A study: The temperature rise has caused the CO2 Increase, not the other way around

Guest post by Lon Hocker

A commonly seen graph illustrating what is claimed to be a causal correlation between CO2 and temperature, with CO2 as the cause. (Image courtesy Zfacts.com)


Differentiating the CO2 measurements over the last thirty years produces a pattern that matches the temperature anomaly measured by satellites in extreme detail.    That this correlation includes El Niño years, and shows that the temperature rise is causing the rise in CO2, rather than the other way around.  The simple equation that connects the satellite and Mauna Loa data is shown to have a straight forward physical explanation.


The last few decades has shown a heated debate on the topic of whether the increase of CO2 in the atmosphere is causing rising temperatures.  Many complex models have been made that seem to confirm the idea that anthropological CO2 is responsible for the temperature increase that has been observed.  The debate has long since jumped the boundary between science and politics and has produced a large amount of questionable research.

“Consensus View”

Many people claim that anthropological CO2 is the cause of global warming.  Satellite temperature data, http://vortex.nsstc.uah.edu/data/msu/t2lt/uahncdc.lt, and Mauna Loa CO2 measurements, ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_mlo.txt, are well accepted and freely available to all researchers.  Figure 1 shows a plot of the Ocean Temperature Anomaly from the satellite data shows a general rising trend.  Shown along with the temperature data is a simple linear model showing the temperature rise as a linear function of CO2 concentration.   This shown linear model is:

Temperature Anomaly =  (CO2 -350)/180

No attempt has been made to optimize this model.  Although it follows the general trend of the temperature data, it follows none of the details of the temperature anomaly curve.  No amount of averaging or modification of the coefficients of the model would help it follow the details of the temperature anomaly.

Figure 1:  Ocean Temperature Anomaly and linear CO2 model

Derivative approach

An alternate approach that does show these details is that the temperature anomaly is correlated with the rate of increase of CO2.  I discovered this independently and roughly simultaneously with Michael Beenstock and Yaniv Reingewertz http://economics.huji.ac.il/facultye/beenstock/Nature_Paper091209.pdf.

Applying this model to the Mauna Loa data not only shows the overall trend, but also matches the many El Niño events that have occurred while satellite data has been available.  The Figure 2, shows the derivative model along with the observed Ocean Temperature Anomaly.  The model is simply

Temperature Anomaly = (CO2(n+6) – CO2(n-6))/(12*0.22) – 0.58

where ‘n’ is the month.  Using the n+6 and n=6 values (CO2 levels six months before and six months after) cancels out the annual variations of CO2 levels that is seen in the Mauna Loa data, and provides some limited averaging of the data.

The two coefficients, (0.22 and 0.58) were chosen to optimize the fit.  However, the constant 0.58 (degrees Celsius) corresponds to the offset needed to bring the temperature anomaly to the value generally accepted to be the temperature in the mid 1800’s when the temperature was considered to be relatively constant.  The second coefficient also has a physical basis, and will be discussed later.

Figure 2:  Ocean Temperature Anomaly and derivative CO2 model

There is a strong correlation between the measured anomaly and the Derivative model.  It shows the strong El Niño of 1997-1998 very clearly, and also shows the other El Niño events during the plotted time period about as well as the satellite data does.


El Niño events have been recognized from at least 1902, so it would seem inappropriate to claim that they are caused by the increase of CO2.  Given the very strong correlation between the temperature anomaly and the rate of increase of CO2, and the inability to justify an increase of CO2 causing El Niño, it seems unavoidable that the causality is opposite from that which has been offered by the IPCC.  The temperature increase is causing the change in the increase of CO2.

It is important to emphasize that this simple model only uses the raw Mauna Loa CO2 data for its input.  The output of this model compares directly with the satellite data.  Both of these data sets are readily available on the internet, and the calculations are trivially done on a spreadsheet.

