Using Catastrophe Theory to Model the Economic Effects of Wildfire Behavior

Document Type

Presentation Abstract

Presentation Date

2-26-1998

Abstract

Wildfire managers are obligated to meet ecosystem management objectives such as cost minimization and efficiency (Williams et al. 1993). This, however, is difficult because each objective is dependent upon wildfire controllability and wildfire behavior. Currently, there is no functional form that defines the relationship between wildfire behavior and controllability and therefore, there is no physical basis for efficient economic analysis. In the first section I generate a fire data set and test it as a cusp catastrophe. Results suggest that catastrophe theory may be an effective tool to model wildfire controllability as measured by the modeled change in fireline intensity, windspeed, initial fuel moisture and fuel loading. The resulting production function relationship presents three management possibilities. The model may be used to; identify environmental factors that systematically predict wildfire controllability and the range over which sudden changes in fire behavior occur; to quantify uncertainty of fire behavior in terms of environmental factors, and; to define a manageable environmental variable that can be used to determine marginal costs and benefits of wildfire management activities. The second section enhances the C+NVC theory by including the physical effects of wildfire behavior and environmental conditions as developed in the first section. To facilitate development of the model I use two factors of production, suppression, which is variable throughout all time periods, and presuppression, which is fixed in the short run and variable in all other instances. I show that the annual C+NVC curve is the economic envelope to the seasonal C+NVC curves. Next, I characterize net value change as a monotonically increasing function of fireline intensity. Because the fire model relates physical effects to fireline intensity, the C+NVC model is enhanced in three ways; the introduction of environmental variables will enable fire managers to assess fire management programs for severe and average expected fire behavior and identify conditions that lead to management uncertainty; fire behavior is defined in terms of intensity and controllability, therefore, the cusp model generates different estimates of suppression efficiency depending upon environmental conditions and expected fire behavior, and; the NVC manifold provides a method by which to evaluate the marginal effectiveness of presuppression.

Additional Details

Thursday, February 26, 1998
4:10 p.m. in MA 109
Coffee/Tea/Treats 3:30 p.m. in MA 104 (Lounge)

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