Communicating the return period of extremes

The concept of return period (recurrence interval) of extreme events is widely used in engineering practice and in the media. In engineering design and risk assessment, the concept of return period is used to determine the expected magnitude(s) of one or more extreme weather events – i.e., the expected magnitude of an event that, if occurred, might cause the failure of a structure. In the media, the concept of return period is used to communicate to the general public the severity of an event. For example, the 2021 summer flood in Northwestern Europe was reported in the news as a one-in-400-year event – an event expected on average once in 400 years. The strength of return period as a metric (in years) to describe the severity of events resides in the straightforward comparison between the average occurrence in years of an event with the average number of years a person can experience and recollect events.

Generally, the return period of a rare event and its magnitude (known as return level) is inferred from limited observations - often derived by extrapolating from a distribution function fitted to the available observations. The distribution is often greatly influenced by the length of observations. These factors make the concept of return period prone to misinterpretation as extreme events are rarely observed in existing records.

Here we provide a new perspective on the return period of extremes determined not only by its exceedance probability but also in relation to the observations used to describe the underlying distribution. Our method offers a straightforward metric, independent of the type of statistical distribution adopted, to quantify and communicate the likelihood of having observed the event of interest in the available observations, ranging from unlikely to very likely. This metric can provide a measure of confidence in the statistical inference of return periods based on the length of record used for inference. We argue that this additional information on likelihood offers important information for designers, planners, and decision-makers.