Direct evidence that CO2 forcing alone determines Global Temperatures

The well known result that CO2 radiative forcing is approximately 5.3 Ln (C/CO) [1] is confirmed here by comparing decadal global temperature anomalies with CO2 concentrations. Positive feedbacks are not needed to explain the observed warming. A value of Transient Climate Response of 1.6C is observed to confirm this. The Moana Loa CO2 measurements when combined with earlier estimates of emissions show that CO2 concentrations have essentially been increasing monotonically since before 1955.  As a result we would expect resultant temperatures to  increase linearly with time [see here], unless there are any positive feedbacks present to increase this rate.

A new method based on a fixed Icosahedral binning  over the surface of the earth allows us  to calculate the decadal averages for each bin and then integrate these to derive the global average temperature for each decade from the 1880s to the 2020s. The big advantage of using decadal temperatures rather than annual temperatures is that natural variability (ENSA, AMO, etc) is simply averaged out.

Figure 1 below shows the result using a 1961-1990 baseline.

The red data-points are the decadal temperatures (left hand scale) while the blue dotted line are the Maona Loa CO2 data combined with NOAA CO2 values before 1955. The data after 2020 extends the linear temperature trend and the exponential CO2 increase to 2050

The linear increase in temperature after 1970 shows that a doubling of CO2 by 2050 if this increasing CO2 emissions trend continues ( blue arrows ) would results in a temperature rise of 1.6C. This is almost identical to the value calculated from directly from radiative forcing from CO2 alone. This proves that proposed feedbacks such as changes in cloud cover or increased water vapour have had no measurable effect so far.

Essentially this implies we have at least 40 years left to develop a reliable low carbon energy source (nuclear).


[1] Myhre et al. New estimates of radiative forcing due to well mixed greenhouse gasses Phys.Rev.Lett., 25, 2715-2718,1998

[2] View the 2000s temperature grid by clicking here 2001-2010 (2000s) Click and spin the globe !

About Clive Best

PhD High Energy Physics Worked at CERN, Rutherford Lab, JET, JRC, OSVision
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45 Responses to Direct evidence that CO2 forcing alone determines Global Temperatures

  1. Demetrios says:

    Does this in any way contradict your previous take on the subject?
    Forgive the layman’s question, but wasn’t Richard Lindzen’s theory that positive feedbacks also played a role?

    • Clive Best says:

      You’re right. It does somewhat contradict the earlier post !

      I think though that this conclusion is correct though. The crucial fact is the linear increase in temperature to an exponential increase in forcing.

  2. forbin says:

    The Greens have done a wonderful Luddite job

    nobody in power wants nuclear – even the French are moving away .

    All possilble carbon fuels will be burnt , if not by the so called West , then by everyone else.

    From other sources the prediction is that fossile fuels will peak in the 2030’s time frame – interesting times ahead.

    pull up a comfy chair and have some popcorn


  3. Peter Ridd says:

    Thanks Clive, Nice graph. Simple prediction and probably as accurate as the GCMs. What are your thoughts on Bjorn Lomborg’s view that we are better off adapting to the modest temperature rise than going net zero? I am strongly pro-nuclear, but we still need coal/oil/gas for many other things than electricity. And there are plenty of advantages from a slightly warmer planet, and from the higher C02 concentrations (such as far faster plant growth rates). I live in the tropics, and heat is far less of a problem now than it was when I was a child 50 years ago – we did not even have fans in the house, no insulation in the ceiling. Now we have a roof with high Infra-Red-emissivity paint, insulation, fans, and air-conditioning which is barely used. Even poor nations can deal with a slightly warmer climate if they can get reliable electricity.

    Peter Ridd

  4. David Johnson says:

    You continue to do “yeomans service” to the decision makers on the planet.
    But data points from 1880?
    Kindly do a statistical analysis of the number and distribution of the raw data spanning 1880 to the present. And note raw data means actually attested to, at this time, in this place. No interpolation or inferred data if you please.
    This will reveal what common sense tells us.

    That we have enough recent data to point to an interesting transient result, maybe. But the error bars on the first 50 years are so large as to be discarded when inferring a linear result with a particular gradient.
    And have you considered doing a comparison of your linear equation with one that models a point of inflexion? Such as in a Sigmoid function.
    I think we need quantify our confidence level.

    David J

  5. Lark reLlez says:

    CO2, O2, N2, CH4, H2O, etc. in an open atmosphere (no lid) all obey the same gas laws and help each other in keeping us Earthlings warm this insight helps us understand CO2’s exact contribution to warming.

  6. Nick Stokes says:

    “The Moana Loa CO2 measurements when combined with earlier estimates of emissions show that CO2 concentrations have essentially been increasing exponentially since before 1955. “
    Not true. What it shows is that {CO2]-200 is exponentially increasing. The offset matters. To use the Myrhe formula, you have forcing=5.35*log((200+A*exp(a*t))/200). That isn’t linear. The slope increases with time.

  7. Clive Best says:

    We can adapt to warmer temperatures as long as they remain stable. Currently the only reliable alternative to hydrocarbons is Nuclear which is the only logical way to maintain living standards and cut CO2 emissions. However we will always likely need to use a small amount of oil and gas for fertilizers, plastics and infrastructure (roads, building etc.) The tropics tend to have their own temperature control in my experience. It warms fast during the day until it triggers a thunderstorm in the early evening cooling everything down for the next day. There is a kind of thermostat control !

  8. Nick Stokes says:

    To give the fuller quote
    “CO2 concentrations have essentially been increasing exponentially since before 1955. As a result we would expect resultant temperatures to increase linearly with time”

    You’re justifying the linear projection by saying that it is the log of an exponential. But that only works if it really is an exponential. The 280 ppm offset negates that.

  9. Clive Best says:

    OK yes you’re right – it is only the incremental increase that is linear. I should have made that clearer, however it doesn’t change the argument for the increase observed post ~ 1960

  10. Everything about geophysical fluid dynamics is nonlinear, and nonlinear is putting it mildly. None of that relates to CO2 as far as I can tell though, as it’s more related to the solution of the Navier-NickStokes equation 😉

  11. dougbrodie1 says:

    How does this conclusion sit with the evidence that increasing global temperatures cause the increase in atmospheric CO2 concentration? See and

  12. Clive Best says:

    Sorry Nick you are of course correct. There is no physical reason why the CO2 levels should increase exponentially. In reality human CO2 emissions have been increasing with time which then yields a CO2 concentration which increases monotonically. This then results in an apparent linear rise in temperature per decade because the forcing goes as log( C/C0) So if CO2 future levels continue increasing on the same trend curve then conclusion is valid. In this worst case the average global temperature rise would then be 1.6C. Of course on an annual basis we may see years with ~ 2C above normal but the underlying trend still follows the decadal average.

    • Scott says:

      Have you presented another Mann Hockey Stick, grafting estimates onto measured CO2 Levels and presenting this as a factual ex
      There is no evidence that the increase in CO2 will result in a logarithmic increase in forcing.
      Although I have seen no studies to confirm this, CO2 is highly phillic to 15um radiation (although there is a lot more H20 in the atmosphere, it appears that most of the 15um radiation is absorbed by CO2 in preference to H20 – as demonstrated through OLR charts).
      The surface only emits a finite quantity of of 15um radiation according to Wiens/SB – around 25W/um in the 14.5-15.5 range.
      According to Dr William Happer, 15um energised CO loses energy through collisions with other molecules in 99.99% or cases, before it re-emits 15um radiation. (Collisions ever nanosec, emissions every second)
      As a result, almost all the 15um radiation is destroyed and converted into kinetic (or other frequency radiations).
      A logarithmic function infers that the absorbance of 15um radiation is infinite, however the amount of radiation available for absorption is limited by 1.0001% the fourth root of temperature increase. This is a logistics function not a logarithmic function.
      Not being a scientist and not having done the experiments, this is only conjecture, but I would bet that nearly all the 15um energy in the lower troposphere is already absorbed and distributed throughout the atmosphere (within the first dew metres), and any increase in CO2 is irrelevant.
      It would be interesting to see an experiment on the effectiveness of absorption by CO2 vs H20 at 15um. Without this all climate speculation is invalid.
      The sources of 15um emissions at the TOA include CO2, H2O? and O3. I have not seen any studies on the percentage each is responsible for the earth’s TOA emissions. It may be that all the 15um emissions observed at the TOA are from O3 rather than CO2.

      • Clive Best says:

        The logarithmic forcing comes from the emissions of Co2 molecules in the infrared.If you calculate the emission height where CO 2 molecules radiate directly to space Then essenTially the tropospaus rises a bit higher to reach energy balance. This “radiative forcing goes as log C/C0


      • Peter Grafström says:

        “15um energised CO loses energy through collisions with other molecules in 99.99% or cases, before it re-emits 15um radiation. (Collisions ever nanosec, emissions every second)
        As a result, almost all the 15um radiation is destroyed and converted into kinetic (or other frequency radiations).”

