Forest Fires: An Example of Self-Organized Critical Behavior

Abstract

R E P O R T S rial. Futtire planeta~y accretion models will ha! e to accolmt for this obse~~,ation. T11e real-izatio~l of a variation in Fe Si ratio among the terrestrial planets \I ill also alter the details of our ~nodels of maltia~~ lna~ltle chemistly and core fomlation sce~larios. Models of core formation in the renestrial planets cannot assume bulk C 1 sitlerophile eleinent abu~ldances.Despite the many complexities concerning their initiation and propagation, forest fires exhibit power-law frequency-area statistics over many orders of magnitude. A simple forest fire model, which is an example of self-organized criticslity, exhibits similar behavior. One practical implication of this result is that the frequency-area distribution of small and medium fires can be used to quantify the risk of large fires, as is routinely done for earthquakes.Frequency-size distributions of natural hazards provide i~nportant information 011 calculating risk and are used ill hazard mitigation ( 1 ). R o b~~s t pon.er-la\\ frequent) -size distributions are associated nit11 self-organized critical behavior. Examples of this beha1 ior are fou~ld in a il~ulnber of conlputer models: the sandpile model ( 2 ) . the slider-block model (31, and the forest fir? nod el ( I ) . The slider-block model is considered to be an analog for eal-tilquakes. Earthqualtes exhibit a power-la~v dependence of occurrence fre-~L I U I C~ on ruphlre area and are co~lsidered to be the type esalllple of self-organized critical behavior in nature ( 5 ) . We found that. under a \vide ~a r i e t y of circ~umsta~lces. forest fires exhibit a pon-er-lan dependence of occurrence fi-equencq on burn area over many orders of magnitude and that actual forest fires call be directly associated n-it11 the forest fire nod el. The only previous major application of the forest fire lnodel lvas to epidemics of measles in isolated populations ( 6 ) . The forest fire model consists of randomly planting trees on a square grid at successi\.e

Power laws reveal phase transitions in landscape controls of fire regimes

“…Each fire is spread independently of the previous fires, so there is no memory in the landscape process. 6 and overlaid a CSR pattern of recorder trees on the SOC grid. The SOC model is initialized with a blank raster grid.…”

“…The latter are well known in thermodynamic and other physical systems, but in ecological systems they are more problematic to specify because of the complex dependencies associated with ecological dynamics 5 . Analyses of power-law behaviour in ecosystems frequently invoke self-organized criticality (SOC) 6,7 to explain how systems evolve to critical points. SOC has been suggested as an overarching mechanism for wildfire dynamics, as realized in a Forest Fire Model 8 (but see Loreto et al 9 ), but it depends entirely on endogenous processes.…”

“…We asked whether a SOC model, which has been proposed to explain power laws in fire-size distributions 6 , can replicate the observed variability in the SD variograms. We built a simple 'forest fire' model 8 but added a CSR pattern (complete spatial randomness) of simulated recorder trees as in the ECDP model, so that a random draw determines whether a recorder tree that experiences fire records that fire with a scar.…”

Age distribution of trees in stationary forest system

“…In the case of forest fires, observations indicate that the size distribution of fires indeed appears as some kind of a power law [25,26,27,28]. However, a single exponent does not necessarily apply to the entire scaling range.…”

“…Firstly, qualitatively different fires may exist due to finite-size effects [31,25]. In other words, stand boundaries may be partly predetermined.…”