|In “A modified impulse-response function representation of the global response to carbon dioxide emissions”, the authors propose a simple modification to the traditional impulse response function (IRF) model in order to account for the effect of past CO2 emissions and temperature change on atmospheric CO2 dynamics, thereby making their modified IFR model (called FAIR) “state dependent”. The authors address a basic issue that I feel is ignored by many people, i.e., Earth System Models (ESMs) show that atmospheric CO2 dynamics is state dependent yet the standard IRF derived from these ESMs is state independent. The FAIR model substantially improves results compared to the standard IRF, illustrating the scientific value of the study. Unfortunately, the paper itself is too poorly written to warrant publication. Some major issues are the lack of sufficient explanations on the simulations, the inadequate structure of the text (both across and within sections), inconsistencies between the actual results and the text describing them, and the poor Figures. Moreover, the authors seem to not have taken previous reviews seriously by reproducing only a part of the comments in their response and by ignoring or misinterpreting many issues raised. |
My suggestion is for the authors to put this paper on the ice for a while, then re-write and submit elsewhere. Overall, the authors should strive for clarity, accuracy, and conciseness. They also need to provide sufficient explanations in the Methods and give attention to details, especially in the Figures. I have identified below several specific elements to consider.
1. Even after reading the paper, I do not really understand the last sentence of the Abstract.
2. I found the Introduction generally good, but maybe the need for the study could be made clearer by noting that the results from Joos et al. (2013) clearly show that: (1) the airborne fraction for a given pulse size depends upon the background state of the atmosphere; and (2) the airborne fraction for a given background state of the atmosphere depends upon the pulse size. Conversely, the standard IRF is state independent...
3. Page 2, line 16. Which “simple climate-carbon cycle models”? MAGICC? Standard IRF? Depending upon the answer, stating that these models have not been “evaluated in terms of their pulse-response behaviour” could be wrong. Similar comment for page 2, line 26.
4. Page 2, line 25. In my opinion Davis and Socolow (2014) did not really evaluate the “required energy-system transitions that are needed to limit warming to below particular thresholds”; they rather estimated emissions from existing infrastructure.
5. Page 3, line 15. The 4-exponentials IRF is for mathematical convenience and does not really correspond to the time dynamics of actual mechanisms, so the “processes” provided in Table 1 are just ‘guiding analogies’. This should be noted here instead of below and made clearer.
6. Page 3, line 18. Replace “i = 1, 4” with “i = 1, ..., 4” or “i = 1‒4” or “i = 1 to 4”.
7. Page 3, line 25. Mention that the authors decided to give a finite (1x10^6) value to \tau_0, as this differs from Myhre et al. (2013). Also mention (here or elsewhere) that for PI-IR, the a_i come from Table S2 of Joos et al. (2013).
8. Page 3, line 25-28. Defining ECS and TCR (and TCRE when mentioned much later in the paper) would probably be worthwhile.
9. Page 3, lines 25-28. The link between the c_j and both ECS and TCR is not clear. The reference to Millar et al. (2015) does not really clarify this point as the latter study presents c_j and d_j in their Supplement only, and under a mathematical form that differs from Eq. (3) considered here. To address this and other comments below, the authors need to add an Appendix or a Supplement in which they: (1) clearly show the mathematical link between the c_j and d_j as appearing in Eq. (3) and both ECS and TCR; and (2) clearly explain how they obtained c_1 = 0.46 and c_2 = 0.27.
10. Page 4, Table 1. Provide the units for c_1 and c_2.
11. Page 5, line 10. iIRF is not the “average airborne fraction over a period of time”, but the product is this average fraction with the length of the integration period.
12. Page 5, line 21 to page 6, line 2. The text is poorly structured; I think the following order would help. First, explain how FAIR uses Eqs. (4) to (6) at each time step, along with Eq. (3) for the temperature. Second, explain how were determined the specific values of r_0, r_C, and r_T (was it simply through trial and error? until finding what?). Third, state that these values work well but could be tuned even more (i.e., the text that currently appears on lines 21-27). Fourth, address the iIRF_100 > 100 years issue (would it really occur in the runs if iIRF_100 had not been limited to 95 years? if yes, the authors need to discuss the implications of this issue later on in the text).
13. Page 5, line 29: “This means the iIRF_100 is only exactly reproduced [...]”. Why?
14. Page 6, line 3. Adding one or two new methodological subsection(s) is required to clearly explain the simulations performed, how FAIR parameters were modified (uncertainty analyses), give the sources of input data (RCP, etc.), etc. Much of the text from the Results should be transferred here and expanded. Below, I refer to these new subsection(s) as “2.3”.
15. Page 6, line 3. Results are discussed as they are presented, which I think is appropriate in this paper. Therefore, the section should probably be named “Results and discussion”.
