The generation and scaling of longitudinal river profiles

Roberts, G. G. and White, N. J. and Lodhia, B. H. (2018) The generation and scaling of longitudinal river profiles. Journal of Geophysical Research-Earth Surface, 124 (1). pp. 137-153. ISSN 2169-9011 DOI https://doi.org/10.1029/2018JF004796

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Abstract

The apparent success of inverse modeling of continent‐wide drainage inventories is perplexing. An ability to obtain reasonable fits between observed and calculated longitudinal river profiles implies that drainage networks behave simply and predictably at length scales of O(102–103) km and time scales of O(100–102) Ma. This behavior suggests that rivers respond in an organized way to large‐scale tectonic forcing. On the other hand, stream power laws are empirical approximations since fluvial processes are complex, nonlinear, and probably susceptible to disparate temporal and spatial shocks. To bridge the gap between these different perceptions of landscape evolution, we present and interpret a suite of power spectra for African river profiles that traverse different climatic zones, lithologic boundaries, and biotic distributions. At wavelengths urn:x-wiley:jgrf:media:jgrf20973:jgrf20973-math-0001102 km, power spectra have slopes of −2, consistent with red noise, demonstrating that profiles are self‐similar at these length scales. At wavelengths urn:x-wiley:jgrf:media:jgrf20973:jgrf20973-math-0002102 km, there is a crossover transition to slopes of −1, consistent with pink noise, for which power scales according to the inverse of wavenumber. Onset of this transition suggests that spatially correlated noise, perhaps generated by instabilities in water flow and by lithologic heterogeneities, becomes more prevalent at wavelengths shorter than ∼100 km. At longer wavelengths, this noise gradually diminishes and self‐similar scaling emerges. Our analysis is consistent with the concept that complexities of river profile development can be characterized by an adaptation of the Langevin equation, by which simple advective models of erosion are driven by a combination of external forcing and noise.

Item Type:	Article
Uncontrolled Keywords:	2018AREP; IA74
Subjects:	02 - Geodynamics, Geophysics and Tectonics
Divisions:	02 - Geodynamics, Geophysics and Tectonics 08 - Green Open Access
Journal or Publication Title:	Journal of Geophysical Research-Earth Surface
Volume:	124
Page Range:	pp. 137-153
Identification Number:	https://doi.org/10.1029/2018JF004796
Depositing User:	Sarah Humbert
Date Deposited:	19 Dec 2018 12:19
Last Modified:	12 Sep 2019 09:41
URI:	http://eprints.esc.cam.ac.uk/id/eprint/4373

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