In this study, the authors deal with the lapse rate in differently humid air masses (subsaturated, supersaturated, big hit) along the flight paths of passenger aircraft. IAGOS measurement data as well as reanalysis data (ERA5) and forecast data (ICON-EU) are used. It is shown that in humid air masses the temperature decrease with altitude is stronger than for dry air masses. 

Overall this manuscript present very interesting results. It fits very well within the scope of ACP. However, some points have not become entirely clear to me. In addition, some aspects should be formulated more precisely. Therefore, I would like to recommend this manuscript for publication with major corrections.

Specific questions and comments:

1. For me it is not clear, why you need the IAGOS data set for this investigation. I understand that comparing measurements with model data is helpful. However, such a statistic could also have been produced without the flight paths from IAGOS. Perhaps you could motivate the use of the IAGOS data more precisely in the text. How is the IAGOS data connected to the case study? Are there measurements available for this event?
2. The exact calculation of the lapse rate, which is included in the statistics, could be explained in more detail. Is the lapse rate calculated from three model levels („lapse rate was calculated from ERA-5 temperature values on the neighboring pressure levels and from these pressure values“ P5L121) or only from two levels („…without further information, it is justified to assume a constant temperature gradient (or lapse rate) between these two levels.“, P5L128)? 
3. In my view, using the lapse rate it is not intuitive to see what is meant by a „large lapse rate“. I would rather use "unstable", "neutral", "stable" for the lapse rate. This brings me to the next point
4. Maybe it is more convenient to use the gradient of the potential temperature, which you also mention in the beginning of 2.4 as a different expression for the stability. This makes it easier to interpret the results, from my perspective. If you want to stay with the temperature gradient, can you motivate this in more detail?
5. By using IAGOS flight paths you most likely have a significant amount of data points within the lowermost stratosphere. How does this influence your results? How many of your data points are above the tropopause? Could there be a contribution to the pdf peak around 0 K/km for the ice subsaturation?
6. Since "big hit" is a rather new term, a brief explanation would be helpful for the reader. In Wilhelm et al. (2021) this term does not occur. How were "big hit" cases defined in this study? This simplifies the reproducibility of the study
7. Regarding the contour figures: please, use the same vertical axis for plotting the ICON-EU and ERA5 results. It is very hard to compare the images side by side with slightly shifted axes. For some figures you show only values above approx. 400 hPa, for other figures you show the whole troposphere. Maybe focus on 500 hPa upwards?
8. Section 4.2: This section seems somewhat speculative to me.
   
   When there is an additional contribution to the lapse rate increase by radiation, why do have all curves their (local) maximum at around the same lapse rate in Fig. 1? Isn’t that contradicting the statement, that the second maximum of the sub saturated pdf is due to the fact, that the air is just too dry? So my question is, why the maxima of all curves overlap. Shouldn't the „big hit“ curve then have the highest lapse rate because the radiative effect is strongest, followed by the supersaturated and then subsaturated curve?
   
   Perhaps a little more light could be shed on the matter by carrying out simple radiation calculations for one exemplary profile per class (subsaturated, supersaturated, big hit), see e.g Fig. 11 of Fusina & Spichtinger, 2010. (Fusina, F. and Spichtinger, P.: Cirrus clouds triggered by radiation, a multiscale phenomenon, Atmos. Chem. Phys., 10, 5179–5190, https://doi.org/10.5194/acp-10-5179-2010, 2010.)

Minor:

1. Please indicate, which ice microphysics is used in ICON-EU
2. P7L168:  „quite a large ISSR“ - maybe a bit more precise, since, as you mentioned, there are also patches of subsaturated air.
3. P8L171 Please discuss here briefly, why ICON-EU shows lower saturation values than ERA5. What is the difference between the two models which could explain this behavior? 
4. P9L192 The feature in 800 hPa is not of interest for this topic, maybe show results only above 500-400 hPa (see my point 7)
5. Is Fig 5 necessary? Maybe include certain temperature isolines into Fig. 3 or 4?
6. Figure 5/6/7: why so many red points (ice supersaturation) in lower regions for ICON-EU compared to ERA5? Additionally, the stippling is not mentioned in the figure caption of Fig 5 and Fig 7. 

Typos

1. P1L24 „and and how long…“
2. P2L33 line break
3. P2L42 remove „even“ ?!
4. P4L98 line break

The study analyses the correlation between larger atmospheric lapse rates and the presence of supersaturation and thin cirrus clouds. It proposes that uplift and adiabatic cooling of an air mass would not result in such high observed lapse rates and suggests that atmospheric radiation effects must be a contributing factor, further enhanced by the presence of ice crystals, given their larger interaction with radiation. One strength of the study’s approach is the combination of in situ and reanalysis and model data, although it is not clear from the manuscript how were the “big hit” cases defined and determined. I would recommend the article’s publication after this aspect is addressed.

Some other suggestions may help the reader understand the methodology and the interpretation of the results:

1. It is clearly stated in the manuscript that the highest lapse rates were found in Big Hit regions, but it is not clear how are these regions identified from the IAGOS data. In other words, is the presence of ice crystals identified and if so, how are natural cirrus and contrails discriminated? This would also help clarifying the sentence in ln 8, which mentions the interaction between high ISS in Big Hit regions and radiation only, leaving out the interaction with ice crystals.
2. Following up on the previous comment, it would be helpful to explain how are the blue and the black lines in Fig. 1 determined in practice from the IAGOS database. From the manuscript it is not possible to understand how this was done. And one of the main outcomes of the study relies on this discrimination.
3. It is not clear from the manuscript why without radiative interaction the results cannot have a physical explanation. A back of the envelope calculation to exemplify this would help the reader understand the need of the radiation hypothesis.

Minor comments:

1. Ln 24, repeated “and”.
2. Ln 154 delete “the”
3. 7 legend, delete “zonal”
4. Ln 291 “distribution” instead of “distributions”