CO2 is Logarithmic Explained

I keep on saying that the “forcing” effects of CO2 are logarithmic while the cooling response of the planet rises exponentially.  I’m not the only one saying this, serious heavy weight skeptics like Lindzen are saying the same thing.  So what do these terms really mean?  OK, a bit of background and then onto the pictures. 

What is often quoted is that CO2 doubling causes an increase in radiance to earth’s surface of 3.7 watts/meter squared, which in turn raises temperatures about 1 degree Celsius.  Why the reference to “doubling”?  Because we’re talking about light and filtering materials.  Consider that you have several pairs of sun glasses, each of which blocks 50% of the light.  If you put two pairs in a row, do they block 100%?  Of course not.  The first pair blocks 50% and the second pair blocks 50% of what is left, which is 25% of the original light.  The third pair would only block 12.5% of the original light.  CO2 suffers from the same law of diminishing returns.  What keeps getting left out of the climate discussion is what happens after the first doubling.  The pre-industrial levels (1900 AD or so) of CO2 are commonly quoted at 278 PPM (parts per million) and the current levels are at about 385 ppm.  If we look at this graph, it becomes pretty clear that we would have to generate a LOT of CO2 to get much more effect than we are already: 

It takes more and more CO2 to get just one more watt...

However, to keep the big picture in mind, we have to also remember that as the earth gets warmer, it radiates heat to space.  The ideal black body formula to calculate how much heat is being dissipated to space is P=(5.76×10^-8)(T^4) where P is power in watts per square meter and T is temperature in degrees K or Kelvin.  To convert from the more common degrees C, just add 273.  The “average” temperature (there’s really no such thing) of earth is often quoted as 15 degrees C or 288 K.  This graph shows how much additional heat the earth sends into space as it gets just a few degrees warmer: 

The warmer something is, the more heat it radiates...

So how much does CO2 in theory heat the planet?  If we use the formula above, we see that increasing the earth’s temperature by just 1 degree, from 288 K to 289 K, results in an increase in earth radiance of 5.5 watts per square meter.  This brings up the obvious question.  If earth radiance goes up by 5.5 watts, how could it be caused by only a 3.7 watt rise?  The climatologists have a variety of explanations for this.  In brief, CO2 doesn’t reflect long wave radiance as many people think, it absorbs it.  This heats the CO2 up, which causes it to radiate more heat, but the photons it releases can be emitted in any direction.  Up, down, sideways…  long story short, some escapes to space and some gets sent back to earth, about 3.7 of the 5.5 additional watts.  This issue alone is a long complicated discussion, but rather than argue it, let’s just accept the numbers.  Doubling CO2 levels from the pre-industrial level of 278 PPM causes an increase of 3.7 watts per meter squared, and that results in a temperature increase of 1 degree C.  The various theories then go on to claim that increased temperatures result in increased water vapour, which is itself a greenhouse gas and supposedly adds another 2 degrees C to the warming.  We’ll debunk both of those, but let’s put aside the water vapour for the moment and just focus on the CO2.  

In order to put the whole thing in perspective, we have to keep in mind two things.  The first is that in order to get a second 3.7 watts (after the first doubling) we would have to double CO2 again.  So the first doubling would be 278 x 2 = 556 PPM = 3.7 watts.  To get to 7.4 watts, we would have to double again to 1,112 PPM.  As the earth heats up though, the amount of additional power required to raise the temperature just one more degree also goes up.  So, to put everything in perspective, let’s take a look at how much CO2 would be required, without water vapour feedbacks, to directly raise the temperature of the earth from 288 K (15 degrees C) by four degrees.  As you look at the graph, just to put things in perspective, consider the two thin lines at the bottom.  The green line is what CO2 was at pre-industrial, and the red line is where we are at after a century of burning fossil fuels: 

Even at double current rates, it would take over a century to get to +2 degrees....

Several things jump out at us.  The first is just how ridiculous the idea of a “tipping point” really is.  The amount of heat the earth radiates to space just goes up too fast for that, and the amount of CO2 that is required to maintain any temperature increase at all goes up even faster.  If we were to double the rate at which CO2 in the atmosphere is increasing in comparison to the last 30 years, it would still take well over a century to get to just two degrees of warming from CO2.  If we tripled the rate, it would take almost four centuries to get to three degrees.  But what about positive feedback from water vapour? 

