the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 30 Jul 2026
Agricultural flood risk under seasonally varying rainfall extremes and crop vulnerability
Abstract. Agricultural systems are highly vulnerable to flooding, particularly when extreme precipitation events occur during sensitive crop growth stages. However, most flood-risk assessments rely on static annual hazard scenarios and simplified design storms, neglecting the combined effects of hydrological seasonality, rainfall temporal structure, and crop phenology. In this study, we propose a probabilistic-hydrological-hydraulic framework for agricultural flood-risk assessment under seasonally varying short-duration extreme precipitation. The approach integrates non-asymptotic multivariate frequency analysis, copula-based dependence modelling among rainfall durations, stochastic microcanonical rainfall disaggregation, hydraulic simulations, and crop-specific flood depth-duration vulnerability functions. Flood-hazard maps are generated at the monthly scale and coupled with seasonally varying crop exposure and vulnerability conditions. The framework is applied to a flood-prone agricultural area in northern Italy. Results show that rainfall temporal structure and event duration substantially influence expected annual losses, with long-duration events generally producing the highest damages due to prolonged inundation and waterlogging conditions. The copula-based multi-duration analysis reveals a considerable uncertainty associated with inter-duration dependence, highlighting that the use of a single representative storm duration may significantly bias agricultural flood-risk estimates. The adopted microcanonical rainfall generator also proved effective in reproducing realistic multi-burst rainfall structures and temporally clustered events, which are particularly relevant for representing cumulative soil saturation and flood persistence processes. Overall, the proposed methodology provides a physically consistent and transferable framework for probabilistic agricultural flood-risk assessment and may support climate-risk analyses, adaptation planning, and flood-risk management in agricultural systems exposed to increasingly complex hydrometeorological extremes.
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Status: open (until 23 Sep 2026)
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RC1: 'Comment on egusphere-2026-4418', Anonymous Referee #1, 19 Aug 2026
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The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-4418/egusphere-2026-4418-RC1-supplement.pdfReplyCitation: https://doi.org/
10.5194/egusphere-2026-4418-RC1 -
RC2: 'Comment on egusphere-2026-4418', Anonymous Referee #2, 23 Aug 2026
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General assessment
This manuscript presents an interesting and well-structured probabilistic framework for agricultural flood-risk assessment, explicitly accounting for the seasonal variability of both rainfall hazard and crop vulnerability. I particularly appreciate the attempt to propagate the uncertainty associated with rainfall duration, inter-duration dependence, and within-event temporal structure through a hydrological-hydraulic modelling chain and ultimately into crop losses. The proposed framework represents a valuable step beyond more conventional approaches based on seasonally invariant hazard scenarios.
The manuscript is generally well written, the methodological workflow is comprehensive, and the results are potentially relevant for both flood-risk assessment and agricultural water management. I therefore recommend moderate revision. My comments mainly concern methodological clarification and some additional discussion that would improve the reproducibility and general applicability of the proposed framework.
Possible alternative based on semi-continuous modelling
The authors may consider mentioning, at least in the Discussion, an alternative modelling strategy based on semi-continuous simulations, particularly for small and/or ungauged catchments. Instead of independently propagating a large number of synthetic design events, one could generate calendarized synthetic precipitation sequences and continuously or semi-continuously propagate the identified flood-producing events through the rainfall-runoff model. Such an approach would naturally retain information on seasonality and antecedent hydrological conditions and could provide a useful alternative to the proposed event-based framework.
I understand that propagating all identified flood waves through a detailed 2D hydraulic model would entail a substantial computational burden — indeed, the computational cost reported in the present study already demonstrates this issue — so I am not suggesting that the authors implement such an approach here. Rather, I think it would be useful to briefly acknowledge it as a potential alternative or future extension, especially for applications to small ungauged basins and when synthetic calendarized precipitation series are available.
Clarification of the SCS-CN implementation
Some additional information on the implementation of the SCS-CN method would be useful. The manuscript states that rainfall-runoff generation is represented through an “event-based approach”, but it is not entirely clear how rainfall losses and effective precipitation are calculated during each synthetic hyetograph. In particular, are cumulative event losses first calculated from total event rainfall and subsequently distributed in time, or is the CN formulation applied incrementally/time-step by time-step during the event?
