Using the Threshold of Motion as a State Variable to Predict Bed Load Hysteresis in Mountain Rivers

Abstract:

While bedload transport hysteresis is common in steep mountain streams, very few transport models predict hysteresis and its causes remain uncertain. A key variable in transport models is the nondimensional shear stress at which bedload movement becomes significant (τ^*_ri). Many factors influence τ^*_ri including clast size, the grain size distribution of the surrounding bed, turbulent intensity, clast protrusion, packing and clustering. Rather than attempt to isolate the myriad competing influences, we present a new model in which τ^*_ri evolves through time as a generalized function of upstream discharge and sediment supply. Discharge serves competing purposes: cumulative flow stabilizes beds by packing and interlocking grains (increasing τ^*_ri), while relatively higher discharge tends to destabilize beds (decreasing τ^*_ri). Sediment supply also influences transport rates at a given discharge. The model term that describes how τ^*_ri varies with supply is similar to the Exner equation. If more sediment enters a reach than leaves, then τ^*_ri decreases. Conceptually this occurs because deposition preferentially fills topographic lows, smooths the bed and increases near-bed velocities. Conversely, when more sediment exits a reach than enters, then τ^*_ri increases because erosion tends to increase bed roughness and move grains from less stable to more stable positions. We compare the new τ^*_ri equation to flume experiments and to field data. The model can predict both clockwise and counterclockwise hysteresis that have been observed in coarse mountain rivers. Finally, we suggest that τ^*_ri should be thought of as a state variable, which influences the evolution of a reach towards the equilibrium condition of transport rate just balancing supply rate.