the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Jun 2026
Climate-sensitive Derived Flood Frequency Analysis Based on Flood Events Characteristics
Abstract. Understanding how flood frequency changes under non-stationary hydro-climatic conditions remains a key challenge in hydrology. This study presents a Bayesian process-based framework for flood frequency analysis that explicitly accounts for the seasonal dependence of rainfall–runoff processes and their sensitivity to climate change. The approach links an event-based rainfall–runoff model with probabilistic representations of storm, soil moisture, and catchment response, allowing the joint propagation of uncertainty from climate drivers to flood quantiles. The process-based structure of the framework also enables the disentangling of individual flood drivers, such as the upward shift of the zero-degree isotherm, long-term changes in soil moisture regimes, and variations in precipitation intensity. The framework is implemented in Austrian hotspots, i.e. groups of similar catchments, using long-term hydrometeorological records and regional climate projections (EURO-CORDEX). Results show that (i) changes in flood frequency are primarily driven by projected increases in precipitation intensity, while temperature and soil moisture act as modulators or amplifiers of this signal; (ii) precipitation changes have larger but more uncertain impacts on floods than temperature and soil moisture variations; (iii) the expected reduction in soil moisture tends to mitigate frequent floods but has mores limited influence on rare events. The proposed methodology provides a transferable tool for assessing climate-sensitive flood hazards in non-stationary environments.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-2808', Anonymous Referee #1, 30 Jul 2026
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AC1: 'Reply on RC1', Luigi Cafiero, 16 Oct 2026
We thank the Reviewer for her/his positive evaluation of our manuscript and for providing constructive, insightful comments that have helped us significantly improve the discussion of our framework. Below is a detailed, point-by-point response to each comment.
1) We acknowledge that the physical and statistical rationale behind the choices below the modeling assumptions needs to be more explicitly stated to improve transparency. We will revise Section 3.2 to briefly summarize why these distributions were selected based on the cited literature. Regarding model simplicity, our assumption is that, even if the model is perhaps too simple for practical design flood estimation, it is not too simple regarding the way different processes transform changes in the inputs in changes in the flood frequency curves.
2) We agree that catchment size and response times dictate different hydrological memories. The choice of a fixed 100-day window was actually the result of preliminary sensitivity analyses. We tested different time windows and found that the 100-day duration consistently provided the highest overall correlation with the inferred event runoff coefficients across the majority of the hotspots. While optimizing this window for each specific hotspot could have marginally improved local performance, a uniform duration was chosen as a reasonable compromise to simplify the framework and ensure consistency in the regional comparison. Furthermore, the event-based Monte Carlo approach was specifically chosen for two main advantages: (1) computational efficiency in propagating Bayesian uncertainty over millions of synthetic events, and (2) the ability to analytically disentangle the individual drivers (precipitation, 0°C line, and soil moisture). We will integrate these aspects into the Discussion section to explicitly address the advantages and limitations of this event-based approach compared to continuous simulations, and to clarify the rationale behind the 100-day window.
3) We thank the reviewer for highlighting the critical interplay between model structure, parameter dimensionality, and overall uncertainty. Regarding the potential underestimation of flood response variability due to model simplification, the comparison with the continuous framework (WETRAX)—presented in Figure 3—demonstrates that our simplified linear rainfall-runoff model captures the key dynamics and peak variability across the target hotspots, without overly dampening the extremes. Nonetheless, we acknowledge that structural assumptions, such as a constant event runoff coefficient and linear routing, inherently omit complex non-linear threshold processes. This constitute an additional uncertainty while our linear reservoir representation provides a parsimonious way to evaluate the sensitivity of flood peaks to climate.
4) We thank the reviewer for this constructive observation. Concerning the high-dimensional parameter space, we fully acknowledge that estimating 25 parameters across the different process distributions inevitably introduces epistemic uncertainty into the derived flood frequency estimates. In accordance with the reviewer's suggestion, we will expand the Discussion section to explicitly address this parameter dimensionality, discuss the associated uncertainties, and outline the structural trade-offs of the framework.
5) Regarding this point, the chosen prior distributions are generally weakly informative and are introduced primarily to regularize the Bayesian inference and ensure computational stability. The only exception is the prior regarding temperature changes, which is more informative but is directly grounded in well-established and documented regional warming estimates. To explicitly verify the robustness of our outputs, we will perform a sensitivity test by doubling the prior variances across the parameters.
