Abstract
Extreme value analysis of sea levels is an essential component of risk analysis and protection strategy for many coastal regions. Since the tidal component of the sea level is deterministic, it is the stochastic variation in extreme surges that is the most important to model. Historically, this modelling has been accomplished by fitting classical extreme value models to series of annual maxima data. Recent developments in extreme value modelling have led to alternative procedures that make better use of available data, and this has led to much refined estimates of extreme surge levels. However, one aspect that has been routinely ignored is seasonality. In an earlier study we identified strong seasonal effects at one of the number of locations along the eastern coastline of the United Kingdom. In this article, we discuss the construction and inference of extreme value models for processes that include components of seasonality in greater detail. We use a point process representation of extreme value behaviour, and set our inference in a Bayesian framework, using simulation-based techniques to resolve the computational issues. Though contemporary, these techniques are now widely used for extreme value modelling. However, the issue of seasonality requires delicate consideration of model specification and parameterization, especially for efficient implementation via Markov chain Monte Carlo algorithms, and this issue seems not to have been much discussed in the literature. In the present paper we make some suggestions for model construction and apply the resultant model to study the characteristics of the surge process, especially in terms of its seasonal variation, on the eastern UK coastline. Furthermore, we illustrate how an estimated model for seasonal surge can be combined with tide records to produce return level estimates for extreme sea levels that accounts for seasonal variation in both the surge and tidal processes.
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Subsequent repeat analyses verified that results were essentially unchanged under order of magnitude changes to the variances.
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Acknowledgements
We are grateful for the helpful and insightful comments of two anonymous referees. Our work was supported by grants connected to the projects Statistics as an aid for environmental decisions: identification, monitoring and evaluation (2002134337) funded by the Italian Ministry for Education and Methods for the analysis of extreme sea-levels and for coastal erosion (CPDA037217) funded by the University of Padova.
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Coles, S., Tawn, J. Seasonal effects of extreme surges. Stoch Environ Res Ris Assess 19, 417–427 (2005). https://doi.org/10.1007/s00477-005-0008-3
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DOI: https://doi.org/10.1007/s00477-005-0008-3