23 Nov 2023
 | 23 Nov 2023
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 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.

Soohyun Yang, Kwanghun Choi, and Kyungrock Paik

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-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


Total article views: 263 (including HTML, PDF, and XML)
HTML PDF XML Total Supplement BibTeX EndNote
204 43 16 263 19 5 4
  • HTML: 204
  • PDF: 43
  • XML: 16
  • Total: 263
  • Supplement: 19
  • BibTeX: 5
  • EndNote: 4
Views and downloads (calculated since 23 Nov 2023)
Cumulative views and downloads (calculated since 23 Nov 2023)

Viewed (geographical distribution)

Total article views: 259 (including HTML, PDF, and XML) Thereof 259 with geography defined and 0 with unknown origin.
Country # Views %
  • 1
Latest update: 25 Feb 2024
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.