Leading Climate Sensitivity Scientist “Admits Mathematical Errors in The AGW Theory”!

Mr. Kyoji Kimoto has asked me to post the following essay, which tells us leading climate sensitivity scientist Dr. Robert Cess admits the IPCC assumptions are erroneous. (Note: Because WordPress didn’t handle some of the scientific notation, I had to cut and paste parts of the text as images).

Dr. Robert D. Cess admits mathematical errors in the AGW theory of the IPCC

by Kyoji Kimoto

Soden & Held [1] shows climate sensitivity is 3°K for 2xCO2 from the 14 GCM studies for the IPCC 4th Assessment Report (2007) as follows:

Climate sensitivity = no-feedback sensitivity (Planck response) x feedbacks

= 1.2°K x 2.5 = 3°K

Here, feedbacks are water vapor, ice albedo, lapse rate and cloud feedback.

In the AGW theory of the IPCC, the central assumption is that the Planck response is 1.2°K. Cess [2, 3] obtained the Planck feedback parameter lambda0 of -3.3(W/m2)/K utilizing eqn (1), giving the Planck response of 1.2K with the radiative forcing RF of 4W/m2 for 2xCO2 as follows:


Coincidently, the Planck response of 1.2°K by eqn (3) is in very good agreement with the Planck response of 1.2 – 1.3°K obtained with one dimensional radiative convective equilibrium model (1DRCM) studies in the literature [4, 5, 6]. Therefore, the Cess method has been followed by many researchers, including the IPCC 1st Assessment Report (1990) and the 14 GCM studies for the IPCC 4th Assessment Report (2007).

It is the sole theoretical basis of the central assumption of the IPCC that the Planck response is 1.2°K at present time [7, 8, 9], because the 1 DRCM study is fudged due to its strong dependence on lapse rate used according to Hansen’s idea expressed in an interview with Spencer Weart held on 23 October, 2000 at NASA.



On 23 August, 2016, Dr. Robert D. Cess gave me the following answer to my mail, admitting his mathematical errors in the derivation from eqn (1) to eqn (3). Dr. Cess was the leading climate scientist of Intercomparison Project of GCMs for the IPCC Assessment Reports. He wrote:

I will try this one more time, and then I will give up. A lot has happened since M&S (1964) and M&W (1967). In modern usage, the no-feedback sensitivity refers to holding all climate parameters fixed except surface temperature. It addresses the question: What would the sensitivity be if there were no interactive climate feedback mechanisms?.  Simply stated, it is a hypothetical reference sensitivity.  NO ONE HAS EVER CLAIMED THAT THE NO-FEEDBACK SENSITIVITY IS A TRUE INDICATION OF THE REAL SENSITIVITY.

The AGW theory of the IPCC is constructed on the Planck response of 1.2°K produced by the mathematically erroneous Cess method. Since Cess has admitted his mathematical errors in the above reply, the theory totally collapses together with the high climate sensitivity of 3°K for a doubling of CO2. It raises sea surface temperature as much as 2°K, thus leading to the various AGW scares such as rapid sea level rise and severer extreme weather in the GCM studies of the IPCC.

Kimoto [11] showed the surface climate sensitivity of 0.14-0.17°K with the surface radiative forcing of 1.1 W/m2 for 2xCO2. It is reduced from the radiative forcing of 3.7 W/m2 at the tropopause due to infrared absorption overlap between CO2 and water vapor plentifully existing at the surface.

Policy based on false science

There is no need for the restriction of fossil fuel usage from the AGW scares claimed by the IPCC with its mathematically erroneous GCM studies. And ratification of Paris climate deal is harmful to mankind due to its useless CO2 regulations causing huge economic losses to the world.


