Moving-Window Detrending for Grain-Roughness Parameterization

Abstract

Detrending is required to enable robust parameterization of surface roughness by removing large topographic trends from fluvial data. A range of detrending methods exist in the literature; however, there is limited presentation of the effect of these methods on output roughness statistics. Here, the results of non-detrended data compared with flat-surface detrending (e.g., removal of bed slope and setup misalignment) and moving-window detrending (e.g., removal of nonlinear bed undulations) are presented for a wide suite of roughness statistics. Digital elevation models (DEMs) of gravel surfaces obtained from the field and the laboratory are analyzed. Roughness statistics include the coefficient of variation of the standard deviation of elevations, standard deviation of elevations, skewness, kurtosis, inclination index, and horizontal roughness lengths from second-order structure functions. Similarities exist between non-detrended data and the data detrended using flat-surface detrending. The moving-window detrending method, which removes larger topographic signatures and roughness scales (e.g., the influence of bed forms), results in lower roughness statistics in the coefficient of variation, standard deviation of elevations, and horizontal roughness lengths. In contrast, higher values of skewness and kurtosis are observed with the moving-window detrending method. These observed differences in roughness statistics for studied detrending methods support the use of a moving-window detrending method for robust grain-roughness parameterization. Furthermore, it is highlighted that comparisons between grain-roughness studies need to ensure that the same procedure of detrending has been applied.