Delayed response model for bankfull discharge predictions in the Yellow River

Delayed response means that channels cannot achieve a new equilibrium state immediately following disruption;the channel requires a response time or relaxation time to reach equilibrium.It follows that the morphological state of fluvial system represents the cumulative effects of all previous disturbances and environmental conditions.A unique feature of the delayed response model for bankfull discharge is that the model is capable of representing the cumulative effects of all previous flow conditions when applied to predict the path/trajectories of bankfull discharge in response to altered flow regimes.In this paper,the delayed response model was modified by readjusting the weight for the initial boundary conditions and introducing a variableβwith respect to time.The modified model was then applied to the bankfull discharge calculations for three selected river reaches of the Yellow River,with each reach having different geomorphic settings and constraints. Results indicated that the modified model can predict accurately the bankfull discharge variation in response to changes in flow discharge and sediment load conditions that have been dramatically altered in the past.Results also demonstrated the strong dependence of current bankfull discharge on the previous years’ flow conditions,with the relaxation time varied from 2 to 14 years,meaning that the bankfull discharge was not only affected by the flow discharge and sediment load in the current year,but also by those in previous 1 to 13 years.Furthermore,the relaxation time of bankfull discharge adjustment was inversely proportional to the long-term average suspended sediment concentrations,and this may be explained by fact that high sediment concentrations may have a high potential to perform geomorphic work and there is more sediment readily available to shape the channel boundary and geometry.