In this paper, we establish a mathematical model of the forest fire spread process based on a partial differential equation. We describe the distribution of time field and velocity field in the whole two-dimensional s...In this paper, we establish a mathematical model of the forest fire spread process based on a partial differential equation. We describe the distribution of time field and velocity field in the whole two-dimensional space by vector field theory. And we obtain a continuous algorithm to predict the dynamic behavior of forest fire spread in a short time. We use the algorithm to interpolate the fire boundary by cubic non-uniform rational B-spline closed curve. The fire boundary curve at any time can be simulated by solving the Eikonal equation. The model is tested in theory and in practice. The results show that the model has good accuracy and stability, and it’s compatible with most of the existing models, such as the elliptic model and the cellular automata model.展开更多
Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. In this paper the assignment and theoretical investigations of the pro...Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. In this paper the assignment and theoretical investigations of the problems of crown forest fire spread in windy condition were carried out. In this context, a study—mathematical modeling—of the conditions of forest fire spreading that would make it possible to obtain a detailed picture of the change in the temperature and component concentration fields with time, and determine as well as the limiting condition of fire propagation in forest with fire break.展开更多
This paper relates to the semi-empirical model based on fire field energy balance and the physical model based on land temperature, aiming to provide a practical way of describing fire spread. Fire spread is determine...This paper relates to the semi-empirical model based on fire field energy balance and the physical model based on land temperature, aiming to provide a practical way of describing fire spread. Fire spread is determined by the characteristics of combustible materials and the agency of meteorological factors and terrains. Combustible materials, such as surface area, have no featured scale, yet the process of forest fire spread contains the self-replicating feature, both of which contribute to the self-similarity of fire spread. Consequently, fire behavior can be described by fractal geometry. In this research, we select Wuchagou forest in Da Hinggan Mountains as the experimental site where a forest fire took place three years ago. The forest fire was detected on low-resolution NOAA-AVHRR images, and fire spread was simulated on high-resolution TM images as another attempt to merge information. Based on remote sensing and GIS, we adopted the method of limited spreading lumping (DLA) to describe growing phenomenon to simulate the dynamic process of fire spread and adjusting shape of the result of fire simulation by the scale rule. As a result, the simulated fire and the actual fire manifest the self-similarity in their spreading shapes as well as the quantitative similarity in their areas.展开更多
文摘In this paper, we establish a mathematical model of the forest fire spread process based on a partial differential equation. We describe the distribution of time field and velocity field in the whole two-dimensional space by vector field theory. And we obtain a continuous algorithm to predict the dynamic behavior of forest fire spread in a short time. We use the algorithm to interpolate the fire boundary by cubic non-uniform rational B-spline closed curve. The fire boundary curve at any time can be simulated by solving the Eikonal equation. The model is tested in theory and in practice. The results show that the model has good accuracy and stability, and it’s compatible with most of the existing models, such as the elliptic model and the cellular automata model.
文摘Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. In this paper the assignment and theoretical investigations of the problems of crown forest fire spread in windy condition were carried out. In this context, a study—mathematical modeling—of the conditions of forest fire spreading that would make it possible to obtain a detailed picture of the change in the temperature and component concentration fields with time, and determine as well as the limiting condition of fire propagation in forest with fire break.
文摘This paper relates to the semi-empirical model based on fire field energy balance and the physical model based on land temperature, aiming to provide a practical way of describing fire spread. Fire spread is determined by the characteristics of combustible materials and the agency of meteorological factors and terrains. Combustible materials, such as surface area, have no featured scale, yet the process of forest fire spread contains the self-replicating feature, both of which contribute to the self-similarity of fire spread. Consequently, fire behavior can be described by fractal geometry. In this research, we select Wuchagou forest in Da Hinggan Mountains as the experimental site where a forest fire took place three years ago. The forest fire was detected on low-resolution NOAA-AVHRR images, and fire spread was simulated on high-resolution TM images as another attempt to merge information. Based on remote sensing and GIS, we adopted the method of limited spreading lumping (DLA) to describe growing phenomenon to simulate the dynamic process of fire spread and adjusting shape of the result of fire simulation by the scale rule. As a result, the simulated fire and the actual fire manifest the self-similarity in their spreading shapes as well as the quantitative similarity in their areas.
