Both of these "proofs" and strawman arguments fail because the troposphere is in horizontal equilibrium due to gravity and center of mass at a particular latitude, but is in complete vertical disequilibrium due to convection and the lapse rate between the surface vertically rising to the tropopause. Further, if an atmosphere was 100% non-greenhouse gases, it would still be subject to gravity and convection calculated by the greenhouse equation, and thus absolutely not isothermal. A container of pure nitrogen with a heat source at the bottom would definitely convect, and convection is what controls the lapse rate and vertical temperature profile in the troposphere.
Basically, the greenhouse equation determines the unique solution for temperature at any height given the opposing vertical disequilibrium from convection and the opposing horizontal gravitational equilibrium at that same height.
Thus, the apparent misunderstanding of these "refutations" has arisen from a false assumption that fails to differentiate vertical and horizontal equilibrium.
We have previously shown the greenhouse equation precisely determines the unique temperature at any vertical height from the surface up to ~11,000 meter top of the tropopause, based upon the local horizontal equilibrium at that particular height.
Satellite observations indeed show a remarkable horizontal equilibrium at a given center of mass of the overlying vertical atmospheric mass:
Newsflash: Heat rises
and the vast majority of that heat rise is vertical due to the vertical, not horizontal, disequilibrium due to the vertical vector of gravitational force with zero horizontal gravitational forcing. Deal with it, and I hope that clears it up.
h/t to ren at Tallbloke's talkshop for posting link to top graphic which was perfect to illustrate this point and said
"It is clear that the troposphere is heated uniformly from the surface of the Earth. Thus, the center of mass of the troposphere is logical."couldn't agree more.