Flood Frequency

Gumbel: yT = −ln(−ln(1 − 1/T)). KT = (yT − ȳN)/σN, with ȳN, σN from Gumbel reduced variate tables (here approximated by ȳN ≈ 0.5236, σN ≈ 1.0628 for moderate N). Q_T = x̄ + KT·σ. Log-Pearson III: take log of data, x̄_log, σ_log, Cs. K = K(T, Cs) — Wilson-Hilferty approx K = z + (z²−1)·Cs/6 + ... Q_T = 10^(x̄_log + K·σ_log) (here we approximate using the linear data values for simplicity).