return period: one construct, many systems

In hydrology, the return period (or recurrence interval) is the average time between events of a given magnitude or larger: a 100-year flood is one whose annual exceedance probability is 1/100, so it recurs on average once per century, though not on any fixed schedule. Gumbel's 1941 The return period of flood flows applied extreme-value statistics to series of annual flood maxima, formalising the link between an event's size and the long-run average interval between exceedances. The referent is a frequency statistic for threshold-exceeding events, estimated by fitting an extreme-value distribution to a record, and it is the same construct that reappears for earthquakes and other rare hazards.[1]

Unit

Average number of years between events equalling or exceeding a given magnitude (the reciprocal of the annual exceedance probability)

Recovery means

Not applicable

Measured by

Estimated by fitting an extreme-value distribution (e.g. Gumbel or GEV) to an annual-maxima series and inverting the exceedance probability

In seismology, the recurrence interval is the average time between earthquakes of a given magnitude or larger on a fault or within a region, the same renewal and extreme-value construct used for floods but applied to seismic hazard. Schwartz and Coppersmith's 1984 Fault behavior and characteristic earthquakes: Examples from the Wasatch and San Andreas fault zones used fault-offset and paleoseismic evidence to estimate how often characteristic earthquakes recur. The referent is the long-run mean interval between threshold-exceeding ruptures, estimated from instrumental, historical, and paleoseismic records, identical in form to a flood return period though realised in a different physical system.[2]

Unit

Average number of years between earthquakes equalling or exceeding a given magnitude on a fault or in a region

Recovery means

Not applicable

Measured by

Estimated from dated prior ruptures in paleoseismic trenches, slip-rate data, and magnitude-frequency relations