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

Abstract

Streamflow-rating curves showing relation between water-surface stage and 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 rating to improve 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 control for 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 flow hydrodynamics. Most of these methods are not widely known or understood, other than by those actively applying them to streamflow gauging stations. Furthermore, underlying physics and scientific justification for these methods has not been examined. Examination of simplifying assumptions that these methods apply to momentum and continuity equations clearly illustrates reasons for limited success of these methods. In this presentation, methods to shift or adjust stage-discharge ratings are described from viewpoint of fundamental hydrodynamics of unsteady nonuniform flow. The simplifying assumptions inherent in these methods are presented and conditions for which error introduced by these assumptions becomes significant are discussed. Introduction: Accurate data describing rate of flow of water (discharge) are used for many purposes, including operational decision making, input for hydraulic and hydrologic models, records for litigation about water rights or damages, calculation of loads and transport of sediment and other water-quality constituents, and for design of water-control and conveyance structures. Because of dynamic nature of hydrologic systems, information typically needed for most hydrologic analyses is a time-series record of discharges. However, direct measurement of discharge in open channels is time consuming and costly. Therefore, most discharge records for streamflow-gauging stations are developed using a calibrated stage-discharge rating to estimate discharge from measured water stages, which permits a fast and relatively inexpensive means to determine discharge (Rantz et al., 1982). Rating curves are established by concurrent measurements of stage, y and discharge, Q and results are fitted graphically or statistically to yield rating curves. The stage-discharge rating has been described as the most important part of a velocity-area current-meter station (Herschy, 1999).