Assessment of uncertainties on stage-discharge rating curves: A large scale application to Québec hydrometric network

Abstract. Rating curves (RC), 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. RC are constructed from gauging measurements and are usually represented by power functions, a mathematical function frequently used to represent stage-discharge relationship of standard hydraulic structures. Uncertainties on 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 on flows have been proposed but are generally too complex for large scale application to hydrometric networks. This paper proposed an approach to develop rating curves and assess the corresponding uncertainties on estimated flow that can be readily applied to large-scale hydrometric networks. This approach takes into consideration possible changes in RC over time due to hydraulic or geomorphologic modifications and assessed if one or two power functions are needed to adequately represent the stage-discharge relationship over the available range of gauged stages. RC at Quebec hydrometric stations have been constructed. Relative differences between flows estimated from the RC and gauged flows are used to assess uncertainties on estimated flow. They were adjusted to normal or logistic distributions with constant (stage-independent uncertainties) or stage-dependent scale parameters (stage-dependent uncertainties). Mean standard deviation on estimated flows for RC with stage-independent uncertainties (75.0 % of the RC) is 6.5 %, while for RC with stage-dependent uncertainties, they increase significantly at low stages reaching values larger than 20 % for some RC at the lowest gauged stage.