Cellular modelling of river catchments and reaches: Advantages, limitations and prospects

The last decade has witnessed the development of a series of cellular models that simulate the processes operating within river channels and drive their geomorphic evolution. Their proliferation can be partly attributed to the relative simplicity of cellular models and their ability to address some of the shortcomings of other numerical models. By using relaxed interpretations of the equations determining fluid flow, cellular models allow rapid solutions of water depths and velocities. These can then be used to drive (usually) conventional sediment transport relations to determine erosion and deposition and alter the channel form. The key advance of using these physically based yet simplified approaches is that they allow us to apply models to a range of spatial scales (1-100 km²) and time periods (1-100 years) that are especially relevant to contemporary management and fluvial studies. However, these approaches are not without their limitations and technical problems. This paper reviews the findings of nearly 10 years of research into modelling fluvial systems with cellular techniques, principally focusing on improvements in routing water and how fluvial erosion and deposition (including lateral erosion) are represented. These ideas are illustrated using sample simulations of the River Teifi, Wales. A detailed case study is then presented, demonstrating how cellular models can explore the interactions between vegetation and the morphological dynamics of the braided Waitaki River, New Zealand. Finally, difficulties associated with model validation and the problems, prospects and future issues important to the further development and application of these cellular fluvial models are outlined.