the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 31 Jul 2026
Compound Risk Assessment of Low River Flows and High Urban Runoff: Frequency of critical drainage conditions in relation to pollutant inputs
Abstract. Urbanization and climate variability increasingly intensify hydrological extremes that impair water quality. A critical compound stress arises when pollutant-rich urban runoff coincides with limited river dilution capacity. To characterize this interaction, we analyze compound events in two directional modes: (i) low river flow paired with corresponding urban runoff, and (ii) high urban runoff paired with concurrent river flow. While these modes represent distinct pathways leading to loss of dilution capacity, the underlying variables exhibit weak and inconsistent dependence, limiting the applicability of conventional bivariate extreme value approaches. To address this limitation, we introduce the Urban-Runoff-to-River-Flow ratio as a direct indicator of dilution stress. A ratio-based extreme value framework is developed using both block maxima and peak-over-threshold approaches, with parameters estimated via maximum likelihood and L-moment methods. The analysis is based on more than two decades of discharge data from three catchments in Lower Saxony, Germany, representing contrasting hydrological regimes. Model performance and compound risk estimates are evaluated against two reference benchmarks: (i) a synthetic benchmark derived from marginal extremes under independence assumptions, and (ii) a conditional benchmark based on historically co-occurring events. Results show that conditional approaches systematically underestimate compound risk in weakly dependent systems, while synthetic estimates provide an upper bound by enforcing coincidence of extremes. In contrast, the ratio-based approach captures the interaction between pollutant loading and dilution capacity more consistently across sites. Overall, the proposed framework provides a robust and physically interpretable method for assessing compound dilution stress, particularly in systems where dependence between drivers is weak or unstable.
Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-4177', Anonymous Referee #1, 03 Sep 2026
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RC2: 'Comment on egusphere-2026-4177', Anonymous Referee #2, 04 Sep 2026
The study addresses an interesting and potentially novel approach to assessing compound stress associated with high urban runoff and low river flow. However, I have several concerns regarding the validation and reliability of the proposed method.
First, the proposed runoff-to-river-flow ratio is a useful indicator, but it is not, by itself, a model of the dependence structure between the two variables. A univariate distribution fitted to the ratio cannot reproduce or simulate the joint behavior of urban runoff and river discharge. The authors should clarify this limitation.
Second, the conclusion that copula modeling is unsuitable because the dependence is weak is not sufficiently justified. Copulas can represent weak dependence, independence, and different forms of tail dependence. Moreover, the negative dependence reported for some cases may be particularly relevant because high urban runoff occurring with low river flow represents the critical compound condition. I recommend comparing the proposed method with an independence copula and selected copula families, including rotated copulas, and evaluating their performance using joint exceedance probabilities and out-of-sample validation.
The “synthetic independence benchmark” also requires correction. Dividing a high urban-runoff return level by a low river-flow return level at the same return period does not represent statistical independence, and the resulting ratio does not necessarily have that return period. Under independence, the ratio distribution should be obtained by independently simulating the two fitted marginal distributions or by analytically deriving the distribution of their ratio. Similarly, dividing separately estimated conditional quantiles does not necessarily produce a valid conditional return level for the ratio.
I am also concerned about the hydrological estimation at the ungauged virtual outlets. River discharge is transferred from gauged locations using drainage-area scaling, but no calibration or independent validation is presented. This is particularly important for Gifhorn, where there is a large difference between the drainage areas of the gauge and the virtual outlet. The authors should validate the scaling procedure using available upstream/downstream gauges or a pseudo-ungauged experiment and compare it, if possible, with a physical or data-driven hydrological model.
Likewise, urban runoff is generated using the Rational Method without validation against observed urban runoff. The application of this event-based method to produce a continuous runoff series through five-minute simulations and superposition needs stronger justification. Calibration, comparison with observed outfall discharge, or benchmarking against a model such as SWMM would substantially improve the reliability of the analysis. Uncertainty in the runoff coefficient, rainfall data, time of concentration, and drainage-area scaling should also be propagated into the final ratio estimates.
Overall, the idea is promising, but substantial methodological clarification and additional validation are required. I therefore recommend major revision.
Citation: https://doi.org/10.5194/egusphere-2026-4177-RC2
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Summary
This manuscript presents a method to quantify the importance of urban runoff compared to river flow from rural areas, which determines how much urban pollutants are diluted. The authors explicitly focus on two sets of compound events, conditioning on either low river flow or high urban runoff. They test different methods for extreme value analysis to analyse the dependence.
Overall impression
The manuscript is well-written with a clear structure and very few typos.
All methods are explained, but I am not an expert on statistics, so I cannot judge if the method is free from errors in the description or application.
I’m missing a discussion comparing the results of your study with previous literature.
I think it would be good to add a paragraph to the conclusion explaining how your study would (eventually) contribute to water quality management.
