The 'Gumbel distribution' is used in hydrology for:
Choose the correct answer
Normal distribution of daily flows
Frequency analysis of annual extreme events (maximum flood, maximum rainfall) — relates return period to magnitude
Groundwater level fluctuation
Daily water demand forecasting
Correct Answer
B. Frequency analysis of annual extreme events (maximum flood, maximum rainfall) — relates return period to magnitude
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Gumbel (Type I Extreme Value) distribution: used for annual maximum flood/rainfall frequency analysis. CDF: F(x) = e^(-e^(-y)) where y = (x-u)/α (reduced variate). Return period T: y = −ln(−ln(1−1/T)). For T=100 yr: y=4.60. Parameters estimated from mean and SD of annual maxima. Used for: design flood, design storm estimation. Check: plot on Gumbel probability paper (linear fit expected).
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