Unit hydrograph applications – choose the comprehensive correct statements Regarding the use of unit hydrographs (UH) for design and analysis, identify the correct statements about duration tolerance, scaling with runoff depth, and transferability to future storms of the same duration.

Introduction / Context:
The unit hydrograph (UH) is a cornerstone of catchment hydrology. It represents the direct runoff hydrograph (DRH) produced by a unit depth of effective rainfall uniformly distributed over the catchment for a specified duration. Once derived, it enables synthesis of storm hydrographs for other runoff depths.

Given Data / Assumptions:

• Linear, time-invariant catchment response within practical limits.
• UH duration matches (or is close to) the effective rainfall duration.
• Runoff depth is in consistent units (e.g., mm or cm).
• Catchment conditions between events are broadly similar.

Concept / Approach:
Under linear superposition, a storm DRH equals the UH ordinates scaled by the runoff depth (in the same units as the unit depth defining the UH). If the UH is a 1 cm UH, multiplying factor = runoff depth (mm) / 10; if a 25 mm UH, factor = runoff (mm) / 25. Limited duration mismatch (≈ ±25%) is commonly tolerable, though using a matching-duration UH is best practice.

Step-by-Step Solution:
Transferability: The UH of a given duration can generate future storm hydrographs of like duration → true.Scaling: Multiply UH ordinates by runoff depth in UH-units → true.Factor example: For a 25 mm UH, factor = runoff(mm)/25 → true.Duration tolerance: ±25% is a commonly cited acceptable range → true.

Verification / Alternative check:
Hydrology texts illustrate convolution of a UH with an excess-rain hyetograph to reproduce storm DRHs, confirming the linear scaling of ordinates and practical duration tolerance.

Why Other Options Are Wrong:

• Each of (a)–(d) is correct individually; hence the comprehensive answer is (e) All the above.

Common Pitfalls:
Confusing UH depth (1 cm or 25 mm) with total rainfall depth; or applying UH outside its climatic/catchment context without adjustment.

Final Answer:
All the above.