Here is a another argument indicating that the effect of the atmospheric trace gas CO2 on the radiation balance of the Earth is small.
We recall the model of blackbody radiation studied on Computational Blackbody Radiation as a collection of oscillators with small damping with equal oscillator internal energy T representing temperature, with oscillator resonance frequencies n varying from 1 to a cut-off set at T and each oscillator radiating
- E_n = gamma T n^2
- E = sum_n gamma T n^2 = sigma T^4
- e = gamma T T^2 = gamma T^3 ~ E/T