Question

By depth-area-duration (DAD) analysis, the maximum average depth of rainfall over a \(10^{3}\) \(\text{km}^2\) catchment due to a 6-hour storm is 80 mm. For the same storm, the maximum average depth of rainfall for a \(10^{4}\) \(\text{km}^2\) catchment, in mm, is

• A. greater than 88
• B. lesser than 80
• C. equal to 80
• D. between 81 and 88

Hint:

Think about how DAD curves behave as the area around a storm centre grows for a fixed duration.

Answer 1

The Correct Option is B

Step 1: Recall what a DAD curve shows.
A depth-area-duration (DAD) analysis plots how the maximum average rainfall depth for a fixed storm duration falls as the catchment area considered gets larger.
The storm data come from actual isohyetal maps, and the average depth is found by area-weighting the rainfall inside successively bigger boundaries drawn around the storm centre.

Step 2: Apply this to the given areas.
Here the duration is fixed at 6 hours, and the average depth for a \(10^{3}\) \(\text{km}^2\) area around the storm centre is 80 mm.
The \(10^{4}\) \(\text{km}^2\) catchment is ten times larger and includes zones further from the storm centre, where rainfall intensity is lower.
Averaging this low-intensity outer rain together with the high-intensity rain near the centre always pulls the average depth down as area grows.

Final Answer:
The average depth for the larger \(10^{4}\) \(\text{km}^2\) catchment must be less than 80 mm. \[ \boxed{\text{lesser than } 80 \text{ mm}} \]