I only really have two comments, but they are potentially pretty major ones:

Section 2.1.1 – I’m not convinced by the accuracy of the sea level data set, since the observed and reanalysis extremes do not correspond well with each other and then the reconstructed data is trained on these contrasting datasets. There are many sites globally where a longer accurate observational sea level record exists, so why not chose a different site?

In the end, you produce a 44 year record of sea level variability. Despite this being a long data set, you only select the annual extremes for the analysis - why do this when in effect this reduces this large data set down to only 44 (suspect) data points. Since the purpose is to assess joint probabilities, this could be done on a larger subset of extremes, e.g. >99^th percentile peaks.

The manuscript proposes a flexible framework for the attribution of the uncertainties associated with joint exceedance probability estimates of river discharge -coastal water levels. The framework is demonstrated at a case study site on the west coast of Sweden. Copula family and the dataset chosen to represent river discharge are found to exert the largest influence on the estimates. The manuscript is overall well written, topical, and the results are interesting, however, I do have several reservations about accepting in its present form. Key literature is missing, the discussion section is subpar, and the novelty of the study is debatable.

General comments

Title is misleading since no river mouth water levels are calculated.

The first paragraph, although not incorrect, is odd in the sense that it stresses that heavy precipitation, storm surge and runoff can be caused by different weather conditions when a key rational for the statistical dependence is that the flood drivers are forced by the same large scale weather conditions.

A more detailed description of the “Weighted Average” and a “Maximum Density” approach in the MhAST toolbox is required for readers unfamiliar with the toolbox.

I do not understand why there is an entire section on univariate (oceanic and fluvial) flooding when the investigation is about compound events. The return levels in the boxplots (Figure 6) are not estimates of the 5- and 30- year fluvial events, they are the fluvial component in bivariate events with those return periods. I am unsure as to whether the bivariate and univariate return periods should be compared and whether statements such as “Moreover, the RL uncertainties for the “Maximum Density” approach are all located within the 95th confidence interval of the

univariate RL.” are meaningful.

The discussion should compare the findings with other similar studies, see Lucey and Gallien (2022) and Santos et al. (2021) for starters.

Specific comments

L13: Statistical copulas do not give a measure of flood risk (at least not directly).

L35: There are a great many other studies that examine the dependence between river discharge and storm surge at sites in Europe that should be cited here (e.g., Ward et al. 2018).

L35, L71 and elsewhere: Be careful to specify that these “interactions” refer to their co-occurrence probabilities and not physical interactions. This would be a good place to introduce frameworks that link statistical and numerical models to account for joint exceedance probabilities and physical interaction to locate the stretches of river where compound flooding is an issue (e.g., Moftakhari et al. 2019, Gori et al. 2020, Jane et al. 2022).  Studies such as Couasnon et al. (2020) and Moftakhari et al. (2017) only carry out statistical modeling and therefore only assess the “potential for compound flooding”, they do not determine “impacts from compound flooding” either in terms of estimating water level or computing inundation depths.

L46: Reference required.

L73: Sentence implies there is a single annual maximum value for each year but of course each year will possess a different annual maximum value.

L76: Technically since the distributions are continuous this would be an “exceedance probability”.

L79: “variable” or “driver” is potentially more accurate language than “factor”.

L81: Is “potential for compound events” more accurate than “a potential compound event”.

L98: What was the other dataset used in the correlation analysis? Also change “statistically insignificant” to “not statistically significant”.

L167 & 169: Could say “paired” instead of “used” as the latter is “used” a lot throughout the paper!

L170: Move references to the end of the sentence.

L185: Null hypothesis in such tests is usually that the correlation coefficients are zero indicating it is reasonable to assume the variables are independent.

L213: “Adopting the “AND scenario” (see above) permitted us to investigate the dependency between sea level and river discharge during extreme events.” The “OR” HS also allow this!

L237: “In the following, we mainly focus on the “OR scenario” yet in the next paragraph, only  the “AND scenario” is discussed! Justification for the “OR scenario” is poor here. By “compound flood risk driven regardless of the situation (oceanographic or hydrological)” I believe you mean you’re interested in compound risk and risk from the oceanographic only and hydrological only events.

