Using catastrophe theory to model wildfire behavior and control
Forest wildfire managers are obligated to meetecosystem management objectives, such as cost minimization andresource allocation efficiency (J.T. Williams, R.G. Schmidt,R.A., Norum, P.N. Omi, and R.G. Lee. 1993. USDA For. Serv.Staffing Pap. Washington, D.C.), which is difficult because eachobjective is dependent upon wildfire controllability andbehavior. Currently, there is no functional formula that definesthe relationship between wildfire behavior and controllabilityand therefore, no physical basis for efficient economic analysis.This paper seeks to (1) identify environmental factors thatsystematically predict wildfire controllability and the rangeover which sudden changes in fire behavior occur, (2) quantifythe uncertainty of fire behavior in terms of the environmentalfactors, and (3) define a manageable environmental variablethat can be used to determine marginal costs and benefits ofwildfire management activities. We develop the theory and providean illustrative example of a cusp catastrophe using simulatedfire data. Preliminary results suggest that catastrophe theorymay be an effective tool to model wildfire controllability asmeasured by the modeled change in fireline intensity, windspeed,initial fuel moisture and fuel loading. Because the use of fuelloading as a control parameter describes the marginal physicaleffects on wildfire behavior, this framework may prove suitableas the production relationship for future economic analysis. Notethat the model specified in this paper is theoretical and shouldnot be applied until validated.