Total Emissivity of the Earth and Atmospheric Carbon Dioxide: A Note from Nasif S. Nahle
Central to the theory of Anthropogenic Global Warming (AGW) is the assumption that the Earth and every one of its subsystems behaviors as if they were blackbodies, that is their “emissivity” potential is calculated as 1.0. 
But this is an erroneous assumption because the Earth and its subsystems are not blackbodies, but gray-bodies. The Earth and all of its subsystems are gray-bodies because they do not absorb the whole load of radiant energy that they receive from the Sun and they do not emit the whole load of radiant energy that they absorb.   
Furthermore the role of carbon dioxide is misunderstood. According to AGW hypothesis, carbon dioxide is the second most significant driver of the Earth’s temperature, behind the water vapor, which is considered the most important driver of the Earth’s climate.  Other authors of AGW discharge absolutely the role of water vapor and focus their arguments on the carbon dioxide. 
What is the total emissivity of carbon dioxide? I will consider this question with reference to the science of radiative heat transfer.
Total Emissivity of the Carbon Dioxide – The Partial Pressures Method
In 1954, Hoyt C. Hottel undertook an experiment for determining the total emissivity of the carbon dioxide and the water vapor . He found that the total emissivity was linked to the temperature of the gas and its partial pressure. As the temperature increased above 277 K, the total emissivity of the carbon dioxide decreased, and as the partial pressure (p) of the carbon dioxide increased, its total emissivity also increased.
Hottel found also that the total emissivity of the carbon dioxide in a saturated state was very low (Ɛcd = 0.23 at 1.524 atm-m and Tcd = 1,116 °C). 
As Hottel diminished the partial pressure of the carbon dioxide, its total emissivity also decreased in such form that, below a partial pressure of 0.006096 atm-m and a temperature of 33 °C, the total emissivity of the carbon dioxide was not quantifiable because it was almost zero.   
After Hottel’s experiment, in 1972, Bo Leckner made the same experiment and corrected and error on the graphs plotted by Hottel. However, Leckner’s results placed the carbon dioxide in a lower stand than that found by Hottel.  
The missing part, however, remained at the real partial pressure of the carbon dioxide in the Earth’s atmosphere and instantaneous temperatures. Contemporary authors, like Michael Modest, and Donald Pitts and Leighton Sissom made use of the following formula to know the total emissivity of the carbon dioxide considering the whole emissive spectrum, at any instantaneous tropospheric temperature and altitude   :
Ɛcd = [1 – (((a-1 * 1 –PE)/(a + b – (1 + PE)) * e (-c (Log10 ((paL)m / paL)^2))] * (Ɛcd)0 
Introducing 7700 meters as the average altitude of the troposphere and the real partial pressure of the atmospheric carbon dioxide (0.00038 atm-m), the resulting total emissivity of the carbon dioxide is 0.0017 (0.002, rounding up the number).
Evidently, the carbon dioxide is not a blackbody, but a very inefficient emitter (a gray-body). For comparison, Acetylene has a total emissivity that is 485 times higher than the total emissivity of the carbon dioxide.
After getting this outstanding result, I proceeded to test my results by means of another methodology that is also based on experimental and observational data. The algorithm is outlined in the following section.
Total Emissivity of CO2 – Mean Free Path Length and Crossing Time Lapse of Quantum/Waves Method
The mean free path length is the distance traversed by quantum/waves through a given medium before it collides with a particle with gravitational mass. The crossing time lapse is the time spent by the quantum/waves on crossing a determined medium; in this case, the atmosphere is such medium.
As the carbon dioxide is an absorber of longwave IR, we will consider only the quantum/waves emitted by the surface towards the outer space.
The mean free path length of quantum/waves emitted by the surface, traversing the Earth’s troposphere, is l = 47 m, and the crossing time is t = 0.0042 s (4.2 milliseconds).  
Considering l = 47 m to know the crossing time lapse of quantum/waves through the troposphere, I obtained the crossing time lapse t = 0.0042 s. By introducing t into the following equation, we obtain the real total emissivity of the atmospheric carbon dioxide:
Ɛcd = [1-(e (t * (- 1/s))] / √π  
Ɛcd = [1-(e (0.0042 s * (1/s))] / √ 3.141592… = 0.0024
Therefore, the total emissivity of the atmospheric carbon dioxide obtained by considering the mean free path length and the crossing time lapse for the quantum/waves emitted from the surface coincides with the value obtained from the partial pressures method:
Ɛcd 1 = 0.0017 = 0.0017
Ɛcd 2 = 0.0024 = 0.0024
The difference is 0.0007, which is trivial in this kind of assessment.
In the introduction I asked: What is the total emissivity of carbon dioxide?
In this note I have calculated the real total emissivity of the atmospheric carbon dioxide at its current partial pressure and instantaneous temperature to be 0.002.
Clearly carbon dioxide is not a nearly blackbody system as suggested by the IPCC and does not have an emissivity of 1.0. Quite the opposite, given its total absorptivity, which is the same than its total emissivity, the carbon dioxide is a quite inefficient – on absorbing and emitting radiation – making it a gray-body.
Accepting that carbon dioxide is not a black body and that the potential of the carbon dioxide to absorb and emit radiant energy is negligible, I conclude that the AGW hypothesis is based on unreal magnitudes, unreal processes and unreal physics.
This blog post was inspired by Chapter 12 of the book ‘Slaying the Sky Dragon.
“This first catechism will be referred to in a later figure as the ‘Cold Earth Fallacy’, and it is based on the erroneous assumption that the earth’s surface and all the other entities involved in its radiative losses to free space all have unit emissivity. The second catechism has already been discussed: the contention that Venus’ high surface temperature is caused by the ‘greenhouse effect’ of its CO2 atmosphere.”
-Dr. Martin Hertzberg. Slaying the Sky Dragon-Death of the Greenhouse Gas Theory. 2011. Chapter 12. Page 163. 
[1.] Hertzberg, Martin. Slaying the Sky Dragon-Death of the Greenhouse Gas Theory. 2011. Chapter 12. Page 163.
[6.] Hottel, H. C. Radiant Heat Transmission-3rd Edition. 1954. McGraw-Hill, NY.
[7.] Leckner, B. The Spectral and Total Emissivity of Water Vapor and Carbon Dioxide. Combustion and Flame. Volume 17; Issue 1; August 1971, Pages 37-44.
[8.] Modest, Michael F. Radiative Heat Transfer-Second Edition. 2003. Elsevier Science, USA and Academic Press, UK.
[9.] Lang, Kenneth. 2006. Astrophysical Formulae. Springer-Verlag Berlin Heidelberg. Vol. 1. Sections 1.11 and 1.12.
[10.] Maoz, Dan. Astrophysics in a Nutshell. 2007. Princeton University Press. Pp. 36-41
[11.] Dr. Hertzberg is an internationally recognized expert on combustion, flames, explosions, and fire research with over 100 publications in those areas. He established and supervised the explosion testing laboratory at the U. S. Bureau of Mines facility in Pittsburgh (now NIOSH). Test equipment developed in that laboratory have been widely replicated and incorporated into ASTM standards. Published test results from that laboratory are used for the hazard evaluation of industrial dusts and gases. While with the Federal Government he served as a consultant for several Government Agencies (MSHA, DOE, NAS) and professional groups (such as EPRI). He is the author of two US patents: 1) Submicron Particulate Detectors, and 2) Multichannel Infrared Pyrometers. http://www.explosionexpert.com/pages/1/index.htm
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