Please refer to the attached supplement PDF file for the comments.

Review Comments for the Manuscript: "Climatology of the terms and variables of transformed Eulerian-mean (TEM) equations from multiple reanalyses: MERRA-2, JRA-55, ERA-Interim, and CFSR."

General Comments:

The manuscript presents an in-depth analysis of the principal variables and terms of the TEM momentum and thermodynamic equations, utilizing datasets spanning over thirty years from MERRA-2, JRA-55, ERA-Interim, and CFSR. The detailed scrutiny of the reanalysis ensemble mean (REM), alongside the notable discrepancies among individual reanalyses, substantially enriches our understanding of atmospheric dynamics and radiative equilibrium from the troposphere to the mesosphere. The study's potential to improve reanalysis datasets and enhance atmospheric modeling and simulation techniques is highly commendable and noteworthy.

Specific Comments:

1. Seasonal Tendency Analysis:

   - The methodology involving DJF and JJA to analyze winter and summer tendencies in the northern hemisphere mainly captures transitions from December 1st to the end of February. This approach may only partially encompass the climatic variations in temperature, wind fields, and stream functions among the different reanalyses throughout the year. Notably, the TEM momentum equation analysis focuses on the differences between states separated by three months rather than the formation of an average state over an entire season. It is recommended to broaden the analysis to include the whole of the annual climatic mean or to analyze TEM terms for additional months. This could provide a more detailed understanding of the discrepancies among the datasets and their underlying causes.

   - The need for more analysis for shorter time cycles, such as monthly budgets, is evident. For instance, events like Sudden Stratospheric Warming (SSW), typically accompanied by significant planetary wave activity, may take place within these three months and might resolve before the end of February. Consequently, the monthly variations in atmospheric momentum and thermodynamics and their causes still need to be addressed.

1. Attribution of Differences in TEM Thermodynamic Terms:

   - The study ascribes specific TEM thermodynamic terms variances to differences in parameters such as ozone and temperature across the datasets. A more detailed discussion and analysis of these parameters, especially ozone distribution, is advised to reinforce this attribution. This would solidify the argument and provide a more transparent explanation of the observed discrepancies, potentially elucidating the underlying mechanisms involved.

Technical Corrections:

- Line 305: Clarification is needed on how the equatorward flow is observed from Figures 1(d) or Figure 4(b).

In conclusion, the manuscript significantly contributes to the field of atmospheric sciences. I think addressing the points mentioned above could significantly enhance the depth and impact of your study. I eagerly anticipate the revised manuscript and am optimistic about the potential of this research to advance our understanding of atmospheric dynamics and modeling.

In this paper, a comparison is made on estimates of the transformed Eulerian mean momentum and thermodynamic budget terms from 4 reanalysis datasets: MERRA-2, JRA-55, ERA-Interim, and CSFR. Their results clearly show differences amongst these datasets. My main concerns on this manuscript are:

1. Presenting the difference magnitudes and large uncertainties shouldn’t be the highlight. The manuscript needs to explain what these differences mean in terms of the physics of the atmosphere for the highlights to be suitable for publication in a journal like Atmospheric Chemistry and Physics. Are the differences enough to suggest that some of the reanalysis suggests a significantly different form of dynamics is occurring? There may also be instances when the difference values may simply be just noise. The noise-signals and physical signals need to be clearly pointed out. Once the authors focus more on what differences actually signify crucial Physics differences amongst the reanalysis datasets, they may be able to improve the organization of the manuscript.
2. In describing the reanalysis datasets somewhere in the methodology, more needs to be said on the differences in the physics that each model is known to already exhibit. These need to be described in a way that would help readers already get an idea of potential differences amongst the model.
3. The results spend too much time describing dynamics that are already well-known. For example, the first sub-section describing REM means may be reduced to solely focus on the issues regarding the calculation of v* or w*. The results need to be re-written in a way that immediately focuses on the physical and/or unphysical differences amongst the reanalysis with one another and/or with REM.
4. Showing DJF dynamics without mentioning sudden stratospheric warming dynamics isn’t a good idea. Your methodology indicates the calculations uses monthly-mean. To mention SSWs requires the use of, at least, daily-mean datasets. You can choose to do this, or instead show one equinox season.

I recommend major revisions for this manuscript.