Coastal flooding compound events can be caused by climate-driven extremes of storm surges and waves. To assess the risk associated with these events in the context of climate variability, the bivariate extremes of skew surge (S) and significant wave height (HS) are modeled in a nonstationary framework using physical atmospheric/oceanic parameters as covariates (atmospheric pressure, wind speed and sea surface temperature). This bivariate nonstationary distribution is modeled using a threshold-based approach for the margins of S and HS and a dynamic copula for their dependence structure. Among the covariates considered, atmospheric pressure and related wind speed are primary forcings for the margins of S and HS, but temperature is the main positive forcing of their dependence. This latter relation implies an increasing risk of compound events of S and HS for the studied site in the context of increasing global temperature.

In the design of offshore platforms, the height of the bottom deck directly affects the safety and engineering cost of the entire platform. It is a very important scale parameter in platform planning. The American Petroleum Institute (API) specification shows that the key to determining the height of the bottom deck lies in the wave height and calculation of the return level of the water increase. Based on the perspective of stochastic processes, this paper constructs a new distribution function model for joint parameter estimation of the marine environment. The new model uses a family of random variables to show the statistical characteristics of design wave height and water increase in both time and space, with extreme value expanded EED-I type distribution used as marginal distribution. The new model performs statistical analysis on the measured hydrological data of the Naozhou Station during the flood period from 1990 to 2016. The Gumbel–Copula structure function is used as the connection function, and the compound distribution model of the wave height and the water increase is used to obtain the joint return level of the wave height and the water increase and through which the bottom deck height of the area is calculated. The results show that the stochastic compound distribution improves the issue of the high design value caused by simple superposition of univariate return levels. The EED-I type distribution still has good stability under the condition of less measured data. Thus, under the premise of ensuring the safety of the offshore platform, less measured data can still be used to calculate the height of the bottom deck more accurately.

The aim of this paper is to analyse extremal events using generalized Pareto distributions (GPD), considering explicitly the uncertainty about the threshold. Current practice empirically determines this quantity and proceeds by estimating the GPD parameters on the basis of data beyond it, discarding all the information available below the threshold. We introduce a mixture model that combines a parametric form for the center and a GPD for the tail of the distributions and uses all observations for inference about the unknown parameters from both distributions, the threshold included. Prior distributions for the parameters are indirectly obtained through experts quantiles elicitation. Posterior inference is available through Markov chain Monte Carlo methods. Simulations are carried out in order to analyse the performance of our proposed model under a wide range of scenarios. Those scenarios approximate realistic situations found in the literature. We also apply the proposed model to a real dataset, Nasdaq 100, an index of the financial market that presents many extreme events. Important issues such as predictive analysis and model selection are considered along with possible modeling extensions.

Inference for clusters of extreme values of a time series typically requires the identification of independent clusters of exceedances over a high threshold. The choice of declustering scheme often has a significant effect on estimates of cluster characteristics. We propose an automatic declustering scheme that is justified by an asymptotic result for the times between threshold exceedances. The scheme relies on the extremal index, which we show may be estimated before declustering, and supports a bootstrap procedure for assessing the variability of estimates.