Fire danger systems have evolved from qualitative indices, to process-driven deterministic models of fire behavior and growth, to data-driven stochastic models of fire occurrence and simulation systems. However, there has often been little overlap or connectivity in these frameworks, and validation has not been common in deterministic models. Yet, marked increases in annual fire costs, losses, and fatality costs over the past decade draw attention to the need for better understanding of fire risk to support fire management decision making through the use of science-backed, data-driven tools. Contemporary risk modeling systems provide a useful integrative framework. This article discusses a variety of important contributions for modeling fire risk components over recent decades, certain key fire characteristics that have been overlooked, and areas of recent research that may enhance risk models.

Understanding the complex relationship between the duration and size of forest fires is important in order to better predict these key characteristics of fires for fire management purposes in a changing climate. Describing this relationship is also important for our fundamental understanding of fire science. Here, we develop and utilize novel techniques for characterizing the distribution of multiple outcomes related to a specific event, placed in the fire science context. In this framework, we jointly model time spent (duration), in days, and area burned (size), in hectares, from ground attack to final control of a fire as a bivariate survival outcome using two broad methodologies: a copula model that connects the two outcomes functionally and a joint modeling framework that connects the two outcomes with a shared random effect. We compare these two methodologies in terms of their utility and predictive power. We also consider how longitudinal environmental variables (e.g., precipitation, drought indices) are best incorporated in this context and the challenges related to the complexity of computation associated with the analysis of two outcomes considered jointly.

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.

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