Question

The rainfall on five successive days in a catchment was measured as 3, 8, 12, 6 and 2 cm. If the total runoff at the outlet from the catchment was 15 cm, the value of the $\varphi -index$ (in mm/hour) is

• A. 0.0
• B. 1.04
• C. 1.53
• D. Sufficient information not available

Answer 1

The correct option is C 1.53



Total depth of rainfall = 31 cm
Total runoff = 15 cm
Infiltration = 31 - 15 = 16 cm
Time of rainfall = 5 days
Considering the whole period of rainfall to be the period of rainfall excess

$\varphi -index=\frac{31-15}{5}=3.2cm/day$

Since the time period (0 to 1 days & 4 to 5 days) are not the period of rainfall excess, these periods are not considered in calculation of $\varphi -index$

$\varphi -index=\frac{31-3-2-15}{5-2}=3.67cm/day$

$=1.53mm/hr.$

Note: Check again if
rainfall intensity $i>\varphi -index$ for all periods of rainfall excess considered in calculation of $\varphi -index$ , if not (i.e., some $i<\varphi -index$) then reconsider the period of rainfall excess.