Modeling the duration and size of wildfires using joint mixture models

Fire duration and fire size are key outcomes for quantifying the survivorship of extended attack fires, here considered to be fires with duration greater than 2 days and size greater than 4 ha. Past studies suggest that these key outcomes are correlated. As well, fire behavior, linked to hidden effects, tends to yield that fires arise from different subpopulations. Indeed, it is not unusual for fire behavior to be identified as arising from normal or extreme subpopulations, for example. Here, we embed these two concepts into a new framework for jointly modeling fire duration and fire size. We develop a bivariate finite mixture framework that can be used to model duration and size with four subpopulations of the outcomes whereby duration and size are either normal or extreme. We utilize a shared random effect model as well as a bivariate Gaussian mixture model for such mixture modeling. We also incorporate the effect of explanatory variables associated with each fire event, on the posterior probability of the component that the fire belongs to, through a Dirichlet model. In an analysis of fire outcomes from British Columbia, Canada, we find that the majority of the fires are of normal or extreme magnitude in both outcomes, with strong evidence indicating correlation between duration and size. The effect of fire center, month, and several environmental covariates are identified as key predictors and we are able to determine through these approaches how these covariates differentially affect the four subpopulations.