Multifractal Analysis and Simulation of the Global Meteorological Network

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. ...