The empirical relationship between water surface elevation (stage) and the volume of water flowing through a channel cross-section (discharge) at a specific location. This rating curve is the fundamental tool for converting continuous stage records into discharge data.
The stage-discharge relationship (also called a rating curve) is a mathematical function relating the water surface elevation (stage) at a gauging station to the corresponding discharge (flow rate) at that location. This relationship is the cornerstone of continuous streamflow monitoring, as it enables conversion of automatically recorded stage data into the discharge time series used for water resource management, flood forecasting, and scientific analysis. Rating curves are developed by making numerous discharge measurements spanning the range of observed flows and plotting each measurement as a stage-discharge pair. The relationship is typically described by a power function: Q = C(h - e)^n, where Q is discharge, h is stage, e is the gauge height of zero flow, and C and n are fitted coefficients. Multiple segments may be needed to represent the full range of flows. Rating curves must be regularly updated because channel geometry changes due to scour, fill, vegetation growth, ice, and debris can shift the relationship. The USGS develops and maintains rating curves for its entire gauging network, with each measurement classified by quality and deviation from the current rating. Compound ratings may be needed for stations affected by variable backwater from downstream confluences, tides, or dam operations. Uncertainty in the rating curve is often the largest source of error in continuous discharge records, particularly for extreme high and low flows where few measurements exist.