MODTRAN is given as an example of a well established tool that uses the same layering method as we do — or indeed anyone wanting a realistic calculation from basic physics of surface temperatures for the Earth, given our solar input.
Cp has already included the radiative effects of CO2.
Only a total plonker would then try to add radiative slabs to alter the now known correct temperatures.
Lapse rates give temperature DIFFERENCES; not temperature itself. The key issue that the greenhouse effect explains is the surface temperature.
You cannot calculate or infer surface temperatures from the lapse rate. You need something more to actually calculate the temperatures themselves, and a realistic estimate always involves numeric calculations at successive altitudes — layers, slabs, levels, slices, whatever you want to call them; and the calculations must involve absorption and emission of IR radiation; and that is governed by the greenhouse gases.
For each layer you are going to need to calculate radiation emitted and absorbed. You can’t do that with Cp.
In the troposphere, where convection establishes the lapse rate, the temperature profile is such that emission and absorption are not in balance; and every level of the atmosphere has a net loss of energy by radiation. At a stable equilibrium, convection supplies energy to make up the difference. This is called radiative convective equilibrium; it is a standard term in atmospheric physics.
In the stratosphere where convection is not involved, the lapse rate is determined by radiation effects alone, and the emission and absorption at each level is in balance. This is called radiative equilibrium; another standard term.
Cheers — Chris