Considering this reversed causality, it is appropriate to use the derivative model to predict the CO2 level given the temperature anomaly.  The plot below shows the CO2 level calculated by using the same model.  The CO2 level by summing the monthly CO2 level changes caused by the temperature anomaly.

Month(n) CO2 = Month(n-1) CO2 + 0.22*(Month(n) Anomaly + 0.58)

Figure 3: Modeled CO2 vs Observed CO2 over Time

Not surprisingly the model tracks the CO2 level well, though it does not show the annual variation.  That it does not track the annual variations isn’t particularly surprising, since the ocean temperature anomaly is averaged over all the oceans, and the Mauna Loa observations are made at a single location.  Careful inspection of the plot shows that it tracks the small inflections of the CO2 measurements.

The Mauna Loa data actually goes back to 1958, so one can use the model to calculate the temperature anomaly back before satellite data was available.  The plot below shows the calculated temperature anomaly back to 1960, and may represent the most accurate available temperature measurement data set in the period between 1960 and 1978.

Figure 4: Calculated Temperature Anomaly from MLO CO2 data

Precise temperature measurements are not available in the time period before Satellite data.  However, El Niño data is available at http://www.cpc.noaa.gov/products/analysis_monitoring/ensostuff/ensoyears.shtml making it possible  to show the correlation between the calculated temperatures and the and El Niño strength.  Note that the correlation between temperature anomaly and El Niño strength is strong throughout the time span covered.

Figure 5: Calculated Temp CO2 from CO2 and ENSO data

An Explanation for this Model

The second free parameter used to match the CO2 concentration and temperature anomaly,  0.22 ppm per month per degree C of temperature anomaly, has a clear physical basis.  A warmer ocean can hold less CO2, so increasing temperatures will release CO2 from the ocean to the atmosphere.

The Atmosphere contains 720 billion tons of CO2 (http://eesc.columbia.edu/courses/ees/slides/climate/carbon_res_flux.gif), the ocean 36,000 billion tons of CO2.  Raising the temperature of the ocean one degree reduces the solubility of CO2 in the ocean by about 4% (http://www.engineeringtoolbox.com/gases-solubility-water-d_1148.html)

solubility diagram - carbon dioxide - CO2 - in water at different  temperatures

Figure 6: Solubility of CO2 in water (While CO2 solubility in seawater is slightly different than in pure H2O shown above in Figure 6, it gives us a reasonably close fit.)

This releases about 1440 billion tons of CO2 to the atmosphere. This release would roughly triple the CO2 concentration in the atmosphere.

We have seen what appears to be about a 0.8 degree temperature rise of the atmosphere in the last century and a half, but nowhere near the factor of three temperature rise.  There is a delay due to the rate of heat transfer to the ocean and the mixing of the ocean.  This has been studied in detail by NOAA, http://www.oco.noaa.gov/index.jsp?show_page=page_roc.jsp&nav=universal,  and they estimate that it would take 230 years for an atmospheric temperature change to cause a 63% temperature change if the ocean were rapidly mixed.

Using this we can make a back of the envelope calculation of the second parameter in the equation.  This value will be approximately the amount of CO2 released per unit temperature rise (760 ppm/C)) divided by the mixing time (230 years). Using these values gives a value of 0.275 ppm /C/month instead of the observed 0.22 ppm/C/month, but not out of line considering that we are modeling a very complex transfer with a single time constant, and ignoring the mixing time of the ocean.


Using two well accepted data sets, a simple model can be used to show that the rise in CO2 is a result of the temperature anomaly, not the other way around.  This is the exact opposite of the IPCC model that claims that rising CO2 causes the temperature anomaly.

We offer no explanation for why global temperatures are changing now or have changed in the past, but it seems abundantly clear that the recent temperature rise is not caused by the rise in CO2 levels.


Lon Hocker describes himself as: “Undergrad physics at Princeton.  Graduate School MIT.  PhD under Ali Javan the inventor of the gas laser.  Retired president of Onset Computer Corp., which I started over 30 years ago.  Live in Hawaii and am in a band that includes two of the folks who work at MLO (Mauna Loa Observatory)!”

