Climate Sensitivity 7: Radiation Only

Suppose as a thought experiment we remove the troposphere with its convection-evaporation/condensation from the atmosphere and consider a system consisting of the Earth together with a stratosphere only governed by radiation. 

The radiation from the Sun would be absorbed partly by the stratosphere and partly by the Earth, all of which would eventually be re-emitted as infrared radiation from the stratopause, the outer surface of the Earth-stratosphere system. The Earth  and the stratosphere would then be in radiative equilibrium at the same temperature, which we can assume to be the 0 C of the present stratopause, which is the Earth black-body temperature balancing that of the Sun. 

The Earth with stratosphere would then act as one black body of temperature 0 C, independent of the transparency of the stratosphere, emitting as infrared radiation whatever was absorbed.

This would be an inhabitable Earth different from the real case at 15 C, and so a model only based on radiation is incompatible with observation.

Nevertheless, let us ask what the climate sensitivity of this system would be, that is the change of temperature dT upon a change of (i) transparency of stratosphere or (ii) insolation dQ?

We have just concluded that (i) gives dT = 0, and in previous posts on climate sensitivity we have shown that (ii) gives  dT = 0.25 dQ.

(i) gives a very small climate sensitivity, while (ii) with  dT = 0.25 dQ by IPCC  is presented as alarming.

Now IPCC with support in e.g.  Radiative Forcing of Climate Change: Expanding the Concept and Addressing Uncertainties (2005) Board on Atmospheric Sciences and Climate argues as follows:

• dQ is estimated to 2.8 W/m2 by using dT = 0.25 dQ with an observed dT = 0.7 C during the 20th century.
• doubled dQ during the 21st century gives dT = 1.5 C: Alarm!

To see if this is Penguin Logic or scientific logic, we must ask from where does the dQ come?

From change of insolation? No because that is not human induced AGW. OK so the change

comes from change of transparency of the stratosphere. But we just noticed that in this case dT = 0, which is not alarming. So we have a clear case of Penguin Logic.

We have seen that in an Earth-atmosphere model with radiation only, there can be no AGW from greenhouse gasses. 

OK, so we have to include the troposphere with convection..., but then the dT = 0.25 dQ no longer can be assumed, so even if we accept some dQ from AGW, its effect on temperature

cannot be estimated by dT = 0.25 dQ, and IPCC does not present any other relation.

The basic question of climate sensitivity needs a complete restart. In IPCC AR5? By some 

Royal Academy?