The contribution of hydraulic modelling to estimated flows in the extrapolated portions of rating curves and evaluation of the uncertainties

Context

The Direction de l’hydrométrie et des prévisions hydrologiques (hydrometry and hydrological forecasting division) of the Ministère de l’Environnement et de la Lutte contre les Changements Climatiques, de la Faune et des Parcs (MELCCFP) is responsible for the operation of hydrometric stations in Quebec. Flows at these stations are estimated using rating curves that connect the water level to the flow of a watercourse. Water levels are then measured and transposed into flows using these curves. The uncertainties associated with the estimated flows are unknown. However, this is important information for the users of the data.

Objective(s)

To quantify uncertainties in estimated flow rates in the extrapolated portions of rating curves
To evaluate the potential contribution of hydraulic modelling to the development of rating curves and the estimation of uncertainties
To propose simplified versions of uncertainty models
To evaluate the effects of seasonality and non-permanent flow conditions on rating curves

Methodology

Adjust the gauging of 173 hydrometric stations operated by the MELCCFP to fit the commonly used equation for the relationship between level and flow at hydraulic structures.
Fit the rating curves, estimate relative deviations from the rating curves, and estimate volumetric flows and fit them to various models.
Examine possible effects of hysteresis (an effect that appears under conditions of transient flow where, for a given level, the flow at high water levels is different from the flow when water levels descend) and seasonality on the rating curves.
Perform an analysis on the uncertainties in extrapolating the rating curves (i.e. for levels above the largest gauged level or below the lowest gauged level) by resampling and by using the hydraulic modelling carried out as part of the INFO-Crue project.
Compare the rating curves obtained from hydraulic modelling with those estimated from gauging. This will make it possible to determine whether hydraulic modelling can provide useful information for the development of rating curves.
Compare the rating curves of the Bayesian rating curve framework (BaRatin method) to the gauging-based rating curves to see when it is advantageous to use this method.

Results

The main results and conclusions of the project are as follows:

Rating curves with their uncertainties were produced for all of the hydrometric stations operated by the Direction de l’hydrométrie et des prévisions hydrologiques.
Problematic rating curves and gauging were identified and will need to be examined in detail.
The standard deviations of the uncertainties for the estimated flows in the interpolated portions were found to be in the order of ±5% to ±10% for most of the rating curves.
Uncertainties in the extrapolated portions (beyond the largest and smallest gauged levels) of the rating curves increase rapidly with the amount of extrapolation. Biases were also observed in the extrapolation of the rating curves.
Certain hydrometric stations and rating curves that are potentially affected by seasonality effects were identified. A more detailed characterization of these sites (type of control and presence of vegetation) will make it possible to identify those that could be subject to a seasonality effect.
No hysteresis effect was detected in the rating curves. Data on the slopes of the sections where the hydrometric stations are located would be required to complete the analysis. It can be assumed that the effects of hysteresis are negligible.
It was difficult to decide on the confidence level to be given to the rating curves estimated from the hydraulic modelling, so no general conclusions could be drawn on the contribution of hydraulic modelling to the development of the rating curves. A case-by-case review is required.
The BaRatin approach adds important hydraulic information, improving the reliability of the rating curves in several cases, particularly in the portions extrapolated from the gauging, for example during the transition to a floodplain. A large-scale application could be quite useful. However, it would require a detailed analysis of each site.
The simplest uncertainty model assumes an average standard deviation in the order of 8.5% to 10% for the flows estimated from the rating curves.

Benefits for adaptation

The project made it possible to better document and evaluate the uncertainties in the estimated flows at the hydrometric stations studied, which could help the MELCCFP’s Direction de l’hydrométrie et des prévisions hydrologiques in its future work.

This project also provided a better understanding of the uncertainties related to the flows estimated by extrapolating the rating curves, as well as the impact of seasonality and hysteresis and the hydrometric stations that are most likely to be affected.