6) We thank the reviewer for this constructive suggestion. The rationale behind our spatial pooling is supported by the fact that intra-hotspot variability is significantly smaller than the inter-hotspot differences. Specifically, the spread of mean event characteristics across individual catchments within the same hotspot is consistently two to three times smaller than the variability observed between different regional hotspots. In the revised manuscript, we will clarify and deepen these aspects. The objective here is not the estimation of flood changes in one individual catchment but in a certain climatic/orographic/geologic zone, which is homogeneous within the hotspots.
7) We agree that consistent axis limits significantly improve visual comparability. We will revise Figure 5 accordingly, harmonizing the axis limits for each variable across all seasonal subplots to enhance the overall readability of the figure.
8) We thank the reviewer for this helpful suggestion. While this aspect was briefly introduced in Section 3.3 ("Propagation of climate change signals"), its visibility and clarity can be improved to avoid any potential ambiguity. In the revised manuscript, we will refine and highlight this explanation.
9) We agree that understanding the relative contributions of temperature, precipitation, and antecedent wetness is crucial. Conceptually, this relative attribution is already embedded in our results, specifically within the scenario-dependent shifts and confidence intervals illustrated in Figure 6 (and detailed for all individual hotspots in the Supplementary Material). However, we recognize that this message may currently require too much effort to extract from the figures and spatial maps alone. Rather than adding another figure that might duplicate existing material, we will carefully re-evaluate how to convey this synthesis more clearly.
Citation: https://doi.org/10.5194/egusphere-2026-2808-AC1
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AC1: 'Reply on RC1', Luigi Cafiero, 16 Oct 2026
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RC2: 'Comment on egusphere-2026-2808', Sepehr Almasi, 21 Sep 2026
Comments:
1. The Stationarity Paradox in a Non-Stationary Study
The core objective of this paper is to analyze flood
frequency under changing, non-stationary hydro-climatic conditions. However, the authors explicitly admit in the discussion that the number of flood-generating events per season was assumed to remain stationary between historical and future periods. This is a severe methodological paradox. Projecting climate-driven changes in flood regimes while artificially fixing the storm frequency negates the primary claim of the paper. The framework must be updated to dynamically extract varying storm frequencies directly from the EURO-CORDEX climate projections.
2. The Synthetic Echo Chamber
The Bayesian stochastic framework is calibrated on a 100-year synthetic dataset hallucinated by the WETRAX weather generator coupled with a distributed rainfall-runoff model. Calibrating a sophisticated statistical model entirely on the artificial outputs of another computer model, rather than against empirical stream gauge observations, is highly problematic. This approach merely propagates and compounds the structural biases of the WETRAX model. The authors must include a rigorous validation section demonstrating the framework's performance against actual, unadulterated observational data from the Austrian hotspots.
3. Hydrodynamic Oversimplification
Despite utilizing computationally heavy regional climate projections and Bayesian inference, the authors compress the complex spatial heterogeneity and hydraulic routing of Alpine catchments into a primitive "linear reservoir" model. Modeling highly diverse catchments as simple linear storage units strips away critical hydrodynamic physics. The authors must provide a dedicated sensitivity analysis proving that this drastic physical simplification does not mask massive structural uncertainties in their extreme flood projections.
4. Statistical Censorship of Compound Extremes
The methodology dictates a "minimum inter-event time of 72 hours" strictly to enforce the statistical independence of successive events. While this satisfies the requirements of extreme value statistics, nature is not bound by a 72-hour stopwatch. By systematically deleting secondary flood peaks that occur within this window, the framework artificially sanitizes the dataset and entirely ignores compound or clustered flood events—which are often the most devastating mechanisms in saturated catchments. The authors must quantify the physical risk being omitted by this statistical convenience.Citation: https://doi.org/10.5194/egusphere-2026-2808-RC2 -
AC2: 'Reply on RC2', Luigi Cafiero, 16 Oct 2026
We sincerely thank Reviewer 2 for his rigorous, constructive, and demanding review. His critique motivated us to introduce a fundamental methodological enhancement regarding non-stationary flood occurrence frequencies, thus allowing us to sharpen the physical and mathematical justification of our derived flood frequency architecture. Below, we address each comment point-by-point.
