Preprints
https://doi.org/10.5194/hess-2023-271
https://doi.org/10.5194/hess-2023-271
23 Nov 2023
 | 23 Nov 2023
Status: a revised version of this preprint was accepted for the journal HESS and is expected to appear here in due course.

Power-Law between the Apparent Drainage Density and the Pruning Area

Soohyun Yang, Kwanghun Choi, and Kyungrock Paik

Abstract. Self-similar structures of river networks have been quantified as diverse scaling laws. Among them we investigated a power functional relationship between the apparent drainage density ρa and the pruning area Ap with an exponent η. We analytically derived the relationship between η and other scaling exponents known for fractal river networks. The analysis of 14 real river networks covering diverse range of climate conditions and free-flow connectivity levels supports our derivation. We further linked η with non-integer fractal dimensions found for river networks. Synthesis of our findings through the lens of fractal dimensions provides an insight that the exponent η has fundamental roots in fractal dimension for the whole river network organization.

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Soohyun Yang, Kwanghun Choi, and Kyungrock Paik

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2023-271', Anonymous Referee #1, 10 Jan 2024
    • AC1: 'Reply on RC1', Kyungrock Paik, 16 Feb 2024
  • RC2: 'Comment on hess-2023-271', Massimiliano Schiavo, 15 Jan 2024
    • AC2: 'Reply on RC2', Kyungrock Paik, 16 Feb 2024

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2023-271', Anonymous Referee #1, 10 Jan 2024
    • AC1: 'Reply on RC1', Kyungrock Paik, 16 Feb 2024
  • RC2: 'Comment on hess-2023-271', Massimiliano Schiavo, 15 Jan 2024
    • AC2: 'Reply on RC2', Kyungrock Paik, 16 Feb 2024
Soohyun Yang, Kwanghun Choi, and Kyungrock Paik
Soohyun Yang, Kwanghun Choi, and Kyungrock Paik

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Short summary
In extracting a river network from a digital elevation model, one should specify the pruning area. As this value grows, the 'apparent' drainage density reduces, following a power function. This power-law reflects the fractal topographic nature of a catchment, and indeed follows the exceedance probability distribution of drainage area, a power-law known in earlier studies. This is supported by analysis of real river networks.