This question was previously asked in

NWDA JE CE 2019 Official Paper

Option 2 : 0.825 cm/hr

**Concept:**

ϕ index of a catchment is defined as the constant infiltration capacity that would yield the actual total runoff for a given rainfall amount.

Mathematically, ϕ_{index} = \(\frac{P_e -R}{t_e} \)

Where,

P_{e} = effective rainfall causing runoff, R = runoff, and t_{e} = effective rainfall period

As we know that, for runoff to occur, **Rainfall intensity (i) > ϕ _{index}**

**Calculation:**

Given,

P = 15 cm, R = 8.7 cm, duration of rainfall = 8 hrs

**Trial 1:** Considering all rainfall values in a period of 8 hrs causes runoff.

∵ We know that, ϕ_{index} = \(\frac{P_e -R}{t_e} \)

⇒ ϕ_{index} = \(\frac{15 - 8.7}{8}\)

∴ ϕ_{index} = 0.7875 cm/hr

\(\because \) We know that, for runoff to occur, i > ϕ_{index},

\(\Rightarrow\) rainfall intensities 0.6 and 0.75 cm/hr are less than ϕ_{index} = 0.7875 cm/hr

\(\therefore \) for trial 2, rainfall intensities **0.6 and 0.75 cm/hr are ignored.**

**Trial 2:**

Total rainfall, P = 1.35 + 2.25 + 3.45 + 2.7 + 2.4 + 1.5 = 13.65 cm, R = 8.7 cm

Duration of rainfall, t = 6 hrs

\(\Rightarrow\) ϕ_{index} = \(\frac{13.65 - 8.7}{6}\)

\(\therefore\)** ϕ _{index }= 0.825 cm/hr**