Fire and Environmental Research Applications Team

Large wildfires can have significant impacts on natural, social, and economic systems. Future climatic scenarios call for an increase in the risk of more severe fires in western forest. Most forest fires are small and do little damage, but they do not occur frequently. In contrast, large fires which do significantly damage are very infrequent events. Commonly, analyses of wildfires use the mean and variance of a probability distribution (e.g. mean fire size, mean area burned, etc.). However, a single extreme event may disrupt the central tendency of the fire occurrence distribution. Catastrophic wildfires are a major concern in public policy; however, these extreme events are not adequately addressed by standard statistics. This paper presents a modeling approach based on the statistics of extreme events to model large forest fires. Large wildfires can be modeled as those exceeding a high threshold. IN the limit of large measurements, the probability structure of extreme fire events will converge to the Frechet-type distribution. However, given the long distribution tail, mean and variance are not finite. For decision making or ecosystem analysis where mean and variance are needed, an alternative using the Truncated Pareto distribution is presented.

Typically, when a large fire occurs the capability of local fire organizations is exceeded and falls into an upper level of decision making, either state, regional, or national. We consider that a decision making level that deals with large fires should be based on models that represent those extreme events. In this paper we offer an analytical approach to model only the large fires that exceed an upper damage threshold. This approach could potentially improve the decision making process for fire management. The statistics of extremes approach can also be used to model only those fire events that may be relevant at large ecological spatial scales.

Alvarado, Ernesto; Sandberg, David V.; Pickford, Stewart G. 1998. Modeling large forest fires as extreme events. Northwest Science. 72 (Special Issue). p.66-75.