Joint spatial modeling of significant wave height and wave period using the SPDE approach

Anders Hildeman, David Bolin, Igor Rychlik

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The ocean wave distribution in a specific region of space and time is described by its sea state. Knowledge about the sea states a ship encounters on a journey can be used to assess various parameters of risk and wear associated with this journey. Two important characteristics of the sea state are significant wave height and mean wave period. We propose a joint spatial model of these two quantities on the north Atlantic ocean. The model describes the distribution of the logarithm of the two quantities as a bivariate Gaussian random field, modeled as a solution to a system of coupled fractional stochastic partial differential equations. The bivariate random field is non-stationary and allows for arbitrary, and different, smoothness for the two marginal fields. The parameters of the model are estimated from data using a stepwise maximum likelihood method. The fitted model is used to derive the distribution of accumulated fatigue damage for a ship sailing a transatlantic route. Also, a method for estimating the risk of capsizing due to broaching-to based on the joint distribution of the two sea state characteristics is investigated. The risks are calculated for a transatlantic route between America and Europe using both data and the fitted model. The results show that the model compares well with observed data. It further shows that the bivariate model is needed and cannot simply be approximated by a model of significant wave height alone.
Original languageEnglish (US)
Pages (from-to)103203
JournalProbabilistic Engineering Mechanics
StatePublished - Feb 9 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-03-10
Acknowledgements: We would like to thank the European Centre for Medium-range Weather Forecast (ECMWF) for the development of the ERA-Interim dataset and for making it publicly available. The data used was the ERA-Interim reanalysis dataset, Copernicus Climate Change Service (C3S) (accessed September 2018), available from “”.


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