eduKateSG · Hydrology · The Gold Standard of Education
Use old flood evidence without turning an uncertain record into a precise story
Choose the explanation you need, or follow all twelve chapters in order.
Full chapter index · Independent practice · Hydrology subject guide
Systematic stream-gauge records are short compared with the recurrence intervals used in some flood decisions. Historical documents, high-water marks and regional information can extend the evidence, but only when the analysis distinguishes what was observed from what would have been noticed.
Bulletin 17C uses the Expected Moments Algorithm, perception thresholds and regional skew to handle this problem within a log-Pearson Type III framework. The central lesson travels beyond one method: absence of a recorded flood is evidence only when the observation system could have detected it.
The numbers below are fictional teaching examples. Real flood-frequency estimates must follow the authoritative regional study, station record and current agency guidance.
Continue from The Gold Standard of Hydrology within The Gold Standard of Education: learning that transfers into life and the How X Works learning library.
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
The systematic period is the interval of regular gauge operation with a defined record of annual peaks. The historical period may begin earlier and contain selected large floods documented by marks, newspapers, surveys or local records.
Do not treat historical years with no listed flood as measured zeros. A town may remember only floods above a bridge deck, while smaller annual peaks went unrecorded. The analysis needs a perception threshold: the level above which a flood would probably have been recorded.
Build a chronology with dates, evidence type, uncertainty and changes in observation. A relocated settlement or newly built bridge can change what was perceptible.
Evidence check: for Separate systematic and historical periods, 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.
Flood-frequency analysis commonly selects one peak per water year at a station. Confirm that peaks belong to the same hydrologic population. Dam construction, diversions, urbanisation or watershed change can divide the record.
Check rating curves and stage-discharge conversions. A historical high-water mark is often a stage observation that must be translated through uncertain channel geometry. Preserve the interval rather than forcing a single discharge.
Distinguish independent rainfall floods from ice jams, dam failures or debris blockages if the adopted method treats them separately. The label “largest flood” does not make mechanisms exchangeable.
Evidence check: for Annual peaks and the analysis population, 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.
CHAPTER 3 OF 12 · Build the worked model
3. Perception thresholds define what absence means
A perception threshold is a discharge or interval above which floods are believed to have been observed during a stated period. Thresholds can vary over time. From 1900–1949, only floods above 800 cubic metres per second may have left reliable evidence; after a gauge opened in 1950, the threshold may be effectively much lower.
For a year with no recorded historical flood, the information is not Q=0. It is that the annual peak likely remained below the applicable threshold. That is censored information.
Support thresholds with evidence: building elevations, newspaper coverage, observer presence, crest-stage marks and search methods. Sensitivity-test plausible alternatives.
Evidence check: for Perception thresholds define what absence means, 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.
The Expected Moments Algorithm can incorporate exact systematic peaks, interval estimates, censored years and perception thresholds. Instead of substituting invented point values for missing floods, it uses the expected contribution consistent with the information available.
Imagine a historical flood estimated between 1,100 and 1,300, followed by 30 years during which any flood above 900 would likely have been recorded and none was. The large interval event and the censored non-exceedance years both inform the distribution.
The attached table shows the information structure. It does not reproduce production software. Use tested implementations and preserve every input flag.
| Period | Information | Perception threshold | Representation |
|---|---|---|---|
| 1970–2025 | Systematic annual peaks | Gauge capability | Exact or interval peaks |
| 1920–1969 | One historical flood in 1938 | 1,000 m³/s | One interval event plus censored years |
| 1870–1919 | No dependable observer record | Unknown | Do not infer non-exceedance |
Evidence check: for Expected Moments Algorithm intuition, 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.
Bulletin 17C fits a Pearson Type III distribution to logarithms of annual peak discharge. The mean, standard deviation and skew of the log values shape the frequency curve. Skew is especially influential in the upper tail.
A station skew estimated from a short record is unstable. One unusually large flood can change it sharply. Regional skew pools information from many suitable stations to estimate the broader tendency.
The distribution is a model, not a physical law. Plot fitted and observed information, examine influential floods and report uncertainty around rare-quantile estimates.
Evidence check: for Log-Pearson Type III and skew, 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.
Bulletin methods combine at-site and regional skew using weights related to their mean-square errors. A precise regional estimate receives more weight; a long, informative station record can contribute more at-site evidence.
Suppose a fictional station skew is 0.40 with MSE 0.25 and regional skew is 0.10 with MSE 0.04. The weighted skew will lie nearer 0.10 because the regional estimate is more precise. Do not average the two values equally.
