The two referees and myself are satisfied by the way the paper has been changed and we do think it has been significantly improved. Referee 1 and myself have additional suggestions, in particular concerning the abstract. It would be good to provide more physical understanding of the computed quantities and results throughout the text.

Major comments:
1) abstract: The abstract is quite short and I am not sure it provides enough physical understanding. In particular, the second paragraph of the abstract is not easy to understand.
a) The physical meaning of "the skewness in planetary waves" should be more clearly explained. There is space to describe the relationship between skewness and degrees of freedom.
b) I would replace "the skewness in planetary waves" by " the skewness in planetary-wave energy".
c) Similar to reviewer 1's comment, I found a bit strange to summarize more the results of section 3.4 and less those of sections 3.2 and 3.3. In my opinion, Fig.6d is an important figure showing the increased synoptic wave energy. Fig.8a completes Fig6d by showing this is mainly coming from wavenumbers 7,8.
d) Maybe one way to describe the results is to start with the zonal mean flow, then planetary waves and finally finish with the synoptic wawes. As it is written now, everything is mixed up in this paragraph and makes the reader confused.
2) Fig.8a and related discussion. The text stays largely focused on what we see on the figures. But there are not enough statements providing a physical meaning of all the quantities computed (see below for more detailed comments on that aspect).
3) Conclusion: there is no attempt to provide a global picture. For instance, the two results on planetary waves are an increase in the skewness and a decrease in the intraseasonal variance. Can these two results be connected to provide a broad picture of the planetary wave behavior during heat waves ? Or are these two results entirely independent ?

Minor comments:
- Line 218: The sentence "We apply bootstrapping with a replacement for different wavenumber ranges for a more robust statistical analysis (Fig. 5)." is not clear to me.
- Figure 5 / caption: "replacement with 1000 simulations" is not clear to me. I am not sure "simulations" is the appropriate wording.
- line 233-234: Fig5a--> Fig6a and Fig5b --> Fig6b
- Paragraph from lines 233-240: Fig6d is an important figure and should be described.
- Lines 249-253: The discussion on the change in PDFs of synoptic Rossby waves is not precise enough and does not refer to any figure. In my opinion, Fig. 6d shows there is more energy is synoptic waves during heat waves as said in the text. But why is this figure not cited in the paragraph ?
- Line 275-278: In my opinion, Fig7f confirms the amplification of wave-3 pattern during heat waves as shown in the cited studies. I think the authors should explicitly say this is a confirmation of previous studies (maybe in another geographical area ?).
- Line 286 / Eq (8): Is Chi_nu the same as Chi^k_n(m) ?
- Eq. (9): what does the superscript "h" mean ? I imagine it refers to heat waves. What about V_nu ? Is it a climatological value ? or is it a value that is computed for every month ?
- The physical meaning of the decreased variance in wavenumber 3 is never provided. Does it mean that wavenumber 3 is quasi-stationary during months marked by heat waves ?
- The zooms in Fig.8a are not clear enough to conclude about the significances of the reduction in wavenumber 3 variance and the increase in wavenumbers 7,8 variance. Both cases show values very close to the 95% confidence. See also referee 1's remark.
- The paragraph from lines 313 to 325 is not easy to read. Please insert "to" after "close" in line 317. I am not sure "barotropicity" exists. Maybe replace by "barotropic structure". The sentence starting by "Note that Fig.9" is difficult to understand.
- Line 347-348: The authors should help the reader to physically interpret the skewness in energy anomalies. If the distributions of the zonal mean state and planetary scale circulation are more skewed than that of synoptic scales, what does that mean physically ? Does it mean that the planetary wave energy is concentrated in a very limited number of planetary scale modes ? In my mind, the reduction of the active degrees of freedom during heat waves means that there are only very specific modes that are excited. Am I right ?

The paper has been significantly improved since the last revision. I appreciate the efforts made by the authors to make the language more easily understandable for the reader and in particular to introduce their methods and results more smoothly in the beginning of the paragraphs/sections. However there are still some paragraphs that need to be more clearly written or reordered. This is the case of the ones describing Fig.5 (see below). Therefore I do think the paper will be ready for publication after a minor revision that addresses the following points:

1) Line 197: The time series of I'_nu is said to define the climatology. This is misleading for the reader since the climatology of the energy is in bracket in Eq(6). I would say I'_nu is the time series of the anomalous daily energies.
2) Line 216: I do not understand the if in parenthesis
3) Lines 228-234: There is no introductory sentences to Fig.5 and its objectives. The paragraph starts discussing robustness of the results and not the results themselves. This is not confortable for the reader.
4) Section 3.2.1: There is an issue on the order of the figures and their description. I do not understand why Fig.6 appears after Fig.5 since the main results of Fig.5 are described after those of Fig.6.
5) Line 312: "is also consistent"
6) Fig. 8b. Please indicate we are looking at variance anomalies of HWs with respect to climatology.
7) Lines 363-367. The sentences miss some precision. Suggestion: "The increase in skewness FOR PLANETARY WAVES REVEALS the decrease in the number of active degrees of freedom during HWs. This aligns with the results of Lucarini and Gritsun (2020) which are based on the atmospheric stability during Atlantic blockings. Based on the χ 2 -skewness, we estimate a reduction of the active degrees of freedom FOR PLANETARY WAVES during Eurasian HWs of about 25% compared to climatology.
8) Line 374: I do not understand the beginning of the sentence: "During HWs, planetary Rossby waves are less active (especially k = 3), and a persistent anomaly... ". Even though the intraseasonal variance of planetary wave k=3 decreases, this wavenumber emerges during HWs and is persistent. So I think saying "planetary Rossby waves are less active" is really confusing.

I am satisfied by the way the paper has been improved and I recommend publication with its current state. Congratulations !