The manuscript "Contribution of physical latent knowledge to the emulation of an atmospheric physics model: a study based on the LMDZ Atmospheric General Circulation Model" studies emulators for all parameterizations of the ICOLMDZ in an idealised aquaplanet configuration. The authors develop four emulators: two FCNs and two UNets, with two sets of input variables: the vertical profile of six state variables and four auxiliary variables in the first set, that are complemented by the vertical laplacian of the state variables in the second set.

Both network architectures are established and have been used to emulate components of GCMs. The main addition by this manuscript is that the authors investigate whether including latent variables as predictors can improve the prediction of physical tendencies. This can be relevant for researchers looking to replace the physical parameterizations with machine-learning based emulators, as stability and accuracy are very important for successful online emulators.

The FCN with vertical laplacians performs similar to the UNet (without vertical laplacians). Considering that the UNet input layer is built up of convolutions that can connect neighboring vertical levels, I find it conceivable that the UNet learns something like a vertical laplacian on the go, without the need to incorporate these predictors explicitly. Incorporating the laplacians also helps with variance, which is underestimated by all emulators.

The methods are outlined clearly and the deep learning code is provided. I believe it would be possible to reproduce the findings, given access to ICOLMDZ and the training dataset. However, ICOLMDZ is not included in the submission.

I would like to ask the authors to address the following points in a revised version of this manuscript:

1. The overall presentation could use some clarification. Due to the nature of the quantities that are evaluated, the figures are quite complex, and the main text discusses findings that are only presented in the supplementary material (S2, S4). I think it would be beneficial to show the figures that are important for building the main narrative in the paper, and move less important subfigures to the supplemental material.
2. Figures 4 and 5 already contain results that are based on the incorporation of the latent variables that is only introduced in a later section (5.2). I find this confusing, as a reader I was not able to interpret the figures while reading the manuscript front to back. I think it would be beneficial to show results once the underlying experiments have been discussed to keep the flow of information.
3. Figure 6 (c-f) contains results that are only introduced later in section 5.2. Again, I find it confusing to see the results early without having the necessary context, and once the context was there in section 5.2 I had to search for the figure to understand the findings.
4. It is obvious that the UNet outperforms the FCN. In the conclusion (Sect. 7), the authors state their interest in coupling both architectures to the dynamical core for an online evaluation. Maybe I am missing a point, but why would it be beneficial to continue working with the FCN if it is outperformed by the UNet? If it is useful to continue with FCN, I would appreciate a short explanation why it should be favored over UNet.
5. Please correct the grammar in the first sentence of section 4.2.

The manuscript presents the development of data-driven parameterizations for the LMDZ Atmospheric General Circulation Model, specifically in an aquaplanet configuration.

In the first experiment, the authors utilize low-level model variables (e.g., temperature, humidity) to emulate the entire subgrid-scale physics. They train two neural networks (NNs): a simple feedforward neural network (DNN) and a UNet with residual blocks. Both NNs struggle to capture sufficient variance in the output variables. The authors attribute this limitation to an inadequate representation of turbulence, particularly in the boundary layer. To mitigate this issue, they incorporate laplacians of part of the variables among the NN input variables, which may enhance the NNs' ability to represent turbulence. This modification leads to improvements in the R² score and the variance of the NN outputs.

The study yields two primary findings:

1. The UNet architecture performs better than the feedforward NN.

2. Incorporating additional variables, thereby embedding physical knowledge into the NNs, can improve their performance.

Overall, the study is comprehensive and well-documented. However, before recommending its publication, I have several suggestions for refinement. 

General comments.

• There are many interesting results in this paper. However, sometimes I was lost in the details and between figures and tables. There are repetitions and reminders of previous results, which make the paper hard to follow. For example, Figure 5 and Table 5 ultimately provide the same information. Tables 3 and 4, as well as Figure 3, could possibly be moved to the Supplementary Material. Additionally, it might be useful to merge Table 4 and Figure 3 by including the total number of parameters on Figure 3. Combining Tables 1, 2, and 6 into a single table would also streamline the presentation. These are suggestions, and the authors can take them or not.
• Please proofread. The grammar can be odd in places.
• Please revise the scale of the colormaps used. The colors are too saturated in Figure 6 (and some of the Figures in the Supplementary) making it difficult to highlight the results.
• Your extrapolation regarding execution times might be correct, but in my experience, estimating the gain when using the NN instead of the physical model is much more complex. It also depends strongly on the strategy chosen to implement the NN. I would not risk providing too many details on this subject.

Point comments.

