Assessment of uncertainties in stage–discharge rating curves: a large-scale application to Quebec hydrometric network

Abstract. Rating curves (RCs), which establish a relationship between stage and discharge at a given cross-section of a river, are largely used by national agencies to measure flow. RCs are constructed from gauging measurements and are usually represented by power functions (also called “power laws”), mathematical functions frequently used to represent stage–discharge relationships of standard hydraulic structures. Uncertainties in estimated flows based on rating curves can be significant, especially for high- and low-flow regimes. It is therefore important to report these uncertainties as accurately as possible. Many approaches estimating the sources of uncertainties in flows have been proposed but are generally too complex for large-scale application to hydrometric networks. This paper proposes an approach to develop rating curves and to assess the corresponding uncertainties in estimated flow that can be readily applied to large-scale hydrometric networks. This approach takes into consideration possible changes in RCs over time due to hydraulic or geomorphologic modifications and assesses whether one or two power functions are needed to adequately represent the stage–discharge relationship over the available range of gauged stages. RCs at Quebec hydrometric stations have been constructed. Relative differences between flows estimated from the RCs and gauged flows are used to assess uncertainties in estimated flow. They were adjusted to normal or logistic distributions with constant (stage-independent uncertainties) or stage-dependent scale parameters (stage-dependent uncertainties). The mean standard deviation of estimated flows for RCs with stage-independent uncertainties (75.0 % of the RCs) is 6.5 %, while, for RCs with stage-dependent uncertainties, they increase significantly at low stages, reaching values larger than 20 % for some RCs at the lowest-gauged stage.