In this work the authors apply information theory to rainfall retrieval from commercial microwave links. Though the theory has been applied to other areas in hydrology, it has not been applied to rainfall retrieval from CML before, and the approach, therefore, is an interesting one. The authors apply the information theoretic framework to two CML processing steps, namely the quantification of precipitation estimates, and the wet-dry classification. They show that considering additional CML variables, as well as external environmental variables can highlight the importance, or weight, of the different parts in the CML processing chain, as well as improve the prediction of the target variables, which is promising.

The article is generally well structured with clearly described sections. It is written to-the-point, though sometimes at the expense of being too brief, particularly on the discussion side. The article does include a comprehensive overview on information theory with references for further consideration, which is nice.

 General comments:

Wet-dry classification

My main comments on the article refers the methodology of the wet-dry classification analysis. As the target variable the authors use manually identified wet and dry timesteps at 1 minute resolution, and the analysis is based on a single CML. In my opinion this strongly hampers the reproducibility and the generalizability of this analysis.

It unclear to me how the authors choose the current link the analysis is based on. Can they show how this framework would behave if a different link is chosen? In other words, how generalizable is this analysis, and how sensitive are the results to the specific link chosen?

The authors also state that the wet and dry timesteps are separated by visually inspecting the total loss attenuation. Is this visual inspection not based on an implicit threshold? And would it then not be possible to apply such a threshold programmatically? For reproducibility it would be important if the authors can show how the analysis would turn out when the wet-dry timesteps are identified programmatically, using a certain condition. Because up-scaling this information theoretic framework in its current form to multiple CMLs, let alone an entire network, does not seem feasible manually.

If this should become too similar to the alternative wet-dry approaches discussed in the article, I suggest using the weather radar data as reference, as is done for the QPE analysis, even though this would change the temporal resolution to 5 minutes. Alternatively a nearby gauge could be used. This would also ensure that wet and dry periods are determined based on actual rainfall sensors.  

Finally, regarding the alternative wet-dry classification approaches the authors suggest two common approaches. Regarding approach B, there are other common approaches in the references listed by the authors that either build on top of the approach by Schleiss and Berne (2010), namely Graf et al., 2020, or that use completely different methodology (Overeem et al., 2013). Therefore to call the approach by Schleiss and Berne (2010) state-of-the-art seems premature, and it would be worthwhile to see how the results from the information theoretic framework compares to other common wet-dry classification approaches, that apparently have been preferred in those publications over the Schleiss and Berne (2010) method.

General textual comments

To me the term ‘external variables’ is not very intuitive and rather vague. On several occasions the authors use ‘environmental’ or ‘atmospheric’ variables. In my opinion exchanging the word external with either environmental or atmospheric would improve the readability of the article.

In the same way, I would consider changing the term ‘internal variables’ to sensor or system variables, as this more directly describes the list of so-called internal variables.

In my understanding the term ‘synoptic’ often refers to large scale weather states, though granted, the term can have different meaning. To avoid confusion, and since in this case the study area is 35x35km, I would suggest simply using the term weather types.

The goal of the article and title

As I read it, the goal of the article is twofold. It is to give insights into the relative importance of different CML processing steps, and subsequently to see how the uncertainty can be reduced by using (qualitative) sensor or environmental variables. For example, in the abstract the authors state they “propose to evaluate CML processing” (L11) and end with the goal to “ultimately facilitate the improvement of CML rainfall estimates” (L24).

In my opinion the title is a little bit vague and does not cover these two goals entirely. I would also add the term “information theory” in the title to immediately make explicit the method used, or make the term “additional variables” more explicit, i.e. additional sensor and environmental variables.

Some suggestions:

- Information-theoretic analysis of processing steps for rainfall retrieval from commercial microwave links.

- Using environmental variables and information theory to gain insights into processing steps for rainfall retrieval from commercial microwave links

Moreover, if my interpretation of the goal of this article is indeed correct I would accentuate that dual goal more clearly in the introduction.

Specific comments:

L54-L56: It is not entirely clear to me what the authors want to say. By “interpretation of the CML data using deterministic models” do they mean estimating rainfall from attenuation suffers from many assumptions in the currently available models? And which CML empirical relations do the authors refer to, the k-R relation? And which variables, total loss? It would be good to be explicit in this paragraph, or give some examples of what you mean.

L59: It is commendable that the authors mention that there are uncertainties associated with gauge-adjusted weather radar too. Since they use this as their reference, a short description in the discussion of the effects this has on their results would be appropriate.

L132: It is appreciated that in the context of this work the authors later (in Fig. 3) explore what a “large enough dataset” is.

L184: Applying a threshold of 0.5mm/h means there are no dry timesteps. Though it makes sense to apply this processing step is isolated like in this analysis, but in a near real-time processing chain there will be dry timesteps present too. Hence a comment, here, or in the discussion, on the implications of this threshold on the results would be appropriate.

L190: As mentioned here and in L117, binning is a subjective choice. It would help to mention based on what user requirements you made your choice, and how your choice reflects the size, distribution and precision of the data.

Section 3.2: please see general comments on wet-dry classification.

L213: “..greater than the threshold.” Which threshold? The detection threshold you are trying to determine, making this an iterative process?

L221: So in the end you use one optimal threshold?

L229: From the text it is unclear to me if, and where, approach A has been used in literature before, or whether it was designed specifically for this analysis.  This would be helpful to show how established this method is.

L241: Please elaborate why you chose for the different temporal resolutions of 15 and 1 minute. This is currently not clear to me from the text.

L280: What is meant by ‘visual shift’?

L303: What is meant with aligned? Aligned temporally?

L312: I recommend adding a table in an appendix with the synoptic types, and how frequently each of the types occurred during the studied period to show how applicable this framework is to the range of different weather types.  Also mention what is the temporal resolution of these synoptic types.

L322: What is meant by “scales”? As in: puts it in perspective?

L327: Regarding the selected results, please state why only these are selected? Are these the most successful combinations of predictors? Perhaps worthwhile to add the other combinations as an appendix.

L349: If the sample size is that important please also add the sample size used for generating Fig. 2 in the caption.

L409-410: The fact that more training data leads to better results, is that the case for all predictors? In other words, could the need for a large sample size not simply be inherently related to the temporal scale of predictors like synoptic type or season?

L379: This should be surprising since TL is used to manually identify the wet-dry timesteps right?

L382: The entire wet-dry classification analysis relies on this one CML. As mentioned in the general comments this is a strongly limiting factor in the generalizability of this analysis.

L419: See general comments on the wet-dry classification and the use of other established wet-dry classification methods. Furthermore, these established methods were often calibrated using weather radar or gauges. It would at least be appropriate to discuss this difference and the effect that has on this comparison, as well.

L436: In case of rainfall events, subsequent timesteps can hardly be considered independent.

L429-444: An additional comment further elaborating on the interpretability of the results would be beneficial. For example, when listing the percentage reduced uncertainties (L329 3%, L332 6%, L337 1.5%, etc.) is this a statistically significant decrease? Also, the percentage decrease in conditional entropy in Fig. 4 is much larger but the scale (x-axis) is much smaller. For the article to be self-contained, also for readers unfamiliar with information theory, a note on how conditional entropy in bits, for example, relates to the number of correctly labeled wet and dry timesteps would help. Such a comment can maybe best be made in the results section.

L440: the comment on climate-specific constraints is appreciated since week or month of year may be of little significance in regions where the intra-annual variability is a lot smaller.

L459-460: It is appreciated that the authors acknowledge this lack of discussion.  

L464: What is meant with “independent”? As in, an additional study?

L478-484: It would be fair to acknowledge the availability of the data as well. For example, synoptic type has a different latency than CML attenuation. How readily available are all these environmental variables and are they able to be incorporated in near real-time?

In addition, please also comment on/acknowledge the dependence of the variables used as predictors, and the influence this has on adding predictors. For example, temperature and month and week of year are not entirely independent variables. Is independence accounted for in the current framework?

Technical corrections:

L293: Conversed as in processed?

L301: The sampling …? area?

L445: This sentence is not clear to me.

Review Report

Journal: Atmospheric Measurement Techniques 

Manuscript Title: Information gain from different processing steps and additional variables for rainfall retrieval from commercial microwave links 

Authors: Anna Špačková, Martin Fencl, Vojtěch Bareš

Overall Assessment

This manuscript presents a novel information-theoretic framework to evaluate uncertainty in rainfall retrieval from commercial microwave links (CMLs) and examines the impact of processing steps and external variables. The study is well-designed, data-rich, and methodologically innovative. However, several issues—particularly in methodological clarity and interpretation of results—require substantial revision. I recommend Major Revision with the following detailed comments. 

Major Concerns and Recommendations

1. Methodological Clarifications Needed: Information-theoretic measures (e.g., entropy, conditional entropy) lack detailed derivation, hindering reproducibility. For example, I suggest the authors expand on discretization steps (e.g., binning strategies for rainfall intensity) and clarify how joint probability distributions are constructed from multivariate data.
2. Deeper Interpretation of Results: Mechanisms behind uncertainty reduction (e.g., synoptic types) are not thoroughly explained. Connecting synoptic types to physical processes (e.g., convective vs. stratiform rain attenuation) may bring more insights. Additionally, you can add spatial plots to illustrate variable-specific impacts on rainfall estimates.
3. I agree with Referee 1's comment. At present, I do not understand why it is necessary to manually label dry or wet data when reference rainfall data is available. However, if this manual labeling is similar to using a simple constant threshold to divide dry and wet data, the so-called reference classification results will inevitably have significant errors. Please explain this issue.
4. Why did this study choose information theory rather than other probabilistic methods? I believe it is necessary to add a comparative discussion in the introduction or methods section to emphasize why information theory is more suitable for this problem.
5. This paper does not explore interactions between predictors. For example, there may be dependencies between CML length and frequency, temperature, and weather type. I suggest including mutual information analysis of variable pairs to identify synergistic effects.
6. The binning strategy (e.g., for rainfall intensity, attenuation) is empirically selected but has not been rigorously tested. In particular, the last binning value exhibits a sudden change compared to the preceding values (see Tables 1 and 2). I recommend conducting a sensitivity analysis on other classification schemes (e.g., equal-frequency bins, dynamic bin widths). Additionally, the authors should rationalize the bin boundaries for high rainfall intensities (e.g., why 50–160 mm/hour is a single bin).
7. As the author mentioned, the ratio of dry period data to wet period data is approximately 97:3. I do not believe that the ROC curve is the best evaluation metric in such an unbalanced sample. Why not try the F1-score or the Matthews correlation coefficient (MCC)?
8. The author states that the rolling standard deviation (RSD) method proposed by Schleiss et al. is the state-of-the-art method for dry-wet classification. I disagree. The RSD method can be considered the most commonly used method, but it cannot be considered the state-of-the-art method. Recently, many machine learning methods have been applied to dry-wet classification, and they exhibit better performance than the RSD method.