Modeling the duration and size of extended attack wildfires as dependent outcomes

Abstract

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.

Modeling the duration and size of wildfires using joint mixture models

“…In this article, we have developed a finite mixture model for the joint modeling of fire duration and fire size. The model can be viewed as an extension of the model by Xi et al (2020) where the joint distribution of the outcomes is separated into components for capturing multimodality in the first stage of the analysis, and the effect of covariates are assessed in the second stage. Compared with existing multivariate frameworks such as the Gaussian mixture model, joint modeling has the flexibility to link outcomes to enable a better understanding of how each outcome is related to the other, in this case, whether and how fire duration and size are connected.…”

“…Note that the marginal distributions of the outcomes can be replaced by other location‐scale distributions, for example, the Weibull or the loglogistic distribution. In an analysis by Xi et al (2020), lognormal models demonstrate the best fit over a variety of alternative models based on the deviance statistic. This analysis though related to the current joint modeling framework, does not utilize a mixture approach, but can be considered as a special simple case of a single component joint model.…”

“…This approach would be conceptually more elegant but would not permit ease of computation as simultaneously considering covariate estimation in the mixture model would be quite computationally intensive. Note that we employed the selected variables from Xi et al (2020) in a related analysis. However, variable selection could be conducted for the two‐stage analysis of the mixture model generally.…”

“…We adopt simple, meaningful ways to summarize environmental variables through their lifetime. As in Xi et al (2020), variables demonstrating a clear trend through their trajectories are centered and regressed against time. The estimated intercept and the slope are used to summarize the trajectory.…”

“…Fires with long durations tend to be large in size, hence fire duration and fire size are often correlated outcomes (Bayham, 2013; Sun, 2013; Xi et al, 2020; Yoder & Gebert, 2012). These authors note indications of multimodality , that is, that there are distinct peaks in the density functions of the outcomes.…”