Dear Mostafa

Thanks a lot for your manuscript. I found it quite interesting, and I would like to suggest that this should not be reviewed as a “brief communication” but as a “research article”. I am not an editor of the journal, so I do not know the formal distinctions, but I think the manuscript has sufficient material to become a paper and it is not brief (its current version has 13 pages). It actually has the size of the papers I like to read.

Other main comments

1. As I said the manuscript is quite interesting but right now it is difficult to read/follow because there is a part (I think) in which the method is applied in simulated wind fields and another part in which the method is applied to observations (I think). So it is not clear if the wind field simulations are actually used within the analysis of the observations or not. This is not clear neither in the abstract nor in the results. So I think that the author should make an effort to explain shortly and clearly the steps of the method, and clarify whether the results are divided into “simulations” and “observations” or if there is some combination: e.g., around lines 124-132 simulations are only used but it seems that after line 133 observations are used
2. The decomposition you are presenting in Eqn. (1) is generally known as “triple decomposition” (see e.g., Buckley and Veron, 2017). As most people working in air-sea interaction perform a decomposition like that in the latter study, it would be nice you describe what the differences are between yours and their type of decomposition. Also why not use their type of decomposition?
3. In section 2.1 it is not quite clear why you start with a Kaimal wavenumber spectrum and not with a Kaimal frequency-based spectrum, which is much more known and popular. Also you mention that \sigma_\beta is an adjustable parameter, but is it? Is it not the standard deviation of the variable? If so then it is not adjustable but computable from the time/spatial series. The one that is adjustable as k_0\beta should be A, or am I missing something?
4. (7): it is not clear if this is a suggestion made by you based on something or if it is already in the literature. It kind of comes suddenly and you need to provide a background for it.
5. Section 3.1. It is important to state which sonic anemometers are you using, I mean which type of sonics. You mentioned you do not filter for mast shadow (by the way you do not mention which is the direction of orientation of the sonics) but are you using sonic-specific corrections for probe distortions? If so, please tell us which.

Specific comments

1. Line 12: add “the” before “air-sea interface”
2. Line 14: add “the” before “significant wave height”
3. Line 15: delete the parentheses.
4. Line 17: what is the dynamic sublayer?
5. Line 19: delete the “the” before MOST and replace “cannot” by “should not”
6. Line 32: add “the” before “suggested”
7. Line 35: I guess it will be better to replace “and the wave” by “and the wave-induced pertubations”
8. Line 38: “u, v, and w… respectively” should be moved to line 35 after “(u, v, w)”
9. Line 42: add “the” before “following 1D Kaimal”
10. Line 53: the ranges of the wave affected band, how do you come with these intervals? Also in some of the intervals the numbers lack units: either 1/m or hz when using one or the other
11. Line 55: “Fig 1a and b” do you mean Fig. 2?
12. Line 60: the ref should be in full parentheses.
13. Line 64: add “the” before “above”
14. Line 70: add “the” before “wave”
15. Line 75: the ref should be in full parentheses.
16. Line 86: replace “waves decay exponentially in vertical” by “waves’ impact decays exponentially in the vertical”
17. Line 89: delete “of” before “wavenumbers”
18. Line 114: “wave-induced elevation” do you actually mean “wave-induced peak”?
19. Line 115 and some others concerning the FINO data. Here, e.g. you mention U_10 and give ranges but there is no 10-m wind speed at FINO
20. Line 117: I understand how you can find out the opposed wind case. But what is your criterion to characterize the other as “swell conditions”.
21. Line 120: add “respectively” after “acceleration”
22. Lines 121 and 122: add units after “0” in when giving L ranges
23. Line 133: did you define the wave age?
24. Caption figure 1 you say “10 m height” but there is not such a thing at FINO. Also add “direction” before “(red markers)”
25. Lines 141-142: the sentence has weird grammar, please rephrase
26. Line 159: what does “In estimated tau” mean? Also what is “dimensionless function for the vertical decay”?
27. Line 166: “growth rate” I am not sure when you make this assumption
28. Figure 4. The lines “Ref” and “Corrected” cannot be distinguish, please change their colors
29. Figure 5: you miss describing frame (d) in the caption
30. Lines 168-169: “Under the wind-sea conditions… atmospheric neutral conditions”. Maybe you showed this but did you mention this in the results section?

