# Correlation between CO2 and Temperature

Here’s the global average temperature anomaly since 1880 (let’s use the data from NASA, shall we?).

Now, I’ll add to that graph the data for atmospheric CO2 concentration. In fact I’ll plot (as a function of time) the quantity 0.0101 x CO2 – 3.265. The triangles in red are yearly average values measured at the Mauna Loa atmospheric observatory in Hawaii; the blue triangles are values measured in the Law Dome ice core (from Antarctica).

I could run statistical tests (OK, I already have) and confirm that the correlation between global temperature and CO2 is strong. It’s very strong. It’s most notable since about 1975; from then until the present, both CO2 and temperature have been rising.

Yet some people don’t think so. They look at the same graph — or a different graph (often one created by some climate denier) and say things like “no correlation between temperature and CO2 except for a brief period from 1980 to 1999″ and “there was a climate hiatus after 1999.”

Look at the graph. If you know how to test these propositions statistically, please do so. Please. Then ponder … what kind of thinker says those things?

Covfefe, anyone?

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### 31 responses to “Correlation between CO2 and Temperature”

1. Robert

Nice to see another article from you.

In response to your “challenge”, I did a couple of simple things with the data. Linear regression of CO2 vs Temp anomaly from 1975 through 2021 gave an R2 value of 0.89 and a P value of 5.74e-23. Linear regression of Log(CO2) vs temp anomaly gave similar values (R2 = 0.89, P = 5.04e-23). So yeah, the relationship (not surprisingly) appears highly statistically significant using these simple tests.

At this point, I’m not sure what kind of “thinker” would still be denying the nature of this relationship.

2. kinimod

I was actually since long thinking about this stunning parallelism and I believe it partly can be explained by a simple model:
The part of the radiation absorbed directly by the oceans doesn’t amount to much temperature increase because of the high thermal mass.
The part of the radiation absorbed by land mostly is transferred into the atmosphere.
90 % of all radiative forcing induced absorbtion ends up in the oceans, so apart from losses to space, which are already accounted for in radiative forcing, this is the main energy flow out of the atmosphere.
The simple model is to assume ocean temperature as constant as well as the thermal resistance of the air – ocean boundary layer. Then the temperature difference air – ocean is proportional to the power flow into the atmosphere i.e. the radiative forcing.
The missing link is the connection of radiative forcing and GHG concentrations. I could neither find a neat relation nor a 1880 – 2022 graph of r.f. – I am sure they are existing, only I did not find them yet. If anybody has a link I would be grateful.
If r.f. is reasonably proportional to CO2 concentrations, the linearity would be explained.

• Al Rodger

Kinimod,
The CO2 forcing (the largest but by no means the entire of forcing) has a simple relationship with CO2 concentrations ΔF = 5.35 x In(C/C0). The effect of using CO2 forcing instead of CO2 concentrations would be to amplify the CO2 effect during the early years. Thus the ΔC(oncentration) post-1960 is 4x ΔC 1880-1960 while the ΔF(orcing) post-1960 is only 3 x ΔF 1880-1960.
This effect (along with the added time allowing those early forcings to act more completely) explains one bit of the denialist nonsense often waved by the likes of Victor the Troll (who we learn inspired this OP from Tamino) aka the composer, musicologist, film maker, media artist, poet and dramatist Dr Victor Grauer from Pittsburg who behaves as a commenter on climatology at a similar level to that of Eric Morcombe’s rendition of Grieg’s piano concerto.

But as CO2 forcing is by no means the entire forcing, the next step would be to add in all GHG forcing and then the other anthropogenic & natural forcings and thus complete the account. This yields a relationship something like that graphed our by SkS here, this all made dramatically wobbly by the volcanic forcings. And because of all those wobbles, it is probably better to engage a climate model to cope with the wobbles, rather than a straightforward mathematical analysis.

• kinimod

Al, thx for this response. I had the logarithmic concentration->forcing relation somewhere in the back of my mind, though not active while writing, and it does indeed not fit to the ‘mind sized model’.
The forcing-temp plot you gave is actually what I was looking for, thx for that. We see there still quite a good fit, though not perfect. The wobbles I just do overlook, given the system inertia I feel this is justified. We see notable deviation around 1885 (less forcing than warming) and 1905 – 1925 (more forcing than warming), which demand an explanation, but since then, the parallelism seem good to me.
So ‘mind sized model’ does not work with the relation co2 concentration -> temperature and what we see is a kind of coincidence, with other effects filling in the lack of co2-concentration induced forcing.
But i m v the forcing -> temperature relationship may be approximatable with the ‘mind sized model’. If this is the case, it gives us a feeling of understanding what’s happening, which at least I find satisfying.

• MarkR

“Then the temperature difference air – ocean is proportional to the power flow into the atmosphere i.e. the radiative forcing.”

I think I’ve worked out why climate model air-ocean temperatures change differently when CO2 increases.

