Return period

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A return period also known as a recurrence interval is an estimate of the likelihood of a flood or river discharge flow of a certain size. It is a statistical measurement denoting the average recurrence interval over an extended period of time.

1 Formula for working out return period or recurrence interval
2 Application
- 2.1 Risk analysis
  - 2.1.1 Example
3 References

[edit] Formula for working out return period or recurrence interval

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

n is number of years on record;

m is the rank of the flood being considered (in terms of the flood size in cumecs).

[edit] Application

Within hydrology return period is important in relating extreme discharge to average discharge. The return period has an inverse relationship with the probability that the event will be exceeded in any one year. For example, a 10-year flood has a 0.1 or 10% chance of being exceeded in any one year and a 50-year flood has a 0.02 (2%) chance of being exceeded in any one year.

It is commonly assumed that a 10-year flood will occur, on average, once every 10 years and that a 100-year flood is such a big discharge that we expect it only to occur every 100 years. While this may be statistically true over thousands of years, it is incorrect to think of the return period in this way. The term return period is actually a misnomer. It does not necessarily mean that the design storm of a 10 year return period will return every 10 years, it could in fact never happen, or happen twice. It is still a 10 years storm though.

The actual formula should be

$T = {m\over{n+1}}$

where

T is the return interval;

m is the ranking, and;

n is number of occurrences.

If the probability of an event occurring is P, and the probability of the event not occurring is Q

$1-P = Q \,$

The binomial distribution can be used to find the probability of occurrence of an event 'r' times in 'n' successive years.

$=nCr \times P^r \times Q^{n-r}$

[edit] Risk analysis

Return period is also useful for risk analysis (such as natural, inherent, or hydrologic risk of failure)^[1]. When dealing with a structure design expectations the return period is useful in calculating the risk of the structure with respect to a given storm return period when given the design life expectation. The equation for assessing this risk can be expressed as

$\overline {R}=1-(1-{1\over T})^n=1-(1-P(X\ge{x_T})^n$