If any reader does genuinely understand the process described in statements of the Second Law* then they would realise that, for there to be no unbalanaced energy potentials, decreases in gravitational potential energy must be offset by increases in kinetic energy. Computationally, using <i>Cp</i> as specific heat and equating PE loss with KE gain, the latter being the energy to raise mass <i>M</i> by temperature difference <i>dT</i> when there is downward molecular movement through a height difference of <i>dH</i> then we get ...
<i>M.g.dH = M.Cp.dT<i />
<i>dT/dH = g/Cp</i>
which is the temperature gradient when thermodynamic equilibrium is attained in non-radiating gases. because of the temperature levelling effect of inter-molecular radiation, so-called GH gases reduce the magnitude of the gravitationally induced temperature gradient, as observed in all significant planetary tropospheres. Thus the thermal profile rotates and the temperature at the base of the troposphere (and in any surface there) is reduced.
* <i>"Processes in which the entropy of an isolated system would decrease do not occur, or, in every process taking place in an isolated system, the entropy of the system either increases or remains constant
"</i>
That version of the 2nd law comes from the textbook <i>An Introduction to Thermodynamics, the Kinetic Theory of Gases, and Statistical Mechanics</i> (2nd edition), by Francis Weston Sears, Addison-Wesley, 1950, 1953, page 111 (Chapter 7, "the Second Law of Thermodynamics").
Note the reference to "every process" which eliminates the climatology invention of "net" effects now being espoused in Wikipedia.