There are plenty of things wrong with that theory.  In principle, the amount of water vapour the atmosphere is capable of holding about doubles for every 10 degree rise in temperature.  The theory goes that just a small rise in temperature would increase water vapour which over all has a much larger greenhouse effect than does CO2.  Estimates range anywhere from double to quadruple the additional warming.  The average quoted most often is 1 degree of warming from CO2 and 2 more from water vapour feedback.  Is this reasonable? 

If the amount of water vapour in the atmosphere always “maxed out” it might be, but we know that doesn’t happen.  Instead, let’s look at what has actually happened.  Since the pre-industrial levels of 278 PPM one hundred or so years ago, CO2 levels have gone up about 38%, not even close to doubling.  In that time, various estimates based on surface station readings around the world have suggested that the earth has warmed up about 0.6 degrees C.   But, we must keep in mind that due to the logarithmic effects of CO2 forcing, and the increased radiance of the earth as it warms, the first 38% has a much larger effect than the next 38%.  In fact, if we go back to our graph and look at where we are now, it is easy to see that whatever effects doubling CO2 actually has, almost 70% of that is already happening: 

Current levels are up 38%.... which means almost 70% of the effects of doubling CO2, are already happening.

Even if we accepted the notion that positive feedback from water vapour triples the effects of CO2, we clearly are not seeing that in actual earth temperatures.  If the rough estimates of CO2 doubling = 3.7 watts per square meter = 1 degree plus 2 more from water vapour were correct, we would have seen a temperature increase over the last century of 2.1 degrees, but we’ve only seen 0.6 degrees.  It could be argued that there are natural cooling fluctuations, and the difference between what the earth’s temperature is now, and what it would have been without the extra CO2 would be 2.1 degrees.  That also seems far fetched given that the earth has been in a general warming trend for the last 300 years, and the rate of warming over the last century has been about the same as the previous ones.  

The more logical explanation is twofold.  First, the effects of CO2 and positive feedback from water vapour have been far over estimated.  Secondly, even doubling or tripling the amount of CO2 we put into the atmosphere would not appreciably change the warming effects of the CO2 levels we have currently… and then not by much.  This isn’t me making numbers up, it is just a matter of extending the IPCC claims and putting them in perspective to show that the worst is already behind us, and is over estimated in any event.  Even if the estimates of CO2 warming were correct (which they clearly are not) the fact is the bulk of the damage (if any) has already happened, and the amount of fossil fuels we would have to burn to appreciably change that is completely beyond our production capacity.

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45 Responses to CO2 is Logarithmic Explained

  1. Pablo Selzer says:

    The misleading allegations of the environmentalists of CO2 emissions destroying our planet are unfounded and not backed up by any statistical studies just EMOTION! They are like “chicken little” telling us the sky is falling when it truly is NOT. What Climatologist would endorse their allegations-NONE.

  2. Dr. Irvin H. Forbing says:

    Are there any peer-reviewed articles that are available to show this logarithmic effect.
    I believe it to be true, but do not have access to such literature.
    Dr. Irvin Forbing

    • davidmhoffer says:

      Any first year radiative physics text book would have more detail and references. I believe Robert G Brown (PhD Physics, Duke University) has put his online now for free.

      • Aerin says:

        Can you please provide links to scientific literature showing this? I have tried to find Robert G Brown’s page on logarithmic CO2 that you mention in your comment and it does not seem to exist.

      • davidmhoffer says:

        Robert G Brown comments frequently at as rbgatduke where you can find any number of comments and articles by him and others on the logarithmic nature of CO2. The official literature from the United Nation IPCC also regards CO2 as being logarithmic, as does any text book on spectrography.

      • Dr. Irvin Forbing says:

        David, an “Aerin” has asked the same question that you have. Here’s is a link, but it may not answer your “scientific link” question.

        You might want to study the Beer-Lambert Law and you will gleen some good info there.

        You might want to try an experiment that Jeffrey Bada of Scripps gave me in his attempt to prove that it was not logarithmic. He had not tried it, but we both did, and CO2 levels could never raise the temps in the experiment more than about 2degC. Bada gave up, but still makes the claim.

        2 1L bottles half filled with water. Place calibrated thermometers in the air of both, then add one alka seltzer (emits CO2) in one bottle, with the other as control (cork both bottles), and put the temp on a graph every 5 min for 1 hour. for both. Do it with increasing “doses” of alka seltzer (CO2) and it will still not change.


