Timescale of the Morphodynamic Feedback Between Planform Geometry and Lateral Migration of Meandering Rivers

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.