Estimating uncertainties in hydraulicallymodelled rating curves for discharge time series assessment

Abstract

Establishing a reliable stage-discharge (SD) rating curve for calculating discharge at a hydrological gauging station normally takes years of data collection. Estimation of high flows is particularly difficult as they occur rarely and are often difficult to gauge in practice. At a minimum, hydraulicallymodelled rating curves could be derived with as few as two concurrent SD and water-surface slope measurements at different flow conditions. This means that a reliable rating curve can, potentially, be developed much faster via hydraulic modelling than using a traditional rating curve approach based on numerous stage-discharge gaugings. In this study, we use an uncertainty framework based on Bayesian inference and hydraulic modelling for developing SD rating curves and estimating their uncertainties. The framework incorporates information from both the hydraulic configuration (bed slope, roughness, vegetation) using hydraulic modelling and the information available in the SD observation data (gaugings). Discharge time series are estimated by propagating stage records through the posterior rating curve results. Here we apply this novel framework to a Swedish hydrometric station, accounting for uncertainties in the gaugings and the parameters of the hydraulic model. The aim of this study was to assess the impact of using only three gaugings for calibrating the hydraulic model on resultant uncertainty estimations within our framework. The results were compared to prior knowledge, discharge measurements and official discharge estimations and showed the potential of hydraulically-modelled rating curves for assessing uncertainty at high and medium flows, while uncertainty at low flows remained high. Uncertainty results estimated using only three gaugings for the studied site were smaller than ±15% for medium and high flows and reduced the prior uncertainty by a factor of ten on average and were estimated with only 3 gaugings.