On Hens, Eggs, Temperatures and CO2: Causal Links in Earth’s Atmosphere
Science is generated by and devoted to free inquiry: the idea that any hypothesis, no matter how strange, deserves to be considered on its merits. The suppression of uncomfortable ideas may be common in religion and politics, but it is not the path to knowledge; it has no place in the endeavor of science. We do not know in advance who will discover fundamental new insights.Carl Sagan 
Clearly, the results […] suggest a (mono-directional) potentially causal system with T as the cause and [CO2] as the effect. Hence the common perception that increasing [CO2] causes increased T can be excluded as it violates the necessary condition for this causality direction.
[…] in other words, it is the increase of temperature that caused increased CO2 concentration. Though this conclusion may sound counterintuitive at first glance, because it contradicts common perception […], in fact it is reasonable. The temperature increase began at the end of the Little Ice Period, in the early nineteenth century, when human CO2 emissions were negligible […].
- To expand the time frame of the investigation backward and forward by exploiting the longest available data series (Section 4).
- To check whether seasonality, as reflected in different phases of [CO2] time series at different latitudes, plays any role that could modify or possibly reverse the detected causality relationship (Section 5).
- To propose and apply a method for investigating the effect of the timescale in causality detection (Section 6).
- To extend the methodology for disambiguating cases in which the type of causality, HOE or unidirectional, is not quite clear (Section 7).
- To exploit the methodology in defining a type of data analysis that, regardless of the detection of causality per se, could shed light on modeling performance by comparing observational data with model results (Section 8).
- To discuss possible extensions of the scope of the methodology, i.e., from detecting possible causality to building a more detailed model of stochastic type (Section 9).
2. Summary of the Stochastic Approach to Causality
- Potentially HOE causal if we have for both some positive and some negative lags j,
- Potentially causal if for all , and
- Potentially anticausal if for all
3. Data and Case Studies
4. Investigating the Maximum Time Span That Modern Data Allow
5. Investigating the Possible Effect of Seasonality
- The system T-[CO2] appears to be potentially causal (unidirectional) in the direction , rather than hen-or-egg causal.
- All characteristic time lags () are positive in the direction (ranging from about 7 to about 10 months), and negative in the direction .
- The explained variance ratio is greater in the direction (about 1/3) than in the direction (around 1/5).
6. On the Timescale of Validity of Results
7. Possible Ambiguities and Disambiguation
8. Comparing Observational Data with Model Results
- There is no essential difference between the results for the periods 1850–2100 and 1850–2021.
- While, as expected, the IRFs differ if they are calculated with or without constraining roughness, the characteristic lags are similar in the two cases (with the exception of in cases #17 and #21).
- In all cases, the lags are negative in the direction and positive in the direction , suggesting a HOE causality with principal direction .
- Clearly, the finding in point 3, resulting from climate model outputs, is opposite to the results found when real measurements are used (NCEP/NCAR Reanalysis temperature and Mauna Loa [CO2] time series).
- Oddly, while the principal direction suggested by the models is , the explained variance is impressively low (10–15%) in this direction and impressively high (reaching 90%) in the opposite direction, .
9. Discussion and Further Results
- The dependence of the carbon cycle on temperature is quite strong and indeed major increases of [CO2] can emerge as a result of temperature rise. In other words, we show that the natural [CO2] changes due to temperature rise are far larger (by a factor > 3) than human emissions (Appendix A.1).
- There are processes, such as the Earth’s albedo (which is changing in time as any other characteristic of the climate system), the El Niño–Southern Oscillation (ENSO) and the ocean heat content in the upper layer (represented by the vertically averaged temperature in the layer 0–100 m), which are potential causes of the temperature increase, unlike what is observed with [CO2], their changes precede those of temperature (Appendix A.2, Appendix A.3 and Appendix A.4).
- On a large timescale, the analysis of paleoclimatic data supports the primacy of the causal direction T → [CO2], even though some controversy remains about this issue (Appendix A.5).
- Terrestrial and maritime respiration and decay are responsible for the vast majority of CO2 emissions , Figure 5.12.
- Overall, natural processes of the biosphere contribute 96% to the global carbon cycle, the rest, 4%, being human emissions (which were even lower in the past ).
- The biosphere is more productive at higher temperatures, as the rates of biochemical reactions increase with temperature, which leads to increasing natural CO2 emission .
- Additionally, a higher atmospheric CO2 concentration makes the biosphere more productive via the so-called carbon fertilization effect, thus resulting in greening of the Earth [34,35], i.e., amplification of the carbon cycle, to which humans also contribute through crops and land-use management .
- All evidence resulting from the analyses of the longest available modern time series of atmospheric concentration of [CO2] at Mauna Loa, Hawaii, along with that of globally averaged T, suggests a unidirectional, potentially causal link with T as the cause and [CO2] as the effect. This direction of causality holds for the entire period covered by the observations (more than 60 years).
- Seasonality, as reflected in different phases of [CO2] time series at different latitudes, does not play any role in potential causality, as confirmed by replacing the Mauna Loa [CO2] time series with that in South Pole.
- The unidirectional potential causal link applies to all timescales resolved by the available data, from monthly to about two decades.
- The proposed methodology is simple, flexible and effective in disambiguating cases where the type of causality, HOE or unidirectional, is not quite clear.
