Hydrology—Unit hydrograph theory: Compared to the peak discharge of a 4-hour unit hydrograph for the same basin, the peak discharge of the instantaneous unit hydrograph (IUH) will be:

Introduction / Context:
Unit hydrographs describe a basin’s direct runoff response to a unit depth of effective rainfall over a specified duration. As the rainfall duration shortens, runoff is concentrated in time, making the hydrograph sharper and peakier. The theoretical limit is the instantaneous unit hydrograph (IUH).

Given Data / Assumptions:

• Same basin, linear system assumption.
• Comparison between a finite-duration (4-hour) unit hydrograph and IUH.
• Unit depth of effective rainfall in both cases.

Concept / Approach:

Reducing rainfall duration for the same unit depth compresses runoff timing and increases peak discharge while preserving total volume (area under hydrograph). Hence, IUH, as the zero-duration limit, has the most concentrated response and the highest peak.

Step-by-Step Solution:

Verification / Alternative check:

Constructing UHs of varying duration from an IUH via convolution shows peaks decrease as duration increases, confirming the relationship.

Why Other Options Are Wrong:

• Equal or lesser contradicts the concentration principle; equal is only a degenerate case.

Common Pitfalls:

• Confusing peak discharge with total volume (which stays constant for a unit depth).

Final Answer:

greater