Regional skew itself depends on station selection, cross-correlation and regression method. Use the published regional value and error for the site; do not borrow from the nearest map label without checking applicability.
| Source | Skew estimate | Mean-square error | Relative influence |
|---|---|---|---|
| Station | 0.40 | 0.25 | Lower |
| Region | 0.10 | 0.04 | Higher |
| Weighted result | Between 0.10 and 0.40 | Method-derived | Closer to regional value |
Evidence check: for Weight station and regional skew, 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.
Very low annual peaks can distort a fitted distribution when the low-flow process differs from the flood process. Bulletin 17C includes procedures for identifying potentially influential low floods rather than applying an arbitrary deletion rule.
Zero or below-threshold values need explicit treatment. A dry channel, a missing record and a peak below a measurement threshold are different observations.
Run the adopted low-outlier procedure and retain sensitivity results. Removing values because they make the fit inconvenient is not analysis.
Evidence check: for Potentially influential low floods and zeros, 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.
A fictional station has systematic annual peaks from 1970–2025. Documents identify an 1938 flood between 1,400 and 1,650. Researchers judge that floods above 1,000 would have been noticed from 1920–1969, while the threshold before 1920 is unknown.
The analysis can use the 1938 interval and the 1920–1969 perception structure. It should not count 1870–1919 as fifty small floods. Those years provide no defensible non-exceedance information.
Repeat the fit with historical thresholds of 900, 1,000 and 1,100. If the one-percent quantile moves substantially, threshold uncertainty is decision-relevant and belongs in the report.
Evidence check: for A worked historical-information audit, 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.
CHAPTER 9 OF 12 · Check evidence and limits
9. Regional skew is not regional flood transfer
Regional skew describes a distribution-shape parameter. Regional regression or index-flood methods transfer quantile or scale information between catchments. They solve related but different problems.
A site can use a regional skew value while estimating mean and standard deviation from its local record. An ungauged site may need a separate regional quantile equation. Name which quantity is borrowed.
Linking methods without tracking dependence can double-count stations. Preserve the study design and software documentation used by the responsible agency.
Evidence check: for Regional skew is not regional flood transfer, 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 and mixed populations
Historical length does not guarantee future relevance. Reservoir operation, urbanisation, wildfire and climate change can alter peaks or observation systems. Test documented changes and avoid combining incompatible regimes only to make the record longer.
For a current design, follow the applicable guidance on nonstationarity or scenario analysis. Do not silently add a climate factor to a historical fit or assume the past distribution remains fixed.
Historical evidence can still inform mechanism and extremes. The claim should match the time period and model actually analysed.
Keep two records: the hydrologic series used by the calculation and the evidence register that justifies each change to it. The register should name the source document, observer, conversion method, uncertainty interval, perception threshold and analyst decision. This separation matters when later evidence changes a historical estimate. A reviewer can revise one input without losing the reasoning that produced the earlier fit.
Archive the software version and complete input file with the report. A printed quantile alone cannot show which thresholds, intervals or skew errors produced it.
Evidence check: for Nonstationarity and mixed populations, 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: a newspaper archive contains no flood reports from 1880–1920, but the town newspaper began in 1905. The years before 1905 do not share the same perception threshold.
Practice two: a high-water mark gives stage but channel reconstruction produces discharge from 1,200 to 1,700. Use interval information and test its leverage instead of choosing the midpoint as exact.
Practice three: station skew and regional skew differ in sign. Check record length, influential peaks, regional applicability and both MSE values before weighting.
Transfer the method to drought or earthquake catalogues by asking the same question: what event would have been noticed in each historical period, and what does silence actually mean?
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.
Is an unreported historical flood a zero?
No. It is usually censored by a perception threshold, and sometimes the observation process is too uncertain to use.
Why use regional skew?
At-site skew is unstable in short records. A defensible regional estimate can reduce sampling error when combined with its uncertainty.
Can I choose the historical threshold after seeing the fit?
Thresholds should come from observation evidence. Test plausible alternatives, but do not tune them for a preferred result.
Does Bulletin 17C remove uncertainty?
No. It provides a structured way to use systematic, historical and regional information while representing important uncertainty.
Authoritative reading begins with the official Guidelines for Determining Flood Flow Frequency—Bulletin 17C, its USGS publication page, and the documented USGS PeakFQ software project. Use the current responsible-agency implementation for real work.
Continue with regional flood frequency and transfer between catchments and annual maxima, partial-duration series and independent peaks. The next useful move is to build a dated table of every observation regime and the flood magnitude that would have been noticed in each.
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.