Rating curve and stage for zero discharge

Rating curve

A rating curve (stage-discharge curve) is the graph or equation that gives the discharge corresponding to the stage at a river gauging section, usually $Q=C(G-a)^b$.

Stage for zero discharge

The stage for zero discharge ($a$) is the gauge height at which flow stops, i.e. the level of the lowest point of the control. It is found as follows.

  G ^
    |           .
 G3-|        .
 G2-|      .        (Q2 = sqrt(Q1*Q3))
 G1-|   .
  a-| .
    +----------------> Q

1. Extrapolation: draw the smooth stage-discharge curve and extend it downward to cut the stage axis at $Q = 0$ (a rough value).
2. Three-point method: pick three points on the smooth curve such that $Q_2=\sqrt{Q_1Q_3}$, read $G_1$, $G_2$, $G_3$, and compute

$$a=\frac{G_1G_3-G_2^2}{G_1+G_3-2G_2}$$

3. Trial on log-log paper: assume several $a$, plot $\log Q$ against $\log(G-a)$. The value that gives a straight line is the stage for zero discharge. If the plotted curve is concave upward, $a$ is too large; if concave downward, $a$ is too small.

 log Q
   |       . (a too small: concave down)
   |     . ____ straight (correct a)
   |   ._.-'
   | .' (a too large: concave up)
   +------------------ log(G - a)

4. Field survey of the lowest point of the control, where possible.