CO2 warms the atmosphere within days-to-weeks, before the ocean really gets to respond[1]. The radiative forcing then drives ocean and air warming. Of all the changes, the most consistent is extra evaporation that cools the ocean surface and eventually that vapour condenses, warming the atmosphere. This explains why the skin layer of the ocean warms less than the air above, at least in climate models.

• Bob Loblaw

Keep in mind that when it comes to altering the climate over a period of decades, it is the radiation balance with space that matters, not the surface changes.

3. mk chen

Correlation means nothing. How do you prove that there is no 3rd, 4th, 5th factors or more that affect both temperature and CO2?

[Response: You sound like the type of thinker who agrees with the nonsense.]

• chrisd

Correlation means plenty if you can establish the physical relation, which had already been done when the Civil War broke out. The correlation is what we call “evidence.”

• Didactylos

Occam’s razor applies here. You need to find your unknown factor that affects both temperature and CO2, and also an extra factor that exactly offsets the known anthropogenic contribution to CO2, and another that exactly offsets the expected effect of increased CO2 on temperature. That’s quite some mental gymnastics!
Of course there are lots of other factors involved, they are just not dominant.
When there is a well-established physical causal link, the correlation should not be a huge surprise.

• How do you prove that a chocolate cake isn’t orbiting Jupiter?

• mrkenfabian

After looking at and quantifying affects from CO2, methane, nitrous oxide, hydrocarbons, stratospheric ozone, tropospheric ozone, stratospheric water vapor, albedo changes from black carbon on snow, albedo from land use changes, atmospheric aerosols, contrails and solar irradiance… that would be have to 13th,14th and 15th factors. And what factors, that haven’t been considered, would those be?

• michael Sweet

Mrkenfabian,
You left off chlorofluorocarbons and cosmic rays ;).

• mrkenfabian

Michael – a moment after clicking on Post Comment I thought of more, eg orbital cycles/variations (although may be included in changes to solar irradiance?) and internal heat/volcanic activity. I’d be curious just how many factors have actually been given consideration – more than I cited, certainly.

The list I gave seems to encompass all the changes that have been looked at and found to have an impact greater than “insignificant” – ie made it into IPCC graphs of changes to radiative forcings. Others have been looked at, quantified and been so small (over the time scales of current climate change) they can be set aside – with quantification and reasoning to support such “omissions”.

• Al Rodger

mrkenfabian,
The factors tabled in IPCC AR5 AII Table 1.2 (which runs to 2011) gives a list of positive & negative climate forcings that were considered significant. It shows CO2 to be 82% of the total post-industrial climate forcing (averaged 2000-11).
The NOAA AGGI gives positive GH forcings which give an equivalent up-to-2011 figure of 63% CO2, a proportion which increases to 65% for the to-2020 figure.
I don’t see any sane argument that points to CO2 not being the big daddy of AGW, especially given its longevity in the atmosphere.

And do note that the commenter mk chen you were replying-to speculates about “factors … that affect both temperature and CO2” implying that, as well as CO2 being but one cause of rising global temperatures, he is unconvinced that rising levels of atmospheric CO2 emanate from chimneys and tail-pipes.

Mind, he is correct to say that “Correlation means nothing” although he forgets to add the adjoiner “…on its own.” And the physics tells us it would be mighty strange if this correlation along with other paleoclimate data didn’t exist.

• Ken Fabian

Thanks Al. The thoroughness is actually impressive – the very opposite of the claimed neglect of other factors besides CO2.But given a mechanism for greenhouse gases to influence global temperatures goes back to the early 1800’s and nothing else that includes a physically plausible explanation has been apparent,the “excess” focus on CO2 seems quite reasonable.

4. Øyvind

Figure 2.10 in AR6 WG1 report shows an estimate of effective radiative forcing (ERF) over the period you ask for. ERF is defined as radiative forcing is the forcing you will find if there was no change in temperature, often simplified to no change in SST and sea-ice. The actual forcing as seen at the Earth during the period is something else since SST has changed over the period. (Table 2.4)

5. Carbomontanus

Hr Tamino

I have allways wondered about that bump or heap around 1940

To me, it is not a hockeystick because that is vulgar. It is a scytch. The Mann with the Scytch….. because that is more threatrening, and what people are so scared of and will not admit.

But, that ERROR in the blade at around 1940 is what I have to repair in all my knives and scytches and try and hammer and weld and grind it away.

Can anyone tell me what that actually is?

• David B Benson

Carbomontanus — The increase in the measured temperature from 1940 to 1945 is an artifact of the difficulty of making ocean temperature measurements during WW2.

• Carbomontanus

Hr Benson

Obviously not, because that follows and shows up earlier than 1940-45.

• Robert

@Carbomontanus & Benson: WW2 is considered by some to have its origin with the invasion of Manchuria by the Japanese in 1931. Also, in Europe, things became bad at least by 1939. You may be able to find other upheavals during these periods. In any case, it would be good to see a reference to the assertion that the global political situation at that time lead to this “artifact”. Not disputing it, just would like to see a credible reference.

