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Parameterizing V-notch Weir Equations for Flow Monitoring in a Drainage Control Structure
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A universal approach for drainage basins.

Erneson A Oliveira1,2,3, Rilder S Pires4, Rubens S Oliveira4

  • 1Programa de Pós Graduacção em Informática Aplicada, Universidade de Fortaleza, 60811-905, Fortaleza, Ceará, Brazil. erneson@eaoliveira.com.

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This study introduces an improved Invasion Percolation-Based Algorithm (IPBA) to efficiently map drainage basins. The research reveals universal power-law behaviors in basin dimensions across Earth and Mars.

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Area of Science:

  • Geohydrology
  • Biodiversity
  • Earth Science
  • Planetary Science

Background:

  • Defining drainage basins is crucial for geohydrology and biodiversity but remains a challenge in Earth Science.
  • Existing methods for delineating drainage basins can be complex and inefficient.

Purpose of the Study:

  • To introduce a novel model for delineating multiple drainage basins using an extension of the Invasion Percolation-Based Algorithm (IPBA).
  • To analyze the statistical properties of drainage basins and anti-basins in terrestrial, lunar, and Martian landscapes.
  • To investigate the origin of Hack's law by relating the Hack's exponent to the fractal dimension of watersheds.

Main Methods:

  • An extended Invasion Percolation-Based Algorithm (IPBA) was developed to delineate drainage basins.
  • The model was applied to both real and artificial datasets, including terrestrial, lunar, and Martian landscapes.
  • Statistical analysis was performed on basin and anti-basin perimeter and area distributions, and Hack's exponent was calculated.

Main Results:

  • Basin and anti-basin perimeter and area distributions exhibit power-law behaviors over several orders of magnitude.
  • The exponents of these power laws are dependent on spatial correlations and invariant to landscape orientation.
  • Terrestrial and Martian results are statistically similar, suggesting similar river dynamics.
  • A theoretical value for Hack's exponent (γ = D/2) was proposed, with empirical measurements for Earth (γ = 0.54 ± 0.01) closely matching the theoretical estimation (γ ≈ 0.55).

Conclusions:

  • The extended IPBA provides a robust and efficient method for delineating multiple drainage basins.
  • Drainage basin characteristics show universal scaling laws across different celestial bodies.
  • Hack's law likely originates from the maximum and minimum lines within landscapes, linked to fractal dimensions.