Forest fire propagation modelling by evolving curves on topography incorporating data assimilation

In this contribution, we present a Lagrangean approach to forest fire modelling. The fire perimeter is represented by a three-dimensional discrete curve on a surface. Our mathematical model is based on empirical fire spread laws influenced by the fuel properties, wind, terrain slope, and shape of the fire perimeter with respect to the topography (geodesic and normal curvatures). The motion of the fire perimeter is governed by the intrinsic advection-diffusion equation. 

To obtain the numerical solution, we employ the semi-implicit scheme to discretize the curvature term. For the advection term, we use the so-called inflow-implicit/outflow-explicit approach combined with the implicit upwind scheme. A fast treatment of topological changes (splitting and merging of the curves) is also incorporated and briefly described .

The propagation model is applied to artificial and real-world experiments. To adapt our model to wildfire conditions, we tune the model parameters using the Hausdorff distance as a criterion. Using data assimilation, we estimate the normal velocity of the fire front (rate of spread), the dominant wind direction and selected model parameters.