In the context of infiltration indices, how does the φ-index differ from the W-index?
- AThe φ-index is always less than the W-index
- BThe φ-index includes the initial losses, while the W-index does notCorrect
- CThe W-index accounts for initial losses, while the φ-index does not
- DThe φ-index is calculated over the entire storm period, while the W-index is not
Solution
Concept
Difference between φ-index and W-index infiltration indices
Formula
W = (P - R - Ia) / te
Step-by-step solution
1. The φ-index is the constant loss rate above which rainfall volume equals surface runoff volume. 2. In computing the φ-index, initial abstractions (depression storage, interception) are lumped into the total loss. 3. The W-index is the average infiltration rate during rainfall excess, with initial losses (Ia) explicitly separated and deducted. 4. Therefore, the φ-index includes initial losses within the loss total, whereas the W-index does not. Answer: B
Explanation
In infiltration analysis, the φ-index is the average rate of rainfall above which rainfall volume equals runoff volume, thereby lumping initial abstractions (depression storage and interception) together with infiltration. The W-index is a refined infiltration index that explicitly separates and deducts initial losses from the total abstraction.
Why the other options are wrong
A) Phi-index is greater than or equal to W-index because it includes initial abstraction. C) W-index explicitly excludes initial loss from the infiltration rate. D) Both indices consider periods where rainfall exceeds infiltration capacity.
Shortcut
Phi-index includes initial loss (Φ ≥ W); W-index deducts initial loss.
Common mistake
Confusing the definition by thinking the W-index includes initial losses instead of separating them out.
Correct answer: B) The φ-index includes the initial losses, while the W-index does not