Simulating transient sediment waves in aggraded alluvial channels by double-decomposition method

Abstract

By using the double-decomposition (DD) method, this study simulates transient sediment waves caused by aggradation described by a diffusion-type partial differential equation (PDE). The DD method solves the PDE by decomposing the solution function for sediment rate into a summation of M number of components, where M stands for the order of approximation. The solution was approximated by considering only the first three terms. The model satisfactorily simulated laboratory-measured aggradation bed profiles with, on average, a mean absolute error (MAE) of 0.70 cm, a root-mean-square error (RMSE) of 0.84 cm, a mean relative error (MRE) of 1.11%, and R2=0.95. The model performance was also tested by using numerical and error-function solutions. In addition, the results obtained from application of the DD solution to hypothetical field cases were found to be theoretically compatible with what may be observed in natural streams. However, sediment wave fronts in later periods of the simulation time reached equilibrium bed levels more quickly, around in the middle section of the channel.