Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Infiltration – indices and equations
Question Statement:
Regarding the hydrologic infiltration indices $\Phi$-index and $W$-index, which of the following statements is always strictly true?
Options:
(A) The $\Phi$-index represents average infiltration and depression storage, and is always greater than or equal to the $W$-index ($\Phi \ge W$)
(B) The $W$-index always exceeds the $\Phi$-index by a factor of 2.0
(C) Both $\Phi$ and $W$ indices account only for surface evaporation, ignoring infiltration
(D) The $\Phi$-index can only be evaluated when rainfall intensity is zero
Answer Key:
A
Step-by-Step Solution & Explanation
- The $\Phi$-index treats initial abstraction ($I_a$, depression storage and interception) as part of infiltration loss ($P_{excess} = P - \Phi \cdot t_e$).
- The $W$-index explicitly separates initial abstraction: $W = \frac{P - R - I_a}{t_e}$.
- Since the loss attributed to infiltration in $\Phi$ includes $I_a$, $\Phi \ge W$ always holds. Option A is correct.