A Published Paper on “wrong formula” for Feedbacks, but How Political?

OK, I’m in favor of the paper from a personal bias point of view. But that doesn’t make it right.

It purports to show that there is a single incorrect formula involving feedback amplification that is shown to be wrong. Scanning the paper, I find evidence and assertion, but not a direct frontal assault. So does it show that formula is the location of the fault, or just that “something is wrong” in the IPCC results? I suspect that will take a long slow read over a pot of tea…

Until then, for your reading pleasure, some links and some light commentary.

First off, I ran into this at TallBlokes, so here’s that link:


His write up (that looks like a direct reblog) doesn’t mention a couple of important things, like who wrote the paper and where it was published. Does give two links. One to where he found it, and one to the PDF itself. (That is also at the site where he ran into a write up.) Here’s a sample:

No rogue equation means no climate crisis.

It says the amount by which climate scientists multiply the direct warming from, say, CO2 to allow for “temperature feedbacks” – changes to the climate because it has warmed that make it warm still further – is equal to the reciprocal of 1 minus a third of the sum of all the feedbacks.

They say the feedbacks, measured in Watts per square meter of the Earth per Celsius degree of direct warming, add up to 2. So the equation tells them to multiply by 3. Just 1 Celsius degree of warming from doubling CO2 in the air suddenly, wrongly becomes 3 degrees. A non-event becomes a crisis.

James Hansen – the former director of NASA’s Goddard Institute for Space Studies (who once said anyone who questioned his math should be tried for “high crimes against humanity”, for which the penalty is death) – had lifted the rogue equation, the Bode system-gain relation, from a 551-page tome by R.W. Bode about feedback amplification in electronic circuits, published 70 years ago.

First off, for folks wanting to get to the meat directly, here’s the PDF location:


And here is the link where TallBloke picked up the story:


So why my hesitancy to just embrace the excitement of a final slam dunk nuking of AGW models and theory? Well, read the paper…

First off, the authors. All folks I like, but the list includes Monckton who is polarizing to the AGW side. Often writing clear, but simplified explanations of what happens. While I like that, it isn’t the typical style of an academic paper. So it could go either way. A real and meaty academic treatment, or an effective position paper that doesn’t really go into enough depth to prove the claims to an academic review level. So reading in detail required to sort that out.

Why models run hot: results from an irreducibly
simple climate model

Christopher Monckton • Willie W.-H. Soon •
David R. Legates • William M. Briggs

OK, we’ve got some decent names here, and it is unlikely you would find such a paper authored by folks not aligned with the Skeptic side of things, but I can see the Warmista True Believers not reading any further than that list of names and dismissing it with a character assassination or two…

Received: 27 August 2014 / Accepted: 12 November 2014 / Published online: 8 January 2015
Science China Press and Springer-Verlag Berlin Heidelberg 2015

It was kicked around for about 4 months, then another 2 getting into publication.

China? It had to go to China to get published? I hear more mud being loaded into slings…

But also Springer-Verlag in Germany. That’s got some chops.

Abstract An irreducibly simple climate-sensitivity
model is designed to empower even non-specialists to
research the question how much global warming we may
cause. In 1990, the First Assessment Report of the Intergovernmental
Panel on Climate Change (IPCC) expressed
‘‘substantial confidence’’ that near-term global warming
would occur twice as fast as subsequent observation. Given
rising CO2 concentration, few models predicted no warming
since 2001. Between the pre-final and published drafts
of the Fifth Assessment Report, IPCC cut its near-term
warming projection substantially, substituting ‘‘expert
assessment’’ for models’ near-term predictions. Yet its
long-range predictions remain unaltered. The model indicates
that IPCC’s reduction of the feedback sum from 1.9
to 1.5 W m-2 K-1 mandates a reduction from 3.2 to 2.2 K
in its central climate-sensitivity estimate; that, since feedbacks
are likely to be net-negative, a better estimate is
1.0 K; that there is no unrealized global warming in the
pipeline; that global warming this century will be < 1 K;
and that combustion of all recoverable fossil fuels will
cause < 2.2 K global warming to equilibrium. Resolving
the discrepancies between the methodology adopted by
IPCC in its Fourth and Fifth Assessment Reports that are
highlighted in the present paper is vital. Once those discrepancies
are taken into account, the impact of anthropogenic
global warming over the next century, and even as
far as equilibrium many millennia hence, may be no more
than one-third to one-half of IPCC’s current projections.
Keywords Climate change Climate sensitivity
Climate models Global warming Temperature
feedbacks Dynamical systems

There follows a bit of historical review, then some “empirical evidence” for hot models (the usual IPPC predictions, er projections, er conjectures, er SWAGs (Scientific Wild Ass Guesses…)) and then it goes into an alternative “model”.

