Unit hydrograph terminology and properties for rainfall–runoff analysis In hydrology, consider the standard unit hydrograph framework used for transforming effective rainfall of a specified duration into direct-runoff hydrographs. Identify the correct set of statements about unit duration, unit storm, reuse across similar durations, and number of possible unit hydrographs for a basin.

Introduction / Context:Unit hydrograph theory is a cornerstone of surface-water hydrology. It provides a linear, time-invariant method to relate a specified duration of effective rainfall (also called excess rainfall) to the basin’s direct runoff response. Understanding the associated terminology and properties ensures correct application in design floods, flood routing, and storm synthesis.

Given Data / Assumptions:

• The unit hydrograph corresponds to a fixed unit duration (for example, 1 hour, 3 hours) and to a unit depth of effective rainfall (commonly 1 cm).
• The rainfall that results in the unit effective rainfall depth over that duration is referred to as a unit storm.
• Hydrologic system is assumed approximately linear and time-invariant for the period of analysis.

Concept / Approach:

Under the linear superposition principle, any complex effective rainfall hyetograph with the same duration increments can be decomposed into scaled and time-shifted unit storms. The resulting direct runoff hydrograph is the sum of scaled and lagged unit hydrographs. Because storms vary endlessly in space and time, many valid unit hydrographs (shapes) can be derived from different events, even for the same unit duration.

Step-by-Step Solution:

Verification / Alternative check:

Classical hydrology texts derive multiple unit hydrographs from different storms for the same basin; each differs slightly yet remains applicable within the linear framework. Synthetic unit hydrographs (Snyder, SCS) further show the non-uniqueness.

Why Other Options Are Wrong:

• Options (a), (b), (c), and (d) are all correct statements; selecting any single one would be incomplete.

Common Pitfalls:

• Confusing gross rainfall with effective rainfall; unit hydrographs respond to effective rainfall only.
• Using a unit hydrograph of one duration to synthesize storms with a different duration without proper conversion.

Final Answer:

All the above.