Statistical modelling of extreme ocean climate with incorporation of storm clustering

Abstract: Knowledge of the extreme ocean climate is essential for the accurate assessment of coastal hazards to facilitate risk informed decision making in coastal planning and management. Clustered storm events, where two or more storms occur within a relatively short space of time, may induce disproportionately large coastal erosion compared to non-clustered storm events. Therefore this study aims to develop a statistical approach to modelling the frequency and intensity of storm events on the eastern and southern coast of Australia, with a focus on examining storm clustering. This paper presents the preliminary analysis of the recently developed methods and results when they are applied to a study site on the central coast of New South Wales, Australia. This study is a key component of the Bushfire and Natural Hazards CRC Project “Resilience to clustered disaster events on the coast - storm surge” that aims to develop a new method to quantify the impact of coincident and clustered disaster events on the coast. Extreme storm events at a given site can be described using multivariate summary statistics, including the events' maximum significant wave height (H), median wave period, median wave direction, duration, peak storm surge, and time of occurrence. This requires a definition of individual storm events, so the current methodology firstly involves the extraction of storm events from a 30-year timeseries of observations. Events are initially defined using a peaks-over-threshold approach based on the significant wave height with the 95% exceedance quantile (2.93 m) adopted as the threshold. Subsequently, these events are manually checked against sea-level pressure data to examine if closely spaced events are generated by the same meteorological system, and if so the events are combined. This means that the final event set is more likely to consist of meteorologically independent storm events. Various statistical techniques are applied to model the magnitude and frequency of the extracted storm events. A number of variations on the non-homogenous Poisson process model are developed to estimate the event occurrence rate, duration and spacing. The models account for the sub-annual variations in the occurrence rate, temporal dependency between successive events, and the finite duration of events. The results indicate that in the current dataset, closely spaced events are more temporally spread out than would be expected if the event timings are independent, which we term anti-clustering. A particular marginal distribution is fitted to each variable, i.e. a Generalised Pareto (GP) distribution for Hsig, and Pearson type 3 (PE3) distributions for duration and tidal residual. Empirical marginal distributions are employed for wave period and direction. The joint cumulative distribution function of all storm magnitude statistics is modelled by constructing the dependency structure using Copula functions. Two methods are tested: a t-copula and a combination of a Gumbel and Gaussian copulas. Comparison of modelled and observed scatterplots shows similar patterns. Goodness-of-fit tests such as Komologorov-Smirnov (K-S) tests, Chi-square tests and AIC and BIC are used to quantitatively evaluate the fitting qualities and to assess model parsimony, along with graphical visualisations, e.g. QQ plots. Based on this approach, a long-term synthetic time-series of storm events (10 years) is generated using the event magnitude and timing simulated with the fitted models. These long-term synthetic events can be used to derive exceedance probabilities and to construct designed storm events to be applied to beach erosion modelling.