In the Gumbel Extreme Value Type I distribution for annual maximum floods, the flood magnitude QT at return period T is:
Choose the correct answer
QT = Qmean + K x S (where K = Gumbel frequency factor = -(sqrt(6)/pi)(0.5772 + ln(ln(T/(T-1)))) approximately)
QT = Q_median only
QT = Q50 for all T
QT = sigma(Q) x T
Correct Answer
A. QT = Qmean + K x S (where K = Gumbel frequency factor = -(sqrt(6)/pi)(0.5772 + ln(ln(T/(T-1)))) approximately)
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Gumbel: y_T = -ln(-ln(1 - 1/T)); Q_T = Q_bar + (y_T - y_n)/S_n x sigma_Q, where y_n, S_n = Gumbel reduced mean and standard deviation (tables for sample size n). For T = 50: y_50 = 3.902. Used for annual maximum series (highest flood per year).
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