Daily streamflow (m3s-1) data between 1969 and 2021 were obtained for UK Benchmark Catchments from the National River Flow Archive (NRFA), as described in . The corresponding catchment-averaged precipitation, potential evapotranspiration, and temperature variables were obtained from CAMELS-GB , derived from the Met Office HadUK-Grid Climate Observations from . A selection of static catchment attributes for each of the catchments were obtained from . The full list of extracted variables and calculated antecedent precipitation totals, used to capture the influence of precipitation during previous days, is presented in Appendix Table .

The temporal span was chosen to maximize the availability of streamflow data for natural benchmark catchments. Benchmark catchments are minimally influenced by anthropogenic influences and were chosen to explore the influence of the WPs as predictors, minimizing the influence of noise from anthropogenic activity. From the full set of benchmark catchments, we selected those for analysis which had at least 95 % of data for each water year (1 October–30 September), and at least 30 complete years of data. For each unique catchment, the normalization of streamflow (m3s-1) to specific discharge (mmd-1) accounted for catchment size variability in the large-sample model and enhanced model generalizability.

These selection criteria resulted in 134 suitable catchments. For the UK-wide analysis, all selected catchments were pooled together. For regional analysis, the catchments were grouped into their corresponding Met Office Hadley Centre Observations Dataset (HadUKP) climate regions using shapefiles . Region names and corresponding abbreviations (e.g., Northern Scotland = NS, Southern Scotland = SS, Central and Eastern England = CEE) are defined in Appendix Table . Daily WP classifications were obtained from the Met Office MO-30 dataset , for the same time period as the catchment streamflow data (1969–2021). These WPs were created using an annealed k-means clustering method of mean sea level pressure (MSLP) from the European Mean sea level Pressure dataset (EMSLP) (1850–2003) . Lower-numbered WPs are associated with weaker MSLP anomalies, are historically more frequent, and occur more often in summer. Higher-numbered WPs are associated with stronger MSLP anomalies, are historically less frequent, and occur more often in winter . The WPs are displayed in Fig. , and the corresponding descriptions from are presented in Appendix Table .

Our analyses focus on winter floods. The winter months of December, January, and February (DJF) were chosen for analysis because most of the largest flood events in the UK occur during this season . Extreme flood events above the 99th percentile were identified for each catchment between 1969 and 2021 using the Peak Over Threshold (POT) method . The 99th percentile threshold was used to capture the most severe events while maintaining an adequate sample size. A 7 d independence window was applied, following . The target variable for modeling was the flood magnitude, defined as the largest specific-discharge value (mmd-1) for each independent event. The resulting sample sizes and regional breakdown of catchments and independent flood events are summarized in Appendix Table .

Our analysis focuses on the day with the highest flood peak, defined in this study as the event-day. While this approach does not capture the full hydrograph duration, it intentionally isolates the peak magnitude of independent events. The POT method is widely recognized for its ability to capture multiple extreme events within a single year, providing a more comprehensive analysis of flood extremes compared to the Annual Maxima (AM) method .

For the identified flood magnitude event days, feature sets 1–6 were compiled from the datasets described above for the UK and regional samples. Feature sets include a combination of: (1) spatial identifiers (latitude and longitude), used as baseline spatial features and to provide location context for the WP classification; (2) the UK Met Office MO-30 WP category on the event day; (3) the antecedent WPs (AWPs) from one to three days prior, representing synoptic scale atmospheric conditions and pre-event circulation; (4) catchment characteristics including aridity index, area, baseflow index, streamflow elasticity, maximum elevation, and runoff ratio; (5) meteorological variables such as event-day precipitation, mean/minimum/maximum temperature, and potential evapotranspiration; and (6) antecedent cumulative precipitation for 1–3 d prior to the event, capturing short-term catchment wetness. The 3 d antecedent window was selected based on the typical response time of small, near-natural UK catchments. Overall, eight regional flood magnitude datasets in addition to the UK national dataset were produced for subsequent modeling. A summary for each region, including the number of catchments, total flood magnitude events, and mean events per catchment is presented in Appendix Table .

