Abstract
Reliable estimates of the occurrence rates of extreme events are highly important for insurance companies, government agencies and the general public. The rarity of an extreme event is typically expressed through its return period, i.e. the expected waiting time between events of the observed size if the extreme events of the processes are independent and identically distributed. A major limitation with this measure is when an unexpectedly high number of events occur within the next few months immediately after a T year event, with T large. Such instances undermine the trust in the quality of risk estimates. The clustering of apparently independent extreme events can occur as a result of local non-stationarity of the process, which can be explained by covariates or random effects. We show how accounting for these covariates and random effects provides more accurate estimates of return levels and aids short-term risk assessment through the use of a complementary new risk measure.Supplementary materials accompanying this paper appear online.
Highlights
Floods and other extreme weather-related hazards are often described in terms of their return period; i.e. the expected waiting time between events if the processes being described are assumed to be stationary
In order to assess the validity of the random effects shown in Fig. 7, the random effect estimates are taken as fixed and the model (2.8) is fitted to the data from the gauge on the River Harbourne, denoted by site H
We show the estimated return level curve based on a generalised extreme value distribution (GEV) fit to the annual maxima from the Harbourne, to Fig. 5
Summary
Floods and other extreme weather-related hazards are often described in terms of their return period; i.e. the expected waiting time between events if the processes being described are assumed to be stationary. A major limitation with the return period as a risk measure is that there are regular occurrences when within the few months following a T year event (T > 50 year) another event of similar or greater severity occurs. This undermines the reputation of statisticians and flood risk managers. We will show that this clustering of independent events can be described by local nonstationarity, a local change in the marginal distribution of the process Ignoring this feature leads to biased return period estimates and an over-optimistic assessment of risk following an extreme event. We provide a practical interpretation of how this risk measure can be used for short-term risk assessment to convey more clearly the reoccurrence chance of extreme events and to help clarify the misinterpretation of an event’s return period
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