Which Came First or Beyond Correlation

An evergreen (you know CO2 makes for more plant growth) of the denial industry is that "you can't show that CO2 CAUSES Climate change". Let Eli fish a few of these poggies out of his Twitter bag

You understand no correlation is definitive. That is why you are reverting to word salads with references to things which are not facts.

The bottom line is there is no correlation between temperature and CO2. That falsifies the AGW theory.

See below. pic.twitter.com/lMDuXRN1kq

— BubbasPossumRanch (@BubbasRanch) June 13, 2023

and another

The idea that earth’s climate, which is immensely complicated, can be dialed hotter simply by increasing CO2, and lower by decreasing, is very poor science.

This chart of geological time clearly shows that CO2 has no meaningful correlation with Earth’s temperature. pic.twitter.com/UQUMGIrWrX

— John Johnson (@JohnK1234abcd) June 19, 2023

But it, of course not, is not just the CO2 has no effect on climate, but the anti-vaxxers and any other delusions of the denial crowd declaring that correlation is not causation. Well, as Eli has been rumored to reply, it can be a pretty strong hint if you understand the mechanism. To be honest, Eli is not very comfortable with any claim that correlation is causation lacking a mechanism, it's the physicist in the Bunny but there is a reason physicists are rare.

Properly speaking this is more a question for Tamino but Eli was trolling the web when up popped the answer Stips, A., Macias, D., Coughlan, C. 

Elisa Garcia-Gorriz & 

X. San Liang 

. On the causal structure between CO2 and global temperature. Sci Rep 6, 21691 (2016) [OPEN].  The abstract says it all

We use a newly developed technique that is based on the information flow concept to investigate the causal structure between the global radiative forcing and the annual global mean surface temperature anomalies (GMTA) since 1850. Our study unambiguously shows one-way causality between the total Greenhouse Gases and GMTA. Specifically, it is confirmed that the former, especially CO2, are the main causal drivers of the recent warming. A significant but smaller information flow comes from aerosol direct and indirect forcing and on short time periods, volcanic forcings. In contrast the causality contribution from natural forcings (solar irradiance and volcanic forcing) to the long term trend is not significant. The spatial explicit analysis reveals that the anthropogenic forcing fingerprint is significantly regionally varying in both hemispheres. On paleoclimate time scales, however, the cause-effect direction is reversed: temperature changes cause subsequent CO2/CH4 changes.

This is not unexpected, indeed a figure that your friendly correspondent has used frequently to describe cause and effect, drives home this conclusion on physical grounds (Figure 1.1 Feedbacks in the climate system by Kurt Lambeck)

The information flow method was developed by X. San Liang in 2014 [SADLY NOT OPEN] for exactly this kind of situation (there is another method for separating cause and effect called Grainger causality)

Given two time series, can one faithfully tell, in a rigorous and quantitative way, the cause and effect between them? Based on a recently rigorized physical notion, namely, information flow, we solve an inverse problem and give this important and challenging question, which is of interest in a wide variety of disciplines, a positive answer. Here causality is measured by the time rate of information flowing from one series to the other. The resulting formula is tight in form, involving only commonly used statistics, namely, sample covariances; an immediate corollary is that causation implies correlation, but correlation does not imply causation.

More in this paper by Liang [OPEN] for those wanting to dive in but let's look at what Stips, et al, find for information flow to global temperature anomaly between 1900 and 2008.

Radiative Forcing	Correlation and Causality–HADCRUT4
	Correlation	Forcing→GMTA [nat/year]	GMTA→Forcing [nat/year]
Total forcing	0.804 ± 0	0.244 ± 0.091	0.036 ± 0.080
Anthropogenic	0.863 ± 0	0.355 ± 0.112	−0.008 ± 0.005
All GHG	0.852 ± 0	0.318 ± 0.108	−0.005 ± 0.003
CO2	0.852 ± 0	0.316 ± 0.108	−0.003 ± 0.003
Aerosol	−0.810 ± 0	0.232 ± 0.095	−0.002 ± 0.006
Cloud	−0.796 ± 0	0.208 ± 0.092	−0.001 ± 0.004
Solar	0.616 ± 0	0.082 ± 0.059	0.035 ± 0.051
Volcanic	0.089 ± 0.267	0.003 ± 0.006	−0.004 ± 0.009
AMO (1900–2008)	0.477 ± 0	0.018 ± 0.043	0.021 ± 0.014
PDO (1900–2008)	0.123 ± 0.204	−0.002 ± 0.013	−0.011 ± 0.025

Larger numbers in the middle column show causation larger numbers in the rightmost column label effects of GMTA.  At least for the 1900 - 2008 period the increase in atmospheric CO2 is the largest cause of the GMTA, although aerosols and clouds also are important. The solar is low as are the AMO and PDO, although they both correlate well with GMTA. As the paper puts it

This is a good real world example that illustrates the basic fact: correlation does not mean causation. It further questions the assumed fundamental role of the AMO for the global climate as speculated in38.

 That should make Mike Mann very happy if he has not seen it. 

Also interesting is the cumulative causality 

Which implies that GHG warming really only became dominant around 1960 e.g. after 1960, CO2 concentration was even more dominent. If information flow is applied to shorter time periods, then other forcings can be temporarily causitive, such as the period a few years after a large volcanic eruption.

But what about paleoclimate?

By calculating the IF in nat per unit time from the 1000 year interpolated PAT time series to CO2 concentration we get 0.123 ± 0.060 nat/ut and −0.054 ± 0.040 nat/ut in the reverse direction. Therefore we have on these long time scales a significant IF only from the temperature data to the CO2, but not in the other direction, exactly opposite to that seen in the data from the last 156 years. This result proves robust against using different ice age/gas age chronologies (SI, Tables SI-5 and SI-6 comparing EDC3 and AICC2012 chronology) and against using the recent corrected CO2 data from Bereiter45 (SI, Table SI-7).

which is just what Figure 1.1 shows. And what about the future, where will increasing GHG concentrations bite the hardest. Stips, Macias and Coughlan have an idea based on information flow

So the next time you hear correlation doesn't prove causality, point them thisaway or to the Nature Scientific Report article.