Atmospheric Temperature and CO2: Hen-Or-Egg Causality?
Πότερον ἡ ὄρνις πρότερον ἢ τὸ ᾠὸν ἐγένετο (Which of the two came first, the hen or the egg?).
Πλούταρχος, Hθικά, Συμποσιακὰ Β, Πρόβλημα Γ (Plutarch, Moralia, Quaestiones convivales, B, Question III).
2. Temperature and Carbon Dioxide—From Arrhenius and Palaeo-Proxies to Instrumental Data
Conversations with my friend and colleague Professor Högbom together with the discussions above referred to, led me to make a preliminary estimate of the probable effect of a variation of the atmospheric carbonic acid [meaning CO2] on the temperature of the earth. As this estimation led to the belief that one might in this way probably find an explanation for temperature variations of 5–10 °C, I worked out the calculation more in detail and lay it now before the public and the critics.
- Indeed, CO2 plays a substantial role as a greenhouse gas. However, modern estimates of the contribution of CO2 to the greenhouse effect differ largely from Arrhenius’s results, attributing 19% of the long-wave radiation absorption to CO2 against 75% of water vapour and clouds (Schmidt et al. ), or a ratio of 1:4.
- During the Phanerozoic Eon, Earth’s temperature varied by even more than 5–10 °C, which was postulated by Arrhenius—see Figure 3. Even though the link of temperature and CO2 is beyond doubt, this is not clear in Figure 3, where it is seen that the CO2 concentration has varied by about two orders of magnitude and does not always synchronize with the temperature variation. Other factors may become more important at such huge time scales. Thus, an alternative hypothesis of the galactic cosmic ray flux as a climate driver via solar wind modulation has been suggested [16,17], which has triggered discussion or dispute [14,18,19,20,21,22,23]. The T–CO2 relationship becomes more legible and rather indisputable in proxy data of the Quaternary (see Figure 4). It has been demonstrated in a persuasive manner by Roe  that in the Quaternary, it is the effect of Milanković cycles (variations in eccentricity, axial tilt, and precession of Earth’s orbit), rather than of atmospheric CO2 concentration, that explains the glaciation process. Specifically (quoting Roe ),variations in atmospheric CO2 appear to lag the rate of change of global ice volume. This implies only a secondary role for CO2—variations in which produce a weaker radiative forcing than the orbitally-induced changes in summertime insolation—in driving changes in global ice volume.
show that properly specified tests of Ganger [sic] causality validate the consensus that human activity is partially responsible for the observed rise in global temperature and that this rise in temperature also has an effect on the global carbon cycle.
study unambiguously shows one-way causality between the total Greenhouse Gases and GMTA [global mean surface temperature anomalies]. Specifically, it is confirmed that the former, especially CO2, are the main causal drivers of the recent warming.
- The short-term effects deserve to be studied, as well as the long-term ones.
- The modern instrumental records are short themselves and only allow the short-term effects to be studied.
- For the long-term effects, the palaeo-proxies provide better indications, as already discussed above.
4.1. Stochastic Framework
- A time reversible process is also stationary (Lawrance ).
- If a scalar process is Gaussian (i.e., all its finite dimensional distributions are multivariate normal) then it is reversible (Weiss ). The consequences are (a) a directional process cannot be Gaussian; (b) a discrete-time ARMA process (and a continuous-time Markov process) is reversible if and only if it is Gaussian.
- However, a vector (multivariate) process can be Gaussian and irreversible at the same time. A multivariate Gaussian linear process is reversible if and only if its autocovariance matrices are all symmetric (Tong and Zhang ).
- If η1 = 0, then there is no dominant direction.
- If , then the dominant direction is .
- If , then the dominant direction is .
4.2. Complications in Seeking Causality
when discussing the interpretation of a correlation coefficient or a regression, most textbooks warn that an observed relationship does not allow one to say anything about causation between the variables.
Determining true causality requires not only the establishment of a relationship between two variables, but also the far more difficult task of determining a direction of causality.
Results from Granger causality analyses neither establish nor require causality. Granger causality results do not reveal causal interactions, although they can provide evidence in support of a hypothesis about causal interactions.
coupled chaotic dynamical systems violate the first principle of Granger causality that the cause precedes the effect.
4.3. Additional Clarifications of Our Approach
- To make our assertions and, in particular, to use the “hen-or-egg” metaphor, we do not rely on merely statistical arguments. If we did that, based on our results presented in the next section, we would conclude that only the causality direction T → [CO2] exists. However, one may perform a thought experiment of instantly adding a big quantity of CO2 to the atmosphere. Would the temperature not increase? We believe it would, as CO2 is known to be a greenhouse gas. The causation in the opposite direction is also valid, as will be discussed in Section 6, “Physical Interpretation”. Therefore, we assert that both causality directions exist, and we are looking for the dominant one under the current climate conditions (those manifest in the datasets we use) instead of trying to make assertions of an exclusive causality direction.
