# Why do 100 year events happen so often?

Analyses of data from rainfall gauges and the use of statistical theory enables one to estimate the probability that a particular rainfall depth will be equalled or exceeded at a particular place, within a particular time interval (duration), and over any given period of time. For example, the probability that 48.2 mm or more will fall in any 1-hour duration in a period of one year at the site of the Bureau's official Melbourne raingauge. Curves representing these values are known as rainfall intensity-frequency-duration (IFD) curves. Rainfall IFD analyses are available for all locations in Australia.

The probability of a particular rainfall amount for a specified duration being equalled or exceeded in any 1 year period can be expressed as a percentage (the annual exceedence probability or AEP) or as "on the average once in every x years" (an average recurrence interval, or ARI, of x years). As an example, for Melbourne, a rainfall amount of 48.2 mm in 1 hour can be expected to be equalled or exceeded on average once every 100 years. In this case, the ARI is 100 years and the AEP is 1%. It is important to note that an ARI of, say, 100 years does not mean that the event will only occur once every 100 years. In fact, for each and every year, there is a 1% chance (a 1 in 100 chance) that the event (in this example, 48.2 mm in 1 hour) will be equalled or exceeded (once or more than once). The use of annual exceedance probability (AEP) to describe the chance of a particular rainfall is preferred as it conveys the probability or chance that exists for each year. The alternative, ARI, is a term which is easily misunderstood.

Statistical theory (see for example, Laurenson, E.M, "back to basics on flood frequency analysis", Civ Eng Trans, 1987) can be used to calculate the chance this (1% AEP) value has of occurring or being exceeded over a longer period, say the 50 years from 2001 to 2050. This chance is calculated to be about 40%. That is, a 1% AEP (100 year ARI) event has a high chance (40%, or between a 1 in 2 chance and a 1 in 3 chance) of being equalled or exceeded over a 50 year period. Similarly, if a storm water drain is designed to cope with a 10% AEP (10-year ARI) rainfall event there is a 10% chance of it's being overtopped next year, a 39% chance in the next 5 years, and 63% chance in the next 10 years.

## The effect of area

The above discussion applies to a particular point or location. If a larger area is considered (say, the whole of a city or town), the chance of receiving an intense rainfall event (say a 1% AEP event) somewhere over the larger area is increased. In practice, the most intense part of a thunderstorm, or of a cold frontal band, is a small area, across which the rainfall values are almost the same. Values for one hour duration taken at points about 5 km apart would be almost totally independent of each other in some storms but partly related in others. For example, one could make a grid of about 100 such points in the greater Melbourne area. The 1-hour, 1% AEP (100 year ARI) value has 1% chance of occurring at *each* of these points in a particular year, which means that there is a good chance (63% assuming full independence of points) of a 1-hour, 1% AEP (100 year ARI) event occurring somewhere in the general Melbourne area in each calendar year. (This is an approximation only as the assumption of independence of - zero correlation amongst - points varies with both the duration of rainfall under consideration and the type of rainfall-producing weather mechanisms which can operate in the area.)

## Add events of different duration

The above reasoning can be repeated using *different durations* for rainfalls of a given probability. If a storm occurred, it would be most severe in terms of rainfall intensity and expected probability of occurrence for some *particular duration*, e.g. it may be a 0.5% AEP (200-year ARI) event at a duration of 1 hour but a 2% AEP (50 year ARI) event for a 30 minute duration, and a 1% AEP (100 year ARI) event for 2 hours duration. On another occasion a storm at a particular locality may peak at a different duration. At any particular place there is a 1% chance in any one year of experiencing a rainfall intensity equal to or greater than the 100 year ARI value for a number of different durations for which the rainfalls are independent, or nearly so. For example, durations of: 5 minutes, 1 hour, 6 hours, and 3 days may display a considerable degree of independence.

Given this range of durations from 5 minutes to 3 days, if one talks simply about the "100-year event" (regardless of the duration at which it occurs) then its probability of occurrence somewhere over a large area, say the greater Melbourne area, is increased significantly above the 63% estimate above - which refers to one duration only.

Thus the reason that some people may perceive the "100-year event" to occur more frequently than its name implies is that, instead of focussing on a single point (raingauge), and a single duration, they include in their considerations an area of significant size and a wide range of durations.

## Drain overtopping and the critical duration

The duration of storm necessary to produce the maximum peak flow for any location in a drainage system is a period known as the time of concentration for that location. This is the time taken for water to flow from the outermost point in the system to the subject location. Storms of a shorter duration (and higher intensity) may cause failure (overtopping) of part of the system upstream of the subject location, but not at that location. Longer storms will not produce a flow in excess of the maximum peak flow of this critical duration storm unless there is a burst of rainfall over a period of time equal to the critical duration within the longer storm that is more intense than the critical duration storm itself."

Note also that a rainfall event of a particular AEP (say 1%) does not necessarily produce a flood magnitude of the same AEP. For example, a 1% AEP rainfall event may occur when the catchment is particularly dry and the resulting flood magnitude may be considerably less than the 1% AEP flood.

*Based on an article by Malcolm Kennedy (1990)*