Combining flow routing modelling and direct velocity measurement for optimal discharge estimation
Authors: Corato G. , Moramarco T. , Tucciarelli T. 
Published: March 2011

Abstract. A new procedure is proposed for estimating river discharge hydrographs during flood events, using only water level data measured at a gauged site, as well as 1-D shallow water modelling and sporadic maximum surface flow velocity measurements. During flood, the piezometric level is surmised constant in the vertical plane of the river section, where the top of the banks is always above the river level, and is well represented by the recorded stage hydrograph. The river is modelled along the reach directly located downstream the upstream gauged section, where discharge hydrograph is sought after. For the stability with respect to the topographic error, as well as for the simplicity of the data required to satisfy the boundary conditions, a diffusive hydraulic model is adopted for flow routing. Assigned boundary conditions are: (1) the recorded stage hydrograph at the upstream river site and (2) the zero diffusion condition at the downstream end of the reach. The MAST algorithm is used for the numerical solution of the flow routing problem, which is embedded in the Brent algorithm used for the computation of the optimum Manning coefficient. Based on synthetic tests concerning a broad prismatic channel, the optimal reach length is chosen so that the approximated downstream boundary condition effects on discharge hydrograph assessment at upstream end are negligible. The roughness Manning coefficient is calibrated by using sporadic instantaneous surface velocity measurements during the rising limb of flood that are turned into instantaneous discharges through the solid of velocity estimated by a two-dimensional entropic model. Several historical events, occurring in three gauged sites along the upper Tiber River wherein a reliable rating curve is available, have been used for the validation. The analysis outcomes can be so summarized: (1) criteria adopted for selecting the optimal channel length and based on synthetic tests have been proved reliable by using field data of three gauged river sites. Indeed, for each of them a downstream reach, long not more than 500 m, is turned out fair for achieving good performances of the diffusive hydraulic model, thus allowing to drastically reducing the topographical data of river cross-sections; (2) the procedure for Manning's coefficient calibration allowed to get high performance of the hydraulic model just considering the observed water levels and sporadic measurements of maximum surface flow velocity during the rising limb of flood. Indeed, in terms of errors in magnitude on peak discharge, for the optimal calibration, they were found, in average, not exceeding 5% for all events observed in the three investigated gauged sections, while the Nash-Sutcliff efficiency was, in average, greater than 0.95. Therefore, the proposed procedure, apart from to have turned out reliable for the rating curve assessment at ungauged sites, can be applied in realtime for whatever flood conditions and this is of great interest for the practice hydrology seeing that, looking at new monitoring technologies, it will be possible to carry out velocity measurements by hand-held radar sensors in different river sites and for the same flood.