The Green Island Formation in Forest Fire Modeling with Voronoi Diagrams

During the last couple of years much attention has been given to an important ecological problem, namely forest wilddre 1]. In a recent report 5] it has been shown that, starting with very simple assumptions, a Voronoi diagram structure 4], 3] naturally emerges as the landscape geometry generated by the spread out of forest wilddre. In this paper, we provide a tool that may help people locate refuge zones inside a forest re using a Voronoi growth model. Forest res is a complex problem with several open questions. In this short communication, we discuss a sub-problem that is a component in a more complex analysis of forest res. Here we assume homogeneous vegetation on a regular topography without a prevailing wind. As a result of this assumption, the re wavefronts radially spread at a constant velocity from the ignition point sites, fP i g. This assumption, although restrictive, is quite reasonable in many locations. For example, in the Planalto region near Brasilia (Brazil), similar conditions are met and often there are forest res that consume high grasslands. Sugarcane plantations is a good example of a single specie homogeneous vegetation that is burned to easy labor access for harvesting. As the re spreads it may close oo regions of vegetation. These regions are termed green islands. They are both good and bad. If someone is caught inside of a green island, then this person has no means of escaping the re because eventually the re will entirely engulf the green island. However, locally, the green island is the last place to get burned up entirely, so it can serve as a temporary refuge zone for people and animals trapped inside of the re. Park rangers routinely set prescribed forest re to prevent a major destructive re in the future. Rangers can use a priori knowledge of islands location to determine where the wildlife will take refuge, and thus they set up stations for rescuing them. In fact, they can use this understanding of island locations to determine where to place the point sources to minimize the loss to wildlife. This paper initially presents the condition, based on the Voronoi diagram, that determines when green islands are spatially formed. Although the green island formation problem has arisen from the forest re application, is has in its own a pure geometrical nature. We consider two types of green islands: simple and complex. A …