Testing Formulations for Incipient Motion of Boulders Reveals the Importance of Fluctuating Force Distributions and Parameter Uncertainty

Rare, high-magnitude floods can rapidly reshape landscapes. Accurate discharge estimates of these large, infrequent events provide critical constraints on flood frequency-magnitude distributions for hazard assessments, and permit quantification of the role large floods play in shaping landscapes and redistributing large volumes of water and sediment. Commonly, flood magnitude is estimated using an incipient motion calculation in which the force necessary to move flood-deposited grains is used to estimate a minimum flow velocity. For large magnitude floods, these velocity estimates are often based on grains from 1 to 10 m in diameter, much larger than the order mm to cm diameter grains on which most incipient motion calculations have been verified, raising questions regarding the accuracy of velocity and discharge inversions for large floods. To address this discrepancy, we explore all probable flow conditions using a Monte Carlo method to simulate incipient motion of large grains during high magnitude floods. We predict a distribution of likely velocity fluctuations at grain motion using a full force balance equation while incorporating reported variability of force-balance parameters and uncertainty in physical parameters such as grain shape. Our results suggest the flow velocity at incipient motion follows a positive power law scaling with grain size that is systematically lower than the relation when not accounting for parameter uncertainty. Testing this finding using a unique natural experiment from a modern glacial lake outburst flood in southern Chile reveals a stronger agreement in the grain size-velocity scaling when accounting for fluctuating force distributions and parameter uncertainty relative to ignoring this variability.