Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Analysis of precipitation data
Question Statement:
By depth-area-duration analysis, the maximum average depth of rainfall over a 10³ km² catchment due to a 6-hour storm is 80 mm. For the same storm, the maximum average depth of rainfall for a 10⁴ km² catchment, in mm, is
Options:
(A) greater than 88
(B) lesser than 80
(C) equal to 80
(D) between 81 and 88
Official Answer Key:
B
Step-by-Step Solution & Explanation
In Depth–Area–Duration (DAD) analysis, for a fixed storm duration, the maximum average depth decreases monotonically as the area increases.
Physical reason: an intense storm cell has limited spatial extent. Over a small area the average can approach the storm-centre intensity; as the averaging area grows to include the storm’s lower-intensity fringes, the areal average is diluted.
Since the area increases tenfold (10³ → 10⁴ km²) for the same 6-hour storm, the maximum average depth must fall below 80 mm. Options (A), (C) and (D) all imply equal or greater depth and are physically impossible.
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