Please find my comments in form of the uploaded supplement.

GENERAL REMARKS

The manuscript introduces a new method to investigate the movements of ice-supersaturated regions (ISSR) in the atmosphere. The authors use two months of data, April and May 2024, from the German Weather Service aviation weather forecast package (WAWFOR) to analyse the occurrence of ISSRs, determine their Centres of Probability (COP) and investigate the movement of the COPs in comparison to the horizontal winds. The analysis is based on a broad application of statistical methods. The two-months case study shows that the ISSRs move largely with the wind fields of embedding air, but with some slight differences.

The topic of the study is of broad interest for the research on contrail occurrence and evolution in the context of aviation climate impacts and fits very well into the scope of the journal. It is carefully designed and presents a new method for tackling this important question. Given the limited data set, the study is an excellent show case for this new method, but the manuscript draws general conclusions which appear to be too broad for this limited data set.

In that context few general questions arise which need to be answered before the manuscript is accepted for publication.

1. The authors should analyse carefully their results with respect to their general applicability, given the limited time span of two months for this analysis. To allow the reader’s own judgement, the investigated area needs to be visualized, e.g., by adding borders and coastlines to Fig. 1. Then, the general weather situation in April and May over this area needs to be described, including their representativeness for spring conditions in general. Once these facts are in place, the results presented can be put into context.
2. The consequences of the presented results need to be discussed in more depth. As one example, the authors present in Fig. 3, that the average speed of ISSRs is slightly lower than that of the wind field around the ISSRs. This finding would mean in consequence, that after a certain time the movements of the ISSR and of the embedding air are decoupled. Furthermore, the weak correlation of 0.28 between the ISSRs pseudo-velocities and the wind velocities indicates a decoupled movement, see Fig. 5. Is this case and if so, what are the consequences?
3. In the same, direction, Fig. 6 clearly shows that the cumulative distribution function of ISSR velocities reaches the 100% plateau value at a significantly lower velocity than the wind speeds. Wind direction and direction of ISSR movement are much closer aligned as is shown in Figs. 7 and 8. A discussion of the consequences of these findings for the movement of ISSR with respect to the embedding air masses would be very helpful.

SPECIFIC COMMENTS

1. On line 90, the authors state a limit of 500 grid points as a lower limit for an ISSR to be considered in their analysis. It would be useful to get an idea of the related size in km distance.
2. On line 93, the term PPC_i is used, please define this quantity.
3. Equation (8) introduces the covariance matrix Q which contains the information about the POC of the ISSR and the principal axes. Figure 2 shows respective results for an exemplary ISSR and the resulting principal axes. However, the position of the COP is understandable given the shape of the ISSR but the principal axes are counter-intuitive. A discussion on of the results is requested.
4. Line 190: The term “kurtosis” should be explained for non-specialists in the applied statistical methods.
5. Line 196: It should be stated at the first mention, that F_Vissr and F_Vwind describe the cumulative distribution functions.
6. Starting on line 252, the authors discuss the differences in velocities between ISSR and wind and use the analogy of a foehn cloud. However, a foehn cloud is triggered by an orographic feature causing lifting of the overflowing air. Since the orographic feature remains at a fixed position the foehn cloud will stay at the same place while the air is flowing through it. But what is the feature creating an ISSR and why should this feature remain at a fixed point? The explanation given here is not very clear and should be sharpened.

MINOR ISSUES

1. The abstract length needs to be reduced since the journal allows max. 250 words, but the current word count is 299.
2. Line 41-42: The use of the terms “material” for ice crystals and “immaterial” for ISSRs is difficult to understand. One possible alternative could be to simply write that cirrus and contrails consist of ice crystals moving with the wind, while ISSR is a thermodynamic feature which may move independent of the wind.
3. Line 62: It should be specified that PPC_prob describes a probability.
4. Line 84: Better use “analogue to” ?
5. Line 97: Better use “defined” instead of “identified” ?
6. Line 118/119: It should be mentioned that u_ISSRand v_ISSRare the cartesian components of the horizontal wind vector.
7. Line 252: The term “material system” for air might be replaced by “… by shifts and rotations of the carrier fluid air …” .
8. Line 271: The term “However”, might be replaced by “On the contrary”.
9. Line 284/285: The abbreviation aCCF should be introduced.