Non-Stationary Flood Frequency Analysis in the UK

This lesson explains the stationarity debate, the trend-testing framework, and the non-stationary generalized extreme value (GEV) approach presented by Faulkner et al. (2020), Can We Still Predict the Future from the Past? Non-Stationary Flood Frequency Analysis in the UK. It then interprets the national findings, the North West pattern, and the example of the Lune at Killington, before critically assessing what the study recommends for design flood estimation and where its limits lie.

1. Why stationarity is debated

Flood frequency analysis has traditionally assumed stationarity: the idea that the statistical properties of floods do not change over time, so the past can be used to estimate future probabilities. Faulkner et al. (2020), Can We Still Predict the Future from the Past? Non-Stationary Flood Frequency Analysis in the UK places this assumption under scrutiny because some UK rivers, especially in recent decades, appear to have experienced an upsurge in flooding.

The paper also shows that the debate is not simply “stationary versus non-stationary” in a straightforward sense. It notes a research debate in which some authors argue that stationary models should often still be preferred when the physical drivers of change and the appropriate model structure are uncertain. In the summary given by Faulkner et al. (2020), Can We Still Predict the Future from the Past? Non-Stationary Flood Frequency Analysis in the UK, stationary models are seen by critics of non-stationary approaches as:

• simpler,
• more theoretically coherent, and
• more reliable for practical application when change processes are not well known.

The same source also reports the argument that a non-stationary model is best justified where there is deterministic information about the process of change, such as increasing urban area. This is important because, in many catchments, the causes of changing floods are uncertain. Trends might reflect climate change, decadal variability, clustering of wet years, or catchment change, and these are not always easy to separate.

So, the stationarity debate in this paper is really about evidence, causation, and usefulness. The question is not only whether flood records contain trends, but also whether those trends are strong enough, interpretable enough, and stable enough to justify changing design practice.

2. Data basis and the logic of the tests

Faulkner et al. (2020), Can We Still Predict the Future from the Past? Non-Stationary Flood Frequency Analysis in the UK applies its analysis to annual maximum flow series. The paper notes that peaks-over-threshold data could potentially provide richer information, but in practice they suffer from data gaps, shorter records, and difficulties in some catchment types, especially groundwater-dominated systems. For that reason, annual maxima provide the main basis for the national assessment.

The study uses four statistical tests for trend. Three are non-parametric and one is parametric:

• Mann-Kendall test – tests for a monotonic upward or downward trend over time.
• Cox-Stuart test – another non-parametric trend test.
• Pettitt test – tests for a change point or step-change in the series.
• Non-stationary frequency distribution fitting – a parametric test based on fitting a non-stationary extreme value model.

The rationale for combining these tests is that they detect different forms of change:

• Mann-Kendall focuses on gradual monotonic change.
• Cox-Stuart provides a second non-parametric check on trend.
• Pettitt detects abrupt shifts rather than smooth trends.
• The parametric non-stationary fit assesses whether allowing distribution parameters to vary improves the flood frequency model.

This combination matters because non-stationarity in flood records may not appear as one simple steadily rising line. A catchment may show a sudden shift, multi-decadal variability, or a trend that mainly affects part of the probability distribution.

3. The non-stationary GEV approach used by Faulkner et al. (2020)

The parametric method in Faulkner et al. (2020), Can We Still Predict the Future from the Past? Non-Stationary Flood Frequency Analysis in the UK fits a non-stationary GEV model to annual maximum flows. In practical terms, the key idea is that at least one parameter of the extreme value distribution can vary with a covariate rather than remaining fixed.

The paper gives a clear example in which the location parameter varies while the other parameters remain fixed. This means the centre of the flood distribution is allowed to shift through time or with another explanatory variable. In the Lune at Killington example shown in the paper, the non-stationary model is explicitly described as a varying location model.

The source also discusses the choice of covariate. A simple option is time, but the authors are cautious about this. They state that although the date 50 years ahead is known, one cannot justify extrapolating time-based trends into the future. Therefore, results are estimated for present-day conditions only when time is used as the covariate.

This is a crucial point for interpretation:

• the model can indicate that the present-day flood regime differs from the long-term stationary estimate,
• but it does not justify simply projecting that same time trend forward indefinitely.

The paper also discusses physically more meaningful covariates that have been used in the literature, including:

• annual rainfall,
• high rainfall percentiles,
• urban extent,
• population, and
• climatic indices.

