Infiltration index from 8-hr rainfall, Bagmati Basin

Total rainfall:

$$P = 0.8+1.8+3.0+4.6+3.6+3.2+2.0+1.0 = 20.0\ \text{cm}$$

Runoff $R = 11.6$ cm, so total loss $= 20.0 - 11.6 = 8.4$ cm. With no initial loss, all of this is infiltration, and the time step is 1 h.

Trial

Assume the hours with rain below $\phi$ are the 0.8 cm and 1.0 cm hours, so these give no excess. Excess is from 6 hours (1.8, 3.0, 4.6, 3.6, 3.2, 2.0), total rain $= 18.2$ cm.

$$18.2 - 6\phi = 11.6 \;\Rightarrow\; \phi = \frac{6.6}{6} = 1.10\ \text{cm/h}$$

Check: $0.8 < 1.1$ and $1.0 < 1.1$ (no excess in those hours, correct); every other hour has rain $> 1.1$.

Answer: Infiltration index ($\phi$-index) = 1.10 cm/h.