• b fagan

@Carbomontanus – here’s a link to NOAA’s Climate at a Glance showing the global annual temperatures from 1920 to 1970.

As a reference, World War II ran from September 1939 to September 1945. In this zoomed-in span, I’m clearly seeing warmer temp start in 1940 and end in 1945.

https://www.ncdc.noaa.gov/cag/global/time-series/globe/land_ocean/ann/3/1920-1970

• b fagan

Well, NOAA Climate at a Glance is down right now, but I’d seen the warm anomaly in global ocean temps during that WW2 timeframe. So I did a search and got some recent papers discussing it. ( I have not read any of them )

Pfeiffer, M., Zinke, J., Dullo, WC. et al. Indian Ocean corals reveal crucial role of World War II bias for twentieth century warming estimates. Sci Rep 7, 14434 (2017). https://doi.org/10.1038/s41598-017-14352-6

Journal of Climate has this: Correcting Observational Biases in Sea Surface Temperature Observations Removes Anomalous Warmth during World War II – Duo Chan and Peter Huybers
https://journals.ametsoc.org/view/journals/clim/34/11/JCLI-D-20-0907.1.xml

And an article on the NOAA PMEL site
New citizen science project launched for U.S. Navy weather observations from World War II
https://www.pmel.noaa.gov/news-story/new-citizen-science-project-launched-us-navy-weather-observations-world-war-ii

6. Oortclooud

The slopes are not similar:

https://woodfortrees.org/plot/gistemp/from:1979/to:2020/trend/plot/uah6/from:1979/to:2020/trend/plot/esrl-co2/from:1979/to:2020

[Response: Perhaps you should read the post more closely.]

• Al Rodger

Oortclooud,
The advice from our host is probably not so helpful as you likely poked both your eyes out trying to count these things we call “number” which are used to assess global temperature and atmospheric CO2 levels. Thus you didn’t notice the “offset” and “scale” functions provided at WoodForTrees. I’m sure that if you had, you would have manipulated the graphical engine there to produce an image showing the actual relationship between GISTEMP/UAH6 and MLO CO2. It is interesting that even such a simplistic analysis demonstrates strange goings-on in that GISTEMP & UAH6 seem to diverge (from each other) through the period 2000 to 2010.

• chrisd

How’s about we dispense with your little y-axis trick and scale the same data more appropriately (like Tamino did):

https://woodfortrees.org/plot/gistemp/from:1979/to:2020/trend/scale:100/offset:320/plot/esrl-co2/from:1979/to:2020

The slopes look pretty similar to me.

• And what exactly leads you to think that the slopes *should* automatically be visually similar when you pick the y-axis scaling for the two variables essentially at random?

• Didactylos

Temperature and CO2 concentration use completely different scales, so comparing the trends visually requires that they be rescaled appropriately.

Just visually matching a short linear trend, the scale can be chosen such that you get a perfect match, or nothing close to a match. Either way, it is virtually completely meaningless. All you can say is both are increasing (although your default scale hides even this much).

Here are the same series with similar scaling to Tamino. Without the Law Dome ice core data, the correlation is less compelling, but the increase is shown clearly:
https://woodfortrees.org/plot/gistemp/from:1880/to:2020/mean:12/plot/uah6/from:1880/to:2020/mean:12/offset:0.5/plot/esrl-co2/from:1880/to:2020/offset:-325/scale:0.01

UAH is an outlier in terms of temperature datasets. RSS uses the same raw data and analyses it much better.

• jgnfld

I haven’t seen anyone compress a slope so well by cherrypicking a y axis since the old denier classic of graphing temps in Kelvin degrees starting at 0 which used to be popular about 20 years ago!

Fine job of propaganda and/or simple ignorance, oort! You are definitely waayyy out there!

7. People who don’t want to see the correlation between CO2 and temperature remove the trend from each dataset and then observe that rapid fluctuations in temperature do not also appear in CO2 concentration. The procedure doesn’t make sense scientifically, but it gives the desired result.

8. tamino-sama,

Great minds think alike. We seem to have posted our responses to Victor at the same time:

https://bartonlevenson.com/GreatStasis.html

9. barry

This ‘skeptic’ CO2/temp correlation appears from time to time.

https://www.woodfortrees.org/plot/uah6/from:1979/normalise/plot/esrl-co2/from:1979/derivative/mean:12/normalise

Look at that! CO2 closely matches monthly temps. Monthly anthropogenic output can’t account for this match. Temps drive CO2!!

I’m not a maths guy, let alone a statistics guy, but it seems to me that this correlates minute fluctuations in the rate of change in atmospheric CO2 with short-term temp fluctuation that can’t possibly account for the total growth over the last century (or the ML record since 1957). I’ve read that ENSO has short-term impact on CO2 due to effects on land biomass.

Ferdinand Engelbeen had a fairly extensive look at it, but it was a little opaque to me and I wondered if there was a clearer breakdown.