Temperature Follows CO2

GMST Follows CO2 Forcings, not Solar Forcings

You could be forgiven for looking at the above graph and thinking that quite obviously temperature (GMST) is following CO2 forcings and not solar forcings. But these facts are inconvenient for the "It's the Sun, stupid" crowd, so they have to figure out a way to turn this on its head. The most common way I've seen is for contrarians to say we have causation reversed. It's actually the increase in GMST that causes CO2 to increase, since warming temperatures causes the oceans to outgas CO2. The mantra I hear from this crowd is that "CO2 always lags temperature," usually followed with "by hundreds of years." Let's examine if this claim makes any sense, looking first at the paleoclimate evidence (where this myth originated) and then the historical evidence, where this claim can be conclusively refuted.

Paleoclimate Evidence

The "CO2 always follows temperature" myth has its origin a misunderstanding of Petit et al 1999[1], where the Vostok ice core data was published, and plots of CO2 and Antarctic temperature (AT) showed what appeared to be a multi-century lag between CO2 and AT proxy data. From the observation that CO2 lagged Antarctic temperature during the last four glacial cycles, contrarians predictably modified this observation by dropping "Antarctic" and adding "always," giving us the familiar refrain, "CO2 always lags temperature." That mantra was never technically correct, but developments since 1999 have shed more light on what was actually going on in the ice core data.

1. In 2012, Shakun et al[2] showed that while CO2 lags AT, it leads changes in GMST. That is, global temperatures follow CO2.
2. In 2013, Parrenin et al[3] re-evaluated the dating of the proxies for AT and CO2 and found that, after correcting the dating of these proxies, CO2 and AT actually rise concurrently with each other.

I go into a lot more detail about this in another post. To summarize, during these glacial cycles orbital forcings triggered regional warming, which caused the outgassing of CO2 from the oceans as ocean waters warm (CO2 is less soluble in warm water). CO2 amplifies this warming signal (as do changes in ice-albedo) so that the more localized warming signal becomes global in scope, and so GMST follows the increase in CO2. Given the resolution of ice core proxy evidence, this looks like AT and CO2 increase at the same time and GMST follows. It's been well understood that CO2 can and does operate as a feedback when orbital cycles trigger warming. Since CO2 changes by ~100 ppm during the glacial cycles, and GMST changes by ~6°C, we can estimate that CO2 increases by ~17 ppm for every 1°C of warming. So it's true that CO2 can lag AT during the glacial cycles (though not by hundreds of years), but GMST still follows CO2. This can be seen below.

GMST Follows CO2 in Paleoclimate Reconstructions

The above graph shows CO2 with Osman's reconstruction [4] of GMST for the last 24,000 years with CO2 data from Vostok (added by me). This clearly clearly shows CO2 increasing prior to the increase in GMST.

Historical Evidence

At other times in the Earth's climate history, perturbations of the carbon cycle from long-term eruptions of large igneous provinces (LIPs) introduce "new" carbon to the carbon cycle by venting carbon to the atmosphere through volcanic activity. Unlike the glacial cycles, which just change the balance of CO2 in the oceans vs the atmosphere, long-term eruptions of LIPs add to the total amount of CO2 to the carbon cycle. When this happens, CO2 concentrations increase in the atmosphere, and the partial pressure of CO2 above the oceans increases, and this causes the oceans to absorb a fraction of the CO2 emissions via to Henry's Law. In these cases, CO2 triggers warming and is the driver of global warming. The human combustion of fossil fuels perturbs the carbon cycle in a similar way. We're taking carbon that has been sequestered from the atmosphere for hundreds of millions of years and adding that carbon to the carbon cycle; the total amount of carbon in the carbon cycle is increasing. That perturbation of the carbon cycle has made the oceans a net carbon sink, taking up a significant fraction of human emissions.

This is pretty easy to demonstrate this to be the case since 1750 with data from the 2025 Global Carbon Budget.[5] We know from historical data that CO2 was about 278 ppm in 1750, which is the equivalent atmospheric carbon mass of 591 GtC. Human emissions from fossil fuel and industry (FFI) and land use change (LUC) has totaled 752 GtC, which would be enough to increase CO2 concentrations by 353 ppm to 631 ppm. However, CO2 concentrations today have only risen to 424 ppm. Human emissions have literally totaled 2.4x the atmospheric growth of CO2. This means that human carbon emissions are responsible for 100% of the increase 147 ppm increase in CO2 and that the land and oceans have become carbon sinks, taking up about 440 GtC of our emissions. 

