Assessing extremal dependence of North Sea storm severity

Abstract

Extreme value theory provides asymptotically motivated methods for modelling the occurrences of extreme values of oceanographic variables, such as significant wave height at a single location. Problems are often multivariate or spatial in nature, where interest lies in the risk associated with joint occurrences of rare events, e.g. the risk to multiple offshore structures from a storm event. There are two different classes of joint tail behaviour that have very different implications: asymptotic independence suggesting that extreme events are unlikely to occur together, and asymptotic dependence implying that extreme events can occur simultaneously. It is vital to have good diagnostics to identify the appropriate dependence class. If variables are asymptotically independent, incorrectly assuming an asymptotically dependent model can lead to overestimation of the joint risk of extreme events, and hence to higher than necessary design costs of offshore structures. We develop improved diagnostics for differentiating between these two classes, which leads to increased confidence in model selection. Application to samples of North Sea sea-state and storm-peak significant wave height suggests that tail dependence changes with wave direction and distance between spatial locations, and that in most cases asymptotic independence seems to be the more appropriate assumption.

You Just Keep on Pushing My Love over the Borderline: A Rejoinder

“…PC priors now exist for models of tail dependence (Kereszturi, Tawn and Jonathan, 2016), the Hurst parameter for fractional Gaussian noise (Sørbye and Rue, 2016a), the degrees of freedom for P-splines (Ventrucci and Rue, 2016), parameters in the Matérn covariance function (Fuglstad et al, 2015), the correlation parameter in bivariate meta-analysis models (Guo, Rue and Riebler, 2015), the autoregressive parameters in an AR(p) process (Sørbye and Rue, 2016b) and the variance in the mean-variance parameterisation of the Beta distribution (Harjanto et al, 2016).…”

On spatial conditional extremes for ocean storm severity

“…A number of recent studies explore the extremal spatial dependence of H S . For example, Kereszturi, Tawn, and Jonathan () assess the extremal dependence of North Sea storm severity using the summary statistics χ and (or equivalently, η ; Coles, Heffernan, & Tawn, ), outlined in Section 3. Estimates for these summary statistics were used to categorise observed extremal dependence as either asymptotic dependence (AD; suggesting that extreme events tend to occur simultaneously) or asymptotic independence (AI; suggesting that extreme events are unlikely to occur together); further discussion of these concepts is given in Section 3.1.…”

Quantification of extremal dependence in spatial natural hazard footprints: independence of windstorm gust speeds and its impact on aggregate losses

“…Similarly, Eastoe et al (2013) applied the coefficient of tail dependence, the χ and χ measures, and the conditional extremes model of Heffernan and Tawn (2004) to estimate the form of extremal dependence in 3 hourly sea surface elevation maxima at 15 locations, identifying, in general, asymptotic dependence. Similarly, more recently, Kereszturi et al (2015) employed the coefficient of tail dependence and χ and χ measures within a comprehensive theoretical framework to assess extremal dependence of North Sea storm severity along four strips of 14 locations within the North Sea.…”