Stage for zero discharge with sketch

The stage of zero discharge ($a$) is the gauge height at which the flow in the river becomes zero (the level of the lowest point of the control). It is needed in the rating equation $Q = C(G-a)^b$.

Methods

1. Field survey: survey the level of the lowest point of the channel control (the bed of the riffle or the lowest point of the section) directly. For sand-bed rivers this level may change from time to time.

2. Trial and error (log-log plot): assume trial values of $a$ and plot $\log Q$ against $\log(G-a)$. The correct $a$ gives a straight line. If the plot curves upward (concave up), the assumed $a$ is too high; if it curves downward (concave down), $a$ is too low.

  a too low        correct a        a too high
  (concave down)   (straight)       (concave up)
  logQ             logQ             logQ
   |     ___        |      /         |         /
   |   /            |    /           |       /
   |  /             |  /             |   _ -
   | /              | /              |_ -
   +------ log(G-a) +------          +------

3. Extrapolation of the arithmetic curve: extend the smooth stage-discharge curve down until it meets the stage axis at $Q=0$. This is a first rough estimate.

4. Three-point (analytical) method: Select three points $(G_1,Q_1)$, $(G_2,Q_2)$, $(G_3,Q_3)$ on the smooth curve with $Q_2^2 = Q_1Q_3$. Then

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

Procedure: choose the lowest and highest points $Q_1$, $Q_3$; compute $Q_2=\sqrt{Q_1Q_3}$; read $G_2$ on the curve; substitute.

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