General comments

   

The core idea of the manuscript, to use polarized microwave observations fromthe MWHS sensor to retrieve ice water path, is certainly of scientific interest given that these observation have not been used for this purpose before. In its current form, however, the manuscript lacks novelty and scientific rigor.

My main criticism is that the authors do very little to tie their results to any reference data, which hampers the credibility of the presented retrieval results. Although they provide a  comparison of the global distributions of monthly mean IWP to ERA5, MODIS and the 2C-ICE product, the latter of which is used as training data for the retrieval, I consider these results insufficient to conclude that the retrieval works reliably given that retrieval artifacts are clearly visible over the Tibetan plateau for the winter time retrievals. 

While I consider the topic fit for publication, major revision will be required to improve quality and relevance of the presented results.

Specific comments

  

• Fig. 4 and 5: I would suggest analyzing only observations from the swath edge or to separate the analysis of observations from edge and center of the swath. This will make it easier to compare your results to observations from conical scanners. I also suspect the scatter plot is misleading here as many markers are likely lying on top of each other. I suggest replacing the scatter plot with a density plot. Information on the hydrometeor content can be added by drawing a contour plot of the distribution of pixels with
  
  $IWP > 10^3$ or $10^2$ on top of the density plot (with a sufficiently different colormap of course).
• l. 177: You cannot reference a results that you haven't yet presented.
• Fig. 5: Please elaborate what causes the low TBs for clear sky observations.
• Sec. 4.2: The presentation of the evaluation needs to be improved. You need to be clearer about what data is used to calculate the error for the cases you present. In particular, you need to state whether for Cases 1 - 5 the changes to the input data are also applied to the validation data. If that is the case,  these error metrics have little meaning as the distribution they are calculated over cannot be expected to represent that of real measurements.
• l. 236: Define relative error. I assume you are referring to the absolute percentage error here. Note that when the absolute percentage error is used to select between models it is biased towards models that underestimate the true value. This together with the fact that you are using  MSE of log(IWP) to train your network, this will likely lead to non-negligible biases in your retrieval. You should therefore also add bias to Tab. 2. I would also suggest adding correlation as an additional metric.
• l. 236: It does not make sense to include the errors over land and ocean here as this is nothing that you can tune. Please move this analysis to the end of this subsection and perform it for the final retrieval configuration.
• l. 263: This is only true if your training data set is too small to include cases with PD from the surface. Otherwise the network can easily learn to handle ambiguous inputs given that it is trained properly.
• l. 268: While the scatter plot is useful here it is insufficient to fully characterize the retrieval. For this you should apply your full retrieval, i.e. the combination cloud classification  and IWP calculation, to all pixels from January 2015. Please provide a table containing at least  bias, MSE, correlation and potentially the relative error calculated for IWP > 100 g/m^2. Here  you can then also assess performance over land and ocean.
• l. 270: This error propagation  doesn't make sense. Even if your relative errors would follow a  Gaussian distribution your mean relative error wouldn't be an estimator of its standard deviation.  This is even less the case for the median absolute error.
• Sec. 4.3.1: Although retrievals of cyclones are certainly scientifically interesting, the retrieval results that you provide are not very meaningful as they can't be tied to any reference value. I  suggest you try to find a co-located overpass of both CloudSat and MWHS. There's a large number of CloudSat Cyclone overpasses available from https://adelaide.cira.colostate.edu/tc/tcs-50km.txt, it should be possible to find one that coincides with an overpass from MWHS within 30 minutes or so. This would allow you to compare your retrieval results to both 2C-ICE as well as the MODIS retrievals andthus add more credibility to the results presented in Sec. 4.3.2.
• Sec. 4.3.2: Please add a figure with the distribution of the zonal mean IWP similar to Fig. 3 in Duncan and Eriksson, 2018. This will allow for a more quantitative evaluation of the retrieval results. I also think a logarithmic color scale (as in Duncan and Eriksson 2018) would be more suitable to display global distributions of IWP in Fig. 15 and Fig 16.

Technical corrections

• l. 4: Missing space after 'Information'
• l. 29 - 31: You cannot conclude that individual measurements can only sense certain properties of clouds only based on their sensitivity to microphysics.
• l. 59: ICI will only have channels up to 668 GHz
• l. 62 - 64: How has MWHS been 'proven to give information about IWP' if it was 'hardly analyzed information
  
  past studies'?
• l. 68: The name is Cloud ProfilING Radar
• Fig. 2 (a): Are there really gaps in the distribution or is that an artifact of the bin boundaries? If the former please explain what could
  
