Modeling memory in gravel-bed rivers: A flow history-dependent relation for evolving thresholds of motion

Abstract. Thresholds of motion (τ*c) strongly control bedload transport in gravel-bed rivers. Uncertainty in τ*c limits the accuracy of predictions of transport and morphologic change. To improve our quantitative understanding of morphodynamic feedbacks in rivers, we propose a flow history-dependent model where τ*c evolves temporally as a function of bed shear stress. Relatively low shear stresses strengthen the bed, increasing τ*c and reducing transport. Larger floods rapidly weaken the bed, decreasing τ*c and increasing transport. We calibrate the model to a 23-year record of flow and bedload transport from the Erlenbach Torrent, Switzerland, and find that the model predicts the field-based τ*c record more accurately than assuming a constant τ*c.  Calibrated parameters describing strengthening are more tightly distributed than weakening parameters, which suggests that flood-induced bed weakening is more stochastic and less predictable than strengthening.