        Date: Tue, 17 Dec 2013 17:23:57 +0000 To:

      • davidmhoffer says:

        Thanks Dr. Forbing.
        The experiment you describe however doesn’t take into account the scale of the atmosphere and the ability of CO2 molecules to absorb and re-radiate repeatedly. That’s one of the problems with trying to do a lab experiment that confirms (or denies) CO2’s effects. We just cannot build an apparatus 14 km tall. There was a very good experiment done in great detail by Heinz Hug which you can find here:

        But be sure to read the criticisms of that experiment which you can get from the pdf linked to right under Heinz Hug’s name at the top of the page. Read together with the experiment itself, it is very informative as to the complexity of measuring the effect in the first place. That said, if you follow the IPCC AR reports themselves, they all assume a ln2 function. If I recall correctly, the formula to arrive at sensitivity due to direct effects of Co2 in isolation is dT=5.35ln2((C2-C1)/C1) which appeared in AR3 and has been carried forward to AR4 and Ar5. I’ve forgotten the precise manner in which it was derived, but even arch skeptics like Roy Spencer and Robert Brown and Richard Lindzen accept it as a reasonable approximation as do arch warmists such as Joel Shore and Kevin Trenberth (all PhD physicists). Spectroscopy however is more a core skill set of chemists, and you’ll find that from both sides of the aisle, PhD chemists come up with the same approximation.

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  6. fireofenergy says:

    So, as things heat up, we are not to worry because that infrared will not FIRST heat things up on Earth first before eventually escaping the excess co2? I don’t think so (and neither do the icecaps, evidently)!
    Bty, why is it sooooo hard to fathom a clean energy infrastructure based NOT on the past of expensive capacity but created far cheaper via upcoming machine automation? Why, I’ll tell you why… It is because that the truth of excess CO2 is also being used as an excuse to further manipulate the people into excess laws and regulations.

    All we need is the industrialists solutions, the technofix and NOT the life sucking politics!

    • Brian H says:

      The energy escaping to space can either increase warming, or escape. Not both. That’s why sat measurements showing monotonic increase of OLR with temps disprove AGW.

      • fireofenergy says:

        More co2 means more warming until escape, right. Unlike the infrared photon, that warming does not dissipate at the speed of light.
        I’m trying to instead not waste my time on the issue anymore, because of the log nature (that we’ll only see a “little” increase in warming despite the fact that most the glaciers are, indeed, retreating).
        I’m learning more about how solar can displace most fossil fuels. Eventually, such solar/battery material will be cheaper than most fossil fuels because automation improves right along with the understanding of physics.

  7. davidmhoffer says:

    Here’s a link to sea ice data where you can see for yourself that while the northern ice cap is below the 1979 to 2008 mean, the southern ice cap is well above it. Which one is it that agrees with you?

  8. warrenlb says:

    What are your Science credentials?

    • davidmhoffer says:

      If you wish to discuss the science by all means. If you wish to have a credential war, I’m not interested. The issues I raise in this post can be confirmed in any physics text book that covers the topic, and indeed they are confirmed in the IPCC literature itself (though very clever wording tends to obscure and distract attention from the core science). If there is an error in my math or my physics, by all means point it out.

      • DerekB says:

        No, credentials matter. It’s not enough to possess the tools, you have to know how to use them.
        Your calculation of the additional radiation from the Earth’s surface at a raised temperature overlooks that 90% of that radiation gets bounced back down by the troposphere. Crudely, you’d need ten times the increased radiation out to balance the increased greenhouse forcing. But that’s an overestimate for yet subtler reasons.

      • davidmhoffer says:

        Uh… no.
        If you needed 10 times as much out to “balance” the increased GHG forcing, by definition, the system would NOT be balanced.
        If you familiarize yourself with the application of Stefan-Boltzmann equations, one of the things that you will discover is that the amount of energy out before CO2 doubles is precisely the same as energy out after CO2 doubles with the exception of the transient period during which the system is realigning itself with warmer surface temps and cooler upper atmosphere temps. But the transient phase is, well, transient. Temporary in other words.

    • Bill Taylor says:

      8th grade science class is all it takes to understand co2 is plant FOOD, required for life as we know it…..and what a TINY role it plays in climate……..and i did get an 8th grade diploma.

  9. How is asking for your credentials an invitation “credential war”?

    Your defensiveness on the topic certainly speaks volumes!

    While one can certainly point out the many, many errors in what you humorously describe as “your math” and “your physics,” is that really a worthwhile exercise when dealing with somebody with no scientific chops whatsoever?

