Frequency-Area Scaling Relationships
During my Master's Thesis (Millington 2003) I worked with Dr. Bruce Malamud to examine wildfire frequency-area statistics and their ecological and anthropogenic drivers. Work resulting from this theis has led to the publication of a peer-review paper (Malamud et al. 2005), a review book chapter (Millington et al. 2006), and several conference presentations.

Briefly, the examination of the frequency-area statistics of wildfires is one method to quantify a wildfire regime. Recent frequency-area studies of wildfire occurrence data for several regions of the world have suggested power-law behaviour over many orders of magnitude, of the form:

where is the frequency of fires with size , and is a constant. Beta is a measure of the ratio of small to medium to large size fires and how frequently they occur. Such a power-law relation is represented on a log-log plot as straight line (e.g. Figure 1).

Figure 1. Power-law frequency-area distribution for wildfire in a region of the conterminous USA.

By normalising for the spatial and temporal extents of the wildfire data, the frequency-area relationship of different regions may be compared and spatially mapped. This is what Malamud et al. 2005 and Millington 2003 did for regions of the USA and Canada. By comparing the frequency-area scaling and other aspects (e.g. vegetation, topography) of distinct regions, investigation into the drivers of wildfire regimes is possble. Finally, this method allows the calculation of the recurrence intervals for wildfires of a given size in a region.

Links
Bailey's Ecoregions - [Link]
Fire Statistics Databases - [Link]
"Why do physicists care about power laws so much?" - [Link]
Statistical Distributions - [Link]