        That is correct but since the collisional equilibrium maintains the population difference and spontaneous emission determines the intensity it doesnt matter that there are a billion dexcitations and excitations in between

        This document by Hermann Harde provides the pertinent equations to understand that aspect
        Research Article
        Radiation Transfer Calculations and Assessment of
        Global Warming by CO2
        It wasnt possible to paste the link but it won’t be difficult to google it

    • David Appleby says:

      In your article you quote the temperature sensivity as 5.3*Ln(C/Co). I think that this should read 5.3*log(C/Co) to get ECS = 1.6K?

  13. Windchaser says:

    “It warms fast during the day until it triggers a thunderstorm in the early evening cooling everything down for the next day.”

    Doesn’t this “thermostat control” of thunderstorms depend on the warmth and height of the troposphere? The thunderstorms only kick in after the rising humid air goes through enough of a temperature drop to cause condensation.

    If the atmosphere as a whole is warmer, this condensation doesn’t then force it cooler. The whole system just shifts to warmer evaporation and warmer condensation points. So it doesn’t work as “temperature control”.

  14. Clive Best says:

    Yes there are huge variations on a monthly and annual scale superimposed on a long term trend. That trend is the decades trend.

  15. Richard Whybray says:

    It is short term data, but the very existance of such extreme daily and monthly figures so early in the record suggests that the warming rate is no longer linear.

    I’m not convinced that the 0.18 C/decade warming rate seen since the 1970s is going to hold through the decades to come.

  16. Al White says:

    The biggest problem with this analysis, indeed with the entire CO2 control knob hypothesis, is that at no other time in the paleoclimate record have changes in the level of atmospheric CO2 led, and thus presumably caused, a rise in temperature. Never. Ever. The concentration of CO2 always follows changes in temperature. Always. On the other hand, temperature tracks fluctuations in the level of solar radiation input into the climate system caused by orbital cycles and varying solar output almost perfectly over any time scale throughout all of climate history. These simple facts, and knowing that the sun is the only meaningful source of heat for the Earth, allow one the luxury of having to look no further to deduce the principle cause of climate change.
    The correlation between rising CO2 and temperature is just that, correlation. Not causation. The recent rise in CO2 concentration is caused by anthropogenic emissions plus rising temperature (through well understood physical processes). The rise in temperature since the Maunder Minimum tracks perfectly with the increase in solar output since 1700 AD. Currently elevated level of total solar irradiance is at or near a 9000-year high. The correlated rises in temperature and CO2 have different causes.
    The fact that CO2 is observed to absorb IR radiation has led climate science down the wrong path for 100 years. Early investigators “assumed” that since laboratory experiments demonstrated IR absorption by CO2, that would then logically translate to a rise in atmospheric temperature. What they weren’t aware of was the fact that solar radiation received by the Earth changes significantly over time. They thought the sun’s radiation was constant. It was, and sometimes still is, referred to as “the solar constant” and was never considered a variable. The amount of energy absorbed by CO2 is minor compared to water vapor and becomes saturated in its effect on temperature at about the current level.

  17. The concept of gradual GHG forced warming precludes large spikes in average temperature. This recent warming is likely something else. And if it is GHG-related in the long term, it’s a behavior not at all understood.

  18. Clive Best says:

    Yes the recent spike is something else and not just another El Niño. The Tonga eruption shot huge amounts of water into the stratosphere. I wonder if this slow descent may have some long term effect, although it is pure speculation.

  19. piton gilbert says:

    There is a big problem in your reasoning.
    Your red curve, base 1961-1990, points to an anomaly of around +1.6°C in 2050.
    It starts from an anomaly of -0.4°C around 1900.
    Therefore, over the period 1900 to 2050, the temperature anomaly would increase by around +2°C.
    During this same period, the CO2 level would increase from 290 to 560 ppm.
    Your curve therefore shows that during the period when the CO2 level is almost doubled, the temperature anomaly increases by at least +2°C…
    This would show that the evolution of the temperature anomaly does not depend solely on the radiative forcing of CO2.

  20. piton gilbert says:

    There is a big problem in your reasoning.
    Your red curve, base 1961-1990, points to an anomaly of around +1.6°C in 2050.
    It starts from an anomaly of -0.4°C around 1900.
    Therefore, over the period 1900 to 2050, the temperature anomaly would increase by around +2°C.
    During this same period, the CO2 level would increase from 290 to 560 ppm.
    Your curve therefore shows that during the period when the CO2 level is almost doubled, the temperature anomaly increases by at least +2°C…
    This would show that the evolution of the temperature anomaly does not depend solely on the radiative forcing of CO2.
    According to your curve, the increase in the temperature anomaly of +1.6°C corresponds to the period where the CO2 rate would increase from approximately 325 to 560 ppm. It’s not a doubling…

  21. Clive Best says:

    Sorry for delay in approving your reply.