Fig.1 Energy budget of the earth adapted from R.V. Dorland (2006)

Er: long wave surface radiation   Ee: evaporation    Et: thermal conduction

Eb: long wave back radiation     Eu: long wave upward radiation

Ew: atmospheric window         Ea: long wave absorbed by the atmosphere

Es: short wave absorbed by the atmosphere    WV: water vapor, CL: cloud


  1. Soden, B.J. and Held, I.M., An assessment of climate feedbacks in coupled ocean-atmosphere models. J. Climate, 2006, 19, 3354-3360.
  2. Cess, R.D., An appraisal of atmospheric feedback mechanisms employing zonal climatology, J. Atmospheric Sciences, 1976, 33, 1831-1843.
  3. Cess, R.D., Potter, G.L., Blanchet, J.P., Boer, G.J., Ghan, S.J., Kiehl, J.T., Le Treut, H., Li, Z.X., Liang, X.Z., Mitchell, J.F.B., Morcrette, J.J., Randall, D.A., Riches, M.R., Roeckner, E., Schlese, U., Slingo, A., Taylor, K.E., Washington, W.M., Wetherald, R.T. and Yagai, I., Interpretation of cloud-climate feedback as produced by 14 atmospheric general circulation models, Science, 1989, 245, 513-516.
  4. Manabe, S. and Wetherald, R.T., Thermal equilibrium of the atmosphere with a given distribution of relative humidity, J. Atmospheric Sciences, 1967, 24, 241-259.
  5. Hansen, J., Johnson, D., Lacis, A., Lebedeff, S., Lee, P., Rind, D. and Russell, G., Climate impact of increasing atmospheric carbon dioxide, Science 1981, 213, 957-966.
  6. Schlesinger, M.E., Equilibrium and transient climatic warming induced by increased atmospheric CO2, Climate Dynamics, 1986, 1, 35-51.
  7. Wetherald, R.T. and Manabe, S., Cloud feedback processes in a general circulation model, J. Atmospheric Sciences, 1988, 45, 1397-1415.
  8. Tsushima, Y., Manabe, S., Influence of cloud feedback on annual variation of global mean surface temperature, Journal of Geophysical Research, 2001, 106, 22,635-22,646.
  9. Tsushima, Y., Abe-Ouchi, A. and Manabe, S., Radiative damping of annual variation in global mean temperature: comparison between observed and simulated feedbacks, Climate Dynamics, 2005, 24, 591-597.
  10. Kimoto, K., On the confusion of Planck feedback parameters, Energy & Environment, 2009, 20, 1057-1066.
  11. Kimoto, K., Will coal save Japan and the world?, Energy & Environment, 2015, 26, 1055-1067.
  12. Schlesinger, M.E., Feedback analysis of results from energy balance and radiative-convective models. In: MacCracken M.C., Luther F.J., (eds) Projecting the Climatic effects of Increasing Carbon Dioxide, DOE/ER-0237 US Department of Energy, Washington DC, pp. 280-319.
  13. Hansen, J., Lacis, A., Rind, D., Russell, G., Stone, P., Fung, I., Ruedy, R.and Lerner, J., Climate sensitivity: Analysis of feedback mechanisms in Climate Processes and Climate Sensitivity, J.E. Hansen and T. Takahashi, Eds. (American Geophysical Union, Washington, D.C., 1984), pp. 130-163.

18 responses to “Leading Climate Sensitivity Scientist “Admits Mathematical Errors in The AGW Theory”!”

  1. Jamie

    When you corrupt science with the promise of a trillion dollar carbon trading floor, when otherwise rational scientists call statistical prediction ‘settled science’, when scientists who dare present counter-hypothesis are called ‘deniers’ and are threatened with jail — it is clear that the scientific method has been abandoned in favor of greed, manipulation, and self-aggrandizement.

  2. BobW in NC

    Sooooooooo… we are talking “pseudoscience”?

    I’ve collected the following characteristics, and climate change (AKA “AGW”) fits every one of them:

    So…The essence of pseudoscience is found in any endeavor that:
    • attempts to present itself as science, but
    • does not adhere to the rigorous standards of the scientific method in how it is performed, or
    • simply can not be performed by the scientific method; specifically, that it…
    • proposes hypotheses that can not be shown to be wrong through data obtained by direct experiment or purposeful, designed observational studies, and
    • uses euphemisms, vague or ambiguous phrasing, and wording that can mean whatever the individual wants it to mean, and finally
    • presents detailed evidence only consistent with its conclusions but that utterly fails to carefully explore (“omits”) evidence that is not consistent with them, and
    • failing to look for evidence inconsistent with its hypothesis, has ever been the foundation of pseudoscience.

    Amen, brother, Amen!

  3. tom0mason

    Dr. Robert D. Cess should be applauded for admitting that there is an error and showing what it means. The sign of a good, honest scientist is being prepared to admit error when they are found.
    All to often these days scientist are shown to be in error and they just bluster their way through, unable to allow and facts impact on their inflated hubris.

