Preprints
https://doi.org/10.5194/os-2022-14
https://doi.org/10.5194/os-2022-14
 
18 Mar 2022
18 Mar 2022
Status: a revised version of this preprint was accepted for the journal OS and is expected to appear here in due course.

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

Tom Howard Tom Howard
  • Met Office, FitzRoy Road, Exeter, EX1 3PB, UK

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 generalised 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.

Tom Howard

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on os-2022-14', Philip Woodworth, 22 Mar 2022
    • AC1: 'Reply on RC1', Tom Howard, 03 Apr 2022
  • CC1: 'Comment on os-2022-14', John Hunter, 11 Apr 2022
    • AC6: 'Reply on CC1', Tom Howard, 28 Apr 2022
  • EC1: 'Comment on os-2022-14', John M. Huthnance, 20 Apr 2022
    • AC2: 'Reply on EC1', Tom Howard, 20 Apr 2022
  • RC2: 'Comment on os-2022-14', Anonymous Referee #2, 21 Apr 2022
    • AC3: 'Reply on RC2', Tom Howard, 28 Apr 2022
  • AC4: 'Comment on os-2022-14', Tom Howard, 28 Apr 2022
  • AC5: 'Comment on os-2022-14', Tom Howard, 28 Apr 2022
    • AC7: 'Reply on AC5', Tom Howard, 28 Apr 2022

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on os-2022-14', Philip Woodworth, 22 Mar 2022
    • AC1: 'Reply on RC1', Tom Howard, 03 Apr 2022
  • CC1: 'Comment on os-2022-14', John Hunter, 11 Apr 2022
    • AC6: 'Reply on CC1', Tom Howard, 28 Apr 2022
  • EC1: 'Comment on os-2022-14', John M. Huthnance, 20 Apr 2022
    • AC2: 'Reply on EC1', Tom Howard, 20 Apr 2022
  • RC2: 'Comment on os-2022-14', Anonymous Referee #2, 21 Apr 2022
    • AC3: 'Reply on RC2', Tom Howard, 28 Apr 2022
  • AC4: 'Comment on os-2022-14', Tom Howard, 28 Apr 2022
  • AC5: 'Comment on os-2022-14', Tom Howard, 28 Apr 2022
    • AC7: 'Reply on AC5', Tom Howard, 28 Apr 2022

Tom Howard

Tom Howard

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Short summary
I show that two different statistical approaches to dealing with rare sea-level extremes caused by storm surges are not incompatible, despite their apparent differences. I suggest a context in which each approach is appropriate. I undertook this research because the two approaches might seem to be incompatible, a situation which I hope that this note helps to clarify. I applied various statistical tests which have appeared in recent literature to sea-level extremes from UK coastal sites.