Statistical Analysis of Large Wildfires

Abstract

Large, infrequent wildfires cause dramatic ecological and economic impacts. Consequently, they deserve special attention and analysis. The economic significance of large fires is indicated by the fact that approximately 94 percent of fire suppression costs on U.S. Forest Service land during the period 19802002 resulted from a mere 1.4 percent of the fires (Strategic Issues Panel on Fire Suppression Costs 2004). Further, the synchrony of large wildfires across broad geographic regions has contributed to a budgetary situation in which the cost of fighting wildfires bas exceeded the Congressional funds appropriated for suppressing them (based on a ten-year moving average) during most years since 1990. In turn, this shortfall has precipitated a disruption of management and research activities within federal land management agencies, leading to a call for improved methods for estimating fire suppression costs (GAO 2004). Understanding the linkages between unusual natural events, their causes and economic consequences is of fundamental importance in designing strategies for risk management. Standard statistical methods such as least squares regression are generally inadequate for analyzing rare events because they focus attention on mean values or typical events. Because extreme events can lead to sudden and massive restructuring of natural ecosystems and the value of economic assets, the ability to directly analyze the probability of catastrophic change, as well as factors that influence such change, would provide a valuable tool for risk managers. The ability to estimate the probability of experiencing a catastrophic event becomes more advantageous when the distribution of extreme events has a heavy-tail, that is, when unusual events occur more often than generally anticipated. Heavy-tail distributions have been used to characterize various types of catastrophic, abiotic natural phenomena such as Himalayan avalanches (No ever 1993), landslides, and earthquakes (Malamud and Turcotte 1999). Several studies also indicate that wildfire regimes have heavy-tails (discussed in section 2 below). For decades, economists have been interested in heavy-tails appearing in the distribution of income (Mandelbrot 1960), city sizes (Gabaix 1999, Krugman 1996), commodity prices series (Mandelbrot 1963a, Mandelbrot