ANALYTICAL FOUNDATIONS FOR FIRE HISTORY IN SCALING AND PROBABILITY THEORY

FALK, D.

Laboratory of Tree-Ring Research, University of Arizona

Scale dependence is an inherent property of fire regimes. I examine three areas of scaling and probability theory as applied to fire history research, using data from Monument Canyon Research Natural Area (MCN), Jemez Mountains, New Mexico.

The event-area (EA) relationship is a scaling function analogous to the species-area relationship for fire events distributed in space and time; the interval-area (IA) relationship, is a related form for fire intervals. Statistical descriptors of the fire regime for the MCN data set, such as fire frequency and mean fire interval, are scale-dependent and show-EA/IA behavior (Figure 1). The slope of the EA/IA is a metric of spatio-temporal synchrony of events across multiple spatial scales and may provide an index of climate entrainment of the fire regime.

Scaling also applies to the temporal distribution of fire events. I outline a theory of fire interval probability from first principles in fire ecology and statistics. Fires are conditional events resulting from interaction of multiple contingent factors that must be satisfied for an event to occur. Outcomes of this kind are multiplicative processes for which a lognormal model is the limiting distribution.

I conclude by outlining a theory of sample size in fire history, beginning with a model of the collector's curve based on accumulation of sets of discrete events and the probability of recording a fire as a function of sample size. All measures of the fire regime at MCN reflect sensitivity to sample size, but a nonlinear regression correction procedure can correct for differences in sample size among composite fire records, increasing confidence in quantitative estimates of the fire regime.

Figure 1.