L245, 337: The term “superposed” implies a decision taken by the practitioner “do not overlap” maybe a clearer description.

L272: “The BB1 copula fit has a 5-year RL of 220 m3/s.” is not correct the BB1 copula fit will have many discharge values associated with a 5-year RL, that depend on the corresponding sea level.

L72: What copulas are you referring to here?

L296: Please explain what the higher return levels are being compared with.

L335: “more significant effect on estimated RLs” more significant effect than what?

L339: Consider re-writing: “This similarity stresses the idea that river discharge predominates over sea-level inputs.” Since the phrase “stresses the idea” is sort of ambiguous furthermore I wonder whether “dominates” is more suitable than “predominates”.

L349: “This study focuses on extreme hydrological events associated with oceanographic conditions and, therefore, concentrates on the RLs of river discharge.” I do not understand the point trying to be made here!

L371: “results” is ambiguous. Is this the “most likely” event?

L417: “The opposite dependency” is a strange turn of phrase.         

L424: Consider changing “The choice of copula has a similar magnitude of its influence on return period statistics as the choice of river discharge input for most of the twelve sets tried” to “Copula choice has a similar influence on return period statistics as the river discharge input for most of the twelve sets tried”.

Appendices: Change “,” to “.” (decimal places).

References

Gori, A., Lin, N., and Xi, D. (2020). Tropical cyclone compound flood hazard assessment: From investigating drivers to quantifying extreme water levels. Earth's Future, 8, e2020EF001660. https://doi.org/10.1029/2020EF001660.

Hendry, A., Haigh, I. D., Nicholls, R. J., Winter, H., Neal, R., Wahl, T., Joly-Laugel, A., and Darby, S. E. (2019) Assessing the characteristics and drivers of compound flooding events around the UK coast, Hydrology and Earth System Science, 23, 3117–3139. https://doi.org/10.5194/hess-23-3117-2019.

Jane, R., Santos, V. M., Rashid, M. M., Doebele, L., Wahl, T., Timmers, S. R., Serafin, K. A., Schmied, L., and Lindemer, C. (2022) A Hybrid Framework for Rapidly Locating Transition Zones: a Comparison of Event- and Response-based Return Water Levels in the Suwannee River FL, Water Resources Research, 58, e2022WR032481. https://doi.org/10.1029/2022WR032481.

Lucey, J. T. D. and Gallien, T. W. (2022) Characterizing multivariate coastal flooding events in a semi-arid region: the implications of copula choice, sampling, and infrastructure, Natatural Hazards and Earth System Science, 22, 2145–2167. https://doi.org/10.5194/nhess-22-2145-2022.

Moftakhari, H., Schubert, J. E., AghaKouchak A., Matthew, R. A., and Sanders, B. F. (2019) Linking statistical and hydrodynamic modeling for compound flood hazard assessment in tidal channels and estuaries, Advances in Water Resources, 128, 28-38. https://doi.org/10.1016/j.advwatres.2019.04.009.

Santos, V. M., Casas-Prat, M., Poschlod, B., Ragno, E., van den Hurk, B., Hao, Z., Kalmár, T., Zhu, L., and Najafi, H. (2021) Statistical modelling and climate variability of compound surge and precipitation events in a managed water system: a case study in the Netherlands, Hydrol. Earth Syst. Sci., 25, 3595–3615. https://doi.org/10.5194/hess-25-3595-2021.

Ward, P. J., Couasnon, A., Eilander, D., Haigh, I. D., Hendry, A., Muis, S., Veldkamp, T. I. E., Winsemius, H. C., and Wahl, T. (2018) Dependence between high sea-level and high river discharge increases flood hazard in global deltas and estuaries, Environmental Research Letters, 13(8), 084012. 10.1088/1748-9326/aad400.

