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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< Ast* <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. 

Channels form meander bends, whether in rivers or on glaciers, volcanoes, coastlines, or the seafloor. Therefore, isolating meander bends is instrumental in characterizing channel shape and its relationship to the surrounding environment. The common approach of delimiting meander bends using inflection points yields isolated arcs that differ from traditional depictions. This study develops a geometric algorithm for mapping meander bends to bridge this gap. The approach accounts for two perceptual factors: observer viewpoint and the scale of significant deviations in the river path. The channel centerline is divided into three elements: arcs of positive/negative curvature, and effectively straight reaches with dimensionless amplitude (A_st*) below a threshold. Meander bends are formed by connecting reaches between arcs of similar curvature and trimming to where the openness, or viewshed, falls below the value for a straight line (180°). A case study for the Beatton River, Canada, shows the method captures the full extents of meander bends and reproduces a common classification (simple vs. compound) and scaling between wavelength and channel width ( 12w_c) from visual interpretation. The number and extents of meander bends change withA_st*; 0.1 < A_st* < 1 prevents over‐segmentation without lumping adjacent meander bends. The approach further indicates two mapping solutions that correspond to viewpoints on opposite sides of the river. By harmonizing the geometric definition of a meander bend with its traditional depiction, this approach advances the quantitative analysis of channels across geologic environments. A companion study tests whether the mapped meander bends have characteristic shapes. 

Abstract Across varied environments, meandering channels evolve through a common morphodynamic feedback: the sinuous channel shape causes spatial variations in boundary shear stress, which cause lateral migration rates to vary along a meander bend and change the shape of the channel. This feedback is embedded in all conceptual models of meandering channel migration, and in numerical models, it occurs over an explicit timescale (i.e., the model time step). However, the sensitivity of modeled channel trajectory to the time step is unknown. In numerical experiments using a curvature‐driven model of channel migration, we find that channel trajectories are consistent over time if the channel migrates ≤10% of the channel width over the feedback timescale. In contrast, channel trajectories diverge if the time step causes migration to exceed this threshold, due to the instability in the co‐evolution of channel curvature and migration rate. The divergence of channel trajectories accumulates with the total run time. Application to hindcasting of channel migration for 10 natural rivers from the continental US and the Amazon River basin shows that the sensitivity of modeled channel trajectories to the time step is greatest at low (near‐unity) channel sinuosity. A time step exceeding the criterion causes over‐prediction of the width of the channel belt developed over millennial timescales. These findings establish a geometric constraint for predicting channel migration in landscape evolution models for lowland alluvial rivers, upland channels coupled to hillslopes and submarine channels shaped by turbidity currents, over timescales from years to millennia.