BaRatin method

To provide operational solutions to the difficult problems of developing, calibrating, reviewing simple and complex rating curves and estimating their uncertainties, the Bayesian BaRatin method (Bayesian Rating curve, Le Coz et al., 2014; Horner et al., 2018) has been developed by INRAE since 2010. The development of methods for quantifying the uncertainties of hydrometric data is one of the team’s research themes, presented here.

The BaRatin method allows the construction of stage-discharge rating curves with uncertainty estimation, combining a priori knowledge on hydraulic controls and the information content of uncertain discharge measurements, a.k.a. gaugings (Le Coz et al., 2014). The equation of the rating curve is derived from the combination of power functions for each of the assumed controls of the site. The user also defines the prior probability distributions of the physical parameters of this stage-discharge equation, “prior” meaning without looking at the gaugings used in the Bayesian estimation. Such a Bayesian estimation is based on the Monte Carlo Markov Chain Method (MCMC) sampling of the posterior distribution of the parameters of the rating curve, inferred from Bayes’ theorem. Physical conflicts between the results and the assumed priors must be verified and may lead to questioning the rating curve model and the estimation of measurement uncertainties.

The BaRatinAGE and BaM! software

BaRatin and its graphic environment BaRatinAGE are open-source and distributed in more than 25 languages (including French and English). The latest version 2.2.1 is available at At the bottom of the page, select the file matching your operating system (Windows or Linux), unzip it in the folder of your choice, and double-click on BaRatinAGE.exe (on Linux: bin/BaRatinAGE).

For any question or comment, please feel free to get in touch with us at Training materials are available here in English, French and Spanish.

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The operational version of BaRatinAGE does not yet deal with time-varying rating curves, but research versions have been developed by Mansanarez (2016) for complex rating curves: stage-gradient-discharge models fortwin-gauge stations subject to variable backwater (Le Coz et al 2016; Mansanarez et al, 2016), stage-gradient-discharge models to treat hysteresis due to transient flows and stage-period-discharge models to treat successive rating shifts due to bed evolution. Ongoing research (PhD by Matteo Darienzo, post-doc by Emeline Perret) focusses on the detection of times and amplitudes of rating shifts, the management of progressive rating shifts due to aquatic vegetation, and real-time application at unstable stations.

These complex rating curve models, as well as the BaRatin simple rating curve model, are already or will be available in the BaM! software (Bayesian Modeling, Renard, 2017). An R interface is under development. In the long term, BaM! and its future working environment will replace the BaRatinAGE software, including the application of the “classic” BaRatin method.

The BaRatinAGE and BaM! software tools have been adopted by the French hydrological services of the Ministry of the Environment (under the national guidance of SCHAPI) and the Compagnie nationale du Rhône (CNR) for the operational management of their rating curves, as well as by the NEON long-term ecological observatories network in the United States (Harrison et al., 2018). They have also been tested by other organizations around the world, such as the USGS in the United States (Mason et al., 2016), and used by other research groups (see list of references hereafter).

Bibliographic references on BaRatin

Darienzo, M., Detection and estimation of stage-discharge rating shifts for retrospective and real-time streamflow quantification, PhD thesis, 2021.

Darienzo, M., Le Coz, J., Renard, B., Lang, M., Detection of stage-discharge rating shifts using gaugings: a recursive segmentation procedure accounting for observational and model uncertainties, Water Resources Research, 57, e2020WR028607, 2021.

Horner I., Renard B., Le Coz J., Branger F., McMillan H.K., Pierrefeu G., Impact of stage measurement errors on streamflow uncertainty, Water Resources Research, 54, 1952-1976, 2018.

Horner, I., Le Coz, J., Renard, B., Branger, F., Lagouy, M., Streamflow uncertainty due to the limited sensitivity of controls at hydrometric stations, Hydrological Processes, 36(2), e14497, 2022.

Le Coz, J., Renard, B., Bonnifait, L., Branger, F., Le Boursicaud, R. Combining hydraulic knowledge and uncertain gaugings in the estimation of hydrometric rating curves: a Bayesian approach, Journal of Hydrology, 509, 573-587, 2014.

