Dear authors,

Following the interactive discussion and the detailed answers to reviewers that you have delivered, the article is now again with reviewers. Sincerely yours,
Michel Crucifix.

Dear authors,

The two referees that read the original version of your manuscript now recommend publication, essentially in its present form. I am of course willing to follow their recommendation, but upon careful reading of the revised manuscript some clarifications are still requested, and I would like also you to consider some more editorial rearrangements.

It might help if I briefly introduce myself as a physicist, with experience in climate physics and modelling with dynamical systems. Some of my recent contributions involve model calibration and selection with Bayesian statistics. I am mainly writing this to help you to understand where the comments come from, bearing in mind that my profile is not atypical for an ESD reader.


A. ON THE STATS
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1. The scientific methodology follows Mayo's account of severe testing. D. Mayo is a philosopher, and perhaps fortunately no philosophical statement is ever perceived as definitive nor uncontroversial. There are certainly zones of frictions between Mayo's discourse and a number of statisticians and this is how ideas evolve, which is perfectly fine. For sure, inference in presence of model discrepancy ("all models are wrong") represents a hard philosophical challenge, one which has no obvious solution. Expressing oneself clearly is part of the challenge. In fact, much of the work done in this article can be justified in fairly simple terms: we challenge competing models as much as we can, with constant concern for the physical meaning of what we are doing. You might want to work harder to track sentences that may appear unnecessarily obscure. E.g.:

- p. 3, l. 28: " It is applied to the substantive null of model adequacy approach described " -> what is the substantive null of model adequacy ?

- The aim of severe testing is to produce highly probed ... : what is "highly probed" ?


2. p. 6, it is written that "the null hypothesis for H2 is H1". Is that clear that H2 U H2 form the set of all possibilities (which is what is implied by this sentence). How would a quadratic trend stand with respect to both ?

B. ON THE PHYSICS
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3. The points 1,2,3 p. 5 are unsatisfactory. The attempt to explain the existence of steps here as a combination between in situ warming and ocean absorption is awkward. The manuscript would be improved by simply acknowledging that there is a physical possibility of step change. In fact, the 3 paragraphs may simply be withdrawn.


4. I can't adhere to the distinction between statistical and physical linearity, which you introduced in response to previous referees comments. Non-linearity does not imply step changes (in fact, strange attractors may respond smoothly to changes in boundary conditions or forcing, and this is the fundamental assumption of linear response theory applied to complex systems, see, e.g., by Lucarini). Use 'smooth' if this is what you mean (or 'continuous' / 'gradual') and don't substitute 'linear' to these concepts.

5. p. 21: the reference to entropy production is, I would say, pretty brave. It is not immediately clear that increased GHG generate increased entropy production. There are also many sources of entropy production on the Earth system and not all are relevant to the dynamics of atmosphere-ocean fluctuations. These statements, without proper framework and citation, might end up being judged as vacuous sophisticated statements, and they may be in the end be detrimental to the manuscript.


C. Other comments:

p. 6 : the text about the 6 tests need to be rewritten in terms of simple sentences, presenting clearly the hypothesis to be tested. Using questions (with question marks) is one option. The semi-telegraphic used here does not suit.

p. 7 : Introduce a section 2.3.1 just after section header.

p. 7, l. 4 : Change "Paraphrasing Mayo and Spanos (2010) to address the results: with very high probability, Tests 1–6 would have produced a result that accords less well with H2/H1 than does H1/H2, if H2/H1 were false or incorrect" -> into "Paraphrasing Mayo and Spanos (2010) to address the results: with very high probability, Tests 1–6 would have produced a result that accords less well with H2 than does H1, if H2 were false or incorrect (and conversely)".

- The LOWESS model is introduced without definition. It will not be obvious to everyone what it is.

- Three times in the manuscript (p. 12, 18 and 32) it is written that internal trends are given 'preference' to shifts. The background to this affirmation is too implicit. I understand that we only accept shifts if we can reject trends. If this is indeed what is meant to be said it should be more explicit.

- The discussion is pretty unusual. The standard practice is to use the discussion section to focus on critical aspects of the methodology and open outlooks for further investigations. Here the discussion has the air of an essay, mixing considerations on climate macro-physics ("homeostatic effect of ocean", "In situ warming is hardly plausible if the atmosphere has no intrinsic heat memory.") with philosophy of sciences ("Most, if not all assessments take up the basic assumptions of those simpler models, forming a consensus mental picture that operates as the dominant paradigm of how climate changes".).
Admittedly, the text is at places much to the point and it conveys a number of relevant ideas. However much care is needed before formulating judgements that may be interpreted as an outsider's opinion about a broad community. Indeed, the stance is at places patronizing "The assumption that the processes involved are timescale invariant indicate that the meaning of seamless has not really been thought through" : thought trough by who ? While I agree that more is to be done about teaching dynamical system concepts in Earth sciences master degrees, we also ought to be fair to a good number of investigators, present on climate science subjects, and who can apprehend many subtleties of non-autonomous, non-linear dynamical systems theory.

In summary, you definitely have the right to express some more informal, though-provoking considerations within of a research article, but I still believe there is considerable scope to shorten and focus the discussion. The manuscript might end up gaining impact in the end.

Thank you for your contribution to ESD, it is my please to confirm acceptance of your article.