A methodology for discharge estimation and rating curve development at ungauged river sites

Abstract

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.