Summary. The total greenhouse effect from CO2 at 280 ppm CO2 is 2.5 C and when CO2 is increased to 460 ppm the additional temperature rise will be 0.2 C if the water vapor staid the same.. When absolute temperature rises 1.5 C the temperature rise will be another 0.057C. When temperature rises 1.5C and relative humidity stays constant there will be a temperature decrease of 0.117C For a total increase of 0.14C. (The temperature rise from 10% increase in water vapor is already taken care of in point 1: The greenhouse effect of water vapor and by adding more CO2 some of that increase must be subtracted out).
At the beginning of the industrialization the CO2 level was 280 ppm. It will be 460 ppm in 2050 if the world keep using CO2 at today’s level, but since China alone plans to build another 1050 coal burning electric plants before then the 2050 level could be higher. If there was no water vapor in the air CO2 alone would contribute 7.1C to the greenhouse effect at 280 ppm, and 7.8C at 460 ppm. To understand why the greenhouse effect increased so little when the CO2 concentration increased 64% let us look at the absorption spectrum for CO2 in the 14.9 micron region.
The CO2 absorption is saturated between 14.2 microns and 15.7 microns at 280 ppm. At 460 ppm it is saturated between 14.0 ppm and 16.0 ppm. Between 13 and 14,2 micron and 16.7 and 18 micron it will absorb more, from about 60% more at low absorption down to almost no extra absorption near saturation. The result is no increased absorption between 14.2 to 15.7 micron; all increase occurs at the edges, so that the total increase will be, not 64% but only 9% if there is only CO2 and no water vapor due to the total saturation of CO2 in the atmosphere for most of the absorption band.
This chart explains the net effect on radiation, from the sun or from the earth.
The incoming solar radiation includes ultraviolet radiation, visible light and near infrared radiation. This is all the heat incoming to the earth, except what is conducted from the earth’s core. All area under the curves of the right half represent greenhouse gases absorption, except the blue area which represents energy radiated into space. The all dominant green-house gas is water vapor but CO2 contributes with absorption bands, at 4.3 microns, 9.4, 10,4 and 14.9 microns. The 4.3 micron absorption is of almost no importance since it occurs at a wavelength where very little radiation is available, neither from the sun, nor from the earth’s black body radiation.
Let us take a closer look at the outgoing black body radiation and the atmospheric window:
The first thing to notice is that no absorption exceeds 100% , so at 14.9 micron wavelength CO2 absorbs 100%, and water vapor absorbs another 80%, the total sum is still 100%. It is impossible to absorb more than 100% of the total energy available for that wavelength. Therefore between the wavelengths 14 and 16 microns all energy is absorbed regardless of CO2 concentration and water vapor concentration. The olive area represents the extra absorption of CO2 at 280 ppm when the water vapor is taken out (you cannot absorb more than 100%). The small yellow slivers represent the extra CO2 absorption at 460 ppm. The white area between the brown total absorption area and the red earth emission line is the total energy emitted through the atmospheric window.
(There exists a good measuring point, where the all dominant greenhouse gases are CO2, Methane, NO2 and O3. At the South Pole in the winter the air is clean, there is almost no water vapor and the winter temperature at the Amundsen–Scott South Pole Station between April and September 2021, a frigid minus-78 degrees (minus-61 Celsius), was the coldest on record dating back to 1957, and the trend is 1 C colder per century. (In the summer humidity increases and for summers the trend is increasing temperatures.) The winter cooling trend is a hint that rising CO2, CH4, N3O and O3 levels are not the dominant factors in temperature rise.)
Besides the absorption window in the 14,9 micron band that absorbs 100% of the available energy water is fundamental and the majority of the energy is already absorbed. But there are smaller absorption in the 10.5, 9.5 and 4.3 micron. The 10.5 and 9.5 micron wavelength do not saturate. so they participate with their full strength when CO2 increases but the 4,3 micron is in a region where there is not much energy emitted , and what is emitted is nearly all absorbed by water vapor. The total greenhouse effect from CO2 at 280 ppm CO2 is 2.5 C and when CO2 is increased to 460 ppm the additional temperature rise will be 0.2 C, if the water vapor staid the same. But the water vapor has increased 10% due to an increase in global temperature by 1.5C. This will lead to a temperature increase from the 2.11% increased absorption from CO2, in the 12.5 to 17 micron band is total CO2 greenhouse effect of 0.2 C x 0.0211 or 0.057C increase when the base increase of water vapor is subtracted out.
The other effect that must be subtracted out is: Temperature is increased 1.5C which results in absolute humidity increase of 10% assuming relative humidity stays constant, so we must subtract out the absorption increase from water vapor in the 12.5 to 14 micron band. The higher wavelengths are of no importance for this calculation since they are already saturated. This amounts to a temperature decrease of 0.117C, so the net temperature increase from a CO2 increase of 64% from 280 ppm to 460 ppm and at the same time water vapor increases 10% is:
0.2 C + 0,057C – 0.117C = 0.14C +- 0.05C.