Correct Answer - Option 1 : 1.2
Concepts:
Phi index (φ index): It is the rate of infiltration exceeding which the volume of rainfall becomes equal to the runoff volume. The relationship of phi-index with precipitation and run off is given by,
\(\phi {\rm{\;index}} = \frac{{{\rm{P}} - {\rm{R}}}}{{\rm{T}}}\)
Where, φ index = phi index of the storm or rainfall,
P = Precipitation due to only that rate of rainfalls which has a value greater than phi index,
T = Duration of effective rainfall,
R = Total runoff.
Note: Rainfall rates lesser or equal to phi index does not contribute to run off, hence they are not considered for calculating runoffs.
Calculations:
As φ index is same for both the storms, so let’s calculate φ index only considering the storm I.
Precipitation due to rainfall caused by Storm I, P = 2 × 5 = 10 cm.
Duration of effective rainfall for Storm I, T = 5 hours.
Total runoff due to Storm I, R = 4 cm.
\(\therefore \phi {\rm{\;index}} = \frac{{{\rm{P}} - {\rm{R}}}}{{\rm{T}}} = \frac{{10 - 4}}{5} = 1.2{\rm{\;cm}}/{\rm{hours}}\)