To address multicollinearity and improve the interpretability of the final feature set, a post hoc feature pruning step was applied to feature set 6 to identify the final feature set 7. Variance Inflation Factor (VIF) analysis, as described in , was used to quantify collinearity among predictors. Predictors with VIF>10 were iteratively removed, prioritizing the retention of physically interpretable variables. The final seventh pruned feature set represents the outcome of a targeted feature selection procedure applied separately to each sample (UK and regional). While feature sets 1–6 are the same across all models to allow direct comparison of process groups, feature set 7 is specific to each data sample. Consequently, the retained features differ slightly by region. Figure  displays the retained and dropped predictors for the UK and the 7 regional feature set models. Table  gives an overview of each additional feature set model, using the data sources described in Table , with abbreviations for model results in Fig. .

Prior to selecting the WPs as a feature set for the RF models, we examined which WPs frequently occurred with extreme flood event days by computing the conditional probability of each WP given that a flood occurred on the day, denoted as “P(WP | flood)”. This analysis was performed for (1) the UK sample dataset and (2) the regional sample datasets. To account for the cumulative influence of synoptic-scale conditions leading to floods, we extended the analysis beyond the day of the event to include AWP categories (up to three days prior).

Next, we developed seven RF regression models, each incorporating a new feature set, as described in Table , to gain insights into the roles of different features as predictors of extreme flood magnitudes (mmd-1), for the UK and regional samples (see Table ). The seven models were run both as a UK-wide model with all catchments pooled and for predefined regional samples (where each region has catchments within corresponding regions). This enhances interpretability by aligning the model structure with established hydro-climatic regions and enables insights into the performance and feature importance of regional and UK samples. That is, each new feature set incrementally incorporates new features, as shown in Table , while the model architecture remains the same. The RF was implemented using the Scikit-learn Python package by . Model performance metrics and Shapley Additive Explanations (SHAP) were calculated based on the test set results. One-hot encoding (1 = TRUE, 0 = FALSE) was applied to the WP and AWP categories to create binary features for the model. A temporal train-test split was applied to all UK and regional models, with events between 1969 and 2010 (80 %) used for training, and events from 2011 to 2021 (20 %) used for testing. This split ensured that later events were unseen during model fitting and hyper-parameter optimization. This temporal validation method has been used in other recent hydrological studies e.g., , respects the temporal sequence of the data, and enables evaluation only on unseen years. Model hyper-parameters were optimized within the training period, using RandomizedSearchCV to balance model complexity and performance. The final configuration selected was: n_estimators = 1000, min_samples split = 10, min_samples leaf = 2, max_depth = None, and bootstrap = True. A sensitivity analysis used to test alternative tree numbers and split parameters was conducted. This also reflects a realistic forecasting scenario where future events are predicted based on past conditions . A three-way split (training: 1969–2000, validation: 2001–2010, test: 2011–2021) was also evaluated but produced very similar model skill. To maximize the available data for learning hydrological relationships, the two-period split was retained, providing an effective balance between robustness and data efficiency.

To quantify predictive uncertainty in the RF models, ensemble-based uncertainty metrics were derived from the final feature set 7 models. For each test-set sample, predictions were obtained from all individual trees within the ensemble. Two complementary metrics were employed. First, the ensemble spread of tree predictions standard deviations (Pred_SD), representing the absolute spread of predictions and thus the model's absolute predictive uncertainty in mmd-1. Second, the coefficient of variation (CV), expressing the relative uncertainty. The results are presented in Fig. .

Overall model performance was evaluated using the coefficient of determination R2 and Percentage Bias (PBIAS), calculated once per model from all test set predictions of flood magnitudes. The overall R2 represents the total proportion of variance in observed flood magnitudes explained by the model at the national or regional scale. For each model, R2 was first calculated for the overall model and then at the catchment level. For the final 7 sets of models, comparisons were performed by re-evaluating the UK model on the exact subset of catchments used in each regional model, using identical test periods. Catchment level R2 values were computed separately for each catchment and then aggregated (median and mean) across catchments within each region. Only catchments with at least ten events were included. This approach provides consistent comparisons across spatial scales and captures both temporal variation within catchments (intra-catchment variability) and variation between catchments (inter-catchment variability). The equations for R2 and PBIAS are provided in Appendix C.

