Fractal characterization of rain-gauge networks and precipitations: an application in Central Italy

Abstract

The measuring stations of a geophysical network are often spatially distributed in an inhomogeneous manner. The areal inhomogeneity can be well characterized by the fractal dimension D_H of the network, which is usually smaller than the euclidean dimension of the surface, this latter equal to 2. The resulting dimensional deficit, (2-D_H), is a measure of precipitating events which cannot be detected by the network. The aim of the present study is to estimate the fractal dimension of a rain-gauge network in Tuscany (Central Italy) and to relate its dimension to the dimensions of daily rainfall events detected by a mixed satellite/radar methodology. We find that D_H = 1.85, while typical summer precipitations are characterized by a dimension much greater than the dimensional deficit 0.15.