Step 1: Understanding the Concept:
We need to match hydrological terms with their definitions.
These are related to rainfall-runoff relationships.
Step 2: Key Formula or Approach:
No specific formula.
Need to know the definitions.
Step 3: Detailed Explanation:
\(\Phi\)-index is an infiltration index (A-III).
Detention storage is short-term storage lost by evaporation (B-I).
Current meter is used for velocity measurement (C-IV).
Stage-discharge relationship is the rating curve (D-II).
Thus, A-III, B-I, C-IV, D-II is the correct matching.
Step 4: Final Answer:
The correct matching is A-III, B-I, C-IV, D-II.
Hence, the correct option is (A).