Coupled model of surface water flow, sediment transport and morphological evolution

This paper presents a mathematical model coupling water flow and sediment transport dynamics that enables calculating the changing surface morphology through time and space. The model is based on the shallow water equations for flow, conservation of sediment concentration, and empirical functions for bed friction, substrate erosion and deposition. The sediment transport model is a non-capacity formulation whereby erosion and deposition are treated independently and influence the sediment flux by exchanging mass across the bottom boundary of the flow. The resulting hyperbolic system is solved using a finite volume, Godunov-type method with a first-order approximate Riemann solver. The model can be applied both to short time scales, where the flow, sediment transport and morphological evolution are strongly coupled and the rate of bed evolution is comparable to the rate of flow evolution, or to relatively long time scales, where the time scale of bed evolution associated with erosion and/or deposition is slow relative to the response of the flow to the changing surface and, therefore, the classical quasi-steady approximation can be invoked. The model is verified by comparing computed results with documented solutions. The developed model can be used to investigate a variety of problems involving coupled flow and sediment transport including channel initiation and drainage basin evolution associated with overland flow and morphological changes induced by extreme events such as tsunami. r 2006 Elsevier Ltd. All rights reserved.