13 Jul 2022
13 Jul 2022
Status: a revised version of this preprint is currently under review for the journal HESS.

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

Soohyun Yang1,a, Kwanghun Choi1, and Kyungrock Paik1 Soohyun Yang et al.
  • 1School of Civil, Environmental, and Architectural Engineering, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 02841, South Korea
  • acurrently at: Department Aquatic Ecosystems Analysis and Management, Helmholtz Centre for Environmental Research – UFZ, Magdeburg, 39114, Germany

Abstract. Self-similar structures of river networks have been quantified as diverse scaling laws. Among them we investigated a power functional relationship between the pruning area Ap and the associated apparent drainage density ρa with an exponent η. We analytically derived the relationship between η and other scaling exponents known for fractal river networks. The derivation is supported by analysis of four real river networks. The relationship between η and non-integer fractal dimensions found for natural river networks is suggested. 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.

Soohyun Yang et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2022-237', Anonymous Referee #1, 16 Aug 2022
    • AC1: 'Reply on RC1', Kyungrock Paik, 06 Oct 2022
  • RC2: 'Comment on hess-2022-237', Anonymous Referee #2, 24 Aug 2022
    • AC2: 'Reply on RC2', Kyungrock Paik, 06 Oct 2022

Soohyun Yang et al.

Soohyun Yang et al.


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Short summary
In extracting a river network from a digital elevation model, one should specify the pruning area. As pruning area grows, the 'apparent' drainage density reduces, following a power function. We suggest that 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. We evaluated this theory by analyzing topographies of four study catchments.