Fire-spotting modelling and parametrisation for wild-land fires

This article describes a mathematical formulation for simulating the effects of firebrands on the propagation of the wild-land fires. Among the different approaches available in literature, this formulation is defined in a way to provide a versatile approach for application to operational wildfire models. Most of the operational wildfire models like WRF-SFIRE and ForeFire model only the evolution of the fire-line according to the definition of the rate of spread, fuel characterisation and the average fire properties and concurrent atmospheric conditions. But this information is not enough to simulate the effects of turbulence and fire-spotting. The formulation presented here can perform as a crucial addition: (1) on the physical aspect by including random fluctuations and (2) on the operational aspect by serving as a post processing application at each time step. The post-processing updates at each time step modify the fire-perimeter obtained from the operational model through a probability density function corresponding to the physical properties of the turbulence and fire-spotting behaviour. A lognormal distribution in convolution with a Gaussian distribution is utilised to emulate the landing distributions of the firebrands. The main aim of this study is to provide a physical parametrisation to the behaviour of the model with respect to the lognormal distribution. The sensitivity of the landing distribution of the firebrands corresponding to the changes in factors like wind speed, fire intensity, radius of firebrand is highlighted through simple and idealized test cases. The results presented in this study provide a tentative outlook towards both qualitative and quantitative assessment of the firebrand landing.