Question

If \( Q \) = depth of runoff in inches, \( P \) = depth of rainfall in inches, \( I_a \) = initial abstraction in inches, and \( S \) = maximum potential retention in inches, then which of the following is the correct equation for the curve number runoff?

• A. \( Q = \frac{(P - I_a)^2}{(P - I_a + S)} \)
• B. \( Q = \frac{(P + I_a)^2}{(P - I_a - S)} \)
• C. \( Q = \frac{(P - I_a)^2}{(P + I_a + S)} \)
• D. \( Q = \frac{(P - I_a)^2}{(P - I_a - S)} \)

Hint:

Use SCS method when rainfall exceeds initial abstraction: \( Q = \frac{(P - I_a)^2}{(P - I_a + S)} \)

Answer 1

The Correct Option is A

The SCS Curve Number method gives the formula: \[ Q = \frac{(P - I_a)^2}{(P - I_a + S)} \quad \text{for } P>I_a \] This formula estimates direct runoff from rainfall using empirically derived relationships between precipitation and soil/land cover characteristics.