Also known as the return period, this is the mean time between occurrences of some event, such as a flood. It is used as the foundation of many design procedures based on acceptable frequencies of occurrence. For urban stormwater drainage design the "event" will be the exceedance of some flood level and the resulting damage.
In general, the ARI can be considered to be the inverse of the probability of exceedance. For example, a 20 year ARI is equivalent to a 1 in 20 or 5% AEP (annual exceedance probability). If ARI is in years, the corresponding probability is in terms of the event occurring in an annual period. This applies to the 1987 rainfall data, but not to the intensity-frequency-duration data issued by the Bureau of Meteorology in 2016.
While ARI has been used in older design guidelines, and will continue to be used in the standard AS/NZS 3500.3, it is replaced by AEP in Australian Rainfall and Runoff 2019.