# Explainer: was the Sydney storm 'once-in-a-century'?

Monday, Apr 27, 2015, 07:49 PM | Source: The Conversation

Kate R Saunders, David Karoly, Peter Taylor

It’s been called the “storm of the century” or a “once-in-a-decade” event, but how often do storms such as the one that lashed New South Wales over the past week really happen?

On April 21 flash floods from extreme rainfall in the Hunter Valley of New South Wales caused substantial damage to bridges and buildings and loss of life. We want to understand how often an event of this size is expected to occur.

The town of Dungog – which saw three deaths and houses washed away – recorded 190 mm of rain, a near record. Nearby Tocal saw a record-breaking 242mm, while Sydney recorded 119 mm.

We’ve analysed the data – while there’s good news for the towns most severely hit in that this level of rainfall really is rare, Sydney can expect similar rainfalls not once-in-a-century, but once every three years.

## How rare is rare?

The problem is: “How can we estimate the frequency of rare extreme events from observations, or events that we are yet to witness, such as a 1-in-500-year event?” To solve this problem we need to model the data and use it to extrapolate outside our observations.

When we’re talking about flash floods and extreme rainfall, we want to know the highest rainfall in a single day or in a few hours, rather than total rainfall over longer periods such as a month or year. The best long-term rainfall observations are for daily rainfall.

One of the Bureau of Meteorology’s observing stations close to Tocal with a long record is Dungog. When we consider the wettest day observed each year at Dungog, the most frequent observed wettest day of the year has approximately 66mm of rain. But in some years the wettest day has over 150mm of rainfall, as you can see in the chart below.

Using the maximum daily rainfall recorded for each year at Dungog Post Office from 1898 to 2015, we can fit a statistical model called a Generalised Extreme Value Distribution, the black line in the chart above. From this extreme value model we can calculate how often an extreme daily rainfall event is expected to occur.

## Returning rains

For example in Dungog, a daily rainfall total exceeding 125mm would be expected to occur on average once every 10 years, and a 200mm plus down-pour would be expected on average once every 100 years.

The rainfall amount corresponding to the flash-flood event in Dungog on April 21 was 190mm. This amount is just slighter than the highest recorded total of 223.5mm in 1946. We estimate an extreme rainfall equal or exceeding 190mm to occur on average once every 75 years, as you can see in the chart below.

So does that mean the residents of Dungog don’t have to worry about an event of this size occurring for the next 75 years? No. An event of this magnitude can occur two years in a row or even in the same year with very low probability. What we mean when we say a 1-in-75-year event is that within a given year an event of this size, daily rainfall equal to or greater than 190mm, is expected with probability 1/75.

As with all statistical models that approximate observed data, there is uncertainty in the estimation. This uncertainty is shown by the dotted lines in the chart above. We can see from this uncertain range that it is not outside the realms of possibility that an event as extreme as this might occur on average once every 33 years as a lower bound (see red line in the chart).

This might seem like a large uncertainty range but, given we are extrapolating from small amounts of data, it is not surprising. What gives confidence to the return levels predicted is they are similar to model predictions at nearby sites such as Branxton.

Sydneysiders can look forward to observing a rainfall event equal or greater than the event on April 21 again soon. The estimated return period for the observed 119 mm of rainfall at Sydney Observatory Hill is that it is only a one in three year event. What Sydney residents need to watch out for is 274 mm of rainfall or more falling in one day. That is a 1 in 100 year event!

What is interesting about this event is that rainfall for the wettest day of the year is normally higher in Sydney, because it is a coastal region, than in Dungog, but that was not the case for April 21.

Kate will be on hand for an author Q&A between 10 and 11am AEST on Wednesday April 29. Post your questions in the comments section below.

Kate Saunders is supported by a Melbourne research scholarship funded by ARC Laureate Fellowship FL130100039.

David Karoly receives funding from the Australian Research Council Centre of Excellence for Climate System Science. He also shares in funding from the European Commission for his role as a Research Director in the EU Centre on Shared Complex Challenges at the University of Melbourne. He is a member of the Climate Change Authority and the Wentworth Group of Concerned Scientists.

Peter Taylor's research is supported by the Australian Research Council Laureate Fellowship FL130100039 and the ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS).