Rough Correlations: Meta-Analysis of Roughness Measures in Gravel Bed Rivers

Bed roughness height (k) is a key parameter for velocity prediction in open-channel flows. There is not yet a firm consensus about whether characteristic particle size D-84 or sigma(z) (standard deviation of the channel thalweg) better describes k in gravel bed streams. A data set of 1,788 flume and 713 field measurements with a wide range of channel morphologies and flow conditions were compiled to test whether D-84 or sigma(z) is a better descriptor of k and to explore the influence of several controls on flow resistance variation. Tests were performed using four well-known flow resistance equations. The results consistently show that sigma(z) outperforms D-84 in predicting velocity and the Smart and Jaggi equation, with sigma(z) as k, outperforms other equations. The data set was grouped based on R/k (R is the hydraulic radius), channel morphologies, and study sites. sigma(z) performs better than D-84 as a measure of k in all morphologies and much better for channels with large instream wood. The analysis shows R/k is a major control on resistance variation as sigma(z) contains more site-specific information like bed structure. The topography measurements for step-pool channels should at least contain measurements on key roughness elements like steps. For gravel-dune or plane-bed channels, the proper resolution should be higher than 1/2 dune wavelength and 2D(84), respectively. The choice of proper reach length relates to both R/k and roughness type. Further, hydraulic geometry functions with either D-84 or sigma(z) as k are proposed, and the relation between the two metrics is discussed.