We consider a model of the atmosphere as two damped oscillators here coupled in series with for simplicity acoustic damping, one with big mass M and velocity V representing O2 and N2, and one with small mass m and velocity v representing the trace gas CO2, both subject to the forcing F.
The analysis of Computational Blackbody Radiation shows that the emission E of the system as the energy consumed by the damping, is given as
- E = d v^2 + D^2 V^2 with dv^2 = D^2V^2 = F^2
- T = mv^2 + MV^2.
- E ~ 2 x D^2/M x T
- epsilon = 2 x D^2/M
In other words, we have in a simple model discovered small emissivity of the system compared with the (maximal) emissivity of the small resonant component, that is small atmospheric emissivity by the presence of the resonant trace gas CO2.