Quantifying the scale of gravel-bed clusters with spatial statistics

Clustering of large surficial particles affect the critical shear stress, bedload transport rate, and ecological processes of gravel rivers. Particle clusters have been the subject of careful study and taxonomy but would benefit from new quantitative, reproducible, statistical analysis, particularly in the gravel size classes where clusters are difficult to reliably resolve by visual, gestalt methods. This study quantified a clustering length scale for a gravel and cobble bed. The size, orientation, and location of 7726 gravel and cobble particles were measured from 100 photographic samples of a symmetrical bar on the Navarro River, California. Nearest neighbor spatial statistics were used to analyze particle associations. Clustering was identified between gravel particles throughout the river bar. Clustering was also identified for large (>d84 of the sample) and medium (between the d50 and d84 of the sample) particles relative to the local gradation. The spatial scale of these large and medium particle clusters were 1.75d84 and 3.0d50, respectively.