- 2081 Baisakh · 4+6 marks
Hyetograph and intensity-duration curve, Lumle tipping bucket
Short answer
Incremental depths from cumulative data give intensities (depth×6). Peak 10-min intensity is 85.2 mm/h in 50–60 min. Maximum intensity-duration values are 85.2, 67.8, 53.2, 49.5, 48.2, 45.2, 41.0, 37.1, 33.9 mm/h for durations 10 to 90 min.
Following are the data of a storm as recorded in a tipping bucket located at Lumle (Lat: 28.3, Long: 83.8) for 1.5 hours:
| Time from beginning of storm (minute) | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 |
|---|---|---|---|---|---|---|---|---|---|
| Cumulative rainfall (mm) | 1.6 | 6.6 | 13.8 | 20.2 | 24.2 | 38.4 | 46.8 | 49.4 | 50.8 |
(i) Plot the hyetograph of the storm. (ii) Plot the maximum intensity duration curve of the storm.
The tipping bucket gives cumulative rainfall at 10-min intervals. The incremental depth in each interval is the difference of successive values, and intensity = depth / (10/60 h) = depth × 6.
(i) Hyetograph
| Interval (min) | Cum. rain (mm) | Incremental depth (mm) | Intensity (mm/h) |
|---|---|---|---|
| 0-10 | 1.6 | 1.6 | 9.6 |
| 10-20 | 6.6 | 5.0 | 30.0 |
| 20-30 | 13.8 | 7.2 | 43.2 |
| 30-40 | 20.2 | 6.4 | 38.4 |
| 40-50 | 24.2 | 4.0 | 24.0 |
| 50-60 | 38.4 | 14.2 | 85.2 |
| 60-70 | 46.8 | 8.4 | 50.4 |
| 70-80 | 49.4 | 2.6 | 15.6 |
| 80-90 | 50.8 | 1.4 | 8.4 |
mm/h (one bar per 10-min interval; each row is approximate)
80 | ##
60 | ##
40 | ## ## ##
20 | ## ## ## ## ## ## ##
5 |## ## ## ## ## ## ## ## ##
+---------------------------
10 20 30 40 50 60 70 80 90 min
(The peak of 85.2 mm/h occurs in the 50-60 min interval.)
(ii) Maximum intensity-duration curve
For each duration the maximum depth is the greatest difference of cumulative ordinates that far apart.
| Duration (min) | Max depth (mm) | Period (min) | Max intensity (mm/h) |
|---|---|---|---|
| 10 | 14.2 | 50-60 | 85.2 |
| 20 | 22.6 | 50-70 | 67.8 |
| 30 | 26.6 | 40-70 | 53.2 |
| 40 | 33.0 | 30-70 | 49.5 |
| 50 | 40.2 | 20-70 | 48.2 |
| 60 | 45.2 | 10-70 | 45.2 |
| 70 | 47.8 | 10-80 | 41.0 |
| 80 | 49.4 | 0-80 | 37.1 |
| 90 | 50.8 | 0-90 | 33.9 |
Example: 30 min: 46.8 (at 70 min) - 20.2 (at 40 min) = 26.6 mm, intensity 53.2 mm/h.
Plot duration (x) against maximum intensity (y). The curve falls from 85.2 mm/h at 10 min to 33.9 mm/h at 90 min.
Answer: Peak 10-min intensity = 85.2 mm/h; maximum intensities are 85.2, 67.8, 53.2, 49.5, 48.2, 45.2, 41.0, 37.1 and 33.9 mm/h for 10 to 90 min.
✓ Answer checked by Claude Sonnet 5.5
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