Section 4: Soil and Water Conservation Engineering
Infiltration, Evaporation & Hydrologic Losses
Subtopic: Phi-index and W-index definitions
Question Statement:
Which of the following statements regarding infiltration indices ($\phi$-index and $W$-index) is/are TRUE?
Options:
(A) The $\phi$-index represents the average rainfall intensity above which the rainfall volume equals the surface runoff volume
(B) The $W$-index explicitly subtracts initial abstraction ($I_a$) and depression storage from total losses
(C) The $\phi$-index is always strictly greater than or equal to the $W$-index ($\phi \ge W$)
(D) During a rainstorm where rainfall intensity is everywhere greater than infiltration capacity, $\phi = W$
Answer Key:
A, B, C, D
Step-by-Step Solution & Explanation
1. By definition, $\phi = (P - R) / t_e$ where $t_e$ is rainfall excess duration (A is true).
2. $W = (P - R - I_a) / t_r$, where $I_a$ is initial abstraction (B is true).
3. Since $\phi$ bundles initial abstraction into the loss rate during excess time ($t_e \le t_r$), $\phi \ge W$ always holds (C is true).
4. When $I_a \approx 0$ and $t_e = t_r$, $\phi$ converges to $W$ (D is true).
All statements A, B, C, D are correct.