Topographic Disorder, Wind Coupling, and Directional Fire Spread: Critical Behavior in a Terrain-Weighted Forest Fire Model
Abstract
We introduce the Terrain-Weighted Forest Fire Model (TFFM), a lattice model in which fire spreads on a spatially correlated Gaussian height field with the asymmetric bond probability pi→ j=clip[e−β+γ(hj−hi),0,1], plus an additive wind bias. Simulations on lattices up to L=8192 reveal a sharp active-to-inactive transition whose critical suppression threshold βc is even in γ, decreases with |γ|, and decreases as the terrain correlation length σh is reduced: slope asymmetry acts as a suppressant because downhill bonds are penalized and fire stalls at local elevation maxima. For rough terrain and low tree density the fire fails to percolate even at zero suppression. Finite-size scaling on a fine β grid at L=2048--$8192$ gives a correlation-length exponent ν=1.8±0.17 from both the susceptibility peak and the width of the transition, and a front-velocity exponent δ=0.34±0.03, identical for smooth and rough terrain; neither matches directed percolation (ν⊥=0.73, ν∥−ν⊥≈0.56) or isotropic percolation (ν=4/3, ≈0.18). The single-seed survival probability at βc is independent of L and decays extremely slowly, with a running exponent falling from ≈0.09 to ≈0.04, excluding directed percolation and pointing to a survival probability that remains finite at criticality, consistent with the L-independent value P*≈0.5 at which Psurv drops to zero. Wind raises βc by a factor of $2−−4$, produces a sharp onset of downwind fire-scar drift at weak coupling, and, at high terrain coupling, decreases the burned fraction at boundary crossing---a terrain-wind competition effect absent from isotropic bond-disorder models. The model yields fire-risk thresholds and fire-scar signatures comparable to satellite burn-scar data.
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BibTeX
@misc{florez2026topographic,
title = {{Topographic Disorder, Wind Coupling, and Directional Fire Spread: Critical Behavior in a Terrain-Weighted Forest Fire Model}},
author = {Juan M. Florez and Eric Suárez Morell and Cristian Millan and J. Restrepo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07763},
eprint = {2609.07763},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07763},
}
RIS
TY - UNPB
TI - Topographic Disorder, Wind Coupling, and Directional Fire Spread: Critical Behavior in a Terrain-Weighted Forest Fire Model
AU - Juan M. Florez
AU - Eric Suárez Morell
AU - Cristian Millan
AU - J. Restrepo
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.07763
UR - https://arxiv.org/abs/2609.07763
AB - We introduce the Terrain-Weighted Forest Fire Model (TFFM), a lattice model in which fire spreads on a spatially correlated Gaussian height field with the asymmetric bond probability p_i→ j=clip[e^−β+γ(h_j−h_i),0,1], plus an additive wind bias. Simulations on lattices up to L=8192 reveal a sharp active-to-inactive transition whose critical suppression threshold β_c is even in γ, decreases with |γ|, and decreases as the terrain correlation length σ_h is reduced: slope asymmetry acts as a suppressant because downhill bonds are penalized and fire stalls at local elevation maxima. For rough terrain and low tree density the fire fails to percolate even at zero suppression. Finite-size scaling on a fine β grid at L=2048--$8192$ gives a correlation-length exponent ν=1.8±0.17 from both the susceptibility peak and the width of the transition, and a front-velocity exponent δ=0.34±0.03, identical for smooth and rough terrain; neither matches directed percolation (ν_⊥=0.73, ν_∥−ν_⊥≈0.56) or isotropic percolation (ν=4/3, ≈0.18). The single-seed survival probability at β_c is independent of L and decays extremely slowly, with a running exponent falling from ≈0.09 to ≈0.04, excluding directed percolation and pointing to a survival probability that remains finite at criticality, consistent with the L-independent value P^*≈0.5 at which P_surv drops to zero. Wind raises β_c by a factor of $2−−4$, produces a sharp onset of downwind fire-scar drift at weak coupling, and, at high terrain coupling, decreases the burned fraction at boundary crossing---a terrain-wind competition effect absent from isotropic bond-disorder models. The model yields fire-risk thresholds and fire-scar signatures comparable to satellite burn-scar data.
ER -