- While we occasionally use statistical tests (namely, the Granger test, Equations (14) and (15)), we opt to use, as the central point of our analyses, Equation (13) (and the conditions below it) because it is more intuitive and robust, fully reflects the basic causality axiom of time precedence, and is more straightforward, transparent (free of algorithmic manipulations), and easily reproducible (without the need for specialized software).
- For simplicity, we do not use any statistic other than correlation here. We stress that the system we are examining is indeed classified as Gaussian and, thus, it is totally unnecessary to examine any statistic in addition to correlation. The evidence of Gaussianity is provided by Figure A1 and Figure A2 in Appendix A.5, in terms of marginal distributions of the processes examined and in terms of their relationship. In particular, Figure A2 suggests a typical linear relationship for the bivariate process. We note that the linearity here is not a simplifying assumption or a coincidence as there are theoretical reasons implying it, which are related to the principle of maximum entropy [67,69].
- All in all, we adhere to simplicity and transparency and, in this respect, we illustrate our results graphically, so they are easily understandable, intuitive, and persuasive. Indeed, our findings are easily verifiable even from simple synchronous plots of time series, yet we also include plots of autocorrelations and lagged cross-correlation, which are also most informative in terms of time directionality.
5.1. Original Time Series
5.2. Differenced Time Series
- For the monthly scale and the causality direction [CO2] → T, the null hypothesis is not rejected at all usual significance levels for lag η = 1 and is rejected for significance level 1% for η = 2–8, with minimum attained p-value 1.8 × 10−4 for η = 6.
- For the monthly scale and the causality direction T → [CO2], the null hypothesis is rejected at all usual significance levels for all lags η, with minimum attained p-value 2.1 × 10−8 for η = 7.
- For the monthly scale, the attained p-values in the direction T → [CO2] are always smaller than in direction [CO2] → T by about 4 to 5 orders of magnitude, thus clearly supporting T → [CO2] as dominant direction.
- For the annual scale with fixed year specification and the causality direction [CO2] → T, the null hypothesis is not rejected at all usual significance levels for any lag η, thus indicating that this causality direction does not exist.
- For the annual scale with fixed year specification and the causality direction T → [CO2], the null hypothesis is not rejected at significance level 1% for all lags η = 1–6, with minimum attained p-value 5% for lag η = 2, thus supporting this causality direction at this significance level.
- For the annual scale with fixed year specification, the attained p-values in the direction T → [CO2] are always smaller than in direction [CO2] → T, again clearly supporting T → [CO2] as the dominant direction.
6. Physical Interpretation
Conflicts of Interest
Appendix A.1. On Early Non-Systematic Measurements of CO2
Appendix A.2. Some Notes on the Averaged Differenced Process
Appendix A.3. Some Notes on Time Directionality of Causal Systems
Appendix A.4. Some Notes on the Alternative Procedures on Causality
Our thoughts and enquiries are, therefore, every moment, employed about this relation: Yet so imperfect are the ideas which we form concerning it, that it is impossible to give any just definition of cause, except what is drawn from something extraneous and foreign to it.
The probabilityof the event occurring in the real world, with f present, is referred to as factual, whileis referred to as counterfactual. Both terms will become clear in the light of what immediately follows. The so-called fraction of attributable risk (FAR) is then defined asThe FAR is interpreted as the fraction of the likelihood of an event that is attributable to the external forcing.
- x = 1: being hot above a threshold;
- y = 1: wearing clothes with weight below a threshold;
- z = 1: sweat quantity above a threshold;
- Cold, heavy clothes:
- Cold, light clothes:
- Hot, heavy clothes:
- Hot, light clothes:
|x||y||z = 0||z = 1|
Appendix A.5. Additional Graphical Depictions
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|Temperature—CO2 Series||Monthly Time Series||Annual Time Series—Sliding Annual Window||Annual Time Series—Fixed Annual Window|
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Koutsoyiannis, D.; Kundzewicz, Z.W. Atmospheric Temperature and CO2: Hen-Or-Egg Causality? Sci 2020, 2, 83. https://doi.org/10.3390/sci2040083
Koutsoyiannis D, Kundzewicz ZW. Atmospheric Temperature and CO2: Hen-Or-Egg Causality? Sci. 2020; 2(4):83. https://doi.org/10.3390/sci2040083Chicago/Turabian Style
Koutsoyiannis, Demetris, and Zbigniew W. Kundzewicz. 2020. "Atmospheric Temperature and CO2: Hen-Or-Egg Causality?" Sci 2, no. 4: 83. https://doi.org/10.3390/sci2040083