Delineation of river bed-surface patches by clustering high-resolution spatial grain size data

Abstract

The beds of gravel-bed rivers commonly display distinct sorting patterns, which at length scales of ~0.1−1 channel widths appear to form an organization of patches or facies. This paper explores alternatives to traditional visual facies mapping by investigating methods of patch delineation in which clustering analysis is applied to a high-resolution grid of spatial grain-size distributions (GSDs) collected during a flume experiment. Specifically, we examine four clustering techniques: 1) partitional clustering of grain-size distributions with the k-means algorithm (assigning each GSD to a type of patch based solely on its distribution characteristics), 2) spatially-constrained agglomerative clustering (“growing” patches by merging adjacent GSDs, thus generating a hierarchical structure of patchiness), 3) spectral clustering using Normalized Cuts (using the spatial distance between GSDs and the distribution characteristics to generate a matrix describing the similarity between all GSDs, and using the eigenvalues of this matrix to divide the bed into patches), and 4) fuzzy clustering with the fuzzy c-means algorithm (assigning each GSD a membership probability to every patch type). For each clustering method, we calculate metrics describing how well-separated cluster-average GSDs are and how patches are arranged in space. We use these metrics to compute optimal clustering parameters, to compare the clustering methods against each other, and to compare clustering results with patches mapped visually during the flume experiment.All clustering methods produced better-separated patch GSDs than the visually-delineated patches. Although they do not produce crisp cluster assignment, fuzzy algorithms provide useful information that can characterize the uncertainty of a location on the bed belonging to any particular type of patch, and they can be used to characterize zones of transition from one patch to another. The extent to which spatial information influences clustering leads to a trade-off between the quality of GSD separation between patch types and the spatial coherence of patches. Methods incorporating spatial information during the clustering process tended to produce a finite number of types of patches. As methods improve for collecting high-resolution grain size data, the approaches described here can be scaled up to field studies to better characterize the grain size heterogeneity of river beds.