Maximum rainfall intensity for 1, 3, 5 hr

The maximum depth for a duration $D$ is the largest sum of $D$ consecutive hourly values; the maximum intensity is that depth divided by $D$. Hourly rainfall (mm) in time order from 7 am: 10, 8, 6, 12, 5, 0, 2, 5, 8, 12, 7, 6, 0, 0 (total 81 mm).

1-hour duration

Largest single hour $= 12$ mm, so $i_{max} = 12/1 = 12$ mm/h.

3-hour duration

Sums of 3 consecutive hours: 24, 26, 23, 17, 7, 7, 15, 25, 27, 25, 13, 6. Maximum $= 8 + 12 + 7 = 27$ mm, so $i_{max} = 27/3 = 9.0$ mm/h.

5-hour duration

Sums of 5 consecutive hours: 41, 31, 25, 24, 20, 27, 34, 38, 33, 25. Maximum $= 10+8+6+12+5 = 41$ mm (first five values), so $i_{max} = 41/5 = 8.2$ mm/h.

Answer: Maximum intensities = 12.0 mm/h (1 h), 9.0 mm/h (3 h) and 8.2 mm/h (5 h).