The paper presents the compound flood risk analysis across the Swedish coast in the presence of low record availability and the choice of copula. While the uncertainty due to the first can’t be averted, the second can be improved by the appropriate choice of copula and its parameter. Often sentences are not clear and require attention in framing. In a few cases, the methodology adopted is not robust and needs a relook. Often, there are misleading interpretations that make the paper weak. The paper can be published after appropriate revisions. The reviews are summarized as below:

1. In Abstract, line 12: “The compound flood risks…. Often estimated using statistical copulas”. This line can be misleading since copulas are one of the methods for estimating joint probability between two random variables. There are other methods as well, for example, joint entropy, or bivariate distributions considering box-cox transformations of associated random variables. Please consider revising/discarding this sentence.
2. Line 27: What about the coastal backwater effects that influence the occurrence of compound flooding?
3. Please use the SI unit for sea level measurement.
4. Line 82: Please use the word ‘copula’ throughout and not the ‘statistical copula’.
5. For processing 13-year sea level observation, a re-analysis coupled observational analysis was performed. In cases of data scarcity, the peak-over-threshold (POT) approach is in use instead of annual maxima. On the other hand, coupling different data sources, as adopted in this study, often results in underestimation due to scale mismatch issues and extremes often underestimated in gridded reanalysis runs. If you are purely interested in observational assessment, the POT approach may be more powerful considering on average 2-3 to events per year, as compared to mixing reanalysis runs with the local tide gauge records.

               On page 5, line 110-125: how you have converted hourly records to daily? The tide gauge records in Sweden are available at a minute-scale temporal resolution.

1. On Fig.3: lower panel, clearly shows that the reanalysis-driven reconstructed sea level observations are largely underestimated, especially at larger return period values. Please show the sea-level observation measurement in meters (SI unit).
2. between lines #145-150: What are the different sources of uncertainty of these models? Please describe number of parameters involve for calibration, forcing data requirements and their temporal resolution. The predictive skills of the hydrologic models in simulating daily river discharge are not discussed at all.
3. Fig. 4: Y axis label: use superscript for the discharge measurement. Further, the uncertainty estimates between E-Hype and S-Hype model can be quantitatively estimated by the ratio of upper bound to the lower bound across higher and lower return levels.
4. Line 177-178: Is it maximum likelihood based estimates of GEV parameters? This might be problematic for estimation of shape-parameters of GEV. Often a Bayesian estimate is proposed.
5. Lines 203-206 and elsewhere: sentences are erroneous, please consider revising. Both ‘OR’ and ‘AND’ approaches are suitable for modelling joint effect: while the former consider a time offset, the later considers co-occurrence.
6. On page 11: line 245: highlights a ‘discrepancy’.
7. Line 251: One do not assign any probability density function to each copula rather derives copula-based joint PDF.
8. On page 13: line 280 onwards – this section and the subsequent ones are very confusing, rather much simpler and statistically robust methods should be adopted. The Gaussian copulas are not good while considering highly skewed data as here. The best method to select copulas are to apply the minimum AIC criteria with small sample corrections (in presence of limited data availability) followed by an appropriate goodness-of-fit measure, such as application of resample-based Cramer von Mises goodness-of-fit statistics.
9. Lines 335-340: Please explain in terms of hazards.
10. Line 339: Coincidence of independence line versus copula-derived dependence PDF does not necessarily stress the hypothesis that river discharge predominates over high sea levels. The other way around can also be possible.
11. Line 376: What is the ‘most likely scenarios’ here?
12. Line 390 and associated section: There are several uncertainties in return levels due to the incorrect and erroneous application of copulas. Please use an appropriate goodness-of-fit measure to select the best-fit distribution. Also, there is not enough evidence that the SL is least sensitive to compound flood hazards; – mere little shift in density contours does not justify this major finding.
13. In section 4: first paragraph, what is the need of extreme sea level analysis using model-derived sea level observations? A purely observational assessment employing different sampling mechanisms can work too. In the second paragraph, the uncertainty resulting from the choice of copula can be constrained by adopting appropriate goodness-of-fit statistics for the selection of the best-fitting copula.