A Note on the Estimation of the Parameters in Logarithmic Stage-Discharge Relationships With Estimates of Their Error

Venetis, Christos

doi:10.1080/02626667009493957

Cited by 30 publications

(36 citation statements)

References 2 publications

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“…Extrapolation of the rating curve is usually based on hydraulic considerations: the equation Q ¼ a(H -H 0 ) b is indeed the usual form of a multi-segmented rating curve (Lambie, 1978;ISO, 1998). Venetis (1970) derived a statistical framework to estimate discharge uncertainties associated with such a power Q(H) relationship.…”

Section: Existing Methods For Extrapolating a Stage-discharge Relatiomentioning

confidence: 99%

Extrapolation of rating curves by hydraulic modelling, with application to flood frequency analysis

Lang¹,

Pobanz

Renard³

et al. 2010

Hydrological Sciences Journal

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Extrapolation of rating curves by hydraulic modelling, with application to flood frequency analysis. Hydrol. Sci. J. 55 (6), 883-898. Abstract This paper illustrates the importance of taking into account the potential errors in discharge estimation in the assessment of extreme floods. First, a summary of the main difficulties encountered in extrapolating rating curves for flood discharge is provided. Then a sensitivity analysis is carried out using a hydraulic modelling approach, applied to eight Mediterranean catchments, and yielding an envelope curve for the stage-discharge relationship, Q(H). To assess the influence of errors in the flood discharge on the uncertainty in estimating extreme floods, a Bayesian framework including a multiplicative error on the rating curve was applied. Its application on two catchments for which historical data are available for the period shows that ignoring the rating curve errors may lead to an unduly optimistic reduction in the final uncertainty in estimation of flood discharge quantiles. Moreover, the quantile values are also affected by taking into account the rating curve errors.Exptrapolation des courves de tarage par modélisation hydraulique, avec application à l'analyse fréquentielle des crues Résumé Cet article illustre l'importance de prendre en considération les erreurs possibles sur l'estimation des débits pour l'estimation des crues extrêmes. Après un rappel des principales difficultés liées à l'extrapolation des courbes de tarage, une analyse de sensibilité par une approche hydraulique fournit une courbe enveloppe pour la conversion des hauteurs de crue en débit, pour huit bassins méditerranéens. Un modèle Bayésien intégrant une erreur multiplicative sur les courbes de tarage permet d'apprécier l'influence des erreurs sur les débits de crue sur l'incertitude d'estimation des crues extrêmes. L'application sur deux bassins versants pour lesquels une information historique est disponible sur la période (1741-2004) montre qu'ignorer les erreurs de courbe de tarage conduit à réduire de façon indûment optimiste l'incertitude finale sur l'estimation des quantiles de crues. De plus, les valeurs des quantiles elles-même sont également affectées par la prise en compte des erreurs de courbe de tarage.

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Section: Existing Methods For Extrapolating a Stage-discharge Relatiomentioning

confidence: 99%

Extrapolation of rating curves by hydraulic modelling, with application to flood frequency analysis

Lang¹,

Pobanz

Renard³

et al. 2010

Hydrological Sciences Journal

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“…Several previous studies have investigated methods of including uncertainties in the stage-discharge relationship, from the first to suggest a statistical framework for those uncertainties (Venetis, 1970) to many modern studies (Petersen-Øverleir, 2004;Moyeed and1271 Clark, 2005;Pappenberger et al, 2006;Reitan and Petersen-Øverleir, 2006;2009;Di Baldassarre and Montanari, 2009;Krueger et al, 2009;Liu et al, 2009). These all rely on fitting a single set of gaugings (i.e.…”

Section: Introductionmentioning

confidence: 99%

Impacts of uncertain river flow data on rainfall‐runoff model calibration and discharge predictions

McMillan

Freer

Pappenberger

et al. 2010

Hydrological Processes

235

217

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10.1002/hyp.7587.abs In order to quantify total error affecting hydrological models and predictions, we must explicitly recognize errors in input data, model structure, model parameters and validation data. This paper tackles the last of these: errors in discharge measurements used to calibrate a rainfall-runoff model, caused by stage–discharge rating-curve uncertainty. This uncertainty may be due to several combined sources, including errors in stage and velocity measurements during individual gaugings, assumptions regarding a particular form of stage–discharge relationship, extrapolation of the stage–discharge relationship beyond the maximum gauging, and cross-section change due to vegetation growth and/or bed movement. A methodology is presented to systematically assess and quantify the uncertainty in discharge measurements due to all of these sources. For a given stage measurement, a complete PDF of true discharge is estimated. Consequently, new model calibration techniques can be introduced to explicitly account for the discharge error distribution. The method is demonstrated for a gravel-bed river in New Zealand, where all the above uncertainty sources can be identified, including significant uncertainty in cross-section form due to scour and re-deposition of sediment. Results show that rigorous consideration of uncertainty in flow data results in significant improvement of the model's ability to predict the observed flow. Copyright © 2010 John Wiley & Sons, Ltd

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“…3 has m -1 segment limits, it is necessary to set h s,0 : h 0,1 and h s,m : ?. This formula is an expanded version of the one-segment rating curve regression equation first formulated by Venetis (1970), who analysed it using a likelihood-based method. This approach was further studied by Reitan and PetersenØverleir (2006), in a paper that illustrated potential difficulties with the likelihood method.…”

Section: Introductionmentioning

confidence: 99%

Bayesian methods for estimating multi-segment discharge rating curves

Reitan

Petersen‐Øverleir

2008

Stoch Environ Res Risk Assess

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This study explores Bayesian methods for handling compound stage-discharge relationships, a problem which arises in many natural rivers. It is assumed:(1) the stage-discharge relationship in each rating curve segment is a power-law with a location parameter, or zeroplane displacement; (2) the segment transitions are abrupt and continuous; and (3) multiplicative measurement errors are of equal variance. The rating curve fitting procedure is then formulated as a piecewise regression problem where the number of segments and the associated changepoints are assumed unknown. Procedures are developed for describing both global and site-specific prior distributions for all rating curve parameters, including the changepoints. Estimation and uncertainty analysis is evaluated using Markov chain Monte Carlo simulation (MCMC) techniques. The first model explored accounts for parameter and model uncertainties in the interpolated area, i.e. within the range of available stage-discharge measurements. A second model is constructed in an attempt to include the uncertainty in extrapolation, which is necessary when the rating curve is used to estimate discharges beyond the highest or lowest measurement. This is done by assuming that the rate of changepoints both inside and outside the measured area follows a Poisson process. The theory is applied to actual data from Norwegian gauging stations. The MCMC solutions give results that appear sensible and useful for inferential purposes, though the latter model needs further efforts in order to obtain a more efficient simulation scheme.

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A Note on the Estimation of the Parameters in Logarithmic Stage-Discharge Relationships With Estimates of Their Error

Cited by 30 publications

References 2 publications

Extrapolation of rating curves by hydraulic modelling, with application to flood frequency analysis

Extrapolation of rating curves by hydraulic modelling, with application to flood frequency analysis

Impacts of uncertain river flow data on rainfall‐runoff model calibration and discharge predictions

Bayesian methods for estimating multi-segment discharge rating curves

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