Question

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Unit hydrograph theory is not applicable to catchment areas larger than 5000 sq.km.
Reason (R): Rainfall is not uniformly distributed on large catchment areas.
In the light of the above statements, choose the most appropriate answer from the options given below:

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

For catchments larger than 5000 sq.km, we typically divide the area into smaller sub-catchments, apply UH to each, and then route the flows through the channels to the main outlet.

Answer 1

The Correct Option is A

Concept: Sherman's Unit Hydrograph (UH) theory relies on two main assumptions: time invariance and linear response.

Step 1: Verify Assertion (A).
The Unit Hydrograph theory assumes that rainfall is uniformly distributed over the entire catchment area for the duration of the storm. For very large catchments ($> 5000 \text{ sq.km}$), this assumption rarely holds true as storms are usually localized. Thus, (A) is correct.

Step 2: Verify Reason (R).
Meteorological reality shows that intense rainfall events (convective storms) have a limited spatial extent. On a large catchment, it is highly likely that one sub-basin receives heavy rain while another remains dry. This spatial variation violates the fundamental "uniform distribution" assumption of UH theory. Thus, (R) is correct.

Step 3: Causal Link.
The inability to meet the uniform rainfall requirement (R) is the exact reason why the theory is restricted to catchments of moderate size (A).