Modeling forest fire spread and spotting process with small world networks

The small world network model is extended to study fire spread through forest fuels. The proposed model includes the short-range radiative and convective effects from the flame as well as the long-range “spotting” effect of firebrands. It uses a weighting procedure on network sites based on the characteristic times of thermal degradation and combustion of a flammable site. First the model is validated against nonspotting fire experiments in homogeneous media. It is then applied to heterogeneous media to illustrate its ability to provide realistic fire patterns. It is found that the concentration of flammable sites, p  , is a good measure of local small world network properties. Front propagation exhibits two thresholds delimiting the spreading/nonspreading transition: the first corresponds to a geometric second-order phase transition line and is inversely proportional to the fire impact length, lclc, according to pcrn=0.5lc−1, and the second is a dynamic threshold resulting from the weighting procedure. The p-dependence of the fractal dimension of the burned area confirms the percolation transition line behavior. Second, firebrands are considered by introducing a characteristic spotting distance. For homogeneous systems, the effect of firebrands on spread rate and burned area is strengthened when the fire impact length decreases and the characteristic spotting distance increases. The head fire goes forward by jumps, especially for small values of the fire impact length. However, the development of spotfires can slow down the overall propagation process. For heterogeneous systems, spread rate and burned area are significantly reduced as the degree of disorder increases. The influence of firebrands then becomes weaker and smoother. The model underlines the existence of critical channels of the propagation cluster, allowing to stop the propagation of fire if they are cut off.