    • davidmhoffer says:

      The math comes straight out of formulas published in the United Nations Intergovernmental Panel on Climate Change, AR1 through AR5. The formula was plugged into an Excel spreadsheet using the built in natural log function and graphed for the range of CO2 concentrations shown. If you think the physics is wrong, by all means, go tell the IPCC, I’m sure they will be glad to hear from you. If you think the math is wrong, go tell the IPCC, they will be glad to hear from you. IF you can demonstrate that the math or physics is wrong, by all means, provide the documentation right here right now with a full explanation as to why. You won’t because you can’t, the reason you whine about credentials is that you have none of your own, you have no working knowledge of the math or physics to challenge me with, so instead you demand my credentials. That’s all you got? Seriously? The fact that CO2 is logarithmic is strewn throughout the IPCC reports, it is strewn throughout every physics paper and climatology paper on sensitivity that I’ve ever read. It is in every radiative physics text book written in the last 100 years.

      If you wanted to point out that I have left out feedbacks from the direct effects of CO2 in my article, you would be correct. But you don’t even have the working knowledge of the subject to notice that. Talk about a lack of scientific chops, LOL.

  10. Brian H says:

    Note the new paper by Bill Gray, . The upper troposphere is dried, not moistened, by cumulus storm clouds. There is no positive feedback, and ECS is consequently about 0.3K, +/- 0.1K.

    Your graphs will be far more graphic with those numbers plugged in!

  11. Alan McIntire says:

    Check out “Voigt Profile” on an online search. At low concentrations of a gas, wattage is proportional to N, at medium concentrations it’s proportional to SQRT(ln N), and at high concentrations, it’s proportional to SQRT(N)

  12. Philip Shehan says:

    A first order calculation of the ECS can be made from the data and compared to the theory. This involves a couple of simplifying assumptions. We ignore the cooling effect on the observed temperature of a reduction in solar activity as measured by sunspots. The Little Ice Age has been attributed to the drop in the number of sunspots during the Maunder minimum and there have been predictions of cooling due to a coming minimum. Note that in the following graph, temperature is rising in line with CO2 concentration while sunspot numbers have been declining. (The sunspot data has an 11 year smoothing to remove the 11 year solar cycle.

    There is also a cooling effect due to the increase in aerosol pollution with rapid industrialization in India and China. Then there is a lag time for the temperature to reach equilibrium for a given CO2 concentration.

    With these caveats in mind, the ECS calculated from Gistemp and UAH satellite data in the following graph. The calculations are from 1958 for the Gistemp data when Mauna Loa CO2 data became available and from 1979 for UAH satellite data which began in that year. The shorter period for the UAH data and the greater “noise” for satellite data (the variation of data points from the trend line) means that the error is larger than for the surface data.

    The resulting calculated ECS for Gistemp and UAH data are 2.6 and 2.3 C respectively. So the actual ECS taking the cooling effects mentioned into account is probably around 3 C. The IPCC range is 1.5 to 4.5 C.

    Gistemp and Muana Loa data from 1958 to June 2017

    Trend 0.157 ±0.022 °C/decade

    This gives a temperature increase for the entire 59.5 year period of

    0.934± 0.131 (The error margin is 14%)

    The rise in CO2 concentration rise in that time is from 315 to 405 ppm. (The error here is small and will be negelected)

    The relationship is logarithmic, and is given by the following equation:

    0.934 = k log(405/315) where k is the proportionality constant

    k = 0.920/0.251 = 3.72

    The temperature rise for a doubling of CO2 concentration is therefore

    3.72 x log2 =

    2.56 ± 0.36 °C

    UAH trend from 1979 (June 2017)

    0. 0.155 ±0.062 °C/decade

    The temperature change for the 38.5year period is 0.600± 0.241 C (40% error)

    Change in CO2 concentration in that period: 338 to 405 ppm

    0.600 = k log(405/338) where k is the proportionality constant

    k = 0.600/0.181 = 3.32

    The temperature rise for a doubling of CO2 concentration is therefore
    3.32 x log2 =

    2.30 ± 0.92 °C

    • davidmhoffer says:

      Well, it is a bit more complicated than that. First, you cannot assume a cooling value from sunspots activity has the historical record has no evidence that such a relationship exists, all the measurements of changes in total insolation due to changes in sun spot activity yield a change in total TSI too small to matter, and even the IPCC says the number is too small to matter (see AR5). You also cannot assume a cooling effect from increased aerosols in India and China without also assuming a warming effect due to the reduction in aerosols due to new air quality laws that have reduce the same massively in Europe and North America. The value you use for k is 3.72, the IPCC and most papers on the subject use 5.35. Recent papers on the topic are clustering around 1.5 deg/doubling or even lower, which is what forced the IPCC to reduce their estimate range in AR5 from 2.0 – 4.5 to 1.5 – 4.5. The high end of that range is supportable by the measure of any papers that have been published in the recent timeframe, the IPCC gave no rationale for retaining the upper estimate, and there just isn’t one.

