Technical note: Tail behaviour of the statistical distribution of extreme storm surges

Abstract

Abstract. The tail behaviour of the statistical distribution of extreme storm surges is conveniently described by a return level plot, consisting of water level (y axis) against average recurrence interval on a logarithmic scale (x axis). An average recurrence interval is often referred to as a “return period”. Hunter's allowance for sea-level rise gives a suggested amount by which to raise coastal defences in order to maintain the current level of flood risk, given an uncertain projection of future mean sea-level rise. The allowance is most readily evaluated by assuming that sea-level annual maxima follow a Gumbel distribution, and the evaluation is awkward if we use a generalized extreme value (GEV) fit. When we use a Gumbel fit, we are effectively assuming that the return level plot is a straight line. In other words, the shape parameter, which describes the curvature of the return level plot, is zero. On the other hand, coastal asset managers may need an estimate of the return period of unprecedented events even under current mean sea levels. For this purpose, curvature of the return level plot is usually accommodated by allowing a non-zero shape parameter whilst extrapolating the return level plot beyond the observations, using some kind of fit to observed extreme values (for example, a GEV fit to annual maxima). This might seem like a conflict: which approach is “correct”? Here I present evidence that the shape parameter varies around the coast of the UK and is consequently not zero. Despite this, I argue that there is no conflict: a suitably constrained non-zero-shape fit is appropriate for extrapolation and a Gumbel fit is appropriate for evaluation of Hunter's allowance.