Difficulty: Easy
Correct Answer: Gumbel’s analytical method (extreme value distribution)
Explanation:
Introduction / Context:
Design discharges for bridges, culverts, and spillways often require flood-frequency analysis rather than just runoff transformation methods. Statistical methods based on extreme value theory are preferred to estimate discharges for specified return periods (e.g., 50-year, 100-year floods).
Given Data / Assumptions:
Concept / Approach:
Gumbel’s method (Type I Extreme Value) fits a theoretical distribution to annual maxima, enabling extrapolation to desired return periods. In contrast, a unit hydrograph converts rainfall to runoff (not a frequency tool), and empirical regional formulae (e.g., California method) are rough and site-limited.
Step-by-Step Reasoning:
Compile annual maximum flood series.Estimate Gumbel parameters (mean and standard deviation or method of moments).Compute reduced variate and derive design flood for the target return period.
Verification / Alternative check:
For many basins, regional frequency analysis (e.g., Log-Pearson Type III) may be adopted by standards. Among the listed options, however, Gumbel’s method is the most directly intended for frequency estimation of extremes.
Why Other Options Are Wrong:
Common Pitfalls:
Final Answer:
Gumbel’s analytical method (extreme value distribution)
Discussion & Comments