This distinction is important because the original SCS-CN method was conceived as an event-scale rainfall-runoff relationship rather than as an infiltration model to be directly applied independently at successive time steps. If an incremental implementation is adopted, its assumptions and limitations should be explicitly discussed. For more process-oriented applications, mixed approaches coupling the CN concept with an infiltration formulation, such as CN4GA-type approaches, could potentially provide a more physically consistent representation of intra-event infiltration dynamics.
Monthly discretization versus broader seasonal groups
The monthly discretization is one of the central characteristics of the proposed framework and is clearly useful for coupling rainfall hazard with crop phenology. However, it also produces a substantial reduction in the effective rainfall sample size. The manuscript itself acknowledges that the monthly analysis results in considerably larger uncertainty than the annual analysis and that, particularly in autumn and winter, the reduced number of events decreases the robustness of the estimated dependence structure.
I therefore wonder whether an intermediate temporal discretization could be considered. For example, groups of two or three hydrologically homogeneous months could reduce the number of parameters, increase the effective sample size, and improve the robustness of both the marginal distributions and the copula dependence structure. Figure 3 already provides results grouped visually into Jan–Mar, Apr–Jun, Jul–Sep, and Oct–Dec, although individual months remain distinguished within each group.
I do not think that the authors necessarily need to replace the monthly analysis, since monthly resolution is useful for crop phenology. However, a short sensitivity analysis, or at least a discussion of the trade-off between temporal resolution and statistical robustness, would considerably strengthen the methodological contribution. A possible compromise could be to estimate rainfall statistics using homogeneous seasonal groups while retaining monthly crop exposure/vulnerability, provided that the underlying precipitation regimes within each group are sufficiently similar.
Definition of monthly probabilities and severity classes
I suggest clarifying more explicitly how the probabilities associated with the return-period/severity classes are calculated. Section 2.1 defines each severity bin through return-period thresholds and associates a representative hydraulic response with each class, but the practical conversion from the return-period scenarios to is not immediately transparent.
Reduction of the synthetic ensemble to P000, P050 and P100
The strategy used to reduce the very large synthetic rainfall ensemble to a manageable number of hydraulic simulations is understandable and necessary. Nevertheless, I think the selection procedure requires a little more explanation. From 36 million synthetic hyetographs, the authors retain three rainfall profiles for each month/return-period/duration combination, referred to as P000, P050 and P100, corresponding to minimum, median and maximum rainfall depths.
Please specify exactly which rainfall quantity is used to rank the hyetographs before extracting these three profiles (total event rainfall, rainfall at the reference duration, 360-min accumulation, etc.). Moreover, using the absolute minimum and maximum of a stochastic ensemble may make the resulting envelope dependent on ensemble size. It would therefore be useful to clarify whether P000 and P100 are literal sample minima/maxima or estimates of distributional endpoints. If they are sample extrema, some discussion of the robustness of this choice compared, for example, with low/high but non-extreme percentiles would be helpful.
Bias in the microcanonical temporal disaggregation
The manuscript provides a useful diagnostic showing that the cascade model increasingly overestimates the wet fraction at finer temporal resolutions, particularly in autumn and winter. Since one of the main conclusions of the study is precisely that the internal temporal organization of rainfall can substantially affect runoff and crop losses, I think the implications of this bias deserve slightly more discussion.
Overall, I find the manuscript methodologically interesting and potentially valuable for agricultural flood-risk assessment. The comments above mainly concern clarification of modelling assumptions, reproducibility, and a broader discussion of alternative modelling strategies.
Citation: https://doi.org/10.5194/egusphere-2026-4418-RC2 -
RC3: 'Comment on egusphere-2026-4418', Anonymous Referee #3, 29 Aug 2026
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The manuscript presents a probabilistic hydrological–hydraulic framework to assess agricultural flood risk under seasonally varying short‑duration extreme rainfall. It integrates multivariate frequency analysis, copula‑based dependence modelling, stochastic rainfall disaggregation, hydraulic simulations, and crop‑specific depth–duration vulnerability functions. Monthly hazard maps are combined with crop phenology to capture how flood timing and duration influence agricultural losses. The framework is applied to a case study in northern Italy to demonstrate that rainfall temporal structure and event duration strongly affect expected damages. The approach highlights the substantial uncertainty associated with multi‑duration rainfall dependence and its propagation into agricultural risk estimates.
