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Oliveira EA, Pires RS, Oliveira RS, Furtado V, Herrmann HJ, Andrade JS. A universal approach for drainage basins. Sci Rep 2019; 9:9845. [PMID: 31285496 PMCID: PMC6614398 DOI: 10.1038/s41598-019-46165-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2018] [Accepted: 06/17/2019] [Indexed: 12/02/2022] Open
Abstract
Drainage basins are essential to Geohydrology and Biodiversity. Defining those regions in a simple, robust and efficient way is a constant challenge in Earth Science. Here, 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 anti-basins 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 = 0.54 ± 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.
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Affiliation(s)
- Erneson A Oliveira
- Programa de Pós Graduacção em Informática Aplicada, Universidade de Fortaleza, 60811-905, Fortaleza, Ceará, Brazil. .,Mestrado Profissional em Ciências da Cidade, Universidade de Fortaleza, 60811-905, Fortaleza, Ceará, Brazil. .,Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60451-970, Fortaleza, Ceará, Brazil.
| | - Rilder S Pires
- Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60451-970, Fortaleza, Ceará, Brazil
| | - Rubens S Oliveira
- Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60451-970, Fortaleza, Ceará, Brazil
| | - Vasco Furtado
- Programa de Pós Graduacção em Informática Aplicada, Universidade de Fortaleza, 60811-905, Fortaleza, Ceará, Brazil
| | - Hans J Herrmann
- Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60451-970, Fortaleza, Ceará, Brazil.,PMMH, ESPCI, 7 quai St Bernard, 75005, Paris, France.,ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, Hit, CH-8093, Zürich, Switzerland
| | - José S Andrade
- Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60451-970, Fortaleza, Ceará, Brazil
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