3. 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 civilisation. More recent developments have concerned hydrology, with drainage basins and river networks analysed through several hydrological variables. Generalised fractal dimensions are seldom reconstructed analytically, as in a few theoritical cases, since in practical applications the numerical estimation is the only possible way. Many alogirithms have been created to acess the fractal dimensions and the multifractal spectrum in general. Two main classess can be distinguished: the Fixed-size Algorithims (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.