Review Report

Manuscript: “The value of visualization in improving compound flood hazard communication: A new perspective through a Euclidean Geometry lens” by “Soheil Radfar, Georgios Boumis, Hamed Moftakhari, Wanyun Shao, Larisa Lee, Alison Rellinger”

General comments

The manuscript introduces the Angles method (based on Euclidean geometry of the so-called “subject space”) for visualizing the dependence structure of compound flooding drivers. Then it is evaluated the utility of the methodology for risk communication through a survey with diverse group of end-users, including academic and non-academic respondents.

The Authors use a geometrical interpretation of Pearson’s correlation coefficient (Eq.s 4-9). This issue is interesting and promising.

However, the Pearson’s correlation coefficient has some weaknesses: 1) problems of existence [see e.g., Salvadori er al. 2007 and De Michele et al. 2005]; 2) represent the linear association between the variables (as highlighted also by the Authors); 3) It is not invariant under monotonous transformation (only linear ones), issue of great importance for the application of Sklar’s theorem and thus copulas applications (see Salvadori er al. 2007). In this respect, why not using the Spearman correlation coefficient? According to the connection between the Pearson’s correlation coefficient and the Spearman’s one, you can write easily Eq.s 3-9 in terms of the pseudo-observations / transformed variables F(Q) and F(S). I suggest to develop this case in substitution (better) or alternative.

In the manuscript you have considered/referred to two variables (Q and S). If you have more than two variables, it could be interesting to say how to proceed, through a pairwise analysis?

Specific issues

Lines 84-87: I suggest to report also the p-value of the correlation coefficients to show the statistical significance.

In eq.(9) it is missing a parenthesis “(”

Line 121 clarify the acronym “CCF”.

Lines 153-154 “From Figure 4, it is clear that the correlation coefficient of the period 1997-2022 is greater than that of 1972-1996 since θ is smaller (thus, the cosine is greater).” I suggest also here to calculate the statistical significance of the estimates of the coefficient, also in light of the non-stationarities claim made by the authors (lines 163-164).

In Figure 8, it is not clear if all the correlations are significant. It is important to clarify which are the significant ones.

Mentioned references

Salvadori G.  et al. 2007. Extremes in Nature: An approach using Copulas, volume 56, Springer, Dordrecht

De Michele C. et al. 2005. Bivariate Statistical Approach to check adequacy of dam spillway. ASCE J. Hydrologic Engineering 10(1), 50-57.

The submitted manuscript „The value of visualization in improving compound flood hazard communication: A new perspective through a Euclidean Geometry lens” proposes as stated in the title: a new visualization method that aims at better representation of bivariate relationships between variables relevant for flood hazard. Unfortunately, I don’t feel that this goal was achieved.

As already noted by the other reviewer, the copula approach has been used for years in visualizing compound hazards. As literature on copulas shows, e.g. https://npg.copernicus.org/articles/15/761/2008/npg-15-761-2008.pdf , probability density function plotted on a graph where marginal distributions transformed to standard normal clearly shows the strength of the correlation (Fig. 3 therein). Further, it can show the structure of the dependency (Fig. 4 therein), which enables visually to detect tail dependence, which can be more relevant to compound hazard probability of occurrence that overall correlation. The authors’ approach focuses only one dimension of the compound problem – not necessary the most important.

Even if one would not like to use the copula approach due to higher complexity (though simply showing data transformed to ranks or standard normal can already be very revealing), I don’t see how presenting the correlations in Fig. 4 as angles improves this compared to e.g. showing three correlations as a bar graph. At least for me, it is not intuitive right away that a large angle with represent a low correlation. In the authors’ survey results, there is clearly lower understanding of correlation in the angles method compared to simply having the numerical value. The authors only compare their approach with a raw scatterplot of particular composure of points. Scatterplots can be enhanced, as noted above, to improve the visibility of correlation.

I will skip any detailed comments, as I am not convinced at all by the authors’ whole approach, which doesn’t contribute to any improvement in visualization of compound hazards.