Uncertainty in stage–discharge rating curves: application to Australian Hydrologic Reference Stations data

Abstract

The purpose of this paper is to determine uncertainty in the gauged range of the stage-gauged discharge relationship for 622 rating curves from 171 Australian Bureau of Meteorology Hydrologic Reference streamgauging Stations (HRS). Water agencies use many methods to establish rating curves. Here we adopt a consistent method across all stations and develop rating curves based on Chebyshev polynomials, and estimate uncertainties from standard regression errors in which residuals from the polynomials are adjusted to ensure they are homoscedastic and normally distributed. Uncertainty in input water level is also taken into account. The median uncertainties in mean response of the available gauged discharge relationship at median daily discharges for the HRS dataset range from +4.5 to −4.2% (95% confidence band) and for individual gaugings from +29 to −22% incorporating a water level uncertainty of ±4 mm. The uncertainties estimated are consistent with values estimated in Australia and elsewhere. ARTICLE HISTORY

The Case for an Open Water Balance: Re‐envisioning Network Design and Data Analysis for a Complex, Uncertain World

“…Extrapolating rating curves beyond the range of measured low-and high-flow discharge introduces additional uncertainty. For example, 30% of published flow values for reference stations in Australia are based in part on extrapolated rating curves (McMahon & Peel, 2019). Control sections such as weirs or flumes help improve discharge measurements (U.S. Department of the Interior, Bureau of Reclamation, 1997), but these can be difficult to size for watersheds with large variability in discharge (Ogden et al, 2013) and may not be a practical choice in streams where the water cannot easily be routed entirely into the control section.…”

CAMELS-AUS: Hydrometeorological time series and landscape attributes for 222 catchments in Australia

“…KF, CC and SCA analysed and compiled the hydrometeorological timeseries and catchment attribute data. MP analysed earlier work (McMahon and Peel, 2019) to provide the uncertainty estimates included in the dataset. KF wrote the initial draft of the manuscript and all co-authors edited and amended it to provide the final manuscript.…”

Evaluating Catchment Models as Multiple Working Hypotheses: on the Role of Error Metrics, Parameter Sampling, Model Structure, and Data Information Content

“…Model parameters are often the only source of uncertainty that is accounted for, i.e. all sources of modeling uncertainty are implicitly lumped into the parameter uncertainty, although uncertainty sources such as model input (Kavetski et al, 2006;Khazaei & Hosseini, 2015;Moallemi et al, 2018;Papacharalampous et al, 2020a;Papacharalampous et al, 2020b;Vrugt et al, 2008), observed data (McMahon & Peel, 2019;Westerberg et al, 2016), and model structural uncertainty (Clark et al, 2015;Fenicia et al, 2011) can be accounted for more explicitly. Even when only parameter uncertainty is accounted for, flux mapping characterizes how uncertainty propagates from parameter space to flux space and hence the impact on model process-representation and MWH (Khatami et al, 2019).…”

“…We acknowledge that in our sensitivity experiment (section 3.1) we introduced idealized errors, while in real-world cases errors could be more complex in nature. Streamflow data are uncertain (McMahon & Peel, 2019;McMillan et al, 2018; and may encompass different epistemic errors and disinformative periods , with complex interactions with each other and other factors involved in model behavior. That said, here we performed sensitivity analysis under ideal conditions to understand the function of each error metric independent of the quality of the data and the model structure.…”