Discharge estimation combining flow routing and occasional measurements of velocity

Abstract. A new procedure is proposed for estimating river discharge hydrographs during flood events, using only water level data at a single gauged site, as well as 1-D shallow water modelling and occasional maximum surface flow velocity measurements. One-dimensional diffusive hydraulic model is used for routing the recorded stage hydrograph in the channel reach considering zero-diffusion downstream boundary condition. Based on synthetic tests concerning a broad prismatic channel, the "suitable" reach length is chosen in order to minimize the effect of the approximated downstream boundary condition on the estimation of the upstream discharge hydrograph. The Manning's roughness coefficient is calibrated by using occasional instantaneous surface velocity measurements during the rising limb of flood that are used to estimate instantaneous discharges by adopting, in the flow area, a two-dimensional velocity distribution model. Several historical events recorded in three gauged sites along the upper Tiber River, wherein reliable rating curves are available, have been used for the validation. The outcomes of the analysis can be summarized as follows: (1) the criterion adopted for selecting the "suitable" channel length based on synthetic test studies has proved to be reliable for field applications to three gauged sites. Indeed, for each event a downstream reach length not more than 500 m is found to be sufficient, for a good performances of the hydraulic model, thereby enabling the drastic reduction of river cross-sections data; (2) the procedure for Manning's roughness coefficient calibration allowed for high performance in discharge estimation just considering the observed water levels and occasional measurements of maximum surface flow velocity during the rising limb of flood. Indeed, errors in the peak discharge magnitude, for the optimal calibration, were found not exceeding 5% for all events observed in the three investigated gauged sections, while the Nash-Sutcliffe efficiency was, on average, greater than 0.95. Therefore, the proposed procedure well lend itself to be applied for: (1) the extrapolation of rating curve over the field of velocity measurements (2) discharge estimations in different cross sections during the same flood event using occasional surface flow velocity measures carried out, for instance, by hand-held radar sensors.