Abstract
The measuring stations of most in situ geophysical networks are spatially distributed in a highly inhomogeneous manner, being mainly concentrated on continents and population centres. When inhomogeneity occurs over a wide range of scales in a space of dimension E, it can be characterized by a fractal dimension Dm. For measuring networks, there is no reason to assume a priori that Dm equals E; it will usually be less than E. The world meteorological network studied here is an example on a surface for which E = 2 (the surface of the Earth) whereas, the network has an empirical dimension Dm ≍ 1.75. Whenever Dm < E, any sufficiently sparsely distributed phenomena (with dimension Dp<E – Dm, here 0.25), cannot be detected—even if the network is infinite. Because these rare phenomena are the most intense, this insufficient dimensional resolution is associated with biases in geophysical statistics, serious difficulties in interpolating measurements to a uniform grid, and problems in calibrating remotely-sensed information.
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Lovejoy, S., Schertzer, D. & Ladoy, P. Fractal characterization of inhomogeneous geophysical measuring networks. Nature 319, 43–44 (1986). https://doi.org/10.1038/319043a0
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DOI: https://doi.org/10.1038/319043a0
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