General Comments:

This paper addresses the interesting questions regarding the development of model errors in temperature and zonal wind in the Met Office UM, using a nudging relaxation and a tendency budget decomposition. These methods are well described, and used to come to some interesting results. In the most part the paper is well written, the results well presented and the conclusions good, however I would suggest a substantial re-write of Section 4 and additional reference to related work before the paper is accepted for publication.

In several places the text would be easier to follow if each panel were given unique identifying letters. Figures 2 and 12 are good, figures 3-11 would benefit from additional labels.

Major comments:

1. L228-238, L430-432: As this is not the first article to identify temperature and wind biases in models, it would be appropriate to provide in the introduction at least a brief review or acknowledgment of the previous work on model temperature and wind biases (particularly the lower stratosphere zonal wind, and tropical tropopause temperature) (in addition to the brief mention of two examples on L555 at the end) and some summary of the existing knowledge. By providing a sufficient overview of the related work that has already been published you will be able to make it much clearer to readers the original contribution that this article makes in the context of the current state of knowledge.

1. Section 4:

As I understand it, the residual term for CNTL is the sum of the parameterised processes, any numerical integration errors and differences arising from the primitive budget equations being different from the actual equations of the UM. The CNTL-GLN difference in the residual is the difference of these in the CNTL and GLN plus the nudging, which is the very short timescale model error in the UM. However there is no single, early, concise explanation of this.

While various aspects of the above are written in various places in various ways, references to components of this and interpretations of the residual often seem confusing. For example lines 302-304 present the similarity as if it were not true by definition. The article could benefit from a concise re-write of lines 327-335 to clearly explain the interpretation of the residual, and moved earlier in the section. Then any subsequent discussion of the residual or any of its components can be re-considered in the context of the earlier explanation to make the section overall more cohesive and consistent.

A consequence of this is: taking the mean CNTL-GLN tendency from dynamics (4b, 6b, 8b, 10b), will this not be disproportionately dominated by the model dynamics bias in the first 6 hours being balanced by the nudging, therefore masking any information about differences between CNTL and GLN at timescales longer than this? If this is what you are trying to address in lines 320-324 it is not clear. With terms being so heavily dominated by the nudging, what information can be gotten from the dynamics/residual at timescales of longer than 24 hours in any quantities including data from GLN?

It is not clear that figure 4 provides any useful information not contained within figures 5 and 6 (and similarly that figure 8 does not show anything not in figures 9-11) other than the contour overlay which could be moved. It may be possible to make this section more concise by removing figures 4 & 8.

L323: This information not shown would perhaps benefit from being shown. With such an emphasis on the Coriolis term in the zonal wind budget, the article would benefit from the inclusion of further discussion of any biases in the meridional wind field.

L330-331: Is this conclusion necessarily true? Unsure if the results provided support this.

L367-370: The sign of the CNTL-GLN difference in physics is the opposite of the sign of the error in 10-b-3 and 10-b-1, which seems to suggest the opposite to what this sentence is saying.

L323-324: By “the error in Coriolis term against truth” do you mean the error in the Coriolis term in CNTL against truth? If so, state this.

Additional specific comments:

All figures: It would benefit the reader if each individual panel were assigned a letter identifier (a), (b), etc.

L33-34: There have been a wide variety of diagnostic methods… It would be appropriate to list some.

L124-128: I can discern what you mean, but it would be beneficial to re-write these sentences to make them clearer.

L191: This is not a general property of all partial differential equations, so remove these opening 4 words (or re-phrase the sentence to make it more accurate).

L253-254: I do not see evidence for this statement. Provide evidence, or clarify that this is not shown.

L262-263 & Figures 2d, 3b, 12a, 12b: The independence of GLN state with forecast lead time seems strange. Is the GLN state at lead times >24 hours truly identical? Can you explain this or comment further on why the differences are zero or imperceptibly small?

L292-293: a decrease in the tropics... State, a decrease in what in the tropics. Similarly for lines 293-295.

Figure 12-14: Are the differences between the dynamics and the sum of the resolved flow components, and the differences between the residual tern and the sum of the nudging + physics, in panels f compared to panels j, larger than one would expect resulting from the model level v.s. pressure level comparison? They seem quite large by eye. Can you comment on this please?

L479-480: This result seems important but it is not shown in this article (nor do you state in the text that it is not shown). With such an emphasis on the Coriolis term in the zonal wind budget, the article would benefit from the inclusion of further discussion of any biases in the meridional wind field.

L483-485: Returning to earlier comments on the interpretations of the residual term – this idea would benefit from further explanation and possibly inclusion of the “not shown” material.

Technical Corrections:

L29: within the first few days

L133-134: 10 degrees in the horizontal … two model levels in the vertical

L136: from December 2018 to February 2019 (or from the December of 2018 to the February of 2019)

L206: the word ‘definitely’ doesn’t need to be here

L242: we focus on three…

L262: but do not depend…

L538: “specially” is the wrong word to use here. One way to rewrite this would be for example “one promising way for operational …”

Review of "Process-based diagnostics using atmospheric budget analysis and nudging technique to identify sources of model systematic errors" by Matsukawa et al. submitted to WCD.

The reviewer would like to thank the authors for their comprehensive study on model-based diagnostics to identify sources of model systematic errors, which could be useful for any NWP and climate models. The method successfully detects sources and origins of model forecast errors in the Met Office Unified Model, which could be common in the state-of-the-art operational and research atmospheric GCMs. I think The paper is comprehensive and well organized as a WCD paper, so that I would already recommend minor revision, though I have several comments below before acceptance.

Specific comments:

1) The relaxation timescale of 6 hours could be practically useful to reduce/erase the initial errors that can grow up in subsequent forecasts. I am curious that how sensitive is "tau" (timescale) to your conclusion? For example, if you choose 12 or 24 hours as tau, you could obtain consistent results, that is, could detect the same origins causing the NH wind field errors?

 The relaxation timescale might be similar with the evaluation time of the Forecast Sensitivity to Observations (Hotta et al. 2017, Prive et al. 2020). The shorter timescales might be more practical for forecasts.

(Hotta et al. 2017, MWR, DOI:10.1175/MWR-D-16-0290.1; Prive et al. 0220, QJRMS, DOI:10.1002/qj.3909)

2) Could you comment in your conclusion part about two topics that could be useful as future studies?

- Budget analysis based on conservation values, potential vorticity or angular momentum (TEM or MIM), could be useful for your further budget analysis. Currently I only refer to a paper by Kobayashi and Iwasaki (2016), though there may be other important studies to be cited.

- As a comparison with the experiment for 2018 boreal winter, additional experiment for an SH winter could be helpful to improve your conclusion (e.g., Yamazaki et al. 2023).

(Kobayashi and Iwasaki 2016, JGR-A, DOI:10.1002/2015JD023476; Yamazaki et al. 2023, WAF, DOI:10.1175/WAF-D-22-0159.1)