The manuscript is well written and very well organized, and the proposed framework is highly relevant for the scientific community, offering a practical perspective for flood‑risk evaluation in support of agricultural management. Further, the simplifying assumptions and limitations of the modelling framework are very well discussed, offering a clear perspective on future research directions.
I consider the manuscript worthy of publication, and I only have a few suggestions — in some cases simply points of curiosity. These comments mainly concern the presentation of the methodology and the results, which could be refined to further enhance reader understanding and improve reproducibility. The comments are listed below, and I hope they will be useful for strengthening a manuscript that is already very strong in its current form.
Figure 1. I assume that vulnerability is crop‑specific; therefore, vulnerability should be zero during months when the crop is absent (already harvested or not yet seeded). Is vulnerability explicitly linked to the crop’s growth stage? And does it depend on crop exposure?
The notation could be improved, for instance by avoiding the use of the same letter—capital and lowercase—for different indices (e.g., for the number of severity classes and for the month index).
Figure 1, line 185 and paragraph title. I understand that “disaggregation” is used here to indicate the separation of the observed rainfall time series at a given raingauge into 12 monthly time series spanning several years (under stationarity). If this interpretation is correct, I suggest using a different term to avoid confusion with the storm‑scale disaggregation performed through the microcanonical random cascade.
After line 195, I recommend stating explicitly that this procedure yields 12 monthly probability distributions of extreme rainfall intensity (for each duration/temporal scale), either at each raingauge or regionally, as described later. Please confirm that this interpretation is correct.
Lines 203–204. The sentence “In the present framework that quantity is the set of ordinary events of a given month block and duration, and not the annual maxima” would be clearer if introduced earlier.
Line 265. The expression “among durations” seems to refer to “among rainfall accumulations/depths at different durations.” Is this the intended meaning? Or do you refer to “durations associated with specific rainfall values”? More generally, the manuscript shows some ambiguity between event duration and time accumulations (the vector ); using distinct terminology would help (see also line 292).
Line 266. Please clarify which variables are being referred to here.
Lines 526, 556, 568, 595, 601, 606, 610, 628, 663, 666, 735. The reference to the corresponding figure is missing.
Could you also indicate the average number of events per month/year corresponding to the threshold , so that the reader can better understand the sample size implied?
Figure 3. The December boxplot is missing from all lower panels.
I also wonder about the difference in crop damage—within your modelling framework—between a temporally variable rainstorm and a homogeneous rectangular hyetograph. Is it possible to disentangle the effects of duration–depth joint variability from those of the intra‑storm temporal distribution? The latter may be relevant, but it is likely influenced by the method used to compute effective rainfall/hydrological losses and by hydraulic propagation (including uncertainties in rainfall spatial averaging and model parameters). Moreover, the microcanonical cascade does not seem fully effective in reproducing the internal storm structure (e.g., wet–dry alternation across scales). A brief comment on this point could strengthen the discussion.
From Fig. S18, it appears that—except for the initial growth stage—damage is zero for flood events lasting less than one day, which I expect to be a very common duration for the flooding event. Is this true? This suggests that most (or all) damage occurs during the initial stage month, depending on crop type, which would substantially simplify the damage simulation. Of course, results depend on flooding recession dynamics, governed by soil moisture and weather conditions. Could you provide additional details on the distribution of flood durations? And which factors primarily control this key variable? This is crucial given the loss function adopted.
Figure 5. To what extent are these results influenced by the method used to compute effective rainfall? A short comment would be helpful.
I believe that additional details on the infiltration model would improve the reader’s understanding of the results.
Line 699. Could you provide more information on flood‑duration distribution in the study area? Is there any evidence of “correlation” with terrain depressions? If yes, this is an important practical proxy for effective management.
Lines 723–725. This issue is mentioned but not shown in the results; presenting it more clearly would strengthen the manuscript.
Citation: https://doi.org/10.5194/egusphere-2026-4418-RC3
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