    The problem with baselines is that knowledge of past temperatures before 1960 is rather poor. Berkeley Earth and Carbon Brief etc. have a habit of using baselines like 1850 – 1900. but of course we have little direct evidence for what global temperatures really were then. SST measurements were non existent apart fro engine room intakes and bucket measurements. There were no measurements in the Arctic, Antarctic, Africa nor much of Asia , so our knowledge is really rather poor.

    However let’s simply accept your argument. I agree that this implies a doubling of CO2 results in a 2C rise in temperature since 1850. Clearly we have to solve this problem of zero carbon energy supply by 2050.

    We have the solution. It is Nuclear Energy. The problem is that climate scientists must also accept this scientific fact.

  22. piton gilbert says:

    While trying to reproduce your chart, I noticed another problem.
    By extending the trend in the evolution of the CO2 rate, which is not quite exponential from 1958 to 2023, 580 ppm will not be reached in 2050, but around 2070 (regression calculations based on monthly data) .
    According to your graph, the temperature anomaly would be around +2°C (base 1961-1990), to which we must therefore add the previous 0.4°C, for a total of at least 2.4°C in the period where the CO2 rate increases from 280 to 580 ppm.
    There is a simpler way to do these calculations, without risk of bias.
    Simply trace the monthly evolution curve of your temperature anomalies since 1958, according to the evolution of the monthly CO2 rate measured at Mauna Loa.
    I had already done so, on November 14, 2022, in the post “Climate Sensitivity to CO2”
    This leads to an evolution of the temperature anomaly of +2.8°C in the period where the CO2 rate is doubled (logarithmic regression).
    We are far from your announced 1.6°C.

  23. Clive Best says:

    Don’t forget these are decadal average temperature which clearly shows a linear increase to the observed CO2 data so far. Yes everything depends on how those CO2 trends evolve over the next 50 years, and that depends on us.
    2.4C increase is indeed possible is you take an earlier baseline.

    I will look at it again in more detail.

  24. piton gilbert says:

    Using ten-year averages or the trend based on monthly measurements since 1975 changes nothing. I have the same straight trend as in your graph.
    What changes is the evolution of the CO2 rate which I calculated from monthly measurements since 1958 by regression.
    It’s not easy to fit the curves together.
    This is why I prefer a graph showing the evolution of anomalies in the same period as that of the evolution of CO2. In this case, there cannot be any bias.
    See : ?rlkey=7hk15u35gqqv2z9jjcctobfwo&dl=0

  25. piton gilbert says:

    See : ?rlkey=7hk15u35gqqv2z9jjcctobfwo&dl=0

  26. piton gilbert says:

    The link to Dropbox does not work.

  27. David Johnson says:

    It is certainly admirable for folks to have and put forward a theory as to how nature works and then make a prediction as to what nature will do next; however doing so is not in itself the same as scientific inquiry. What troubles me the most about your [Clive’s] post and many of the replies is the rush to certitude. What I observe is an attitude that believes that in a few sentences and one diagram one can definitively say that we know “the magic number” and it is 1.6C per doubling of CO2. There has to be either a hubris or an ideological conviction that underlies such an attitude.

    Please everyone let’s step back and admit that we know no such thing. Complex phenomena are often found to be either inherently chaotic at the margins or multi-dimensional. Almost the entire popular “climate change debate”, of which this blog is an example or indeed most of the locus of publicly funded climate / weather research around the globe, is based on a presumption that there is “a number”. We just need to find what it is. Once we know it, we can extrapolate into the far future and then working backwards with magisterial authority make policy for all 8 billion souls, all the while congratulating ourselves for our magnanimity and prescience.

    One a separate tack, has anyone considered the falsifiability of the 1.6C per doubling hypothesis by looking at ‘extreme’ cases – compare historical evidence of temperature with CO2 levels 4 times, 8 times the pre-industrial baseline. Does the climate record support the claim that with 3 doublings = 8 times we see a minimum and relatively stable temperate 1.6C x 3 = 4.8C higher that pre-industrial times?

    And as atmospheric physicist Richard Lindzen reminds us, “climate” has historically been defined to be that basket of extensive metrics we directly experience such as temperature, rainfall, wind speed and sea level; all of which are expressed as 30 year averages. Decadal data shows way too much volatility and is closer to weather than climate. And since the discovery of the Pacific Decadal Oscillation (PDO) and Atlantic Multi-decadal Oscillation (AMO) we have realised that even 30 years may be too short a time span to capture the real variation we observe.

