Summary

In this manuscript, the authors apply a compound flood risk assessment (CFRA) to the coastal regions of the contiguous United States. In contrast to several previous studies, they do not only perform a bivariate extremes analysis between storm surge and river streamflow (referred to in their manuscript as data-based CFRA), but they couple their statistical analysis to a large-scale river-routing model and population exposure information (referred to in their manuscript as physics-based CFRA). Their main finding appears to be that their metrics, such as the marginal and joint exceedance probabilities and Kendall’s rank correlation, differ substantially depending on the type of CFRA. The authors use their results to argue that ‘data-based’ CFRA alone does not provide a holistic view of CFRA and provides a biased view, hence different types of CFRA need to be considered. Although my experience in this field is limited, I think that this contribution is welcome and useful, and I also found it well written. I do have several comments, though, that I hope will help to improve the manuscript.

Comments:

-‘Data-based CFRA’: I am not sure if this is a commonly used term, but it is ambiguous to me because ‘physics-based CFRA’ is also based on data. Would it be possible to find terminology that more clearly distinguished the two types of CFRA? Perhaps ‘statistics-based’ and ‘dynamics-based’ or so?

-Figures: for the maps, color schemes are used that I doubt are color-blind friendly/perceptually uniform. Could the authors please check and modify their figures where necessary?

L64-L92: I am missing an introduction of existing large-scale compound flood risk studies with similar aims, such as https://nhess.copernicus.org/articles/23/823/2023/. I would encourage the authors to include a paragraph on such studies and explain the similarities and differences with their own manuscript. The same comment applies to the Discussion section.

L144: Kendall’s rank correlation is computed, but it is not clear to me if/what lag is allowed between the two variables. Could the authors please also discuss how the samples for which the rank correlation is computed are conditioned, i.e., are cases in which one of the variates but not necessarily both variables are extreme (two-sided) also considered or not, and why (not)?

Section 2.1: information about declustering of the peak events seems to be missing, although declustering is necessary to avoid dependence in the extremes. Could the authors please explain if/how their data was declustered?

L318-332: this paragraph discusses figures that are not part of the main manuscript. I would either include both the discussion and those figures in the manuscript or put both in the supplements, and only briefly refer to them. Its current form is inconvenient to read in my opinion.

Section 3.2.1: A comparison with the results of previous (‘data-based’) studies in this region (e.g., Wahl et al., 2015; Nasr et al., 2021) would provide useful context, but is missing. Could this be added?

L400-402: while I appreciate this remark, data that covers a longer period cannot simply be obtained. Could the authors please explain/discuss how they imagine a dataset such as the GTSM reanalysis being extended back in time with reasonable confidence? In the absence of such data, how can we get a sense of how uncertain the results of the present study are given the relatively short period used? This seems especially relevant given the underrepresentation of tropical cyclones in the observations/reanalysis data. And what about the influence of temporal variability on the dependence between the two variates examined? (e.g., Wahl et al., 2015)

L440-445: The open access to the code used for the paper is commendable. I strongly recommend doing the same for the output data instead of sharing it ‘upon request’.

Minor issues:

L55: ‘across rivers and estuaries’: I suggest changing this to ‘different rivers and estuaries’, unless variation within a river or estuary is meant.

L103 could the authors please comment on using a river routing model v.s. using a hydrological model that also includes groundwater? I am not an expert, but I can imagine that changes in groundwater also affect the propagation time between upstream and the coastal interface?

L114: It only becomes clear later why the 2^nd boundary condition is used (i.e., in eq. 6). It would be helpful to briefly motivate the 2^nd boundary condition here already. Besides, it is not clear where this fixed level is derived from – is it the mean level in GTSM?

L119: ‘statistical model’ please specify what this refers to.

L175: ‘using an R-package’ please specify which package.

L192: is this necessary? Can the authors not just change the scale of the relevant plots?

L200: to avoid confusing this section for a results section, I suggest replacing ‘investigate’ with ‘review’ or ‘discuss’. Additionally, I found this section not as well connected to the rest of the manuscript. Perhaps some sentences could be added as to why these uncertainty sources are introduced here.

L206-207: would be more consistent to define the different types of uncertainty in the same order as they are introduced.

L252: ‘shift’ is this the same as ‘lag’? If so, I think that would be a clearer term.

L258: I suggest to change +/- 5 days to: a window of 10 days around the extreme, if this is indeed the intended meaning.

Section 2.2.4: please consider putting this in a table, for a clearer overview.

L279: ‘elevation gradient’ – would it be worth plotting the gradient instead of the elevation itself in figure?

L286-287: could use some more explanation, in my opinion.

L298: I think this needs to be ‘Section 2.2.4 at 24 river basins’, correct?

This work has proposed a compound flood (CF) risk assessment (CFRA) framework for coastal regions in the contiguous United States (CONUS). Compound flood is a significant research topic, and this study is timely to contribute to expand the literature. Overall, this work reads smooth and has included great simulations and analysis. Below are some comments on the manuscript. 

1.    The scientific question was not quite clear. Is the objective to build a framework for assessing compound flood risk or to understand the risk across the U.S. coast? When reading the manuscript, it feels like the former was the main objective.   

2.    Line 160-165: “We consider 𝑄 and 𝑆𝑆 to be dependent of each other when they display a significant positive correlation (p-value<0.05).” Can we ignore the dependence if the p-value is smaller than 0.05. The authors need to better justify the selection of p-value. 

3.    Line 170-175: Which copula did the authors choose to quantify the dependence and why?

4.    Line 53: change “not available” to “unavailable”

5.    Line 87: “has accounted”

6.    Line 108-111: Why did the authors use GRFR runoff forcing? ERA5 land and NLDAS also provide runoff.

7.    Fig.7’s caption is unclear. “Figure 7: The Kendall's correlation coefficient (𝝉).” What is this 𝝉 and how to define it?

8.    Fig.8’s caption is also unclear. Please specify each term and variable for (𝑷𝑸,𝑺𝑺) in  the figure. 

9.    In terms of storm surge events, is it possible to identify storm surge caused by tropical cyclones, extratropical cyclones etc.? How well is GTSM data validated by observations? Given the GTSM products are forced by ERA5 data, it would be useful to validate the GTSM’s storm surge. 

10.    Figs 2-4: I would suggest that the authors add labels for geographical locations/states. It is hard to know where the locations are in these figures.  

11.    While it is not reported in this work, the authors could add discussions on the compound flood risk in the future given the climate projection.

12.    In Section 3.2 CFRA, it would be better to add more discussions on the results across different coastal regions and the reason why there is spatial discrepancy in the results such as joint exceedance probability. Is the discrepancy in the risk across different regions due to differences in extremes Q or in SS (e.g., storm type, frequency or track), or in both?