Methodology
Exceedance probability
metric.exceedance.probability
Definition
The chance that the river will rise above this flood level somewhere in the forecast period, based on running the weather model 40 times with slightly different starting conditions.
Interpretation and pitfalls
How sure are we that the river will rise above this level? This number tells you what fraction of our 40 forecast runs predicted a flood at this level.
We run the forecast 40 times with slightly different starting weather conditions. Some runs predict heavy rain, some predict less. If 15 of those 40 runs show the river rising above the **HQ10** level (the level you'd expect in a once-every-10-years event), we report a 38% exceedance probability.
It is not a 38% chance of flooding
A 38% exceedance probability is **not** the same as a 38% chance of flooding. It's the share of our forecast scenarios that crossed the line — not a literal probability of nature itself.
The number has wide uncertainty
With only 40 forecasts to sample from, the uncertainty in this number is ±10–15 percentage points. A reported 38% could really be anywhere from 23% to 53%.
Formula
Empirical first-crossing exceedance probability from the 40-member ICON-EPS ensemble at threshold Q_T.
This is the empirical probability under the ensemble's implicit sampling distribution. The 40 members are perturbed via LETKF-based initial-condition perturbations and SPPT stochastic physics, so they sample initial-condition and model uncertainty but not parameter or structural uncertainty.
Finite-sample binomial confidence intervals at N=40 are non-trivial. For p̂ = 0.5, the 95% CI ≈ [0.34, 0.66]. For decision-relevant thresholds (p̂ near a cost–loss threshold), bootstrap the CIs and report them.
Calibration is suspect for rare events
At small ensemble size, calibration is suspect for rare events. Consider a Brier-score decomposition (Reliability − Resolution + Uncertainty) on historical verification before trusting probabilities below 10% or above 90%.
References
- Hersbach, H. (2000). Decomposition of the continuous ranked probability score for ensemble prediction systems. Weather and Forecasting, 15(5), 559–570.
- DWD (2024). ICON-EPS Documentation — Numerical Weather Prediction Models.