• Eq. (2): Is this an approximation?
• line 231: Is it a 1D UNet? I recommend revising the first sentence of the paragraph to state that you used (rather than developed) the UNet architecture.
• line 315: Even though I ultimately agree with you on choosing the UNet instead of the DNN, I find that this is not immediately 'obvious'.
•  line 380: 'It appears that the U-Net architecture has a better ability to capture the reference tendency than the DNN': wasn't this already the conclusion of Section 4.1?
• line 465: I don't understand this sentence.
• line 485: Did the model converge during the 'training with Δ' experiment using the same settings as in the ‘initial training’ experiment?
• line 499-501: Is it a global R² score or only for the wind components?

In the manuscript "Contribution of physical latent knowledge to the emulation of an atmospheric physics model: a study based on the LMDZ Atmospheric General Circulation Model", the authors compare two Neural Network (NN) architectures, Dense Neural Networks (DNNs) and U-Nets, for their ability to emulate tendencies produced by a conventional physics package. They find that U-Nets generally outperform DNNs in capturing the variability of these physical processes. The study demonstrates that feature engineering by integrating physical knowledge, such as including the Laplacians of state variables as additional predictors, can improve the accuracy of both investigated NNs, particularly for the DNN.

I think this research could contribute to the development of more skillfull ML emulators of subgrid physics, but it has significant limitations as it is only trained on data produced by an aquaplanet setup without any topography and the performance of the emulators is only evaluated offline. An evaluation of the online performance, coupled to the aquaplanet ICOLMDZ setup would certainly be more meaningful than the offline evaluation.

Some of the findings presented in this manuscript appear to be preliminary and would benefit from more thorough evaluation. I will elaborate on this in the following points:

Major comments

1. From my perspective the biggest issue, as mentioned, is that the developed emulators are only evaluated offline. A small stability/performance test of the DNNs/U-Nets coupled online would be very insightful.
2. Line 160: Why don't you consider 2D outputs such as precipitation. I am sure the physics package of ICOLMDZ also parameterizes some 2D fields.
3. Line 198: Why do you choose one every 20 cells and not a random subset? With this fixed "step size" you potentially overfit to these locations, don't you? What about evaluation on full data set, it is mentioned here, but you never come back to that as far as I saw?
4. Line 224: You only tried this particular setup (6 layers and 512 neurons in each layer) and no hyperparameter optimization at all?
5. Line 483: To judge impact of adding additional predictors adding a plot learning/validation curves to assess convergence would be helpful. Also, best to train multiple models to see if the improvement is "statistically significant"
6. Line 562: The discussion is very short and not complete, you should add some limitation of you study, e.g, the aquaplanet setup.

Minor comments

1. Eq. (2): I doubt that the ICOLMDZ uses as simple Euler step for time integration.
2. Line 242: Please provide more details how you "reformatted" the input to 2D tensors. You are using 1D convolutions as previous developed ML physics schemes using U-Nets, right?
3. Eq. (8-13): I don't think explaining the computations of means, variances, and metrics in such detail is necessary, but that is ultimately your choice.
4. Line 420/Figure 8: Why do you choose a random timestep and not multiple ones and take a median/mean profile? Also, it could be helpful to plot A,B, and C in the same figure for easier comparison.
5. Line 423: What physical process is represented by the thermals opposed to convection and turbulence?
6. Line 436: "This is also the case for gravity wave drags from precipitations" - Do you mean convectively coupled waves, or what should "gravity waves from precipitation" mean?
7. Line 470: Is delta z really fixed and if so, what is this fixed distance?
8. Line 613: You should mention the CPU inference time of your models as well and mention that even if you are able to use the GPU for inference during coupling, you have an overhead from copying the data from CPU to GPU as long as ICOLMDZ is not running on the GPU as well.
9. Line 631: Watt-Meyer et al., 2024 did not emulate a physics package but derived the subgrid physics by coarse graining from high-resolution simulations

Typos/Grammar

1. Line 19: The second "numerical" is redundant
2. Line 201-203: "These numbers of samples are multiplied by the length of the input vector X′ and the output vector Y′, for all the three subsets, which correspond to variables aggregated over the vertical dimension" What do you mean by multiplied by length of ..., to get the number overall size of the input data?
3. Line 229: "It is trained with the learning rate scheduler of 10^{−3} ..." What exact scheduler did you use? I assume the factor 10^{-3} indicates some decay or did you mean learning rate of 10^{-3}?
4. Line 230: I wouldn't say that "a U-Net is a CNN architecture" but that it uses convolutional layers
5. Line 246: "Once the models had been built, we trained them." Not necessary to state this.
6. Line 257: "In this article" - You mean section I think
7. Line 284: "We will sometimes compute the RMSE on specific subsets of the test dataset to exhibit performances that vary for instance across latitudes or vertical levels." - "exhibit" does not fit here
8. Line 333: "..., we examine them study by latitude belts, ..."
9. Line 416: "We decided to carry out this study on three grid cells..." - please use columns instead of grid cells here
10. Line 429-431: please rewrite the sentence
11. Line 535: reformulate "with these new learning"
12. The word "Indeed" is overused throughout the manuscript.