What Is the Greenhouse Effect, Really?

This post connects to previous posts on Climate Sensitivity and the Incorrect Postulate of Climate Alarmism.

Above is the Wikipedia pictorial explanation of the Green House Effect GHE (from IPCC): Of the incoming radiation from the Sun of 235 W/m2, the surface of the Earth absorbs 168 W/m2, and then by the GHE recirculates 324 W/m2. The recirculation is believed to be driven by reradiation (absorption and emission) by the atmosphere of infrared radiation from the surface of the Earth with the following key motivation:

• The ability of the atmosphere to capture and recycle energy emitted by the Earth surface is the defining characteristic of the greenhouse effect. 
  

OK, we learn that GHE amounts to "recycling of energy". We understand that recycled energy is not new input energy, just recirculation of whatever comes in from the Sun (235 W/m2) and eventually gets radiated away from the top of the atmosphere (235 Watts/m2). 

It is like the cash flow in a company with cash-in = cash-out, and a certain amount of recirculation between different branches of the company. 

How is the size of the GHE effect, the recirculating radiation, computed, that is the 324 W/m2? (And what drives the recirculation?)

Well, let's see what else of interest is presented in the above figure: Yes, the surface temperature T_S of the Earth is indicated to be 14 C. Is there a connection between 324 W/m2 and  T_S=14 C? There should be, since the whole idea is that GHE is responsible for T_S = 14 C, instead of the surface temperature without any atmosphere, which is  estimated to T_B = -18 C. Thus the GHE is viewed to increase the surface temperature by 32 C.

The idea could be that if by recycling the input to the Earth surface is not 168, but instead 168 + x, then  to get rid of that extra input x the surface temperature would have to increase by 32 C. By Stefan-Boltzmann's Radiation Law we would then get

             (168 + x)/235 =  (288/255)^4 = 1.64, that is   x = 230  W/m2.

OK, not so bad, but not quite the same:  230 vs 324. 

We make a new try: Suppose that the atmosphere reradiates the fraction c of the radiation from the Earth. Then trivial radiation balance gives 

                       (168 + x) c = x, that is x = 168/(1-c)  

and so x = 324 corresponds to  c = 0.48. Yes, why not assuming that the reradiation coefficient

is about 0.5. With x = 230 we get c = 0.27, also conceivable. 

In either case, the GHE does not include the real physics of heat transfer in the atmosphere (convection coupled with condensation-evaporation), just some very simplistic radiation assumptions. The whole concept of the GHE with its recycled radiation seems to have very 

simplistic basis.

IPCC now uses this very simplistic basis to compute climate sensitivity (without feed back) according to the rule dQ = 4 dT on the same simplistic (discussed in previous posts), and comes up with a global warming of 1 C upon doubling of CO2, as the starting point of climate alarmism. The physical basis of this results seems to be too simplistic to be able to have any scientific significance. 

The whole idea of GHE as an explanation of the temperature distribution through the atmosphere from 15 C at the Earth surface to -50 C at the tropopause to 0 C at the stratopause, seems utterly strange. How is possible that the GHE is not seriously challenged by serious scientists?

Note that the top picture by NASA does not include any "recycled energy" but instead  23% "carried (by convection) to clouds and atmosphere by latent heat in water vapour".