Fire Spread Modeling using Probabilistic Cellular Automata

The paper clearly specifies a probabilistic CA with six states and an explicit local rule f that maps the current cell state and its neighbours at time t to the next state at time t+1, including Rules 1–5 and an EMPTY sink after burning, and it references a lightning probability and a wind-driven modulation of spread via an ODE and a synthesized pb function; it also states that parameters are fitted by minimizing the discrepancy between predicted and observed burned area using a non-linear optimization routine. However, it provides no formal statements or proofs about (i) the Markov property/time-homogeneity of the global process, (ii) almost-sure finite-time absorption under p_lightning = 0, or (iii) existence of a minimizer for the calibration objective on a compact parameter set. The candidate solution supplies these missing hypotheses (e.g., finite burning durations, p_lightning = 0, time-invariant parameters) and gives a correct, standard argument: the CA on a finite grid induces a time-homogeneous Markov chain; with finite per-cell burn durations and no spontaneous ignition, the chain hits the absorbing set almost surely in finite time; and continuity plus compactness ensures the calibration objective attains a minimum. Hence, the paper’s exposition is incomplete on these theoretical points, while the model’s solution is correct given mild, explicit assumptions consistent with the paper’s rules and intent. The states and rules are described in Table 1 and the local update f is explicitly defined in the paper, supporting the Markov framing; lightning and wind mechanisms are discussed; and optimization to match burned area is noted, but without formal guarantees or objective definition, which the candidate provides.