Sediment yield in rivers at different time-scales

The present thesis is devoted to a particular topic regarding the fluvial sub-systems, namely the evaluation of the annual amount of sediment yield through a given cross-section of a river. This problem has been largely investigated in literature and the resulting models can be classify in different groups depending on the morphological characteristics they take into account and their complexity. In any case the large quantity of data required is always the main problem. With this work we want to find simple relationships that require the lesser number of data as possible, so we have made our evaluations at a basin-scale and assumed for the river the Local Uniform Flow hypothesis (LUF). Accordingly, each river reach is defined by its length, width, slope and bottom composition, while the watershed area is collapsed in its barycentre which coincides with the upstream end of the LUF reach. A basic state, called equilibrium and represented by a stationary rating curve (a monomial relation between the solid and the liquid discharge of Engelund-Hansen type) is first identified, with the purpose to evaluate the deviations of the real solid transport from the equilibrium value, deviations that depend on the time-scale considered. In particular we have developed three models, valid in three different time-scales. For the short-term analysis we use the 1-D deterministic solution of the harmonic river which provides the delay and attenuation of the perturbation of the solid transport with respect to the equilibrium condition. In other words we link the actual deviations of the solid transport recorded downstream with previous perturbations of the liquid discharge, happened upstream. For a pluri-annual time-scale we integrate the 1-D morphodynamic model to a zero-dimensional model. As the water and sediments inputs to the river are concentrated in its upstream end, the width of the entire river is assumed to be constant, while the slope and the grain-size composition are considered to be variable in time. The resulting mathematical model is implicit and non-linear, but at this time-scale we simplify it in order to find a simple and generic analytical solution for the pluri-annual morphological evolution of the river. Finally, for very long-term analysis we integrate numerically the exact 0-D morphodynamic model to predict the morphological reactions of a river at geological time-scale. In this case we schematize the river with two contiguous LUF channel, representing the highland and the lowland parts of the real watercourse respectively. In this way, this model can simulate the typical behaviour of natural rivers showing a grain-size segregation (fining) in the downstream direction, accompanied by smaller slopes, without the computational costs necessary for a complete one-dimensional model. Some comparisons and numerical applications have been made.