SHAP values quantify each feature’s contribution to individual predictions, providing insights into local and global influences on the target variable . By applying SHAP analysis to the test sets for the 7 sets of models, model interpretability is assessed on unseen data. This approach allows for the evaluation of generalization performance and feature influence during the independent testing period. SHAP, derived from cooperative game theory, is a powerful explainable AI tool used to interpret the outputs of machine learning models . For each prediction in the test set, SHAP values represent the extent to which a feature contributes to deviations from the mean prediction . Compared to feature importance derived from Gini impurity, SHAP is more robust as it provides insights into both the direction and magnitude of the relationship between predictors and the target variable and enables analysis of local and global effects . See equations for SHAP calculation in Appendix C.

The dominance of cyclonic WPs on flood-event days (Fig. a), such as WP 30 in the UK sample, is consistent with previous work linking these synoptic regimes to enhanced UK precipitation and flooding potential . Regional differences in the most frequent flood-associated WPs (e.g., WP 23 in NS) indicate that synoptic circulation provides a broad-scale atmospheric context. However, the resulting flood response likely depends on how that context interacts with regional hydro-climatic conditions and catchment properties . Spatial variability may also reflect differences in the precipitation footprints and storm tracks associated with individual WPs. Moreover, coastal exposure and orographic enhancement in western regions could be playing a role.

WP 21 provides an example of how frequency on flood-event days can differ from circulation types associated with widespread extreme precipitation. Previous analyses have shown that WP 21 can be associated with elevated precipitation across multiple UK regions . In the present analysis, WP 21 occurs frequently on flood-event days in several regions (notably SE, SS, and NW; Fig. a), but WP 30 remains the most frequent type overall. This reinforces that the circulation type most strongly linked to extreme precipitation does not necessarily correspond to the type that co-occurs most frequently with flood events. This is because flood occurrence and magnitude also depend on antecedent wetness, catchment storage, and hydrological memory . Consequently, the same WP can produce different flood responses in different catchments and under different pre-event conditions.

The antecedent analysis (Fig. b) further indicates that the synoptic context preceding flood events is not limited to the event-day circulation type. The reduced dominance of WP 30 three days prior to events, alongside more frequent occurrence of other cyclonic types (e.g., WPs 20 and 29), is consistent with the importance of multi-day circulation sequences in conditioning catchment wetness through cumulative rainfall . These results motivate the inclusion of antecedent circulation descriptors as candidate predictors in the subsequent modeling framework, while also highlighting the potential for non-linear interactions between atmospheric regime, precipitation, and catchment state.

The conditional probability patterns (Fig. a) provide synoptic-scale context for winter flood-event days, but the translation from circulation type to flood response is not one-to-one. The same WP can coincide with flood events more frequently in steep, fast-response catchments that are already wet, but less frequently in drier or more permeable catchments with higher infiltration capacity, reflecting the importance of antecedent wetness, storage, and hydrological memory .

The antecedent analysis (Fig. b) indicates persistence of cyclonic circulation in the days preceding flood events. In particular, higher-numbered cyclonic types are more common three days prior to events, while WP 30 becomes less dominant and WPs 20 and 29 occur more frequently. This supports the interpretation that multi-day synoptic sequences condition catchment wetness through cumulative rainfall and soil saturation, which can increase the likelihood of flood generation .

The magnitude distributions (Fig. ) demonstrate that WPs associated with frequent flood-event occurrences are not necessarily those associated with the highest flood magnitudes. Although WP 30 most frequently co-occurs with flood-event days (Fig. ), it is not associated with the highest median or mean flood magnitudes (Fig. a). WP 30 represents a broad cyclonic regime that can persist for several days and affect large areas, which may favor frequent flood-event occurrences rather than the largest peak magnitudes . WP 30 could be driving lower intensity but longer duration events, especially in larger catchments where prolonged rainfall is a more important factor for flood generation, and be associated with duration rather than event peak. In contrast, WP 23 is associated with higher flood magnitudes in this event-based analysis, highlighting the importance of considering both the frequency of flood-conducive circulation types and the intensity of the flood magnitudes linked to those types .