Data and calcs available on request


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Response of a warmist worm to this paper: http://images.clipartof.com/thumbnails/35089.jpg

Quinn the Eskimo

Along similar lines is The Acquittal of CO2, by Jeffrey A. Glassman, http://www.rocketscientistsjournal.com/2006/10/co2_acquittal.html.
The Abstract:

Carbon dioxide in the atmosphere is the product of oceanic respiration due to the well‑known but under‑appreciated solubility pump. Carbon dioxide rises out of warm ocean waters where it is added to the atmosphere. There it is mixed with residual and accidental CO2, and circulated, to be absorbed into the sink of the cold ocean waters. Next the thermohaline circulation carries the CO2‑rich sea water deep into the ocean. A millennium later it appears at the surface in warm waters, saturated by lower pressure and higher temperature, to be exhausted back into the atmosphere.
Throughout the past 420 millennia, comprising four interglacial periods, the Vostok record of atmospheric carbon dioxide concentration is imprinted with, and fully characterized by, the physics of the solubility of CO2 in water, along with the lag in the deep ocean circulation. Notwithstanding that carbon dioxide is a greenhouse gas, atmospheric carbon dioxide has neither caused nor amplified global temperature increases. Increased carbon dioxide has been an effect of global warming, not a cause. Technically, carbon dioxide is a lagging proxy for ocean temperatures. When global temperature, and along with it, ocean temperature rises, the physics of solubility causes atmospheric CO2 to increase. If increases in carbon dioxide, or any other greenhouse gas, could have in turn raised global temperatures, the positive feedback would have been catastrophic. While the conditions for such a catastrophe were present in the Vostok record from natural causes, the runaway event did not occur. Carbon dioxide does not accumulate in the atmosphere.


Looking at the graph – Modeled CO2 vs. Time – comparing measured CO2 to Model predictions – any reasonable, scientificly trained person would have to believe that CO2 controls the temperature of the seasons to believe CO2 controls global temperature rises.
Use some common sense Warmers.

Jim G

The first rule of regression analysis, or any other correlation method, is to beware of implied cause and effect. Many dependent variables can be correlated to many independent variables but cause and effect should not be implied. The stock market’s swings with the length of women’s skirts was a classic used many years ago. Another rule is to beware of exogenous variables. The hypothesis that increase in co2 is caused by temperature increase is just as viable as the AGW hypothesis but also just as subject to potential effects of other variables. I love this site for its lack of “lemming instinct” and challenge of the conventional wisdoms of the day. However, I think we many times are picking at flycrap in trying to disprove what has never been scientifically proven in the first place.


Good grief, Lon! I hope you are’nt dependent on AGW grants.
You would be out of a job before you know it!
Very elegant to think of the derivate, I must say. Well done!

This is one of the first things an undergraduate geology student learns (a warmer ocean has lower CO2 solubility.) That is why limestone reefs form in the tropics.
Some climate “scientists” could avoid embarrassing themselves by learning some basic science – before getting their PhD

Calcite can be either dissolved by groundwater or precipitated by groundwater, depending on several factors including the water temperature, pH, and dissolved ion concentrations. Calcite exhibits an unusual characteristic called retrograde solubility in which it becomes less soluble in water as the temperature increases.


I made quickly a similar calculation with woodfortree.org
the result is astonishing


For this to be true, the proxy CO2 records that show it almost perfectly flat for the last 1000 years have to be wrong.
Obviously possible, but without addressing it, you have a pretty weak presentation.

Make data and calculations available online please! Let’s follow the practices we want from others.


Wow. Someone tell Willis.

Keith G

Lon, this is very well done. However, I am simply stunned that this has never been done before. There have been numerous posts here and debates on RealClimate about the fact that CO2 rise/fall lags temperature rise/fall. You’d think that explaining the CO2 variation would be one of the key products of MLO. So what do they say?


