Birth-death-suppression Markov process and wildfires

TL;DR

This paper introduces a birth-death-suppression Markov process model for wildfires, analyzing extinction probabilities and burn sizes, and develops spectral methods for bounded population processes to support wildfire suppression decision-making.

Contribution

It presents a novel birth-death-suppression Markov process model for wildfires and applies spectral analysis using Pollazcek polynomials to analyze bounded burn scenarios.

Findings

Derived probabilities for extinction and burn size outcomes.

Developed spectral integral representations for bounded population processes.

Laid groundwork for real-time wildfire risk metrics and suppression strategies.

Abstract

Birth and death Markov processes can model stochastic physical systems from percolation to disease spread and, in particular, wildfires. We introduce and analyze a birth-death-suppression Markov process as a model of controlled culling of an abstract, dynamic population. Using analytic techniques, we characterize the probabilities and timescales of outcomes like absorption at zero (extinguishment) and the probability of the cumulative population (burned area) reaching a given size. The latter requires control over the embedded Markov chain: this discrete process is solved using the Pollazcek orthogonal polynomials, a deformation of the Gegenbauer/ultraspherical polynomials. This allows analysis of processes with bounded cumulative population, corresponding to finite burnable substrate in the wildfire interpretation, with probabilities represented as spectral integrals. This technology is developed in order to lay the foundations for a dynamic decision support framework. We devise real-time risk metrics and suggest future directions for determining optimal suppression strategies, including multi-event resource allocation problems and potential applications for reinforcement learning.