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Quite often the discharge at a site is estimated using the rating curve developed for that site and its development requires river flow measurements, which are costly, tedious and dangerous during severe floods. To circumvent the conventional rating curve development approach, Perumal et al. in 2007 and 2010 applied the Variable Parameter Muskingum Stage-hydrograph (VPMS) routing method for developing stage-discharge relationships especially at those ungauged river sites where stage measurements and details of section geometry are available, but discharge measurements are not made. The VPMS method enables to estimate rating curves at ungauged river sites with acceptable accuracy. But the application of the method is subjected to the limitation of negligible presence of lateral flow within the routing reach. To overcome this limitation, this study proposes an extension of the VPMS method, henceforth, known herein as the VPMS-L in method, for enabling the streamflow assessment even when significant lateral inflow occurs along the river reach considered for routing. The lateral inflow is estimated through the continuity equation expressed in the characteristic form as advocated by Barbetta et al. in 2012. The VPMS-L in , is tested on two rivers characterized by different geometric and hydraulic properties: 1) a 50 km reach of the Tiber River in (central Italy) and 2) a 73 km reach of the Godavari River in the peninsular India. The study demonstrates that both the upstream and downstream discharge hydrographs are well reproduced, with a root mean square error equal on average to about 35 and 1700 m 3 s −1 for the Tiber River and the Godavari River case studies, respectively. Moreover, simulation studies carried out on a river stretch of the Tiber River using the one-dimensional hydraulic model MIKE11 and the VPMS-L in models demonstrate the accuracy of the VMPS-L in model, which besides enabling the estimation of streamflow, also enables the estimation of reach averaged optimal roughness coefficients for the considered routing events. [ABSTRACT FROM AUTHOR]