Bidi Burning

Bushfires and Mathematical Knot Theory

A Seminar by David Ward

Bushfire mosaics are very important in maintaining a diversity of habitats for both plants and animals.  They can also protect water catchments, and nearby human settlements.

I In a previous seminar for the Water Corporation of WA (2007), I showed, through Graph Theory, how a bushfire mosaic can easily be lost through ill-advised fire exclusion (‘Does God Play Dice?’), followed by an inevitably large and uncontrollable bushfire.

In this seminar I show how, where a bushfire mosaic has been lost, it can be restored through a simple strategy drawn from mathematical Knot Theory.  The strategy is extremely flexible, and could be used along tracks and creeks.

The Nyoongar word for a track is ‘bidi’.  There were many throughout the south-west before Europeans arrived, and Nyoongar burning would have been most frequent close to such tracks and creeks, so maintaining a relatively fine mosaic.  Further out, the mosaics were most likely coarser.  We can learn from the traditional custodians of the land.

   To the right I show a mosaic developed using Knot Theory.  Once established, the patches could be burnt at any cyclic interval, from biennially up to the number of patches in the mosaic.  However, in the absence of fire suppression by humans, the mosaic will inevitably coarsen if fire is excluded from any patch for more than the return period of fire in that patch.  Self-organisation by bushfire mosaics is unavoidable.  For upland jarrah forest the return period for fire is, beyond any shadow of doubt, 2-4 years.

   Further, bushfire mosaics have a fractal quality, in that each burnt patch can be, in itself, a mosaic of second order burnt and unburnt, due to the presence of rocks, or moist, shady places, aspect , animal diggings etc.  This second order mosaic will be most pronounced when fires are frequent and mild, in low fuel.  It will disappear when long fire exclusion and heavy fuel loads create large, fierce fires.  A good example of such total burnout, due to heavy fuel, was at Mt Cooke a few years ago.  There are others, notably in National Parks, where long fire exclusion has been attempted.  Due to poor fire policy, King’s Park bushland has been damaged by two fierce fires since 1980.  Overseas, Kruger National Park burned fiercely in 2001, due to ill-advised fire exclusion.  Twenty humans were killed, plus large animals such as elephant and rhino.  In 1988, Yellowstone National Park burned fiercely for the same reason.

By mosaic burning along tracks and creeks, the Water Corporation, and DEC, could protect Wungong water catchment from future uncontrollable bushfires.  It would definitely benefit two iconic plants, the balga (Xanthorrhoea preissii) and the djiridji (Macrozamia riedlii).  It would also help to protect humans, such as resident catchment rangers, recreationists on the Bibbulman Track and Munda Bidi, and residents of Bedfordale and Jarrahdale.