    Too many ‘scientists’ act like spoiled children with their favorite unchallengeable toy theory.

  4. AlecM

    Actually, the real error is far more profound than admitted by Cess. His claim that Earth’s mean outgoing Longwave Radiation (OLR), emitted at -18 deg C, to its mean surface exitance, emitted at +15 deg C, is its radiant emissivity is a serious scientific error.

    This is because a radiant emissivity calculation requires identical geometry AND emission temperature. What’s worse is the implication that the difference of surface exitance and OLR, termed the ‘clear atmosphere greenhouse factor, is absorbed in the atmosphere. This is junk science at its worst.

    To claim this absorption and thermalisation exists gives 40% extra atmospheric warming than reality. To offset this imaginary heating, the 1-D model by Wang et al which apparently legitimised Cess’ 1.2 K CO2 climate sensitivity, assumed negative convection. This was admitted by Hansen, part of that team, to an AIP interviewer in 2000 to be ‘a fudge’ but he claimed the 3-D models were fine.

    They are not fine: presumably to make the scam less detectable the UK’s Hadley Centre replaced negative convection with a Kirchhoff’s Law of Radiation argument which to provide imaginary ‘back radiation’ in the Atmospheric Window had to use incorrect cloud optical physics. That same ‘fudge’ also creates imaginary ‘positive feedback’.

    We have all been conned by people who knew they were conning us.i

  5. tom0mason


    I am amazed but not that surprised at
    “They are not fine: presumably to make the scam less detectable the UK’s Hadley Centre replaced negative convection with a Kirchhoff’s Law of Radiation argument which to provide imaginary ‘back radiation’ in the Atmospheric Window had to use incorrect cloud optical physics. That same ‘fudge’ also creates imaginary ‘positive feedback’.”

    If there was one area that Cess investigated extensively it was clouds, and cloud optical properties. He more than anyone should be able to see clear through Hadley’s errors, as well as the Hansen fudge.

  6. JamesG

    Read that email again; he does not admit any error! From the intemperate tone of the email I doubt he even considered the question in the first place. The shouty last sentence just means that he still believes the ‘real sensitivity’ is 3K regardless of the no-feedback number and does not like any pesky skeptic amateur impuning otherwise.

    1. wert

      He admits error, but believes it is in the other direction. Who knows. I don’t.

      This ‘high school physics’ is bound to be in error, no doubt.

    2. ScottM

      Sure, it isn’t an admission of a mathematical error. It’s a restatement of conditions inherent in the definition. It would only be a mathematical error if the math were inconsistent with those conditions.

    3. Jamie

      He ‘believes’the real sensitivity is 3K … Sounds more like faith to me than ‘settled science’.

      1. ScottM

        You put “believes” in quotes, as if you are quoting *him* rather than *yourself*.

        1. Jamie

          I am quoting you:

          “he still believes the ‘real sensitivity’ is 3K”

          And since we are on the subject, why are you so hostile to those who propose counter-hypothesis to the warmists, after all that is the scientific method … not ‘he still believes.’

          You warmists have to get your ‘beliefs’ straightened out before you go off peddling them as ‘settled science.’

          1. ScottM

            Apologies, it was JamesG that said it. Now you owe me an apology for a similar misattribution. And another for the accusation of hostility. I am open to rational arguments, rationally presented; I also will not hesitate to call out irrationality when I see it.

  7. ScottM

    Kimoto cites his own paper, which errs in assuming that the evaporation and thermal conduction terms follow the same 4th power law as radiation, and thus will have comparable magnitude in the derivative. I wonder if he will cop to the error.

    1. AlecM

      Yup: I have picked this out. However, he has been working in parallel to me and has provided some key information, in particular that in year 2000, Hansen admitted 1976_Wang_etal.pdf (on the NASA repository of papers) used imaginary ‘negative convection’, which does not exist, to justify Cess’ claims earlier that year.

  8. Jeremy

    Pierre Gosselin, you may recall, back in 2008, two years before the equal hottest year on record so far, said he thought that Earth would become icy cold by 2020, writing (archived here):

    Pierre Gosselin says:
    October 23, 2008 at 2:03 am
    -2.5°C by 2020!

