Summary

This paper engages with an important and genuinely underexplored problem: how to rigorously assess the risk that a proposed aviation climate mitigation measure will fail to deliver a net climate benefit, given the substantial uncertainties in aviation climate metrics. The motivation for critically examining Prather et al. (2025) (hereafter PGP) is reasonable, that paper does leave a number of methodological questions open. Unfortunately, the present manuscript does not succeed in either of the two goals it appears to pursue: it neither constitutes a sufficiently focused or complete critique of PGP, nor does it develop an alternative framework that is demonstrably more sound. For these reasons, and as elaborated below, I do not think the manuscript is suitable for publication in its current form. I do not believe these issues can be resolved through revision without what would amount to a substantially new paper, and I therefore recommend rejection, while encouraging the author to consider the paths forward suggested at the end of this review.

Major Comments

1. Unclear scope and contribution

The most fundamental problem with this manuscript is that it pursues two distinct goals simultaneously, a critique of PGP and the presentation of an alternative framework, without fully achieving either. This ambiguity undermines the paper throughout. A focused critical response to PGP, limited to identifying specific mathematical or conceptual errors, would more naturally take the form of a correspondence or comment submitted to Nature, where PGP was published. The present venue and format imply that the paper is making a positive contribution beyond critique, but the alternative framework presented here is not developed to a standard that would justify publication on its own terms. The author should decide which goal is primary and restructure accordingly. As it stands, the two goals pull against each other: the critique sections are sometimes too detailed for a paper primarily presenting new methodology, while the alternative framework is not developed rigorously enough to stand as an independent contribution.

2. The most important weakness of PGP is not addressed

The paper raises several legitimate concerns about PGP's mathematical presentation, but conspicuously omits what is arguably the most fundamental weakness of that paper and of the present one: the premise that a GWP-like metric provides a reliable basis for determining whether a mitigation action delivers a genuine climate benefit. GWP and GWA are time-horizon-dependent, globally and temporally averaged quantities that aggregate very different physical processes into a single number. The scientific literature contains extensive debate about whether such metrics are appropriate for decision-making, particularly when comparing long-lived forcing agents like CO₂ with short-lived ones like contrail-induced cirrus, see for example Shine et al. (2005, Climatic Change, 68, 281–302), who proposed alternatives to GWP precisely because of its limitations in comparing gases with very different atmospheric lifetimes, and Shine (2009, Climatic Change, 96, 467–472), who argued explicitly for a fundamental reappraisal of GWP as a policy metric. Fuglestvedt et al. (2010) provide a thorough overview of the metric landscape in the transport context, and Lee et al. (2021, 2023) discuss at length the difficulties of applying such metrics to aviation non-CO₂ effects specifically. By accepting the GWA framework as a valid foundation and confining the critique to mathematical implementation, this paper implicitly endorses a premise that deserves much more scrutiny. A paper positioning itself as a rigorous examination of PGP's methodology should engage seriously with this deeper issue.

3. The assumption that ERF changes are free of uncertainty is not justified

The central methodological claim of the alternative framework is that the right-hand side of the risk inequality, the ratio of ERF changes due to a mitigation measure, can be treated as a known, certain quantity because it is determined by a concrete operational or technical decision (lines 200–202). This assumption is very difficult to justify in practice and the paper does not seriously defend it. ERF changes are not directly controlled by operators; they are emergent outcomes of operational decisions mediated by complex atmospheric and microphysical processes. The change in contrail ERF resulting from a rerouting decision, for example, depends on ambient humidity, temperature, aircraft type, contrail microphysics, and radiative conditions — all of which carry substantial uncertainty. Further, ERF varies over the lifetime of a contrail, suggesting that even absent uncertainty, there wouldn’t be a one-to-one mapping between a re-routing decision and an ERF change, although this issue could be avoided by instead considering something like lifetime-integrated ERF. Treating ΔERFs as essentially known while locating all relevant uncertainty in the impulse response function parameters is not a physically motivated choice. It is an assumption made for mathematical convenience, and one that is arguably less realistic than PGP's treatment.

