A Geometric Algorithm to Identify River Meander Bends:1. Effect of Perspective

Abstract

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 ($\lambda \approx$ 12w_c) from visual interpretation. The number and extents of meander bends change with A_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.