  Intense wildfires impact nature, humans, and society, causing catastrophic
damage to property and the ecosystem, as well as the loss of life. Forecasting
wildfire front propagation is essential in order to support fire fighting
efforts and plan evacuations. The level set method has been widely used to
analyze the change in surfaces, shapes, and boundaries. In particular, a signed
distance function used in level set methods can readily be interpreted to
represent complicated boundaries and their changes in time. While there is
substantial literature on the level set method in wildfire applications, these
implementations have relied on a heavily-parameterized formula for the rate of
spread. These implementations have not typically considered uncertainty
quantification or incorporated data-driven learning. Here, we present a
Bayesian spatio-temporal dynamic model based on level sets, which can be
utilized for forecasting the boundary of interest in the presence of uncertain
data and lack of knowledge about the boundary velocity. The methodology relies
on both a mechanistically-motivated dynamic model for level sets and a
stochastic spatio-temporal dynamic model for the front velocity. We show the
effectiveness of our method via simulation and with forecasting the fire front
boundary evolution of two classic California megafires - the 2017-2018 Thomas
fire and the 2017 Haypress.
