Derivation and investigation of mathematical models for spotting in wildland fire

Spotting in the context of wildland fire refers to the creation of new fires, downwind from an existing fire front, where the new fires result due to the launch, and subsequent fuel bed ignition upon landing, of burning plant material released from the main front. We will present a new integro-partial differential equation (i-PDE) model which includes both local spread, combustion/extinguishment, and non-local spread due to spotting. We will also present a new model for firebrand transport in the atmosphere, which allows us to incorporate existing physical or empirically-based submodels existing in the literature to obtain the spotting distribution. We will use the spottting distribution to investigate the problem of fire fronts breaching obstacles to local fire spread, such as a highway or river, and the spotfire distribution appears as a kernel for the integral term in our i-PDE model. We then investigate travelling wave solutions to the i-PDE model, demonstrating that spotting can increase the rate of spread, or cause acceleration of a fire front's advance.