Theoretical Examination of Historical Shifts and Adjustments to Stage-Discharge Rating Curves

Streamflow-rating curves showing the relation between water-surface stage and the flow discharge have been a widely used tool in hydrology for over a century. Despite their wide-spread application, several problems with stage-discharge ratings have been recognized, resulting in development of many empirical methods to adjust or shift the rating to improve the agreement between ratings and measurements. Among these are methods to account for looped ratings during unsteady flow, stage-slope-discharge ratings to account for variable downstream backwater conditions, and shifts to account for changes to the "control" for the rating. Although these methods have been commonly applied to compute discharge records for streamflow-gauging stations for over half a century, they have achieved only a limited degree of success because of simplifying assumptions on the flow hydrodynamics. Most of these methods are not widely known or understood, other than by those actively applying them to streamflow gauging stations. Furthermore, the underlying physics and scientific justification for these methods has not been examined. Examination of the simplifying assumptions that these methods apply to the momentum and continuity equations clearly illustrates the reasons for the limited success of these methods. In this presentation, methods to shift or adjust stage-discharge ratings are described from the viewpoint of the fundamental hydrodynamics of unsteady nonuniform flow. The simplifying assumptions inherent in these methods are presented and conditions for which the error introduced by these assumptions becomes significant are discussed.