[1] A methodology for estimating discharges and development of rating curves at ungauged river sites is presented. The methodology employs a routing method, which is an extension of the variable parameter Muskingum stage hydrograph (VPMS) routing method developed by M. Perumal and K. G. Ranga Raju, for routing a given upstream stage hydrograph in a channel reach characterized by trapezoidal compound cross section to arrive at the stage hydrograph at the downstream site. Furthermore, the VPMS method also enables us to estimate the discharge hydrographs at the upstream and downstream sites. It is assumed that there is no lateral flow within the routing reach. For establishing the rating curve at the ungauged river site the following concept employed in the development of the VPMS method can be conveniently exploited: During unsteady flow, there exists a one-to-one relationship between the stage estimated at the ungauged site and the corresponding steady discharge, which occurs somewhere downstream of that location, and using the method employed in the VPMS method, one can estimate that steady discharge. By linking this discharge with the stage estimated at the ungauged site the rating curve can be established. This approach of developing the rating curve is verified for a number of hypothetical data sets, obtained using the MIKE 11 model, which is used as the benchmark model in this study. Furthermore, the appropriateness of the proposed extended VPMS routing method is verified using two sets of experimental data on unsteady flows, obtained from a laboratory channel with rectangular compound flow section. The methodology is also field tested using six sets of concurrent stage hydrograph data obtained at the upstream and downstream sites of a 15 km reach length of the Tiber River in central Italy, out of which only one set of data was used for calibrating the reach-averaged Manning's roughness coefficient. The close reproductions of the rating curves and discharge hydrographs recorded at the upstream and downstream sites demonstrate that the proposed methodology can be confidently used for rating curve development and discharge estimation at ungauged sites, thus avoiding the manual discharge measurement at any river site not subjected to backwater effects.Citation: Perumal, M., T. Moramarco, B. Sahoo, and S. Barbetta (2007), A methodology for discharge estimation and rating curve development at ungauged river sites, Water Resour.

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Two variants of the Muskingum flood routing method formulated for accounting nonlinearity of the channel routing process are investigated in this study. These variant methods are: (1) The threeparameter conceptual Nonlinear Muskingum (NLM) method advocated by Gillin 1978, and (2) The Variable Parameter McCarthy-Muskingum (VPMM) method recently proposed by Perumal and Price in 2013. The VPMM method does not require rigorous calibration and validation procedures as required in the case of NLM method due to established relationships of its parameters with flow and channel characteristics based on hydrodynamic principles. The parameters of the conceptual nonlinear storage equation used in the NLM method were calibrated using the Artificial Intelligence Application (AIA) techniques, such as the Genetic Algorithm (GA), the Differential Evolution (DE), the Particle Swarm Optimization (PSO) and the Harmony Search (HS). The calibration was carried out on a given set of hypothetical flood events obtained by routing a given inflow hydrograph in a set of 40 km length prismatic channel reaches using the Saint-Venant (SV) equations. The validation of the calibrated NLM method was investigated using a different set of hypothetical flood hydrographs obtained in the same set of channel reaches used for calibration studies. Both the sets of solutions obtained in the calibration and validation cases using the NLM method were compared with the corresponding solutions of the VPMM method based on some pertinent evaluation measures. The results of the study reveal that the physically based VPMM method is capable of accounting for nonlinear characteristics of flood wave movement better than the conceptually based NLM method which requires the use of tedious calibration and validation procedures.

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