Le Coz, J., Renard, B., Bonnifait, L., Branger, F., Le Boursicaud, R. Uncertainty Analysis of Stage-Discharge Relations using the BaRatin Bayesian Framework. 35th IAHR World Congress 08/09/2013-13/09/2013, Chengdu, China, 9 p, 2013.

Le Coz, J., Moukandi N’kaya, G. D., Bricquet, J.-P., Laraque, A., Renard, B., Estimation bayésienne des courbes de tarage et des incertitudes associées : application de la méthode BaRatin au Congo à Brazzaville, Proc. IAHS, 384, 25-29, 2021.

Mansanarez, V. Non unique stage-discharge relations: Bayesian analysis of complex rating curves and their uncertainties, PhD thesis, 2016.

Mansanarez, V., Le Coz, J., Renard, B., Vauchel, P., Pierrefeu, G., Lang, M. Bayesian analysis of stage-fall-discharge rating curves and their uncertainties, Water Resources Research, 52, 7424-7443, 2016.

Mansanarez, V., Renard, B., Le Coz, J. Lang, M., Darienzo, M., Shift happens! Adjusting stage-discharge rating curves to riverbed morphological changes at known times, Water Resources Research, 55, 2876-2899, 2019.

Perret, E., Le Coz, J., Renard, B., A rating curve model accounting for cyclic stage-discharge shifts due to seasonal aquatic vegetation, Water Resources Research, 57, e2020WR027745, 2021.

Bibliographic references using BaRatin

Ahrendt, S., Horner-Devine, A. R., Collins, B. D., Morgan, J. A., Istanbulluoglu, E., Channel conveyance variability can influence flood risk as much as streamflow variability in western Washington State. Water Resources Research, 58, e2021WR031890, 2022.

Francke, T., Foerster, S., Brosinsky, A., Sommerer, E., Lopez-Tarazon, J.A., Güntner, A., Batalla, R.J., Bronstert, A., Water and sediment fluxes in Mediterranean mountainous regions: Comprehensive dataset for hydro-sedimentological analyses and modelling in a mesoscale catchment (River Isábena, NE Spain), Earth System Science Data, 10(2), 1063-1075, 2018.

Garcia, R., Costa, V., Silva, F., Bayesian rating curve modeling: alternative error model to improve low-flow uncertainty estimation, Journal of Hydrological Engineering, 25(5): 04020012, 2020.

Gouy, V., Liger, L., Ahrouch, S., Bonnineau, C., Carluer, N., Chaumot, A., Coquery, M., Dabrin, A., Margoum, C., Pesce, S., Ardières-Morcille in the Beaujolais, France: A research catchment dedicated to study of the transport and impacts of diffuse agricultural pollution in rivers, Hydrological Processes, 35(10), e14384, 2021.

Henn, B., Painter, T.H., Bormann, K.J., McGurk, B., Flint, A.L., Flint, L.E., White, V., Lundquist, J.D., High-Elevation Evapotranspiration Estimates During Drought: Using Streamflow and NASA Airborne Snow Observatory SWE Observations to Close the Upper Tuolumne River Basin Water Balance, Water Resources Research, 54(2), 746-766, 2018.

Kastali, A., Zeroual, A., Remaoun, M., Serrano-Notivoli, R., Moramarco, T. Design Flood and Flood-Prone Areas under Rating Curve Uncertainty: Area of Vieux-Ténès, Algeria, Journal of Hydrologic Engineering, 26(3), 05020054, 2021.

Kastali, A., Zeroual, A., Zeroual, S., Hamitouche, Y., Auto-calibration of HEC-HMS Model for Historic Flood Event under Rating Curve Uncertainty. Case Study: Allala Watershed, Algeria, KSCE Journal of Civil Engineering, 26(1), 482-493, 2022.

Kazimierski, L.D., García, P.E., Ortiz, N., Morale, M., Re, M., Aforos de ríos y arroyos en la Cuenca Matanza-Riachuelo. Elaboración de relaciones altura – caudal (curvas HQ). Informe LHA 05-397-21, Instituto Nacional del Agua (INA) – ACUMAR, Ezeiza, Argentina, 2021.

