A return period, also known as a recurrence interval or repeat interval, is an average time or an estimated average time between events such as earthquakes, floods,[1] landslides,[2] or river discharge flows to occur.
It is a statistical measurement typically based on historic data over an extended period, and is used usually for risk analysis.
Examples include deciding whether a project should be allowed to go forward in a zone of a certain risk or designing structures to withstand events with a certain return period.
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.
In any given 100-year period, a 100-year event may occur once, twice, more, or not at all, and each outcome has a probability that can be computed as below.
Also, the estimated return period below is a statistic: it is computed from a set of data (the observations), as distinct from the theoretical value in an idealized distribution.
One does not actually know that a certain or greater magnitude happens with 1% probability, only that it has been observed exactly once in 100 years.
Even if the historic return interval is a lot less than 1000 years, if there are a number of less-severe events of a similar nature recorded, the use of such a model is likely to provide useful information to help estimate the future return interval.
One would like to be able to interpret the return period in probabilistic models.
An alternative interpretation is to take it as the probability for a yearly Bernoulli trial in the binomial distribution.
That is disfavoured because each year does not represent an independent Bernoulli trial but is an arbitrary measure of time.
This question is mainly academic as the results obtained will be similar under both the Poisson and binomial interpretations.
, the probability of exceedance within an interval equal to the return period (i.e.
), the probability of a given number r of events of a return period
This is valid only if the probability of more than one occurrence per unit time
then Take where Given that the return period of an event is 100 years, So the probability that such an event occurs exactly once in 10 successive years is: Return period is useful for risk analysis (such as natural, inherent, or hydrologic risk of failure).
The probability of at least one event that exceeds design limits during the expected life of the structure is the complement of the probability that no events occur which exceed design limits.