Multifractal Analysis and Simulation of the Global Meteorological Network

Y. Tessier, S. Lovejoy, D. Schertzer
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引用次数: 31

Abstract

Abstract Taking the example of the meteorological measuring network, it is shown how the density of stations can be characterized by multifractal measures. A series of multifractal analysis techniques are applied (including new ones designed to take into account the spherical geometry) to systematically test the limits and types of network multiscaling. These techniques start with a network density defined by grids or circles and proceed to systematically degrade their resolution (no a priori scaling assumptions are necessary). The multiscaling is found to hold over roughly the range 20 000 to 200 km (limited by the finite number of stations—here about 8000). Special attention is paid to qualitative changes in the scaling behavior occurring at very low and high density regions that the authors argue are associated with multifractal phase transitions. It is argued that the density was produced by a universal multifractal process, and the three corresponding universal multifractal parameters are estimated. ...
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全球气象网络的多重分形分析与模拟
摘要以某气象测量网为例,介绍了用多重分形测度来表征站点密度的方法。应用了一系列多重分形分析技术(包括考虑球面几何的新技术)来系统地测试网络多重尺度的极限和类型。这些技术从网格或圆定义的网络密度开始,然后系统地降低它们的分辨率(不需要先验的缩放假设)。发现多尺度在大约20,000至200公里的范围内保持不变(受限于有限数量的站点-这里大约有8000个)。特别注意在极低和高密度区域发生的标度行为的质变,作者认为这些质变与多重分形相变有关。认为密度是由一个普适多重分形过程产生的,并估计了对应的三个普适多重分形参数. ...
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