Mathematics of Information Technology and Complex Systems



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Forest Fires and Spread in Heterogeneous Landscapes

Project leader:
Dr. Thomas Hillen, Professor, Director of the Applied Mathematics Institute, University of Alberta

Each year, thousands of forest fires burn in Canada, consuming millions of hectares. Although important for the ecology of a forest ecosystem, fires threaten native species and human life and property. It is therefore important that the fire management community have access to decision support tools to help fight and manage forest fires.

Since 1925, Canadian researchers have investigated the influence of weather, fuel type, fuel moisture, and landscape topography on the spread of forest fires. Such research led to the publication of fire hazard tables. Since the 1970s, computer guided prediction tools have been developed. In May 2002, the first version of the software tool “Prometheus” was released, which has now become the state-of-the-art computational fire growth prediction tool.

The objective of this project is to develop a complete, multi-scale approach to the mathematical modelling of forest fire spread and control. The dynamics of a forest fire can be roughly divided into three scales. On the microscopic scale, we will consider local information such as fuel type, moisture and wind and weather conditions as well as stochastic effects include local wind conditions.

On the mesoscopic scale, we use local information to compute a rate of spread (ROS) of the fire front. We plan to further develop the models of Richards from 1990, 1995, and 1999 and those in the software package, all which are mesoscopic models.

Finally, on the macroscopic scale are mathematical models which still use local information however, the unknown function is a macroscopic object. Here we will follow two approaches: the level set method to describe the evolution of the fire front and reaction-advection-diffusion equations for the energy release rate and for the temperature distribution.