- 2073 Shrawan · 12 marks
Intensity-duration graph from mass curve ordinates
Short answer
From the mass curve, maximum depths over each duration are converted to intensity. Intensities are 84.0, 70.0, 61.3, 57.0, 52.0, 47.5, and 37.3 mm/h for 15, 30, 45, 60, 90, 120, and 180 min, respectively.
A storm commenced at 7:00 hours. The ordinates of the rainfall mass curve of this storm in mm as recorded by a recording rain gauge at 15 minute intervals are 0, 9.5, 17.0, 27.0, 40.5, 49.0, 63.0, 84.0, 95.0, 102.0, 110.0, 112.0 and 112.0. Plot the intensity duration graph by computing the maximum rainfall intensities for durations of 15, 30, 45, 60, 90, 120 and 180 minutes.
Mass curve ordinates (mm) at 15-min intervals from 07:00: 0, 9.5, 17.0, 27.0, 40.5, 49.0, 63.0, 84.0, 95.0, 102.0, 110.0, 112.0, 112.0.
Incremental rainfall (mm) per 15 min: 9.5, 7.5, 10.0, 13.5, 8.5, 14.0, 21.0, 11.0, 7.0, 8.0, 2.0, 0.
For each duration , the maximum depth is the largest difference of mass curve ordinates minutes apart (found by sliding the window along the curve), and .
| Duration (min) | Max depth (mm) | Period (from 07:00) | Max intensity (mm/h) |
|---|---|---|---|
| 15 | 21.0 | 90-105 min | 84.0 |
| 30 | 35.0 | 75-105 min | 70.0 |
| 45 | 46.0 | 75-120 min | 61.3 |
| 60 | 57.0 | 45-105 min | 57.0 |
| 90 | 78.0 | 30-120 min | 52.0 |
| 120 | 95.0 | 0-120 min | 47.5 |
| 180 | 112.0 | 0-180 min | 37.3 |
Checks: 30 min = 14.0 + 21.0 = 35 mm; 1 h = 84.0 - 27.0 = 57 mm; 2 h = 95.0 - 0 = 95 mm.
Intensity-duration graph: plot duration on the x-axis and maximum intensity on the y-axis:
mm/h
84 |*
70 | *
61 | *
57 | *
52 | *
47.5| *
37 | *
+---------------------------
15 30 45 60 90 120 180 min
The intensity falls steadily as the duration increases.
Answer: Maximum intensities = 84, 70, 61.3, 57, 52, 47.5 and 37.3 mm/h for 15, 30, 45, 60, 90, 120 and 180 min.
✓ Answer checked by Claude Sonnet 5.5
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