Climate change alarmists have been saying that doubling the amount of CO2 in the air will result in a temperature increase of 1.2°C and that everyone agrees, even most deniers. The only question is supposed to be secondary forcing, mostly due to water vapor, which increases or decreases the 1.2°C.

The basic temperature increase of 1.2°C is called radiative forcing or temperature sensitivity. It seems strange that the number would be so unquestionable, when humans don't have the slightest ability to quantitate the complexities and randomness of climate activity. Some say the number is produced by a simple calculation, sometimes attributed to the Stefan-Boltzmann equation (SBE). The SBE simply states how much radiation is given off by matter at a given temperature; and all matter is assumed to be the same. It says nothing about saturation, convection, pressure or absorption spectrum. In fact, it does not apply to the finger print radiation absorbed by greenhouse gasses; it only applies to black body radiation. I claim that it is inappropriate for gasses, because they don't have a two dimension radiative surface.

Steve McIntyre attempted to trace the source of the number in the IPCC reports. There is no source to be found. All citations lead to nothing. The discussion of this subject on his web site is found here: http://www.climateaudit.org/?p=2570, January 7, 2008.

Near the origins of the equations in question is a publication by Hansen et al, Journal of Geophysical Research, August 20, 1988, claiming that radiative forcing by carbon dioxide follows an equation which now takes the form of, rf = 5.35 ln C/C₀, and that this result can be converted to a global temperature of 0.75°C ±0.25°C for each watt per square meter.

Norm Kalmanovitch did an evaluation and criticism of the Hansen publication and determined that the source of the numbers would have been the claimed increase in CO2 of 100 ppm since the industrial revolution combined with a supposed temperature increase of 0.6°C. He said that no more than 0.1°C can be attributed to carbon dioxide, since a pre-existing increase accounts for 0.5°C due to the rebound from the "little ice age." I would go farther and mention the total fabrication of temperature data based upon the juggling of worthless thermometer measurements.

More relevant than the actual numbers is the total contempt for the basic science of the subject. The equation for radiative forcing shows about 4 W/m² for doubling the amount of CO2 in the air. Gasses such as the atmosphere do not have a surface for the supposed watts per square meter. The concept webs into transfer measurements, where a hypothetical surface might exist for a spacecraft looking down upon the earth. But for CO2 that surface is above the stratosphere and therefore has no relationship to temperatures near the earth's surface.

The IPCC documents state that indeed the center of the main absorption peak for CO2 saturates, but the shoulders do not saturate, and they yield the increase in heat with increased concentration of CO2. The applicable part of the shoulders would be about one part per thousand of the total absorption curve. It would absorb over several kilometers instead of the ten meters at the center of the absorption peak. So the supposed 4 W/m² increase is spread over several kilometers, which means it must be viewed in terms of cubic meters instead of square meters. Four watts dispersed through five thousand cubic meters of air is not going to produce 0.75°C x 4 = 3°C temperature increase.

With a specific heat of air of 1.012 Kj/Kg/K, an average density of the troposphere of 0.51 Kg/m³ and the heat spread over 5,000 m³, that's 2550 Kg of air. Four watts is a kilo-joule every 250 seconds. It thereby takes 22 days to heat that much air 3°C. If it keeps heating for 44 days, the temperature increase is 6°C. It starts to boil water in 747 days.

There is no definable relationship between rate of heat added and resulting temperature. It depends upon rate of heat loss. Nature equilibrates at some point, and humans have not the slightest ability to determine how the equilibration occurs, which means the numbers and equations are totally contrived.

How nature equilibrates was demonstrated by Lindzen and Choi, who used satellite measurements of radiation emitted by the earth and showed that as surface temperatures increase, more radiation escapes into space. described on Forcing page

Similar fakery: Fake Data—The Hockey Stick Graph