eduKateSG · Hydrology · The Gold Standard of Education
Transfer flood evidence between catchments without pretending they are interchangeable
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Full chapter index · Independent practice · Hydrology subject guide
An ungauged catchment has no long local record, yet a bridge, culvert or floodplain decision still needs an estimate. Regional flood-frequency analysis borrows information from gauged catchments that are sufficiently similar. Its value comes from pooling evidence; its danger comes from transferring a relationship across a boundary where it no longer holds.
This guide explains homogeneous regions, the index-flood method, regional regression, mixed gauged–regional estimates and extrapolation. The numerical examples are fictional. They show the arithmetic and the audit trail, not a design value for any real site.
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Full chapter index
See the mechanism · Chapters 1–2
Build the worked model · Chapters 3–5
Test what changes · Chapters 6–8
Check evidence and limits · Chapters 9–10
Practise and continue · Chapters 11–12
CHAPTER 1 OF 12 · See the mechanism
1. Why regionalisation is a model, not a shortcut
A short record contains few rare floods. A 20-year gauge can observe ordinary variability but gives unstable estimates for a one-percent annual exceedance probability. Nearby gauges provide additional information if their flood-generating processes, measurement quality and catchment controls are comparable.
Regionalisation assumes some features can be shared. An index-flood approach may share a dimensionless frequency curve while allowing each catchment its own scale. A regression approach relates flood quantiles to drainage area, rainfall, slope, storage, soils or urbanisation.
The region is therefore part of the model. Administrative borders and map proximity are not enough. State why the stations are pooled, which differences remain, and how a site that does not fit will be handled.
Evidence check: for Why regionalisation is a model, not a shortcut, preserve the observation before the interpretation. Record the decision quantity, annual probability and design horizon. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
Begin with the quantity needed: peak discharge, flood volume, stage or duration. State whether the probability is annual exceedance probability, recurrence interval shorthand or an event-rate measure. Do not mix annual maxima with partial-duration estimates without converting them to a common scale.
A “100-year flood” is better described as a flood magnitude with a one-percent chance of being exceeded in a year under the model. It is not scheduled once per century. Multiple exceedances can occur in a short period.
Record the relevant design life and consequence. A screening estimate for a field visit can tolerate different uncertainty from a safety-critical design. The same regional equation should not silently serve every decision.
Evidence check: for Define the decision and probability scale, preserve the observation before the interpretation. Record gauge quality, missing periods and rating changes. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
For each gauge, record period of record, missing intervals, rating-curve changes, regulation, diversions, land-use change and whether historic floods were incorporated. Use a consistent extraction rule and quality-control process.
Catchment descriptors must also be reproducible. Drainage area depends on the outlet and digital elevation model. Rainfall statistics depend on period and gridded product. Urban fraction depends on classification date. Store the data version, not only the final number.
Inspect hydrographs and station notes. A long nominal record with an unstable rating may contribute less than a shorter well-measured record. Pooling does not erase systematic error; it can spread it.
Evidence check: for Assemble comparable station data, preserve the observation before the interpretation. Record descriptor definitions, data versions and regulation. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
Let Q_i(T) be the T-year flood quantile at station i and μ_i a site-specific scale such as the mean annual flood. The index-flood model writes Q_i(T)=μ_i q(T), where q(T) is a dimensionless regional growth factor shared by the region.
Suppose three fictional stations have index floods of 100, 160 and 250 cubic metres per second. At a selected probability, their dimensionless sample ratios are 1.80, 1.72 and 1.88. A regional factor might be estimated near 1.80 with uncertainty. An ungauged site with an estimated index flood of 130 would then have a corresponding quantile near 234, before accounting for estimation error.
The arithmetic is easy. The scientific task is defending the shared q(T). Plot each station’s dimensionless curve and residuals. If one station has snowmelt floods while the others are tropical rainfall catchments, scaling may not create homogeneity.
| Station | Index flood | Selected quantile | Dimensionless ratio |
|---|---|---|---|
| A | 100 | 180 | 1.80 |
| B | 160 | 275 | 1.72 |
| C | 250 | 470 | 1.88 |
| Target | 130 | 234 | 1.80 regional |
Evidence check: for The index-flood idea, preserve the observation before the interpretation. Record dimensionless ratios and the chosen site scale. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
Homogeneity does not mean identical hydrographs. It means the remaining differences are consistent with the regional model and sampling variability. Compare climate regime, flood season, geology, storage, urbanisation and regulation. Use formal discordancy and heterogeneity measures where the adopted method defines them.
Avoid circular selection: choosing only stations whose fitted curves already agree can make the final test look better than it is. Define physical inclusion rules first, then examine statistical diagnostics. Document exclusions and sensitivity to borderline stations.
Large regions increase sample size but can blend different mechanisms. Small regions preserve process similarity but leave high sampling uncertainty. Treat the boundary as a sensitivity analysis rather than a fact drawn once on a map.
Evidence check: for Test regional homogeneity, preserve the observation before the interpretation. Record physical inclusion rules before statistical diagnostics. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
At a gauged site, the index flood may be estimated from the local annual maxima, sometimes with weighting or bias correction. At an ungauged site, it is often predicted from a regression on catchment descriptors. A log-linear form might relate log μ to log area, rainfall and storage.
Imagine a fictional fitted relation μ=3.2 A^0.72 R^0.45 S^-0.20 with variables defined in specific units. Substituting an ungauged catchment’s descriptors yields a scale estimate. Unit changes, zero storage and descriptor error can invalidate a mechanical calculation, so the equation must travel with definitions and applicability limits.
