If the addition of optical thickness to some band is able to sufficiently cool the uppermost layers sufficiently, OLR would be reduced in
the optically thicker bands as well; if warming occurs in uppermost layers, OLR would increase in
the optically thicker bands.
OLR increases in the optically thinner bands would lead to atmospheric warming in general, but this has to be accompanied by OLR decreases somewhere, such as in
optically thicker bands (and always in the band where optical thickness was added, assuming positive lapse rates everywhere as is the case in a 1 - dimensional equilibrium model with zero solar heating above the tropopause, or at least not too much solar heating in some distributions), which will tend to cause cooling of upper levels.
Not exact matches
However, some of the OLR and upward fluxes in upper levels in general come from other levels, especially in
optically -
thicker bands.
Warming must occur below the tropopause to increase the net LW flux out of the tropopause to balance the tropopause - level forcing; there is some feedback at that point as the stratosphere is «forced» by the fraction of that increase which it absorbs, and a fraction of that is transfered back to the tropopause level — for an
optically thick stratosphere that could be significant, but I think it may be minor for the Earth as it is (while CO2 optical thickness of the stratosphere alone is large near the center of the
band, most of the wavelengths in which the stratosphere is not transparent have a more moderate optical thickness on the order of 1 (mainly from stratospheric water vapor; stratospheric ozone makes a contribution over a narrow wavelength
band, reaching somewhat larger optical thickness than stratospheric water vapor)(in the limit of an
optically thin stratosphere at most wavelengths where the stratosphere is not transparent, changes in the net flux out of the stratosphere caused by stratospheric warming or cooling will tend to be evenly split between upward at TOA and downward at the tropopause; with greater
optically thickness over a larger fraction of
optically - significant wavelengths, the distribution of warming or cooling within the stratosphere will affect how such a change is distributed, and it would even be possible for stratospheric adjustment to have opposite effects on the downward flux at the tropopause and the upward flux at TOA).
The atmosphere is
optically «
thick» in those
bands
Likewise, the emission of CO2 within its absorption
bands is just as effective as its interception, therefore this energy is partitioned throughout the atmosphere and radiated back to earth in its majority (because the escape of energy through the
optically thick higher levels of the atmosphere reduces the flux, whereas the earth is still
optically close by and a ready recipient of IR radiation.
Quadrupling the CO2 makes the portions of the spectrum in the yellow
bands optically thick, essentially adding new absorption there and reducing the transmission of infrared through the layer.