- Furthermore, the methodology defines a type of data analysis that, regardless of the detection of causality per se, assesses modeling performance by comparing observational data with model results. In particular, the analysis of climate model outputs reveals a misrepresentation of the causal link by these models, which suggest a causality direction opposite to the one found when the real measurements are used.
- Extensions of the scope of the methodology, i.e., from detecting possible causality to building a more detailed model of stochastic type, are possible, as illustrated by a toy model for the T-[CO2] system, with explained variance of [CO2] reaching an impressive 99.9%.
- While some of the findings of this study seem counterintuitive or contrary to mainstream opinions, they are logically and computationally supported by arguments and calculations given in the Appendices.
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A.1. Notes on Carbon Cycle and its Dependence on Temperature
Appendix A.2. Investigation of Causality between Albedo and Atmospheric Temperature
|Albedo, α: CERES, TERRA; T: NCEP/NCAR; period: 2000–2022||24||3||1.08||2.90||0.24||0.13||9.1 × 10–4|
|25||–3||–0.31||–2.46||0.24||0.06||3.6 × 10–4|
Appendix A.3. Investigation of Causality between El Niño, Atmospheric Temperature and CO2
|: NOAA; T: NCEP/NCAR; |
|26||3||4.14||3.85||0.46||0.33||8.1 × 10–4|
|27||3||–2.15||–0.93||0.46||0.30||2.3 × 10–3|
|: NOAA; [CO2]: Mauna Loa, |
|28||11||11.62||11.15||0.32||0.24||6.6 × 10–4|
Appendix A.4. Investigation of Causality between Ocean Heat Content, Atmospheric Temperature and CO2
|OMT0–100: NOAA; T: NCEP/NCAR; period: 1955–2022||30||ΔOMT0–100||0||2.42||0.98||0.68||0.53||7.1 × 10–3|
|31||ΔOMT0–100||0||–2.15||–0.93||0.68||0.52||3.8 × 10–3|
|OMT0–100: NOAA; [CO2]: Mauna Loa; period: 1958–2022||32||ΔOMT0–100||2||2.22||2.93||0.46||0.35||5.8 × 10–4|
|33||ΔOMT0–100||–2||−2.73||–2.82||0.46||0.21||5.6 × 10–3|
Appendix A.5. Notes on the T-[CO2] Relationship on Large Timescales
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|Monthly timescale, varying Δt|
|T year||1||5||7.70||6.35||0.48||0.31||1.3 × 10–5 *|
|2||–5||–5.67||–5.49||0.48||0.23||7.3 × 10–4 *|
|T year||3||8||7.75||6.86||0.56||0.34||3.1 × 10–4 *|
|4||–8||−6.31||–6.30||0.56||0.23||4.4 × 10–3 *|
|years||5||8||8.19||7.08||0.57||0.31||3.4 × 10–4 *|
|6||–8||−6.31||–6.31||0.57||0.21||4.5 × 10–3 *|
|years||7||9||10.65||10.32||0.53||0.29||1.0 × 10–4 *|
|8||–9||−6.28||–6.28||0.53||0.14||3.8 × 10–3 *|
|years||9||8||11.00||11.00||0.47||0.27||5.6 × 10–5 *|
|10||–8||−6.55||–6.54||0.47||0.11||3.6 × 10–3 *|
|years||11||6||11.74||12.15||0.45||0.31||3.4 × 10–5 *|
|12||6||9.98||11.13||0.45||0.33||7.6 × 10–6|
|13||–6||−6.33||–6.31||0.45||0.12||7.7 × 10–3 *|
|T year||14||10||9.76||8.91||0.40||0.35||2.0 × 10–4 *|
|15||–10||–8.51||–8.35||0.40||0.18||1.1 × 10–3 *|
|Annual timescale, year|
|T: CMIP6 mean, SSP2-4.5; [CO2]: SSP2-4.5, 1850–2100, w/o roughness constraint||16||0||–3.75||–6.20||0.36||0.90||0.095|
|As #16 and #17 but for 1850–2021||18||0||–6.23||–8.58||0.31||0.72||0.10|
|As #16 and #17 but with roughness constraint||20||0||–3.65||–5.55||0.36||0.84||3.5 × 10–5|
|21||0||6.86||1.63||0.36||0.13||7.7 × 10–3|
|As #18 and #19 but with roughness constraint||22||0||–7.34||–8.99||0.31||0.64||8.3 × 10–5|
|23||0||11.26||14.77||0.31||0.13||9.4 × 10–3|
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Koutsoyiannis, D.; Onof, C.; Kundzewicz, Z.W.; Christofides, A. On Hens, Eggs, Temperatures and CO2: Causal Links in Earth’s Atmosphere. Sci 2023, 5, 35. https://doi.org/10.3390/sci5030035
Koutsoyiannis D, Onof C, Kundzewicz ZW, Christofides A. On Hens, Eggs, Temperatures and CO2: Causal Links in Earth’s Atmosphere. Sci. 2023; 5(3):35. https://doi.org/10.3390/sci5030035Chicago/Turabian Style
Koutsoyiannis, Demetris, Christian Onof, Zbigniew W. Kundzewicz, and Antonis Christofides. 2023. "On Hens, Eggs, Temperatures and CO2: Causal Links in Earth’s Atmosphere" Sci 5, no. 3: 35. https://doi.org/10.3390/sci5030035