16. Page 6, lines 11-13. These two sentences are not necessary.
17. Page 6, lines 13+. Two undiscussed elements stroke me when looking at Fig. 1. First, one would expect PI-IR to end up with lower atmospheric CO2 than historical observations (because PI-IR CO2 sinks work with pre-industrial efficiency throughout) but this is not the case; why? I think this is because PI-IR was obtained by Joos et al. (2013) under a pulse of 100 GtC, whereas historical annual emissions were much lower and therefore initially had less impact on CO2 sinks efficiency. The authors should provide this explanation (if they agree with it) as it addresses the issue and strengthens their point about the inadequacy of state-independent IRF model. Second, PI-IR CO2 sinks are less efficient than FAIR CO2 sinks until about year 2000 (Fig. 1c). This seems mathematically impossible when looking at parameter values in Table 1 and the different equations... unless \alpha in FAIR has a value < 1. I think the authors should explain this here, and also give in the Methods the initial value of \alpha (about 0.16, right?) when C_acc and T are still equal to zero (i.e., when iIRF_100 is equal to r_0). The way FAIR is introduced, I initially thought \alpha would always be > 1 and got confused.
18. Page 6, lines 16-17. “The AR5-IR displays a too large [...]”. This sentence is a poor description of Fig. 1c, as no single model is really “consistent with the observations”. The authors can only state that AR5-IR is always higher than FAIR and that both are much more stable than observations.
19. Page 7, line 6. Mentioning the social cost carbon one time in the Introduction is OK, but coming back to this concept throughout the paper seems out of place (has the paper been written for another journal?) and pointless (a model of CO2 dynamics needs to give good results to be useful for any application, not just the social cost of carbon); please remove. Similar comment for page 2, line 13; page 6, lines 15-17; and page 13, line 13.
20. Section 3.1. The text should refer to the results in Fig. 1d, Fig. 2c, and Fig. 2d or these panels should be removed. With a current total of 28 Figure panels, less would probably be better.
21. Page 7, lines 15-19. This is Introduction-type text, not for the Results.
22. Section 3.2. The authors often mention iIRF_100, but this variable is not shown in the Figures. The authors should present airborne fraction results instead or add a Table with iIRF_100 results.
23. Page 7, lines 20-26. The majority of this text belongs to 2.3, along with the explanations about how “fully-coupled”, “biogeochemically-coupled”, and “radiatively-coupled” results were obtained. I also suggest removing Fig. 3a, which is more ‘methodological’ (i.e., diagnosed emissions required to reach a particular CO2 level) and not really interesting in itself.
24. Page 7, lines 31-32. All models show a rapid temperature increase followed by a relatively stable value, not just the “fully-coupled” FAIR model.
25. Page 8, lines 1-3. Cumbersome sentence; please rephrase.
26. Page 8, lines 18-26. The majority of this text belongs to 2.3, where the decision to maintain the same ratio between r_T and r_C needs to be justified. But in fact, I even suggest removing Fig. 4 from the paper as I do not believe it adds much value.
27. Page 8, line 27. Actually, the FAIR model is able to “successfully capture much of the response” only for the well-behaving models (i.e., no major year-to-year variability); this should be noted.
28. Page 8, line 31 to page 9, line 8. The majority of this text belongs to 2.3, with possibly some elements to the Introduction.
29. Page 8, lines 5-12. The authors apparently misunderstood Zickfeld and Herrington (2015). The issue with the results of Ricke and Caldeira (2014) is not so much that they did not “account for feedbacks on the carbon cycle and fail[ed] to capture the plateau of CO2-induced warming” as that they did not account for the effect of the pulse size on the shape of the temperature response (because they used a state-independent IRF model): for very large pulses, there is no longer an early warming peak followed by a plateau. FAIR is able to capture this change of shape from small pulses leading to an early warming peak (Fig. 8d) to large pulses without an early warming peak (Fig. 5a), whereas the standard IRF model is not (Fig. 5a). Although this outcome further illustrates the scientific value of FAIR, this change of shape occurs for pulses > 1000 GtC (also see Zickfeld and Herrington, 2015) and is therefore of little practical relevance for real emission scenarios. Given the amount of results presented, I thus suggest removing Fig. 5 from the paper as I do not believe it adds much value. If the Figure is kept, the text describing its results should be made accurate.
30. Page 9, lines 14-31. The majority of this text belongs to 2.3, where the ‘stopping rule’ for the different %/yr simulations should be given (until quadrupling initial CO2?). The long sentence on lines 23-26 adds little value.
31. Page 10, line 3. Why does a “constant airborne fraction necessarily give an approximately quadratic increase” and what is “approximately quadratic” (e.g., an exponent of 1.8)?
32. Page 10, lines 6-8. Cumbersome sentence; please rephrase.
33. Page 10, lines 8-10. Specify that these results are for “radiatively-coupled” experiments.
34. Page 10, lines 10-14. Cumbersome sentence; please rephrase.
35. Page 10, line 15. The “cumulative airborne fraction” could be more clearly defined: it is the fraction of all past emissions that are still in the atmosphere.
