A new method for the assessment of the fractal dimensions of river networks at given hierarchical orders is presented. It is based on the analogy between river networks and DLA processes. Starting from the outlet section of each drainage area, two tangents to the river network tips can be drawn, forming an internal angle. A supplementary angle is then defined, from which the fractal dimension of a river network is easily computed. An analogous procedure can be followed considering the tangents to the drainage divide. The 'supplementary angle method' (SAM) has been tested on the Corace river network and basin (Calabria, Italy). An empirical relation linking the fractal dimensions computed on river networks and on basin areas has been obtained. A comparison of results from the SAM and the standard box-counting method has been performed, showing an increasing agreement for higher hierarchical orders.
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