Fractal Characterisation of Geophysical Measuring Networks and its Implication for an Optimal Location of Additional Stations: An Application to a Rain-Gauge Network

Summary

The locations of measuring stations are often inhomogeneously distributed in space, possibly because of both geophysical interests and access problems. The areal inhomogeneity of a network can be well characterised by its fractal dimension, that is an index ranging progressively from 0 (when all stations are distributed on a single point or on isolated points) to 2 (when all stations are uniformly distributed). Appreciating the scaling region, inside which the station-co-ordinates are fractally distributed, provides valuable information both on the minimum detectable scale and on the minimum resolvable dimension. The increase in the measuring capability of a network must occur through its strategic enlargement resulting in a compromise between the fractal dimension increase and local topographic necessities. An application to a rain-gauge network belonging to the Naples Section of the Italian Hydrographic Service is reported.