A robust stage-discharge rating curve model based on critical flow from a reservoir

Hydrometric gauging stations are often sited in reservoirs such as lakes and river pools since they possess favourable features for streamflow determination. By applying the equations which govern critical flow from a reservoir along with a spline representation of the known geometric characteristics of the reservoir outlet, a new method is developed for estimating the stage-discharge relationship in reservoir-like situations. The proposed rating curve model is amenable to least squares estimation using the available stage-discharge measurements. The proposed model is shown by theory to be general, and includes both normal uniform flow from a reservoir and the classical power-law rating curve model as special cases. Using geometric data and stage-discharge measurements from two Norwegian gauging stations, it is demonstrated that (a) the proposed model is more appropriate than the classical power-law rating curve model when performance is measured by the AIC statistic and the sizes of the jackknife standard deviations of the predicted discharges, and (b) the proposed model displays a superior performance over the power-law model in both upwards and downwards extrapolation.