General comments

The reviewed manuscript presents a study aimed at estimating the potential of the Ice Cloud Imager (ICI), a satellite instrument to be launched in 2026 as part of the EUMETSAT Polar System, to retrieve vertical profiles of ice water content (IWC) and mean mass diameter of ice particles. For this purpose, the authors propose using quantile regression neural networks trained on simulated ICI observations. They demonstrate that ICI's 13 channels spanning 183-664 GHz frequencies contain sufficient information about the IWC vertical distribution to reliably retrieve this quantity in the range of 3-14 km with an estimated vertical resolution of 2.5 km and IWC values varying from 0.01 to 1 g/m³. Above and below this layer, the retrieval errors become high. The authors compare their retrievals with existing DARDAR radar-lidar products and show statistical consistency with this product. This result suggests that ICI, once launched and operational, will be capable of complementing the existing ice cloud observations with broader spatial coverage.

The study is topical, the manuscript is well organized and well written, and I would not hesitate to recommend its publication in the journal provided that the minor issues listed below are addressed. This is the reason I've chosen "accepted subject to minor revisions".

Specific comments

In the Introduction, the authors provide the rationale for such a method and for retrieving the vertical profile of ice water content instead of estimating the ice water path in the column. One of the arguments they present is the radiative effects of cloud ice, and I agree with this in general. It is clear that the same mass of ice can be distributed within the cloud limits in a number of ways, and the radiative transfer and radiative effects for these distributions will not be the same. For example, the emission depends on temperature, and a cloud with top-to-bottom IWC(z) falloff will not be equivalent to a bottom-to-top IWC(z) falloff, despite the fact that their IWPs are the same. However, it has already been shown using the same DARDAR dataset and DISORT calculations that the absolute differences for short-wave and long-wave fluxes estimated with and without knowledge of IWC(z) shape do not exceed 2 W/m² at the top of the atmosphere, 2.7 W/m² at the surface, and 4 W/m² in the atmosphere. If these results are cloud amount weighted, these values reduce to 0.5 W/m^2, 0.5 W/m^2, and 1 W/m², respectively. From this point of view, it would be useful to provide an example of a real physical situation for which the error of using constant IWC instead of a real IWC(z) profile would lead to misinterpretation of a physical phenomenon or model validation.

Section 3.2. Retrieval model implementation

I am not an expert in neural network training, but my experience with forward and inverse problems tells me that adding noise to the simulated radiance increases the chances of retrieving an incorrect original profile, especially in the case of an ill-posed problem. Indeed, this is a typical self-consistency test in any method, for which the input data are passed through the forward simulator, then modified by realistic noise, and then passed through the retrieval procedure to compare with the reference data. However, I'm not sure that the training dataset should be modified by noise. It's true that the real data will be noisy, but the training process using noise-free data should yield similar weights to the neural network's nodes and paths as a noise-perturbed one, but this training will take less time/data and be more physical. Later on, its accuracy will be reduced by using noisy data, but the neural network itself will be "cleaner". Could you please comment on this? Will one still require 9.4 million cases to train the neural network (line 216), or can one achieve the same results using 10 times fewer profiles, but without noise?

Lines 199-200: Indeed, the retrieval of Dm and Zm does not make sense if ice water path equals zero, but this is somewhat evident. Could you please rephrase these sentences?

5.1. Retrieval Ice Water Content

In this section, the authors spend considerable time explaining the effects related to averaging kernels, but they do not mention them explicitly, despite the fact that they show them in Fig. 12 and Fig. 13. I would say that the text of this section could be made much more compact and understandable for the reader if the authors moved these figures here.

Fig. 3, 7, 9, 10: It would be interesting to see the differences between the reference and test panels either in absolute or relative values in a third (added) panel. I am somewhat concerned about the striping mentioned in this section. Wouldn't it be better to smooth/denoise the input data to avoid this effect? Perhaps one could run the retrieval twice – once for original profiles and once for smoother ones – and if the results differ strongly, then use the second solution.

Review comments for “The Ice Cloud Imager: retrieval of frozen water mass profiles” by May and Eriksson

This manuscript presents a comprehensive study of the vertical profiling capability of ice water mass (IWC) and mass-weighted effective diameter (Dme) from an upcoming spaceborne passive sub-millimeter radiometer instrument called Ice Cloud Imager (ICI). Starting from an established quantile regression neural network (QRNN) framework that this team used previously for retrieving column integrated mass (IWP) and averaged Dme, the authors applied the same ML architecture to retrieving the profiles of IWC and Dme using the same training database constructed from global active radar measurements that can provide the “truth” profiles with an arbitrary vertical resolution set at 500 m. They found that decent prediction (i.e., error <=100%) can be achieved for a wide range of IWC values between roughly 5 – 11 km, with degraded performance below or above this altitude range. The integrated IWC is consistent with the previously retrieved IWP, demonstrating the physical consistency. Similar conclusions were drawn for Dme profile retrieval as well, although it in general performance worse with larger biases. A substantial amount of the pages is then dedicated to understand the real “physical” vertical resolution using the averaging kernel method as well as the degree-of-freedom estimation, and lastly some sensitivity study was carried out to inspect whether the pseudo-high resolution enabled by the ML algorithm would significantly distort the results with regards to different cloud structure and microphysics.

