This paper presents an interesting assessment of controls on annual streamflow variability, with a particular focus on the synchronicity between precipitation and potential evaporation. This factor turns out the second most important control on annual streamflow variability (following the more commonly considered annual precipitation) in an analysis of 4122 catchments from four continents (out of 3 tested variables: P, PET, and the phase and strengh of P vs PET). The work thereby suggests that introducing the synchronicity between precipitation and potential evaporation as an independent variable can significantly improve predictions of annual streamflow variability. Overall, the work seems like it could become useful and relevant, but I also have several issues at present. Essentially, the paper seems to be prepared in a rush, with bullet point statements throughout the entire paper, inconsistencies in figures, labels, etc. In addition, the writing itself also lacks specicificity at times. Therefore, at present, I cannot fully scientifically judge the paper, and have only commented on the presentation. Once the presentation is improved, I’d happily review the science part more carefully. 

1. The paper also seemed to be hastily prepared. I strongly believe a careful revision of all text would be needed to ensure the reader is informed effectively and thereby the writing meets HESS’ standards. The extent to which this is needed goes beyond what I can comment on within a reasonable amount of time.
2. The connection with existing literature needs to be strengthened

Section 1.3. This list of studies is useful. However, the overview overlooks many large-sample hydrological studies that have already pointed (and quantified) clear links between precipitation seasonality (relative to PET or T seasons) and (mean) annual streamflow rates. For example:

-Jawitz, J. W., Klammler, H., & Reaver, N. G. F. (2022). Climatic asynchrony and hydrologic inefficiency explain the global pattern of water availability. Geophysical Research Letters, 49, e2022GL101214. https://doi.org/10.1029/2022GL101214  

-Padrón, R. S., Gudmundsson, L., Greve, P., & Seneviratne, S. I. (2017). Large‐scale controls of the surface water balance over land: Insights from a systematic review and meta‐analysis. Water Resources Research, 53(11), 9659-9678.

Berghuijs, W. R., Sivapalan, M., Woods, R. A., & Savenije, H. H. (2014). Patterns of similarity of seasonal water balances: A window into streamflow variability over a range of time scales. Water Resources Research, 50(7), 5638-5661.

In addition, it may be useful to point out that Potter et al. (2005) concluded something that opposes the main findings of the current manuscript. Namely, that rainfall seasonality was not reflected in the mean annual water balance

Also note that more asynchronicity indices exist, for example, in papers listed above, but also other works such Willmott, C. J., & Feddema, J. J. (1992). A more rational climatic moisture index. The Professional Geographer, 44(1), 84–88. 

1. The methods should more clearly explain the synchronicity function. The ∩ and ∪ operatators are not extremely widely used in hydrology, and could use a clearer explanation. In general, a visualization, such as provided in the 2018 study that is referenced tom would be helpful. Technically the work also does not explicitly test for phase shifts (only quantifies some indirect effects of that, so the work should reconsider its title. 
2. The choice for a particular example is completely arbitrary and not explained. It is fine to provide a “random” example but then provide to explain the method, and not halfway the results.

Detailed comments

• The writing of the paper could benefit from fewer sections and less bullet points, and writing it as a more fluent story (I guess this is also partly personal taste, but I believe this may benefit readers of HESS(D) so please at least consider it). 
• Make sure that figures are prepared more carefully. Right now, subscript in the text does not appear as subscript anymore in figure captions (e.g. Fig. 1, Fig 6) or figures are made extremely inefficiently (e.g. Figure 2  is spread over 4 pages, some simple redesign could convey the same information more clearly using much less space (e.g. write correlation coefficients within panel, write y-label only at most left column, write x-labels only at most bottom row, skip created whitespace between panels, show moving average within scatter to make relationships between points clearer, make subpanels 25% less wide and high but increase resolution of figure (more dpi/vector). With all these adaptations, one can make a clearer figure that just fits on one page (likely). 
• Why remove all the catchments with reservoirs? Would testing this also across more human-impacted reservoirs not make the study more relevant (either by showing the findings apply to a wider range of conditions or by showing the contrasts in behaviors)?
• The study talks about elasticities (which are defined as % change in response per % in driver), but uses sensitivities (which express mm/y change in response per mm/y in driver). The paper reflects on this use of language but why is does it choose to have this inconsistency between the terms and definitions, and not use conventions?
• L41: The wording of this sentence suggests this is the only way of assessing climate impacts, which is not the case. For example add the word “can”, and the issue would be solved.
• L146: define if your aridity index is PET/P or P/PET.
• Figure 1: Fix subscript labels
• Figure 4: add hypen following R^2. Do something to make the overlap in markers more clear. 
• Figure 5: x markers are hard to read 
• Figure 6: Fix labels (p-valuye, E_0). The Figure also has an inefficiently large size for something that could be displayed much smaller (of the font was adapted)

The authors present a very interesting study investigating the impact that synchronicity within each year of monthly precipitation (P) and monthly Potential Evapotranspiration (PET) has on annual streamflow (Q) anomalies. The authors explore this across 4122 catchments from 9 countries around the world using mostly CAMELs or equivalent catchment datasets. Overall, this manuscript is well written and easy to understand and is likely to be very interesting to a wide readership as it seeks to quantify what has long been suspected of being important but hitherto has not been quantified successfully.

