General comments

This paper deals with evaluation of ML emulators of radiative parameterizations in General Circulation Models. In particular, authors aim to verify if the results of model calculations with original parameterization and with its ML emulator are identical. Comparisons have been performed between results obtained with GFS at C96 horizontal resolution and an hybrid deterministic-statistical GFS (HGFS), in which the original parameterization schemes have been replaced with shallow-NN-based emulators of LW and SW RRTMG developed for CFS.

The problem has been explained clearly, the topic discussed in this work is very interesting, so the manuscript is potentially suitable for publication. It furnishes a good contribution in the context of existing literature. However, before I can recommend the publication, several issues must be addressed.

My main concern is about the organization of the paper, since in the present form it is not so easy to be read. In particular:

• The Introduction is too long and does not allow the reader to have a clear frame of the problem under study. I suggest to split it into two parts: one about the main concepts, a synthesis of the state of art, and the aims of the present work; another one about all the other technical details of the emulators developed at ECMWF, NCEP et al…
• The title of Section 2 does not reveal the content. It is true that authors explain the differences between the two models, but they also explain how they have modified the setup of GFS in order to perform the tests described.
• The discussion section is interesting, but the concepts described are quite generical and not specifically linked to the results obtained in the present work. In particular, concepts expressed in subsection 4.1 would fit better into the Introduction. Subsection 4.2 is mainly theoretical: I suggest to shorten it and to move it in another section.
• Analysis of results is mainly qualitative and performed only through analysis of Figures. I suggest to add some Tables with numerical values of specific indicators (bias, rmse etc…) in order to have a detailed quantification of the differences. In other words, Results section must be strengthened, since it is quite weak in the present form.
• Similarly, the Conclusion section is too generical and quite weak.

Specific comments

Line 60: What do you mean with “results are physically identical” ?

Lines 70-71: I suggest to introduce a sentence to make a better link between the concept expressed in the paragraph 65-70 with the one expressed afterwards.

Lines 151-154: In my opinion, this paragraph is not properly linked with the previous text, but rather seems a “stand alone” one.

Lines 195-196: Avoid using stand-alone sentences.

Line 211: “e-folding” is scientific jargon. I suggest to avoid it.  

Lines 203-208: “In addition … or HGFS”. This paragraph does not fit well into the “Results” section. I would move it into the previous section.

Line 207: “with radiative transfer emulators developed in 2011”. This sentence is too generical, please use more precise terms.

Line 216-218: “Note, that… experiments”. I think that this information is not so relevant for the reader, being more related to management policies of the supercomputing center.

Figures 1-2-3: Put a proper label on horizontal and vertical axes. Put the unit of measure on the colorbar.

Line 230: Explain the meaning of TOA (Top of Atmosphere).

Figures 2-3 (caption): “Vertical coordinate shows model level number.” It seems to me that latitude values are shown on the vertical axis, please clarify.

Line 279. Acronym SNN is introduced here for the first time. Explain the meaning.

Unfortunately, the paper does not convince me in the current form. The paper is separated into two parts. The first part shows that a neural networks emulator that was developed for one model can be used within a different model and obtain reasonable results. This is interesting in principle. However, the new model is changed significantly to allow for the application of the old emulator (e.g. in terms of vertical resolution) and the quality of the solution with the neural network is not evaluated sufficiently. The second part is a long discussion on what should be done to obtain emulators that are working in different environments. While the discussion is interesting in principle, it is not backed up by the results of the first part (e.g. as only a single (shallow) neural network has been tested). The arguments of the discussion are intuitive, but most of them are not backed up by powerful references or by numerical experiments. I therefore think that the paper is not suitable for GMD in the current form. I hope the authors can improve the paper along the following suggestions.

Major comments:

The figures 1-3 do not leave me convinced that the neural network configuration is good enough. Can you show results that would convince me that the GFS version with 64 vertical levels is producing something useful (e.g., by comparing it against the default model with 127 vertical levels)? Can you show more diagnostics that compare GFS and HGFS for quantities that are no mean fields or at least provide plots of variability? Can you show vertical profiles that compare the neural network emulator and the default radiation scheme to visualise how different the solutions are?

Each sub-section of section 4 should show a clear connection to the numerical simulations. If this is not possible, the content should be either removed or backed up with a theoretical study. Section 4.1 should become part of the introduction. Section 4.2 should be backed up by experiments because it otherwise remains speculative. The argument that SNNs are better than DNNs as they are more generalisable is not backed up with simulations and we also do not learn how non-linear the ML solution needs to be from the paper. Section 4.3 is also not backed up by any experiments. Section 4.4 and section 4.5 read like chapters of a textbook and are not very relevant for a paper that is not training new emulators.

Minor comments:

The description of radiation schemes in general is rather long with machine learning only starting at l.55

The neural network solutions that are used in the paper are not described in sufficient detail in Section 2.

l.65: I do not think that this very general statement holds. I am sure that I could break forecast skill with an unbiased, random, uncorrelated error if I wanted to.

l.77: I do not understand “blackbody cloud”

l.118: Why do you need to store the entire training data set for regression trees?

Figure 1: I assume that this does not cover the entire year 2018 but rather 1^st Feb 2018 – 1^st Feb 2019, correct?

Figure 2 and 3 are not “zonal means” as indicated in the captions. The vertical coordinate is not the “model level number”.

l.208: " hybrid deterministic-statistical GFS" -- Why do you call it “hybrid”?

l.248: This should be moved to the introduction.

l.185: Yes, OK, the number of possible model states is increased. But how do you know that this is leading to difficulties in the emulation? I do not think that this can be shown mathematically.

l.281: It is hard for me to believe that there is no universal theorem for DNNs