Round 1

Reviewer 1 Report

Dear Editor,

The present submitted paper (sci-2319544) is sophisticated and more comprehensive, relating to the published version in 2020. (sci2040083). The two works arouse the scientific community's interest with an imposing title (Hen Or Egg-the causal relationship) and an even more striking and bold conclusion that starts to "boil over" the discussion in the "backroom".

The first study (2020) used global temperature data from satellites (UAH) and ground-based (CRUTEM4 ) as well as  CO₂ data from several sites from 1980–2019. The authors present their earlier work on the T - CO₂ relationship, in which they used satellite-based temperature series (UAH) for the lower troposphere. In addition to the satellite-based temperature, in the present work, the authors used surface reanalysis data from the NCEP and NCAR centres as a data set, which allows going back in time. Thus, they extended their analysis for a 65-year time span. Regarding the CO₂ concentration measurements, recent ones (Mauna loa) and the South Pole complete data set (NOAA, 1975-2021) have been included in the analysis.

In recent works, the authors [ref.,4,5] developed an integrated theoretical framework that investigated causality in a comprehensive approach (theoretical and applied), identifying several problems in identifying causal relationships to formulate necessary conditions in determining causality. These conditions could be implemented through an algorithm. So, they developed an efficient algorithm which can be implemented in large-scale open systems. This framework was presented in studies, especially in hydrology and climatology. For example, the difference in the relationship of global mean temperature with CO₂ concentration was presented in 30 case studies on an annual basis.

The conclusion from the analysis suggests a unidirectional potentially causal connection with Temperature as the cause and CO₂ as the effect. Furthermore, this direction of causality holds for the entire period covered by observations, i.e. 65 years, and for all time scales resolved by these data.

The submitted manuscript is a highly structured paper and fully covered by a solid theoretical analysis, documented and supported by original and relevant references. The work is supported by an excellent theoretical background and a coherence that certifies the value of the results.

Besides, the research work and the scientific and research footprint on the international scene of the authors are a guarantee.

Dear editor, publishing the work (sci-2319544) in your journal would be a good decision!

P.S:  It is a fact in the history of science that the directed universality of a scientific theory, over time, creates a bias that traps scientific judgment. This paper is of great interest to the readership. Still, I suspect that only a tiny part of the scientific community will have the courage to positively use this paper as an excellent reference. One of the reasons is that in approaching science, dogmatic theories are always a factor of adverse influence on the acceptance of another point of view.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Review of On hens, eggs, temperatures, and CO₂: causal links in Earth’s atmosphere

I have divided the study into four interlinked themes that the authors discuss.  Just for your information, I suggest references, and you may have a look at them- or not. None of them are to my own work.

A summary.

1.      Impulse response function. The authors show that temperature precedes CO₂ during the period 1948 to 2022 by using a technique called Impulse response function, IRF.  The study is a continuation of the authors previous studies. The authors, in the present article, focus on “hydrological and climate applications” (line 89). They list seven applications. (lines 93 to 109) and list eleven the main case studies in their Table 1.

2.      Comparison with observations. In section 8 the authors compare modelling results with observations. They find that the modelling studies suggest CO₂ → T, whereas the observations suggest T → CO₂. I find this exercise quite interesting and would think that many more modelling studies should have made similar exercises. (Lines 447 ff.)

3.      Alternative sources for CO₂ increase. The authors claims that the increase in terrestrial and maritime respiration in the last 65 years period is 3.4 times greater than the CO₂ emission by fossil fuel combustion.

4.      Lead-lag network. In the discussion section the authors show a schematical picture of possible causal links in the climate system (Figure 13).

The authors conclude the case studies with five observations (lines 427 to 437).  The main conclusion is that, based on observations, there is a direction DT →  Dln CO_{2. .} However, I would prefer that they had addressed the seven applications in lines 93 to 109 more directly.

Major concerns

The IRF. I suppose I could have disentangled the difference between their IRF method and normal cross correlation, but if the authors state that difference more clearly, it would be fine. They use the same nomenclature as for cross correlations, e.g., eq (2) is called the explained variance ratio. In equation (5) they define a roughness constant, E, which is the second derivative, -the acceleration of g(h) where g(h) = IRF is a function of the time lag, line 112 and Fig 3. Thus, I suppose E is the sharpness of the peaks in e.g., Figure 3. Maybe I am wrong? To me, IRF functions very much like R².  Maybe I am wrong again, but it would be nice to be explained the difference.

I am not sure why you report “mean” and “median”, do you sometimes make a choice?

I am not very fond of too much background information, just sufficient to explain what the problem is, but maybe you could mention a little bit more about alternative methods? Kestin et al. (1998) could be one source.

