Extreme rainfall over multiple time-scales

Hydrologists are interested in the behaviour of extreme rainfall over different time aggregations. So, for example, it is possible to have an hour of very extreme rainfall within a day for which the total rainfall is not particularly unusual. The converse is also true.

Extremes occurring at different timescales present different problems for hydrologists and civil engineers, so statistical ‘growth curves’, which plot the probability of an event against its severity, are calculated for each time-scale (1-hour, 6-hour, 24-hour, 5-day etc.) separately. However, there is a great deal of interest in the idea of modelling the different growth-curves simultaneously. This would enable a greater efficiency in terms of using data to model extremal behaviour, as well as allowing hydrologists to make predictions where information for a particular time-scale was not available (e.g. what is the distribution of hourly extremes at a site where only daily data is available?). Further, the multivariate behaviour of extremes recorded over different time-scales may serve to characterize the extremal rain climate at a particular location, and serve as an instrument for observing and quantifying climate change.

In this project we will start by investigating the time-scale dependent behaviour of extreme rainfall from data collected at 200 sites in the UK, consisting of daily records for about 150 locations, and hourly records for about 50 locations. Statistical methods for extreme values will feature largely in the analysis, which is likely to involve a fair amount of statistical computation. Bayesian methods are also likely to be prominent, and there is notable scope in this project to get involved in the theoretical issues relating to extremes recorded over multiple aggregations.