River discharge or streamflow (the volume of water flowing through a cross-section per unit of time) is one of the most important variables in hydrology. Hydrometric time series are the basic data used in most hydrological studies. They are used to make decisions about the management of water resources and aquatic environments, and to prevent the risks of flooding, erosion and river pollution. Quantifying hydrometric uncertainties is therefore crucial, both to optimise measurement processes and to enable data to be used appropriately.

This open-access article (Le Coz et al., 2024) provides an overview of the tools developed by the Groupe Doppler Hydrométrie for quantifying the uncertainties in hydrometric data.

Streamgauging uncertainty

Quantifying the uncertainty of river discharge measurements comes up against a number of specific difficulties (complex measurement in a natural environment, in a turbulent flow, lack of a precise reference or discharge standard, etc.). While respecting the general framework of metrology (GUM JCGM 2008 and other reference documents), methods adapted to very different streamgauging techniques need to be developed.

In particular, we have developed the following methods for composing uncertainties: Q+ (Le Coz et al. 2012; Le Coz et al. 2015; for current meter gauging, implemented in the Barème and Jacinthe operational software), Flaure (Despax et al., 2016, for current meter gauging) and Oursin (Despax et al., 2023; for moving-boat ADCP gauging, implemented in the QRevInt operational software).

In addition, the uncertainty decomposition approach using interlaboratory experiments has been adapted to the hydrometric context, with single-factor (Le Coz et al., 2016) or multi-factor (Despax et al., 2019) experimental designs. These calculations are implemented in the QRame operational software, for moving-boat ADCP gauging or any other streamgauging technique.

Uncertainty of rating curves and discharge time series

Streamgaugings are used to estimate stage-discharge rating curves (or even more complex models) used to establish discharge time series from quasi-continuous water level records at hydrometric stations. We have developed the BaRatin Bayesian method (Le Coz et al. 2014; Horner et al., 2018; Kiang et al., 2018; implemented in the BaRatinAGE operational software), which combines two sources of uncertain information (prior knowledge of hydraulic controls, and the gaugings) to estimate the rating curve within a probabilistic framework. Alternative models have been developed for complex rating curves (twin-gauges for variable backwater: Mansanarez et al., 2016, rating shifts: Mansanarez et al., 2019, hysteresis: Perret et al., 2022, aquatic vegetation: Perret et al., 2021) and the detection of rating shifts in retrospect and in real time (Darienzo et al., 2021). These methods will gradually be transferred to operational tools.

References

Darienzo, M., Renard, B., Le Coz, J., Lang, M. (2021). Detection of stage-discharge rating shifts using gaugings: A recursive segmentation procedure accounting for observational and model uncertainties. Water Resources Research, 57(4), e2020WR028607.

Despax, A., Perret, C., Garçon, R., Hauet, A., Belleville, A., Le Coz, J., Favre, A.-C. (2016) Considering sampling strategy and cross-section complexity for estimating the uncertainty of discharge measurements using the velocity-area method, Journal of Hydrology, 533, 128–140

Despax, A., Le Coz, J., Hauet, A., Mueller, D. S., Engel, F. L., Blanquart, B., Renard, B., Oberg, K. A. (2019) Decomposition of uncertainty sources in acoustic Doppler current profiler streamflow measurements using repeated measures experiments. Water Resources Research, 55(9), 7520–7540.

Despax, A., Le Coz, J., Mueller, D. S., Hauet, A., Calmel, B., Pierrefeu, G., Naudet, G., Blanquart, B., Pobanz, K. (2023). Validation of an uncertainty propagation method for moving-boat acoustic Doppler current profiler discharge measurements. Water Resources Research, 59(1), e2021WR031878.

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

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. (2018) A comparison of methods for streamflow uncertainty estimation, Water Resources Research, 54(10), 7149–7176.

Le Coz, J., Camenen, B., Peyrard, X., Dramais, G. (2012). Uncertainty in open-channel discharges measured with the velocity-area method, Flow Measurement and Instrumentation, 26, 18-29

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

Le Coz, J., Camenen, B., Peyrard, X., Dramais G. (2015). Erratum – Uncertainty in open-channel discharges measured with the velocity-area method, Flow Measurement and Instrumentation, 46, 193-194.

Le Coz, J., Blanquart, B., Pobanz, K., Dramais, G., Pierrefeu, G., Hauet, A., Despax, A. (2016). Estimating the uncertainty of streamgauging techniques using field interlaboratory experiments, Journal of Hydraulic Engineering, 142(7), 04016011

Le Coz, J., Renard, B., Lang, M., Calmel, B., Mendez Rios, F., Hauet, A., Despax, A., Perret, Bonnifait, L. (2024). Développement d’outils pour la quantification des incertitudes des données hydrométriques, LHB-Hydroscience.

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

Mansanarez, V., Renard, B., Le Coz, J. Lang, M., Darienzo, M. (2019)  Shift happens! Adjusting stage-discharge rating curves to riverbed morphological changes at known times, Water Resources Research, 55(4), 2876–2899.

Perret, E., Renard, B., Le Coz, J. (2021). A rating curve model accounting for cyclic stage-discharge shifts due to seasonal aquatic vegetation. Water Resources Research, 57(3), e2020WR027745.

Perret, E., Lang, M., Le Coz, J. (2022). A framework for detecting stage-discharge hysteresis due to flow unsteadiness: Application to France’s national hydrometry work. Journal of Hydrology, 608, 127567.