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Opinion

The Mathematics of Connectivity and Bushfires: A Note from David Ward

By jennifer
April 29, 2009

HUNGARY has produced many outstanding mathematicians and physicists. Perhaps there is a connection with rampant violin playing.

One of these was Paul Erdös who was the twentieth century’s most prolific mathematician, with 1475 papers to his credit. He rivals Leonhard Euler, the Swiss genius of the eighteenth century. There is a worthwhile biography of Erdös called ‘The Man Who Loved Only Numbers’, by Paul Hoffman (1998).

On a recent thread at this blog (Wise Men Excluded from Bushfire Royal Commission), I raised the issue of fuel connectivity, and suggested that it helped to explain the uncontrollable spread of bushfires over large areas of Victoria a few months ago.

The tonnage of available fuel determines the intensity, and convection column strength, and the number of flying embers, but connectivity determines ground spread. Wind is important, but large fires, of course, create their own wind. It seems to me that the application of Occam’s Razor makes climate superfluous to the argument, beyond there being weather dry enough for a fire to burn. Given dry fuel, fierce fires can occur even at mild temperatures. Surely we have all lit a pot-belly stove on a winter’s day.

Although I doubt if he had ever seen a bushfire, or a gumtree, Erdös had useful ideas on connectivity in networks. With a Hungarian colleague, he published papers about ‘giant patches’. These form when random connections are made between a set of random points (Erdös and Renyi 1959, 1960).

The idea of networks (connected graphs) originated, in Europe at any rate, with Euler, when he solved the puzzle of the seven Bridges of Königsberg. Recent applications have been in neural networks in the brain, disease epidemics, and the growth of the world wide web. ‘Six degrees of separation’ may ring a bell for some.

With regard to bushfire, as fire is excluded from a large area, formerly disconnected fuel patches join up, and this process suddenly accelerates as ‘cliques’ of patches start connecting. Some have called this phenomenon a ‘connectivity avalanche’. Once a certain threshold is passed, bushfire can spread uncontrollably. Ember showers, due to heavy fuel burning, can obviously accelerate the process by causing another level of connectivity.

I give this information for those constructive contributors who are interested in ideas about bushfire management. Probably I should publish it quickly before someone from academia claims it. Those involved in research will know the sequence: a) Rubbish, b) Well, perhaps in some cases, c) Of course, and I thought of it first.

Fuel reduction burning reduces both fuel quantity, and, importantly, connectivity. The restoration of something like Aboriginal patch burning, by both reducing fuel, and disrupting connectivity, would make large bushfires a thing of the past, no matter what the weather. The bush would be healthier, and safer for native animals, not to mention humans. Should I mention erosion and water supplies? Or the fact that mild fires sequester enormous amounts of carbon as charcoal, but very hot fires create mainly ash, and volatilize much of the nutrients?

*******************

David Ward lives in Western Australia and comments at this blog under the alias 'Green Davey'.

The picture is of grass trees at Scott River, Western Australia, taken in January 2007, following a "mild, patchy burn".

Previous contributions from Mr Ward include:

Nyoongars, Noolbengers and No Fires
https://climatelab.com.au/blog/2007/02/nyoongars-noolbengers-and-no-fires-a-note-from-david-ward/ 

Parachutes & Prescribed Burning
https://climatelab.com.au/blog/2007/01/parachutes-prescribed-burning-a-note-from-david-ward/

Noongars Knew Best (Part 2)
https://climatelab.com.au/blog/2005/09/noongars-knew-best-part-2/

Noongars Knew Best
https://climatelab.com.au/blog/2005/06/noongars-knew-best/

Good Causes

Comments

  1. Steve,
    I'm happy to state that i'm pro burning (current operational experience in WA) and i will respond, as expected, because I dont think you give a full picture of the FRB in this case before stating that it was of no value..I find this unusual if you were being objective.

    As a fire scientist you would know that a prescribed burn can vary in its intensity based on the conditions under which it is done. Your reference to woody material being left after the burn suggests that it was a mild one.. I am assuming you made a mistake in mentioning that the "fine fuels were no(?) reduced" as it is the fine fuels which are most important in producing a successful fuel reduction burn ..If they weren't reduced I would suggest that the FRB was patchy at best and not successful in reducing fuel levels prior to the fire.

    You do not mention the levels of ground fuel pre burn..In one area it may need a few mild burns in heavy fuels before the "available fuel" levels are brought down to an acceptable level without causing severe canopy scorch.. So without an understanding of fuel levels prior to the FRB your comment cannot be taken at face value... one burn may not have been enough to reduce the fire hazard to a remotely manageable level.

    I'm not saying that you are wrong about it being a canopy fire however, I dont think you have represented all the facts relating to the FRB prior to the fire that would give an true indication as to whether it had made a difference or not.

  2. To all those angry people who write on this site defending their own personal pro-FRB dunghills.

    As in the course of my profession over the last 7 weeks, I have done much walking along the waterways all around the Marysville area employed by an agency.

    As an experienced fire scientist (25 years - yes there is more than one of these people on the continent), I can tell you that it was obvious which areas to the south, west and east of Marysville were fuel reduced. The simple facts are this. The coarse woody debris (logs, etc.) present prior to the fire was still there afterwards. The fine fuels at ground level had no been reduced prior to the fire. And yes, it appears as if the area burnt was more than a 2 km radius from the town at least to the south and west.

    And do you know what, the fuel reduction burning in these areas appeared to make absolutely no difference to the extreme fire intensity experienced (and presumably the rate of forward spread) - it was a fast mostly canopy fire. In many areas, it was so intense that Mountain Ash fruit was combusted in the canopy (there will be no regeneration), and the radiant heat from this canopy fire has even killed the Bracken rhizomes in the soil (despite the ground fuel being reduced). It was an extreme event on an extreme weather day, and no amount of fuel reduction (burn back to the coast if you want) would not have made any difference.

    So, when all of you pro-fuel reduction burn, burn the continent as the cure-all for everything, types respond to this as anticipated, I'll then tell you the story of the negative ecological impacts that FRB has on veg. Based on scientific fact, not twisted logic.

    By the way, for the record, I do believe in FRB around infrastructure to reduce the ground intensity in lesser events, but 350,000 ha across the States per annum .....

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