4. The contrail lifetime argument exposes an internal inconsistency

This issue is made concrete by examining what the left-hand side of equation (17) actually contains. The author claims that the relevant uncertainties reside in the parameters of the impulse response functions K_C(H), specifically the atmospheric lifetimes and decay timescales. For CO₂ this is reasonable; the multi-timescale decay of atmospheric CO₂ perturbations is a genuine and well-studied source of uncertainty. For contrail-induced cirrus, the impulse response function does include a lifetime parameter, and there is some genuine uncertainty in mean contrail lifetime. However, contrail lifetime is short enough (hours to at most a few days) that the integral K_CiC(H) is relatively insensitive to the precise value of that lifetime for any climatologically relevant time horizon H, the uncertainty in K_CiC(H) is small compared to the overall uncertainty in contrail climate forcing. This means that while the left-hand side of equation (17) carries some contrail-related uncertainty, it captures only a narrow slice of the total uncertainty associated with contrail forcing. The much larger sources of contrail climate uncertainty, including radiative properties, coverage, microphysics, and the relationship between operational decisions and actual contrail ERF, are not parameters of the impulse response function and therefore do not appear on the left-hand side at all. They must instead reside on the right-hand side, precisely where this paper claims everything is known. This is not a minor technical quibble; it is a structural problem that undermines the paper's central claim about where the relevant uncertainties lie.

5. The conclusion undermines the case for publication

The author states in the conclusions that "the method is not mature enough to base practical decisions on" and that "the stochastic model for the uncertainties is close to arbitrary." While this intellectual honesty is appreciated, it raises a question the paper does not adequately answer: what is the positive contribution being made? If the proposed framework is acknowledged to be immature and not actionable, and if its mathematical relationship to PGP is closer than claimed, then the manuscript needs to articulate much more clearly what a reader should take away from it. Scientific papers presenting methodological frameworks that are not yet fit for use need to make a compelling case for why the framework is nonetheless a meaningful step forward. That case is not made here.

Minor Comments

• Section 2.1 (exchange rate vs. trade-off ratio): The conceptual distinction drawn here is interesting and potentially valuable, but it is developed at greater length than its ultimate role in the paper justifies. If the paper were reframed as a pure conceptual/theoretical contribution, this section could anchor it more effectively.
• Section 3.4 (equilibrium temperature change example): This section is one of the more self-contained and readable parts of the paper. The finding that the result is good for climate as soon as the contrail ERF reduction exceeds approximately 2.63 times the CO₂ ERF increase (under the best-estimate sensitivity factors) is useful and concrete. However, the subsequent risk analysis here suffers from the same problems identified in Major Comment 4. The uncertainty in λ_ERF for contrails is very large relative to that for CO₂ precisely because contrail forcing is so uncertain, which again suggests the real uncertainty is not where the framework places it.
• Section 4.3: The demonstration that NOₓ emissions must be included in the trade-off calculation for contrail avoidance is a valid and useful point. This would be worth preserving in any future revised work.
• The suggestion in the conclusion that ensemble weather forecast methods (Borella et al., 2026; Hanst et al., 2025) represent a more promising direction is well-taken, but feels somewhat tangential to the rest of the paper. If this is the author's preferred path forward, it might be worth a separate short perspective piece rather than a brief mention at the end of a paper focused on a different methodology.

Recommendation and Paths Forward

For the reasons outlined above, I recommend rejection of the manuscript in its current form. The issues identified are not, in my view, resolvable through revision without producing what would effectively be a new paper. I want to be clear that this recommendation reflects the mismatch between the paper's scope and its execution, not a judgment that the underlying questions are unimportant. Indeed, they are important, and the aviation climate community would benefit from rigorous work on them.

I would suggest the author consider two potential paths forward. First, the specific mathematical criticisms of PGP, particularly the point about uncertain quantities appearing on both sides of the risk inequality, could be developed into a focused comment or correspondence submitted to Nature. This way the comment would reach the audience most directly engaged with PGP. Second, if the goal is to develop a genuinely alternative framework, the author should begin from a more critical examination of whether GWP-like metrics are an appropriate foundation at all, resolve the ERF uncertainty problem identified above, and ensure that the uncertainty structure of the proposed framework reflects the actual physical sources of uncertainty in aviation climate science rather than mathematical convenience. That would be a substantial and valuable contribution.