The authors compare the pattern in Figure 2 and figure 4 left panel, and say that they agree well with the empirical function for time lags up to 10 years (I do not see that this is clear) (line 281)-

The authors apply their method to climate series. I am wondering if their method require the series to be stationary or if there are other criteria for when it can be applied.

I would have anticipated references to more recent literature. For example, Shakun et al. (2012), (Parrenin et al. 2013).  With respect to smoothing 1^st differencing is a normal procedure in economics and Estrella (2005) make a choice.

On line 492 to 496 you show that there can be several “potential causes of the temperature increase”. But with several causes, at least cross correlation could give different lead-lag relations?

Comparison with observations. I agree with the authors on the utility and importance of comparing lead-lag relations for observations and models. There are studies that do this, however.

Alternative causes for CO₂ increase. Maybe I misunderstand, if is it temperature that increases respiration (Eq A17) don’t you then have the egg and hen dilemma? If respiration increases, would not CO₂ uptake in plant material also increase?

Lead-lag relations. This is nice, but shouldn’t you compare with other studies?  Methodically, you would have “Methods based on Granger causality...”  for example in Moraffah 2021. Causal inference for time series analysis.... Issue-wise there are a lot of studies on LL relations between ocean oscillations (variabilities) and other climate series.

Minor comments

Line 128. You may have a positive LL relation in your nomenclature, but still have a negative correlation, I suppose?

Line 270. Yes, timescales are important, the term “disentangling” is often used in that context (Wills et al. 2018).

Line 302. This is a normal procedure for detrending in economics.

Lines 393. Nice

Line 332 anticausal?

Line 433.  ... is opposite... point 3 ...real measurements →I would anticipate characterization of data in point 3.

Line 678. But see Hansen et al. (2022)

Estrella, A. (2005). "Why does the yield curve predict output and inflation?" Economic Journal 115(505): 722-744.

Hansen, J. E., M. Sato, L. Simons, L. S. Nazarenko, K. von Schuckmann, N. G. Loeb, M. B. Osman, Pushker Kharecha, Qinjian Jin, George Tselioudis, Andrew Lacis, Reto Ruedy, 9, Gary Russell, Junji Cao and J. Li11 (2022). Global warming in the pipeline.

Kestin, T. S., D. J. Karoly, J. I. Yang and N. A. Rayner (1998). "Time-frequency variability of ENSO and stochastic simulations." Journal of Climate 11(9): 2258-2272.

Parrenin, F., V. Masson-Delmotte, P. Kohler, D. Raynaud, D. Paillard, J. Schwander, C. Barbante, A. Landais, A. Wegner and J. Jouzel (2013). "Synchronous Change of Atmospheric CO2 and Antarctic Temperature During the Last Deglacial Warming." Science 339(6123): 1060-1063.

Shakun, J. D., P. U. Clark, F. He, S. A. Marcott, A. C. Mix, Z. Y. Liu, B. Otto-Bliesner, A. Schmittner and E. Bard (2012). "Global warming preceded by increasing carbon dioxide concentrations during the last deglaciation." Nature 484(7392): 49-54.

Wills, R. C., T. Schneider, J. M. Wallace, D. S. Battisti and D. L. Hartmann (2018). "Disentangling Global Warming, Multidecadal Variability, and El Nino in Pacific Temperatures." Geophysical Research Letters 45(5): 2487-2496.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

I would like to congratulate the authors for the excellent work submitted to the journal. The importance of discussing the discussed topic is of unique relevance to environmental science as a whole. I do not have any contribution to the methodological, conceptual, statistical or formatting improvement of the work. Congratulations to the authors. I strongly recommend the publication.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Dear authors. You have responded to all my concerns. I just have two minor- minor comments. R2.14 2 "multiplying one of the two series  by -1" ?

anticausal - anti would mean it is not causal- so you prove it is not causal? Or, causality goes the other way ?   I suppose I could understand if I thought harder.

Author Response

>Dear authors. You have responded to all my concerns.

We are glad and thankful that you found our responses satisfactory.

> I just have two minor- minor comments.

We have fixed both.

>R2.14 2 "multiplying one of the two series  by -1" ?

We have explained it by changing the text as follows:

"In the opposite case (if the processes are negatively correlated), by multiplying one of the two series by -1 we make the correlation positive."

> anticausal - anti would mean it is not causal- so you prove it is not causal? Or, causality goes the other way ?   I suppose I could understand if I thought harder.

We have explained it by adding the following text:

"Note that anticausal means that the actual causality direction is opposite to that assumed."

Overall, we thank you very much for the careful reading, the constructive attitude and the helpful comments.