Return period

A return period, also known as a recurrence interval (sometimes repeat interval) is an estimate of the likelihood of an event, such as an earthquake, flood or a river discharge flow to occur. It is a statistical measurement typically based on historic data denoting the average recurrence interval over an extended period of time, and is usually used for risk analysis (e.g. to decide whether a project should be allowed to go forward in a zone of a certain risk, or to design structures to withstand an event with a certain return period). The following analysis assumes that the probability of the event occurring does not vary over time and is independent of past events.

Recurrence interval = ${\displaystyle {n+1 \over m}}$

For floods, the event may be measured in terms of m³/s or height; for storm surges, in terms of the height of the surge, and similarly for other events.

The theoretical return period is the inverse of the probability that the event will be exceeded in any one year (or more accurately the inverse of the expected number of occurrences in a year). For example, a 10-year flood has a ${\displaystyle 1/10=0.1}$ or 10% chance of being exceeded in any one year and a 50-year flood has a 0.02 or 2% chance of being exceeded in any one year.

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