Aviation has much discussed effects on climate through its CO2 and non-CO2 emissions. The non-CO2 effects have inherently much larger uncertainties than the CO2 effects (in terms of effective radiative forcing, ERF). Mitigation measures tend to focus on technology, operations, and fuels, and often have so-called ‘tradeoffs’, where the non-CO2 effects may be reduced at the expense of an increase in CO2 effect. Prather et al address this. The present paper is a critique of the Prather et al approach, and as such is an important contribution. However, the present draft has some shortcomings which could be successfully addressed.

This is an important paper in the debate over operational mitigation approaches for aviation. Thus, some extra effort bringing some clarity, particularly to the style of presentation is worthwhile.

Abstract

The tone is quite critical of the original work and could be phased more equitably and factually. For example, “…leaves, to this author’s opinion, many issues open for discussion” could be “ leaves some issues open for discussion’ – indeed the original authors (Prather et al; hereafter PGP25) highlighted this. “Vague” could be “less clear”. The sentence “Unfortunately…” could be “The method proposed by PGP25 may have some shortcomings that are addressed with derivations presented here” (omit the next sentence). Remove “unfounded” “…suffer from a degree of arbitrariness” could be “..are highly dependent on the assumptions made, some of which are subjective or ‘user choices’” The last sentence needs to be put in context of what the present paper found in a more positive way (rather than the abstract reading as a list of criticisms of PGP25). At the moment, the last sentence is uninterpretable. Indeed, what this relates to is a rather passing comment at the end of the paper, which seems incomplete.

The abstract is currently letting a good paper down significantly and needs a complete re-think and re-write. Instead of focusing on the PGP25 problems and rather critical statements, the author should focus on some of the significant findings and interpretation that are present in the discussion.

Introduction

L10, the referencing is extensive but the outline non-specific. It would be helpful so say something like “a number of mitigation strategies have been proposed that require developments in technology, operations, and fuel type”.

L14 refers to tradeoffs, but is non-explicit. Many mitigation strategies do indeed imply compromises or tradeoffs, but the main problem lies in tradeoffs between short-lived climate forcers and CO2. This is the nub of the problem. There are other SLCF-SLCF tradeoffs but these are usually technological and of lesser consequence. It would be helpful to the reader to get to the core of the problem that is being addressed by PGP25 and the present paper. L15-21 identify the problem but not the critical issue (SLCF vs CO2) but omits to mention that the outcome of ‘positive for climate’ is potentially one that could even change sign over time.

L27 introduces the PGP25 metric but does not illuminate. Is it an AGWP per activity? In which case it is worthwhile to explain what the “Global Warming” is, since AGWP itself is a misnomer – it is simply an integrated RF over a user-chosen time horizon.

L32 “ad hoc, without derivation” is overly harsh. Please rephrase. Similarly, for the next two sentences, “not convincingly justified”, “vague” could be rephrased.

Critical review of the method of PGP

L41 I find the critique of PGP25 here entirely justified and the PGP25 sentence quoted rather muddles the history and usage of CO2 equivalence metrics. A tradeoff is an extension of the original intended usage of GWPs, as an exchange rate mechanism but has rather different implications. L:48 Example 1 is rather strange, going to the length of equating an individual source of CH4, and is not really illustrating successfully the equivalence/exchange rate mechanism originally intended. As originally conceived, GWP is a reporting convenience that recognizes different GHGs (and balances of a country, or sector) that by necessity requires an exchange rate mechanism, since the end effect of releasing (e.g.) 1 kg of CH4 is not the same as 1 kg of CO2. Also, by necessity, a time horizon (TH) needs to be specified, a compromise and subjective user choice that has been extensively debated in the literature since the concept of GWP was introduced in the late 1980s. Example 2 is correct, but seems unnecessarily off topic, and could be restated as the SLCF vs CO2 tradeoff, which has already been stated for NOx/fuel (and thus CO2), earlier. Example 3, is more to the point but identical in principle to Example 2.

L60, this is an oversimplification in that it omits the aspect of TH. TH has the potential to change the ‘outcome’, and should at least be acknowledged here.