Regarding ocean acidification, if the rising temperature is providing less CO2 for the same “amount” of ocean water, should the ocean pH not be rising?

Old Goat

Just as we suspected all along, but what will it take to convince those who wear the blinkers? Especially as for a variety of reasons it doesn’t suit them to know…


What one can invent with a simple spreadsheet and two Mauna Loa friends!

Malaga View

Looks like good science to me… and makes good sense too!!!
Thank you!

Dear Lon Hocker,
A confirmation of your argument in this article is evidenced by the paleobiological register. In this graph I eliminated the temperature line for the correlation between the mass fraction of carbon dioxide in the atmosphere and the area of continents flooded is seen clearer. You can see the expansion of the oceans happens many years before any increase of the mass fraction of the carbon dioxide in the atmosphere:


I seem to recall that on a geologic timescale CO2 lags temperature by about 600-800 years. How can this be reconciled with the about 6 months lag found in this study?


Do you mean ‘nowhere near the factor of three rise of CO2 concentration’ in the second to last paragraph before the Conclusion?


An inconvenient paper. Congratulations!


If this was true how do we explain that the CO2 levels in ice core data are almost totally flat before 1850. (you’d think same process would have applier during e.g. MWP)
1) global temperature variation has been very small (and current warmins IS unprecedented) – not likely
2) ice core CO2 data can not be trusted – not likely
3) this mode breaks down prior to 1850

Peter Miller

This is one of the few times I disagree with you.
Your hypothesis is dependent on the oceans being saturated with carbon dioxide – the current level is circa 90ppm, a very long way from saturation level at current global temperatures.
REPLY: You might look at who wrote it before disagreeing with me. – Anthony

Steve from Rockwood

At first glance this would appear to be a brilliant discussion. I can’t get over Figure 2. And he plays in a band. Nice work.

richard telford

Well this post get one thing right, almost. There is a relationship between atmospheric CO2 concentrations and El Niño. Congratulations for finding this relationship over 30 years after it was first described by Bacastow in Nature. If your research had extended to reading this paper, you would have learnt that the main driver is not the ocean, but vegetation dynamics.
Your model captures the short term variability, but cannot explain the trend (because your analysis removed the trend!). The short term variability is interesting, but it is the trend is of most concern.
And how does your model account for the changing carbon isotopic ratio (the Seuss effect); the decline atmospheric in O2 concentrations; that the ocean is undersaturated in CO2, so is absorbing not emitting CO2. Simple – it cannot.
El Niño events have been recognized from at least 1902, so it would seem inappropriate to claim that they are caused by the increase of CO2.
This is a strawman. Nobody is claiming that El Nino is caused by the increase in CO2, indeed, there is evidence for El Niño throughout the Holocene (Rodbell et al. 1999 – Science)


So…what does Willis Eschenbach think of this?

Andrew W

From Wiki: “Henry’s law is used to quantify the solubility of gases in solvents. The solubility of a gas in a solvent is directly proportional to the partial pressure of that gas above the solvent. ”
Over the last 150 years the partial pressure of CO2 has risen by about 35%, so CO2 is moving into the oceans, not out of them.


The guys who believe that CO2 causes Global Warming do not use to drink gasified beverages but just one, in these original 6 flavors which do not contain any CO2 whatsoever:
Cherry, Grape, Lemon-Lime, Orange, Berry, Strawberry.
Same flavors found in their ideology too.
That’s the problem!

D. Cohen

Your article makes a very good point, but in retrospect the same argument can be made based on the annual variation of the CO2 data. No one (that I know of) argues that the annual CO2 variation is due to anything but the annual temperature cycle, therefore we already know that — for the annual CO2 cycle — changes in temperature cause changes in CO2 concentration. From that data alone we should expect multiyear temperature changes (like El Nino events) also to cause changes in the CO2 concentration.


Olli: The problem with ice core data is that the resolution is very low – the CO2 values one gets are like a several hundred year long moving average. But if you look closely at the graph presented here recently, you may at least see a very faint trace of the LIA.


