Flood-frequency prediction: For estimating floods of a specified return period at a site using annual-maximum series, which of the following methods is generally regarded as the most reliable among the choices given?

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:

  • Annual maximum (or peak-over-threshold) discharge records are available.
  • Objective is to estimate a quantile associated with a chosen return period.


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:

  • Unit hydrograph: A runoff transformation tool; not a statistical frequency method.
  • California method: Empirical and regional; less reliable than analytical fitting of extremes.
  • Rational method without frequency: Lacks statistical basis for return period selection.
  • None of these: Incorrect because Gumbel is suitable.


Common Pitfalls:

  • Confusing hydrologic transformation tools with statistical frequency tools.
  • Applying empirical regional equations outside their calibration region.


Final Answer:
Gumbel’s analytical method (extreme value distribution)

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