Rating curve equation and daily discharge hydrograph

Equation of the rating curve

The stage-discharge relation at a gauging section is

$$Q = C\,(G-a)^{b}$$

where $Q$ = discharge (m$^3$/s), $G$ = gauge height (m), $a$ = gauge height for zero discharge (m), and $C$, $b$ = constants of the section ($b\approx1.5$ to $2.0$). It plots as a smooth, upward-curving line on arithmetic paper and as a straight line on log-log paper.

 G (stage)                 log Q
  |        .'               |       . /
  |      .'                 |     . /  slope = b
  |    .'                   |   . /
  |  .'                     | . /
  |_.'___________ Q         +---------- log(G-a)
  a

Daily discharge hydrograph from the daily stage hydrograph

1. Obtain the daily mean stage for each day, as the average of the observed gauge readings, or from the area under the recorder chart (stage hydrograph).
2. Use the rating curve (equation or table) to read the discharge corresponding to each day's mean stage: $Q_i = C(G_i-a)^b$.
3. Where the stage changes rapidly in a day, compute discharge for shorter intervals, or use the discharge for each reading and then average.
4. Apply shift corrections if the control has changed in the period.
5. Plot $Q_i$ against time (days) to get the daily discharge hydrograph.

 stage G        rating curve      discharge Q
  |   /\                            |   /\
  |  /  \      ---> Q=f(G) --->     |  /  \
  |_/____\___ t                     |_/____\__ t

The sum of the daily discharges gives monthly and annual volumes.