1 PREDICTING THE DEVIATIONS FROM THE CURVE OF SEDIMENT TRANSPORT VS WATER FLOW G. Di Silvio 1 , M. Nones 1 and M. Bisiacco 2 1. Hydraulic, Maritime, Environmental and Geotechnical Engineering Department, University of Padua, Padua, Italy 2. Department of Information Engineering, University of Padua, Padua, Italy ABSTRACT By means of an analytical solution of the one-dimensional, two grainsize-classes morphodynamic model (Fasolato et al., 2009) it has been shown that any river reach, no matter how irregular its geometry, sorted its sediments and variable its water flow, reaches and maintains an equilibrium configuration (namely a stationary morphological situation), under the only condition that the reach’s boundaries are always in equilibrium. This means that the bathymetry of the river reach and the grainsize composition of the bed should in principle remain constant in time (even in presence of variable input of water and sediments), provided that water and sediments entering the reach are related by a unique relation (equilibrium transport formula). Such a condition, however, is hardly satisfied, especially in the farthest mountain branches of the hydrographic network, as the formation mechanisms of water- and sediment- input are quite variable and seasonally delayed. As these initial perturbations with respect to the equilibrium conditions propagate with a certain attenuation along the river, they give place to the well-known instantaneous deviations from the average curve of sediment transport vs water flow. In the present paper a general approach is suggested to predict these deviations. The approach is based on the deterministic analytical solution for the “harmonic river” (Fasolato et al., 2009), combined with a recursive model of the ARMA type. The recursive empirical model for a certain river (calibrated against a relatively small dataset of regular measurements) will provide the “instantaneous” sediment discharge as a function of the “instantaneous” water flow (equilibrium component) and the water flow measured at one or more previous times (non-equilibrium components). With the aid of the deterministic model, the calibrated parameters of the recursive model may be given a physical meaning which may be somehow transferred to other rivers with only a very limited and sparse sediment transport measurements. 1. INTRODUCTION As opposed to the basic configuration of uniform plane flow, that conveys a uniform solid discharge of a uniform grainsize material, as typically considered by ordinary experimental conditions in a laboratory, a natural river reach is affected by a lot of variability in time and space. This variability concerns not only hydrology (time-depending water flow), but also sediment input (solid transport rate and grainsize composition) and geometry (bottom profile and river width). If we assume that during the year all these quantities, except water and sediment inputs remain constant, the relationship between instantaneous water flow and instantaneous sediment transport will be provided by a unique curve (corresponding to the “equilibrium” transport formula), while the transport composition will remain constant. Deviations from the “equilibrium” curve, in terms of total transport and grainsize composition, is by far more important in the upper portions of mountainous watershed, where frequent debris flow and landslides change the local morphology and increase many fold the ordinary transport (Di Silvio et al., 1991). These changes propagate slowly and progressively damped over long distances, from their