Semi-implicit time integration of the Exner equation for bedload transport over a non-erodible layer: Application to a tidal sandbank model

Existing morphodynamic models that consider bedload sediment transport over non-erodible layers often rely on small morphological time steps or numerical filtering techniques for stability. A time-integration method of the Exner equation that can simulate bedform evolution over large timescales without relying on numerical fixes appears to be lacking. In this research, we provide two semi-implicit time-integration methods and propose a method to incorporate the non-erodible layer without numerical fixes, applied to a tidal sandbank model. As shown by our results, both methods work well, and are computationally fast. The newly developed model is compared against a conventional approach, which violates the non-erodibility condition, is computationally less efficient due to the need for small time steps, and introduces new uncertainty by adding more parameters. Our new method to deal with the non-erodibility allows for large morphological time steps and is a suitable method to study tidal sandbank dynamics in sediment-scarce environments.