      Throwing math at the problem is a waste of time until we have a firm grasp of natural variability which we do not. If calculating sensitivity were as trivial as you present above, the climate models would be hitting their projections dead on. They aren’t even close.

      • Philip Shehan says:

        I used the term “first order” because it is a calculation from the observed temperature data without quantitatively apportioning the part dues to CO2 alone, but I do give an indication of why it is likely to be an underestimate of ECS due to cooling contributions from other forcings.
        I mention that reduced sunspot numbers indicate a cooling contribution due to reduced solar activity.

        “First, you cannot assume a cooling value from sunspots activity has the historical record has no evidence that such a relationship exists…”

        I agree that the correlation is not definitive, but skeptics are very fond of pointing to the correlation between the little ice age and the Maunder and Dalton minima of sunspot activity. So much so that there has been much speculation that we are heading for a new Little Ice Age because of a new minimum sunspot period. In fact that is why I produced this graph in the first place. Not for the ECS calculation which I had done previously without refering to sunspots, but to dispute the claim being made that a new sunspot minimum would mean lower temperatures because the warming due to increasing CO2 was greater than any such temperature reduction effect of lower sunspot numbers.

        WFT also has a total solar irradiance data:

        The raw data, smoothed (to remove 11 year solar cycle) and trend values show a reduction in total solar irradiance..

        But I am quite prepared to give the benefit of the doubts to those who say that here has been no reduction in solar activity over the last 50 years. In fact the NASA calculation referred to below says that this the case.That would mean that the calculated value of the ECS, 2.6 and 2.3 are not too low, at least as far as solar contributions are concerned.

        There is still the matter of a cooling effect from increased particulate pollution due to rapid industrialisation over the past few decades , especially in India and China. Again this is an assumption that I have produced no quantitative data on, but it would seem to be well founded:

        It is true that the west has ‘cleaned up it’s act over recent decades, but Nasa calculations indicate that there has been an overall substantial cooling effect due to aerosol pollution and other anthropogenic factors such as deforestation. Although Nasa’s calculations show no change in solar radiation, the overall effect is that the observed temperature is lower than that due to only the warming contribution of increased CO2 concentration.

        I also mentioned that there is a time lag for the temperature to reach equilibrium at a given CO2 concentration. This is why it is said that even if CO2 emissions were to cease tomorrow a further temperature rise of up to 0.6 C is “locked in”.

        If a 10 year lag period is introduced into the Gistemp Mauna Loa data (Mauna Loa Data from 1958 to 2007.5 and the Gistemp data from 1968 to 2017.5), the calculated ECS is 3.2 ± 0.5 °C. For UAH it is 3.1 ± 1.5 °C. The uncertainty for the UAH data is much higher because the time for the temperature data is now only 29.5 years, compared to 49.5 for the Gistemp data.

        “The value you use for k is 3.72, the IPCC and most papers on the subject use 5.35.”

        That is because I have calculated the k factor directly from the CO2 and temperature data, with the simplifying assumption that the temperature change is entirely due to CO2 concentration change, ignoring cooling contributions mentioned above. That is why I said that the calculated ECS derived from the calculated k value is likely to be an underestimate.

        If most papers on the subject used a value of 5.35, ( Where does this come from?) the ECS would be 5.53 x log 2 (log to the base e) = 5.53 x 0.639 = 3.83 C. I consider that to be too high. Apparently you do too.

        The reason the IPCC gave for reducing the lower end from 2 to 1.5 C is that the long, high end “tail” in the probability curves for individual determinations skewed the values to a higher value. That is it is not a symmetrical curve like a normal distribution.

        That is also why there are a number of clearly too high values of 7 degrees and higher which the IPCC does not put in its range of likely values. Monckton spends a lot of time on these straw man values in his alleged “proof” of an ECS of 1.9 C.

        That is why the IPCC reduced the lower bound value. It was not because of some recent calculations having lower values.

