We describe work in progress in modeling wildland firespread and tuning the resulting models to historic or idealized firespread data. Modeling wildland firespread has acquired a high priority in recent years, as ecosystems in which burning has been actively suppressed for a century erupt in catastrophic fires. Modelers would like to predict fire damage, control fires in real time with limited resources safely deployed for optimal effectiveness, and formulate long-term strategies for prescribed burns to reduce the incidence of catastrophic fires.

Modeling efforts are on-going at many levels of fidelity, from simple models amenable to low-memory, low-flop-intensity implementation (e.g., on the laptops of firechiefs in the field), to rich models approaching the goal of first principles, for which a single simulation taxes the most powerful computers in the national labs for weeks. Our current efforts are at the simple end of the fidelity spectrum, with a single "forward" problem consisting of the advance of a closed curve representing an idealized firefront over a two-dimensional domain characterized by topography, areal fuel density, windfield, and other factors. Due to the economic and safety importance of firespread modeling, there is an extensive literature of empirical models with similar limited input requirements. Surprisingly, in view of the importance claimed for these models, attempts to parameterize them with real data seem to be in their infancy, including our own very recent forays.

We employ a level set method, for which the primary modeling requirement is a rule for the instantaneous advance of an infinitesimal element of fire perimeter arc, normal to itself. In this talk, we provide a brief technical background of the firespread problem and its forward solution using level sets (in contrast with other approaches), we describe our own contributions to the modeling based on early studies, and focus the discussion on the parameter estimation problem.

This is joint work with Vivien Mallet of Ecole de Ponts et Chausees (Paris) and Francis Fendell of TRW (Redondo Beach). It is part of a larger project ("Caliente"; see http://www-2.cs.cmu.edu/~caliente/) on PDE-constrained optimization.