Catchment size modulates these WP-magnitude relationships (Fig. b). Smaller catchments display wider spreads and higher upper-tail magnitudes under WPs 23 and 30, consistent with their shorter response times and sensitivity to intense rainfall. Larger catchments exhibit narrower distributions, reflecting spatial averaging and storage effects that can dampen peak responses. These differences further support that synoptic-scale regimes provide a necessary but insufficient descriptor of event-scale flood magnitude without accounting for catchment state and response characteristics.

Finally, changes in the frequency of specific circulation types could have implications for future flood hazards. For example, under RCP8.5, reported an increase in the occurrence of WP 23, which may be particularly relevant for regions where this WP is already prominent on flood-event days (e.g., NS; Fig. ). This motivates future work linking circulation-type projections to hydrological impacts using predictors that better resolve catchment states and event-scale forcing.

Feature set 7 is the final pruned specification. Latitude/longitude and WP/AWP predictors were excluded, and the remaining predictors were pruned for collinearity (Appendix Fig. ). This means that the results for feature set 7 reflect skill attributable to the retained hydrometeorological and catchment-relevant predictors, while spatial proxies and WP/AWP categories do not contribute to (and in some regions reduce) predictive performance. A brief sensitivity check indicated that increasing model complexity did not materially change test performance, supporting the robustness of the final specification.

The UK pooled model consistently outperforms the regional models across feature sets, reaching R2=0.84 in feature set 6 and R2=0.83 in feature set 7 (Fig. a). The statistically significant improvement from the feature set 1 baseline (R2=0.66) is consistent with the advantages of pooling information across a larger and more diverse set of near-natural catchments, which can improve the ability of machine-learning models to learn generalizable relationships from limited extreme-event samples .

Across regions, model performance varies substantially, reflecting differences in dominant hydrological regimes, within-region heterogeneity, and event sample composition. The SW region achieves the highest regional performance (R2=0.83 in feature set 6; R2=0.82 in feature set 7), while the NW exhibits a large improvement relative to baseline (+0.35) reaching R2=0.75. In contrast, SS and ES show more modest improvements, reaching feature set 7 R2 values of 0.60 and 0.54, respectively, consistent with the constraints of smaller regional samples.

CEE exhibited the lowest performance (R2=0.37 in feature set 6 and 0.33 in feature set 7), despite having the largest dataset. This region's low relief, permeable, and chalk dominated terrain can mean that floods are more groundwater and storage driven rather than influenced by event precipitation . The CEE region is therefore likely less sensitive to short-duration rainfall predictors. Similarly, the SE region has low performance, reaching R2 of 0.49 with hydrometeorological features and up to 0.60 by feature set 7, although this is not statistically significant compared to the baseline model (feature set 1). This aligns with previous work showing that the SE is difficult to model without explicit groundwater representation . These results underscore that regions dominated by slower-response processes require predictors that capture longer-term hydrological memory.

The changes in skill across feature sets highlight which predictor groups are most informative for event-scale flood magnitude estimation. In most regions, the inclusion of WP and AWP predictors (feature sets 2–3) does not improve performance relative to the spatial baseline and can reduce skill, suggesting limited incremental predictive information at daily resolution for peak magnitude estimation. This is consistent with the view that synoptic-scale circulation descriptors may not resolve the fine-scale variability associated with local precipitation extremes and catchment-scale runoff generation processes . In contrast, the largest gains in R2 occur once event-day hydrometeorological variables and short-window antecedent precipitation indices are included (feature sets 5–6), reinforcing the importance of forcing and antecedent wetness in conditioning peak magnitudes in many UK catchments .

