Bayesian analysis of stage–fall–discharge models for gauging stations affected by variable backwater

Petersen‐Øverleir, Asgeir; Reitan, Trond

doi:10.1002/hyp.7417

Cited by 26 publications

(48 citation statements)

References 32 publications

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“…Venetis () was among the first to recommend that rating curve uncertainties should be treated within a statistical framework. The classical statistical approach has been rigorously updated by Moyeed and Clarke (), Petersen‐Øverleir and Reitan () and Reitan and Petersen‐Øverleir (; ; ) using a variety of techniques including multi‐segment fitting and Bayesian estimation. Fuzzy methods have been favoured by other authors using, for example, ‘limits of acceptability’ approaches (Liu et al ., ), envelope curves (Pappenberger et al ., ; Krueger et al ., 2010a) and fuzzy set theory (Shrestha et al ., ; Shrestha and Simonovic, ; ).…”

Section: River Discharge Uncertaintymentioning

confidence: 98%

Benchmarking observational uncertainties for hydrology: rainfall, river discharge and water quality

McMillan

Krueger

Freer

2012

Hydrological Processes

405

366

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This review and commentary sets out the need for authoritative and concise information on the expected error distributions and magnitudes in observational data. We discuss the necessary components of a benchmark of dominant data uncertainties and the recent developments in hydrology which increase the need for such guidance. We initiate the creation of a catalogue of accessible information on characteristics of data uncertainty for the key hydrological variables of rainfall, river discharge and water quality (suspended solids, phosphorus and nitrogen). This includes demonstration of how uncertainties can be quantified, summarizing current knowledge and the standard quantitative results available. In particular, synthesis of results from multiple studies allows conclusions to be drawn on factors which control the magnitude of data uncertainty and hence improves provision of prior guidance on those uncertainties. Rainfall uncertainties were found to be driven by spatial scale, whereas river discharge uncertainty was dominated by flow condition and gauging method. Water quality variables presented a more complex picture with many component errors. For all variables, it was easy to find examples where relative error magnitudes exceeded 40%. We consider how data uncertainties impact on the interpretation of catchment dynamics, model regionalization and model evaluation. In closing the review, we make recommendations for future research priorities in quantifying data uncertainty and highlight the need for an improved ‘culture of engagement’ with observational uncertainties. Copyright © 2012 John Wiley & Sons, Ltd.

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Section: River Discharge Uncertaintymentioning

confidence: 98%

Benchmarking observational uncertainties for hydrology: rainfall, river discharge and water quality

McMillan

Krueger

Freer

2012

Hydrological Processes

405

366

View full text Add to dashboard Cite

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“…To bring new solutions to this problem, this work builds on the avenue opened by Petersen‐Øverleir and Reitan []. The Bayesian approach they introduced appears to be a promising way to analyze stage‐fall‐discharge relations and the related uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Bayesian analysis of stage‐fall‐discharge rating curves and their uncertainties

Mansanarez¹,

Coz²,

Renard³

et al. 2016

Water Resources Research

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Stage‐fall‐discharge (SFD) rating curves are traditionally used to compute streamflow records at sites where the energy slope of the flow is variable due to variable backwater effects. We introduce a model with hydraulically interpretable parameters for estimating SFD rating curves and their uncertainties. Conventional power functions for channel and section controls are used. The transition to a backwater‐affected channel control is computed based on a continuity condition, solved either analytically or numerically. The practical use of the method is demonstrated with two real twin‐gauge stations, the Rhône River at Valence, France, and the Guthusbekken stream at station 0003⋅0033, Norway. Those stations are typical of a channel control and a section control, respectively, when backwater‐unaffected conditions apply. The performance of the method is investigated through sensitivity analysis to prior information on controls and to observations (i.e., available gaugings) for the station of Valence. These analyses suggest that precisely identifying SFD rating curves requires adapted gauging strategy and/or informative priors. The Madeira River, one of the largest tributaries of the Amazon, provides a challenging case typical of large, flat, tropical river networks where bed roughness can also be variable in addition to slope. In this case, the difference in staff gauge reference levels must be estimated as another uncertain parameter of the SFD model. The proposed Bayesian method is a valuable alternative solution to the graphical and empirical techniques still proposed in hydrometry guidance and standards.

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“…Traditional statistical approaches [e.g., Venetis , ; Clarke , ; Clarke et al ., ; Petersen‐Øverleir and Reitan , ] base their discharge uncertainty bounds on the residual variance from a regression function or the variance of the parameter estimates for the rating curves, but do not explicitly incorporate measurement uncertainty in the gauging data. Bayesian approaches [e.g., Moyeed and Clarke , ; Petersen‐Øverleir and Reitan , ; Reitan and Petersen‐Øverleir , ; Le Coz et al , 2014; Juston et al ., ] offer the advantage of incorporating hydraulic knowledge of the gauging station to set informative priors on the rating‐curve parameters and deriving a likelihood function that accounts for uncertainty in the individual stage‐discharge measurements [e.g., Le Coz et al ., ]. Alternative approaches [e.g., Krueger et al ., ; Guerrero et al ., ; Jalbert et al ., ; Westerberg et al ., ; McMillan et al ., ] have tended to concentrate on non‐stationary rating curves where the typical assumptions made in statistical approaches may result in biased uncertainty estimates.…”

Section: Introductionmentioning

confidence: 99%

A novel framework for discharge uncertainty quantification applied to 500 UK gauging stations

Coxon

Freer

Westerberg

et al. 2015

Water Resources Research

192

189

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Benchmarking the quality of river discharge data and understanding its information content for hydrological analyses is an important task for hydrologic science. There is a wide variety of techniques to assess discharge uncertainty. However, few studies have developed generalized approaches to quantify discharge uncertainty. This study presents a generalized framework for estimating discharge uncertainty at many gauging stations with different errors in the stage-discharge relationship. The methodology utilizes a nonparametric LOWESS regression within a novel framework that accounts for uncertainty in the stagedischarge measurements, scatter in the stage-discharge data and multisection rating curves. The framework was applied to 500 gauging stations in England and Wales and we evaluated the magnitude of discharge uncertainty at low, mean and high flow points on the rating curve. The framework was shown to be robust, versatile and able to capture place-specific uncertainties for a number of different examples. Our study revealed a wide range of discharge uncertainties (10-397% discharge uncertainty interval widths), but the majority of the gauging stations (over 80%) had mean and high flow uncertainty intervals of less than 40%. We identified some regional differences in the stage-discharge relationships, however the results show that local conditions dominated in determining the magnitude of discharge uncertainty at a gauging station. This highlights the importance of estimating discharge uncertainty for each gauging station prior to using those data in hydrological analyses.

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Bayesian analysis of stage–fall–discharge models for gauging stations affected by variable backwater

Cited by 26 publications

References 32 publications

Benchmarking observational uncertainties for hydrology: rainfall, river discharge and water quality

Benchmarking observational uncertainties for hydrology: rainfall, river discharge and water quality

Bayesian analysis of stage‐fall‐discharge rating curves and their uncertainties

A novel framework for discharge uncertainty quantification applied to 500 UK gauging stations

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