The Vostok ice core data is freely available online for both CO2 and reconstructed temperature:
It is visually obvious that temp leads CO2, it should be relatively trivial to extend your analysis back 400 thousand years.


stevengoddard says:
Interesting point, as any carbonate increases its solubility in its “mother liquor” H2CO3, carbonic acid. The warmer the water the lesser CO2 content, the higher the pH, the lesser calcite solubility.


What I like about this site is that papers are presented, and are subjected to criticism.
We get a hypothesis and then that hypothesis is subjected to analysis by the group mind from various perspectives.
If only we had a word to describe this kind of analytical approach to trying to discern the truth. 🙂

Not as elegant as E=MC^2 perhaps, but if confirmed, just as great a breakthrough for humankind.


Peter Miller says:
June 9, 2010 at 1:30 pm
I’d agree…since the oceans are well below saturated, the oceans aren’t a likely driving force. There are plenty of other natural sources of CO2 that have temperature-related equilibria that AREN’T the oceans…anyone have thoughts on this?
Also, what is the warmist argument to the oceans being below saturation with respect to CO2? Doesn’t this imply that CO2 concentrations used to be far higher?

Quinn the Eskimo

Kagiso, have a look at Glassman’s article. He did, in 2006, the analysis on the Vostok records that you recommend, with the conclusion stated in the abstract above.

I cannot see the logic of this. It claims there is a close correlation of temperature with rate of CO2 increase. Then it jumps to saying that the CO2 increase must be caused by the temperature. Why? Why not temp rise caused by rate of CO2 increase? Youdon’t change the causality by just rearranging the terms in the correlation equation.
The sea water chemistry is very bad. There is a large volume of dissolved CO2 equivalent, mainly as bicarbonate. But only about 1% is free CO2. Just using water solubility curves and relating them to total CO2 is quite wrong.


Greg Said: “For this to be true, the proxy CO2 records that show it almost perfectly flat for the last 1000 years have to be wrong.
Obviously possible, but without addressing it, you have a pretty weak presentation.”
What makes you think the proxies are as accurate as measured values? What makes you think proxies are accurate at all? A physical relationship can be demonstrated, but when the comparisons are run against actual measurements, they diverge from measured values and no one has provided a reasonable explanation, just arm waving to this point.

“No one (that I know of) argues that the annual CO2 variation is due to anything but the annual temperature cycle, therefore we already know that — for the annual CO2 cycle — changes in temperature cause changes in CO2 concentration.”
Surely it’s much more the biological uptake during the growing seasons?
As there is far more land vegetation in the nothern hemisphere the seasonal fluctuations are not cancelled out by the southern hemisphere.


That’s nonsense, with due respect. Laws apply everywhere. You can check what this post presents by just buying a carbonated beverage and holding it in your hand before opening it, the warmer the bottle the more CO2 gas will go out when opened. The other way is simply impossible: to increase the temperature of the solution while increasing at the same time CO2 solubility, unless you increase pressure.

Les Johnson

Lon: Good job. This is nearly identical to something I was trying to do with Lucia.
Instead of using coefficients, though, I found a good match by shifting the CO2 rate of change by 3-12 months, with the best correlation at 6 months.
This is the CORREL function in Excel, using CRUT3 data, from 1998.
CORREL 1998-99 raw 0.834
CORREL 1998-99 12 mon MA 0.937
CORREL 1998-99 24 MA 0.994
This is CRUT3 data, from 1960:
CORREL all data (raw) 0.426
CORREL 12 mon MA 0.634
CORREL 24 mon MA 0.699
This is UAH data, from 1998 to present.
CORREL 1998-99 raw 0.887
CORREL 1998-99 12 mon MA 0.986
CORREL 1998-99 24 MA 0.989
This is UAH data, from 1980 to present.
CORREL all data (raw) 0.463
CORREL 12 mon MA 0.678
CORREL 24 mon MA 0.674


Nick Stokes:
As an oriental philosopher would say: “You can’t fart unless you eat first”


Nick Stokes says:
June 9, 2010 at 2:09 pm
“Then it jumps to saying that the CO2 increase must be caused by the temperature. Why?”