This is due to both biological processes (including photosynthesis in land and oceans) and Henry's Law, which states that the amount of CO2 dissolved in the oceans is proportional to the partial pressure of CO2 in the atmosphere above the oceans. As CO2 increases from human emissions, the land takes up a fraction of our emissions (greening) and the oceans take up another fraction of our emissions (ocean acidification). And in the oceans, there are two dynamics at play related to Henry's Law:

1. Human carbon emissions generates an atmosphere-to-ocean CO2 flux.
2. Ocean warming from increased CO2 causes an ocean-to-atmosphere CO2 flux

Both of these occur at the same time, but as I discuss in another post the CO2 flux to the oceans is about 10x greater than the flux to the atmosphere. And this should make intuitive sense. Ocean warming has been slower than land warming, so the oceans have warmed by about 1°C. If CO2 was increasing as it was during the glacial cycles, we should see only about a 17 ppm increase in CO2 (about 36 GtC). But CO2 has increased by 147 ppm (312 GtC) or almost 9x as much as would be expected from ocean warming, and the land/ocean sinks have taken up the remainder of 752 GtC - 312 GtC = 440 GtC. Since both the land and oceans are net carbon sinks, they cannot be sources for the increase in CO2. This means necessarily that CO2 is not following the increase temperature as the oceans outgas CO2 in response to warming. The mass-balance data we have from our emissions rules out that possibility, and this can be confirmed with four other independent lines of evidence I describe here. So we can conclusively rule out the possibility that CO2 has lagged temperature since 1750. There are no natural carbon sources on land or the ocean to contribute to an increase in atmospheric CO2. It has to be human emissions.

These conclusions are also supported by the Stips et al 2016 [6] analysis of CO2 and T causality, which found both 1) causation in the direction of AT -> CO2 using ice core data for the last 800K years and 2) causation in the direction of CO2 -> GMST using historical data, consistent with the theoretical predictions of climate science. They are also confirmed by the fact that current global warming has not yet eclipsed the peak warmth of the last interglacial (LIG) about 120,000 years ago. This make sense if GMST lags CO2, since it takes time for the Earth's climate system to reach full equilibrium with a rapid change in forcings. However, if CO2 always lags warming, and if current warming is causing the 147 ppm increase in CO2, then we would expect even warmer temperatures during the LIG to be followed by CO2 concentrations in excess of current CO2 concentrations. But that doesn't happen. The highest concentration of CO2 during the Quaternary is about 300 ppm.

I should also note that some have used some somewhat comical mathematical tricks to get around this problem. They differentiate CO2 and temperatures to show that variability in CO2 lags variability in temperature, and they (wrongly) claim that because of this lag, CO2 always follows temperature. I have a couple posts on this here and here. The observations regarding variability in CO2 are real, since ENSO does effect the carbon sink, but this is a natural control on the variability of atmospheric CO2, not the long-term increase in CO2. These arguments make conclusions about the long-term signal from data that has removed the long-term signal by differentiation. It's easy to create the impression that there is no long-term trend if you detrend your graph. And none of the people making this argument can explain 1) where the additional CO2 comes from supposedly caused by temperature or 2) why the increase in atmospheric CO2 tracks so closely with human emissions.

In fact, it's long been documented that GMST increases linearly with cumulative emissions, and the relationship is quite strong (r^2 = 0.88). A simple regression between GMST and cumulative emissions shows that global warming has been occurring at a rate of about 0.018°C for every 10 GtC emissions. This is of course approximate, since it doesn't account for emissions of other GHGs or changes in aerosol pollution. However, this value is within the CI for the IPCC's value of 0.0165°C for 10 GtC.

So it's technically true that AT can lead CO2 by a very small amount of time when local warming is triggered by orbital cycles. In this case, the dominant CO2 flux is from the oceans to the atmosphere, but global warming follows CO2. However, for perturbations of the carbon cycle from volcanic activity or human emissions, the dominant CO2 flux is from the atmosphere to the oceans, and the oceans acidify. This happened during the PETM, which led to a mass extinction of benthic foraminifera. And the oceans are acidifying now in response to human carbon emissions as well. 

References:

[1] Petit, Jean Robert et al (1999): Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature, 399(6735), 429-436, https://doi.org/10.1038/20859

[2] Shakun et al, “Global Warming Preceded by Increasing Carbon Dioxide Concentrations during the Last Deglaciation” Nature 484(7392):49-54 · April 2012
https://www.researchgate.net/publication/223987444_Global_Warming_Preceded_by_Increasing_Carbon_Dioxide_Concentrations_during_the_Last_Deglaciation

[3] Parrenin, F. et al. “Synchronous Change of Atmospheric CO2 and Antarctic Temperature During the Last Deglacial Warming.” Science 339, 1060 (2013).
DOI: 10.1126/science.1226368
https://pdfs.semanticscholar.org/d61d/0fbcb5828af1d434d1bd0282ed36e0f00d2a.pdf

[4] Osman, M.B., Tierney, J.E., Zhu, J. et al. Globally resolved surface temperatures since the Last Glacial Maximum. Nature 599, 239–244 (2021). https://doi.org/10.1038/s41586-021-03984-4

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[6] Stips, A., Macias, D., Coughlan, C. et al. On the causal structure between CO2 and global temperature. Sci Rep 6, 21691 (2016).
https://www.nature.com/articles/srep21691