Uma abordagem generalizada para a definição e caracterização de bacias hidromorfológicas

Abstract

Drainage basins play a fundamental role in Hydrology and Geomorphology. However, the lack of a proper definition for these regions still represents an open problem. Here, we propose a new hierarchical algorithm to define all sub-basins of a given (basin) landscape. We introduce a model to delineate multiple drainage basins through an extension of the Invasion Percolation-Based Algorithm (IPBA). In order to prove the potential of our approach, we apply it to real and artificial datasets. We observe that the perimeter and area distributions of basins and antibasins display long tails extending over several orders of magnitude and following approximately power-law behaviors. Moreover, the exponents of these power laws depend on spatial correlations and are invariant under the landscape orientation, not only for terrestrial, but lunar and martian landscapes. The terrestrial and martian results are statistically identical, which suggests that a hypothetical martian river would present similarity to the terrestrial rivers. Finally, we propose a theoretical value for the Hack's exponent based on the fractal dimension of watersheds, γ = D/2. We measure γ = 0.52 ± 0.01 for Earth, which is close to our estimation of γ ≈ 0.55. Our study suggests that Hack's law can have its origin purely in the maximum and minimum lines of the landscapes. We too apply our method to the Amazon basin and find that the obtained sub-basins are consistent with those reported in the literature. Finally, we also observe that the perimeter and area distributions of subbasins exhibit long tails following approximately power-law behaviors and that their exponents decrease with the hierarchy of the sub-basins.