Exceedance Probability Plot
Chart overview
An exceedance probability plot ranks observed annual maxima and plots them against their empirical frequency, then fits extreme value distributions such as Gumbel or GEV to extrapolate return levels for rare events.
Key points
- Civil engineers and hydrologists use it to estimate the 100-year flood discharge, design storm infrastructure, and assess climate-driven changes in extreme event frequency.
- The log-probability axes linearize many extreme value distributions for easy visual assessment of fit.
Example Visualization
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"Create an exceedance probability plot from my annual maximum values. Plot observed data as scatter points using the Weibull plotting position, fit and overlay a Gumbel or GEV distribution curve, add a secondary x-axis showing return period in years, use log scale on the x-axis, and shade the 95% confidence interval."
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Python Code Example
Console Output
Figure saved: plotivy-exceedance-probability.png
Common Use Cases
- 1Estimating the 100-year flood discharge for bridge design from gauge records
- 2Analyzing trends in extreme rainfall intensities under climate change scenarios
- 3Comparing fitted distributions (Gumbel vs. GEV) for wind speed extremes
- 4Reporting design return levels for coastal storm surge assessments
Pro Tips
Use the Weibull formula (rank / (n+1)) for unbiased plotting positions on the empirical points
Always show the 90% or 95% confidence interval to communicate extrapolation uncertainty
Add a secondary top x-axis labeled with return periods (2, 5, 10, 50, 100, 200 years)
Note the period of record length in the title since extrapolation beyond 3x the record is unreliable
Scientific Chart Selection Cheat Sheet
Not sure whether to use a Violin Plot, Box Plot, or Ridge Plot? Download our single-page reference mapping the most-used scientific chart types, exactly when to use them, and the core Matplotlib/Seaborn functions.