In the study, seasonal rainfall covariates are explored, and each covariate is centred and scaled by subtracting its mean and dividing by its standard deviation. According to Faulkner et al. (2020), Can We Still Predict the Future from the Past? Non-Stationary Flood Frequency Analysis in the UK, this helps reduce standard errors in parameter estimation.

The paper further distinguishes between:

• conditional return levels – flood estimates conditional on a particular covariate value or year, and
• marginal return levels – flood estimates that average over the distribution of the covariate.

The marginal return level is conceptually attractive because it accounts for non-stationarity without conditioning on one specific rainfall or climate state. However, the paper warns that marginal return levels become difficult when the covariate distribution is not well bounded or well approximated, and this problem is compounded by uncertainty in annual maximum series.

4. National-scale findings

The headline national result reported in Faulkner et al. (2020), Can We Still Predict the Future from the Past? Non-Stationary Flood Frequency Analysis in the UK is that the non-stationary frequency distribution identified evidence of trend at many more stations than the non-parametric tests. The excerpt shows:

• 343 stations (67%) showed no evidence of trend under the non-stationary frequency distribution,
• while 166 stations (33%) showed evidence of trend (compared with 117 stations, 23%, with an increasing Mann-Kendall trend).

This suggests two important conclusions.

1. Evidence of non-stationarity is widespread enough to matter operationally. The issue is not confined to a handful of unusual gauges.
2. Model-based detection is more sensitive than simple non-parametric tests. That does not automatically make it more correct, but it means that practical conclusions may depend strongly on method choice.

The paper also reports Pettitt test change points through time, indicating that in some stations change is better represented as a shift rather than a smooth monotonic trend. This supports the broader message that “trend” in flood records can take several forms and should not be reduced to one single statistical pattern.

5. Why the North West stands out

A major substantive finding in Faulkner et al. (2020), Can We Still Predict the Future from the Past? Non-Stationary Flood Frequency Analysis in the UK is the strength of trends in north-west England. The paper explicitly notes that many strongly significant trends occur in catchments in this region and that many of these catchments remain largely rural.

This is significant because it weakens some simple alternative explanations. The authors state that:

• urbanisation is not an adequate explanation for many of the strongest trends, and
• changes in agricultural land management are unlikely to explain trends as large as those observed.

The source also notes that some of the rivers with the strongest trends are relatively natural and have not been channelised or embanked. This pushes interpretation toward broader hydroclimatic drivers, though the paper remains careful not to claim that short records can cleanly distinguish progressive climate change from decadal variability or clustering.

In teaching terms, the North West results illustrate a central practical dilemma:

• there is strong statistical evidence that recent flood regimes differ from older assumptions,
• yet the physical attribution is not precise enough to support unlimited extrapolation.

That is exactly why the authors favour using non-stationary methods to estimate present-day risk, while remaining cautious about long-range trend projection.

6. Interpreting the Lune at Killington example

The Lune at Killington is used in Faulkner et al. (2020), Can We Still Predict the Future from the Past? Non-Stationary Flood Frequency Analysis in the UK as an example comparing stationary and non-stationary flood frequency analysis.

The table reproduced in the source gives the following model parameters:

• Stationary model: μ = 223, σ = 76.7, ξ ≈ −0.01
• Non-stationary model (varying location): μ0 = 171, μ1 = 2.47, σ = 68.7, ξ = 8.54 × 10−5

These parameter values show that the preferred non-stationary formulation allows the location parameter to increase with the covariate. In plain language, the distribution of annual maximum floods has shifted upward relative to what a stationary model assumes.

The associated figure compares stationary and non-stationary estimates for several annual exceedance probabilities (AEPs), including the 1% AEP. The implication is that present-day design floods at this site are higher under the non-stationary model than under the stationary model.

The confidence intervals shown for the 1% AEP are also important. They remind us that:

• non-stationary models may change the central estimate, but
• uncertainty around rare-event estimates remains substantial.

So the Lune at Killington example is not just evidence that “non-stationary is bigger.” It demonstrates something more nuanced:

• a non-stationary model can materially alter current design estimates,
• especially for rare floods such as the 1% AEP event,
• but these revised estimates are still uncertain and should not be treated as exact truths.

7. What the results mean for design flood estimation

Faulkner et al. (2020), Can We Still Predict the Future from the Past? Non-Stationary Flood Frequency Analysis in the UK directly links these findings to flood risk management. The paper notes that non-stationary analysis may affect both the design and the economic justification of flood mitigation schemes.

