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Fractal dimension of the hydrographic pattern of three large rivers in the Mediterranean morphoclimatic system: geomorphologic interpretation of Russian (USA), Ebro (Spain) and Volturno (Italy) fluvial geometry

Donadio Carlo1, Magdaleno Fernando2,3, Mazzarella Adriano1, Kondolf George Mathias4

1 DiSTAR, Dipartimento di Scienze della Terra, dell’Ambiente e delle Risorse, Università degli Studi di Napoli Federico II, Largo San Marcellino 10, 80138 Napoli, Italy

2 CEDEX, Centre for Studies and Experimentation on Public Works, Ministry of Public Works - Ministry of Agriculture, Food and Environment, Alfonso XII 3, 28014 Madrid, Spain

3 Technical University of Madrid, Alfonso XII 3, 28014 Madrid, Spain

4 LAEP, Department of Landscape Architecture and Environmental Planning, University of California, Berkeley, 202 Wurster Hall 2000, 94720 Berkeley, CA, USA.

Pure and Applied Geophysics, 2014

Doi: 10.1007/s00024-014-0910-z



Fig. 1 Donadio et al. 2014 vetrina DiSTARBy applying fractal geometry analysis to the drainage network of three large watercourses in America and Europe, we have calculated for the first time their fractal dimension. The aim is to interpret the geomorphologic characteristics to better under stand the morphoevolutionary processes of these fluvial morphotypes; to identify and discriminate geomorphic phenomena responsible for any difference or convergence of a fractal dimension; to classify hydrographic patterns, and finally to compare the fractal degree with some geomorphic-quantitative indexes. The analyzed catchment of Russian (California, USA), Ebro (Spain), and Volturno (Italy) rivers are situated in Mediterranean-climate regions sensu Köppen, but with different geologic context and tectonic styles. Results show fractal dimensions ranging from 1.08 to 1.50. According to the geological setting and geomorphic indexes of these basins, the lower fractal degree indicates a prevailing tectonics, active or not, while the higher degree indicates the stronger erosion processes on inherited landscapes.

Key-words: Fractal dimension, fluvial geomorphology, Mediterranean climate, USA, Europe



Fig. 1 – a) Drainage network of Russian (R) - California (USA), Ebro (E) - Spain, and Volturno (V) - Italy, rivers; b) Log of number of pairs C of the areal coordinates of the three rivers (R Russian, E Ebro, V Volturno), with mutual distance smaller than R, as a function of log(R) (m). Dashed line is the random distribution with fractal dimension DC = 2; solid line is DC inside the scaling region (dotted lines); c) Diagram of a comparison between the values of fractal dimension (DC) of fluvial drainage networks calculated with the correlation integral in this paper and some derived from literature, the river sinuosity (S, open box), the basin drainage density (Dk, solid triangle), and the stream order (i) sensu Strahler (1957). In the upper part of the diagram the 2D-fractal dimension refers both to Mediterranan climate rivers (left), i.e., the three ones analyzed (1 solid circle: R Russian, E Ebro, V Volturno) and those from the literature (2 solid star:Turcotte 1997; Del Monte et al. 1999, 2007), and to rivers flowing in different morphoclimatic systems (right), derived from the literature (3, open circle: Garnett 1986; Peckham 1995; Turcotte 1997; Andrews 2006), separated by a dashed line. The curve divides a region (below) with prevailing active or recent tectonics (low DC) from the region (above) mainly characterized by erosion processes (high DC), which have structured and modelled the current fluvial geometry. The lower part of the diagram shows particularly the relation between drainage density (Dk) of the three studied river basins and the other parameters. The dotted lines represent the limits of DC intervals between the main Mediterranean-type drainage patterns identified: (I) rectangular, (II) subdendritic, (III) dendritic, (IV) pinnate, and parallel