Reed, D.W. 1988. How likely a 10,000-year flood? BHS Circulation No. 20, November 1988, 13 [also appeared in BNCOLD News & Views].
Return
Return periods can get the hydrologist a bad name.
A flash flood in January inundates a town centre, leading to insurance claims totally six figures. The river has been gauged since 1968. The January flood has an estimated peak of 22 m3/s, just over three times the "mean annual flood". Rapid reference to a regional flood growth curve indicates a return period of 350 years: an "outlier".
The water authority reassures the public that it was a freak event and staff return to thinking about the National Rivers Authority, and problems that recede less easily.
In October an almost identical event occurs; the flood "returns". The local MP says that the authority might as well have said it was a 0.35-year flood. Pity the hydrologist; trying to explain that the river has no memory of the previous event only makes matters worse.
Roulette
Perhaps a safer way of describing a 350-year event is to quote an annual non-exceedance probability of 0.9971. The river engineer will still understand it, and the layman might just twig that there's an element of roulette.
Reservoirs
Recognizing the 10,000-year flood as the event with an annual non-exceedance probability of 0.9999 is useful to the reservoir engineer too. Consider that there are a thousand major impounding reservoirs in the UK for which a 10,000-year event would present a severe test of spillway facilities. Simple probability suggests that we might expect such an event to occur at one or other of these 1,000 reservoirs about once in ten years on average. That we don't appear to experience such exceedances quite this often, might be taken to indicate that the hydrologist is over-egging the 10,000-year flood.
In fact things aren't that simple. Flood events at one site are not entirely independent of flood events at neighbouring sites.
Research
Recently completed research at the Institute of Hydrology, Wallingford, has yielded a model to describe the spatial dependence seen in extreme rainfall.
The model is built on data from 400 long-term daily raingauges and many shorter term ones. Interestingly, many of the long-term gauges are for reservoired catchments - installed originally to help determine a fair division of resources between water abstracted for supply and releases to the river in "compensation".
Risk
But what does the spatial dependence model tell us about reservoir flood risk? Well, it provides a procedure for assessing the annual collective risk of a T-year exceedance for a network of critical sites. The method uses the concept of an equivalent number of independent sites.
The effect of spatial dependence in rainfall is judged to make the thousand impounding reservoirs equivalent to only about 250 independent sites. Thus we can expect an exceedance of the 10,000-flood to occur four times less frequently than the once in ten years assessment made earlier.
Rider
A sting in the tail is that, when an event giving rise to an exceedance does occur, it may well affect several sites simultaneously. This "clustering" of exceedances is evident in past incidents such as the Mendip floods in July 1968.
Reference
The collective risk assessment procedure is given in Flood Studies Supplementary Report No. 18, available from the Institute of Hydrology, Wallingford, Oxon OX10 8BB (Tel: 0491-3800). The research on which it is based was funded by the Department of the Environment, contract no. PECD7/7/135.