地形无序、风耦合与定向火势蔓延：地形加权森林火灾模型中的临界行为
Topographic Disorder, Wind Coupling, and Directional Fire Spread: Critical Behavior in a Terrain-Weighted Forest Fire Model
- Universidad Central de Chile（智利中央大学）
- Universidad Técnica Federico Santa María（弗雷德里科·圣塔玛利亚理工大学）
- Universidad de Antioquia（安蒂奥基亚大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出地形加权森林火灾模型，揭示地形坡度与风耦合对火势传播临界行为的影响，发现新的临界指数并预测火灾风险阈值。
AI中文摘要：
我们引入了地形加权森林火灾模型（TFFM），这是一个晶格模型，其中火势在空间相关的高斯高度场上传播，并具有非对称键概率 $p_{i\to j}=\mathrm{clip}[e^{-\beta+\gamma(h_j-h_i)},0,1]$，外加一个加性风偏置。模拟至 $L=8192$ 揭示了尖锐的活跃-非活跃转变，其临界抑制阈值 $\beta_c$ 关于 $\gamma$ 为偶函数，随 $|\gamma|$ 增大而减小，并随地形成相关长度 $\sigma_h$ 的减小而减小：坡度不对称性起到抑制作用，因为下坡键受到惩罚，火势在局部高程极大值处停滞。对于粗糙地形和低树木密度，即使在零抑制下，火势也无法渗透。有限尺寸标度给出了前沿速度指数 $\delta=0.34\pm0.02$，对于平滑和粗糙地形相同，且既不匹配有向渗透（$\nu_\parallel-\nu_\perp\approx0.56$）也不匹配各向同性渗透（$\approx0.18$）。在 $\beta_c$ 处的单种子存活概率与 $L$ 无关，且衰减极慢，运行指数从 $\approx0.09$ 降至 $\approx0.04$，排除了有向渗透，并表明在临界点存活概率保持有限，与 $P_{\rm surv}$ 降至零时的 $L$ 无关值 $P^*\approx0.5$ 一致。在这些尺寸下无法分辨关联长度指数，这与淬火关联无序引起的缓慢交叉修正一致。风将 $\beta_c$ 提高了2-4倍，在弱耦合下产生下风火痕漂移的急剧起始，并在高地形耦合下降低边界穿越时的燃烧比例——这是各向同性键无序模型中不存在的地形-风竞争效应。该模型产生的火灾风险阈值和火痕特征与卫星燃烧痕迹数据相当。
英文摘要：
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 $p_{i\to j}=\mathrm{clip}[e^{-β+γ(h_j-h_i)},0,1]$, 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 $ν=1.8\pm0.17$ from both the susceptibility peak and the width of the transition, and a front-velocity exponent $δ=0.34\pm0.03$, identical for smooth and rough terrain; neither matches directed percolation ($ν_\perp=0.73$, $ν_\parallel-ν_\perp\approx0.56$) or isotropic percolation ($ν=4/3$, $\approx0.18$). The single-seed survival probability at $β_c$ is independent of $L$ and decays extremely slowly, with a running exponent falling from $\approx0.09$ to $\approx0.04$, excluding directed percolation and pointing to a survival probability that remains finite at criticality, consistent with the $L$-independent value $P^*\approx0.5$ at which $P_{\rm surv}$ 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.
