Understanding Shifts in Wildfire Regimes as Emergent Threshold Phenomena

Abstract

Ecosystems driven by wildfire regimes are characterized by fire size distributions resembling power laws. Existing models produce power laws, but their predicted exponents are too high and fail to capture the exponent's variation with geographic region. Here we present a minimal model of fire dynamics that describes fire spread as a stochastic birth-death process, analogous to stochastic population growth or disease spread and incorporating memory effects from previous fires. The model reproduces multiple regional patterns in fire regimes and allows us to classify different regions in terms of their proximity to a critical threshold. Transitions across this critical threshold imply abrupt and pronounced increases in average fire size. The model predicts that large regions in Canada are currently close to this transition and might be driven beyond the threshold in the future. We illustrate this point by analyzing the time series for large fires (>199 ha) from the Canadian Boreal Plains, found to have shifted from a subcritical regime to a critical regime in the recent past. By contrast to its predecessor, the model also suggests that a critical transition, and not self-organized criticality, underlies forest fire dynamics, with implications for other ecological systems exhibiting power-law-like patterns, in particular for their sensitivity to environmental change and control efforts.

Epidemic cholera spreads like wildfire

“…This distribution is fat-tailed, with the frequency of the larger epidemics over-represented relative to what would be expected for an exponential or a bell-shape distribution with a characteristic, most frequent, size. This pattern is similar to those described for the size distributions of natural disasters such as earthquakes and wildfires151617. This similarity is particularly apparent when the size distribution for cholera epidemics is compared to that of fires for a region with aggressive wildfires such as the Boreal forest of the Northern hemisphere (Fig.…”

“…This motivates us to better characterize these size distributions with a recently developed minimal forest-fire model that is both spatially explicit and stochastic17; this model represents an extension of the well-known Drossel-Schwabl model (hereafter DSM18). The original forest fire model was proposed in the context of self-organized criticality (hereafter SOC19) and applied to both wildfires in nature15 and childhood diseases such as measles20.…”

“…The original forest fire model was proposed in the context of self-organized criticality (hereafter SOC19) and applied to both wildfires in nature15 and childhood diseases such as measles20. The extension we consider here was recently shown to better explain the observed variation in empirical size distributions of wildfires, in particular the values and full spread of the exponents of these power-law-like patterns observed across ecoregions1617.…”

“…Hereafter we refer to the limit of infinite σ as the “SOC limit” of our model. Although models exhibiting the 2 nd order phase transition and DSM have been independently studied quite extensively17181920212223, the model presented here is to our knowledge the only one capable of bridging these two distinct phenomena by varying a single parameter, σ . This feature gives our model the ability to generate a family of size distributions that remain power-law like regardless of considerable variation in parameters.…”

Land cover, more than monthly fire weather, drives fire-size distribution in Southern Québec forests: Implications for fire risk management

“…This allows a more accurate representation of the upper tailed behaviour of FSDs. Regional variations in the upper tail behaviour of FSDs have also been found [24,29], but we know of no studies that have modelled this variation in relation to environmental factors. Moritz et al [30] proposed that parametric models, in which the distributional parameters are functions of environmental covariates, could be used to shed light on the effect of these factors on FSDs.…”