Review of “Downscaling atmospheric chemistry simulations with physically consistent deep learning”

Geiss et al. produce an interesting use case of upsampling/downscaling CNNs for the purpose of producing higher resolution chemistry simulation coarse forecasts from process models. I think the main interest, and perhaps the novelty, is in their adaption of widely used CNNs to ensure that to high resolution output is physically realistic and consistent. I am not aware of this being done before, so I think this is of interest to the community and therefore GMD.

Overall, I thought the message of the paper was clear and tells a compelling story as to how these upsampling methods can be useful. I particularly liked how the introduction contains all the relevant details though I think some terminology could use more explanation (comments about this are later in the review). I have no major concerns about this manuscript, and any minor comments and thoughts are included below. Thank you for a nice and interesting paper!

Major comments

Section 1.1 and 3.1: I think the introduction of the technical language could be improved a bit. GMD will have readers who don’t understand what CNNs are or why we’d want to use one for image processing. I think perhaps a couple of plain text sentences about CNNs and why they’re useful would benefit this section. There’s also language used without introduction such as 3-layer, vanishing gradients, convolutional kernels, and deeper CNNs, that could be explained more. I don’t disagree at all with what you’ve written, I just think the audience (GMD) and the manuscript will benefit from a little more explanation.

Minor comments

L23: It’d be worth clarifying that you mean small ‘spatial’ lengthscales as small temporal lengthscales are equally important.

L92: It’s not immediately apparent to me why being able to train a CNN on log-normally distributed data is a result of your work. Wouldn’t a standard approach be to scale your date before training?

L160: What’s a spatial chip?

L174&177: There are numerous other loss functions that will account for the issue of the loss dominating for large concentrations (negative log likelihoods, normalised loss etc)

L201: Unit for this value 4x10^6 would be useful?

L203: Neither a ReLU nor an ELU will enforce non-negative outputs. I believe this sentence to be incorrect and it should be updated.

L271: What was the motivation for using MAE to evaluate. I personally would have thought MSE alongside so evaluation of fractional errors to be more informative.

L275: This could be a limitation in my understanding, but I thought SSIM values are between 0 and 1, not -1 and 1.

Table1: What’s the intuition behind CO and it’s fairly similar performance (for LOG-SSIM, but not MAE) across the downscaling methods?

Figure 2 and others: Representing ship tracks only really shows that the CNN learns that these are stationary features right. If we moved this ship track elsewhere, I’d imagine the CNN wouldn’t upscale that well. Is this right?

Figure 6: About the ‘ringing artifacts’. Should we be concerned that the interpolation methods (particularly the CNN) are producing upsampled output that contains these harmonic artifacts?

Sec5: What’s the additional computational cost of using VSR methods as opposed to SISR?

Typographical comments

L114 (and throughout): I don’t think chemicals should be in LaTex math mode. If using LaTex, try using the chemformula package and \ch{} command.

L159: Mention explicitly that SLP is sea level pressure?

L415: As far as I can tell, GCM hasn’t been introduced.

Other thoughts

L111: I really appreciated the forethought in scaling to a fairly standard (non-square model resolution)

Sec3.4: I think this is all very sensible and a nice solution to the conservation problem

I really appreciated the availability of the code and the video supplement. I thought these were useful additions.

General Comments

This manuscript describes the effort to use deep convolutional neural networks (CNNs) to downscale atmospheric chemistry simulations, focusing on NO₂, SO₂, CO, O₃, and PM_2.5. The authors develop and evaluate the performance of SISR-CNNs and VSR-CNNs, demonstrating that these new methods outperform nearest neighbor, bilinear, and bicubic interpolations, as well as "Clim." Especially, the authors develop methods that can strictly enforce physical conservation laws within CNNs, perform large and asymmetric resolution changes (8 x 10) between common model grid resolutions, account for non-uniform grid cell areas, super resolve log-normally distributed datasets, and leverage additional inputs such as high-resolution climatologies and model state variables. This work is significant not only for the community of atmospheric chemists but also for climate modelers. This manuscript is well written, and it should be published after the authors address my comments listed below.

Specific Comments

(1) Perhaps I misunderstood, but I do not fully grasp how the conservation enforcement layer works. According to equations (3) and (4), the output from this layer appears to be P (mixing ratio in a single low resolution grid cell)? How does this layer interface with the output layer ("0.25° x 0.25° Resolution Output")? Any variable transformations occurring here? For gradient descent to update the parameters, I am under the impression that "weights" and "biases" are needed, but I cannot locate such parameters in this conservation enforcement layer. It would be helpful for readers to have more information.

(2) I would like to bring to the authors' attention some related prior work that develops a CNN kernel for unstructured grids for spherical signals, which may enhance the model's performance. I believe a short discussion would be beneficial. https://openreview.net/forum?id=Bkl-43C9FQ

(3) If I'm correct, SISR-CNNs and VSR-CNNs can only process "one pollutant" at a time? Or they can process "multiple pollutants" (such as RGB channels in an image) simultaneously?

(4) Line 110: There are multiple ways to degrade or prepare low resolution data, making the term "degraded" unclear. Readers may believe, for instance, that the authors conducted simulations with two resolutions separately (using a nested mesh for example). Consequently, I believe that "2-D averaging" should be made explicit here.

(5) Line 171-174: Any citations to support the argument made in factor (1)? Glorot and Bengio (2010) spoke about normalized Initialization for deep feedforward neural networks, but not for convolutional neural networks.

(6) Additional information about the runtime would be beneficial for users. For instance, the number of GPUs used and the training time for SISR-CNNs and VSR-CNNs.

Technical Corrections

Line 190: What is "a-priori"? Is this a typo?