In feature set 7, performance remains similar to feature set 6 in the UK model and in several regional models, indicating that the pruning step removes redundant predictors while retaining most of the information relevant to prediction. The small reduction in R2 between feature sets 6 and 7 reflects the expected trade-off between interpretability and predictive performance and supports the use of a reduced, physically interpretable predictor set for subsequent process attribution.

PBIAS results (Fig. b) indicate a general tendency towards the underestimation of peak magnitudes in the test period across many regions, consistent with the scarcity of observations in the upper tail and the inherent difficulty of learning extreme responses from limited event samples. NS shows comparatively smaller bias and includes cases of overestimation, suggesting region-specific differences in error structure. The largest biases in CEE co-occur with low R2, further indicating that key storage-related processes are not fully represented by the current predictor set. Predictive uncertainty derived from RF ensemble spread (Appendix Fig. ) provides additional context, with generally low median uncertainty across samples but increased uncertainty in regions with lower skill.

Catchment-level evaluation complements pooled-scale metrics by isolating within-catchment temporal predictability in the test period. Unlike the aggregate results discussed previously, which combine inter- and intra-catchment variability across regions, this analysis calculates R2 individually for each catchment based on its test events and then compares these values between the UK and the corresponding regional models. Figure  shows these per-catchment R2 distributions, with matched comparisons between the UK and regional models. At the regional scale, the southwest (SW) maintained high aggregated R2 values, but per-catchment performance revealed wide variability (ranging from -0.94 to 0.69), highlighting heterogeneity in local dynamics. This indicates that regional models can generalize well to broader regional trends but may not consistently capture localized hydrological processes driving flood magnitudes. Similar variability was observed in other regions, suggesting that model skill depends strongly on individual catchment characteristics, data density, and the distinct hydrometeorological drivers of extremes. Across all regions, the UK model outperformed regional models in 54.9 % of matched catchments (Appendix Fig. ), confirming that large-sample pooled models generally provide stronger generalization and robustness .

However, regional models achieved higher performance than the UK-wide model in 45.1 % of catchments, demonstrating that locally trained models can still outperform larger models when regional hydrological characteristics are strongly distinct. Scatter-plots of per-catchment R2 values in Appendix Fig.  show that regional models sometimes outperform the UK model, particularly in regions with coherent hydrological regimes, suggesting that local models retain value where region-specific flood processes dominate. The stronger overall UK performance reflects the model's ability to leverage greater data diversity and capture inter-catchment variability, consistent with established findings in large-sample hydrology . Despite this, the relatively modest catchment-level R2 values in many regions highlight persistent challenges in modeling intra-catchment variability of the largest fluvial floods at the event scale. Limited extreme event records for individual catchments (often <20 events) constrain model learning and increase noise, reducing temporal prediction reliability. These data constraints likely explain some of the low or negative R2 values observed in smaller or more heterogeneous catchments. Overall, this analysis reveals that while pooled UK models achieve higher generalisation, regional and catchment-specific processes still drive substantial local variability. Aggregated metrics may therefore mask poor local model skill, emphasising the importance of targeted feature engineering and model designs capable of balancing generalisation with sensitivity to local catchment dynamics.

Our analysis of dominant processes indicates that flood magnitude predictions are primarily controlled by a combination of climatic context, catchment features, and event-scale forcing, with aridity, catchment area and precipitation related features consistently among the most important (Figs.  and ). SHAP summary plots show both the direction and magnitude of individual predictor effects on model output, whereas mean absolute SHAP values summarize the overall contribution of each predictor across all events (Figs.  and ). Regional differences in predictor rankings indicate that the relative importance of climatic context, hydrometeorological forcing, and static catchment attributes varies between hydro-climatic regimes (Figs.  and ).

In the highest-performing UK model, the aridity index is the most influential feature overall, followed by precipitation (event day) and cumulative precipitation on the day before. The aridity index, though static, represents a long-term control on catchment response by defining the climatic water balance under which hydrological processes operate . Lower aridity (e.g., wetter conditions) is associated with higher flood magnitudes, suggesting that catchments with persistently higher moisture availability are more efficient at converting rainfall into runoff. While the aridity index does not vary from event-to-event, its importance reflects the underlying hydro-climatic context and catchment wetness, which influence flood potential by setting the background (long-term) hydro-climatic conditions under which individual storms occur. The aridity index captures broad spatial gradients in climate and hydrology that may have previously been represented by latitude and longitude in the simpler earlier model feature sets. However, aridity provides a more physically interpretable and hydrologically meaningful descriptor of spatial variability across UK catchments.

Across both the UK and regional models, precipitation on the event day consistently emerges as a dominant predictor of extreme flood magnitudes, while antecedent precipitation plays a secondary role. In nearly all regions, the SHAP distributions confirm this behavior, with positive SHAP values associated with higher rainfall leading to higher predicted flood magnitudes. This consistency demonstrates that the models capture key physical processes, reflecting similar findings from other UK ML-based hydrological studies .

In the SW and NW regional models, feature rankings largely mirror the UK model but reveal important regional nuances. Aridity remains a key control, but antecedent precipitation one day prior to the event gains prominence. In the SW, this could be explained by the mechanism of soil saturation and cumulative rainfall in modulating flood magnitudes . The SW model also attributes greater influence to topographic and temperature-related variables, consistent with elevation-driven orographic enhancement of rainfall and temperature-linked variability in evapotranspiration and antecedent wetness that together shape flood response in steep, maritime catchments . In contrast, lower-performing regions such as CEE and SE show a weaker dominance of dynamic predictors. Here, static features such as baseflow index, area, or elevation rank higher. This further reflects the importance of capturing slower, groundwater-influenced flood generation processes characteristic of these permeable, low-relief catchments.

Finally, while SHAP values provide valuable insight into model behavior, they represent associations rather than direct causal relationships. Non-linear feature interactions may amplify or mask underlying process signals. Therefore, SHAP-based interpretability should be used alongside physical reasoning to avoid over-interpreting model-derived relationships . Overall, the SHAP analysis supports that the models capture physically consistent mechanisms governing flood magnitudes, with the dominance of rainfall intensity and climatic wetness, while highlighting region-specific sensitivities to antecedent and physiographic factors.

This study has several limitations that future research can address. First, uncertainty in flow observations remains a major challenge, particularly for extremes. High-flow discharge estimates are often derived by extrapolating stage–discharge rating curves beyond the range of direct gauge measurements and are sensitive to both rating curve uncertainty and stage measurement error which can be substantial during flood conditions . In addition, the use of daily discharge can under-represent the magnitude of short-lived flood peaks because daily averaging smooths the hydrograph . Future work could include quality-controlled sub-daily discharge where available to provide an improved representation of peak magnitudes .

The selection of near-natural catchments was a deliberate decision to isolate natural processes; this may have reduced variability and limited the data sample size. Static features have proven to be highly important in the models, but they do not directly capture dynamic processes such as soil moisture infiltration, groundwater levels, and snowmelt. Incorporating additional dynamic variables such as snowmelt and groundwater datasets could significantly improve predictive performance in future work. Moreover, uncertainty in precipitation data also constrains model accuracy. No rainfall product will perfectly represent local conditions, and this limitation can be amplified when modeling extremes. The inclusion of WPs was motivated by their use in operational tools (e.g., Fluvial and Coastal Decider), and their potential to capture more predictable synoptic scale drivers of floods. However, despite WP-flood associations, their use in flood magnitude estimations proved limited in this study. This is likely due to a scale mismatch between the spatial resolution of the WPs and the localized behavior of flood events. Future research could aim to capture more accurately the synoptic and antecedent conditions driving floods.

Furthermore, while aggregated UK and regional metrics provide a useful overall picture, they may obscure substantial heterogeneity at the catchment scale. The lower and more variable catchment-level R2 values observed in this study highlight the importance of developing multi-scale evaluation frameworks that explicitly assess local predictive skill and uncertainty. Finally, the study's deliberate design to focus exclusively on DJF events in near-natural catchments exceeding the 99th percentile threshold means that the findings represent a subset of hydrological regimes and may not fully generalize to managed or urbanized systems.