Basic physics shows how the IPCC exaggerates alleged warming from CO2 by 10 times

Re-blogged from Dr. Claes Johnson, Professor of Applied Mathematics, KTH:

Leaked Climate Sensitivity of 0.3 C

The leaked Second Order Draft IPCC AR5 essentially repeats the AR4 estimate of a climate sensitivity of 3 C:

• Equilibrium climate sensitivity is likely in the range 2°C–4.5°C, and very likely above 1.5°C. The most likely value is near 3°C. Equilibrium climate sensitivity greater than about 6°C–7°C is very unlikely. 

Let me here  leak the following update of my previous 10 times smaller estimate of climate sensitivity coming down to 0.3 C, based on the following argument using the standard numbers of 

• Earth surface temperature: + 15 C
• top of the atmosphere TOA temperature: - 18 C at 5 km altitude
• lapse rate: 6.5 C/km 
• dry adiabatic lapse rate: 10 C/km
• transported from surface to TOA by thermodynamics: 120 W/m2 
• transported from surface to TOA by radiation: 60 W/m2.

Assuming that thermodynamics reduces the lapse rate from 10 to 6.5 C/km, thermodynamics would thus have the effect of decreasing the temperature increase from TOA to Earth surface by 5 x 3.5 = 18 C, thus with a relative decrease of 18/120 = 0.15 Cm^2/W. 

The corresponding number for radiation would be an increase of 33/60 = 0.5 Cm^2/W. 

The combined effect would thus be with a partition of 2/3 thermodynamics and 1/3 radiation:

• 1/3 x 0.5 - 2/3 x 0.15  = 1/6 - 1/10 = 5/30 - 3/30 = 2/30 = 1/15 Cm^2/W.

An assumed radiative forcing of 4 W/m2 would thus lead to a warming of  4/15 C, which is less than 0.3 C, thus a factor 10 smaller than IPCC's most likely value of 3 C.

Do you say that the above argument is simplistic? Yes, it is, but it may well be more realistic than the IPCC argument  leading to a climate sensitivity probably inflated by a factor 10.

See Negative Climate Sensitivity, the followup post to the above