Analytical and numerical insights into wildfire dynamics: Exploring the advection-diffusion-reaction model

Understanding the dynamics of wildfire is crucial for developing management and intervention strategies. Mathematical and computational models can be used to improve our understanding of wildfire processes and dynamics. This paper presents a systematic study of a widely used advection-diffusion-reaction wildfire model with non-linear coupling. The importance of single mechanisms is discovered by analysing hierarchical sub-models. Numerical simulations provide further insight into the dynamics. As a result, the influence of wind and model parameters such as the bulk density or the heating value on the wildfire propagation speed and the remaining biomass after the burn are assessed. Linearisation techniques for a reduced model provide surprisingly good estimates for the propagation speed in the full model.

[1]  A. Navas-Montilla,et al.  A family of well-balanced WENO and TENO schemes for atmospheric flows , 2023, J. Comput. Phys..

[2]  P. Baker,et al.  Human‐Driven Fire Regime Change in the Seasonal Tropical Forests of Central Vietnam , 2023, Geophysical Research Letters.

[3]  S. Stephens,et al.  Fire return intervals explain different vegetation cover responses to wildfire restoration in two Sierra Nevada basins , 2022, Forest Ecology and Management.

[4]  R. Bradstock,et al.  The 2019–2020 Australian forest fires are a harbinger of decreased prescribed burning effectiveness under rising extreme conditions , 2022, Scientific Reports.

[5]  N. Koutsias,et al.  Global warming is shifting the relationships between fire weather and realized fire-induced CO2 emissions in Europe , 2022, Scientific Reports.

[6]  Christopher H. Guiterman,et al.  Mechanisms of forest resilience , 2022, Forest Ecology and Management.

[7]  G. Miguez-Macho,et al.  Spatial and temporal expansion of global wildland fire activity in response to climate change , 2022, Nature Communications.

[8]  N. Baranovskiy,et al.  Mathematical Simulation of Forest Fuel Pyrolysis and Crown Forest Fire Impact for Forest Fire Danger and Risk Assessment , 2022, Processes.

[9]  Anabelle W. Cardoso,et al.  Understanding and modelling wildfire regimes: an ecological perspective , 2021, Environmental Research Letters.

[10]  T. Banerjee,et al.  Spatial and temporal pattern of wildfires in California from 2000 to 2019 , 2021, Scientific Reports.

[11]  S. Coats,et al.  Human-driven greenhouse gas and aerosol emissions cause distinct regional impacts on extreme fire weather , 2021, Nature Communications.

[12]  L. M. Villada,et al.  Exploring a Convection–Diffusion–Reaction Model of the Propagation of Forest Fires: Computation of Risk Maps for Heterogeneous Environments , 2020, Mathematics.

[13]  Mauro Innocente,et al.  Physics-based model of wildfire propagation towards faster-than-real-time simulations , 2020, Comput. Math. Appl..

[14]  L. M. Villada,et al.  Implicit-Explicit Methods for a Convection-Diffusion-Reaction Model of the Propagation of Forest Fires , 2020, Mathematics.

[15]  Adrián Navas-Montilla,et al.  Depth-averaged unsteady RANS simulation of resonant shallow flows in lateral cavities using augmented WENO-ADER schemes , 2019, J. Comput. Phys..

[16]  E. Siirila‐Woodburn,et al.  Watersheds dynamics following wildfires: Nonlinear feedbacks and implications on hydrologic responses , 2019, Hydrological Processes.

[17]  O. Viedma,et al.  Wildfires and the role of their drivers are changing over time in a large rural area of west-central Spain , 2018, Scientific Reports.

[18]  C. A. Cansler,et al.  Fire and tree death: understanding and improving modeling of fire-induced tree mortality , 2018, Environmental Research Letters.

[19]  M. Innocente,et al.  A two-dimensional reaction-advection-diffusion model of the spread of fire in wildlands , 2018 .

[20]  Shahid Habib,et al.  Biomass burning, land-cover change, and the hydrological cycle in Northern sub-Saharan Africa , 2016 .

[21]  Cristina Santín,et al.  Global trends in wildfire and its impacts: perceptions versus realities in a changing world , 2016, Philosophical Transactions of the Royal Society B: Biological Sciences.

[22]  E. Crooks,et al.  Lack of symmetry in linear determinacy due to convective effects in reaction-diffusion-convection problems , 2016 .

[23]  B. Perthame.  Parabolic Equations in Biology: Growth, reaction, movement and diffusion , 2015 .

[24]  Thomas Hillen,et al.  The Effect of Wind on the Propagation of an Idealized Forest Fire , 2009, SIAM J. Appl. Math..

[25]  A. Sullivan.  Wildland surface fire spread modelling, 1990–2007. 3: Simulation and mathematical analogue models , 2009 .

[26]  Jonathan D. Beezley,et al.  A wildland fire model with data assimilation , 2007, Math. Comput. Simul..

[27]  A. Sullivan,et al.  Wildland surface fire spread modelling, 1990–2007. 2: Empirical and quasi-empirical models , 2007, 0706.4128.

[28]  M. Isabel Asensio,et al.  A convection model for fire spread simulation , 2005, Appl. Math. Lett..

[29]  M. I. Asensio,et al.  On a wildland fire model with radiation , 2002 .

[30]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[31]  K. P. Hadeler,et al.  Travelling fronts in nonlinear diffusion equations , 1975 .

[32]  E. Neafsey,et al.  Fire in the Earth System , 2009 .

[33]  C. Vreugdenhil.  Numerical methods for shallow-water flow , 1994 .