The logic is straightforward:

• If estimated design floods increase, then structures may need to protect against larger events than previously assumed.
• The costs of schemes are strongly influenced by protection against rare floods such as the 1% AEP event.
• The benefits of schemes, however, are often dominated by avoided damages from more frequent floods.

This creates a practical tension. Non-stationary estimates can increase capital requirements for walls, storage, or other measures, but the economic case for those upgrades depends on how changing flood probabilities are translated into expected damages over time.

The paper states that Cumbrian scheme appraisals were piloting non-stationary analysis where there was evidence for it. This signals a selective, evidence-based implementation rather than immediate universal replacement of stationary methods.

8. Critical assessment of the recommendations

8.1 Strengths of the recommendations

The recommendations in Faulkner et al. (2020), Can We Still Predict the Future from the Past? Non-Stationary Flood Frequency Analysis in the UK are persuasive in several ways.

• They respond to observed data. The study is motivated by actual UK gauge records, especially in places where recent flooding has clearly intensified.
• They avoid blind extrapolation. The paper is careful not to treat a time trend as a physically certain forecast far into the future.
• They are operationally relevant. The focus is on present-day design estimation and appraisal decisions, not only on theoretical statistics.
• They acknowledge spatial variation. The strongest case for non-stationary treatment appears in regions such as the North West rather than uniformly everywhere.

In that sense, the paper offers a pragmatic middle position: retain awareness of stationary methods, but permit non-stationary analysis where the evidence is strong and where it materially affects decisions.

8.2 Limitations and cautions

The same source also reveals several limitations that should temper how far its recommendations are taken.

• Attribution remains uncertain. The paper explicitly notes the difficulty of distinguishing progressive climate change from decadal variability or flood-rich and flood-poor clustering over relatively short records.
• Time is a weak physical covariate. A time-varying model may fit historical change, but time itself does not explain the hydrological mechanism, which is why the authors do not justify extrapolating it far forward.
• Annual maximum series are information-limited. The paper notes that peaks-over-threshold could be richer, but practical issues prevented wider use. This means conclusions are drawn from one extreme value per year, which can limit inference.
• Rare-event uncertainty remains high. Even with a better-fitting non-stationary model, estimates such as the 1% AEP flood still carry wide uncertainty.
• Marginal return levels are not straightforward. The source explains that these can be difficult when the covariate distribution is not well bounded or well approximated.

These limitations matter because design flood estimation needs more than a statistically improved fit to past data. It also needs defensible interpretation, consistency across practice, and a robust basis for future-facing investment decisions.

8.3 Implications for engineering judgment

A critical reading of Faulkner et al. (2020), Can We Still Predict the Future from the Past? Non-Stationary Flood Frequency Analysis in the UK suggests that non-stationary analysis should be treated as a decision-support tool, not as an automatic replacement for all existing methods.

For design flood estimation, that implies:

• use non-stationary analysis where there is strong local evidence of change,
• interpret increases in design flow alongside confidence intervals and physical understanding,
• be especially cautious when using time as the sole covariate, and
• avoid assuming that historical trend rates can simply be projected across a full asset life.

The study therefore supports more adaptive and regionally sensitive design practice, especially in places like north-west England, but it does not support abandoning critical judgment or treating non-stationary outputs as precise forecasts.

9. Key takeaways

• The stationarity debate is not settled; it turns on evidence, causation, and practical usefulness.
• Faulkner et al. (2020), Can We Still Predict the Future from the Past? Non-Stationary Flood Frequency Analysis in the UK uses four trend tests: Mann-Kendall, Cox-Stuart, Pettitt, and a parametric non-stationary frequency model.
• The non-stationary GEV approach mainly allows distribution parameters, especially location, to vary with a covariate such as time or rainfall.
• Nationally, the model-based non-stationary test detects evidence of trend at many stations, more than the non-parametric tests.
• North-west England stands out for strong trends, many in largely rural and relatively natural catchments.
• At the Lune at Killington, the non-stationary varying-location model implies higher present-day design floods than the stationary model, including for the 1% AEP event.
• The paper recommends cautious use of non-stationary analysis for present-day conditions and scheme appraisal where evidence is strong.
• Main limitations include uncertain attribution, difficulty extrapolating time trends, uncertainty in rare-event estimates, and challenges in using marginal return levels.