How Certain Is a Design Flood?

Research question

What can the available national experiments say about uncertainty in a design flood, and where must their interpretation stop? The central question is not how to manufacture one wider bar. It is how to keep unlike evidence legible: method performance across held-out stations, disagreement within the gauging network, sampling within finite AMAX records, and sensitivity to assumptions that have not yet been tested together.

Terminology and taxonomy

Natural uncertainty concerns varying weather, antecedent state and catchment response. Data uncertaintyconcerns measurement, rating, record quality and descriptor evidence.Parameter uncertainty concerns quantities fitted from finite evidence. Structural uncertainty concerns the assumptions in the transfer, pooling or response model. Model-family uncertainty concerns the adopted probability family when more than one family remains plausible.

The natural, data, parameter, structural and model-family uncertainty layers are conceptually separate, but they can overlap and are not assumed independent. A difficult flood measurement can affect a fitted parameter and a validation residual at the same time. “Layer” is therefore an evidence label, not a claim of statistical orthogonality.

Evidence layer 1: population validation scatter

Donor-adjusted SM2025 was evaluated on 918 spatial-cluster held-out stations, with donor availability restricted to the training folds. Its median absolute QMED error was 23.4% and its FSE was 1.538. Those values describe out-of-sample performance across the frozen validation population. They mix whatever residual effects remain in that design; they do not identify a structural component in isolation.

The factor is population cross-validation scatter, not a site-specific confidence interval. Applying it to one example is a useful way to show multiplicative scale, but it does not attach a local coverage level or account for evidence that was not part of that validation statistic.

Evidence layer 2: network self-consistency

Across 85 adjacent same-river pairs, area-scaled QMED disagreement had a median of 12.2%, Q1–Q3 6.6–34.5% and P90 58.8%. This is a network self-consistency diagnostic only. It asks whether paired gauged records agree after a simple area scaling, not how uncertain either member is at a named project site.

River-name pairing is heuristic, and disagreement can reflect several overlapping causes: measurement, non-linear area scaling, tributaries, regulation, differing record periods or genuinely different catchment response. The distribution cannot identify one cause, establish an irreducible floor or be transferred as an individual-site interval.

Evidence layer 3: within-record sampling

The growth revalidation resampled years within each of 874 gauged stations and recomputed the fitted targets. Near the approximately 40-year record length studied, median within-record GF100 sampling variability was about ±13.0%. The experiment isolates one finite-record question more directly than a comparison between different stations.

The result belongs to GF100, the selected cohort and the frozen resampling design. It is not a universal design-flow allowance. It does not include QMED error, network data disagreement, structural assumptions, model-family choice or future non-stationarity.

Worked population factor

For an illustrative estimate of 10.00 m³/s, dividing by 1.538 gives 6.50 m³/s and multiplying by 1.538 gives 15.38 m³/s: approximately 6.5–15.4 m³/s. The separate worked table keeps the formula, rounded result, interpretation and 918-station scope together.

This is factor arithmetic, not an interval calibrated for the example site. The lower and upper values must retain the population-validation label wherever they are reproduced.

Why mechanical combination is invalid

The three numerical results do not share a target. The FSE concerns QMED prediction residuals across held-out stations; the same-river distribution concerns paired network disagreement; and ±13.0% concerns within-record GF100 sampling. Their cohorts, estimands and dependence structures differ.

They are therefore not combined mechanically. Adding 23.4%, 12.2% and 13.0% would treat unlike summaries as commensurate components. Multiplying 1.538 by new factors inferred from the other percentages would assume conversions and independence that have not been established. A joint result would need an explicit probabilistic model, stated covariance assumptions and validation against the quantity it claims to cover; none is supplied by these studies.

Model-family protocol status

A proposed protocol would fit GLO, KAP3 and GEV in parallel to the same frozen evidence, retain valid fits, and report how the resulting growth factors differ while holding the index flood and evidence custody fixed. This would be a sensitivity display, separate from validation scatter and finite-record sampling.

The protocol is not yet demonstrated. The cited artefacts contain no completed parallel-family envelope, so no family range, coverage or performance achievement is claimed here.

Practical reporting pattern

1. State the adopted design-flow estimate, method and evidence date.
2. Report population validation performance with its target, cohort, validation design and sample size.
3. Report site and network data diagnostics as diagnostics, including record quality and reasons they may not transfer.
4. Report finite-record sampling evidence for the statistic actually studied, with its record-length and cohort scope.
5. Report structural and family sensitivities separately, marking unexecuted protocols as open research.
6. Do not publish a combined total unless a joint model, dependence assumptions, coverage target and validation evidence are explicit.

Limitations

• The QMED experiment reports population performance; it does not calibrate the worked factor for the illustrative estimate.
• Same-river pairing is heuristic, area scaling is simplified and the diagnostic does not attribute disagreement to individual causes.
• The GF100 result belongs to the selected 874-station cohort, the approximately 40-year record-length experiment and its within-station resampling design.
• Natural variability and non-stationarity are named in the taxonomy but are not quantified by the three cited experiments.
• Dependence and overlap between evidence layers have not been fitted, so the report supplies no joint uncertainty distribution.
• The proposed GLO/KAP3/GEV comparison has not been executed as a completed family-envelope study.

What we do not conclude

• We do not convert the 918-station FSE into local coverage for the illustrative estimate.
• We do not treat the 85-pair network distribution as an error floor or transfer it to an individual site.
• We do not treat ±13.0% GF100 sampling variability as a universal design-flow allowance.
• We do not add the reported percentages or multiply them into one uncertainty factor.
• We do not assume that natural, data, parameter, structural and family effects are independent.
• We do not present GLO/KAP3/GEV spread as a completed or achieved uncertainty envelope.

Disclosure boundary

This report discloses the three research questions, broad cohort and validation designs, exact aggregate tables, worked-factor arithmetic, interpretations, claim statuses, source revisions and the point at which each conclusion stops. Its evidence sources are the frozen Hydrometric QMED revalidation, same-river network study and growth revalidation only.

It withholds raw station records, exact donor and feature engineering, learned coefficients, per-station residuals, private data-construction mechanics, customer information and deployable workflow logic. That boundary permits audit of the public claims without exposing the implementation needed to reconstruct the proprietary method.