Review Statistical modelling of extreme ocean environments for marine design: A review Philip Jonathan a,n , Kevin Ewans b a Shell Projects and Technology Thornton, Chester CH1 3SH, UK b Sarawak Shell Bhd., 50450 Kuala Lumpur, Malaysia article info Article history: Received 8 August 2012 Accepted 5 January 2013 Available online 28 February 2013 Keywords: Review Extreme Covariate Multivariate Bayesian Return value abstract We review aspects of extreme value modelling relevant to characterisation of ocean environments and the design of marine structures, summarising basic concepts, modelling with covariates and multi- variate modelling (including conditional and spatial extremes). We outline Bayesian inference for extremes and reference software resources for extreme value modelling. Extreme value analysis is inherently different to other empirical modelling, in that estimating the tail (rather than the body) of a distribution from a sample of data, and extrapolation beyond the sample (rather than interpolation within) is demanded. Intuition accumulated from other areas of empirical modelling can be misleading. Careful consideration of the effects of sample size, measurement scale, threshold selection and serial dependence, associated uncertainties and implications of choices made is essential. Incorporation of covariate effects when necessary improves inference. Suitable tools (e.g. based on additive models, splines, random fields, spatial processes) have been developed, but their use is restricted in general to academia. Effective modelling of multivariate extremes will improve the specification of design conditions for systems whose response cannot be easily characterised in terms of one variable. Approaches such as the conditional extremes model are easily implemented, and provide general- isations of existing marine design approaches (e.g. for primary and associated variables). Software is available, but again generally only for academic use. Modelling spatial dependence rigourously will provide single extreme value models applicable to spatial neighbourhoods including complete ocean basins, avoiding the need for procedures such as site pooling. Indeed, once the model is established, the metocean engineer may not ever need to perform further extreme value analysis for that basin in principle. Spatial extremes is an area of active research in the statistics community. A limited number of appropriate models have been deployed (e.g. for precipitation, temperature and metocean applica- tions). Software is available, but again for specialist use. Bayesian inference provides a consistent framework for inference and is rapidly becoming the standard approach in academia. It appears inevitable that, in time, Bayesian inference will also be regarded as the standard in ocean engineering applications. Implementation of Bayesian methods requires some expertise. Software is available, but again generally only used by statistical specialists. & 2013 Elsevier Ltd. All rights reserved. Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/oceaneng Ocean Engineering 0029-8018/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.oceaneng.2013.01.004 n Corresponding author. Tel.: þ44 151 272 5421; fax: þ44 151 44 5384. E-mail addresses: philip.jonathan@shell.com (P. Jonathan), kevin.ewans@shell.com (K. Ewans). Ocean Engineering 62 (2013) 91–109