lutes, S.R. Winterstein, A dynamic inverse FORM method: design contours for load combination problems. Probab. Eng. Mech. 44, 118–127 (2016)
R. Montes-Iturrizaga, E. Heredia-Zavoni, Environmental contours using copulas. Appl. Ocean Res. 52, 125–139 (2015)
R. Montes-Iturrizaga, E. Heredia-Zavoni, Multivariate environmental contours using C-vine copulas. Ocean Eng. 118, 68–82 (2016)
M.J. Muliawan, Z. Gao, T. Moan, Application of the contour line method for estimating extreme responses in the mooring lines of a two-body floating wave energy converter. J. Offshore Mech. Arctic Eng. 135(03,1301), 1–10 (2013)
J.M. Niedzwwecki, J. van de Lindt, J. Yao, Estimating extreme tendon response using environmental contours. Eng. Struct. 20, 601–607 (1998)
NORSOK: NORSOK Standard N-003:2017. Action and action effects (2017). Edition 3
T. Øyri, Contour methods for deepwater riser systems. NTNU (2014). Master Thesis
D. Randell, G. Feld, K. Ewans, P. Jonathan, Distributions of return values for the ocean wave characteristics in the South China Sea using directional-seasonal extreme value analysis. Environmetrics 26, 442–450 (2015)
D. Randell, K. Turnbull, K. Ewans, P. Jonathan, Bayesian inference for nonstationary marginal extremes. Environmetrics 27, 439–450 (2016)
E. Ross, D. Randell, K. Ewans, G. Feld, P. Jonathan, Efficient estimation of return value distributions from non-stationary marginal extreme value models using Bayesian inference. Ocean Eng. 142, 315–328 (2017)
K. Saranyasoontorn, L. Manuel, Design loads for wind turbines using the environmental contour method. In: 44th AIAA Aerospace Sciences Meeting and Exhibit, pp. AIAA 2006–1365. American Institute of Aeronautics and Astronautics (AIAA) (2006)
F. Serinaldi, Dismissing return periods!. Stoch. Environ. Res. Risk Assess. 29, 1179–1189 (2015)
F. Serinaldi, C.G. Kilsby, Stationarity is undead: Uncertainty dominates the distribution of extremes. Adv. Water Resour. 77, 17–36 (2015)
F. Silva-González, E. Heredia-Zavoni, R. Montes-Iturrizaga, Development of environmental contours using Nataf distribution model. Ocean Eng. 58, 27–34 (2013)
J.E. Stopa, K.F. Cheung, Periodicity and patterns of ocean wind and wave climate. J. Geophys. Res. Oceans 119, 5563–5584 (2014)
E. Vanem, Statistical analysis of univariate extremes and bivariate distributions of wave data and climate change projections. Tech. Rep. 2014-1672, Rev. 02, DNV GL (2014)
E. Vanem, Non-stationary extreme value models to account for trends and shifts in the extreme wave climate due to climate change. Appl. Ocean Res. 52, 201–211 (2015)
E. Vanem, Uncertainties in extreme value modeling of wave data in a climate change perspective. J. Ocean Eng. Mar. Energy 1, 339–359 (2015)
E. Vanem, Joint statistical models for significant wave height and wave period in a changing climate. Mar. Struct. 49, 180–205 (2016)
E. Vanem, A comparison study on the estimation of extreme structural response from different environmental contour methods. Mar. Struct. 56, 137–162 (2017)
E. Vanem, E.M. Bitner-Gregersen, Alternative environmental contours for marine structural design—a comparison study. J. Offshore Mech. Arctic Eng. 137(051601), 1–8 (2015)
E. Vanem, A.B. Huseby, B. Natvig, A Bayesian hierarchical spatio-temporal model for significant wave height in the North Atlantic. Stoch. Environ. Res. Risk Assess. 26, 609–632 (2012)
E. Vanem, A.B. Huseby, B. Natvig, Modeling ocean wave climate with a Bayesian hierarchical space-time model and a log-transform of the data. Ocean Dyn. 62, 355–375 (2012)
S. Winterstein, T. Ude, C. Cornell, P. Bjerager, S. Haver, Environmental parameters for extreme response: Inverse FORM with omission factors. In: Proceedings of 6th International Conference on Structural Safety and Reliability (1993)
S.R. Winterstein, Environmental contours for sub-populations: effects of wind-wave direction and cut-out wind speed. Tech. Rep. TN 2016-071, Probability-Based Engineering (2016)
S.R. Winterstein, A.K. Jha, S. Kumar, Reliability of floating structures: extreme response and load factor design. J. Waterway Port Coast. Ocean Eng. 125, 163–169 (1999)
S. Yue, P. Rasmussen, Bivariate frequency analysis: discussion of some useful concepts in hydrological application. Hydrol. Process. 16, 2881–2898 (2002)
Acknowledgements
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Vanem, E. A simple approach to account for seasonality in the description of extreme ocean environments. Mar Syst Ocean Technol 13, 63–73 (2018). https://doi.org/10.1007/s40868-018-0046-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40868-018-0046-6