Allied & ICAR Exam Bank • ALLIED_1181 MCQ • 1 Mark

Section 4: Soil and Water Conservation Engineering

Hydrology and Runoff

Subtopic: Gumbel's Flood Frequency

Question Statement:

In Gumbel's extreme value Type I distribution for flood frequency analysis, the reduced variate $y_T$ corresponding to return period $T$ is given by:

Options:

  • (A) y_T = -\ln\left(\ln\left(\frac{T}{T - 1}\right)\right)
  • (B) y_T = \frac{T}{T - 1}
  • (C) y_T = \ln(T)
  • (D) y_T = \exp(T)

Answer Key:

A

Step-by-Step Solution & Explanation

The cumulative distribution is $F(x) = \exp(-\exp(-y))$. For exceedance probability $1/T$, $F(x) = 1 - 1/T = \frac{T-1}{T} \implies -y = \ln(-\ln(F)) \implies y_T = -\ln\left(\ln\left(\frac{T}{T-1}\right)\right)$.
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