Discharge and bed roughness estimation from water level data analysis

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.