## torsdag 15 april 2010

### On Climate Sensitivity 4

IPCC climate alarmism with a climate sensitivity/global warming of 1.5 - 4.5 degrees Celcius upon doubling of CO2 in the atmosphere, is based on the following argument:

Stefan-Boltzmann's Radiation Law states that a black body radiates heat Q which scales like the fourth power of its temperature T in degrees Kelvin K, that is

Q = c TTTT ,

where c is a constant. Differentiation gives

dQ = 4 c TTT = 4 Q/T .

It is known that the Earth radiates about 273 Watts per squaremeter at a temperature of about 273 K or 0 Celcius C, which gives the crucial relation

dQ = 4 dT

connecting change of radiation dQ to change of temperature.

IPCC now argues that dQ from doubling of CO2 is about 4 Watts per squaremeter, and thus
the corresponding global warming dT = 1 C (the same as 1 K). By positive feed back this is then
elevated to 1.5 - 4.5 C.

The global warming of dT = 1 C is presented as rock solid basic physics which cannot be questioned, because that would amount to violate Stefan-Boltzmann.

To get perspective, let us compare with an even simpler argument: Changing Q=273 with
say dQ = 2.73 (instead of 4 to make it simple) corresponds to 1% and a corresponding 1% change of T=273 would amount to a global warming of dT of about 3 C.

This seems too big even to IPCC, but corrected by the marvellous factor 4 from differentiation, it becomes the starting point of global warming with climate sensitivity dT of about 1 C.

But is it scientifically correct to use Stefan-Boltzmann's Law to compute dT =1 C? Or

Let's see: The atmosphere acts like an window insulating the Earth surface at a temperature of 15 C from the radiating upper atmosphere at 0 C.  It acts like a window separating the inside of a room at say 15 C from the outside at 0 C.

But this situation is not described by Stefan-Bolzmann's Law, but rather by the even more fundamental Fourier's Law stating that heat transfer is proportional to temperature difference with a certain heat transfer coefficient.

Now according to IPCC, doubled CO2 corresponds to 1% increase of radiative forcing, which
can be translated to a 1% decrease of heat transfer coefficient, that is 1% better insulation, which would require a 1% increase of temperature difference inside-outside to maintain heat balance. But 1% of 15 C is 0.15 C.

The basic climate sensitivity thus appears to be 0.15 C (by Fourier's Law), rather than the commonly presented rock solid 1 C (by Stefan-Boltzmann's Law).

To reach a climate sensitivity of 4.5 C starting from 0.15 C requires a positive feed back factor of 30. What can be the science behind a so large positive feed back factor? IPCC does not give any clue, and nobody else... Maybe  climate sensitivity is about 0.15 C? Barely noticable?

This post is also put up as the knol Climate Sensitivity.