Dear Dr. Avakumović,

Since both reviewers found that the manuscript contained potentially valuable ideas and results, and in light of your thorough replies, I invite you to revise your manuscript for reconsideration by both reviewers. I agree with reviewer 2's suggestion that section 4 of your manuscript is worth expanding on in your revisions, and am happy with the fit of this manuscript with Earth System Dynamics' scope, especially since the focus is on the climate modeling tool, and not the potential economic application. I look forward to reading your revised submission.

Best regards,
Dan Kirk-Davidoff

Dear Dr. Avakumović,

I thank you for your extensive revisions in response to the reviewers comments, and thank the reviewers for their careful reading and advise. In considering the first reviewer's comments about the clarifying the central point of your paper, it seems to me that your main point corresponds to this reviewer's second option, with some shading towards the third option: demonstrating the usefulness of the Green's Function approach to diagnosing the origin of deviations from a constant TCRE. I agree that the paper could be easier to follow if this point were consistently emphasized. In particular, I'm not sure that the one-box model is crucial to the central arguments of the paper, and would suggest that you consider dropping it, or else using to introduce the Green's function approach and demonstrate the effect of structural model uncertainty, and then putting it aside in the discussion of scenario and state-depedency.
I encourage you to revise the paper once more in light of both reviewers' comments, and look forward to reading the revised manuscritpt.

Best regards,
Dan Kirk-Davidoff

Dear Dr. Avakumović,

Thanks for your careful revisions of your manuscript. I am now pleased to recommend it for publication in ESD, subject to a several clarifying technical corrections recommended by the second reviewer (who worked generoulsy and assiduously to identify them). Please look over all of them, and make all changes that you agree clarify your intent. I appreciate your patience and hard work in responding to the reviewers comments and recommendations. I've appended the list of technical corrections here, for convenience.

Best regards,
Dan

lines 3-5: I had a really hard time understanding the sentence. Is the
following change an accurate reflection of what you meant? “In this paper,
the deviations of the carbon budget and the strict linear relationship implied
by the carbon budget are examined through the lens of the function of
the temperature response to an emission pulse (i.e, pulse response), and
its relation to TCRE” -> “In this paper, the deviations of the carbon
budget from the strict linear relationship implied by the TCRE is examined
through the lens of impulse response and its relationship with a non-linear
TCRE.”
• line 5: “deviations” -> “deviation”
• line 6: “The former stems from the scenario choice, the emission pathway,
under the fixed cumulative emissions” -> “The former stems from the
scenario choice, i.e. the specific emission pathway for a given level of
cumulative emissions”
• lines 8-9: “This paper shows how the pulse response in role of a Green’s function gives a unifying perspective on both scenario and state-dependence”
-> “This paper shows how the pulse response, viewed as a Green’s function,
gives a unifying perspective on both scenario and state-dependence”
• line 10: “independency” -> “independence”
• line 10-11: “under the given constraints” -> “for a given set of constraints”
• line 12-13: The sentence as written is very confusing. Does the following
change clarify the intended meaning? “Moreover, using pulse response as
a Green’s function in the optimization program, the” -> “Moreover, using
the pulse response, the”
• line 13: “full” -> “reduced-complexity”. ESM people would rightly have a
fit if we called FaIR a full model.
• line 19-21: “Green’s function approach is eligible to diagnose both models’
carbon budget scenario-dependency, leaving investigation with other and
1
more complex models to future work.” -> “The Green’s function approach
can be used to diagnose both models’ carbon budget scenario-dependency,
paving the way for future investigations and applications with other and
more complex models.”
• line 63: “with the changing” -> “with changing”
• lines 64-65: “Moreover, this paper shows that state-dependency of TCRE
leads to a non-linear carbon budget equation, as the non-constant TCRE
leads to breakdown of linearity given by Eq. 1.” This sentence goes in
circles (non-linear TCRE leads to non-linearity because it breaks the linear
assumption). I suggest deleting it.
• line 67: “and not from the climate conditions of the system” -> “and not
from the intial climate conditions of the system”. If you have a different
pathway, then you have different climate conditions along the way to
reaching the same cumulative emissions so I don’t think it is correct to
imply that the climate conditions are entirely the same.
• line 68: “utilizing the high-complexity” -> “utilizing high-complexity”
• line 87: “of Green’s function” -> “of a Green’s function equation” ? The
phrase “in the context of Green’s function” doesn’t make any sense to me.
• line 91: “independency” -> “independence” (again, probably worth doing
a search for independency throughout, independency is an anarchic term
for independence)
• line 92: ‘full model’ -> “FaIR” or whatever other model you mean. I
wouldn’t use the term ‘full model’ anywhere in your paper because it is
unclear and the idea of a ‘full model’ doesn’t really make sense (all models
have limitations, so what makes one model full while another is not).
• line 99: as above re ‘full model’ (and, as above, I strongly suggest removing
the phrase ‘full model’ from the manuscript entirely)
• line 108: “left out” -> “left”
• line 113: “in context” -> “in the context”
• line 114: “implications on” -> “implications for”
• line 117: as above re ‘full model’
• line 123: as above re ‘full model’
• line 125: “deviation” -> “the deviation”
• line 132: “changing pulse” -> “pulse” (changing is already implied by other
words in the sentnce)
• line 167: “the Green’s” -> “Green’s”
• line 253: “45 years” -> “45 years farther” (or further)
2
• line 265: “previous” -> “the previous”
• lines 303-304: I didn’t understand this sentence: “This way, assuming any
function for the state dependency is avoided; rather, it is deducted from
mapping v(T) (Fig. 7, right graph)”
• line 305: “due to negative” -> “due to the negative”
• lines 307-308: “due to an an increasing probability of a climate system
bifurcation thresholds” What does this mean and what reference do you
have for this?
• line 321: “shown in next” -> “shown in the next”
• line 359: ‘full model’ (as above)
• line 361: ‘full model’ (as above)
• line 366: refer to the analysis you have which shows this (Appendix A)
• line 415: “exhibiting the same” -> “exhibiting deviations of the same”
• line 416: “especially precise for lower cumulative emissions” -> “with
the Green’s function approach being especially close to FaIR for lower
cumulative emissions”
• line 427: “Namely, in” -> “Namely,”
• lines 429 - 431: There are some missing words in this sentence so it doesn’t
really make sense
• line 490: ‘had’ -> ‘has’
• line 495: ‘full model’
• line 515: ‘linearities’ -> ‘non-linearities’ ?
• line 518: ‘linear’ -> ‘linear (when viewed at the same time point)’ or
something like this? The pulse isn’t constant so there must be some time
element assumption in here no?
• line 540: “with FaIR” -> “with FaIR or some other model that captures
the scenario- and state-dependent effects discussed here”
• line 662: ‘full model’ (as above)