Dear editor and authors, please find attached my review comments. I look forward to reading the revised manuscript!

This study uses 10 years of ERA5 data, along with existing thermodynamic theory on contrail formation and persistence, to investigate the probability of persistent contrail formation for different aircraft/engine designs and the factors that constrain it. Additionally, relationships between the mixing line slope (part of the thermodynamic theory of contrail formation) and persistent contrail formation probability are derived using the study’s data, which are highly relevant to the assessment of novel technologies in the context of aviation’s climate impact.

The paper is quite well-written, and the visualizations are mostly excellent. The methodology is sound. I feel like some of the findings (e.g. ice supersaturation is the most limiting factor, but less so for technologies with steeper mixing lines) could have been approximated through physical reasoning and already available climatologies on temperature and humidity. The study’s results are still highly valuable, but I would have liked to see some hypotheses / comparisons based on less refined analyses to better appreciate the merits of the approach taken here.

In my opinion, the most valuable results of the paper are the “simple” relationships derived for the probability of potential persistent contrail formation as a function of the mixing line slope. I expect these to be incredibly useful within a tool such as AirClim, in order to assess the impact of changes to aircraft fleets.

Overall, the study is within the scope of the journal, presents novel findings, and is well-written. I therefore recommend its acceptance subject to addressing my comments below.

Major comments

• Given that the results of this study are likely going to be used in climate impact assessments, I would appreciate more comparisons of the obtained results to observations or other studies. For example, how do the numbers in Figure 3 compare to observations from e.g. IAGOS? Does the occurrence of ice supersaturation found in ERA5 (potentially limited to an appropriate geographical region) match that found by IAGOS?
• There are several discussions in the paper regarding the way in which persistent contrail formation regions change due to modifying certain parameters. See for example the paragraph starting at L327. A figure (or two) illustrating such a situation would really help the reader, and also serve as a test for the hypotheses formed here and there.

General comments

Did the authors experiment with visualizing persistent contrail formation regions as the intersection of 3 different regions (each satisfying one of the individual constraints)? Perhaps this could be a nice plot to add to figure 2.

The abbreviation “limfac” is used in many figures, but I do not believe it is defined anywhere.

Many occasions where citations are not in chronological order: these should be re-ordered.

Many occasions where a “the”  is missing before “horizontal direction” or “vertical direction”. I’ve included some of those in my line-by-line comments below, but at some points I stopped marking them.

Line-by-line comments

L18: Would replace “no effect” with “little effect”

L20: should this be “resulting aircraft-induced cloudiness”?

L21: effective radiative forcing (so first letters not capitalized). Same goes for the abstract.

L23:  isn’t “alternative fuels” descriptive enough?

L25: “contrails can form”

L26: “ice nuclei” if the water vapour condensed on these particles, doesn’t that make them cloud condensation nuclei and not necessarily ice nuclei?

L36: “Contrails slowly sink”. This is not necessarily true, I believe. There are processes that can lead to contrails moving upward, such as radiative heating.

L36: “and often mixing with natural cirrus”. Could you provide a reference for this statement?

L37: “trap outgoing longwave radiation”. It is more physically correct to state “reduce outgoing longwave radiation”, I believe.

L39: Not clear whether the warming effect dominates because of many night-time contrails or because day-time contrails are more warming than cooling, or a combination of both.

L41: “over-proportional” should not be hyphenated I believe. I also think the wording could be better, perhaps by simply stating the results from the cited studies (e.g. x% of flights contribute y% of the total contrail radiative forcing…)

L45: there are other studies that could be cited here, such as Agarwal et al. (2022) and Geraedts et al. (2024)

L47: should “the persistent contrail formation” be “persistent contrail formation” ?

L48: what is “individual avoidance”?

L51: “vertical” and “zonal” might be better terms to use here?

L58: This section is somewhat at odds with an earlier section which states “However, due to the large variability in the properties and concentration of the ambient aerosols (e.g. Brock et al., 2021; Voigt et al., 2022), the resulting ice crystal number and radiative effect of the subsequent contrails are currently highly uncertain.”

L82: “hybrid electric” this is hyphenated in most other places in the manuscript

L96: is this sentence missing a “are described”?

L99: The introduction actually states that this is due to expansion of the exhaust plume, which is not necessarily the same as isobaric mixing I believe.

L100: How is this “thermodynamic approximation” if you describe the mixing process as isobaric?

Equation 1: Shouldn’t CON (used in the text) and H2O be non-italic?

Equation 3: Symbol “h” not introduced.

L121: bar on c_p is not placed appropriately.

L123: “define it to be”

L129: “written as”

L130: “is tangent to” would be a more exact description, I think

Equation 5: Units here are written using italics whereas that is not the case in the main text.

L151: “to limit required computational resources” ?

L153: “last” or “latest” ? Or “previous” ?

L160: What are the implications of ignoring liquid droplets in the plume?

Table 1: Abbreviation “JA1” not introduced

Table 1: Why not just state some of the Q values as MJ/kg?

Table 1: G missing units.

L189: “We use numpy.random.choice” Without replacement I presume?

L201: What are “further ERA5 variables”? Perhaps better to say “variables other than the relative humidity” ?

L236: “in the horizontal direction” ?

Figure 2: What is “limfac edge” in the colormap label?

L259: “Saved to file” can just be “saved” right?

L299: “acts like” these are different physical processes, right? Perhaps different wording might be more appropriate?

L311: “in the horizontal direction”?

L312: “conducive to persistent contrail formation” Shouldn’t this be “for all ambient conditions satisfying persistence and droplet freezing”?

L321: “in the vertical direction”

L330: Are there any examples of this happening?

L351: “conservatively regrid” What does this mean?

L363: Why the number of varying significant digits reported?

L368: Why the negative latitudes if you already specify that they are on the Southern hemisphere?

Figure 6: I suggest using different colors for the lines here as one might confuse the fact that they represent different pressure levels with differing aircraft designs. Perhaps use colors from a sequential colormap? Also, no need to have “.0” behind all the pressure levels in the legend.

Table 3: I suggest to use italics for the symbols.

L456: This sentence is quite hard to read, consider splitting it up.

L473: “towards to poles” should be “towards the poles” ?