Environmental and Ecological Statistics

, Volume 21, Issue 2, pp 189–220 | Cite as

Bayesian hierarchical spatio-temporal modelling of trends and future projections in the ocean wave climate with a \(\text{ CO }_2\) regression component

  • Erik Vanem
  • Arne Bang Huseby
  • Bent Natvig


Bad weather and rough seas continue to be a major cause for ship losses and is thus a significant contributor to the risk to maritime transportation. This stresses the importance of taking severe sea state conditions adequately into account, with due treatment of the uncertainties involved, in ship design and operation in order to enhance safety. Hence, there is a need for appropriate stochastic models describing the variability of sea states. These should also incorporate realistic projections of future return levels of extreme sea states, taking into account long-term trends related to climate change and inherent uncertainties. The stochastic ocean wave model presented in this paper exploits the flexible framework of Bayesian hierarchical space-time models. It allows modelling of complex dependence structures in space and time and incorporation of physical features and prior knowledge, yet at the same time remains intuitive and easily interpreted. Furthermore, by taking a Bayesian approach, the uncertainties of the model parameters are also taken into account. A regression component with \(\text{ CO }_2\) as an explanatory variable has been introduced in order to extract long-term trends in the data. The model has been fitted by monthly maximum significant wave height data for an area in the North Atlantic ocean. The different components of the model will be outlined in the paper, and the results will be discussed. Furthermore, a discussion of possible extensions to the model will be given.


Bayesian hierarchical modelling Climate change MCMC Modelling the effects of climate change Ocean waves Spatio-temporal modelling Stochastic processes 



The authors want to express their thanks to Dr. Andreas Sterl at KNMI for kindly providing the significant wave height data used in this analysis and for clarifying some issues discovered when investigating the data. Thanks also to Dr. Pieter Tans for kind permission to use the NOAA ESRL \(\text{ CO }_2\)-data. The data on future projections of atmospheric concentration of \(\text{ CO }_2\) were obtained from the IPCC.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OsloBlindernNorway

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