References

Buckley M.P. and Veron F. (2017) Airflow measurements at a wavy air-water interface using PIV and LIF. Exp. Fluids. 58:161

Wave-Turbulence Decomposition holds significance for both the wave and atmospheric communities. However, it is a considerable challenge for the decompositon. Within this study, the author introduces a method for decomposing wave and turbulence fluctuations. The concept is intriguing and certainly warrants publication. Prior to the manuscript's publication, I have outlined several comments that the author may wish to consider addressing.

Several established methods for wave-turbulence decomposition have been utilized in previous studies. To provide context, I recommend that the author furnish an overview of these methods in the introduction. This should encompass the work conducted by Hristov et al. (2003, 2014), the spectral method outlined by Veron et al. (2008) and Grare et al. (2013), as well as the interpolation method described by Rieder and Smith (1998) and Högström et al. (2015).

In light of these established techniques, it would be beneficial for the author to address whether their proposed method has been compared to these prior approaches. Specifically, have the results obtained using the author's method demonstrated good agreement with those generated by the aforementioned methods? Furthermore, it would be pertinent to explore the strengths and limitations of the author's method in comparison to the existing alternatives. Within the scope of this study, a comparison has been made between the method developed by Hristov and the approach outlined by Veron et al. in 2008. It is noted that the results obtained from these two methods show an acceptable level of agreement, as previously established by Wu et al. in 2008. This comparison adds credibility to the validity of the author's method. Incorporating this comparative analysis would provide a more comprehensive understanding of the novelty and effectiveness of the author's proposed approach in relation to the existing methodologies.

The presence of multiple layers of sonic sensors introduces an intriguing opportunity for validation. It would be highly compelling to ascertain whether the wave coherence contribution as discussed in Section 2.2 aligns with the findings derived from the methods detailed in Section 2.1 across the various sensor layers. This comparative analysis could yield valuable insights into the consistency and reliability of the outcomes.

It is not easy to follow the connection between sections 2.1, 2.2, and 2.3. Please consider restructuring it.

For section 2.3: Eq. 11 is only valid for the surface. Thus, it should not have the dependent on z which is confused the readers.

In the manuscript, you use many “we”. Since there is only one author, it should be “I” instead.

Reference:

Hristov, T.S., Miller, S.D. and Friehe, C.A., 2003. Dynamical coupling of wind and ocean waves through wave-induced air flow. Nature, 422(6927), pp.55-58.

Hristov, T. and Ruiz-Plancarte, J., 2014. Dynamic balances in a wavy boundary layer. Journal of Physical Oceanography, 44(12), pp.3185-3194.

Veron, F., Melville, W.K. and Lenain, L., 2008. Wave-coherent air–sea heat flux. Journal of physical oceanography, 38(4), pp.788-802.

Grare, L., Lenain, L. and Melville, W.K., 2013. Wave-coherent airflow and critical layers over ocean waves. Journal of Physical Oceanography, 43(10), pp.2156-2172.

Rieder, K.F. and Smith, J.A., 1998. Removing wave effects from the wind stress vector. Journal of Geophysical Research: Oceans, 103(C1), pp.1363-1374.

Högström, U., Sahlée, E., Smedman, A.S., Rutgersson, A., Nilsson, E., Kahma, K.K. and Drennan, W.M., 2015. Surface stress over the ocean in swell-dominated conditions during moderate winds. Journal of the Atmospheric Sciences, 72(12), pp.4777-4795.

Wu, L., Hristov, T. and Rutgersson, A., 2018. Vertical profiles of wave-coherent momentum flux and velocity variances in the marine atmospheric boundary layer. Journal of Physical Oceanography, 48(3), pp.625-641.