Definition of a unit hydrograph (runoff depth basis) A unit hydrograph is the direct-runoff hydrograph produced by a rainstorm of a specified duration that generates a runoff depth of:

Introduction / Context:The unit hydrograph (UH) concept is a cornerstone of surface-water hydrology. It represents the time distribution of direct runoff resulting from a unit depth of effective rainfall of a given duration over a catchment.

Given Data / Assumptions:

• Catchment is linear and time-invariant during the event (superposition and proportionality hold approximately).
• “Unit” depth conventionally means 1 cm (10 mm) of effective rainfall excess.
• Specified duration refers to the rainfall excess duration (e.g., 1 hour UH, 4 hour UH).

Concept / Approach:A UH is defined so that its ordinates scale linearly with rainfall excess. If a storm produces D cm of effective rainfall of the same duration, the resulting direct-runoff hydrograph is D times the UH ordinates.

Step-by-Step Solution:

Verification / Alternative check:Hydrology handbooks and standard texts uniformly adopt 1 cm as the unit runoff depth in metric practice; some analyses may use 1 inch in US customary units.

Why Other Options Are Wrong:

• 5, 20, 25, and 30 mm are not the conventional “unit” depth; they would define non-standard hydrographs.

Common Pitfalls:Confusing rainfall depth (gross) with effective rainfall (excess). The UH is tied to runoff excess after abstraction losses.

Final Answer:10 mm (i.e., 1 cm)