A Geometric Algorithm to Identify River Meander Bends: 2. Test for Characteristic Shapes

Abstract

River meander bends are widely considered to have recurring shapes. Formal classifications of meander bends have provided an important framework for basic research and practical applications in river engineering and restoration. However, the central role of expert interpretation in both mapping and classifying meander bends leaves persistent uncertainty for whether their shapes do form patterns or instead represent a continuum of forms. This study analyzes meander bend shapes derived in a companion paper about the Beatton River, Canada, to test whether meander bends show repeating shapes without the prior assumption that such patterns exist. Meander bends are compared using Fréchet distance, a curve similarity measure, and evaluated for common shapes using agglomerative hierarchical clustering. The case study indicates that normalizing meander bend coordinates by wavelength and amplitude yields clusters of meander bends with internally consistent shapes. Characteristic meander bends for each cluster are derived by averaging the normalized coordinates and rescaling by the mean amplitude and wavelength for the source meander bends. Whereas automatically mapped meander bends vary in number and extent with a dimensionless amplitude threshold (A_st*), the characteristic meander bends are generally robust against variation in this parameter within its effective range (0.1 $\le$ A_st* $\le$ 1). By establishing a test for characteristic shapes among populations of multifarious meander bends, the analysis enables new tests for environmental controls on channel form, a standard for assessing the fidelity of numerical models for planform evolution, and a method to design nature-based templates for river restoration and engineering.