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 Irstea 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 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 (Lundquist et al., 2016; Osorio and Reis, 2016; Storz, 2016; Zeroual et al. 2016).
The BaRatinAGE software
BaRatin and its BaRatinAGE graphical environment are available in French and English with a free individual license. To obtain the software and subscribe to the user mailing list, simply write to: firstname.lastname@example.org.
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.
References on BaRatin
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.
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.
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, submitted.
References using BaRatin
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.
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.
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, 2018 (in press).
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.
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.
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.
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.