Tuesday, June 20, 2023

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

and another

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. . 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


ForcingGMTA [nat/year]

GMTAForcing [nat/year]

Total forcing

0.804 ± 0

0.244 ± 0.091

0.036 ± 0.080


0.863 ± 0

0.355 ± 0.112

−0.008 ± 0.005


0.852 ± 0

0.318 ± 0.108

−0.005 ± 0.003


0.852 ± 0

0.316 ± 0.108

−0.003 ± 0.003


−0.810 ± 0

0.232 ± 0.095

−0.002 ± 0.006


−0.796 ± 0

0.208 ± 0.092

−0.001 ± 0.004


0.616 ± 0

0.082 ± 0.059

0.035 ± 0.051


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.


  1. Awesome! Thanks for posting this. I reposted the citation and the abstract on ResearchGate, where I am involved in a protracted battle with several self-proclaimed geniuses who have disproved the greenhouse effect, and question everything from the mathematics of energy balance to carbon budgets.

  2. Sorry to see these tired old lie promoters get a new lease on life. Thanks for doing the heavy lifting.

  3. Eli,

    Apparently there is a paper from 2021 that says the technique used in the paper you cited (and I re-cited) was not valid, although the conclusion was still accurate:

    Coulombe, P.G., Göbel, M. 2021. On Spurious Causality, CO2, and Global Temperature. Econometrics 9(3), 33; https://doi.org/10.3390/econometrics9030033

  4. Secular trends show weak power in any correlation. You really need detailed structure to make assertions.

  5. Sorry about the long delay, I saw tamino reposting and checked here.

    Those who cite "Correlation is not causation" simply don't understand that pretty much all so-called "true experiments" are analyzed by the very same mathematical methods. The sole difference relies on the procedures themselves which ASSUME such things as actual random assignment, complete experimenter conscious and unconscious objectivity, etc.

    As another example, most of what is said about stars is information gained NON-experimentally as the most important basic data source in astronomy is from spectroscopy performed at various wavelengths and how well the [gasp on] correlations [gasp off] between the observed spectra are to the predicted spectra from [gasp on] models [gasp off].


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