Unit hydrograph selection: The best (most informative) unit period for a unit hydrograph is approximately equal to the basin lag divided by which number?

Introduction / Context:
Hydrologists select a unit hydrograph duration to represent the catchment response to a unit depth of effective rainfall. Choosing an appropriate unit period is important for accurate runoff modeling and design flood estimation.

Given Data / Assumptions:

• Basin lag (time from centroid of excess rainfall to peak of direct runoff hydrograph) is known or can be estimated.
• Objective is to choose a practical unit duration that captures catchment dynamics without over-smoothing.

Concept / Approach:
A commonly used guideline is to select the unit duration as a fraction of the basin lag so that the hydrograph adequately represents the catchment response while remaining manageable for computations and convolution. A typical recommendation is about one-third of the basin lag.

Step-by-Step Reasoning:
Let T_lag be the basin lag.Choose unit duration T_u such that T_u ≈ T_lag / 3.This balances temporal resolution with the need to avoid an excessively short unit that introduces noise and numerical instabilities.

Verification / Alternative check:
Hydrology texts and practice often suggest a range (about one-third to one-fifth of lag); adopting one-third is a standard rule-of-thumb for routine problems and objective-type questions.

Why Other Options Are Wrong:

• 2: Too short; may cause spiky unit hydrographs.
• 4 or 5 (or 6): Unit duration becomes too long, smoothing the response and losing definition of peak timing.

Common Pitfalls:

• Selecting unit duration equal to storm duration rather than basin dynamics.
• Using an excessively long duration leading to underestimation of peak discharge.

Final Answer:
3