Stage at zero discharge from rating data

Use the three-point method on the smooth curve with $Q_2 = \sqrt{Q_1Q_3}$.

Take the lowest and highest points: $(G_1,Q_1)=(20.80,100)$ and $(G_3,Q_3)=(24.00,1000)$.

$$Q_2=\sqrt{100\times1000}=316.2\ \text{m}^3/\text{s}$$

Reading $G_2$ from the curve by interpolation between $(21.95, 300)$ and $(22.37, 400)$:

$$G_2 = 21.95 + \frac{316.2-300}{400-300}\times(22.37-21.95) = 22.018\ \text{m}$$ $$a=\frac{G_1G_3-G_2^2}{G_1+G_3-2G_2}=\frac{20.80\times24.00-22.018^2}{20.80+24.00-2\times22.018}=\frac{499.20-484.79}{0.764}=18.86\ \text{m}$$

Check by trial on the log-log plot (least-squares fit of $\log Q$ against $\log(G-a)$ for trial $a$):

The straightest line occurs at $a \approx 18.9$ m, which agrees with the three-point result.

Answer: Stage for zero discharge $\approx 18.9$ m.

(The result is sensitive to the point selection, so the trial plot is preferred as a check.)