        Published values come from models and paleodata which have relatively large uncertainties. This is why various groups come to different values, And the IPCC gives the likely range as 1.5 to 4.5, or 3 ±1.5 C.

        In AR4 the IPCC gave the mot likely value of 3 C. They did not do so in AR5, because of the skewed high end tail problem mentioned.

        That is why I decided to a purely empirical calculation based solely on observed temperature and CO2 data, ignoring the likely cooling effects of other forcings. The values i derived were 2.6 and 2.3 C which as i said is probably an underestimate as likely cooling contributions were ignored, putting the actual ECS at around 3 C, in the middle of the IPCC range.

        “Throwing math at the problem is a waste of time until we have a firm grasp of natural variability which we do not. If calculating sensitivity were as trivial as you present above, the climate models would be hitting their projections dead on. They aren’t even close.”

        Throwing math at the problem is the only way the ECS value will be more accurately determined by whatever method. That is how quantitative science works.

        Other methods use models and paleodata. I decided to take a purely empirical approach using recent instrumental temperature and CO2 data. I have noted certain simplifications and given the calculated uncertainties.

        The results are 2.6 C for Gistemp and 2.3 C for UAH satellite data, well within the IPCC range, even ignoring any cooling forcings.

        You cannot dismiss the maths unless you can point to an error in it.

      • davidmhoffer says:

        You cannot dismiss the maths unless you can point to an error in it.

        You have a boatload of “if’s” that underlie your calculations. The math can be completely correct, if a single assumption is wrong, the result is meaningless. Since we have insufficient data to quanitfy natural variability, or even the underlying trend that is probably still playing out from the Little Ice Age, nothing we calculate stands on firm ground. If you believe you are correct, by all means, publish your projections for global temps in the future based on various RCP scenarios, then wait and see if you are correct. A whole lot of very smart people with a whole lot of compute power have put together a whole lot of models in which there are no math errors, yet they cannot produce accurate projections. See the problem? The math is right, the underlying assumptions upon which the math is based are wrong.

        As for your quip about what skeptics say about the Maunder Minimum, blah, blah, blah, sorry, but you don’t get to paint with that broad a brush. It is not a homogeneous group.

      • Philip Shehan says:

        There are in fact no ‘ifs’ in the calculation from the data itself.

        I have introduced some assumptions or ifs to argue that the actual value may be higher thn calculated, and i have provided reasons in the from of calculations and data from other sources as why those assumptions are probably correct.

        Regarding the sunspots and solar activity as measured by total solar irradiance. I presented data for both that shows that they both decreasing in agreement, although the former data only goes back to 1975.

        But as I said. fine. lets not consider those assumptions. Let’s just look at how much of a rise there is in temperature for a rise in CO2 concentration, free of assumptions.
        You are left with the calculated ECS values of 2.6 and 2.3 C.

        (Monckton introduces a bucketload of assumptions into his alleged mathematical “proof” that the IPCC got the ECS too high, while coming up with values in agreement with the IPCC range, albeit at the other end. That is why I put this calculation in the comments there. My critique of his assumptions resulted in his Lordship making his usual ad hom attacks, complaining that I had critiqued his lecture to the Heartland Institute conference precisely as he had invited people to do without reading his unpublished paper, referring to my kindergarten education (I have a PhD in Nuclear Magnetic Resonance) and calling me a paid Marxist.)

        You have introduced your own evidence free assumption to claim that the ECS is actually lower, namely that there is still a rebound effect from the end of the little ice age operating. You have provided no evidence for that claim.

        “If you believe you are correct, by all means, publish your projections for global temps in the future based on various RCP scenarios”.

        Again, I have not based the calculation on any RCP scenarios. I have simply done the maths.

        I have not submitted this for publication for the reason that I began with. It is a ‘first order’ calculation, precisely because I do not have access to a whole lot of computer power and detailed data etc or the inclination to do so. It simply put on this blog and others for consideration.

        And yes there is a lot of assumptions and uncertainties. that go into calculating the ECS from paleodata and models which is why there are a range of values from these methods.
        is why as i have stated, i decided to see what a purely empirical approach gave.

        All I am saying is that calculation based on data produces ECS values well within the IPCC range. That is the IPCC range has not been falsified by this approach. Skeptics are very fond of Popper and falsification. The calculation based on empirical instrumental data alone supports the ECS being within the IPCC range.

        I make no stronger claim for the results.

