Question

The rainfall during three successive 2 h periods are 0.5, 2.8 and 1.6 cm. The surface runoff resulting from this storm is 3.2 cm. The $\varphi$ index value of this storm is

• A. 0.20 cm/h
• B. 0.28 cm/h
• C. 0.30 cm/h
• D. 0.80 cm/h

Answer 1

The correct option is C 0.30 cm/h

Total rainfall=0.5 + 2.8 + 1.6 = 4.9 cm
Surface runoff = 3.2 cm
Infiltration = 4.9 — 3.2 = 1.7 cm
Time of rainfall = 6 hr

If infiltration is assumed constant, infiltration rate will be

$\frac{1.7}{6}=0.28cm/hr$

But this infiltration rate cannot be possible throughout the time period of 6 hrs because

From 0-2 hr :
$\text{rainfall rate =}\frac{0.5}{2}=.25cm/hr$

which is lesser than infiltration rate and infiltration rate cannot be more than rainfall rate.

Now, taking time period from 2 to 6 hrs

Excess rainfall duration = 6 - 2 = 4 hrs
Total rainfall = 2.8 + 1.6 = 4.4 cm
Surface runoff = 3.2 cm

(because from 0 - 2 hrs, storm will not contribute in surface runoff)

Infiltration = 4.4 - 3.2 = 1.2 cm

$\varphi -index=\frac{\text{Infiltration}}{t_e}=\frac{1.2}{4}$
= 0.30 cm/h

For t = 2 to 4 hrs,
$\text{Rainfall intensity}=\frac{2.8}{2}=1.4cm/hr>\varphi$

For t = 4 to 6 hrs,

$\text{Rainfall intensity}=\frac{1.6}{2}=0.8cm/h>\varphi$
Hence
$\varphi -index=0.3cm/h$

Alternative approach
Total rainfall = 0.5 + 2.8 + 1.6 = 4.9 cm
Total runoff = 3.2 cm
Time of rainfall = 6 hours

Considering whole period of rainfall to be period of rainfall excess.

$\Rightarrow \varphi -index=\frac{4.9-3.2}{6}=0.283cm/h$

$\varphi -index$ denotes losses and it cannot be greater than rainfall intensity. The intensities of rainfall are 0.25 cm/h, 1.4 cm/h and 0.8 cm/h for the three storms. Out of these, 0.25 cm/h is lesser than $\varphi -index$ obtained. Hence it is not the period of rainfall excess.

Again, considering the other two rainfall excess,

$\Rightarrow \varphi -index=\frac{2.8+1.6-3.2}{4}$

= 0.3 cm/h