What it does
A “100-year flood” is the flow with a 1 % chance of being equalled or beaten in any year. It is estimated by fitting a probability distribution to the largest flow of each year at a river gauge, the annual maximum series, and reading off the flow for the return period you need.
This tool fits four common distributions side by side:
- GEV (generalised extreme value) by L-moments, used in the UK and many other countries.
- Log-Pearson type III on the logarithms of the flows, the long-standing US method, with the station skew or one you type (for example a regional skew).
- Gumbel, by L-moments and by ordinary moments, the simplest choice.
It shows the flood for any return period with a bootstrap range, the return period of a flow you give, and the chance of at least one such flood over a span of years.
How to use it
- Paste a year and the year’s peak flow per row, or open a CSV or text file. A single column of peaks also works. Use 10 to 1,000 years.
- Type the flow unit for the labels.
- Choose the main distribution. All four appear in the table and chart; the main one gets the range and the headline.
- For log-Pearson III, leave the skew blank to use the record’s own skew, or type a regional skew.
- Type the return period you want, a flow to find its return period, and a span of years (such as a mortgage or a design life) for the chance of a flood in that time.
What the results mean
- The chart has the recorded peaks at their plotting positions (the largest of n years plots at n + 1 years with Weibull) and the four fitted curves. Where the curves agree, the answer is fairly safe; where they spread apart, the choice of distribution matters.
- The range comes from 1,000 resampled records. A 40-year record cannot pin down a 500-year flood, and the range says so.
- L-skewness τ3 describes the shape: about 0.17 for a Gumbel shape, higher for records with a few very large floods.
- The Grubbs-Beck screen flags peaks that look too large or too small for the rest; check them (a dam break, a gauge fault, a dry year) rather than deleting them blindly.
- The chance in a span of years is 1 − (1 − 1/T)^N: a 100-year flood has about a 26 % chance of happening at least once in 30 years.
Worked example
The made-up record has 40 annual peaks from 1985 to 2024, averaging 484 m³/s, with a largest of 920 m³/s. L-skewness is 0.169, close to the Gumbel shape, so the GEV shape k is almost 0. The GEV gives a 100-year flood of about 1,016 m³/s; log-Pearson III with the station skew (−0.05) gives 987 m³/s, Gumbel by L-moments 1,017 m³/s and by moments 996 m³/s. A flow of 800 m³/s has a return period of about 20 years (GEV) or 21 years (log-Pearson III). No outliers are flagged.
FAQ
Which distribution should I use? Follow the guidance in your country: GEV or generalised logistic in the UK, log-Pearson III in the US, GEV or LP3 in Australia and Canada. If they disagree a lot, the record is too short to tell, and the range is the honest answer.
Can I use daily flows? No. Use one value per year, the largest. Taking several floods from one year breaks the independence the method assumes. Peaks-over-threshold analysis is a different method.
Does it allow for climate change? No. It assumes the floods come from an unchanging distribution. Check the record for a trend first (the Trend and anomaly analyser can help) and follow local guidance on climate allowances. For design, use the official method and a qualified engineer.
Where the numbers come from
- L-moments and the GEV fit by Hosking's (1985) approximation for the shape: Hosking, J. R. M. and Wallis, J. R. (1997), Regional Frequency Analysis: An Approach Based on L-Moments (equations only). Gumbel by moments and L-moments and the Kite standard error: standard hydrology texts such as Chow, Maidment and Mays (1988), Applied Hydrology.
- Log-Pearson type III by moments of the log flows, the station skew, and the Grubbs-Beck outlier screen with its approximate K_N equation: US Interagency Advisory Committee on Water Data, Bulletin 17B (1982), public domain. The newer Bulletin 17C (2019) method (expected moments and the multiple Grubbs-Beck test) is not reproduced.
- Plotting positions (Weibull, Gringorten, Cunnane) and the percentile bootstrap: standard statistics. The Pearson III frequency factors are computed exactly from the gamma distribution, not read from printed tables.
- Checked against SciPy (pearson3, gumbel_r, genextreme, gammainc) in the tests. The example record is made up, drawn at random by fibub.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-08.