El Niño events have been recognized from at least 1902, so it would seem inappropriate to claim that they are caused by the increase of CO2. Given the very strong correlation between the temperature anomaly and the rate of increase of CO2, and the inability to justify an increase of CO2 causing El Niño, it seems unavoidable that the causality is opposite from that which has been offered by the IPCC. The temperature increase is causing the change in the increase of CO2.

There are several comments of this nature. I advise people to read the article through before going off half-cocked.

Some related graphs: showing temperature as a functon of CO2 change per year
Sylvain (12:57) thanks for that wood-for-trees graph link
The ocean does not have to be saturated to affect the rate of absorption of CO2

Keith in Hastings UK

Meantime the warmist gravy train & call to penal action keeps going, with no apparent regard for new thought such as the above. See the new UN climate chief’s remarks just reported:
here in UK, it lokks as if the “climate change” budget/action plan is to be spared even the desparate deep budget cuts the Govt have promised to cut the deficit.
So: keep blogging etc – perhaps there is just a political decadal oscillation…..

Alan Siddons

One minor correction.
“The Atmosphere contains 720 billion tons of CO2”
No, at the present concentration that figure would be around 831 billion metric tons. And that’s in CARBON weight. In CO2 weight it’s 3044 Gt. Same applies to the ocean figures. This doesn’t detract from Hocker’s basic idea, though. By my own rough estimate, a 0.5% release of CO2 from the oceans since around 1850 would closely mimic the reported trend. If Ernst Beck is correct, however, there’s really no trend at all.


Andrew W @ June 9, 2010 at 1:50 pm
Henry’s law assumes constant temperature.


I believe the abnormal ‘bump’ in the temperature anomaly you see in data between 1939 and 1946 is attributed data gathered from ships not using the usual shipping lanes during World War II.

Anne van der Bom

glacierman says:
“Looking at the graph – Modeled CO2 vs. Time – comparing measured CO2 to Model predictions – any reasonable, scientificly trained person would have to believe that CO2 controls the temperature of the seasons to believe CO2 controls global temperature rises.
Use some common sense Warmers.”
Any reasonable, scientifically trained person would have done some thinking before saying such a thing.
The seasonal variation of CO2 levels result in a forcing in the order of tens of mW/m². The difference in average solar radiation between summer and winter runs in the hundreds of W/m² (depending on the latitude). That is a difference of four orders of magnitude. Methinks someone else than the warmers must use some common sense.


Lon – Your analysis fails to consider one simple over-riding factor – We can reasonably estimate the amount of CO2 emissions into the atmosphere over at least the last half-century based on the known usage of petroleum/coal/etc.. (Hopefully, no one will argue that the burning of fossil fuels does not cause CO2 emissions). Based on the amount of CO2 emitted from the burning of fossil fuels, the increase in atmospheric CO2 concentrations should actually greater than what has occured. The oceans are absorbing CO2, not releasing it.
Anthony – I am what one might call a “lukewarmer” and think that Pielke Sr probably has the best summary of man’s influence on climate (in short, CO2 is but one of several anthropogenic forcings and the emphasis on CO2 only is inappropriate). I also am very skeptical of the gloom and doom predictions of many that advocate that global warming of a few degress will be catastrophic. I check your site nearly daily since I often find interesting and informative information here. Also, I think the work you have done with the surfacestations project and the questions you have raised regarding the development of the various global temperature indices are very important. I also know that you want to present a wide variety of viewpoints and ideas. That being said, I wish you would use a little more discretion or prescreening before posting guest posts with what are clearly flawed analyses. It really affects your credibility on the stuff you discuss which is good.

That temperature rise precedes any Co2 rise can be traced back to 1660.