Why is the claim that greenhouse gases warm up the Earth by 33°C wrong

 The claim that greenhouse gases warm up the Earth by 33°C refers a joint statement by national academies of Brazil, Canada, China, France, Germany, India, Italy, Japan, Russia, UK and USA in 2005: “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.”  This claim has been widely endorsed since by numerous academic institutions including the IPCC around the world. 

However, this claim turns out false; it is simply a result of misuse of the Stefan-Boltzmann law by climate scientists.  When deriving this conclusion, climate scientists made technical errors:

1)      treating  the Earth as a blackbody while it never is;

2)      using wrong temperature quantity that is not the temperature quantity defined by the physics essence of the Stefan-Boltzmann law;

3)      classifying temperatures raised by greenhouse gases as a different physical quantity outside the Stefan-Boltzmann  as well as other related physics laws.

Detailed analysis is summarized in a ppt presentation, which can be downloaded from this Acribd link:

https://www.scribd.com/document/358487453/CaoJ-CC2-2014

  

Common errors in the use of the Stefan-Boltzmann equation

Climate scientists make technical errors in their use of the Stefan-Boltzmann equation.

The Stefan-Boltzmann equation is simple: a black-body object with surface temperature, T, emits energy per unit time and unit surface area, J, the energy flux density:

            J = σ T⁴                                                                                                                           (1)

where σ is the Stefan-Boltzmann constant equal to 5.67 x 10^-8 (W/m²K⁴). 

When the Stefan-Boltzmann law is applied to the Earth-Atmosphere system, climate scientists often make one or more of these technical errors:

i)        a coefficient ε in the range 0 to 1, called emissivity should multiply the right hand side when applied to objects that are not black bodies; 

ii)       a failure to specify correctly the “surface” and “surface temperature” of the Earth-Atmosphere system;

iii)     a failure to specify whether or not a layer of air is a single object or a cluster of objects.

 Following statements (methodologies) have been proven a result of misuse of the Stefan-Boltzmann equation:

1) the 33°C greenhouse warming effect for the Earth;

2) the 390 W/m² surface radiation in the Earth Energy Budget;

3) the 1˚C CO₂ non-feedback climate sensitivity; and

            4) the formula for emission by a layer of air.

There is no surprise that scientists can make errors, but it is perhaps a surprise that the technical errors have been shared by so many scientists across a discipline to such an unprecedented extent. 

The full article (PDF file) can be downloaded from link:  http://jonova.s3.amazonaws.com/guest/cao-jinan/jcao_common-errors-stefan-boltzman_aug2012.pdf