Kiang, J.E., Gazoorian, C., McMillan, H., Coxon, G., Le Coz, J., Westerberg, I., Belleville, A., Sevrez, D., Sikorska, A.E., Petersen-Øverleir, A., Reitan, T., Freer, J., Renard, B., Mansanarez, V., Mason, R. A comparison of methods for streamflow uncertainty estimation, Water Resources Research, 54(10), 7149-7176, 2018.

Lang, M., Darienzo, M., Le Coz, J., Renard, B., Evaluation des incertitudes et de l’homogénéité de longues séries de débits de crue sur le Rhin à Bâle (1225-2017) et Maxau (1815-2018), LHB-Hydroscience, 2022.

Laraque, A., Le Coz, J., Moukandi N’kaya, G.D., Bissemo, G., Ayissou, L., Rouché, N., Bricquet, J.-P., Gulemvuga, G., Courbes de tarage du fleuve Congo à Brazzaville-Kinshasa, LHB-Hydroscience, 2022.

Lundquist, J.D., Roche, J.W., Forrester, H., Moore, C., Keenan, E., Perry, G., Cristea, N., Henn, B., Lapo, K., McGurk, B., Cayan, D.R., Dettinger, M.D. Yosemite hydroclimate network: distributed stream and atmospheric data for the Tuolumne River watershed and surroundings, Water Resources Research, 52, 7478-7489, 2016.

Maldonado, L.H., Firmo Kazay, D., Romero Lopez, E.E., The estimation of the uncertainty associated with rating curves of the river Ivinhema in the state of Paraná/Brazil, IAHR RiverFlow 2018 conference, E3S Web of Conferences, 40, 06029, 2018.

Mason, R.R. Jr., Kiang, J.E., Cohn, T.A. Rating curve uncertainty: An illustration of two estimation methods, IAHR River Flow conference, St. Louis, Missouri, USA, 12-15 July, 729-734, 2016.

Ocio, D., Le Vine, N., Westerberg, I., Pappenberger, F., Buytaert, W. The role of rating curve uncertainty in real-time flood forecasting, Water Resources Research, 53, 4197-4213, 2017.

Osorio, A.L.N.A., Reis, D.S. A Bayesian approach for the evaluation of rating curve uncertainties in flood frequency analyses, World Environmental and Water Resources Congress, West Palm Beach, Florida, USA, May 22-26, 482-491, 2016.

Osorio, A.L.N.A. Modelo bayesiano completo para análise de frequência de cheias com incorporação do conhecimento hidráulico na modelagem das incertezas na curva-chave [Full Bayesian model for flood frequency analysis with incorporation of hydraulic knowledge in the modeling of uncertainties in the rating curve], Master thesis, Universidade de Brasília, Brazil, 161 p, 2017.

Perret, E., Le Coz, J., Renard, B., Courbes de tarage dynamiques pour la végétation aquatique saisonnière, LHB-Hydroscience, 2022.

Qiu, J., Liu, B., Yang, Z., Peng, W., Uncertainty analysis of estimated discharge based on stage-discharge rating curves [in Chinese], Shuikexue Jinzhan/Advances in Water Science, 31(2), 214-223, 2020.

Qiu, J., Liu, B., Yu, X., Yang, Z., Combining a segmentation procedure and the BaRatin stationary model to estimate nonstationary rating curves and the associated uncertainties, Journal of Hydrology, 597, 126168, 2021.

Sikorska, A.E., Renard, R. Calibrating a hydrological model in stage space to account for rating curve uncertainties: general framework and key challenges, Advances in Water Resources, 105, 51-66, 2017.

Storz, S.M. Stage-discharge relationships for two nested research catchments of the high-mountain observatory in the Simen Mountains National Park in Ethiopia, Master thesis, Bern University, Switzerland, 87 p, 2016.

Vieira, L.M.D.S., Sampaio, J.C.L., Costa, V.A.F., Eleutério, J.C., Assessing the effects of rating curve uncertainty in flood frequency analysis, Revista Brasileira de Recursos Hidricos, 27, e11, 2022.

Zeroual, A., Meddi, M., Assani, A.A. Artificial neural network rainfall-discharge model assessment under rating curve uncertainty and monthly discharge volume predictions, Water Resources Management, 30, 3191-3205, 2016.