Gumbel distribution is used to model
- ADaily rainfall
- BMonthly temperature
- CAnnual maximum floodCorrect
- DDaily evaporation
Solution
Concept
Probability distribution used to model extreme values, specifically annual maximum floods in hydrology.
Step-by-step solution
1. Identify the purpose of flood frequency analysis in hydrology. 2. Recognize that Gumbel's Extreme Value Distribution is standard for analyzing extreme events like annual maximum floods. 3. Match with the correct option.
Explanation
The Gumbel distribution, also known as the Extreme Value Type-I distribution, is widely used in hydrology for predicting extreme hydrological events such as annual maximum floods, maximum rainfall, and maximum wind speeds.
Why the other options are wrong
A: Daily rainfall is typically modeled using Log-Pearson Type III or normal distributions. B: Monthly temperature follows a normal distribution. D: Daily evaporation is usually modeled using normal or log-normal distributions.
Shortcut
Gumbel = Greatest/Maximum flood.
Common mistake
Confusing Gumbel distribution with normal distribution used for mean values.
Correct answer: C) Annual maximum flood