---
title: "IDF curve and DAD curve"
subject: "Engineering Hydrology"
chapter: 2
key: "semester_5/engineering_hydrology:idf-dad"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/idf-dad
site: BCT Engineering
---

# IDF curve and DAD curve

Engineering Hydrology · Chapter 2: Precipitation

- Asked in: 2079 Bhadra, 3+3 marks; 2079 Baisakh, 2+2 marks (asked 2 times)
- Video: [DAD & IDF Curves | Engineering Hydrology](https://www.youtube.com/watch?v=lz55t5M8kOA) — APSEd
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/idf-dad
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-2

## Question

Explain about IDF curve and DAD curve.

## Short answer

IDF curves relate rainfall intensity to duration and return period, derived from frequency analysis; intensity decreases as duration increases. DAD curves show average precipitation depth over an area for different durations; depth decreases with increasing area. Both are used in design storm estimation.

## Answer

#### IDF curve (Intensity-Duration-Frequency)
An IDF curve shows the relationship between **rainfall intensity** $i$, **duration** $D$ and **frequency (return period)** $T$ of storms at a place. Intensity decreases with duration, and for the same duration a rarer storm (higher $T$) has a higher intensity.

**Development:** From annual maximum rainfall of various durations (5 min to 24 h), a frequency analysis (Gumbel, Log-Pearson III) gives the depth for each return period. Intensity = depth / duration is plotted against duration on log scales, one curve per return period.

```text
 i (mm/h)
  |\
  | \\   T = 100 yr
  |  \\\  T = 25 yr
  |    \\\ T = 5 yr
  +-------------- D (min)
```

An empirical form is $i = \dfrac{K T^x}{(D + a)^n}$. IDF curves are used to get design rainfall for storm drains, culverts and small catchments (rational method).

#### DAD curve (Depth-Area-Duration)
A DAD curve shows the **average rainfall depth** over an area for storms of different **durations**. For a given duration, the average depth decreases as the area increases, and for the same area a longer duration gives a larger depth.

**Development:** From isohyetal maps of a storm for 6, 12, 24 h, etc., the average depth within each isohyet and the area enclosed are computed, and plotted as depth against area for each duration.

```text
 Depth
  | \____  24 h
  |  \____ 12 h
  |   \____ 6 h
  +-------------- Area (km2)
```

DAD curves are used to estimate the probable maximum precipitation (PMP) and the design storm for large catchments, flood control and spillway design.

## Check yourself

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

1. For a given return period, intensity with duration:
   A. Decreases as duration increases
   B. Increases
   C. Is constant
   D. Is zero
   Answer: A. Longer storms are less intense. (Key point: IDF trend)

2. For same duration, a higher return period gives:
   A. Lower intensity
   B. Higher intensity
   C. Same intensity
   D. No rain
   Answer: B. Rarer storms are heavier. (Key point: Return period)

3. In a DAD curve, for a given duration, average depth:
   A. Increases
   B. Is constant
   C. Decreases as area increases
   D. Equals zero
   Answer: C. Rain spreads thinner over large area. (Key point: DAD trend)

4. DAD curves are used to estimate:
   A. Storm drain size for small catchments
   B. Gauge number
   C. Evaporation
   D. PMP and design storm for large catchments
   Answer: D. IDF is for small catchments. (Key point: Use)

## Related in Engineering Hydrology

- [DAD curve procedure and isohyetal area data](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Adad-curve-procedure-isohyetal) — Engineering Hydrology, chapter 2
- [Presentation of precipitation data, IDF curve](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apresent-precip-data-idf) — Engineering Hydrology, chapter 2
- [Peak discharge by rational method with IDF equation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Arational-idf-20ha-25yr) — Engineering Hydrology, chapter 6