A Comparison of Methods for Streamflow Uncertainty Estimation

International audienceStreamflow time series are commonly derived from stage-discharge rating curves, but the uncertainty of the rating curve and resulting streamflow series are poorly understood. While different methods to quantify uncertainty in the stage-discharge relationship exist, there is limited understanding of how uncertainty estimates differ between methods due to different assumptions and methodological choices. We compared uncertainty estimates and stage-discharge rating curves from seven methods at three river locations of varying hydraulic complexity. Comparison of the estimated uncertainties revealed a wide range of estimates, particularly for high and low flows. At the simplest site on the Isère River (France), full width 95% uncertainties for the different methods ranged from 3 to 17% for median flows. In contrast, uncertainties were much higher and ranged from 41 to 200% for high flows in an extrapolated section of the rating curve at the Mahurangi River (New Zealand) and 28 to 101% for low flows at the Taf River (United Kingdom), where the hydraulic control is unstable at low flows. Differences between methods result from differences in the sources of uncertainty considered, differences in the handling of the time-varying nature of rating curves, differences in the extent of hydraulic knowledge assumed, and differences in assumptions when extrapolating rating curves above or below the observed gaugings. Ultimately, the selection of an uncertainty method requires a match between user requirements and the assumptions made by the uncertainty method. Given the significant differences in uncertainty estimates between methods, we suggest that a clear statement of uncertainty assumptions be presented alongside streamflow uncertainty estimates

Relations hauteur-débit non univoques : analyse bayésienne des courbes de tarage complexes et de leurs incertitudes

Complex rating curves, with stage and additional variables as inputs are necessary to establish streamflow records at sites where the stage-discharge relation is non-unique. Within the same Bayesian framework, hydraulically-based methods are introduced and tested to develop complex rating curves and estimate their uncertainties: stage-gradient-discharge (SGD) models to address hysteresis due to transient flow, stage-fall-discharge (SFD) models to address variable backwater at twin gauge stations, stage-period-discharge (SPD) model to address net rating changes due to bed evolution. Each model was applied to contrasting hydrometric stations and evaluated through sensitivity analyses. For each of the three sources of non-uniqueness in the stage-discharge relation, the proposed Bayesian methods provide not only quantitative uncertainty analysis but also efficient solutions to recurrent problems with the traditional procedures for complex ratings.Les courbes de tarage complexes, qui prennent en entrée la hauteur d'eau et des variables supplémentaires, sont nécessaires pour établir les chroniques de débit des cours d'eau là où la relation hauteur-débit n'est pas univoque. Dans le même cadre bayésien, des méthodes à base hydraulique sont proposées et testées pour construire les courbes de tarage complexes et estimer leurs incertitudes : des modèles hauteur-gradient-débit (SGD) pour résoudre l'hystérésis due aux écoulements transitoires, des modèles hauteur-dénivelée-pente (SFD) pour résoudre le remous variable aux stations à double échelle, le modèle hauteur-période-débit (SPD) pour résoudre les détarages nets dus aux évolutions du lit. Chaque modèle a été appliqué à des stations hydrométriques variées et évalué grâce à des analyses de sensibilité. Pour chacune des trois sources de non-univocité de la relation hauteur-débit, les méthodes bayésiennes proposées fournissent non seulement une analyse d'incertitude quantitative mais aussi des solutions efficaces à des problèmes récurrents que posent les procédures traditionnelles pour les courbes de tarage complexes

Estimating uncertainties in hydraulicallymodelled rating curves for discharge time series assessment

Establishing a reliable stage-discharge (SD) rating curve for calculating discharge at a hydrological gauging station normally takes years of data collection. Estimation of high flows is particularly difficult as they occur rarely and are often difficult to gauge in practice. At a minimum, hydraulicallymodelled rating curves could be derived with as few as two concurrent SD and water-surface slope measurements at different flow conditions. This means that a reliable rating curve can, potentially, be developed much faster via hydraulic modelling than using a traditional rating curve approach based on numerous stage-discharge gaugings. In this study, we use an uncertainty framework based on Bayesian inference and hydraulic modelling for developing SD rating curves and estimating their uncertainties. The framework incorporates information from both the hydraulic configuration (bed slope, roughness, vegetation) using hydraulic modelling and the information available in the SD observation data (gaugings). Discharge time series are estimated by propagating stage records through the posterior rating curve results. Here we apply this novel framework to a Swedish hydrometric station, accounting for uncertainties in the gaugings and the parameters of the hydraulic model. The aim of this study was to assess the impact of using only three gaugings for calibrating the hydraulic model on resultant uncertainty estimations within our framework. The results were compared to prior knowledge, discharge measurements and official discharge estimations and showed the potential of hydraulically-modelled rating curves for assessing uncertainty at high and medium flows, while uncertainty at low flows remained high. Uncertainty results estimated using only three gaugings for the studied site were smaller than ±15% for medium and high flows and reduced the prior uncertainty by a factor of ten on average and were estimated with only 3 gaugings

Estimating uncertainties in hydraulicallymodelled rating curves for discharge time series assessment

