Modelling fire-return interval T: stochasticity and censoring in the two-parameter Weibull model

Fire frequency analysis in Portugal (1975 - 2005), using Landsat-based burnt area maps

“…Single-censored fire intervals were those for which one of those dates was unknown. Ignoring single-censored data is likely to lead to incorrect fire frequency estimates (Polakow and Dunne 1999;Oliveira 2008;Moritz et al 2009).…”

“…the actual occurrence of fire is a probabilistic event (Polakow and Dunne 1999). Thus, fire frequency can be described by a set of statistical models that describe the probability of fire.…”

“…Thus, fire frequency can be described by a set of statistical models that describe the probability of fire. In fire frequency studies, the Weibull distribution has been widely used because of its flexibility, ability to model a range of positively skewed distributions and for better fitting fire history data than most alternatives (Johnson 1992;Polakow and Dunne 1999). McCarthy et al (2001) considered that there was little a priori biological justification to use the Weibull function for analysing fire frequency and that its choice by several authors was essentially due to mathematical convenience.…”

“…The Weibull model for fire frequency data can be characterised by any one of the following functions: cumulative mortality distribution, F(t) (distribution function), time since fire distribution, A(t) (survival function), fire interval distribution, f(t) (probability density function) and hazard of burning distribution, l(t) (hazard function): 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 Fire frequency analysis in Portugal using Landsat Int. J. Wildland Fire E It is also characterised by three parameters: a scale parameter (b), a shape parameter (c) and a shift location parameter (e) that is assumed to be zero in fire frequency analyses (Polakow and Dunne 1999). For a detailed review of the topic see Johnson and Gutsell (1994) and Dodson (2006).…”

“…In other Mediterranean regions of the world, Polakow and Dunne (1999) modelled the fire return interval in the Cape of Good Hope Nature Reserve (75.5 km 2 ), South Africa, from 1934 to 1992. They found that the probability of burning increased with time since fire and estimated a multi-century long fire cycle.…”