How stage-discharge relationship is established

A stage-discharge relationship (rating curve) at a gauging site is established as follows.

1. Select the site with a stable, permanent control and a straight reach.
2. Install a gauge (staff gauge or automatic recorder) and note the datum.
3. Measure discharge at various stages, from low to flood, by the area-velocity (current meter) method, and simultaneously record the stage. A minimum of about 15 to 20 measurements covering the whole range is desirable.
4. Plot the stage $G$ against discharge $Q$ on arithmetic paper; draw a smooth curve through the points.
5. Fit the equation $Q = C(G-a)^b$:
   • Find $a$, the stage at zero discharge (by trial, or the three-point method $a=\dfrac{G_1G_3-G_2^2}{G_1+G_3-2G_2}$ with $Q_2=\sqrt{Q_1Q_3}$).
   • Plot $\log Q$ against $\log(G-a)$; a straight line is obtained when $a$ is correct; its slope is $b$ and intercept is $\log C$.
6. Check the correlation and test the curve by new measurements.
7. Extrapolate the curve above the highest measured stage by the log-log straight line or the conveyance (Manning) method.
8. Review periodically: if the points depart from the curve (shifting control), apply shift corrections or draw a new curve.