        Skeptics will keep in mind the points you and i have both raised when they consider the probability of the accuracy that the resulting value.

        I consider the Nasa calculations of the contributions of forcings useful in this regard:

        Of course I understand [SNIP!} will make every opportunity to come up with reasons to dismiss it.

        mod ~ that term isn’t allowed. Call skeptics anything you want, but that term was coined for the specific purpose of associating skeptics with holocaust denial and isn’t permitted here. Thank you.

  13. Philip Shehan says:

    Pardon the typos and sloppy edits above.

    • Philip Shehan says:

      With regard to errors a correction on this data:

      Regarding the sunspots and solar activity as measured by total solar irradience. I presented data for both that shows that they both decreasing, although the data for the former is only from July 1978.

      • davidmhoffer says:

        So, over 25+ years you’re showing a decline in TSI of roughly 1/2 w/m2. Keep in mind that is the raw TSI. Subtract 30% for albedo, divide by 4 for earth being a rotating sphere and you are left with an effective change in forcing of less than 1/10th of a w/m2. Sure, technically as measured it is declining, but effectively you’re showing exactly what I said earlier. It is too small to matter.

        Going back to your math, allow me one more crack at explaining to you. IF, and ONLY if, you knew exactly what the temp of the earth would be today if CO2 had not risen over the time period in your calcs, can you calculate sensitivity. That is precisely the problem. You don’t know, no one knows, which is why the value is so hard to determine. All the correct math in the world doesn’t change that one fact.

        As for Popper, you profoundly misunderstand his philosophy.

        Logically, no number of positive outcomes at the level of experimental testing can confirm a scientific theory, but a single counterexample is logically decisive

        Your math is not an experiment. You can’t run an experiment on Earth, so you don’t know what the temp would be without additional CO2. You arrive at a value within the IPCC range and claim that the IPCC range has not been falsified by this approach. The fact is that the IPCC range can be neither confirmed nor falsified by this approach.

      • Philip Shehan says:

        No, what I was showing was that in response to your claim that sunspot number is not a good indicator of temperature, never mind that skeptics repeatedly insist that it is and that the Maunder and Dalton minima were responsible for the LIA and that the current decline leading to another minima will see the onset of another little ice age,

        I put up data showing that for the period in which TSI and sunspot data overlap, there is an excellent match in the decline of both. Here it is again

        This suggests that sunspot numbers are an indicator of total solar iradiance and therefore contribution of solar forcing to temperature.

        BUT AGAIN, I stated that is you do not wish to accept the likelyhood that the sun is making a cooling contribution THEN DON’T. FINE BY ME. The same goes for the argument on particulates or time lag.


        They were simply added as a statement of reasons (with evidence0 as to why the actual ECS may be higher than the one I calculated.

        Note that the relative scaling of sunspot numbers to the temperature and CO2 data in thisngraph is arbitrary, set only to demonstrate the qualitative fact that CO2 and temperature a are rising while sunspot numbers are falling. It gives no indication of the significance of any cooling contribution of reduced sunspot numbers to the observed temperature.

        But as you concede that there is a cooling effect but it is too small to matter , you are agreeing that it is a cooling effect, so the sun is not adding to the observed temperature, so it is not leading to an overestimate of the ECS as others have asserted when I discuss this.

        That it has little effect is also consistent with the NASA calculation i have put up twice.

        We will just stick to the figures ignoring any such arguments.

        The ECS is then 2.6 and 2.3 C for gistemp and UAH data respectively.

        ” IF, and ONLY if, you knew exactly what the temp of the earth would be today if CO2 had not risen over the time period in your calcs, can you calculate sensitivity. That is precisely the problem. You don’t know, no one knows, which is why the value is so hard to determine. All the correct math in the world doesn’t change that one fact.”

        And let me have a crack at explaining this to you once again.

        We we do know what global temperatures and CO2 concentrations were at past dates (Not exactly. Empirical data has uncertainties, which I have included for the temperature data and transferred to the ECS calculated from that data as per scientific practice. I stated before I have neglected the uncertainties for the CO2 data which is negligable compared to that for the very “noisy” temperature data.) We know the present global temperature and CO2 concentrations.

        It is PRECISELY because we have data for both the temperature rise and the CO2 rise that we can calculate the ECS.

        If there were no CO2 rise WE COULD NOT because if concentration was still 315 ppm as it was in 1958, log (315/315) = log 1 = 0. You cannot divide the temperature change by zero so you cannot calculate k or the ECS. What this actually means is that there is no dependence of temperature on CO2 concentration.