However, my main concern with this manuscript is the metric used to quantify the synchronous precipitation index (Equation 1, λ). The authors present an interesting discussion of their thought process for selecting λ in the Appendix (please direct the reader to that discussion near Equation 1 as I nearly missed it). λ was developed in de Lavenne and Andréassian (2018), where an excellent explanation of how to calculate λ is provided on page 269.

The selection of an appropriate metric for this analysis is critical. While I agree that λ is the best option from those presented in the Appendix, I am still not convinced that λ is doing what the authors think it is doing. For example, if P = 5 mm every month and PET = 40 mm every month for 12 months (a very water limited year) then the numerator of Eq.1 = 60 and the denominator of Eq.1 = 480 and λ = 0.125. In this case, 100% (not 12.5%) of the P is available for evaporation as P < PET every month and there is always sufficient PET to evaporate all the P. Whereas, if P = 40 mm every month & PET = 5 mm every month for 12 months (a very energy limited year) then the numerator = 60 and the denominator = 480 and λ = 0.125. In this case, 12.5% of the P is available for evaporation as P > PET every month and there is only sufficient PET to evaporate 12.5% of P. Therefore, the statement that λ represents the percentage of P that is most easily accessible to evaporation is only true if P > PET. When P < PET then all the P is available for evaporation.

Also, I am not convinced that the comment by de Lavenne and Andréassian (2018) that a high value of λ is associated with evaporation favoured over streamflow and a low value with streamflow favoured over evaporation is the case. The two examples above with the same λ value of 0.125 indicate both evaporation favoured over streamflow (PET > P) and streamflow favoured over evaporation (P > PET). Therefore, I think a better metric than λ is required for this analysis.

As a reviewer, I don’t have a recommendation at hand that would solve this issue. However, I think a synchronous precipitation index should include a component that indicates how much P exceeds PET during the year as this will have an impact on streamflow anomalies, which is the subject of this manuscript. Would a better synchronous precipitation index (λ-New) be to check if P>PET in a given month, take the difference (P-PET) if P>PET and zero if P<=PET. Then over the year, sum the P-PET differences and divide by the sum of P. For this metric, λ-New = 0 when PET is always > P and increases from 0 the larger the P-PET difference relative to total P becomes. I encourage the authors to consider this metric or any other better metric they can develop.

I am hopeful that the results presented in this manuscript will become even better once a better synchronous precipitation index is used in the analysis.

Specific comments

Line 32: Hydrological year definition – I am pleased to see that a single hydrological year definition has not been used for the entire world. However, one definition for the Northern Hemisphere and another for the Southern Hemisphere leaves plenty of scope for key periods of synchronicity between P and PET within a year to encounter the arbitrary start or end of the hydrological year. Why not used a hydrological year defined at each catchment based on the month with the lowest monthly Q as the start of the hydrological year? If the authors wish to keep the current two definitions, then please add to the Supplementary Material results of a comparison of the overall results with the two hydrological years versus individual catchment hydrological years. Alternatively, an explanation of why the results aren’t expected to change due to hydrological year definition would be appropriate to add in the Notations section.

Line 103: “seasonality of rainfall” – I think you mean “synchronicity between precipitation and potential evaporation” here.

Line 140: I agree that re-computing the PET with a common equation is a good idea. It would be good to add to this paragraph some examples of the PET equations used in the datasets to give a sense of the diversity of PET that they contain.

Figure 1 Caption: You mentioned that the catchments beyond the orange line are leaky and beyond the blue line are gaining. Another possible interpretation is that there are errors in the P, Q and PET data that become apparent in this Turc-Budyko plot. I think it would be good to acknowledge that data errors could be causing some of the unexpected points in these two plots.

Equation 4: The first term on the right-hand side should be eQ/P, not eQ/Eo.

Lines 199 – 200: correct the synchronicity variable name. It should not be V as used in this sentence in four places.

Table 3: One option here would be to use the Adjusted R^2, which adjusts the R^2 value based on the number of parameters used in the equation. This would make the Adjusted R^2 value more comparable across models with a different number of variables included. A commented is made later on that adding an extra variable is expected to increase R^2, which is true. The adjusted R^2 is designed to take that issue into account.

References

de Lavenne, A. & V. Andréassian. 2018. Impact of climate seasonality on catchment yield: a parameterization for commonly-used water balance formulas. J. Hydrol., 558: 266–274. https://dx.doi.org/10.1016/j.jhydrol.2018.01.009