36. Page 10, lines 29-34. This is Introduction-type text, not for the Results.
37. Page 11, lines 1-5. Much more details about what was done and how it was done (i.e., which was the range of c_j values used) must be provided in 2.3 and possibly the new Appendix/Supplement. Figs. 7a and 7b should also be better introduced.
38. Page 11, lines 8-13. This sentence is confusing: it seems to imply that the increasing airborne fraction was due to changes in FAIR parameters (r_0, r_T, r_C, and c_j) *through time*. I rather assume that the increasing airborne fraction results from the structure of FAIR that leads to an ever-increasing \alpha, with changes FAIR parameters being responsible for the blue shading.
39. Page 11, lines 14-23. FAIR results in Fig. 7d do not show a “straight-line relationship between cumulative carbon emissions and human-induced warming”, the downward curvature being obvious starting from 500 GtC at least (not only at high cumulative emissions as mentioned). Please specify that the TCRE value provided is valid for 1000 GtC only.
40. Page 11, lines 24-26. This is Introduction-type text, not for the Results.
41. Page 11, line 28 to page 12, line 10. This text is not really related to FAIR and could easily be deleted. If not, it should be moved to a new subsection 3.5.
42. Page 11, line 30. Gillett et al. (2013) highlighted the policy relevance of TCRE, not TCR.
43. Page 12, lines 10-16. The majority of this text belongs to 2.3, where explanations must be much improved. In particular, the c_j (not TCR and ECS) were changed in FAIR; how?
44. Page 12, lines 16+. The text should refer to the results in Fig. 8b or this panel should be removed.
45. Page 12, lines 17-23. The majority of this text belongs to 2.3, where the IPT equation and the distribution (shape and values) of d_1 must be justified. I also suggest combining what remains of this paragraph with the next one, as they are logically linked (i.e., there are no results for d_1 uncertainty only, right?).
46. Page 12, lines 24-27. The majority of this text belongs to 2.3, where the values chosen must be justified, the 300 random draws approach must be explained, and the “median” shown in Fig. 8 must be defined (is it the median of the 300 draws or the result obtained with the median values of the parameter distributions?).
47. Before the Conclusions. A short discussion of the following point is missing: the idea behind FAIR is to adjust the standard IRF time constant based on iIRF_100, which is by definition for a time horizon of 100 years. Do you expect FAIR to perform well for time horizons of 1000 years and more? Would this require expanding the time horizon of iIRF?
48. Page 13, line 10. Strictly speaking, the authors did not show that “including both explicit CO2 uptake- and temperature- induced feedbacks are essential”. One could hypothesize that FAIR may give similar results working with temperature-induced feedback only but using a higher value of r_T (or with CO2 feedback only but using a higher value of r_C).
49. Page 15. The same study is referenced under both Meinshausen et al. 2011a and 2011b.
50. The Figures along with the related legends and captions are very poor. Here is only a subset of all the issues I saw.
- Fig. 1 caption: these results are for the historical period, so why the “RCP scenarios”?
- Many panels lack the x-axis title.
- There is often an overlap between axis scales (e.g., Fig. 1d bottom left) or with the panel letter (e.g., Fig. 5a bottom left).
- Axes are not labelled consistently, for example “CO2 concentration” vs. “CO2 Concentrations” vs. “Atmospheric concentration”, or “Airborne Fraction” vs. “Airborne fraction” vs. “Fraction of CO2 impulse remaining”.
- Results are often ‘cut’ because the scale is not large enough (e.g., Fig. 2c).
- Why aren’t MAGICC results shown on Figs. 2c and 2d; I presume they are available?
- Fig. 2c shows results with very different scales, while Fig. 2d shows too many results. Fig. 2 should have 6 panels: a) as currently, b) as currently, c) temperature for RCP8.5, d) temperature for RCP2.6, e) temperature vs. emissions for RCP8.5, and f) temperature vs. emissions for RCP2.6.
- Fig. 3 caption: the shading is grey, not black.
- The legends of Fig. 6a and 6c should both appear in 6a as they apply to all panels of Fig. 6. The legend of Fig. 6b should be ordered logically.
- Fig. 6 caption: replace “cumulative total carbon uptake” by “cumulative ocean and land carbon uptake”.
- There is no purple bar in Fig. 7a, in contradiction with both the legend and caption. There is no purple bar in Fig. 7d, in contradiction with the caption.
- Why aren’t AR5-IR results shown in Figs. 7a and 7b?
Davis and Socolow (2014). Environmental Research Letters 9, 084018.
Gillett et al. (2013). Journal of Climate 26, 6844-6858.
Joos et al. (2013). Atmospheric Chemistry and Physics 13, 2793-2825.
Millar et al. (2015). Climatic Change 131, 199-211.
Myhre et al. (2013). IPCC AR5, WG1, Chapter 8.
Ricke and Caldeira (2014). Environmental Research Letters 9, 124002.
Zickfeld and Herrington (2015). Environmental Research Letters 10, 031001.