1) We agree with the reviewer that allowing the Poisson arrival rate m to vary would improve the assessment done in the paper. In the revised manuscript, we will update the parameter m under climate change based on the climate projections from the CORDEX ensemble. Unlike the observational events used to calibrate the Bayesian framework, which were identified from observed flood hydrographs, climate model outputs lack direct discharge records. We will therefore adjust parameter m by extracting independent precipitation events from CORDEX based on tailored hydrometeorological criteria, such as duration, intensity, and phase thresholds, and scaling the arrival rate according to the projected changes in their seasonal frequency. We will update the methodology and simulation results accordingly to account for this non-stationarity.
2) Even though we do not clearly understand what is meant by “hallucinated” in this context, we can see the point raised here. Regarding the choice of the WETRAX continuous framework, our primary goal is to disentangle and isolate the individual impacts of specific flood drivers within a controlled, process-based environment. Relying on a distributed hydrologic model provides complete and internally consistent long-term series of all hydrometeorological state variables and fluxes. Nevertheless, we agree with the reviewer that grounding this framework against real-world observations would allow the simulated dynamics to mirror empirical flood responses. In an ideal world, with sufficient and reliable observation data, one could obtain the events and their characteristics directly from them. Here we accept the compromise of assuming that the complex WETRAX model represents the hydrological processes reasonably well. We therefore will not build our framework on observed data. In the revised manuscript, we will expand the validation section to benchmark the continuous simulations against observed stream gauge data across the Austrian hotspots. We will report quantitative metrics assessing the performance of both the distributed hydrological model and the weather generator, while citing the foundational literature that introduces the WETRAX+ chain across Austria.
3) In the revised manuscript, we will clarify that our objective is not the calibration of operational baseline flood frequency curves, e.g., to be used to produce hazard maps. Instead, our goal is to evaluate how flood frequency curves shift in response to climate perturbations, meaning our primary interest lies in capturing process sensitivity and propagating change signals. Within Derived Flood Frequency Analysis, adopting a parsimonious linear reservoir model is, in our opinion, sufficient to decouple and attribute the individual effects of climate drivers, at least as an approximation. Furthermore, this analytical formulation makes the required Monte Carlo sampling of millions of synthetic events computationally tractable. Moreover, Figure 3 shows that event-by-event peak discharges simulated by the linear reservoir align well with those from the continuous distributed model (WETRAX+) across all ten hotspots. Accordingly, we will revise the discussion to transparently discuss the boundaries and trade-offs of the linear routing scheme. However, we believe that a dedicated sensitivity analysis of the physical simplification of the derived distribution approach is out of the scope of this paper.
4) We do not clearly understand how the "omitted physical risk " could be quantified, but an additional discussion on compound events is indeed a good addition to the paper. Adopting a minimum inter-event time of 72 hours may cluster compound flood events into individual ones. The procedure is applied to satisfy the independence assumption underpinning extreme value modeling and Poisson-based Derived Flood Frequency Analysis. Consequently, our current setup does not evaluate explicitly potential climate-induced shifts in the occurrence frequency or temporal clustering of successive flood events, which can be a key driver of extreme runoff. In the revised manuscript, we will address this limitation in the Discussion section, contextualizing our findings using recent literature on flood clustering and compound events.
Citation: https://doi.org/10.5194/egusphere-2026-2808-AC2
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AC2: 'Reply on RC2', Luigi Cafiero, 16 Oct 2026
Data sets
Supplementary material - Climate-sensitive Derived Flood Frequency Analysis Based on Flood Events Characteristics Luigi Cafiero https://doi.org/10.5281/zenodo.20051452
Model code and software
Supplementary material - Climate-sensitive Derived Flood Frequency Analysis Based on Flood Events Characteristics Luigi Cafiero https://doi.org/10.5281/zenodo.20051452
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The manuscript presents an interesting and timely contribution to climate-sensitive flood frequency analysis. The proposed framework is original in the way it combines event-based derived flood frequency analysis, Bayesian inference, and climate-change perturbations of key flood-generating processes. In my opinion, the work is scientifically sound, well structured, and potentially suitable for publication. The modelling assumptions are generally well motivated and supported by previous literature, and the paper provides useful insights into the relative role of precipitation, temperature-related processes, and antecedent catchment conditions in shaping future flood frequency.
I therefore recommend publication after minor revisions. My comments mainly concern clarifications of some modelling choices, additional discussion of the implications of the adopted framework, and a few suggestions to improve the presentation of the results.