# How Extreme is Extreme?

The recent floods in Eastern Australia have been described as "once in a lifetime" events. Cyclone Yasi was the "largest ever".  They have certainly been events that no-one would want to experience more than once.  In their aftermath, there have been demands for action to better plan for such events.

Less devastating but more common problems of an extreme nature also need to be planned for.  For example, a key question when planning electricity generation capacity is, what might be the highest electricity demand next summer, or in the next 20 or 30 summers?  As with floods, it is important to understand the possible extremes so that there is only a low chance that electricity supply cannot meet demand.  Similarly engineers designing offshore facilities need to plan for the largest wave likely to occur.  But how do you plan for an event that has not been observed before?

Questions about extreme values are inherently statistical - they ask, what is the probability that a certain level will be exceeded?  The answers are often in the form of rates.  Hence the talk of the "one hundred year flood", meaning that there is a probability of 1% of a flood occurring in any given year. Estimating such probabilities is critical in planning since there is often a trade off between the extra cost of building infrastructure to cope with such an event and the cost of rebuilding after such an event.  A proper understanding of the risks is essential for good planning.

These questions are different from many in statistics that are concerned with averages and what is most likely to occur.  (If you are coping with a cyclone, it is of no comfort to know what the average wind is, or being told that the weather is usually calm.)  These different questions require different statistical tools.  Fortunately this has been an active area of study - theory and practical - for statisticians over the past fifty years.

A particularly exciting development of recent years has been the combining of extreme value theory applied to data such as weather records with large numerical models of the consequences of such weather.  Classic studies of this type involve modelling floods, where detailed numerical models of water flow, taking into account the topography of the land, can give an estimate of exactly what flood might be expected at any location in a flood plain.  These models are critical in Australia - while we have a dry climate, it is also a climate of extreme events.  Floods occur more often than most people are conscious of.  Everyone is aware of the Brisbane River floods, but floods in Perth, in 1872 and 1926, devastated a city more known for its dryness rather than its rain.

Data Analysis Australia statisticians have applied extreme value methods to a variety of problems from environmental to financial, most recently understanding maximum likely demands for electricity.  Today, peak electricity demand is strongly driven by air conditioning and hence there is a need to understand the extremes in weather - temperature and humidity - and the link between such weather and electricity use.  These models have helped clients lower costs and ensure more reliable systems.