    Some powerful cycles appear to be aligning to deliver a vicious deep freeze.

    – Solar cycles

    – Ocean cycles – PDO, AMO, etc.

    – and the 100K year ice-age cycle

    There are some things to keep in mind:

    1. Climate does not change gradually.

    2. Climate changes abruptly, without warning.

    3. Temperatures over the last 2 million years have been colder than today’s 95+% of the time.

    4. Warm, like today, is in fact highly unusual.

    5. Our current interglacial has been abnormally long.

    6. Interglacial are more often much briefer, short-lived spikes.

    6. Thus, the climate dice are not in our favour!

    Ice ages have occurred right ON SCHEDULE for the last 3 million years.

    And if you examine the interglacial temperature peaks, i.e the brief optimums between the cold intervals, you’ll see our modern optimum is indeed prolonged. More often the interglacials are just brief spikes that suddenly nosedive back into prolonged deep-freezes. Now the sun is going to sleep, and the oceans are reversing to boot!

    My prediction is we’ve started a nasty cold period that will make the 1960s look balmy. We’re about to get caught with our pants down.

    And a few molecules of CO2 is not going to change it.

    Here is what Pierre’s prediction looks like. In six years from now, according to Pierre Gosselin, the temperature will drop to 2.5 degrees Celsius below that at the beginning of the 20th century:

  9. Dodgy Geezer

    OK – so the maths is suspect. That can be sorted – a new paper can be published.

    Unfortunately, the policy directives resulting from the AGW theory are not so easy to change. Human society cannot just stop rapidly and go in another direction. Planck’s point that science advances by funerals is much more applicable to policy directives.

    We will have to wait for all the current politicians and activists to die before we can actually start building any new power stations…

  10. bobl

    A lot wrong here.

    Problem numero UNO is the unsubstantiated assumption that Outgoing Longwave Radiation should equal incoming insolation – Hmm sounds on the surface reasonable but totally indefensible. If that was true then the “Climate” is a lossless perpetual motion machine.

    What’s wrong with that radiative balance is what is left out. Things like

    Lightning and other electrical energies
    Bulk kinetic energies driven by heat (waves and wind)
    Energy absorbed in Photosynthesis
    Surface absorption and other heat sinks – eg polar ice
    Entropy losses (eg rocks cracking, weathering, movement of masses)
    Chemical processes eg Mammals turning sunlight + Cholesterol into Vitamin D

    on the other side of the ledger

    Volcanic heat
    Friction caused by gravitationally/derived wind/tides
    Energy introduced by the constant flexing of the earths crust by the gravitation of the moon/sun (bend a wire back and forth and see what happens)
    Centripetal forces from the rotation of the earth causing constant flows from equator to poles.
    Bioenergy for example humans emit around 200Watts at rest and 800 Watts or more when active, multiply that by 7 Billion, then account for the bioactivity of all other species or even say Termites or plankton or rats and mice.
    Solar wind

    The idea that OLR=Insolation is “Not even wrong” it’s properly stated as

    OLR = Insolation + NRG – NRL

    NRD = Non Radiative Gains
    NRL = Non Radiative Losses

    Climate science ASSUMES that NRG and NRL are negligible ( less than 1000th of ) compared with Insolation but has *never* proved it so. Without knowing the magnitude of NRL and NRG accurately the whole of climate modelling is utterly meaningless.

    Lets take a look at JUST ONE – Bioheat.

    On earth there is around 1 -4 Trillion Carbon tonnes of live biomass, since Carbon is about 30% of the mass of an organism we can estimate live biomass is around 3E 15 Kg – 1.2 E16 kg from this we can say that the average biomass per square meter is 3 E15 / 5.1 E14 = 5.9 – 1.2E16 / 5.1 E14 = 23 kg biomass per square meter or around the equivalent of 0.1 – 0.5 people per square meter. If these organisms generate bioheat at the same rate as humans say 300W average per 50 kg then the total bioheat into the “Climate” is around 0.1 x 300 = 30W per square meter – 150 W per square meter or 10% up to 40% of the insolation from the sun at the surface. Clearly a significant heat source, certainly not negligible.

    Yet bioheat doesn’t factor into the climate heat balance. Bioheat must be one of those special kinds of heat that doesn’t radiate…