  cause them. In the case of the latter please select the bin boundaries to avoid them.
• l. 167: Please typeset unit according to manuscript preparation guidelines.
• l. 170: Figure should be abbreviated with Fig. except at the beginning of a sentence.
• l. 222: Please also provide false alarm rate and probability of detection since accuracy alone can be misleading for imbalanced datasets.
• l. 289: Specify channel in which the low TB are observed
• l. 325: showed -> shown
• l. 341: The different measurement resolution of Modis and MWHS cannot affect the retrieved mean on a  5x5 degree grid.
• l. 344: Given that there are obvious artifacts in the retrieval results, I don't think that this can be concluded.
• l. 365: This discussion of the limitations of the neural network retrieval is too superficial. First of all, once the code is written extracting more co-locations is extremely easy, so I don't think there is a valid excuse to use a training data set that oneself deems too small. Moreover, although there are uncertainties  related to the co-locations of the CloudSat and MWHS observations, these uncertainties are represented in  the training data and can thus be predicted using for example quantile regression neural networks. The real  issue are the uncertainties in the 2C-ICE data as these are much harder to quantify and cannot be predicted.
• l. 385: You cannot conclude that performance is good for the Cyclone cases because you don't have any reference to compare to.

The paper develops the Neural Network for the FY/MWHS to retrieve global IWP parameters using the correlations between the CloudSat 2C-ICE IWP products and the MWHS BT measurements when collocations happen. Although the statistical NN method does not use any forward model calculations to involve physical radiative transfer processes, it provides a simple and quick way to obtain the global IWP coverage from the FY/MWHS observations. However, the entire methods including finding collocations, developing NN, and analyzing results have so many similarities to the paper in Holl et al., 2010; 2014, which raises concerns about the significance and novelty of this work. Further, major issues as summarized below exist in the developed methods. Due to these weaknesses, the manuscript is recommended to be rejected in the present form.

Section 2.2, lines 133-144

The procedure of finding collations is one of the key steps in the entire study, but the descriptions shown in lines 133-144 in Sect 2.2 are very vague. For example, the MWHS footprint size should change with the scanning angles since the instrument has a cross-track scanning mode. How accurate is it to always approximate the MWHS footprint using a constant circular pixel? How do you address the spatial response function inside each MWHS footprint? Also, when the MWHS scanning angle is too large, its field of view is likely to be different to that of the nadir-looking CPR even though the two sensors have similar geolocations, and readers might wonder how reprehensive the collations are in such situations. The sampling errors due to insufficient CPR pixels in each MWHS measurement are mentioned, but it is still not clear how significant the errors are and what the authors did to minimize the negative effects.



Section 2.2, figures 1-3

The random IWP cases in the collocation database essentially represent our prior knowledge about the ice cloud distribution. Considering that the topic of this paper is to address the global water path distribution, the collation database is expected to sample the global IWP coverage without biases. The results in fig.3, however, show that the latitudinal distribution of the dataset is highly ununiform. This suggests improper weights are given to the random database cases, and therefore systematic biases are introduced during NN retrievals. How to make the collocation database cases to distribute according to our prior knowledge needs to be addressed.



Section 2.2, figures 4 and 5

The biggest problem of this study is the dramatic lack of validation and evaluation of the essential collocation database. Since there are so many error sources in collocating, adequate work on validating the dataset and evaluating the mismatch errors is necessary. The only results serving such purposes are given in figures 4 and 5, but the results are very confusing. The figures show that the BT observations spread over identical ranges no matter the ice clouds exist or not, at least in the way the authors show. How could you retrieve ice cloud parameters if the BT observations do not respond to the ice cloud change at all? Besides, I suspect that the collocation database should have many physically unreasonable cases due to various error sources, right? If so, the method to filter out the meaningless cases needs to be illustrated. Also, the effects of various error sources on the database and the retrieval accuracies need to be thoroughly analyzed. Overall, solid evidence must be provided to assure the critical collocation database is robust.



Section 4.2

Figures. 7 to 10 and table 2 show the statistics of the retrieval results using different inputs, and they are the primary results of this paper. However, the results become unpersuasive since the collocation database is not established, validated, and evaluated properly. Lines 270-273 give the estimations of the retrieval errors by combining the 2C-ICE product errors and the NN retrieval errors, but the errors from the collocation finding procedure are not considered. The testing dataset is obtained in the same way as the training dataset, which means the two datasets share the same inherent collocation errors. Besides, no descriptions and explanations of fig.10 are given, and more discussions should be added in the revision. 



Section 4.3.1

Figures 11 to 14 show a case study to retrieve IWP of the typhoon Rammasun using MWHS measurements. Again, validations of the retrieval results are completely missing. The statements say that “the structure and the distribution of IWP are consistent with the characteristic of TB (line 324)” and therefore “the performance of the two neural networks appears to be good (line 328)”, which are very crude. Besides, the atmospheric and cloud microphysical statistics in typhoon are likely to be very dissimilar to the globally averaged microphysics in the collocation database. Using a different training dataset with more accurate prior information should make the typhoon retrievals better. Also, the plots of BT measurements in figures 11 -13 occupy too much space. You should provide more analytical results instead of merely showing the instrument observations.



At last, there are many grammatical errors, and an English revision is necessary to improve the manuscript.