Modelling evolution of bed profile and grain size distribution in unsurveyed rivers

The water flow and sediment transport equations have been linearized and analytically solved under the hypothesis of quasi-equilibrium conditions. This solution permits to reconstruct the river bathymetry from planimetric data, the only ones available from satellite images for most of the large rivers of the world. The linearized quasi-equilibrium solution provides a criterion to evaluate the accuracy of the approximate (uniform-flow) model, compared to the regular (steady-flow) model. For non-equilibrium conditions, a further constraint on time resolution should be added, which is however generally satisfied for long-term morphological simulations. The uniform-flow solution presents many advantages which become crucial for long-term numerical computations at watershed scale. The article provides a detailed numerical comparison of the accuracy and resolution of both steady- and uniform-flow models, with an application to the evolution of the lower Zambezi River, which confirms the theoretical criterion. The accuracy of the uniform-flow solution appears to improve when the river is schematized with a coarse computational grid although, of course, with a corresponding loss of spatial resolution.