Modeling wildfire incident complexity dynamics

Abstract

Wildfire management in the United States and elsewhere is challenged by substantial uncertainty regarding the location and timing of fire events, the socioeconomic and ecological consequences of these events, and the costs of suppression. Escalating U.S. Forest Service suppression expenditures is of particular concern at a time of fiscal austerity as swelling fire management budgets lead to decreases for non-fire programs, and as the likelihood of disruptive within-season borrowing potentially increases. Thus there is a strong interest in better understanding factors influencing suppression decisions and in turn their influence on suppression costs. As a step in that direction, this paper presents a probabilistic analysis of geographic and temporal variation in incident management team response to wildfires. The specific focus is incident complexity dynamics through time for fires managed by the U.S. Forest Service. The modeling framework is based on the recognition that large wildfire management entails recurrent decisions across time in response to changing conditions, which can be represented as a stochastic dynamic system. Daily incident complexity dynamics are modeled according to a first-order Markov chain, with containment represented as an absorbing state. A statistically significant difference in complexity dynamics between Forest Service Regions is demonstrated. Incident complexity probability transition matrices and expected times until containment are presented at national and regional levels. Results of this analysis can help improve understanding of geographic variation in incident management and associated cost structures, and can be incorporated into future analyses examining the economic efficiency of wildfire management.

Figure 1. Model of the evolution of wildfire incident complexity dynamics through time.

At each time step (day), suppression actions and environmental conditions jointly influence the complexity of the incident. Stochasticity in system evolution is due to partial control and natural variation. System evolution begins with incident detection and ends with containment. Adapted from .

Figure 2. Forest Service Region numbers and names for the continental United States.

Figure 3. Conceptual representation of Markov Chain model of incident complexity dynamics.

Here only three states – high complexity, low complexity, and incident contained – are used to simplify presentation of the system. The contained state is presented as an absorbing state (i.e., P_CC = 1).

Figure 4. Three-state Markov Chain model of national-scale incident complexity dynamics, a simplified representation of the results presented in Table 3.

Due to rounding the presented transition probabilities may not sum perfectly to 1.00.