The manuscript by Sperber and Gierens, 2023 introduces a new cirrus parameterization that avoids saturation adjustment and can be implemented in models using one-moment microphysical schemes. The scheme adds an additional prognostic variable describing the in-cloud humidity to the reference model using the saturation adjustment assumption. The authors describe and compare the results of their scheme with the benchmark stochastic model and the reference saturation-adjusted cloud model, demonstrating the advantage of their parameterization.

This is a valuable study that could potentially in the long-term lead to improvements in coarse-resolution models using simple, 1-moment microphysical schemes and the saturation adjustment assumption. Such simplified representations of cirrus are common in current weather prediction models. Overall, it is a very nice parameterization development study that has some potential for improving ice supersaturation forecasts. However, I have a number of questions that should be addressed before the study can be published in its final form.

General comments:

1. The conditions where the new parameterization improves the modeled moisture fields the most (slow, constant updraft) are most likely to be associated with heterogeneous freezing at lower supersaturations. If this is the case, and nucleation occurs at lower supersaturations, the advantage of your scheme would probably be smaller compared to the cases presented. Also, even if your scheme removes one of the biases, bias due to the lack of heterogeneous ice nucleation may persist.
   
   I am wondering which of the two biases could have larger implications on the simulated supersaturation fields, particularly in the context of a weather model. Please, discuss!
   
   
   
   Also, I think it might be worthwhile to add an additional sensitivity test assuming an idealized type of heterogeneous ice nucleation. This test might give some more clues about the importance of the new parameterization.
   
   Indeed, I know that weather models typically don't have either interactive or prescribed aerosol fields that could modify cirrus formation. However, prescribing an aerosol or ice nucleating particle climatology would be a fairly straightforward task.

1. How realistic is the assumption of a constant updraft for periods longer than 12 hours? Does this really occur in the real atmosphere? How well are such processes simulated by weather models?
2. A number of studies point to the importance of rapid temperature/updraft variations in the formation of cirrus, particularly in the context of homogeneous freezing. The manuscript mentions the inclusion of such variability in the scheme. However, I didn't understand how such fluctuations are included in the new scheme. Could you explain this better? What if the variability were larger/smaller?
3. I believe the authors hate to provide a data availability statement, as per https://www.atmospheric-chemistry-and-physics.net/policies/data_policy.html

Specific comments:

Page 1, abstract: I’m missing a sentence on the conditions in which the new scheme is improving humidity most compared to saturation adjustment

Page 2, first paragraph: I like the sharp focus on contrails. However, from the climatic point of view, the scheme would have likely a much larger impact on natural cirrus coverage and their radiative effects.

Page 5, equation 10: Why is the assumption of a hyperbolic supersaturation? Where does this come from?

Page 6: Why can’t growing ice crystals decrease the relative humidity to 100%?

Section 2.2: please note that I did not go through the equations, but I just tried to qualitatively understand the concept of the new scheme. An illustration/schematic could help to effectively convey the key concept of the new scheme.

Section 3: Visualizing the updrafts considered in the considered cases would improve the clarity of the results, particularly for the cosine-like cases.

Figure 4 and 8: based on the caption I expect an increase in updraft from 2 to 5 cm/s. Please, just plot the updraft.

Page 18, lines 364-370: Would be great to see that in a separate sensitivity test and a new figure.

Page 19, lines 404-405: language, please rewrite the sentence. Saturation adjustment => parameterization using saturation adjustment (or similar)

Page 19, line 408: “keeps getting restored” => is that true? I guess it’s simply continuous?

Page 19, line 426-427: suggestion “…a significant improvement compared with a saturation adjustment scheme…”

see attached report