For a watershed with fair pasture cover, if potential infiltration s = 10 cm and storm rainfall P = 12 cm, what is the direct runoff depth Q?

Introduction / Context:Quick event-based runoff estimates often use simple abstractions where a potential infiltration depth s is subtracted from rainfall depth P to compute direct runoff Q. This is useful for rapid checks and teaching fundamentals before applying full SCS-CN or infiltration-capacity models.

Given Data / Assumptions:

• Potential infiltration s = 10 cm.
• Storm rainfall P = 12 cm.
• Neglect other abstractions (interception, depression storage) for this simplified calculation.

Concept / Approach:If rainfall does not exceed potential infiltration, no direct runoff occurs. If it exceeds s, the excess becomes runoff. Hence: Q = max(0, P − s). This linear model captures the threshold behavior simply and is commonly introduced in hydrology courses.

Step-by-Step Solution:

Verification / Alternative check:While SCS-CN could give a slightly different value depending on I_a and S, the question clearly frames the simple potential-infiltration model, so the linear result stands.

Why Other Options Are Wrong:

• 3 cm, 5 cm, 8 cm: Do not match P − s = 2 cm for the specified s and P under this model.

Common Pitfalls:

• Accidentally using P/s or other ratios instead of the threshold subtraction.
• Forgetting that runoff cannot be negative.

Final Answer:2 cm