"Adiabatic cooling" refers to the process of reducing the temperature of something by allowing it to expand without adding or removing heat. It occurs when air or a gas expands, causing its molecules to spread out, which in turn lowers its temperature.
Full definition
Possibly, the solution to this is that in the real atmopshere the movement of this level is severely constrained (mainly
by adiabatic cooling) and so can not rise enough to produce your solution.
I would suggest these small aerosols have a large effect on the
saturated adiabatic cooling and heating cycles and the transport of water vapor latent heat poleward.
The meridional stratification contrast is created
by adiabatic cooling and warming by the residual circulation, as this circulation must be deflected vertically to avoid the mixing barrier at the jet maximum.
This causes the relative humidity to increase due to
the adiabatic cooling.
«Increase GHG... atmosphere expands... thus it cools...» Fine so far, but note that the expansion due to radiation pressure is of order only 1 part in 1E11, so
the adiabatic cooling is only of order 1 nanokelvin (and that much only if you go from optically thin all the way to optically thick).
The Process of
Adiabatic Cooling and Heating.