Quantifying Variability of Incipient‐Motion Thresholds in Gravel‐Bedded Rivers Using a Grain‐Scale Force‐Balance Model

Predicting thresholds of sediment motion is critical for a range of applications involving sediment transport. However, thresholds for sediment motion can vary over an order of magnitude for a single characteristic flow and bed configuration. Lacking simple ways to incorporate this variability, many assume thresholds are constant for rough, turbulent flow. Here, we quantify variability of incipient‐motion thresholds based on a commonly used grain‐scale force‐balance model, with model parameter distributions determined from published experiments. We show that variability in the threshold of motion within the 2D force‐balance model occurs predominantly due to variability in the lift coefficient and grain protrusion, and secondarily due to drag coefficient variability. For a known grain size, the mean threshold of motion, and variability about the mean, can be predicted from a family of power laws. These power laws can be altered with site‐specific parameter distributions, allowing for site‐specific application to well‐studied reaches and other planets. Using compiled flume and field data we show that constraining force‐balance parameter distributions with independent data results in narrower distributions of the predicted threshold of motion, consistent with constrained flume experiments. This analysis highlights that while the threshold of sediment motion is variable, the magnitude of variability is predictable within the force‐balance model based on site‐specific physical constraints of local flow and bed conditions. Understanding what flow velocities are needed for rivers to move gravel and boulders is critical for river management, reducing flood hazards, understanding river ecosystems, and the long‐term evolution of landforms such as deltas and mountain ranges. However, accurate predictions of sediment transport are made challenging by large variability in flow conditions observed when a particular size of sediment is moved by a river. In this work we use an existing theory to explore the expected flow conditions and flow variability needed to move sediment. These results allow for more accurate river restoration and engineering designs and more sustainable river management. Using a grain force‐balance model and observed parameter distributions, we quantify expected variability in incipient‐motion thresholds Predicted distributions of incipient‐motion thresholds match those observed in laboratory experiments and natural rivers A power law can describe m