On the equilibrium profile of river beds

Despite the wide spectrum of perturbations of flow and sediment transport experienced by rivers as a result of hydrologic variations, the paradigm of morphodynamic equilibrium has long been present in the geomorphological literature where it is traditionally associated with the semiempirical notion of formative discharge, whereby the unsteady forcing is taken as morphologically equivalent to some effective steady forcing. Here we investigate the mechanisms responsible for maintaining a quasi-equilibrium bed profile of a river reach sufficiently short to have no significant tributary inputs. More importantly, we assume the channel banks to be fixed, hence, the case we have in mind is that of rivers protected by levees which cannot respond to hydrologic forcing by changing their width like natural rivers. Employing a 1-D model of river morphodynamics, we first determine the equilibrium profile of the river reach for given steady forcing conditions and discuss the capability of this approach for interpreting bed profiles observed in the field by applying it to the terminal reach of the Magra River, Italy. Field observations turn out to be reasonably well fitted by the equilibrium profile associated with a steady effective discharge, which however differs from the typical formative discharge (meanannual flood) for natural channels with erodible banks. Finally, we clarify how fluctuations of the hydrodynamic forcing associated with the recorded historical sequence of hydrologic events of variable intensities have acted to maintain the river equilibrium. Key Points The average bed profile may experience a state of morphodynamic equilibrium Unsteady forcing is morphologically equivalent to some effective steady forcing We present a mathematical approach able to determine the equilibrium profile