Erosion caused by overland flow: An interpolation method

► We provide a new approximate analytical solution during non-steady erosions. ► Overland flow is considered as an example. ► Complex physical dynamic processes are considered during the erosion. ► The contribution of both finer and coarser soil particles is explored. ► An interpolation between short and long times is developed. A new general method has been obtained to solve the physically-based equations describing the dynamics of sediment adjustment through time following erosion on a plane soil surface. This method is based on exploiting differences in behavior between smaller and larger sediment particles in their ability to form a protective layer by net deposition of previously eroded sediment. The utility of this approximate solution was verified by comparison with a numerical solution, for the particular case when a steady over land flow of water is the cause of the erosion.