Statistical measures of extremal dependence illustrated using measured sea surface elevations from a neighbourhood of coastal locations

The extremal dependence of stationary time-series at pairs of locations can be summarised using one or more of a number of statistics. We illustrate the application of the coefficient of tail dependence, the χχ and χ¯ statistics, and the conditional extremes model of Heffernan–Tawn to estimate the extremal dependence in time-series of 3-h maxima of sea surface elevation across a spatial array of measurement gauges at the US Army Corps of Engineers' Field Research Facility on the Atlantic coast of North Carolina. Although the original data are non-stationary, we induce stationarity on a site-by-site basis using a non-parametric model to remove the mean trend. Subsequently, we find that pairs of locations are generally asymptotically dependent. Parameter estimates for the Heffernan–Tawn model, although uncertain, suggest that characteristics of conditional extremes vary systematically with distance from the conditioning site.

► We discuss extremal dependence between sea surface elevation at different locations.
► A range of statistical measures for extremal dependence are reviewed.
► All locations are found to be asymptotically dependent on the central location.
► There is some systematic variation in the level of dependence with distance.
► We also find some differences in behaviour in long- and cross-shore directions.