For a watershed with fair pasture cover, if s is the potential infiltration (cm) and P is the storm rainfall (cm), what is the expression for direct runoff depth Q (cm)?

Introduction / Context:
Event-based runoff estimation commonly starts with simple abstractions that subtract initial or potential infiltration from storm rainfall. For small catchments and quick estimates, a linear 'potential infiltration' model is frequently used.

Given Data / Assumptions:

• Potential infiltration capacity during the event is s (cm).
• Storm rainfall depth is P (cm).
• Land cover: fair pasture (used only to contextualize plausible s values).
• Neglect other abstractions (interception, depression storage) for this simplified model.

Concept / Approach:
The simplest rainfall–runoff abstraction assumes that if rainfall does not exceed the infiltration capacity, no direct runoff occurs. When rainfall exceeds the potential infiltration, the excess becomes direct runoff. This yields a piecewise linear relation:

Step-by-Step Solution:

Verification / Alternative check:
While more sophisticated models (e.g., SCS-CN: Q = (P − Ia)^2 / (P − Ia + S)) exist, the question explicitly frames 'potential infiltration s' in a simplified sense; thus, the linear excess-rainfall model is appropriate.

Why Other Options Are Wrong:

• (P − s)^2 / P: Not a standard form; can distort low/high P behavior.
• P / (1 + s): Nonphysical scaling; lacks threshold.
• P − s/2: Ignores full infiltration potential.
• s − P: Would give negative runoff for P > s.

Common Pitfalls:

• Confusing this linear model with SCS-CN; always check definitions.
• Forgetting that Q cannot be negative.
• Ignoring other abstractions (interception, depression storage) in detailed studies.

Final Answer:
Q = max(0, P − s)