Flood Frequency with a Short and Inconsistent Record
A river has 22 years of annual peak-flow records. The two highest peaks (3,100 and 2,850 m³/s) occurred in the last 5 years; the rest range from 400 to 1,600 m³/s. A log-Pearson III fit to all 22 years gives a 100-year flood of 2,600 m³/s. A dam was built upstream 12 years ago, and the catchment above the gauge is now regulated. A bridge designer wants to use the 2,600 m³/s figure directly.
1. Evaluate the appropriateness of applying the 22-year log-Pearson III result directly to the bridge design.
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Several problems compound:
- Record length: 22 years is short. A 100-year estimate is an extrapolation well beyond the data; confidence intervals are very wide (often ±40% or more).
- Non-stationarity: the dam was built 12 years ago and the two largest peaks are in the last 5 years. Regulated catchments change the peak distribution - usually reducing peaks, but the recent large events contradict a simple reduction and may reflect changed routing, spillway releases, or a wetter period.
- Inconsistency: a fitted 100-year value of 2,600 m³/s is lower than two observed peaks (3,100 and 2,850). A distribution that predicts a rarer event smaller than events already seen is suspect - likely the fit is distorted by the many low values or by the skewed tail.
Judgement: do not use 2,600 m³/s directly. The record mixes pre- and post-dam conditions and the fitted value conflicts with the observed maxima. The design should at minimum use the observed maximum as a floor and treat the fitted value with explicit uncertainty.
2. Propose how you would restructure the analysis and what value you would carry forward as a defensible design basis.
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Restructuring:
- Split the record at dam completion: 10 years pre-dam, 12 years post-dam. Analyse the post-dam period separately for current conditions, but note 12 years is far too short for a 100-year estimate.
- Do not extrapolate from 12 points. Instead, use the post-dam record to characterise the change (ratio of post- to pre-dam peaks for comparable events) and apply that adjustment to a longer regional or pre-dam dataset.
- Regional flood-frequency analysis: pool with nearby unregulated gauges to lengthen the effective record, then transfer by catchment-area scaling.
- Check the tail: the two ~3,000 m³/s events are real and must be honoured. A fit that ignores them is not credible.
Defensible basis: carry forward a design peak of at least 3,100 m³/s (the observed maximum) as a lower bound, with an explicit freeboard/uncertainty allowance, and state clearly that the 100-year estimate is uncertain. Recommend a sensitivity range (e.g., 3,100–4,000 m³/s) rather than a single number, and require the designer to justify the chosen value against the observed maxima.