Streamflow rating uncertainty: Characterisation and impacts on model calibration and performance

Common streamflow gauging procedures require assumptions about the stage-discharge relationship (the 'rating curve') that can introduce considerable uncertainties in streamflow records. These rating uncertainties are not usually considered fully in hydrological model calibration and evaluation yet can have potentially important impacts. We analysed streamflow gauge data and conducted two modelling experiments to assess rating uncertainty in operational rating curves, its impacts on modelling and possible ways to reduce those impacts. We found clear evidence of variance heterogeneity (heteroscedasticity) in streamflow estimates, with higher residual values at higher stage values. In addition, we confirmed the occurrence of streamflow extrapolation beyond the highest or lowest stage measurement in many operational rating curves, even when these were previously flagged as not extrapolated. The first experiment investigated the impact on regional calibration/evaluation of: (i) using two streamflow data transformations (logarithmic and square-root), compared to using non-transformed streamflow data, in an attempt to reduce heteroscedasticity and; (ii) censoring the extrapolated flows, compared to no censoring. Results of calibration/evaluation showed that using a square-root transformed streamflow (thus, compromising weight on high and low streamflow) performed better than using non-transformed and log-transformed streamflow. Also, surprisingly, censoring extrapolated streamflow reduced rather than improved model performance. The second experiment investigated the impact of rating curve uncertainty on catchment calibration/evaluation and parameter estimation. A Monte-Carlo approach and the nonparametric Weighted Nadaraya-Watson (WNW) estimator were used to derive streamflow uncertainty bounds. These were later used in calibration/evaluation using a standard Nash-Sutcliffe Efficiency (NSE) objective function (OBJ) and a modified NSE OBJ that penalised uncertain flows. Using square-root transformed flows and the modified NSE OBJ considerably improved calibration and predictions, particularly for mid and low flows, and there was an overall reduction in parameter uncertainty.