Research Paper: Estimation of Environmental Contours Using a Block Resampling Method
Ed B. L. Mackay, Philip Jonathan
A new method for estimating joint distributions of environmental variables is presented. The key difference to previous methods is that the joint distribution of only storm-peak parameters is modelled, rather than fitting a model to all observations. This provides a stronger justification for the use of asymptotic extreme value models, as the data considered are approximately independent. The joint distribution of all data is recovered by resampling and rescaling storm histories, conditional on the peak values. This simplifies the analysis as much of the complex dependence structure is resampled, rather than modelled explicitly. The storm histories are defined by splitting the time series into discrete blocks, with the dividing points defined as the minimum value of a variable between adjacent maxima. Storms are characterised in terms of the peak values of each parameter within each discrete block, which need not coincide in time. The key assumption is that rescaling a measured storm history results in an equally realistic time series, provided that the change in peak values is not large. Two examples of bivariate distribution are considered: the joint distribution of significant wave height (Hs) and zero up-crossing period (Tz) and the joint distribution of Hs and wind speed. It is shown that the storm resampling method gives estimates of environmental contours that agree well with the observations and provides a rigorous method for estimating extreme values.