        But as we do have data for the time periods, we can calculate what he logarithmic dependence is.

        And it is 2.6 ± 0.4 °C and 2.3 ± 0.9 °C for each doubling of CO2 concentration for Gistemp and UAH temperature data respectively. (There re no exact numbers when dealing with empirical data.)

        “As for Popper, you profoundly misunderstand his philosophy.”

        Regarding Popper and falsifiability. I mentioned that because I frequently have to respond to people who quote that at me. I suspect that none of these people had ever heard of Popper or read anything by or about him except that “skeptic” blogs keep quoting him on falsifiablilty.

        I knew about Popper long before his name was conscripted into the climate debate by “skeptics” i own and have read The Logic of Scientific Discovery. I have read otyher works by and about Popper. i have a graduate qualification in the History and Philosophy of Science which i undertook part time while working as a research scientist because i had an interest in the subject.

        I sometimes explain to these instant experts that whereas Popper is an extremely important figure in the discipline, his ideas, including that on falsifiability are not the be all and end all on the subject. For example there are those of Thomas Kuhn, who coined the term paradigm shift. I have his book, The Structure of Scientific Revolutions too. And before i get the usual smart alec replies from “skeptics”, I have also read it. And other works by others in the field.

        As a scientist I can attest that Kuhn’s ideas of how scientists actually work are more in accordance with reality than Popper’s.

        But as far as Popper’s test for falsifiability goes, the results of my calculation means that the IPCC range for the ECS passes it.

        “Your math is not an experiment. You can’t run an experiment on Earth, so you don’t know what the temp would be without additional CO2.”


        Once more.

        Correct. My maths are not an experiment. Never claimed they were. They are a calculation.


        The temperature and CO2 measurements are the data showing how much the temperature has risen with additional CO2. That is the experimental data I use in my calculation.

        I already explained that. Go back and read it if you still don’t get it.

      • davidmhoffer says:

        To run an experiment, you need two earths, one with additional CO2 and one without. You don’t have the other one.

        You claim your calculations are independent of such considerations anyway, they’re not. Your calculations are inclusive of many such considerations, and since you don’t know their sign or magnitude, you don’t know how they affect your results.

        Not matter. You understand that CO2’s effects are logarithmic. Excellent.

      • Philip Shehan says:

        No you don’t need two earths. You only need data from one earth.
        Th calculation is based on temperature and CO3 data. Their magnitudes are as given. The signs of the values are positive.

  14. Philip Shehan says:

    Pardon the typos again.

    • davidmhoffer says:

      If you believe that you have experimentally valid data from a single Earth and that this satisfies Popper…. Wow. Per Einstein… That’s not right. That’s not even wrong.

      • Philip Shehan says:

        So what is this if it is not data from a single earth?

        The rise in CO2 concentration since 1958

        The rise in global average temperature since 1958:

        The calculated rise in temperature with doubling of CO2 from this data is .is 2.6 ± 0.4 °C

        The expected value for a rise in temperature with doubling of ECS according to the theory of anthhropogenic global warming is between 1.5 and 4.5 °C.

        Does the observed data falsify the theory?

        And actually the saying “That is not even wrong” is not attributed to Einstein. It is attributed to Wolfgang Pauli who was known to be somewhat ascerbic. He is also known for the Pauli exclusion principle.

        I did tell you that I have a lot of books on the history and philosphy of science and a post graduate qualification in the discipline.

      • davidmhoffer says:

        If you have to ask that question, it doesn’t matter how many books you have.

      • Philip Shehan says:

        The questions are simple enough. Is that data, and does the data falsify the theory?
        Your refusal to answer looks means you are throwing in the towel.

      • davidmhoffer says:

        You’re right, I’m throwing in the towel. You’re unable to understand that your calculations are based on a false premise. You don’t understand what an experiment actually is. You’re terribly proud of your math and insist it is correct while ignoring the physics which you have insufficient data to quantify and apply the math to and think it is OK to do that. You quote Popper, and seem to think that having his book means you understand. There really is little point in explaining to you further.

      • Philip Shehan says:

        You however have demonstrated that you qualify for the “d” word

        Further attacks of this sort and not only will I snip the comment as I did this one, I will also ban you.

      • Philip Shehan says:


  15. Philip Shehan says:


  16. William H Smith says:

    The general idea for saturation in spectral lines can be found here:

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