Wednesday, November 23, 2011

False assumption of black-body earth surface leading to false illusion of global warming

The false assumption that the earth surface is a black body surface has been identified being a fatal technical error leading to false illusion of global warming.

The Stefan-Boltzmann law states that a black-body object with surface temperature, T, emits energy σT4 per unit time and unit surface area, where σ is the Stefan-Boltzmann constant equal to 5.670373 x 10-8 (W/m2K4).  For an object with any surface, it emits ε σT4, where ε is surface emissivity of the object.  ε is a value between 0 and 1; 0 is literally for white and transparent bodies, and 1 for black bodies.  Most substances are grey bodies with 0 < ε < 1. 

When the Stefan-Boltzmann law is applied to calculate the Earth’s outgoing emission flux, Qe, one shall write:
     Q=  4prε  σT4
where, r, is radius of the Earth,  and T is the Earth’s mean surface temperature; 4pr2 constitutes of the surface area of the Earth.
In current climate research, ε is either missing in the expression or asserted to be unit.  By taking ε = 1, one has assumed the earth surface a black-body surface, which means that almost everything on the earth surface ¾ ocean, soil, snow and vegetations etc are all objects with black-body surface!  Truly this is illogically wrong. 

For a given outgoing flux, Qe, the calculated mean earth surface temperature T for ε = 1.0 becomes lower than that for ε < 1.0.    

This technical error has led to a widely spreading misunderstanding that the Earth would be much colder should there is no greenhouse gas effect.  With ε = 1.0, one obtains T = -18°C, which is then compared with actual mean near surface air temperature 15°C.  The difference 33°C has been considered a common measure of the greenhouse effect [e.g. Lucis et al. “Atmospheric CO2: Principal Control Knob Governing Earth’s Temperature” Science 33, 356-359 (2010)].

Numerous documents have made similar statements without realising the value of -18°C is incorrect.  The Joint Science Academies’ Statement: Global Response to Climate Change (2005) by academies of Brazil, Canada, China, France, Germany, India, Italy, Japan, Russia, UK and USA stated:
“The existence of greenhouse gases in the atmosphere is vital to life on Earth – in their absence average temperatures would be about 30 centigrade degrees lower than they are today.”
CSIRO’s Science and Solutions for Australia – Climate Change (2010) writes:
“The surface of the planet would be more than 30°C cooler than it is now without this natural greenhouse effect, and life as we know it would not be possible.”
After quoting the Science paper, the Australian Climate Commission Report – The Critical Decade (2011) continues:
“In fact, without these long-lived greenhouse gases, the Earth’s temperature would drop rapidly and drive the planet into an ice-bound state.”

It is a collective error in current climate research.  One can find the error in peer reviewed academic publications as well as in climate science textbooks.  It may prove to be the most expensive technical error we ever had in the human history.  (By Dr. J. Cao, Australia)


  1. Hi Dr Cao

    First, let me applaud you on your courage shown by posting these thought provoking articles.

    May I ask you to clarify the following..

    "With ε = 1.0, one obtains T = -18°C, which is then compared with actual mean near surface air temperature 15°C"

    I was under the impression that -18DegC is obtained by using (1-albedo) or .7 not 1.

    e.g. 1,368 W/m2 x (1 - albedo) = 4 x s x T4

    (where s is the SB constant)

    Or, using Earth's average albedo of 0.31 and solving for T:

    T4 = [1,368 W/m2 x (0.69)] / 4s

    Which yields T = 254 K ( = -19° Celsius = -3° Fahrenheit)



  2. Hi Oguzhan;

    Thanks for your comment.

    Yes, you are right. -18°C was obtained as you've shown. My point is the equation should be:

    1,368 W/m2 x (1 - albedo) = ε x 4 x s x T4

    where, ε has been proven 0.702 rather than 1.0 in a separate paper.
    J. Cao

  3. Nice post. Marginally related is that the emissivity (e) of liquid water must be virtually zero in the IR. Before my time carbon-arc movie projectors used a half-inch layer of water to filter out all the IR, which would o'wise burn up the film. It's not likely that water could reflect or transmit any IR. ~2/3 of Earth surface is H2O - certainly not even close to a BB. RSS

  4. Better yet, adding to the poor application of scientific principles employed by the "climate" scientists, it appears that the basic program modeling the planet was designed for describing star energy budgets. They scaled it down to a very cold, smaller star and called it a planet.

    They apparently still assume that the Earth absorbs sunlight and emits energy, like a star, from all sides 24/7 and do not allow for a half-lit planet which is emitting and not absorbing energy over half its surface at any given time.

    This situation is so far from reality, it HAS to fail.

    Charles HIgley

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  6. To Ron and Charles Hlgley;

    From laboratory IR spectra, we know nothing on earth is black body - even pitch black is only around 0.97. Water perhaps is 0.7-0.8 or so.

    In calculation how much the Earth absorbs the solar radiation, everybody knows to multiply a coeffient a (absorptivity = 1 - albeto), but it is forgotten to multiply a coeffient e (emissivity) in calculation using the Stefan-Boltzmann law for how much the Earth emits.