There is a growing group of scientist attempting to pin the lack of warming tail on atmospheric pressure. They are right but wrong because they assume that pressure is the horse and surface temperature the cart. Local temperature and pressure and that potential temperature/energy makes up the wagon.
If the surface emits photons at 270K degrees in the spectrum of a greenhouse gas, the energy absorbed by that greenhouse gas is dependent on the temperature of the gas. Simple right?
Well, the total energy of the gas absorption is dependent on the pressure of the gas which is dependent on the density ie thermal mass of the gas layer.
Think about the thermosphere. It has a high temperature and no significant heat. No significant heat because it has no significant thermal mass. So the average potential temperature of the average radiant layer of the gas has to be considered.
Potential temperature is commonly used in meteorology. It relates the temperature of a parcel of air at one temperature and pressure to another. CO2 absorbs photons of the right wave length and energy to fill its absorption spectrum. The total energy of the absorption spectrum is approximated by it Planck envelop which is related to the fourth power of temperature. As the gas layer grows colder the energy it absorbs decreases rapidly, by the fourth power of the temperature.
This is fairly well known in climate science and expected to be observable as greater warming in the upper part of the troposphere. The troposphere radiant layer should be about 1.2 degrees warmer than the surface emitting the outgoing long wave radiation absorbed by the greenhouse gases in that layer. According to the theory of global warming, that should produce about 1.0 degrees of warming at the surface. Only one problem, the surface is not emitting the photons absorbed by the average radiant layer.
Because the surface atmosphere in most regions is effectively saturated by the abondance of greenhouse gases due to the higher density and pressure of the lower atmosphere, energy absorbed by the surface ghgs is transferred by collision warming the air mass which cools adiabatically with the reduced density of the air mass so it rises to a new lower pressure level. That air mass or parcel of air contains the same energy in a larger volume. If it were forced back to the surface, the temperature felt at the surface would directly proportional to the energy of the parcel. But, that is an adiabatic process, not added or removed, the only thing that changes is the pressure. When that parcel at the lower pressure emits photons, it is no longer adiabatic, something changed. It gave up some of its heat to something outside of that parcel.
The photon emitted from the parcel has an energy dependent on the temperature of the parcel at that altitude. If that parcel is higher in altitude meaning lower in temperature, the energy emitted reduce by the fourth power of the temperature from the source of the absorption to the temperature of the emission. At the surface, the free path length is extremely short so this is not a significant factor. As altitude increases the free path length increase so it begins to become significant.
When that greenhouse gas is not a gas, but a liquid or solid version of water, latent heats leaps frog the mean free path length. Now it gets interesting.
The potential energy of the packet of water or ice crystals is much greater than the energy of the gases at the lower pressure. The gases at altitude can only absorb in their spectrum which has wave length AND energy constraints. The gas can absorb a photon at the proper wave length with greater energy, but can only emit photons based on its energy envelop, on average, constrained by the fourth power of its temperature.
While this is all very well known, the equations used by climates scientists do not appear to include the impact of the average radiant layer of the greenhouse gases which increases in altitude with warming. The Planck response limits the amount of warming until the entire radiant layer reaches sufficient energy to return sufficient energy to be felt at the surface.
Natural convection, diffuses the energy absorbed vertically and horizontally increasing the rate of cooling in the average radiant layer. While temperature can be used in the laws of thermodynamic, it can only be used when the energy and the work done by that energy are consistent with the change in temperature. That is not the case in our complex climate system.
Energy is fungible, the work done is not. So the potential temperature of the climate system, which includes the energy of that parcel of atmosphere, must be considered.