Delineation of gravel-bed clusters via factorial kriging

Gravel-bed clusters are the most prevalent microforms that affect local flows and sediment transport. A growing consensus is that the practice of cluster delineation should be based primarily on bed topography rather than grain sizes. Here we present a novel approach for cluster delineation using patch-scale high-resolution digital elevation models (DEMs). We use a geostatistical interpolation method, i.e., factorial kriging, to decompose the short- and long-range (grain- and microform-scale) DEMs. The required parameters are determined directly from the scales of the nested variograms. The short-range DEM exhibits a flat bed topography, yet individual grains are sharply outlined, making the short-range DEM a useful aid for grain segmentation. The long-range DEM exhibits a smoother topography than the original full DEM, yet groupings of particles emerge as small-scale bedforms, making the contour percentile levels of the long-range DEM a useful tool for cluster identification. Individual clusters are delineated using the segmented grains and identified clusters via a range of contour percentile levels. Our results reveal that the density and total area of delineated clusters decrease with increasing contour percentile level, while the mean grain size of clusters and average size of anchor clast (i.e., the largest particle in a cluster) increase with the contour percentile level. These results support the interpretation that larger particles group as clusters and protrude higher above the bed than other smaller grains. A striking feature of the delineated clusters is that anchor clasts are invariably greater than the D₉₀ of the grain sizes even though a threshold anchor size was not adopted herein. The average areal fractal dimensions (Hausdorff-Besicovich dimensions of the projected areas) of individual clusters, however, demonstrate that clusters delineated with different contour percentile levels exhibit similar planform morphologies. Comparisons with a compilation of existing field data show consistency with the cluster properties documented in a wide variety of settings. This study thus points toward a promising, alternative DEM-based approach to characterizing sediment structures in gravel-bed rivers.