General comments
I think the title “Compound Risk Assessment of Low River Flows and High Urban Runoff: Frequency of critical drainage conditions in relation to pollutant inputs” could be shortened. In the text, you never use the term “critical drainage conditions”. Maybe “Compound Risk Assessment of Low River Flows and High Urban Runoff in relation to pollutant loading”?
Urban runoff was simulated with the rationale method. There were no data for validation. How sensitive are your results to the choices for model parameters in the rationale method? If you had estimated the imperviousness, slope or channel length differently, how much would the effect be on the urban runoff peaks and following analyses and conclusions?
Did you see any peaks in the observed river flow indicating large outflow from cities, as qualitative validation of the urban runoff model?
It looks like the gauge in Celle in in the middle of the city. Does this gauge already measure some of the urban runoff? If yes, can you use that as qualitative validation of your urban runoff simulation? And, if yes, is some of the urban runoff counted twice, both in the numerator and denominator of the ratio?
You briefly mention seasonality of the extremes in both time series in Appendix A (610-611), but I think it’s important to mention this in the main text, to get a feeling for the dynamics. When do the high urban runoff events take place and when do the low river flow events take place?
Specific comments
Table 1 & Fig. 1: How different are the river discharge dynamics at the three gauges? Does the mountainous area in the south make Celle and Rethem very different from Grafhorst? Can you show example timeseries for each area in the supplement, for a full year and both urban runoff and river flow?
129 “the runoff coefficient C was determined from the proportion of impervious surfaces within the catchment”: Do you mean “for the runoff coefficient C, the proportion of impervious surfaces within the catchment was taken”? Or was there some other step in between? Does all water from impervious surfaces go to the river in these cities, or does some go to a wastewater treatment plant?
Fig. 4 can be improved – the data points are difficult to see because they are clustered in a small part of the figure. Perhaps scatter density plots work better. Then you don’t need the contour lines. I also think you can remove the histograms – then you can use the full space for the scatter plots. It looks like you can reduce the y axes to 100. If you make the y axes 0-100 and twice as long as the x axes (0-50), then the scale is the same on both axes and it’s directly clear which (urban/river) is bigger, especially when you add a 1:1-line. If you put the four figures then next to each other, then you can cut off the labels of the y axes of panels 2-4 because they are the same anyway. Write out the small text in the figures (speamanr etc) in readable text (capitals, spaces, p=0.62 instead of p=6.22E-1)
Fig 4, 5, 6: Can you show the results for the other rivers and window sizes in a supplement?
367 “The dependence between the two variables remains consistently weak across all seasons.”: Why “remains”? (Maybe I missed an earlier comment about this.)
267-370 “Spearman correlation coefficients range from approximately 0.03 in spring to 0.01 in winter, with Pearson coefficients indicating similarly negligible association. This reflects the fundamentally different governing mechanisms of the two processes: urban runoff is driven by short-duration 370 storm pulses, whereas river flow integrates catchment-scale storage and responds over multi-day timescales.”: Did you see differences between the three catchments? And if yes, can you explain the differences with catchment or urban characteristics?
309-401 “their fitted distributions reflect contrasting tail behavior: urban runoff extremes are characterized by increasing magnitudes toward higher return periods, whereas the associated river flow exhibits a pronounced shift toward low-flow conditions.”: I don’t understand this. Isn’t it by definition the case that the higher urban runoffs are at the higher return periods? That’s how you order them. Or do you mean that they increase more quickly? But then I would expect the curve in the left panel of Fig 5 to turn up in the upper right corner. I also don’t understand the second half of the sentence. What do you mean with “pronounced shift”? Where can I see that in the figure?
429-430 “Overall, the Weibull distribution is the best-suited of the three-parameter distribution functions. In individual cases, however, the GEV and Pearson III distributions are favored”: Isn’t Weibull a type of GEV?
Appendix: I am not sure what the rules are at HESS for appendices and supplements. The appendix is now quite long – maybe a supplement is better for the extra figures and tables. Make sure you refer to all the supplementary figures and tables in the appendix/supplement in the main text.
Appendix A: I think it’s more informative if you reduce the x-axis to 365 days and not aggregate the urban runoff to monthly values. Then you can also see how long the memory of the urban runoff is.
Textual/technical comments
124: (Kuichling, 1889) > Kuichling (1889)
233: by (Sarigil et al., 2024)) > by Sarigil et al. (2024))
245: Rob J. Hyndman > Hyndman (also in reference list)
274: by (Pickands III, 1975) > by Pickands III (1975)
274 : by (Grimshaw, 1993) > by Grimshaw (1993)
278 “…extreme value analysis, which is introduced in the following section.” > remove “which is introduced in the following section”, because you already introduced it in the methods section
538: Gifhorns > Gifhorn
Figures: Check all figures for font sizes. Some are very small.
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Good luck!