Climate Sensitivity 6: The SuperFerry

Global Climate is like a SuperFerry powered by radiative forcing  Q = 273 Watts/m^2 from the Sun, and radiating back the same to outer space from the top of the stratosphere at T = 273 K = 0 C, according to Stefan-Boltzmann's Radiation Law

                                                     Q = c TTTT .

You don't easily change the trajectory of a SuperFerry, but is it easy to change Global Climate?

Is Global Climate sensitive to changes in radiative forcing? If we remember a tiny bit of Calculus, we may get the idea to differentiate Stefan-Boltzmann's Law to get 

                             dQ = 4 c TTT dT = 4 Q/T dT = 4 dT .

Beautiful! You can now say that if you change radiative forcing by 4 Watts/m^2 , roughly 1% of

the incoming/outgoing 273 Watts/m^2, then dT = 1 Kelvin K (or 1 Celsius C). See Climate System Modeling by Kevin Trenberth.

You have just derived the basis of IPCC climate alarmism: 1% change of forcing is small, but 

a corresponding 1 C of global warming is alarming, in particular if you combine it with various positive feed backs to inflate it up to 4.5 C. The alarm clock sounds because the radiative forcing from doubling CO2 in the atmosphere is, guess, about 4 Watts/m^2. 

Voila: A small extra radiative forcing dQ = 4 Watts/m^2 from CO2 threatens to destroy human civilization by global warming with dT = 1.5 - 4.5 C.

As further support, the formula dQ = 4 dT is fed into a Climate Model in two ways: The Sea Surface Temperature SST is increased by 1 C, and the radiative forcing by dQ = 4 Watts/m^2, and the Climate Model then with the help of a supercomputer and a bit of positive feed back,

delivers global warming of 1.5 - 4.5 C. 

The formula dQ = 4 dT is presented by IPCC as rock solid undeniable fundamental physics which cannot be disputed by any sane person. Even skeptics like Richard Lindzen (and the Reference Frame) buys this formula but then seeks to compensate by negative feed back to bring down 1 C to the less alarming 0.5 C. 

But wait! We applied Stefan-Boltzmann to the top of the stratosphere, and did not have a chance to use a very important piece of information: 

                                                 SST = 15 C.

And global warming concerns change of SST, the temperature at the surface of the Earth,

which is very different from the temperature at the top of the stratosphere. 

If we think of it, we understand that the atmosphere acts like an insulating medium connecting

surface temperature to outer atmosphere temperature, in a similar way as an isolating window connects the inside of  a room (at say 15 C) to the outside (at say 0 C). 

Now, no sane engineer would seek to determine the inside temperature of a building by using only Stefan-Bolzmann's Radiation Law. A sane engineer would instead use Fourier's Law stating that the heat flow through a window is proportional to the temperature difference inside-outside. 

Using Fourier's Law we understand that 1% change of forcing corresponds to 1% of the temperature difference, that is 0.15 C. 

The sane engineer would thus conclude that, modulo positive/negative feed backs) the climate

sensitivity is 0.15 C, almost a factor 10 smaller than the 1 C of IPCC climate alarmism.

So what do you say?  Or the Royal Academy?