A Global Warming Calculation. Doubling CO2 to 800ppmv makes one fifth of a degree warming.

So since around COP26, in some of my spare time. I calculated just how much CO2 (and water vapour), absorbs heat radiation from earth. Based on the 3 (4 for H20) strongest absorption lines in the HITRAN database that come from absorption of a photon by the ground state. Going from 400 ppvm CO2 to 800 ppvm, increases absorbtion by just 1.1 Watts per square meter. Below is the chart of absorption by part per million watts of CO2 in the atmosphere.

I have made the code public, at my github. Finishing off a paper with the details of the calculation, but it is basically integrating over latitude, frequency and height, the absorption line and line width with a Lorentzian Line shape. Lorentz is known to be larger than actually absorption at frequencies away from the peak, so this is an over estimate. So how much heating does the extra 1.1 Watts cause. If all the heat goes into the emission, then by Stefan Boltzaman, https://en.wikipedia.org/wiki/Climate_sensitivity, Note 2, 1 Watt is 1 Kelvin (or C) warming. But that for any warming, some of that heat going into evaporating water, so the temperature change well be lower. I will look at evaporation at a later time. Updating this post, now I have done climate sensitivity including rainfall calculation, while the naive temperature increase is about 1.1Kelvin, with rainfall it is only a sixth of that about 0.167 Kelvin.