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

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.