Basic Evidence of Low Emissivity of CO2

A basic estimate of the radiative forcing of CO2 as atmospheric trace gas from its main resonance at wave number 667, can be obtained as follows from Planck's Law in the form

• R(n,T) = gamma T n^2 for n < 4T,

where n is wave number, T ~ 300 K is temperature and R(n,T) is radiation per unit of wave number and gamma is a constant. The total outgoing long wave radiation OLR from the Earth surface at temperature T assuming the atmosphere to be transparent,  is then equal to the integral of R(n,T) over 0< n < 4T:   

• OLR = gamma * 64/3 T^4 .

Adding the trace gas CO2 will block radiation in an interval around 667 ~ 2T of width 1 (motivated on Computational Blackbody Radiation as a basic phenomenon of near-resonance), with a blocking effect B given by

• B = gamma * 4 T^3 . 

The emissivity of an atmosphere with CO2 as trace gas can then be estimated as the relative blocking effect B/OLR = 12/64 T < 0.001 of the main resonance at 667.

This is similar to the estimate 0.002 presented in a previous post, with the doubling resulting from the weaker spectral lines away from the main resonance.

Notice that the blocking effect of the main resonance of CO2 is in principle independent of concentration, which can be seen as an extreme form of logarithmic dependence with full effect at saturation already for small concentration.

The radiative forcing corresponding to an emissivity of 0.002 will be smaller than 0.5 W/m2 (as 0.2% of a total of about 200 W/m2), which is a factor 10 smaller than the 3.7 W/m2 serving as the basis of CO2 alarmism predicted by Modtran.

With the emissivity from the main resonance at 667 very small, the 3.7 W/m2 must result from the Modtran models of line broadening for spectral lines on the "shoulders" of the spectrum away from 667. CO2 alarmism thus critically depends on theoretical models of a phenomenon, which is so subtle that experimental evidence appears to be impossible.