Reed, D.W. 1991. Deducing the rarity of extreme events. Paper to IWEM River Engineering Section, Leamington Spa, 10 May 1991, 17 pp.
Deducing the rarity of an extreme event is sometimes politic and sometimes useful. If a recent event has caused known losses, deducing its rarity may go a long way to proving or disproving the benefit of an improvement scheme. Unfortunately, such assessments are seldom straightforward. If the frequency analysis minefield is successfully crossed, there remains the difficulty of "saying it right"; rarity assessments quoted in return period form are all too often misinterpreted.
The principal technical difficulties in frequency analysis are that estimates have to be made from statistically small samples, and that the true form of the distribution of extremes is unknown. An added difficulty is sociological in origin: the "Guinness Book of Records" syndrome. This is the behaviour by which the number of extremes occurring in a year is less an index of climatic extreme than a product of the time, ingenuity, and computation expended in the hunt, and the size of region over which the search is made.
A fundamental difficulty is in deciding what constitutes the extreme event. A flood is often adequately characterized by its peak flow, and comparisons made with the highest peak flows recorded in each year of record, through an "annual maximum" analysis. In contrast, the assessment of drought rarity is obscured by seasonal factors and operational peculiarities which affect the extent to which a resource system is sensitive to a particular duration or timing of the extreme. To quote the "worst" return period without reference to the system characteristics may be expedient in explaining one shortfall but incredible thereafter.
After charting the problems, the argument is set forth that a deeper understanding of dependence is necessary if environmental extremes are to be better understood and more convincingly estimated. The paper distinguishes three types of dependence: that between successive values of a variable (temporal dependence), that between values of a variable observed at several sites (spatial dependence), and that between variables that interact (multivariate dependence).
Important progress has been made in modelling spatial dependence and it is now possible to place extreme rainfall observations in a regional context. Also reported is the outcome of an investigation of intersite dependence in flood data. Here the focus of attention is the sensitivity of design estimates to a region-wide extreme event, such as the 27 December 1979 storm which led to serious flooding in much of South Wales and the West of England.
Where progress has been less heartening is in the development of general solutions to "joint probability problems". Fluvial-tidal interactions are of particular concern as drainage authorities seek to maintain or improve drainage standards in coastal areas; yet general solutions appear to be little nearer than a decade ago. Increased user awareness, both of the problems and the theoretical principles, may lead to frustration unless short-cut solutions are found.
The paper provides something of a review of UK practice and pitfalls, and begins with a brief tour of contexts in which rarity assessments arise.