Comparing Meander Sizes of Alluvial and Bedrock Channels to Loop-Erased Random Walks: Implications for Controls on the Sizes of Meander Bends
Abstract
The scale of meandering rivers is so visually apparent as to provide a compelling means for falsifying hypothesized equations governing flow through channel bends. If equations governing alluvial hydraulics provide insufficient explanations of planform in some cases, then objective determination of non-random planform scales in the general case is necessary. It follows, then, that accurate measurement of meander wavelength requires an estimation of the probability that the measured length is the result of random chance. We make that estimate by comparing meander wavelengths measured from 1) digitized natural alluvial and bedrock channel centerlines and 2) loop-erased random walks (LERW). Meander wavelengths are measured as the straight-line distance between bend cross-over locations, which are identified from the extrema of streamwise direction, ϕ(s), where s is streamwise distance. We estimate the corresponding probability density function from the sample comprising the wavelength measurements from the set of variably smoothed direction series, and we bootstrap confidence limits around our estimated probability densities by 1,000 trials of resampling with substitution. Wavelengths for each centerline are normalized by their respective discretization, which corresponds to half of the mean channel width for the natural streams. The estimated peak dimensionless wavelength of the LERW is 2.6 with upper and lower 95% confidence limits of 3.1 and 2.1, respectively. The estimated dimensionless wavelengths of natural meanders are all greater than the LERW upper limit, nor do they have overlapping 95% confidence intervals, suggesting that non-random representative wavelengths are present in natural meanders. Peak dimensionless meander wavelengths range from 4 to 10 and 12 to 30 for alluvial and bedrock meanders, respectively. The larger bedrock wavelengths imply that the magnitude of formative flow events increases with bank resistance.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2016
- Bibcode:
- 2016AGUFMEP51A0860Z
- Keywords:
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- 1824 Geomorphology: general;
- HYDROLOGYDE: 1825 Geomorphology: fluvial;
- HYDROLOGYDE: 1856 River channels;
- HYDROLOGYDE: 1862 Sediment transport;
- HYDROLOGY