Realistic wildfire growth simulations applying a differentiable parametric representation of the fire front based on Composite Bézier curves

Modelling the evolution of a forest fire in Wildland Urban Interface (WUI) areas is still a major challenge in the field of forest fire simulation. Most existing forest fire spread simulators are based on polygonal representations of the fire perimeter, which often fail to capture the complexities of fire behaviour in these areas. Elliptical Wave Propagation (EWP) based simulators rely on this type of forest fire perimeter representation, that is, they represent the fire perimeter as a series of points connected by straight lines where the evolution of the fire front is performed by evaluating the spread of each perimeter point using as the spread direction the direction of the normal vector at each of them. To this end, EWP-based simulators have been built on top of the Richard model, which uses a differentiable parametric representation of the fire front. However, due to the polygonal representation used by EWP-based simulators, these cannot exploit the mathematical potential of using a parametric representation of the fire perimeter, which could compromise the accuracy of the simulations.
To address these limitations, we propose a novel parametric representation of the fire front using Composite Bézier Curves (CBC). The proposed wildfire perimeter representation improves the realism of the fire shapes being smooth and rounded. The first implementation of this proposal was done keeping the original method of normal vector calculation. This approach has been called Composite Bézier Curves using Neighbours (CBCN). However, an improved methodology has also been proposed where a more accurate method for calculating the normal vector directions is used, which is aligned with the curvatures of the fire front, thereby improving the overall modelling of fire dynamics. This advanced proposal has been called Composite Bézier Curves using Differentials (CBCD). Both proposed methodologies have been integrated into FARSITE, a well-known EWP-based forest fire spread simulator. Traditional polygonal representation (LIN) and the new CBC-based approach (CBCN and CBCD) were tested in ideal scenarios and two real cases. The obtained results show that any CBC-based representation generates more realistic fire shapes and they also enhance the simulator’s ability to model fire spread in WUI areas, with CBCD being the proposal that obtains the best results.