One-dimensional hydrodynamic models based on the Saint-Venant equations (the SVN model) are used widely for river stage prediction. Errors that originate from simplifying assumptions, improper specification of initial and boundary conditions, uncertainty in parameters, channel geometry, observed data, and solution methods produce the inconsistencies between actual flow and that represented by the SVN model; this problem is especially apparent in tidal rivers. All of these simplifications and sources of imprecision can accumulate and introduce substantial errors in application. Total errors due to the causes mentioned above are treated as an error function, which is introduced as an additive term in the SVN model momentum equation. The function is constructed using a Fourier series approximation of discrepancies between simulated and observed flow. By combining the SVN model with the error function, a river stage correction approach (the ISV model) is proposed to take account of unconsidered errors in application. The tidal reach of the Qiantang River is selected as the study case and results based on a classification of flood events show that the ISV model generally performs better than the SVN model alone. It indicates that the approach could help guide improvements on the SVN model performance.