Regression residuals quantify unexplained variation among calibration catchments. Prediction uncertainty for a new site includes coefficient uncertainty, residual variance and descriptor uncertainty. Reporting only the point estimate hides the main reason regionalisation is needed.
Evidence check: for Estimate the site scale, preserve the observation before the interpretation. Record regression residuals and descriptor uncertainty. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
An alternative fits a separate equation for each annual exceedance probability, such as Q_0.01 as a function of catchment properties. Official regional studies often publish equations, standard errors, parameter ranges and maps of applicable regions.
Separate equations need not produce a perfectly coherent frequency curve. If independently fitted quantiles cross, review the method. An index-flood model has internal scaling coherence but may fit poorly where growth curves differ. Choose by diagnostics and the authoritative regional study, not convenience.
The attached fictional table compares estimates from a local short record, an index-flood model and quantile regression. Differences are not votes to average blindly. They point to assumptions that need investigation.
| Annual exceedance probability | Short local record | Index-flood model | Regional regression |
|---|---|---|---|
| 0.20 | 142 | 151 | 148 |
| 0.10 | 171 | 184 | 179 |
| 0.02 | 235 | 268 | 251 |
| 0.01 | 262 | 302 | 279 |
Evidence check: for Regional regression for flood quantiles, preserve the observation before the interpretation. Record published applicability ranges and model coherence. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
At a short-record gauged site, local data and the regional model both contain information. A weighted estimate can reduce variance when weights reflect their relative precision and dependence. The exact procedure should follow the adopted regional method.
Do not treat the regional estimate as independent if the target gauge helped fit it. A leave-one-out regional prediction is useful for validation. If the local estimate departs sharply from neighbours, check rating curves, outliers, regulation and catchment descriptors before deciding it is merely noisy.
Historic flood information can extend the effective record, but it has perception thresholds and dating uncertainty. Include it through a method that represents censored or interval information rather than pretending every unobserved year had no large flood.
Evidence check: for Combine gauged and regional evidence, preserve the observation before the interpretation. Record dependence between local and regional evidence. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
Check every descriptor against the calibration range. A catchment twice as large as any study basin, far more urban or dominated by a reservoir is an extrapolation even if it lies inside the mapped region. Regression software will still return a number; the number may have no demonstrated error behaviour.
Distance from the centre of the predictor space can be more revealing than any single range. A site may be ordinary in area and rainfall separately but unusual in their combination. Flag leverage and show the nearest comparable calibration stations.
If no defensible region applies, use a broader uncertainty range, collect targeted measurements or build a process model with independent calibration. Manufacturing precision is not a substitute for data.
Evidence check: for Extrapolation and the edge of the map, preserve the observation before the interpretation. Record leverage and distance from calibration catchments. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 10 OF 12 · Check evidence and limits
10. Nonstationarity, regulation and change
Regional equations usually describe a stated historical period under an assumption about how flood-generating processes behave. Urban growth, wildfire, drainage alteration, reservoir operation and climate change can shift the relationship. A long record crossing a change point is not automatically more representative of the future.
Separate an attribution question from a design question. For attribution, preserve pre-change and post-change evidence. For design, use guidance that explicitly handles current or projected conditions. Do not append an arbitrary percentage to a regional estimate without a documented scenario method.
Reservoirs can reduce some peaks and increase others through operating rules or coincident releases. Treat regulated and unregulated basins as different populations unless the regional method models regulation.
Evidence check: for Nonstationarity, regulation and change, preserve the observation before the interpretation. Record change points, land use and operating rules. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
Practice one: an ungauged basin lies inside a published region, but its urban fraction is 70 percent while the calibration maximum is 18 percent. The equation is an extrapolation. Seek an urban method or targeted data rather than hiding the mismatch.
Practice two: one gauge has a dimensionless one-percent quantile of 3.1 while every other station lies between 1.6 and 2.0. Check data quality and flood mechanism, then repeat the regional fit with and without it. Exclusion requires a process reason, not a desire for a smoother curve.
Practice three: a ten-year local record gives a much lower estimate than the regional model. Examine whether the decade was unusually dry, whether the regional model includes the site, and how the adopted weighting procedure handles sampling variance.
Transfer the framework to drought, low flow or rainfall intensity only after redefining the statistic and regional mechanism. Similar mathematics does not guarantee similar hydrology.
Evidence check: for Independent practice and transfer, preserve the observation before the interpretation. Record the donor station that is genuinely most comparable. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
What is an index flood?
It is a site-specific scale used with a dimensionless regional growth curve. The exact estimator must be defined by the method.
Is the nearest gauge always the best donor?
No. Similar flood mechanisms and catchment controls can matter more than straight-line distance.
Can I use a regional equation outside its predictor range?
It will produce a number, but its published accuracy may not apply. Label the extrapolation and seek another line of evidence.
Why show several estimates?
Agreement can support robustness; disagreement reveals sensitivity to record length, pooling and model form. Choose through a declared method rather than averaging by intuition.
Authoritative starting points include the USGS National Streamflow Statistics regional application, the USGS index-flood methods reference, and a worked USGS regional flood-frequency study. Use the official study and current agency guidance for the real location.
Continue with partial-duration series and independent flood peaks, paired catchments and attribution, and flow-duration curves and drought sequences. The next useful move is a one-page transfer sheet listing the target descriptors, calibration ranges, donor stations, residuals and the condition that would make the region unacceptable.
Evidence check: for FAQ, sources and the next useful move, preserve the observation before the interpretation. Record the boundary at which transfer should stop. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.