It should also be noted that three are, as PGP25 noted, other CO2 equivalence metrics, notably the Global Temperature change Potential (GTP, Shine et al., 2005) and an alternative derivation of the GWP, the GWP* (Allen et al., 2015). These at least need to be mentioned as context somewhere (not necessarily in detail), earlier in the introduction of the concept and usage of CO2 equivalence emissions.

L67 “impossible”, at this point in the reading of the m/s, I would judge this to be incorrect (although the reader is directed forwards). Surely, the risk-analysis method will contain intrinsic uncertainties, and required some degree of user discretion and caution, but “impossible”?

2.2 Tradeoff risk

L78 – 80. This is a poor characterization of a particular GWP, in this case CH4. It is not a “best guess”, it is the best estimate of a ratio of an integrated RF from a pulse emission of CH4 divided by the same mass pulse emission of CO2. Both nominator and denominator have uncertainties, and the calculation will have assumptions of, e.g. background CO2 concentrations and TH selected. Dismissing it as a “best guess” is incorrect. The last part of L80 is correct in that the intrinsic uncertainties will make the decisions uncertain (in the sense of the efficacy of those decisions).

L98 “..if the GWA ratio is large…” I do not understand this. Surely, the success of the outcome is not simply dependent on the size of the ratio but the size of the uncertainties, particularly, in the nominator?

Finally, I note the PGP have themselves provided comments which are generally very helpful and I would recommend that the author consider these comments.

L156, for clarity and accuracy, please refer to CO2 equivalent emission metrics, not ‘climate metrics’ (see IPCC 1r6 glossary for what a ‘climate metric’ is generally agreed to be).

L213 I don’t understand this assertion. Yes, it is the ‘deltas’ that matter, but to some degree these will be dependent on the size of the absolutes, surely? For example, if the global ERF of contrail cirrus were 5 mW/m2, rather than 50 mW/m2, then that would affect the decision as to whether a mitigation measure was worthwhile. Hence, at this point, I disagree with the assertion and agree with that of PGP25 on “pressing need”.

L350 Bickel et al. (2025) are quite clear that an ERF for a single flight cannot be computed from a global computation, nor a local climate sensitivity parameter.

L364-367. Absolutely. This is the core finding. This has been potentially misrepresented or misunderstood by Voigt companion commentary to the PGP25 paper.

L404 Commendable – a widely ignored point. In general, there is a likelihood that an upwards vertical displacement for the purposes of avoidance will increase aviation induced ozone, and vice versa. Again, but for different reasons, the ERF of an individual flight is virtually impossible to compute robustly with chemistry-climate model. Similarly, the direct forcing of water vapour may operate similarly for altitudinal shifts.

L441 – L444. While agreeing completely, the author has not at any point dug into the practical difficulties that ERFs are only correctly computed with GCMs. Global integrations of plume calculations to derive a global RF, which is then corrected to an independent ERF/RF ratio are (as pointed out here and by Bickel et al. 2025) not valid. Avoidance calculations are carried out with plume calculations, at present, with mostly the single CoCIP model. The RF change of a flight is therefore not necessarily consistent with the global ERF (actually two different metrics), and an ERF of a single flight with a plume model without a coupled water vapour/energy budget, using a globalized adjustment is invalid.

L472 “hardly” could be replaces with “not” on the basis of the arguments presented.

L479 – L486 I understand what the author is alluding to, but I think that this is confusing issues. Presumably “weather forecasts” refers to accurate prediction of ice-supersaturation (for the formation of the individual persistent contrail in itself). PGP25’s work, seems to assume perfect prediction of contrail formation and persistence and deals with the tradeoffs of delta ERFs. I think that this point would be better dropped into the argument earlier, when summarizing the assumptions of the PGP25 work, rather than alluding to alternative methods later.

Final comments

I think in revising the paper, a better summary of what PGP25 are saying could be provided (see their comments on the present paper), rather than the sole focus on the mathematics of their risk calculations. They do indeed outline reservations over the usefulness and make some recommendations. Unfortunately, Nature-stable publications like “headlines” and the well-intentioned caveats of authors can get lost.

Style – the paper is extensively written in the first person, e.g. “to my feeling” L426, “To my view” L479, which I think is better phrased more passively voiced