Establishing a reliable stage-discharge (SD) rating curve for calculating discharge at a hydrological gauging station normally takes years of data collection. Estimation of high flows is particularly difficult as they occur rarely and are often difficult to gauge in practice. At a minimum, hydraulicallymodelled rating curves could be derived with as few as two concurrent SD and water-surface slope measurements at different flow conditions. This means that a reliable rating curve can, potentially, be developed much faster via hydraulic modelling than using a traditional rating curve approach based on numerous stage-discharge gaugings. In this study, we use an uncertainty framework based on Bayesian inference and hydraulic modelling for developing SD rating curves and estimating their uncertainties. The framework incorporates information from both the hydraulic configuration (bed slope, roughness, vegetation) using hydraulic modelling and the information available in the SD observation data (gaugings). Discharge time series are estimated by propagating stage records through the posterior rating curve results. Here we apply this novel framework to a Swedish hydrometric station, accounting for uncertainties in the gaugings and the parameters of the hydraulic model. The aim of this study was to assess the impact of using only three gaugings for calibrating the hydraulic model on resultant uncertainty estimations within our framework. The results were compared to prior knowledge, discharge measurements and official discharge estimations and showed the potential of hydraulically-modelled rating curves for assessing uncertainty at high and medium flows, while uncertainty at low flows remained high. Uncertainty results estimated using only three gaugings for the studied site were smaller than ±15% for medium and high flows and reduced the prior uncertainty by a factor of ten on average and were estimated with only 3 gaugings

Estimating the long-term evolution of river bed levels using hydrometric data

The stage-discharge measurements and rating curves accumulated over decades at hydrometric stations are a valuable source of information on the long-term evolution of river bed levels. However, the methodology to extract meaningful geomorphic information from such hydrometric data is not straightforward. We introduce an original method to estimate the parameters of successive rating curves by Bayesian analysis in sequence. These parameters reflect the physical properties of the channel features that control the stage-discharge relation: low-flow riffles, main channel, floodway (bars), floodplain, etc. The dates of rating changes are assumed to be known in existing hydrometric records. The uncertainty interval of each parameter is estimated, assuming, however, that no rating change has been ignored by the station manager. It is thus possible to clearly distinguish overall trends of the channel bed level from the local evolution of riffles and to evaluate whether the observed temporal changes are significant compared to the estimation uncertainties

Estimating the long-term evolution of river bed levels using hydrometric data

The stage-discharge measurements and rating curves accumulated over decades at hydrometric stations are a valuable source of information on the long-term evolution of river bed levels. However, the methodology to extract meaningful geomorphic information from such hydrometric data is not straightforward. We introduce an original method to estimate the parameters of successive rating curves by Bayesian analysis in sequence. These parameters reflect the physical properties of the channel features that control the stage-discharge relation: low-flow riffles, main channel, floodway (bars), floodplain, etc. The dates of rating changes are assumed to be known in existing hydrometric records. The uncertainty interval of each parameter is estimated, assuming, however, that no rating change has been ignored by the station manager. It is thus possible to clearly distinguish overall trends of the channel bed level from the local evolution of riffles and to evaluate whether the observed temporal changes are significant compared to the estimation uncertainties

A comparison of methods for streamflow uncertainty estimation

Streamflow time series are commonly derived from stage-discharge rating curves, but theuncertainty of the rating curve and resulting streamflow series are poorly understood. While differentmethods to quantify uncertainty in the stage-discharge relationship exist, there is limited understanding ofhow uncertainty estimates differ between methods due to different assumptions and methodologicalchoices. We compared uncertainty estimates and stage-discharge rating curves from seven methods at threeriver locations of varying hydraulic complexity. Comparison of the estimated uncertainties revealed a widerange of estimates, particularly for high and low flows. At the simplest site on the Isère River (France), fullwidth 95% uncertainties for the different methods ranged from 3 to 17% for median flows. In contrast,uncertainties were much higher and ranged from 41 to 200% for high flows in an extrapolated section of therating curve at the Mahurangi River (New Zealand) and 28 to 101% for low flows at the Taf River (UnitedKingdom), where the hydraulic control is unstable at low flows. Differences between methods result fromdifferences in the sources of uncertainty considered, differences in the handling of the time-varying nature ofrating curves, differences in the extent of hydraulic knowledge assumed, and differences in assumptionswhen extrapolating rating curves above or below the observed gaugings. Ultimately, the selection of anuncertainty method requires a match between user requirements and the assumptions made by theuncertainty method. Given the signi ficant differences in uncertainty estimates between methods, we suggestthat a clear statement of uncertainty assumptions be presented alongside streamflow uncertainty estimates

Hydrological post event survey after the autumn 2014 floods in the Cévennes region in France: results and first hydrological analyses

International audienceDuring the autumn 2014, an exceptional succession of intense rain events and associated flash floods have hit a large territory extending from the Hérault to the Gard and Ardèche regions in south east of France. These events caused 17 casualties and estimated damages ranging from 550 to 600 billion euros (FFSA). On several upstream watersheds, the reported floods seem to be the largest observed from human memory, and may therefore become reference events for flood risk prevention. A post event survey was organised within the Hymex framework in order to document the first 3 events which occurred successively from the 15th of September to the 15th of October. A total of 64 peak discharge values were estimated, enabling a detailed description of observed hydrological reactions. The analysis of this dataset confirms the very significant peak discharge levels, which remain however significantly below the envelope curves and the discharge values observed during some other historical events in this region (for instance the 2002 flood). A detailed hydrological analysis of this dataset based on rainfall runoff simulations is now in progress. It is worth noting that some of the affected areas were already hit by the 2002 and 2008 events, for which post event surveys were already conducted: therefore, a comparison of the hydrological reactions for these three events will be possible. The proposed communication will include the presentation of the characteristics and consequences of the main flood events, the dataset obtained from the post event survey, and the first lessons derived from the hydrological analysis