Are channel networks statistically self-similar?

Research Article| December 01, 1997 Are channel networks statistically self-similar? Anicet A. Beauvais; Anicet A. Beauvais 1Institut Français de Recherche Scientifique pour le Développement en Coopération, 32 Avenue Henri Varagnat, 93143 Bondy Cedex, France Search for other works by this author on: GSW Google Scholar David R. Montgomery David R. Montgomery 2Department of Geological Sciences, University of Washington, Seattle, Washington 98195-1310 Search for other works by this author on: GSW Google Scholar Author and Article Information Anicet A. Beauvais 1Institut Français de Recherche Scientifique pour le Développement en Coopération, 32 Avenue Henri Varagnat, 93143 Bondy Cedex, France David R. Montgomery 2Department of Geological Sciences, University of Washington, Seattle, Washington 98195-1310 Publisher: Geological Society of America First Online: 02 Jun 2017 Online ISSN: 1943-2682 Print ISSN: 0091-7613 Geological Society of America Geology (1997) 25 (12): 1063–1066. https://doi.org/10.1130/0091-7613(1997)025<1063:ACNSSS>2.3.CO;2 Article history First Online: 02 Jun 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn Email Permissions Search Site Citation Anicet A. Beauvais, David R. Montgomery; Are channel networks statistically self-similar?. Geology 1997;; 25 (12): 1063–1066. doi: https://doi.org/10.1130/0091-7613(1997)025<1063:ACNSSS>2.3.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGeology Search Advanced Search Abstract Scaling properties of both field-mapped and threshold-delineated channel networks were studied by applying the box-counting method to three drainage basins in the western United States. This method involves (1) examination of power-law relations between the box size, ϵ, and the number of boxes, N, that intersect channel segments across a range of box sizes appropriate for the method and then (2) examining the standardized residuals for the least squares linear regressions of log N vs. log ϵ used to calculate a fractal dimension (D). For each channel network, the slope of the log N vs. log ϵ relation varies from 1 at small length scales to 2 at large length scales, a range that defines the limits to the applicability of the box-counting method. At length scales below which this slope equals 1, the plots simply record the linear aspect of streams; the length scale defining an upper limit to the application of the box-counting method corresponds to a box size large enough to intersect a channel in each box. Although a fractal dimension may be meaningfully defined only between these upper and lower length scales, neither the field-mapped nor the artificially delineated networks that we examined exhibit discrete fractal dimensions within this range. Instead, the slope of the log-log plot systematically varied with box size. The consistent lack of log-linear plots for the networks that we examined violates a fundamental requirement for fractal geometry and contrasts with general assertions about the fractal nature of river networks. A strong correlation between mean source-area size and the length scale above which the slope of plots implies D = 2 indicates that, although channel networks are not statistically self-similar, they are space filling at length scales greater than twice the mean source-basin length. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.