---
title: "Application of probability plots"
subject: "Engineering Hydrology"
chapter: 6
key: "semester_5/engineering_hydrology:probability-plots-application"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/probability-plots-application
site: BCT Engineering
---

# Application of probability plots

Engineering Hydrology · Chapter 6: Flood Hydrology

- Asked in: 2080 Bhadra, 3 marks
- Video: [Using Probability for Hydrologic Analysis](https://www.youtube.com/watch?v=i5p7D30exUw) — Videos produced by Peter Rogers
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/probability-plots-application
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-6

## Question

Discuss application of probability plots with figure.

## Short answer

A probability plot graphs event magnitude against exceedance probability/return period on specially scaled paper so that a chosen distribution plots as a straight line. It is used to estimate design floods by extrapolation, assess distribution fit, find return period of observed events, and analyze risk and reliability.

## Answer

A **probability plot** shows the magnitude of an event (e.g. flood or rainfall) against its probability of exceedance, or return period, on a paper designed so that the assumed distribution plots as a **straight line** (normal, log-normal, Gumbel paper). Plotting positions are $P=m/(N+1)$ or $T=(N+1)/m$.

```text
 Q
  |                     o  <- extrapolated
  |                  /
  |               o/
  |            o /
  |         o  /
  |      o   /
  |   o    /     (best-fit line)
  +--+-----+-----+-----+---- T (yr) or P (%)
    1.1    2     10    100
```

#### Applications
1. **Flood estimation:** read the flood of a required return period (e.g. 50 or 100 years) by extending the straight line beyond the record (extrapolation) for design of dams, bridges and culverts.
2. **Choice of distribution:** the closeness of the points to the line shows whether Gumbel, normal, log-normal or log-Pearson III fits the data.
3. **Return period of a past event:** read T for an observed flood or rainfall.
4. **Risk and reliability:** the probability of a design value being exceeded in the structure's life.
5. **Design rainfall and low-flow (drought) analysis,** and comparison between stations or regions.
6. **Checking the parameters,** e.g. the mean flood plots at about T = 2.33 years on Gumbel paper.

## Check yourself

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

1. What is special about a probability plot?
   A. It uses time on x
   B. The assumed distribution plots as a straight line
   C. It shows hydrographs
   D. Everything plots as a circle
   Answer: B. Probability paper is scaled so the chosen distribution is linear. (Key point: Purpose)

2. How is a design flood read?
   A. Average the points
   B. Count points
   C. Extend the best-fit line to the required T
   D. Take the maximum
   Answer: C. Extrapolation gives design floods beyond the record. (Key point: Extrapolation)

3. What does closeness of points to the line show?
   A. Catchment area
   B. How well the distribution fits
   C. Gauge location
   D. Rainfall depth
   Answer: B. Points scattered from the line suggest another distribution fits better. (Key point: Choice of distribution)

## Related in other subjects

- [Interpret box plots of four plants](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Amultiple-box-plots-four-plants) — Probability and Statistics, chapter 1
- [ANOVA table: wheat varieties on four plots](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Aanova-wheat-varieties-plots) — Probability and Statistics, chapter 6