Correlation Between CO2 and Temperature on Various Time Scales

You sometimes hear that, at least on certain time scales, CO2 and global temperature (GMST) don't correlate very well or even that the two go in opposite directions. The implication drawn from this is that CO2 can't be the primary driver of climate changes. What I want to show here is that this claim is categorically false. On virtually all time scales in the Phanerozoic, CO2 and GMST correlate very well, especially when taking into consideration that GMST correlates with the log of CO2. 

The best way for me to demonstrate this point is to simply show the correlation. Where I can, I convert CO2 to forcings (using RF = 5.35*ln(CO2/280)) and and plot CO2 forcings on the x-axis and GMST on the y-axis. This gives us two advantages: first, it allows us to calculate the r^2 for that correlation, and second, the slope of the correlation gives us an indication of sensitivity - that is, the temperature response to changes in CO2 forcings. A few caveats are in order here, though:

1. CO2 isn't the only driver of climate changes, so a simple regression of CO2 and GMST only reflects sensitivity accurately when other forcings are either negligible or cancel out.
2. When other forcings (other GHGs, aerosols, etc) play a more significant role, you may see some deviation between CO2 and GMST; this is expected because while CO2 may be the primary or dominant driver, it's not the only driver.
3. Natural variability (like ENSO) on decadal time scales explain why some years are warmer than the CO2 trend and some are cooler than the CO2 trend.
4. Sometimes there is a lack of correlation because of data poverty (few datapoints) and/or biases that affect proxy measurements of CO2 or GMST. So when we see time frames where there is less of a correlation, that could be due either to the effect of other forcings or data poverty/biases affecting the reconstruction.
5. The further back in geologic time we go, the more likely that data poverty and biases will play a significant role when the correlation is less strong.

We don't have perfect data, but one thing is pretty clear: during time frames when we have the best and most accurate data, we also find the strongest correlation between CO2 and GMST. 

Last 75 Years

The data since 1950 is very good, and the correlation is very strong, with an r^2 = 0.91. The slope of this correlation is 0.682 C/W/m^2, which implies a TCR = 2.5 C. However, the reduction of aerosol pollution since the 1980s is not accounted for here, so we can't make too much of this; I strongly suspect that not accounting for aerosols biases the slope towards higher sensitivity.

Nevertheless, the there is no denying the strength of the correlation on this time scale. And yes, I know that correlation does not mean causation, but this post is not about demonstrating causation. I'm simply rebutting the claim that there is a lack of correlation on some time scales.

Last 175 Years

Since 1850, the correlation between CO2 and GMST is still quite strong with an r^2 = 0.88. The slight reduction in correlation is mostly due to cool SSTs between 1900-1930 and warm years during WWII. In a couple recent post, I covered some data biases that may have affected the 1900-1930 time frame. Nevertheless, the slope here is 0.632 C/W/m^2, which implies a TCR = 2.3 C. Again this assumes all other forcings are negligible or cancel out. 

You can see areas where GMST deviates slightly more on during times where radiative forcings were smaller than when they are larger, but overall, the correlation remains undeniable.

Last 2000 Years

Over the last 2000 years, both GMST and CO2 are hockey stick shaped. For this time frame, I haven't found a good way to plot the correlation with CO2 forcings on the x-axis, but if I do, I'll add that to this post. But it's pretty clear that GMST varies strongly with CO2. The temperature series here is from Pages2K.

Last 24,000 Years

If we extend our time scale back tot the time of the last glacial maximum, we still see a strong correlation between CO2 and GMST. This reconstruction comes from Marcott & Shakun 2021 (I added CO2 to the graph), and clearly lower CO2 correlates with cooler temperatures. The largest deviation between the two comes from the mid-Holocene (about 7000 years ago) during the so-called Holocene "conundrum." It's possible that seasonal biases are affecting the GMST reconstruction here, or also possibly that other forcings are at work here.

And yes, I'm well aware of claims that CO2 lags temperature in these glacial cycles. That claim is based on outdated evidence. While warming from orbital cycles likely triggered a CO2 response, GMST warming actually follows CO2.

Last 800,000 Years

Extending back to the last 800,000 years allows us get a good chunk of the glacial cycles of the Quaternary, especially those cycles that follow the Mid-Pleistocene Transition. Panels B and D below show global temperatures (B) and various forcings with CO2 in red (D). Accounting for these forcings allowed their model to reproduce the GMST variability quite well, as you can se in Panel A. One very valuable aspect of this study is that it shows the relative magnitude of the forcings affecting GMST, and on these time scales, while CO2 is the dominant forcing, it is not the only forcing.

Last 66 Million Years

Emily Judd's recent paper has produced the most comprehensive large scale reconstruction of both CO2 and GMST for the Phanerozoic. She also performed a simple regression of CO2 and GMST for the Cenozoic and most of the Phanerozoic. In her reconstruction the correlation is r^2 = 0.94 and temperature increases ~8.2 C for 2xCO2 on geologic time scales. Since there are other known forcings at work here, most importantly the the long-term increase in solar luminosity, this value should not be taken as an Earth System Sensitivity estimate, but it still shows that changes in CO2 does a very good job of explaining changes in GMST on geologic time scales.

Last 485 Million Years

When Judd extends her reconstruction to the last 485 million years of the Phanerozoic, In her reconstruction the correlation drops to r^2 = 0.52 and temperature response decreases to ~7.7 C for 2xCO2 on geologic time scales. Issues of data poverty are significant on this time scale, especially in the Mesozoic, but overall the correlation is quite good.

The scatter from the overall trend is largest between 500 ppm and 1200 ppm CO2, and most of it comes from a portion of the Mesozoic, where there evidence of warm temperatures without a corresponding increase in CO2. Judd's paper refers to this as the Mesozoic Conundrum. It seems likely this will be resolved with more proxy data for CO2 and GMST as well as a better accounting of other forcings that may be at work here.

Conclusion

It's remarkable to me that the evidence we have shows such good correlation even as far back as time scales of hundreds of millions of years. Obviously there is still work to be done, but the evidence we have is clear enough to show that there is a robust correlation between CO2 and GMST on decadal centennial, millennial and on geologic time scales. And while there certainly are other forcings at work, and CO2 does not explain all changes in GMST, the data we have broadly supports the conclusion that CO2 is the dominant driver of changes in GMST.