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On the theory of drainage area for regular and non-regular points.

Publication ,  Journal Article
Bonetti, S; Bragg, AD; Porporato, A
Published in: Proceedings. Mathematical, physical, and engineering sciences
March 2018

The drainage area is an important, non-local property of a landscape, which controls surface and subsurface hydrological fluxes. Its role in numerous ecohydrological and geomorphological applications has given rise to several numerical methods for its computation. However, its theoretical analysis has lagged behind. Only recently, an analytical definition for the specific catchment area was proposed (Gallant & Hutchinson. 2011 Water Resour. Res.47, W05535. (doi:10.1029/2009WR008540)), with the derivation of a differential equation whose validity is limited to regular points of the watershed. Here, we show that such a differential equation can be derived from a continuity equation (Chen et al. 2014 Geomorphology219, 68-86. (doi:10.1016/j.geomorph.2014.04.037)) and extend the theory to critical and singular points both by applying Gauss's theorem and by means of a dynamical systems approach to define basins of attraction of local surface minima. Simple analytical examples as well as applications to more complex topographic surfaces are examined. The theoretical description of topographic features and properties, such as the drainage area, channel lines and watershed divides, can be broadly adopted to develop and test the numerical algorithms currently used in digital terrain analysis for the computation of the drainage area, as well as for the theoretical analysis of landscape evolution and stability.

Duke Scholars

Published In

Proceedings. Mathematical, physical, and engineering sciences

DOI

EISSN

1471-2946

ISSN

1364-5021

Publication Date

March 2018

Volume

474

Issue

2211

Start / End Page

20170693

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Bonetti, S., Bragg, A. D., & Porporato, A. (2018). On the theory of drainage area for regular and non-regular points. Proceedings. Mathematical, Physical, and Engineering Sciences, 474(2211), 20170693. https://doi.org/10.1098/rspa.2017.0693
Bonetti, S., A. D. Bragg, and A. Porporato. “On the theory of drainage area for regular and non-regular points.Proceedings. Mathematical, Physical, and Engineering Sciences 474, no. 2211 (March 2018): 20170693. https://doi.org/10.1098/rspa.2017.0693.
Bonetti S, Bragg AD, Porporato A. On the theory of drainage area for regular and non-regular points. Proceedings Mathematical, physical, and engineering sciences. 2018 Mar;474(2211):20170693.
Bonetti, S., et al. “On the theory of drainage area for regular and non-regular points.Proceedings. Mathematical, Physical, and Engineering Sciences, vol. 474, no. 2211, Mar. 2018, p. 20170693. Epmc, doi:10.1098/rspa.2017.0693.
Bonetti S, Bragg AD, Porporato A. On the theory of drainage area for regular and non-regular points. Proceedings Mathematical, physical, and engineering sciences. 2018 Mar;474(2211):20170693.
Journal cover image

Published In

Proceedings. Mathematical, physical, and engineering sciences

DOI

EISSN

1471-2946

ISSN

1364-5021

Publication Date

March 2018

Volume

474

Issue

2211

Start / End Page

20170693

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences