The Black River near Washago is in central Ontario, Canada, and drains a watershed of approximately 1506 km² upstream of the Water Survey of Canada gauge 02EC002, which has over 100 years of streamflow records. The watershed is characterised by a humid continental climate, with cold, snowy winters and warm, humid summers. The climate is strongly influenced by the Great Lakes, which moderate seasonal temperatures and enhance precipitation (Whitfield and Cannon, 2000). Hydrologically, the Black River is classified as a mixed-regime system, with a dominant nival (snowmelt) component; the nival fraction is approximately 0.7 (Burn and Whitfield, 2023). The primary flood-generating mechanisms are spring snowmelt and rain-on-snow events, which have historically produced the highest flows (Buttle et al., 2016). The watershed contains a high proportion of wetlands, which play a key role in sustaining groundwater recharge, and maintaining baseflow during dry periods.

The Moyie River is in southeastern British Columbia within the South BC Mountains region and drains an area of approximately 1480 km² upstream of the Water Survey of Canada gauge 08NH006, which provides a 90-year observational record. The watershed lies within a complex mountainous terrain characterised by steep slopes, dense forest cover, and variable elevations. The climate is strongly influenced by elevation and orographic effects, resulting in a continental to subalpine climate with distinct seasonal patterns. Winters are cold with substantial snowfall, while summers are warm and relatively dry (Whitfield and Cannon, 2000). The hydrologic regime is snowmelt-dominated, with peak flows typically occurring in late spring to early summer (May–June). Rain-on-snow events in late winter or early spring also contribute to flood risk, particularly when rapid warming occurs on an established snowpack (Buttle et al., 2016).

The Lahave River at West Northfield is in Nova Scotia and drains an area of approximately 1250 km² upstream of the Water Survey of Canada gauge 01EF001, providing 108 years of continuous daily flow records. The watershed is situated within a coastal, lowland physiographic region and is characterised by rolling hills, mixed forest, and numerous lakes and wetlands. The region experiences a humid maritime climate, with relatively mild winters, cool summers, and high precipitation distributed evenly throughout the year. This climate is strongly influenced by proximity to the Atlantic Ocean, which moderates seasonal temperature fluctuations and contributes to frequent rainfall. The area is also regularly affected by storms, including tropical cyclones and hurricanes, due to its exposure to Atlantic storm tracks (Whitfield and Cannon, 2000). Hydrologically, the Lahave River exhibits a rainfall-dominated regime, with flood events occurring year-round, but most frequently in the fall and winter when intense rainfall coincides with saturated soil conditions. Rain-on-snow events may also contribute to elevated flows during transitional seasons; however, snow accumulation is generally lower than in inland or higher-elevation watersheds (Buttle et al., 2016). Figure 1 shows the location of three study watersheds.

The Hydrologiska Byråns Vattenbalansavdelning – Environment Canada (HBV-EC) model (Hamilton et al., 2000) was used to simulate watershed streamflow. A lumped representation of HBV-EC was implemented within the Raven Hydrological Modelling Framework version 3.8 (Craig et al., 2020). The HBV-EC model conceptualises catchments as a soil moisture zone atop two stacked buckets, representing upper and lower storage layers. Its structure includes three primary routines: a snow routine, soil routine, and runoff generation routine (Hamilton et al., 2000). The snow routine uses a classic degree-day approach to estimate snowmelt rates. The model partitions snowmelt and precipitation into evapotranspiration and runoff based on water and energy balance principles. Runoff is divided into surface and subsurface flow, which is further partitioned between the upper and lower buckets according to soil moisture dynamics (Seibert and Vis, 2012). A lumped version of HBV-EC was used to simulate the average temporal dynamic of catchment behaviour without requiring detailed spatial information. HBV-EC was selected due to its demonstrated strong performance in Canadian landscape (Beck et al., 2016; Stahl et al., 2008; Zégre et al., 2010), its widespread use for flood simulations (Fischer and Schumann, 2021; Sikorska et al., 2015), its parsimony, ease of implementation, and its computational efficiency (Seibert and Bergström, 2022).

The model was run using daily time series of measured discharge, precipitation, maximum and minimum temperature, which were sourced from Environment Canada. The HBV-EC models were calibrated to a truncated discharge dataset using a combination of manual and automated approaches. Manual calibration followed a stepwise process: (1) parameters controlling the long-term water balance were adjusted to achieve volumetric flow simulations; (2) parameters governing snowpack process were calibrated to accurately simulate the freshet; (3) parameters influencing soil moisture dynamics were refined to improve recession and baseflow representation. Once an acceptable parameter set was identified through manual calibration, the Dynamically Dimensioned Search (DDS) algorithm (Tolson and Shoemaker, 2008) was employed for further optimisation. The objective function minimised the daily discharge Kling-Gupta Efficiency (Gupta et al., 2009) often the last 30 years to ensure the best fit between simulated and observed hydrographs. The final set of parameters was evaluated against the long-term water balance, hydrographs, flow duration curves, and peak flows. Across all experiments, HBV calibration used only a 30-year daily streamflow subset.

The REM approach is a tool for propagating uncertainty into hydrological model predictions. It achieves this by incorporating samples of model error into deterministic predictions (Farmer and Vogel, 2016). REM combines deterministic predictions from process-based hydrologic models with stochastic components that characterise the uncertainties in model predictions (Montanari and Koutsoyiannis, 2012). This integration is accomplished by leveraging the statistical properties of the observed residual error, defined as the difference between observed and simulated streamflow (Vogel, 2017). By effectively characterising and modelling these residuals, the REM approach enables the generation of probabilistic streamflow estimates, accounting for uncertainties inherent in deterministic model outputs (Honti et al., 2013). REM characterises residual uncertainty as the discrepancy between simulations and observations. This residual term implicitly reflects the combined effects of forcing uncertainty, parameter uncertainty, and structural model error, without separating their individual contributions. This formulation is consistent with established error-modelling frameworks in hydrology (Li et al., 2016; McInerney et al., 2017).

In this study, the residual error model is developed for the annual maxima, aligning with the requirements of flood frequency analysis. While much of the literature has focused on REM applications at the daily streamflow – where model errors are often non-normal, heteroscedastic, and autocorrelated – our approach focuses on modelling these properties for annual maxima. The statistical properties of annual maxima residuals require careful treatment to avoid biased estimates of extremes.

The selection of the REM structure was guided by diagnostic analyses of the statistical properties of the raw residuals, including variance behaviour, temporal dependence, and distributional characteristics. To address the heteroscedasticity – where errors tend to increase with larger streamflow – we apply a Box–Cox transformation (Box and Cox, 1964) with a power parameter fixed at 0.2, following the recommendations of McInerney et al. (2017). The innovation, or random component of the REM, follows a Gaussian distribution with a flow-dependent residual mean (Li et al., 2016). The parameters of REM were inferred using the method-of-moments (Hazelton, 2011). For the detailed REM formulation, including the model equations, readers are referred to Hunter et al. (2021) and Romero-Cuellar et al. (2024).

In this study, we employed CoSMoS (Complete Stochastic Modelling Solution) (Papalexiou, 2018) as the stochastic weather generator (SWG). CoSMoS is an R package designed for the stochastic simulation of univariate, multivariate, or random field non-Gaussian time series. It implements a flexible framework that unified, extends, and improves the theory of stochastic modelling for hydroclimatic process, preserving key statistical characteristics such as marginal distributions, autocorrelation structures, and intermittency (Papalexiou, 2018). The core assumption underlying CoSMoS is that any process can be generated by transforming a parent Gaussian process.

For this study, we inferred the parameters of the generalized gamma distribution, autocorrelation structure, and dry-period distribution of daily precipitation using 30 years of gauge-based observations, with statistics estimated separately for each calendar month. Similarly, for maximum and minimum temperatures, we estimated the monthly marginal distributions and autocorrelation structures. Using the inferred parameters, CoSMoS was used to generate long-term (e.g., 1000 synthetic years) daily time series of precipitation, maximum temperature, and minimum temperature. These synthetic meteorological forcings were then used to drive the hydrologic model, enabling the simulation of annual maximum flows and the estimation of flood frequency distributions.

To adapt CoSMoS for flood frequency purposes, we implemented two key modifications: (1) a bootstrap-based smoothing strategy across monthly boundaries to address abrupt discontinuities in statistical properties, and (2) the introduction of physical constraints on extreme precipitation to prevent unrealistically long-tailed behaviour in the generalized gamma distribution. These constraints help avoid infinite or implausible values in simulated extremes. Full details of these modifications are provided in the Supplement (Sect. S2).

Following calibration of the hydrologic model, fitting of the stochastic weather generator (SWG), and inference of the residual error model (REM) parameters, the process-based flood-frequency analysis proceeds in two stages. First, the SWG generates 1000 years of synthetic meteorological forcings, which are transformed into streamflow using the calibrated hydrologic model. The annual maximum flow is then extracted from each synthetic year, producing a deterministic sequence of 1000 simulated annual maxima.

Second, the REM is applied to each simulated annual maximum to generate 1000 residual-error realizations. This procedure produces 1000 REM-corrected annual-maximum sequences, each containing 1000 years of flood values. For each corrected sequence, the annual maxima are ranked and assigned annual exceedance probabilities using the Weibull plotting-position formula. Flood quantiles are then estimated for the selected return periods, resulting in an ensemble of 1000 flood-frequency curves.

The central UQ-flood estimate at each return period is obtained from the median of the ensemble, while the 95 % predictive interval is defined by the 2.5th and 97.5th percentiles. This interval represents variability across the residual-error realizations, conditional on the synthetic meteorological sequence, calibrated hydrologic model, fitted SWG, and selected REM formulation.

A Bayesian at-site flood-frequency analysis based on the Generalized Extreme Value (GEV) distribution was used as a secondary statistical benchmark for the central flood-quantile estimates. Long-record empirical annual-maximum-flow estimates remained the primary observational benchmark. The GEV distribution was selected because it is grounded in extreme-value theory and is widely used to model annual maximum flows in hydrologic applications (Coles, 2001; Jenkinson, 1955; Vogel and Wilson, 1996; Zaghloul et al., 2020).

The GEV distribution was fitted to the observed annual maxima under two data configurations: the full available record and the same 30-year record used to develop UQ-flood. Bayesian inference was used to characterize uncertainty in the GEV parameters and corresponding flood quantiles (Liang et al., 2012; Parkes and Demeritt, 2016). Markov chain Monte Carlo sampling was applied to draw from the joint posterior distribution of the GEV location, scale, and shape parameters. Posterior mean flood quantiles were used as the central estimates, and the 2.5th and 97.5th percentiles of the posterior flood-quantile distributions defined the 95 % credible intervals.

The analysis was implemented using the extRemes R package (Gilleland and Katz, 2016). The adequacy of the fitted GEV distributions was evaluated using quantile plots, probability plots, and return-level plots for each watershed under both the short-record and long-record configurations. The diagnostics did not indicate important concerns with the fitted GEV models. The complete diagnostic results are presented in Figs. S2–S7 of the Supplement.

Central flood-quantile estimates were evaluated at return periods of T=2, 5, 10, 20, 50, 100 years. For each return period, the interval width was calculated as: 1URT=qT97.5-qT2.5 Where qT97.5 and qT2.5 denote the upper and lower limits, respectively, of the 95 % interval for the flood quantile associated with return period T.

The GEV and UQ-flood intervals represent different conditional uncertainty components. The Bayesian GEV credible intervals primarily characterize sampling and parameter uncertainty conditional on the observed annual-maximum sample and selected statistical model. In contrast, the UQ-flood intervals represent predictive variability across residual-error realizations conditional on the calibrated hydrologic model, fitted stochastic weather generator, and selected REM formulation. Consequently, their widths were not compared as equivalent measures of precision or performance. Instead, the GEV results were used to provide statistical context for evaluating the central UQ-flood estimates against the long-record observational benchmarks.

This study quantifies uncertainty in discharge quantiles associated with specified annual exceedance probabilities (AEPs), rather than uncertainty in plotting positions or order statistics. The focus is therefore on vertical uncertainty – i.e., uncertainty in discharge for a fixed return period – which is the quantity most relevant for flood-risk assessment and engineering design.

To estimate confidence intervals for discharge quantiles, we adopt an analytical approach based on fitting parametric probability distributions to annual maximum flow (AMF) data. Several candidate distributions (e.g., Weibull, exponential, gamma, and lognormal) are fitted using maximum likelihood estimation. Model selection is guided by a combination of visual diagnostics (density plots, Q–Q plots, and cumulative distribution function comparisons) and statistical criteria, including the Akaike Information Criterion (AIC) and goodness-of-fit statistics. The selected distribution provides the basis for estimating uncertainty in discharge quantiles corresponding to target AEPs.

For a given AEP, the corresponding non-exceedance probability is defined as: 2p=1-1AEPN+1 Where N is the sample size and AEP is expressed in years. The uncertainty in this probability estimate due to finite sample size is modelled using the beta distribution, consistent with the analytical framework of Baâ et al. (2001). The lower and upper bounds of the 95 % confidence interval are computed as: 3x0.05=qbeta0.025,p,N-p+1x0.95=qbeta0.975,p,N-p+1 These bounds are then transformed into flow quantiles using the cumulative distribution function (CDF) of the selected parametric model: 4Q0.05=F-1x0.05Q0.95=F-1x0.95 where F-1 is the inverse CDF (quantile function) of the fitted distribution. This procedure yields confidence intervals for discharge quantiles that explicitly reflect sampling uncertainty conditional on the assumed statistical model. It provides a transparent, closed-form alternative to resampling-based methods and is well suited for comparative analyses across multiple basins. We emphasize that this approach differs conceptually from methods that quantify uncertainty in exceedance probabilities or order statistics (horizontal uncertainty), such as fractional order statistics (e.g., Serinaldi, 2009). While such approaches are valuable – particularly for estimating uncertainty beyond the observed sample maximum – the present study prioritizes uncertainty in discharge for fixed design return periods.

To evaluate the proposed UQ-flood framework, we designed a numerical experiment focused on two questions: (1) whether the central flood-quantile estimates obtained using 30 years of observations are consistent with long-record observational benchmarks, and (2) how explicitly accounting for hydrologic-model error through the residual error model affects process-based flood estimates.

Long-record empirical annual-maximum-flow estimates were used as the primary benchmark. A Bayesian GEV analysis was retained as a secondary statistical benchmark for the central flood-quantile estimates. Because the UQ-flood and GEV intervals characterize different uncertainty components, their widths were not compared as equivalent measures of precision or performance.

The evaluation consists of two main components:

Evaluation under different observational record lengths

UQ-flood was developed using 30 years of observed meteorological and streamflow data. Its central flood-quantile estimates were evaluated against:

Empirical annual-maximum-flow estimates derived from the full available observational record.

For the Black River and Moyie River watersheds, the HBV-EC hydrologic model, CoSMoS stochastic weather generator, and residual error model were calibrated or inferred using observations from 1 January 1991 to 31 December 2020. For the Lahave River watershed, the corresponding period extended from 1 January 1992 to 31 December 2021. These periods represented the most recent complete 30-year observational records available for the respective watersheds. For each watershed, the same period was also used for the short-record GEV analysis, ensuring consistency across the modelling and statistical comparisons.

The UQ-flood framework was further evaluated for the Moyie River and Lahave River watersheds, shown in the left and right panels of Fig. 5, respectively. As in the Black River analysis, the long-record empirical annual-maximum estimates provide the primary benchmark. Bayesian GEV estimates based on the full and 30-year records provide secondary statistical benchmarks, while the process-based simulation without REM is included to assess the contribution of residual-error correction. UQ-flood was developed using 30 years of meteorological and streamflow observations in both watersheds.

The central UQ-flood estimates remain within the confidence intervals for the long-record discharge quantiles across the evaluated return periods. However, neither UQ-flood nor the long-record GEV is uniformly closest to the empirical estimates. For Lahave River, UQ-flood is closer to the empirical estimate at the 50-year return period, whereas the long-record GEV is closer at the 100-year return period. For Moyie River, the two approaches produce similar estimates at lower return periods, while the long-record GEV is closer to the empirical estimate at the 50-year return period. These results are notable because UQ-flood uses only 30 years of observations, whereas the long-record GEV uses the full available annual-maximum series. The corresponding numerical estimates are provided in the Supplement (Table S1).

The UQ-flood and GEV uncertainty intervals represent different conditional uncertainty components, and their widths are therefore not compared as equivalent measures of precision or performance. Instead, the evaluation focuses on whether the central estimates are consistent with the long-record observational benchmarks. The confidence intervals for the empirical discharge quantiles are particularly important at high return periods, where the observed plotting positions are affected by greater sampling uncertainty.

For both watersheds, the process-based simulations without REM underestimate the long-record empirical flood quantiles. Applying the REM shifts the process-based estimates toward the observational benchmarks, demonstrating the importance of representing hydrologic-model discrepancies at the annual-maximum scale. Overall, the additional case studies show that UQ-flood produces central estimates consistent with the observational confidence intervals and that the REM corrects systematic biases in the uncorrected process-based simulations. However, the relative proximity of UQ-flood and GEV to the empirical estimates varies by watershed and return period, and neither approach is uniformly closest across all cases.

Uncertainty is an established consideration in flood frequency analysis, and conventional statistical methods provide confidence or credible intervals for estimated flood quantiles (England et al., 2018). These intervals are valuable for characterizing sampling and parameter uncertainty conditional on the observed flood sample and selected probability model, but they do not necessarily represent uncertainty arising from a process-based modelling chain. In process-based FFA, flood estimates are additionally affected by the representation of meteorological variability, hydrologic-model structure and parameters, antecedent conditions, and errors in simulated flood peaks; the relative importance of these components may also vary with return period and watershed characteristics (Arnaud et al., 2017; Cameron et al., 2000; Newman et al., 2021). Process-based simulation therefore does not eliminate uncertainty associated with short observational records but redistributes it across a broader set of modelling assumptions and components. This distinction is important when interpreting the present results: the UQ-flood and Bayesian GEV intervals characterize different conditional uncertainty components and should not be compared directly as equivalent measures of overall precision. Accordingly, the GEV analysis is retained as a secondary statistical benchmark, while the primary evaluation focuses on whether the central UQ-flood estimates remain consistent with the long-record observational benchmarks and whether the residual error model corrects systematic biases in the process-based flood estimates.

The UQ-flood framework presented in this study offers a complementary approach to existing methods by integrating process-based hydrologic simulation with a residual error model (REM) and a stochastic weather generator. This integration supports a shift towards process-based uncertainty quantification that is consistent with hydrologic processes. Rather than replacing existing methods, UQ-flood aims to enhance uncertainty characterisation by propagating uncertainty from model inputs through to flood quantile estimates. In this context, incorporating error models into continuous simulation frameworks may help improve bias correction and support more transparent flood risk estimation.

A key contribution of UQ-flood is the integration of a process-based hydrologic model, a stochastic weather generator, and a residual error model developed specifically for annual maximum flows. Although these components have been used separately in previous flood-frequency studies, their integration allows systematic hydrologic-model discrepancies to be corrected at the same scale as the target design variable.

The annual-maximum formulation addresses an important mismatch in process-based FFA. Hydrologic models are commonly calibrated using daily streamflow metrics that emphasize overall hydrograph behaviour, water balance, and seasonal dynamics. However, satisfactory daily-flow performance does not guarantee unbiased simulation of annual flood peaks, which may be particularly sensitive to antecedent conditions, threshold processes, snowmelt–rainfall interactions, and upper-tail behaviour. This limitation was evident in the simulations without the REM, which systematically underestimated flood quantiles across the study watersheds. By modelling the residual relationship between observed and simulated annual maxima, the REM corrects these systematic discrepancies and represents residual predictive variability at the scale directly relevant to flood-frequency estimation.

UQ-flood uses a sequential modelling structure in which the hydrologic model, stochastic weather generator, and REM are developed separately. This structure is statistically less complex than fully joint Bayesian approaches that simultaneously infer parameters across the complete modelling chain. However, UQ-flood should not be interpreted as free from subjective or user-defined decisions. Hydrologic-model selection and calibration, weather-generator selection and configuration, REM specification, and transformation choice can all affect the resulting flood estimates. Moreover, long continuous simulations can remain computationally demanding.

The Box–Cox transformation parameter was fixed at λ=0.2, following previous hydrologic residual-error studies that identified this value as suitable for representing heteroscedastic streamflow errors. Nevertheless, the fixed value remains a modelling assumption, and its influence was not evaluated in this study. Future applications should assess whether the selected transformation and residual-error structure adequately represent the residual characteristics of the watershed and flood regime under consideration.

UQ-flood does not require fitting a parametric probability distribution directly to the synthetic annual-maximum series. Instead, flood quantiles are estimated empirically from the REM-corrected sequences using plotting positions. This avoids imposing a parametric form on the final synthetic flood sample, but it does not remove the assumptions embedded in the hydrologic model, weather generator, or REM. The framework should therefore be viewed as a complementary process-based approach rather than a replacement for conventional statistical FFA.

Overall, the contribution of UQ-flood lies in explicitly representing hydrologic-model error at the annual-maximum scale. The framework corrects systematic biases in deterministic process-based simulations and propagates residual predictive variability into flood-quantile estimates.

UQ-flood remains conditional on the choices and assumptions within its modelling chain. The UQ-flood interval represents residual predictive variability, whereas statistical FFA intervals primarily characterize sampling and parameter uncertainty conditional on a selected probability model. Because these intervals represent different uncertainty components, their widths should not be compared as equivalent measures of overall precision.

Flood estimates are influenced by hydrologic-model structure and calibration, stochastic weather-generator selection and configuration, and residual-error-model specification. In this study, CoSMoS initially produced implausibly long-tailed precipitation extremes in very long simulations, requiring a constraint to preserve physical plausibility. UQ-flood is not restricted to CoSMoS and could use other meteorological sampling approaches, including stochastic storm transposition (Wright et al., 2020), reforecast ensemble pooling (Brunner and Slater, 2022), or convection-resolving climate simulations (Dallan et al., 2024). However, all synthetic sequences represent the climate conditions reflected in the calibration period and should not be interpreted as future-climate projections.

A core assumption of UQ-flood is that process-based hydrologic models can derive more useful information than purely statistical extrapolation from short records. That is, expert knowledge about watershed processes – such as water balance, storage, and runoff generation – enables the model to constrain future flood behavior more effectively than sampling-based uncertainty alone (Su and Tung, 2013). In this sense, UQ-flood acts as a more intelligent flood sampler, embedding physical understanding directly into the generation of extreme event ensembles.

The present analysis does not propagate uncertainty in streamflow measurements, rating curves, hydrologic-model parameters, or weather-generator parameters. These uncertainties may be important for rare floods and should be incorporated in future applications. Moreover, UQ-flood requires sufficient meteorological and streamflow observations to calibrate the modelling components and characterize annual-maximum residuals.

Transferability depends on whether the hydrologic model and meteorological generator adequately represent the dominant flood-generating processes. The modular framework can accommodate alternative lumped or distributed models, but this flexibility does not guarantee reliable performance in different or ungauged watersheds. Applications to ungauged basins would require regionalization or parameter-transfer methods and case-specific evaluation.

The current implementation uses annual maxima, but UQ-flood is not structurally limited to this formulation. A peaks-over-threshold extension could use more high-flow information from short records but would require explicit treatment of threshold selection, event independence, declustering, exceedance frequency, and event magnitude. Future work should also use event-scale diagnostics to investigate how hydrologic-model performance, meteorological simulation, residual-error characteristics, and flood-generating mechanisms contribute to differences among watersheds.

The findings across the three case studies highlight the potential practical value of UQ-flood for flood risk management and engineering design. For watersheds with long flow records, UQ-flood produced flood quantile estimates consistent with those obtained using conventional statistical flood frequency analysis (FFA), while yielding narrower uncertainty intervals. Under short-record conditions, such as a 30-year record, UQ-flood also provided robust and actionable flood estimates, whereas conventional statistical FFA produced substantially wider uncertainty intervals that may be impractical for design and planning purposes. These findings suggest that UQ-flood can help address the limitations of local data scarcity, a common challenge in operational flood risk assessment.

From a practical perspective, improved characterization of uncertainty can support more informed design and investment decisions. Uncertainty intervals that are excessively wide can complicate the selection of design floods, potentially contributing to overdesign and unnecessary costs or underdesign and increased flood risk. In applications such as infrastructure planning, floodplain mapping, and insurance risk assessment, more informative uncertainty estimates can support the prioritization of investments, the evaluation of alternative design options, and the development of climate-resilient infrastructure.

UQ-flood also provides a process-based framework for interpreting and communicating flood estimates. By combining hydrologic simulation, explicit bias correction, and residual uncertainty propagation, the framework links flood quantile estimates to modeled hydrologic processes and observed model performance. This provides a complementary perspective to conventional statistical FFA, in which estimates depend primarily on the selected probability distribution and the available sample of annual maximum flows. Nevertheless, the process-based nature of UQ-flood does not eliminate uncertainty associated with model structure, parameter estimation, or the representation of hydrologic processes; these sources of uncertainty should be considered when interpreting results and applying them to engineering decisions.

Finally, the UQ-flood is conceptually aligned with the emerging design simulation approach (Fischer et al., 2025), which emphasizes process-based flood estimation to inform engineering design. Within this context, UQ-flood offers a framework for incorporating quantified uncertainty into decisions such as the selection of design floods and safety factors. Rather than relying exclusively on fixed safety margins, engineers and decision-makers can use uncertainty estimates to evaluate the robustness of alternative design choices against specified risk tolerances. The potential benefit is a more transparent and evidence-based balance between infrastructure costs and flood safety, particularly in watersheds where limited observational records constrain conventional flood frequency analysis.