Modeling wildfire dynamics through a physics-based approach incorporating fuel moisture and landscape heterogeneity

TL;DR

The paper addresses how fuel moisture and landscape heterogeneity influence wildfire spread by developing a macroscopic Advection-Diffusion-Reaction framework for a two-phase porous medium. It advances by introducing moisture via the apparent calorific capacity method and exploring four moisture variants (NM, S2M, S3M, C2M) within a consistent ADR structure that also incorporates wind, local radiation via the Rosseland approximation, and topography. Key contributions include detailed derivations from energy and mass balances, a robust finite-volume numerical implementation with SSP-RK3 time stepping, and extensive parametric analyses in 1D and 2D that illuminate when moisture and radiation dominate fire behavior and how topography modulates spread. The work assesses the model’s behavior against laboratory and field observations, demonstrates the sensitivity of rate-of-spread to moisture, wind, and surface cover, and provides guidance on model choices and calibration for predictive wildfire dynamics.

Abstract

Anthropogenic climate change has increased the probability, severity, and duration of heat waves and droughts, subsequently escalating the risk of wildfires. Mathematical and computational models can enhance our understanding of wildfire propagation dynamics. In this work, we present a simplified Advection-Diffusion-Reaction (ADR) model that accounts for the effect of fuel moisture, and also considers wind, local radiation, natural convection and topography. The model explicitly represents fuel moisture effects by means of the apparent calorific capacity method, distinguishing between live and dead fuel moisture content. Using this model, we conduct exploratory simulations and present theoretical insights into various modeling decisions in the context of ADR-based models. We aim to shed light on the interplay between the different modeled mechanisms in wildfire propagation to identify key factors influencing fire spread and to estimate the model's predictive capacity.

Figures (20)

• Figure 1: Plot of idealized, S2M-approximated, and S3M-approximated $h$-$T$-curves. Note the relations $\Delta h_{\mathrm{sen},1}=h_w-h_{\infty}$ and $\Delta h_{\mathrm{sen},2}=h_{pc}-(h_w+ML_w)$.
• Figure 2: Comparison of the simulations using the two combustion functions. (a) Comparison of the combustion function using the Arrhenius law in Eq. \ref{['eq:psi_arrhenius']} and with a constant term in Eq. \ref{['eq:psi_constant']}. (b) Solutions of the ADR model \ref{['eq:model1b']} using the two combustion functions. The graphs widely overlap.
• Figure 3: Comparison of the solution profiles for the temperature $T$ and the fuel $Y$ at a fixed time with and without radiation. The parameter $k_c$ differs in the two cases for compensating the lack of radiation.
• Figure 4: Comparison of the traveling wave profiles for the temperature $T$ and the fuel $Y$ at a fixed time for two-stage moisture models (S2M, C2M) with the three-stage moisture model S3M. The moisture content is $M=0.1$, the wind speed is $w=0$, and the live/dead ratio is $r=1$.
• Figure 5: Comparison of traveling wave profiles for the temperature $T$ and the fuel $Y$ for two-stage and three-stage moisture models with fixed $x=350$ m, and parameters $M=0.1$, $r=1$, $w=0$. Left: Phase portrait of the solutions at a fixed $x$; right: time-dependent solutions showing the traveling wave profiles.

Theorems & Definitions (6)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5
• Remark 6