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Volume 4, issue 4 | Copyright

Special issue: Frontiers in geomorphometry

Earth Surf. Dynam., 4, 799-818, 2016
https://doi.org/10.5194/esurf-4-799-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 31 Oct 2016

Research article | 31 Oct 2016

Catchment power and the joint distribution of elevation and travel distance to the outlet

Leonard S. Sklar1, Clifford S. Riebe2, Claire E. Lukens2, and Dino Bellugi3 Leonard S. Sklar et al.
  • 1Department of Earth and Climate Sciences, San Francisco State University, San Francisco, CA 94132, USA
  • 2Department of Geology and Geophysics, University of Wyoming, Laramie, WY 82071, USA
  • 3Department of Earth, Atmospheric and Planetary Sciences, MIT, Cambridge, MA 02139, USA

Abstract. The delivery of water, sediment, and solutes by catchments is influenced by the distribution of source elevations and their travel distances to the outlet. For example, elevation affects the magnitude and phase of precipitation, as well as the climatic factors that govern rock weathering, which influence the production rate and initial particle size of sediments. Travel distance, in turn, affects the timing of flood peaks at the outlet and the degree of sediment size reduction by wear, which affects particle size distributions at the outlet. The distributions of elevation and travel distance have been studied extensively but separately, as the hypsometric curve and width function. Yet a catchment can be considered as a collection of points, each with paired values of elevation and travel distance. For every point, the ratio of elevation to travel distance defines the mean slope for transport of mass to the outlet. Recognizing that mean slope is proportional to the average rate of loss of potential energy by water and sediment during transport to the outlet, we use the joint distribution of elevation and travel distance to define two new metrics for catchment geometry: "source-area power", and the corresponding catchment-wide integral "catchment power". We explore patterns in source-area and catchment power across three study catchments spanning a range of relief and drainage area. We then develop an empirical algorithm for generating synthetic source-area power distributions, which can be parameterized with data from natural catchments. This new way of quantifying the three-dimensional geometry of catchments can be used to explore the effects of topography on the distribution on fluxes of water, sediment, isotopes, and other landscape products passing through catchment outlets, and may provide a fresh perspective on problems of both practical and theoretical interest.

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To better understand how rainfall, erosion, and other landscape processes create patterns of outflow from catchments, we developed a new way of measuring how the land surface is organized. Each hillslope area, where water and sediment are sourced, has an elevation above the catchment outlet and a horizontal distance that materials must travel to reach the outlet. We combined these attributes in a new metric that captures how the production and loss of energy varies within and between catchments.
To better understand how rainfall, erosion, and other landscape processes create patterns of...
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