ratingcurve

A rating curve, also known as a stage-discharge curve, is the relationship between water stage (the height of the water surface) and discharge (the flow rate) at a gauging station. It is used to estimate river discharge from continuous stage measurements.

Construction involves collecting paired observations of stage and discharge over time. Stage is measured with staff gauges, stilling wells, or sensors, while discharge is determined using methods such as velocity-area measurements, current meters, weirs, or calibrated structures. The resulting data form a curve that translates a given stage into a corresponding discharge.

Form and representation: rating curves are typically monotonic and nonlinear, with varying slope across the range of stages. They are often expressed as piecewise functions or fitted with smooth mathematical forms such as polynomials, power relations, or splines. In practice, separate segments may be used for low, moderate, and high flows to better capture the river’s response.

Applications: rating curves enable conversion of continuous stage records into discharge time series, supporting flood forecasting, hydrologic modeling, reservoir and dam operation, and water resources planning and management.

Maintenance and uncertainty: rating curves can change over time due to sediment deposition or scour, channel modification, vegetation, ice effects, or changes in streambed structures. Re-rating or updating curves is common. Uncertainty arises from measurement errors, natural variability, and extrapolation beyond the range of observed data; confidence intervals are often quantified.

See also: stage, discharge, hydrograph, gauging station, hydrometry.