Theoretical Development of Stage-Discharge Ratings for Subcritical Open-Channel Flows

Ratings relating stage and flow discharge have been traditionally established through measurements of discharge and concurrent stage. Inherent in this approach are several difficulties and shortcomings that have resulted in widely recognized problems in developing and applying ratings, such as looped ratings. Purely empirical methods that attempt to improve the agreement between ratings and measurements have met with limited success. This paper suggests a theoretical basis for discharge ratings that reflects the hydraulics of unsteady, nonuniform, subcritical flow. Simplification of the Saint-Venant equations for rating applications results in an approximation of the dynamics of flow that is summarized in the hydraulic performance graph, from which discharge ratings can be developed and updated theoretically. The resulting ratings apply a quasi-steady approximation of the flow, along with semiempirical correction factors developed for the site to estimate the discharge using the same information that is needed for “stage-fall-discharge ratings,” while addressing some of the shortcomings of this type of rating. Comparison of ratings developed using the resulting procedure against laboratory and field observations yields encouraging results.