Compliance Process of the Geo-morphological indices of the watershed with the Multi-fractal Properties of the River Network

Fractal geometry is used as a suitable tool for analysis of the sub-basin geomorphology and the river networks characteristics. It is also practical for very other complicated natural phenomena. Some of the most important indices of multi-fractals are generalized fractal dimensions, Singularity spectrum and the scaling coefficient. The main object of this article is the anlysis and evaluation of Walnut Gulch Watershed based on multi-fractal analysis of the river network images and geomorphology characteristics. To achieve this goal we inserted the required data in GIS template and Arc Map software. We also developed MATLAB codes for non-linear analysis. The selected analysis method here to define the fractal dimension of the river networks in the sub-basins is the Box Counting. During this process, first we obtain the fractal dimensions for each of the considered sub-basin with developed MATLAB codes and then the generalized fractal dimensions, Singularity spectrum and the scaling coefficient of the sub-basins are derived. In the last step, sub-basins geomorphologic characteristics such as: µ, SL, S, T, BS and Re are compared to the multi-fractal characteristics. The results showed that significant relationships between the geomorphologic characteristics of the sub-basins with multifractal features which may be extended to other watersheds if more studies are managed.