Bayesian hierarchical spatio-temporal modelling of trends and future projections in the ocean wave climate with a CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{ CO }_2$$\end{document} regression component

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 CO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{ CO }_2$$\end{document} 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.