Procedures in multifractal analysis of river networks: a state of the art review

Multifractal theory was developed by a number of workers in different fields of scientific research, together making a large contribution to civilization. More recent developments have concerned hydrology, with drainage basins and river networks analysed through several hydrological variables. Generalized fractal dimensions are seldom reconstructed analytically, as in a few theoretical cases, since in practical applications the numerical estimation is the only possible way. Many algorithms have been created to assess the fractal dimensions and the multifractal spectrum in general. Two main classes can be distinguished: the Fixed-Size Algorithms (FSA) and the Fixed-Mass Algorithms (FMA). Different methods are briefly illustrated in this paper and applications of FSA to natural river networks and hydrological response are shown.