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Δ𝐸=133.26+0.044[𝐶𝑂2]
It’s just a numerical coincidence that the 0.044 looks like the molar mass of CO2. That equation gives 0.044 * 380 = 16 W/m2, which is the reduction in surface downwelling IR if you remove all the CO2 from the present day atmosphere (e.g., see Table 1 of Zhong and Haigh, 2013, Weather, https://doi.org/10.1002/wea.2072, pdf).
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