ratingcurves

A rating curve is a relation used in hydrology and hydraulic engineering to describe the connection between the water surface stage at a river or stream cross-section and the discharge flowing through that cross-section. It is typically expressed as Q = f(H), where Q is discharge and H is water level or stage. Rating curves enable the conversion of a continuous water level record into a continuous discharge record, provided the curve is valid for the observed conditions.

Development of a rating curve involves collecting paired observations of stage and discharge at the same cross-section over a range of flow conditions. Stage is measured with staff gauges or pressure transducers, while discharge is determined using velocity-area methods, current meters, or acoustic Doppler techniques. The paired data are plotted and a curve or piecewise function is fit, often with separate segments for low, normal, and high flows. Rating curves can be empirical, based on observed data, or semi-empirical, with physics-informed forms. In practice, curves may be updated periodically to reflect changes in channel geometry or measurement accuracy.

Applications of rating curves include estimating daily or continuous discharge from stage records, flood forecasting and hydrograph routing, water resources management, and calibration of hydrological models. They also underpin storage accounting for reservoirs and environmental flow assessments. Interpretation requires awareness of nonstationarity and changing hydraulic conditions.

Limitations include sensitivity to channel modifications, sedimentation, ice, debris, and backwater effects from downstream or upstream structures. Because curves are valid only for the conditions under which they were developed, rating curves require regular validation and updating, and extrapolation beyond the observed range should be approached with caution.