IDF Curves from Raw Rain — Gumbel (EV1)

OpenHydroLab · Real Met Office gauge — Drumalbin 00987, Lanarkshire (MIDAS-Open hourly rain, 1991–2024). Every number on screen is computed live from the embedded record — nothing is faked.

① Extract annual maxima (AM)

How the dataset is prepared, per duration D:
  1. QC the years — keep only ≥90 % complete (27 of 34 survive).
  2. Slide a D-hour window over the hourly record; keep the wettest position.
  3. Intensity = window depth ÷ D. One value per year → the AM series.
Dry spells fast-forward automatically. The window scan replicates the published extraction exactly — each finished pass is checked against the archived AM value.

② Frequency — design point

④ Design catchment — Rational method

Aha demo: in stage ① play the 1-h pass, then the 24-h pass — the winning windows sit in different storms (an August cloudburst vs a December front): longer windows scoop more depth but lower intensity. Then in stage ④ look at the Qp(D) curve: it peaks exactly at D = tc — shorter storms never wet the whole catchment, longer storms are weaker. That is why the design storm lasts tc.

Dataset — Drumalbin 00987

Record (hourly)1991–2024
Usable years (≥90 %)27 of 34
AM durations1·2·3·6·12·24 h
Extraction check0 / 6 verified
Sub-hourly durations (15–30 min) would need pluviograph data — an hourly gauge cannot resolve them.

② Gumbel fit (MoM) at D =

α = (√6/π)·σ ≈ 0.7797σ,  ξ = μ − 0.5772α
Mean intensity μ
Std dev σ (n−1)
Scale α
Location ξ
i_T = ξ + α·y_T,  y_T = −ln[−ln(1−1/T)]
Reduced variate y_T
Design intensity i_T
Design depth i_T·D

Risk over the design life

P(X≥1) = 1 − (1−p)ⁿ,  p = 1/T
Annual probability p
Exactly once in n yr
Exactly twice in n yr
At least once in n yr
Binomial P(X=r) = C(n,r)·pʳ(1−p)ⁿ⁻ʳ. Example 4 (T=50): n=20 → 0.272; twice, n=15 → 0.032; ≥once, n=20 → 0.332.

③ Fitted IDF equation (Sherman)

i = a·Tm / (D + b)n
a
m
b
n
RMSE over 36 points

④ Rational method Qp = C·i·A/3.6

t_c = 0.0195·L0.77·S−0.385 min (Kirpich)
Time of conc. t_c
Storm duration D
i(D, T) from IDF
Peak discharge Q_p
SI unit cross-check
P(≥1 exceed. in n yr)