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This is a subject on which I have posted several articles in the past. I agree with some but not all of Jinan’s claims.
Firstly, the warmists derive the -33C by assuming an albedo for earth of 0.3 as Jinan mentions however one needs to recognize that most of this albedo is due to clouds which are water vapour. Without green house gases ie: without water vapour earth’s albedo would be more like that of the moon (0.12) so the received radiation would be higher (390 * .88) leading to a surface temperature of 279K or +6C.
Now Jinan makes the point that the surface emissivity is much less than 1, in fact more like 0.7 derived from the albedo. I have to disagree with this, the albedo comes from reflection of visible light by clouds. The liquid water surface which comprises 70% of earth’s surface has an emissivity in the thermal infrared of about 0.96 which is indeed very close to 1. Land may have a somewhat lower emissivity but even there, surface covered by vegetation has a high emissivity in the thermal infrared.
Jinan makes the point that one must consider each wavelength region separately and here I totally and absolutely agree with him. This is to me is a fundamental error make by warmists when the talk about an equivalent radiation altitude. In the atmospheric window the atmosphere is transparent and the emission comes directly from the surface (or from cloud tops where the surface is covered by clouds). At green house gas absorption wavelengths the atmosphere is opaque and emission comes from the top of the green house gas column exactly as Jinan claims, and as he correctly states the temperature of the gas at this altitude is more like -50C (basically the tropopause or very low stratosphere) certainly not +14C. If anyone has any doubt about this point, I invite them to look at Earth’s emission spectrum as seen from space (Nimbus satellite). At these wavelengths the emissivity of the atmosphere is exactly 1. This comes about because emissivity always equals absorptivity. If the gas column absorbs all the energy radiated form the surface it has an absorptivity of 1 hence an emissivity of 1 as well.
It is Jinan’s point 2.4 which I disagree with most. It is not necessary to consider the emission of each molecule separately. For a layer of air thick enough to absorb all energy radiated up from below the layer as a whole has an emissivity of 1 (at that wavelength of course) and can be treated as a black body emitter at that wavelength (which means one can apply Planks law which defines energy emitted at a particular wavelength NOT Stefan Boltzman law which defines emission for an object which is a black body at all wavelengths).
As to the sensitivity to doubling CO2; we know there is a logarithmic relationship between ghg concentration and energy retained. We know how much energy CO2 currently retains simply by looking at the emission spectrum of Earth as seen by the Nimbus satellite. Without CO2 the emission temperature at around 14.7 microns would be that of the surface +14C instead of what it actually is -50C. We can either integrate Planks law over the wavelength absorption range of CO2 or graphically look at the reduction in area under the curve of the emission spectrum to space the result is 27 watts/sqM. We also know the total absorbance of the CO2 column at 280 PPM and it is about 2000 abs. That represents 10-11 doublings from the point at which the line center saturates (which is where the logarithmic relationship starts) so the incremental effect of doubling CO2 is 2.7 watts/sqM (I disagree with the warmists 3.7 watts/sqM figure). My calculation ignores the impact of clouds. If this is taken into account the 2.7 watts/sqM figure is reduced somewhat because cloud tops are cooler than the surface thus without CO2 the emission to space would be less than a surface at +14C would imply.
This comment is already too long so let me finish by re-iterating, I agree with much but not all of what Jinan states but my conclusions do indeed agree with his.