Wednesday, October 31, 2012
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