MULTIFRACTAL ANALYSIS AND SIMULATION OF THE GLOBAL METEOROLOGICAL NETWORK

Taking the example of the meteorological measuring network, it is show n how the density of stations can be characterized by multifractal mea sures. A series of multifractal analysis techniques are applied (inclu ding new ones designed to take into account the spherical geometry) to systematically test the limits and types of network multiscaling. The se techniques start with a network density defined by grids or circles and proceed to systematically degrade their resolution (no a priori s caling assumptions are necessary). The multiscaling is found to hold o ver roughly the range 20 000 to 200 km (limited by the finite number o f 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 universa l multifractal process, and the three corresponding universal multifra ctal parameters are estimated. The minimum and maximum orders of singu larities present in the network are estimated, as well as the minimum- and maximum-order statistical moments that can be reliably estimated. The results are then used to simulate the effects of the finite numbe r of stations on a network with the same statistical properties, and h ence to quantitatively show that the observed breaks in the multiscali ng can be accounted for by the finiteness. A growing number of geophys ical fields have been shown to exhibit multiscaling properties over va rious ranges, and in this paper it is discussed how the bias introduce d by the network clustering can be removed by new ''multifractal objec tive analysis'' procedures.