Forest fires and other examples of self-organized criticality

We review the properties of the self-organized critical (SOC) forest-fire model. The paradigm of self-organized criticality refers to the tendency of certain large dissipative systems to drive themselves into a critical state independent of the initial conditions and without fine-tuning of the parameters. After an introduction, we define the rules of the model and discuss various large-scale structures which may appear in this system. The origin of the critical behavior is explained, critical exponents are introduced, and scaling relations between the exponents are derived. Results of computer simulations and analytical calculations are summarized. The existence of an upper critical dimension and the universality of the critical behavior under changes of lattice symmetry or the introduction of immunity are discussed. A survey of interesting modifications of the forest-fire model is given. Finally, several other important SOC models are briefly described.Comment: 37 pages RevTeX, 13 PostScript figures (Figs 1, 4, 13 are of reduced quality to keep download times small

Power-law behavior reveals phase transitions in landscape controls of fire regimes

In low-severity fire regimes of the American West and elsewhere, landscape memory of fire events is registered in fire-scarred trees, with temporal record lengths often exceeding 200 years^1-5^. Understanding the environmental controls on historical wildfires, and how they changed across spatial scales, is difficult because there are no surviving explicit records of either weather or vegetation (fuels). We show how power laws associated with fire-event time series arise in limited domains of parameters that represent critical transitions in the controls on landscape fire. We used stochastic simulations iteratively with Monte Carlo inference to replicate the spatio-temporal structure of historical fire-scar records in forested watersheds of varying topographic complexity. We find that the balance between endogenous and exogenous controls on fire spread shifts with topographic complexity, where in the most complex landscapes the endogenous controls dominate and the pattern exhibits criticality. Comparison to an self-organized criticality (SOC) model^6,7^ shows that the latter mimics historical fire only in a limited domain of criticality, and is not an adequate mechanism to explain landscape fire dynamics, which are shaped by both endogenous and exogenous controls. Our results identify a continuous phase transition in landscape controls, marked by power laws, and provide an ecological analogue to critical behavior in physical and chemical systems^8-11^. This explicitly cross-scale analysis provides a paradigm for identifying critical thresholds in landscape dynamics that may be crossed in a rapidly changing climate

Evaluation of WRF-Sfire Performance with Field Observations from the FireFlux experiment

This study uses in-situ measurements collected during the FireFlux field experiment to evaluate and improve the performance of coupled atmosphere-fire model WRF-Sfire. The simulation by WRF-Sfire of the experimental burn shows that WRF-Sfire is capable of providing realistic head fire rate-of-spread and the vertical temperature structure of the fire plume, and, up to 10 m above ground level, fire-induced surface flow and vertical velocities within the plume. The model captured the changes in wind speed and direction before, during, and after fire front passage, along with arrival times of wind speed, temperature, and updraft maximae, at the two instrumented flux towers used in FireFlux. The model overestimated vertical velocities and underestimated horizontal wind speeds measured at tower heights above the 10 m, and it is hypothesized that the limited model resolution over estimated the fire front depth, leading to too high a heat release and, subsequently, too strong an updraft. However, on the whole, WRF-Sfire fire plume behavior is consistent with the interpretation of FireFlux observations. The study suggests optimal experimental pre-planning, design, and execution of future field campaigns that are needed for further coupled atmosphere-fire model development and evaluation

A Note on Mathematical Modelling of Elliptical Fire Propagation

Mathematical modelling of forest fire propagation in time plays a key role in existing fire propagation predicting systems. Such systems are capable of simulating the growth of fire front in time and space and predicting spatial and temporal fire behaviour. In our previous papers, we studied mathematical foundations of the elliptical fire propagation model implemented in several advanced simulation systems.The model is based on Huygens' principle applied on fire propagation assuming locally elliptical fire spread. However, in the literature various other mathematical representations of local fire propagation have been reported, such as double ellipse, lemniskata, oval shape, tear shape, and others. Such types of local fire propagation have been experimentally observed in certain conditions during laboratory and field fires. In this paper, we demonstrate several simple examples of fire propagation corresponding both to the elliptical and non-elliptical local fire propagation in homogeneous conditions

Unmanned Aerial Systems for Wildland and Forest Fires

Wildfires represent an important natural risk causing economic losses, human death and important environmental damage. In recent years, we witness an increase in fire intensity and frequency. Research has been conducted towards the development of dedicated solutions for wildland and forest fire assistance and fighting. Systems were proposed for the remote detection and tracking of fires. These systems have shown improvements in the area of efficient data collection and fire characterization within small scale environments. However, wildfires cover large areas making some of the proposed ground-based systems unsuitable for optimal coverage. To tackle this limitation, Unmanned Aerial Systems (UAS) were proposed. UAS have proven to be useful due to their maneuverability, allowing for the implementation of remote sensing, allocation strategies and task planning. They can provide a low-cost alternative for the prevention, detection and real-time support of firefighting. In this paper we review previous work related to the use of UAS in wildfires. Onboard sensor instruments, fire perception algorithms and coordination strategies are considered. In addition, we present some of the recent frameworks proposing the use of both aerial vehicles and Unmanned Ground Vehicles (UV) for a more efficient wildland firefighting strategy at a larger scale.Comment: A recent published version of this paper is available at: https://doi.org/10.3390/drones501001

The Victorian Naturalist

v.114 (1997

Scaling, Propagation, and Kinetic Roughening of Flame Fronts in Random Media

We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density, below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with mean field theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time dependent width and equal time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.Comment: Standard LaTeX, no figures, 29 pages; (to appear in J. Stat. Phys. vol.81, 1995). Complete file available at http://www.physics.helsinki.fi/tft/tft.html or anonymous ftp at ftp://rock.helsinki.fi/pub/preprints/tft