Step 1: φ-index Explained.
The φ-index method determines direct runoff from a catchment area. Direct runoff equals total rainfall minus the φ-index, multiplied by the number of days.
Step 2: Calculate Total Rainfall.
Total rainfall over five days:
\[
2 + 6 + 9 + 5 + 3 = 25 \, \text{cm}
\]
Step 3: Calculate Total Direct Runoff.
For each day, subtract the φ-index (3 cm/day) from the daily rainfall, then sum the results:
\[
\text{Total direct runoff} = (2 - 3) + (6 - 3) + (9 - 3) + (5 - 3) + (3 - 3)
\]
\[
\text{Total direct runoff} = (-1) + 3 + 6 + 2 + 0 = 16 \, \text{cm}
\]
Step 4: Conclusion.
The total direct runoff is 16 cm, thus option (2) is correct.
Final Answer:
\[
\boxed{16 \, \text{cm}}
\]