On discharge simulation from observed stage hydrographs

The accuracy of three methods for estimating the discharge hydrograph from observed stages was investigated. In particular, besides of the classic approach based on the Jones formulation [1], the influence on stage-discharge relationship of diffusive term, as proposed by Fenton [2], and inertial terms, as derived by Marchi [3], was analyzed. The methods were verified by comparing their results with those of a one-dimensional hydraulic model for a synthetic experiment reported in literature and characterized by substantial unsteady flow effects. The first two approaches were able to simulate adequately the discharge hydrograph when the celerity and diffusivity values were set through the mean flow. However, when peak flow or base-flow was used, they were found slightly accurate; the maximum error was in peak discharge and increased up to 15% and 4% for Fenton and Jones formulation, respectively. Whereas, the Marchi approach not depending from celerity and diffusivity parameters, gave an error on peak discharge equal to –2.7%. In addition, the error in estimating the width of the hysteresis loop of the flood was –6% for the Marchi approach and up to 35% for the other methods. The results show that the Marchi model should be more suitable in representing the stage-discharge relationship especially for real time forecasting applications. Finally, the models were applied to a flood event observed at a gauged section of the Upper Tiber river. As during the flood the unsteady effects were negligible, it was found that all methods were in accordance with the kinematic approximation, whichever discharge value was used for estimating the celerity and diffusivity parameters.