Global fire size distribution: from power law to log-normal

Wildland fires are one of the main alleged examples of Self-Organised Criticality (SOC), with simple SOC models resulting in the expectation of a power-law fire size frequency distribution. Here, we test whether fire size distributions systematically follow a power law and analyse their spatial variation for eight distinct areas over the globe. For each of the areas, we examine the fire size frequency distribution using two types of plots, maximum likelihood estimation and chi-square tests. Log-normal emerges as a suitable option to fit the fire size distribution in this variety of environments. In only two of eight areas was the power law (which is a particular case of the log-normal) not rejected. Notably, the two parameters of log-normal are related to each other, displaying a general linear relation, which extends to the sites that can be described with a power law. These results do not necessarily refute the SOC hypothesis, but reveal the presence of other processes that are, at least, modulating the outcome of SOC in some areas.

Fire regime from 1973 to 2011 in north-western Patagonian grasslands

Fire is one of the most important disturbances in terrestrial ecosystems and has major ecological and socioeconomic impacts. Fire regime describes the variation of individual fire events in time and space. Few studies have characterised the fire regime in grasslands in spite of the importance of these ecosystems. The aim of this study was to describe the recent fire regime (from 1973 to 2011) of north-western Patagonian grasslands in terms of seasonality, frequency and burned area. Our study area covered 560 000 ha and we used a remote sensing approach combined with statistics obtained from operational databases. Fires occur during the summer in 2 of every 3 years with a frequency of 2.7 fires per year and a mean size of 823 ha. Fire size distribution is characterised by many small fires and few large ones which would respond to a distribution from the power law family. Eighty per cent of the total area affected by fire was burned in the span of a few years, which were also widespread fire years in forests and woodlands of north-western Patagonia. This work contributes to general knowledge about fire regimes in grasslands and we expect that our results will serve as a reference to further fire regime research.

Relationships between annual plant productivity, nitrogen deposition and fire size in low-elevation California desert scrub

Although precipitation is correlated with fire size in desert ecosystems and is typically used as an indirect surrogate for fine fuel load, a direct link between fine fuel biomass and fire size has not been established. In addition, nitrogen (N) deposition can affect fire risk through its fertilisation effect on fine fuel production. In this study, we examine the relationships between fire size and precipitation, N deposition and biomass with emphasis on identifying biomass and N deposition thresholds associated with fire spreading across the landscape. We used a 28-year fire record of 582 burns from low-elevation desert scrub to evaluate the relationship of precipitation, N deposition and biomass with the distribution of fire sizes using quantile regression. We found that models using annual biomass have similar predictive ability to those using precipitation and N deposition at the lower to intermediate portions of the fire size distribution. No distinct biomass threshold was found, although within the 99th percentile of the distribution fire size increased with greater than 125 g m–2 of winter fine fuel production. The study did not produce an N deposition threshold, but did validate the value of 125 g m–2 of fine fuel for spread of fires.

What do we know about forest fire size distribution, and why is this knowledge useful for forest management?

Forest fire size distribution (FSD) is one of the suite of indicators of forest fire regimes. It is applied in forest fire management, particularly for planning and evaluating suppression efforts. It is also used in forest management in the context of emulating natural fire disturbances. Given the recent growth in research and applied interest in this topic, we review and synthesise the state of knowledge on FSD, and identify sources of knowledge uncertainties and future research directions. Based on literature, it is common for forest fires to follow the power law probability distribution, particularly the truncated subtype, under a variety of forest types and forest and fire management practices. Other types of FSD are also observed, but under specific circumstances. Although there is evidence that observed FSDs vary both over space and time, the knowledge is too fragmented to generalise the cause–effect relationships for such variation. As well, it is not clear how the various methods of studying FSD and their spatio-temporal scales influence derivations of FSDs. We suggest that a hypothetico-deductive research approach, combining empirical studies with process-based simulations is an effective means to advance the knowledge of FSD. We suggest caution in the use of FSD in forest management because applying different distributions or even different parameters for the same distribution may result in great fire size class differences and thus different implications for forest management.

A parametric model of the fire-size distribution

This paper developes statistical models of the size distribution of lightning-caused wildfires in the boreal mixedwood forests of Alberta, Canada, for the intervals 1980––1998 and 1961––1998. Above any minimum threshold size [Formula: see text]3 ha, the logarithm of fire size is approximately exponentially distributed. However, computer simulations using the best-fit distribution would over predict the frequency of large fires, and thus the mean rate of disturbance. A truncated exponential distribution, which places an upper bound on fire size, is more suitable and, according to probability plots, provides an excellent fit to the data. I estimate the maximum fire size in the study area to be [Formula: see text] 650 000 ha. This estimate is insensitive to the choice of lower bound for fire sizes (between 3 and 1000 ha) and to the choice of sampling interval. Parametric modelling of fire sizes using covariates derived from forest inventory data shows that the expected size of a fire is positively related to the abundance of pine forest in the vicinity of the point of detection and negatively related to the abundance of recently logged or burnt areas. This implies that variation in forest structure and disturbance history impose marked spatial variability on the fire size distribution. Other covariates, such as periodic indices of fire weather, could readily be evaluated in this framework.