Overall this is a solid work which pushes both the theoretical understanding of the true profiling capability from ICI for two different variables as well as advances the practical retrieval algorithm. The methodology design is strict, and experiments are well-designed and well-executed. The writing is clear for most parts, and the logic flows naturally without significant disruption. Given the solid foundation this work paves in pushing one step further toward developing a new satellite product, which is going to be extremely useful, I’d support final acceptance and publication of this work. However, there is some room for improvements, especially the lack of a strategy for accurate cloud flagging using the quantile distribution or uncertainty so to remove the “fake” small IWC retrievals, and the lack of discussion on real physical vertical resolution for different cloud types. While I believe missing discussing these components won’t necessarily significantly degrade the impact of your work, they should be included (which might require more than simple additional works) so to make your product ultimately useful.

• Major concerns:

1. Since your ML prediction actually predicts the distribution (or quantiles), it is a pity that the discussion on how to use the quantiles to develop a IWC or Dme flagging algorithm, especially given the fact that your results contain so many small IWC/Dme values that are apparently unreal but just ML artifacts because the training focuses on learning the distribution. For example, the fake “near-empty” clouds near the freezing layer in Fig. 3 case, the much larger integrated IWC value compared to your retrieved IWP in the clear-sky regime in the Fig. 7 case, the spike in Fig. 6, and the “better-than-CloudSat” in the lower sensitivity threshold suggested in your Fig. 4 PDF comparisons. My guess is the PDF width from your prediction for these small IWC cases should be larger than your retrieved IWC value, but as the errorbar was never used for filtering, I don’t know if that’s the case or not. Ultimately if these become operational or research products for ICI, you’ll be required to provide a quality flag or something similar to let the user know which retrievals are not trustworthy. My suggestion is to try playing with different thresholds (e.g., standard deviation, 75^th quantile – 25^th quantile, etc.) to develop a flagging algorithm and show the confusion matrix to demonstrate both clear-sky and cloudy-sky are accurately captured. Also, please use the flagging mechanism to update Fig. 3, 4, 5, 6, and 7.
2. With the same IWP value, the clouds could be top-heavy (i.e., developing), U-shape (i.e., mature), or bottom-heavy (i.e., decaying). The scientific value of profile retrieval mainly lies in being able to differentiate cloud vertical structure, and potentially understand better the system life stage. The three cases shown in Fig. 15 demonstrate that your algorithm could achieve this capability. However, the averaging kernel and DoF discussions all focusing on the mean vertical resolution for all training samples. I would strongly recommend updating the averaging kernel results for different types of cloud. Given the fact that your training samples are big, you can use some clustering method (e.g., PCA, k-clustering) to separate them into a few representative types, and then compute the results for each cloud type. There is no way that the ~ 2.5 km vertical resolution can be achieved for all kinds of ice clouds between 5-15 km, so it would be much more appreciated if readers can be informed the real physical resolution that can be achieved for different cloud types. I’m especially interested to see how multi-layer clouds can be resolved in your proile retrievals.

• Minor points:

1. As mentioned in this work, the operational ICI products include mean mass height Zm and mass-weighted column averaged Dme. Could you check if your retrieved IWC can give you the mean mass height that’s consistent with Zm, and your Dme and IWC profile retrievals can yield agreement with mass-weighted column averaged Dme? I’m especially curious about the former.
2. Your ML retrieval results suggest degradation happens above 12 km, but later on your averaging kernel experiments find the vertical resolution can be achieved stably below 15 km. Why this discrepancy?
3. In the averaging kernel experiment, Dme response function is bi-model, but IWC response function is not. Do you know why they are inconsistent? Does this suggest ICI is mostly useful for sensing ice particles in anvils and cloud bottom? But the vertical resolution of 5 km at 10 km strikes me… Please elaborate your thoughts.
4. Line 170: why using the mean instead of the peak of the predicted PDF? The PDF could be very skewed for many cases.
5. 5b vs. 5a: I can understand why your training database has low bias near the tropopause because your database doesn’t include the CALIPSO measurements whil DARDAR has. But why your PBL cloud ice are also low-biased compared to DARDAR?
6. 8a: There is a consistent and significant low-bias in the 1:1 correlation, but then the MFE is very small, indicating the retrieval results are good. Why? Is MFE a good measure for such a situation? Maybe you should use RMSE or MAE?