So we have the surprising logical conclusion that GHGs should actually facilitate atmospheric cooling by
permitting upward radiation which could not otherwise occur.
James Shearer's comment about «If the emissivity of the layer is low, most of the
additional upward radiation can pass right through the layer without warming it» is one of those it depends things.
When upward radiation close to the right frequency hits a CO2 molecule, it can excite the vibrational mode at that frequency.
He uses Kirchhoff's law and the two energy balances (ground to lower atmosphere, upper atmosphere to space) to derive the result: The long
wave upward radiation from the surface is limited to 1.5 times the short wave downward radiation from the Sun.
Given this, it is quite clear that any reduction in the efficiency
of upward radiation (by, say, reflecting it right back down again), will have to be compensated for by increasing the air / sea (skin) temperature difference, hence having a warmer subsurface temperature.
But then there's feedbacks within the stratosphere (water vapor), which would increase the stratospheric heating
by upward radiation from below, as well as add some feedback to the downward flux at TRPP that the upward flux at TRPP would have to respond to via warming below TRPP.
The internal kinetic energy is taken as the upward long wave energy flux at the top of the atmosphere, and the potential energy is
the upward radiation flux from the surface.
This result is used to determine the fraction of
the upward radiation from the surface that is transmitted directly to space (rather than absorbed by the atmosphere), which is 1/6.
The current theory does not assume an energy balance between the surface and the lower atmosphere, and allows
the upward radiation from the surface to be twice the short wave downward radiation from the Sun.