Long-term Morphodynamics of a Schematic River Analysed with a Zero-dimensional, Two-reach, Two-grainsize Model

At the basin scale, neglecting localized deviations caused by geological constraints like knick-points, alluvial rivers commonly exhibit a concave profile and a progressive sediment fining in the downstream direction. Although this configuration is, perforce, not in equilibrium, yet it usually shows a quasi-stationary behaviour at the very long (historical and geological) time-scale. A zero-dimensional, two-reach, two-grainsize hydro-morphological model is presented and applied to a schematic river. The description of the processes involved is done assuming several reasonable and verified simplifications, giving reason of the extremely slow evolution of many alluvial rivers and providing a quantitative approach to evaluate their ‘response time’. Different from previous analytical formulations, the response time appears here to be affected, among others, by the granulometry of the sediment input. Applications of the model to different geometries demonstrate that the present riverine morphology at the basin scale will persist practically stationary for extremely long periods of time (centuries and even millennia), if the climatic forcing remain unchanged and no anthropogenic perturbations are introduced in the system.