    I realise many well meaning folks will be unimpressed with that restriction – but I contend that we need to be very cautious before penciling in the next 30 year data point.

  28. Bob Peckham says:

    I find the points made by Al White to be quite convincing, and worthy of much more attention. I would just ask Al if he could provide references to the most reliable/recent graphs showing that “The rise in temperature since the Maunder Minimum tracks perfectly with the increase in solar output since 1700 AD” ?.
    Also are there any calculations showing that the variations in solar output are sufficient to account for the observed temperature variations ? (Earlier reading on this had led me to believe they were too small).

  29. Peter Grafström says:

    From the curves in the diagram, were T is approximately linear from 1970 to 2050,
    I read
    1970 T=0 c=328ppm
    2050 T=1.6 c=560ppm
    TCR is the transient temperature rise for a doubling of CO2
    For other ratios this ought to be correct no?
    DT=1.6=TCR*ln(560/328)/ln2=0.772TCR=> TCR=2.07K

  30. David Nichols says:

    The atmosphere is a highly non-linear chaotic system. How can our entire climate system with even more complexities be linearly related to a trace gas that has one small absorption band at 15 microns? H20 and clouds are the Earth’s primary greenhouse gases. CO2 concentrations never dominates our climate system based on ice core data. The present warming trend could be mostly natural given we are coming out of a Little Ice Age that ended in the 1800s. Certainly, increasing CO2 leads to a small amount of warming, but changes in the Sun and natural cycles could easily explain much of our present warming. Anyway, I do enjoy your page and work.

    • >> “The atmosphere is a highly non-linear chaotic system.”

      Perhaps certain aspects of the atmosphere are chaotic, but there are fundamental behaviors that are still inscrutable yet likely perfectly deterministic. Consider the QBO cycle of equatorial stratospheric winds, which is a nonlinear interaction of the sun and moon’s nodal cycles. The QBO frequency is EXACTLY (365.242/27.212 mod 1) where the 2 numbers are the respective nodal cycles and “mod” is a modulo math result — i.e. nonlinear aliasing in short.

      Forget CO2 for a moment, this is the kind of behavior that stands climate science on its head and will cause researchers to rethink the foundations of their numerical simulations.

  31. Thomas Martin says:

    I have been asking for years for an experiment that demonstrates the premise that doubling CO2 from present 420ppm to 840ppm will raise a parcel of air’s temperature by at least 2.7F to 8.1F as required by the mann made global warming theory.

    So far I have seen nothing. Not only is CO2 highly adsorptive – it is highly emissive so it apparently stores no heat Like an electrical wire stores no electricity.
    For laughs Look at Bill Nyes Climate science 101 on youtube.. about 4 min.. hilariously he does not even has his thermometer in the experiment that demonstrates his “truth” and frankly that is an excellent microcosm of the flawed science that hides from real debate .

  32. You don’t seem to understand that temperature and heat are different things. The temperature of the Earth’s thermosphere for example is very high even though little heat is stored in it. The fact that the CO2 stores virtually no heat is irrelevant considering how important it is in transforming radiation from one spectral wavelength to another and at what altitude this occurs.

  33. gymnosperm says:

    CO2 does not transform radiation. It emits in the same bands it absorbs. Since it has fairly low emissivity, and prefers dancing to spitting photons, it transfers energy kinetically to its 2500 neighbors, inducing them to radiate at their own spectrum.
    In the tropics, satellites at 70km “see” CO2 radiating at the temperature of the tropopause

    • “CO2 does not transform radiation.”

      I didn’t fall off the turnip truck yesterday. Of course it transforms radiation. Most of the radiation that eventually heats the earth is in the visible part of the spectrum. That which leaves the earth is mainly in the infrared and since CO2 causes reabsorption and redirection of IR (some back downward), there will be many cycles of re-emission from the gray-body earth as the full spectrum readjusts to a new spectral profile.

      That’s the problem with people that only know a little bit of physics — they use some grain-of-truth aspect and completely misinterpret the actual understanding of what’s happening.

      • gymnosperm says:

        The spectrum of the earth changes with warming, overwhelmingly from increased solar absorption, the absorption and emission spectra of CO2 do not. The earth sports many more absorbers and radiators than CO2. This is why earthlight spectra change with temperature. Different materials kick in. What changes absorption and emission spectra of CO2, and what you are confusing with transforming, is atmospheric pressure.

  34. Take some physics classes, preferably starting with statistical mechanics where you can learn about partition functions, leading up to S-B.

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