Modeling fire interval data from the American southwest with the Weibull distribution

Abstract

In this study, the Weibull distribution is tested as a possible model for fire interval data derived from dendrochronologically-dated fire scars from four sites in the American Southwest. Two- and three-parameter Weibull distributions were fit to fire interval data sets, and additional statistical descriptors based on the Weibull were derived to improve our understanding of the range of variability in presettlement fire regimes. The three-parameter models failed to provide improved fits versus the more parsimonious two-parameter models, indicating the Weibull shift parameter may be superfluous for Southwestern fire regimes. The Weibull Modal Interval (MOI) was a superior overall measure of central tendency, and appears to identify a common underlying structure in Southwestern fire regimes independent of habitat type and environmental gradients. Unusually short and long fire intervals were identified by the lower and upper exceedance intervals (LEI and UEI) and the Maximum Hazard Interval (MHI) based on the Weibull hazard function. Model statistics were nearly identical between two pairs of sites that were 260 kilometers distant that differed in topography, vegetation, and land-use history. However, differences were observed between sites only 10 kilometers apart, suggesting the influence of local factors (e.g., topography and substrate) over regional influences (e.g., climate). Although the Weibull models helped quantify the historical range of variability in presettlement fire regimes, ecological interpretations of the Weibull parameters proved difficult.

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

“…Similar analyses in ecosystems such as tropical savannas, which display much shorter fire rotation periods than temperate ecosystems, ought to allow for assessment of changes in parameter estimates between time series spanning several times the fire rotation period. Inclusion of SC fire intervals in the analysis has, by far, the strongest effect on parameter estimates (in agreement with Polakow andDunne 1999 andMoritz et al 2009), an effect that increases with fire rotation period and is important as most available studies have relied solely on complete fire interval data (Grissino-Mayer 1999;Lloret and Marí 2001;Vázquez and Moreno 2001;Díaz-Delgado et al 2004;Fisher et al 2009;Kraaij 2010). Our results show that exclusion of SC data leads to overestimation of fire frequency and hazard of burning dependence on fuel age.…”

Canopy disturbance history of old-growth Quercus alba sites in the eastern United States: Examination of long-term trends and broad-scale patterns

“…We analyzed the distribution of disturbance interval data to determine whether the MDRI or WMRI was most appropriate for each forest region (i.e. MDRI was used for normally distributed return interval data, WMRI was used for return interval data best modeled by the Weibull distribution; Grissino-Mayer, 1999;Rentch et al, 2003a). MRTC and R:n are relativized descriptors of canopy disturbance and allow for comparisons of disturbance chronologies of different lengths and sample sizes.…”

Predicting spatio-temporal variability in fire return intervals using a topographic roughness index

“…Choice of independent variables considered in the regression was based on documentation of human and land use history of the Ozark Highlands (Rafferty, 1985;Stevens, 1991). The dependent variable, mean fire return interval, was defined as the average time (years) between subsequent fires occurring at the fire history sites (approximately 1 km 2 areas) (Baker, 1989;Grissino-Mayer, 1999). We conducted a multiple regression analysis using SAS software (SAS Institute, 1990) and the PROC REG (ordinary least squares) command.…”