On Climate Sensitivity 3

Summarizing the previous Climate Sensitivity posts 1 and  2, we have

• The Earth seen as a black body without atmosphere would according to Stefan-Boltzmann's radiation law have a surface temperature 21 times smaller than that of the Sun.
• Assuming the surface temperature of the Sun to be 5700 K (or 5250 K) we obtain a black body Earth surface temperature of 273 K (250 K). Without atmosphere the temperature would be 0 Celcius (-23 C). Not pleasant. Like during a cloudfree dry air night in Sahara.
• With atmosphere (with clouds and water vapour) the Earth surface temperature is 288 K. 
• The upper atmosphere must act like a blackbody and radiate whatever comes in at 273 K (250 K).
• The net insolation to the Earth-atmosphere is 69% of a total incoming radiation of 380 W/m^2 = 262 W / m^2.
• The temperature effect of the atmosphere per unit net insolation, is 15/262 (38/262)
• A radiative forcing of 1 W/m^2 thus can be estimated to give a temperature rise of 0.06 (0.14) C.
• The radiative forcing from doubling CO2 in the atmopshere is estimated to be 2-4 W/m^2, which would give a climate sensitivity of 0.12-0.24 (0.28-0.56) C. 
• IPCC AR claims the climate sensitivity to be in the interval 1.5 - 4.5 C. The IPPC upper bound is about 40 times the above lower bound. The IPPC lower bound is about 3 times the above upper bound. 
• The estimated feed back factor changing the above simple radiation estimate is thus a factor 3 - 40.  

I don´t see IPCC (or anyone) presenting physical mechanisms capable of producing so large feed-back factors (can it be some dark energy popping up?). Concerning the origin of 

the 1.5 - 4.5 interval, note what Wikipedia controled by IPCC writes:

• The standard modern estimate of climate sensitivity - 3°C, plus or minus 1.5°C - originates with a committee on anthropogenic global warming convened in 1979 by the National Academy of Sciences and chaired by Jule Charney. Only two sets of models were available; one, due to Syukuro Manabe, exhibited a climate sensitivity of 2°C, the other, due to James E. Hansen, exhibited a climate sensitivity of 4°C. "According to Manabe, Charney chose 0.5°C as a not-unreasonable margin of error, subtracted it from Manabe’s number, and added it to Hansen’s. Thus was born the 1.5°C-to-4.5°C range of likely climate sensitivity that has appeared in every greenhouse assessment since..."^[7]
  

On the contrary, the fact that the early Earth with a weaker Sun  was not deep frozen indicates that the global mean temperature really is quite insensitive to varying insolation. In particular, global mean temperature (whatever that means) does not vary much over glacial and interglacial periods.  See the recent WUWT post Lies, Damned Lies, Statistics and Graphs..

Compare also A Complete List of Things Caused by Global Warming (if there are any...)

This conforms with the position of Lindzen and Spencer that climate sensitivity is small.

Spencer also gives an argument that you can fool yourself to believing in high climate sensitivity if you notice from measurements only a small energy imbalance between hot and cold years, because the system is never in equilibrium because the insolation varies with changing cloud cover. 

To sum up: We have seen that global mean temperatures can vary under constant radiative forcing, as an expression of the internal dynamics of the coupled ocean-atmosphere system. 

From this observation you can fool yourself (and the World) that a small change in the radiative forcing will have a large effect on global temperatures.  This is what IPCC seems to be doing. 

Mathematically this is is an illposed problem: You are trying to compute a derivative Df(x),

of a function f(x), namely climate sensitivity, with f(x) the temperature as function of forcing x.

But you only know the value of f(x) (+ perturbations) for one value of  x (or values very close to x). Now Df = df/dx where df is change in f and dx is change in x, and if dx = 0 (or very small) then Df is not well defined,  that is Df is illposed. 

Accordingly IPCC puts climate sensitivity in the interval 1.5 - 4.5 (or bigger) ,which is so large that it carries no information of value, except that 4.5 (or bigger) looks scary. It could as well be 0 - ∞ . And the true value seems to be close to 0. While the value ∞ is used in IPCC alarmism.

Note that the usual way of estimating climate sensitivity is to differentiate

Stefan-Boltzmann's Radiation Law Q = c T^4 to get dQ=4cT^3dT, which with dQ = 3 gives 

the commonly  predicted value of dT = 1, that is a climate sensitivity of 1 C, which is the further inflated by positive feed back to 1.5 - 4.5 C.  

But this argument lacks logic because it only focusses on black body radiation, and does not 

take into account that the atmosphere acts as an insulating layer, for which case the above

(simple) computation shows a climate sensitivity of at most 0.3 C.