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. 

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