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The indirect measurement technique for discharge estimation, based on water level data analysis in two different river sections, is extended to the case of existing significant tributary flow between the two sections. The methodology is based on the calibration of a numerical flow routing algorithm, solving the Saint-Venant equations in diffusive form along the main channel between the two measurement sections. The first calibration parameter is the average Manning's roughness coefficient holding in the main channel, the other ones are relative to the rating curve of each tributary channel, estimated per unit roughness coefficient and per unit slope immediately before the junction of the tributary with the main channel. The new methodology is tested against different flood events observed along one gauged river reach: the Alzette river basin, in Luxembourg. The applied MAST hydraulic model solves the diffusive wave equations using the observed stage hydrograph at the upstream section as boundary condition. The observed stage hydrograph at the downstream section is used as benchmark function for the computation of the objective function to be minimized trough calibration. Field tests include comparison of the numerical results with historical discharge and water depth data available in the Alzette river.

Water level data measured at the two ends of a reach are used to compute both the average n Manning roughness coefficient and the discharge hydrograph in the upstream section of the reach. The methodology is first introduced for the simple case of homogenous roughness and large slope, when the kinematic assumption holds for the momentum equation. In the more general case, when subcritical flow can occur along the channel, an approximation of the downstream boundary condition is required to make always identifiable the calibration problem. In this case, the calibration problem is solved by 1) associating to each possible n value the solution of a flow routing problem, with assigned upstream water level conditions, 2) selecting among all the feasible n values the optimal roughness coefficient that provides the best match between the computed and the measured water depths hydrograph in the downstream section, according to a selected functional error. The DORA diffusive model is adopted for the solution of the flow routing problem and the Brent algorithm is applied for the search of the minimum of the functional error. The choice and the computation of the initial conditions along the reach, for each possible n value, are discussed. An application to a set of data already available in literature and collected at two gauged sections in the Tiber river (Italy), follows.