After exploring and calibrating the model for a while, the paper goes on to review / critique the IPCC / ARx models and results. The “meat” of the claim for a wrong formula seems to come in on page 129 (numbering starts at 122, so this is only 7 pages of paper text. Also note some formulas got a bit mangled in the PDF cut / paste):

8.3.1 The CO2 forcing
Delta F sub t

RCP 8.5 is the ‘‘business-as-usual’’ scenario in AR5.
However, the assumptions underlying it are unrealistic (see
Discussion). In the more realistic RCP 6.0 scenario,
atmospheric CO2 concentration, currently 400 ppmv, is
projected to reach 670 ppmv by 2100, so that DFt from
2015 to 2100 will be 5.35 ln(670/400), or 2.760 W m-2

8.3.2 The feedback sum f

A plausible upper bound to f may be found by recalling that
absolute surface temperature has varied by only 1 % or 3 K
either side of the 810,000-year mean [40, 41]. This robust
thermostasis [42, 43], notwithstanding Milankovich and
other forcings, suggests the absence of strongly net-positive
temperature feedbacks acting on the climate.
In Fig. 5, a regime of temperature stability is represented
by g(sub infinity) ≤ 0.1, the maximum value allowed by process
engineers designing electronic circuits intended not to
oscillate under any operating conditions. Thus, assuming
g(sub infinity) ≤ 0.5, values of f(sub infinity) fall on [-1.6, +0.3], giving Lambda(sub infinity) on
[0.21, 0.35]. Where f(sub infinity) is thus at most barely net-positive, the
corresponding equilibrium-sensitivity interval is well constrained,
falling on [0.8, 1.3] K. Of course, other assumptions
might be made; however, in a near-perfectly thermostatic
system, net-negative feedback is plausible, indicating that the
climate—far from amplifying any temperature changes
caused by a direct forcing—dampens them instead. Indeed,
this damping should be expected, since temperature change is
not merely a bare output, as voltage change is in an electronic
circuit: temperature change is also the instrument of self equilibration
in the system, since radiative balance following
a forcing is restored by the prevalence of a higher temperature.
Also, in electronic circuits, the singularity at g(sub infinity) = +1,
where the voltage transits from the positive to the negative
rail, has a physical meaning: in the climate, it has none. A
damping term absent in the models is thus required in Eq. (7)
and may be represented in Eq. (1) by a reduction of Lambda (sub infinity).

OK, that looks more like an assertion to me than a proof… but I’m not prone to writing papers and think more in terms of math proofs (which I rather enjoyed doing years ago).

The rest of the paper seems to set about showing the “simple model” more closely matches observations, so must be the right one (or the more correct one). While I tend to agree with that claim, I’m not sure better wiggle matching is “proof” (though is grounds for using this model over the clearly more wrong IPCC / ARx ones).

At any rate, there’s the links, the story, and the paper. See what you think of it.

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About E.M.Smith

A technical managerial sort interested in things from Stonehenge to computer science. My present "hot buttons' are the mythology of Climate Change and ancient metrology; but things change...
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5 Responses to A Published Paper on “wrong formula” for Feedbacks, but How Political?

  1. tallbloke says:

    Thanks EM, I didn’t have time to go into it, as I’m puzzling over gravity and phi again as I juggle too many batons…

  2. Steve C says:

    I’ve played with too many amplifiers that oscillate and oscillators that won’t not to have a grim appreciation of feedback conditions. They can be right buggers to keep sweet even when you think you understand ’em and have full control. I don’t think I’ve ever seen a definitive equation-level explanation of climate code though, so hope to see one ere too long so I can see this equation in situ and work out what’s going on.

    Also, the character assassination has already started … on WUWT

    Sigh. So damn easy to write the script yourself, but still they expect you to believe fantasy is reality.

  3. E.M.Smith says:


    Been there, done that ;-)

    In fact, doing such juggling now as I prepare for a move across a continent and / or find a job in Florida and have my life up in the air in any case…

    hope my overview “dive” helps, and thanks to you for the pointer to the paper.

    @Steve C:

    I downloaded the code for one of the models. It’s a strange mix of oversimplification of reality with horridly long and complex implementation / operations. Haven’t had the time or courage yet to try to uncomplexify it back to a statement of “what does this do?”.

    Near as I can tell, they just glue bits on as each Grad Student gets their Ph.D. and it has not real “spec” or design docs. Oh Well…

    And then there is that predictable foaming at the mouth of the attack dogs with hydrophobia…

  4. omanuel says:

    One incorrect formula in the Standard Climate Model does not make up for seventy years (2015 – 1945 = 70 years) of purposeful deceit in astronomy, astrophysics, climatology, cosmology, geology, meteorology, nuclear, particle, planetary, solar & theoretical physics, using deceptive:

    1. Standard Solar Models
    2. Standard Nuclear Models
    3. Big Bang Model of Cosmology
    4. Manipulation of Observations and Experimental Measurements that were made with public funds from the US DOE, NASA, EPA, NOAA, etc., etc.

    FEAR of deceitful government science that hid the Creator, Destroyer and Sustainer of every atom life and world in the solar system has induced mental, emotional and spiritual illness in society worldwide.

    FEAR is the most powerful emotion and easily overwhelms logic.

    FEAR of nuclear annihilation in 1945 is the root cause of today’s social insanity, induced by common knowledge politicians, world leaders, their puppet scientists and perhaps even members of the medical and banking community are lying.

  5. omanuel says:

    As usual, the liars themselves are the last to recognize the problem.

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