Streamflow rating uncertainty: Characterisation and impacts on model calibration and performance Jorge L. Pe ~ na-Arancibia a, * , Yongqiang Zhang a , Daniel E. Pagendam b , Neil R. Viney a , Julien Lerat d , Albert I.J.M. van Dijk e, a , Jai Vaze a , Andrew J. Frost c a Land and Water Flagship, CSIRO, Black Mountain, GPO 1666, Canberra, ACT 2601, Australia b Digital Productivity and Services Flagship, CSIRO, EcoSciences Precinct, PO Box 2583, Brisbane, QLD, Australia c Bureau of Meteorology, PO Box 413, Darlinghurst, NSW 1300, Australia d Bureau of Meteorology, GPO Box 2334, Canberra, ACT 2601, Australia e Fenner School of Environment & Society, Australian National University, Canberra, ACT 0200, Australia article info Article history: Received 23 June 2014 Received in revised form 2 September 2014 Accepted 9 September 2014 Available online Keywords: Modelling Calibration Ensemble Stage-discharge Rating curve Nadaraya-Watson Heteroscedasticity Uncertainty abstract 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 (hetero- scedasticity) 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 un- certainty bounds. These were later used in calibration/evaluation using a standard Nash-Sutcliffe Effi- ciency (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. Crown Copyright © 2014 Published by Elsevier Ltd. All rights reserved. 1. Introduction Streamflow data are generally estimated from stage measure- ments through a stageedischarge relationship (the ‘rating curve’), developed through measurement of flow using manual methods (estimation of flow velocity combined with estimates of river width and height for subsections of the river) and relating that to measured flow height at various points in time; then interpolation/ extrapolation of that relationship across all height-flow levels using regression techniques to produce a curve. Several sources of un- certainty can be accounted for in this procedure including mea- surements of flow height, width and shape of the river cross- section and inaccuracies in the measurement of the velocityearea relationship (Domeneghetti et al., 2012). Another source of uncer- tainty arises from the regression techniques used to derive the stageedischarge relationship. The classical approach for deriving * Corresponding author. CSIRO Land and Water, GPO Box 1666, Canberra ACT 2601, Australia. Tel.: þ61 (2)6246 5711; fax: þ61 (2)6246 5800. E-mail address: jorge.penaarancibia@csiro.au (J.L. Pe~ na-Arancibia). Contents lists available at ScienceDirect Environmental Modelling & Software journal homepage: www.elsevier.com/locate/envsoft http://dx.doi.org/10.1016/j.envsoft.2014.09.011 1364-8152/Crown Copyright © 2014 Published by Elsevier Ltd. All rights reserved. Environmental Modelling & Software 63 (2015) 32e44