ARI and AEP Explained

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You are in: HAS Home > Design IFD Rainfall > ARI_AEP

ARI and AEP

The Average Recurrence Interval (ARI) and the Annual Exceedance Probability(AEP) are both a measure of the rarity of a rainfall event.

What is ARI?

ARI is defined as:

The average, or expected, value of the periods between exceedances of a given rainfall total accumulated over a given duration.

It is implicit in this definition that the periods between exceedances are generally random.

What is AEP?

AEP is defined as:

The probabilty that a given rainfall total accumulated over a given duration will be exceeded in any one year.

How does AEP relate to ARI?

With ARI expressed in years, the relationship is:

Formula for converting values from ARI to AEP

which results in the following conversion table:

ARI (years)	AEP
1	0.632
2	0.393
5	0.181
10	0.095
20	0.049
50	0.020
100	0.010

ARIs of greater than 10 years are very closely approximated by the reciprocal of the AEP.

For a more detailed account, see Back to Basics on Flood Frequency Analysis by E.M. Laurenson, Civil Engineering Transactions, 1987, pp. 47 to 53.

Why use AEP instead of ARI?

Australian Rainfall and Runoff (Inst. Engrs Aust.,1987), states:

Use of the terms "recurrence interval" and "return period" has been criticised as leading to confusion in the minds of some decision makers and members of public.Althougth the terms are simple superficially, they are sometimes misinterpreted as implying that the associated magnitude is only exceeded at regular intervals, and that they are referring to the elapsed time to the next exceedance.

The use of the term ARI can lead to confusion. It is preferable, therefore, to express the rarity of a rainfall event in terms of AEP. For example, a rainfall total of 159mm falling in 3 hours at Darwin Regional Office has a 0.010 (i.e. 1%) probabilty of being equalled or exceeded in any one year can be easier to understand than the equivalent statement of a rainfall total of 159mm in 3 hours has an average recurrence interval of 100 years.

Last Modified: 06 April 2006, Hydrometeorological Advisory Service.

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