论文标题
法国地中海地区的多重分点过程和野火的空间分布
Multifractal point processes and the spatial distribution of wildfires in French Mediterranean regions
论文作者
论文摘要
我们引入了一类简单而宽的多重空间点模式,即强度是多重型的COX过程,即具有与随机多裂度度量相对应的随机强度的泊松过程类别。然后,我们通过标准期望最大化程序提出了最大似然方法,以估计所有尺度上这些强度的分布。这提供了在各种数值示例中验证的简单框架,以估算缩放定律,因此提供了此类空间点过程的多重属性属性。在这种方法中研究了在法国地中海野火数据库中收集的野火分布,这特别使我们能够计算与年度火灾事件发生可能性的空间分布相关的统计矩。我们表明,对于每个顺序$ Q $,这些瞬间显示出明确的缩放行为,并具有非线性缩放指数$ζ_Q$的非线性频谱。因此,从我们的研究中,似乎可以通过非平凡的多重分子奇异性频谱来描述Widlfire IGNITION年度风险的空间分布,并且不能降低这种风险,从而每$ km^2 $提供许多事件。我们的分析是通过对强度对数的直接空间相关估计来证实的,该强度对数的特殊形状逐渐降低形状对应于多型级联的标志。随着时间的推移,多型特征似乎是恒定的,并且在所研究的三个区域中相似。
We introduce a simple and wide class of multifractal spatial point patterns as Cox processes which intensity is multifractal, i.e., the class of Poisson processes with a stochastic intensity corresponding to a random multifractal measure. We then propose a maximum likelihood approach by means of a standard Expectation-Maximization procedure in order to estimate the distribution of these intensities at all scales. This provides, as validated on various numerical examples, a simple framework to estimate the scaling laws and therefore the multifractal properties for this class of spatial point processes. The wildfire distribution gathered in the Prométhée French Mediterranean wildfire database is investigated within this approach that notably allows us to compute the statistical moments associated with the spatial distribution of annual likelihood of fire event occurence. We show that for each order $q$, these moments display a well defined scaling behavior with a non-linear spectrum of scaling exponents $ζ_q$. From our study, it thus appears that the spatial distribution of the widlfire ignition annual risk can be described by a non-trivial, multifractal singularity spectrum and that this risk cannot be reduced to providing a number of events per $km^2$. Our analysis is confirmed by a direct spatial correlation estimation of the intensity logarithms whose the peculiar slowly decreasing shape corresponds to the hallmark of multifractal cascades. The multifractal features appear to be constant over time and similar over the three regions that are studied.