- 2078 Kartik · 6 marks
Mass curve, hyetograph, depth-duration curve
Short answer
The mass curve and hyetograph are constructed from the data. Maximum depths for durations of 5, 10, 15, 20, 30, 40, and 50 minutes are 0.7, 1.3, 1.6, 1.8, 2.5, 2.9, and 3.1 cm, respectively.
Following are the rain gauge observations during a storm. Construct the mass curve of precipitation, hyetograph and maximum depth-duration curve.
| Time since commencement of storm (min) | Accumulated rainfall (cm) |
|---|---|
| 5 | 0.1 |
| 10 | 0.2 |
| 15 | 0.8 |
| 20 | 1.5 |
| 25 | 1.8 |
| 30 | 2.0 |
| 35 | 2.5 |
| 40 | 2.7 |
| 45 | 2.9 |
| 50 | 3.1 |
Step 1: Incremental depth and intensity (5-min intervals)
| Time (min) | Cum. rain (cm) | Increment (cm) | Intensity (cm/h) |
|---|---|---|---|
| 5 | 0.1 | 0.1 | 1.2 |
| 10 | 0.2 | 0.1 | 1.2 |
| 15 | 0.8 | 0.6 | 7.2 |
| 20 | 1.5 | 0.7 | 8.4 |
| 25 | 1.8 | 0.3 | 3.6 |
| 30 | 2.0 | 0.2 | 2.4 |
| 35 | 2.5 | 0.5 | 6.0 |
| 40 | 2.7 | 0.2 | 2.4 |
| 45 | 2.9 | 0.2 | 2.4 |
| 50 | 3.1 | 0.2 | 2.4 |
Intensity = increment / (5/60 h) = increment × 12.
Mass curve: plot accumulated rainfall (y) against time (x) from the first two columns, a rising curve that ends at 3.1 cm at 50 min and is steepest between 10 and 20 min.
Hyetograph: a bar chart of the increment (or intensity) against time.
cm/h
8.4 | ##
7.2 | ## ##
6.0 | ## ## ##
3.6 | ## ## ## ##
2.4 | ## ## ## ## ## ## ## ##
1.2 |## ## ## ## ## ## ## ## ## ##
+------------------------------
5 10 15 20 25 30 35 40 45 50 min
Maximum depth-duration: for each duration the largest rainfall in any consecutive period is found from the mass curve.
| Duration (min) | Max depth (cm) | Period of occurrence (min) | Avg intensity (cm/h) |
|---|---|---|---|
| 5 | 0.7 | 15-20 | 8.4 |
| 10 | 1.3 | 10-20 | 7.8 |
| 15 | 1.6 | 10-25 | 6.4 |
| 20 | 1.8 | 10-30 | 5.4 |
| 30 | 2.5 | 10-40 | 5.0 |
| 40 | 2.9 | 10-50 | 4.35 |
| 50 | 3.1 | 0-50 | 3.72 |
Plot depth (or intensity) against duration. The depth increases with duration while the average intensity falls from 8.4 cm/h (5 min) to 3.72 cm/h (50 min).
Answer: Maximum depths = 0.7, 1.3, 1.6, 1.8, 2.5, 2.9 and 3.1 cm for 5, 10, 15, 20, 30, 40 and 50 min.
✓ Answer checked by Claude Sonnet 5.5
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