---
title: "Intensity-duration curve from storm record"
subject: "Engineering Hydrology"
chapter: 2
key: "semester_5/engineering_hydrology:intensity-duration-30min-5hr"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/intensity-duration-30min-5hr
site: BCT Engineering
---

# Intensity-duration curve from storm record

Engineering Hydrology · Chapter 2: Precipitation

- Asked in: 2075 Chaitra, 6 marks
- Video: [Maximum Intensity and Depth of Rainfall](https://www.youtube.com/watch?v=T2-4Nn0JZWs) — Revit for Civil Engineers
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/intensity-duration-30min-5hr
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-2

## Question

The rainfall depth with time during a storm at a station is given below. Compute maximum average intensities of the rainfall for durations 30 minutes, 1 hr, 2 hr, and 5 hr and plot the resulting intensity duration curve.

| Time (hr) | 06:00 | 06:30 | 07:00 | 07:30 | 08:00 | 08:30 | 09:00 | 09:30 | 10:00 | 10:30 | 11:00 | 11:30 | 12:00 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rainfall (mm) | 0 | 6 | 6 | 5 | 8 | 5 | 9 | 13 | 6 | 4 | 3 | 2 | 0 |

## Short answer

Maximum consecutive depths are divided by duration: 13 mm in 0.5 h gives 26.0 mm/h; 22 mm in 1 h gives 22.0 mm/h; 35 mm in 2 h gives 17.5 mm/h; 65 mm in 5 h gives 13.0 mm/h.

## Answer

The maximum average intensity for a duration $D$ is the greatest rainfall depth in any $D$ consecutive hours divided by $D$. Rainfall in each 30-min interval (mm): 6, 6, 5, 8, 5, 9, 13, 6, 4, 3, 2, 0 (total 67 mm).

| Duration | Critical period | Max depth (mm) | Max intensity (mm/h) |
|---|---|---|---|
| 30 min | 09:00-09:30 | 13 | 26.0 |
| 1 h | 08:30-09:30 | 22 (9+13) | 22.0 |
| 2 h | 07:30-09:30 | 35 (8+5+9+13) | 17.5 |
| 5 h | 06:00-11:00 | 65 | 13.0 |

Checks: 2 h = 8 + 5 + 9 + 13 = 35 mm; 5 h = 6+6+5+8+5+9+13+6+4+3 = 65 mm (the five-hour window starting 06:00; the window 06:30-11:30 gives only 61 mm).

**Intensity-duration curve:** plot duration (x-axis) against maximum intensity (y-axis):

```text
 mm/h
 26 |*
 22 |   *
 17.5|        *
 13 |                       *
    +------------------------
     0.5   1    2         5   h
```

The curve falls with duration because the intense part of the storm is spread over a longer time.

**Answer: 26.0, 22.0, 17.5 and 13.0 mm/h for 30 min, 1 h, 2 h and 5 h.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is the maximum average intensity for a duration D computed?
   A. Greatest depth in any D consecutive hours divided by D
   B. Total storm depth divided by D
   C. Average of all 30-min depths times D
   D. Depth in the first D hours divided by D
   Answer: A. Take the critical window of length D with the greatest depth and divide by D. (Key point: Maximum average intensity)

2. What is the 30-min maximum intensity?
   A. 13 mm/h
   B. 26 mm/h
   C. 22 mm/h
   D. 6.5 mm/h
   Answer: B. Max 30-min depth is 13 mm (09:00-09:30), so 13/0.5 = 26 mm/h. (Key point: 30-minute maximum)

3. Why is the 5-h depth 65 mm and not 61 mm?
   A. Both windows are equal
   B. The 61 mm window is the correct one
   C. The 06:00-11:00 window gives the greatest depth; 06:30-11:30 gives only 61
   D. Rainfall after 11:00 is excluded
   Answer: C. The maximum over all 5-h windows is 65 mm (06:00-11:00), so intensity 13 mm/h. (Key point: 5-hour window)

4. Why does maximum intensity fall with longer duration?
   A. Rain gauges under-record
   B. Less rain falls overall
   C. The mass curve flattens to zero
   D. The intense part of the storm is averaged over a longer time
   Answer: D. The peak burst is diluted by lighter rain in longer windows. (Key point: Shape of curve)

## Related in Engineering Hydrology

- [Hyetograph and intensity-duration curve, 6:00-12:00 storm](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ahyetograph-intensity-duration-6to12) — Engineering Hydrology, chapter 2
- [Intensity-duration graph from mass curve ordinates](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aintensity-duration-15-180min) — Engineering Hydrology, chapter 2
- [Maximum rainfall intensity for 1, 3, 5 hr](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Amax-intensity-1-3-5hr-7am) — Engineering Hydrology, chapter 2
- [Hyetograph and intensity-duration curve, Lumle tipping bucket](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Atipping-bucket-lumle) — Engineering Hydrology, chapter 2
- [Mass curve, hyetograph, depth-duration curve](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Amass-curve-hyetograph-mdd) — Engineering Hydrology, chapter 2
- [Intensity-duration curve and depth-area curve](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aidf-depth-area-curve) — Engineering Hydrology, chapter 2

## Related in other subjects

- [Techniques for average depth of rainfall](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aaverage-rainfall-techniques) — Hydro Power, chapter 2