Mathematics the new weapon against extreme bushfires

Mathematics the new weapon against extreme bushfires

13 October 2016

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Australia —  Mathematicians say new research could be a game-changer in predicting the movements of catastrophic bushfires.

Number-crunching has long been used to understand how fire behaves, but until recently the formulas have lacked the flexibility to predict the movement of extreme bushfires, such as the Black Saturday disaster of 2009.

“Fire, like with most of nature, is inherently mathematical,” Jason Sharples from the University of New South Wales said.

“Think about a flat piece of ground with some fuel on it, if you stick a match on it, [providing there is no wind] the fire will actually spread as a circle, which is a mathematical object.

“When you add extra complexity into the landscape, things get a little bit more complicated than just a circle, but it’s still mathematics which is underpinning how the fire spreads.”

There is a lot at stake in getting the formulas right, because the sudden change of direction by a massive bushfire is a matter of life and death.

Dr Sharples specialises in the applied mathematics of bushfires and has been studying phenomena such as vorticity-driven lateral spread, eruptive fire spread and mass spotting.

“These are all examples of what I would call dynamic fire spread,” he said.

“These phenomena really typify where the new paradigm of fire-spread modelling is going.”

New knowledge, new formulas

He said, throughout the 20th century, traditional mathematical modelling of bushfires relied on rigid formulas that did not allow for the fast-changing, dynamic nature of extreme fires.

With simple fires, the models can rely on fixed data, such as wind speed, wind direction, fuel density, humidity, and the angle of slopes.

That goes out the window when a bushfire becomes extreme, because those numbers are no longer fixed.

“The underlying assumption I refer to is the quasi-steady assumption,” Dr Sharples said.

“You are assuming that over the course of the fire-spread, the fire is spreading more or less at a constant rate of spread.

“That assumption is valid for a simple fire.

“The problem is that you are precluding any sort of dynamic effects in your fire-spread.”

It is only in the past five years that mathematicians have really focussed on embracing the shifting variables that truly reflect how massive fires spread.

When an extreme bushfire gets going, it becomes powerful enough to influence and feed off the atmosphere around itself.

At this point, Dr Sharples explained, the event becomes “both a fire and a storm”, having a huge impact on the direction and speed of air movements around the fire.

These fast-changing factors are critical in fire fighters’ efforts to protect property and human life.

From a mathematician’s point of view, once a fire begins to affect the direction and speed of air movements, then more sophisticated models are required to account for them.

The good news is there are now mathematical models that can account for these movements, boosting authorities’ ability to predict the fire’s next move.

Bizarre behaviour

One of the least understood behaviours displayed by bushfires has been their ability to move at right angles to the wind direction.

It contradicts our instinctive belief that fire will always spread with the direction of the wind, given a flat surface.

The ramifications of this lateral movement can be a matter of life and death, throwing fire fighters’ tactics into chaos.

Again, these bizarre movements occur because the fire has affected air movements, in this case creating vortexes, like spiralling columns of air, which push the fire sideways.

Flames ‘exploding’ uphill

Another example of extreme fire movement is when large flames burn on a slope.

Any flame sucks in air from all sides, but when this occurs on a slope there can be less air available on the uphill side, simply because there is less space there.

As a result, the flame sucks in more air than is available on the uphill side, creating a space with lower pressure.

Air from the downhill side rushes up to fill the void, creating a violent surge of air and fire that bursts up the slope like an explosion.

Mathematicians are just starting to develop models to predict this behaviour, factoring in the slope angles, wind, temperature and other variables.

Few would expect the battlefront against catastrophic bushfires to be led from the desktops of applied mathematicians.

Dr Sharples said the traditional infantry of fire fighters, fire trucks and helicopters would always lead the charge, but if mathematical modelling continued to improve, those fighters could be armed with better information to plan their movements in life and death situations.

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