小尺度森林火灾的渐近幂律分布

森林火灾系统是一个自组织临界性系统，它的表现之一就是火灾的尺度分布满足幂律规律。然而实际数据分析表明，在尺度最大和最小的两个区域，火灾分布与幂律规律存在较大的差异。对小尺度火灾的偏离现象，研究者通常猜测是由于小面积火灾记录数据遗漏较多造成的，目前尚没有一个理论上的依据，而小尺度火灾的分布规律对大尺度火灾的预测起看关键作用。为了解释这种偏离现象，该文将火灾看作一个生灭过程，并对火灾蔓延和熄灭的机理进行了分析，最终得到了森林火灾分布与火灾尺度的定量依赖关系及其机理。将该文的结果与日本近年来全国范围内的森林火灾统计数据进行了对比，表明该文得到的结果与真实数据得到较好符合，并且成功解释了小尺度森林火灾分布与幂律关系的偏离现象。该研究可望对深入认识火灾系统的自组织临界性和防治火灾具有一定的实际意义。

Asymptotic Power-law Distribution of Small Forest Fires

The forest fire system is a self organized critical system and the distribution of forest fires satisfies power law relation. However, it has been observed that fire distribution deviates power law when fire size is very small or very large. The deviation of small fires is usually attributed to the absence of small fire records, while the theoretical explanation is not available nowadays. To understand the deviation of small fires, forest fire is treated as a Birth Death process and the spreading as well as the extinguishment of forest fire is analyzed. The dependence of fire distribution on fire size and its mechanism are obtained and the reason of the deviation of small fire is explained. The analytical results are then compared with actual forest fire records in Japan and it shows good accordance. The study may be useful to understand the self organized criticality of fire system and may have practical implications on forest fire protection.