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 says nothing about saturation, convection, pressure or absorption spectrum.

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.

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

Addendum—Explanation:

The basic equation (radiative forcing = 5.35 ln C/C₀) is an offshoot of the so-called radiative transfer equations—but a misapplication of the concept.

The transfer equations indicate how much radiation is converted to heat, and how much passes through a gas, as the concentration of the absorbing gas increases. With an increase in concentration, more radiation is absorbed creating heat, and less passes through.

Climatologists, being physicists, figured that the radiative transfer equations would be how to determine how much radiation is converted to heat by carbon dioxide in the atmosphere. But there were a few glitches.

The first glitch is that such equations do not hold when there is no longer any radiation passing through the gas—a condition called saturation. Carbon dioxide in the atmosphere saturates at the center of its main peak in ten meters (Heinz Hug). That means it uses up all radiation at the wavelength which it absorbs within ten meters. There is a lower concentration of CO2 molecules on the shoulders of the absorption peaks (which are in a different energy state), but even those use up all radiation in a longer distance. Where the concentration is one tenth of that at the center of the peak, the distance is ten times as much, or 100 meters.

Another glitch is that absorption bands of other greenhouse gasses, particularly water vapor, overlap those of CO2.

So someone, perhaps James Hansen, took the general equation for radiative transfer and tailored it to fit the assumed result that CO2 was producing. The assumed result was that an increase in CO2 from 280 to 380 ppm since the industrial revolution caused a 0.6°C temperature increase.

That assumption is highly subjective and invalid for both the CO2 increase and temperature. The CO2 increase came from ice core measurements which are totally worthless for CO2. Direct measurements show almost as much CO2 in the air a century ago as now. The assumed temperature increase is also more contrivance than measurement.

Then the ultimate glitch is that radiative transfer is only applicable to a homogeneous and definable condition, where rate of heat loss is known. No one knows what heat does in the complexities of the atmosphere. To assume what the heat does before writing an equation to determine what it does is a closed loop of logic.

So the modified equations were designed to show that whatever was happening in the past is what will happen in the future. That assumption is nothing resembling science. Science is measuring, not assuming. There is no allowance for change in extending the past into the future (even if the past were evaluated properly). Yet the computer models do the same thing. They are tested and aligned upon the assumed events of the past, and they extend the past into the future. Any six-year-old can extend a line from the past into the future. So computer models could not predict the leveling off of temperatures over the past eight years including a decline over the past few years. The models had to show whatever the past showed.

Kalmanovitch Paper — shows the source of the fudge factor, at Icecap, November 25, 2008

Another Source of Kalmanovitch Paper — at Geoplasma

 

Question: How do we know carbon emissions cause climate change? Vicky Pope, Chief Climate Advisor at the Met Office, UK: If there were no carbon dioxide (CO2) in the atmosphere it would be a lot colder. The link between CO2 and temperature is a matter of basic physics and has been known for 200 years. But human activity is upsetting the balance. http://blogs.mirror.co.uk/science/2009/12/global-warming-forget-the-clim.html

 

The Other Side of the Story by Alarmists

This subject is described on the Real Climate web site— the usual reference for alarmists—exactly as I describe it on the page titled Disputed Area, except with the conclusion that the result is significant rather than irrelevant. Their conclusion is explained with this image:

(Image at Real Climate)

As the CO2 concentration increases, the slopes on the absorption curves absorb more infrared. This would be irrelevant at ground level, but it supposedly prevents more radiation from going into space at the top of the troposphere. But is the amount a lot of very little? I explain why it is very little, while alarmists say it is a lot. Is there a science to resolve this dispute? None what-so-ever. In fact, the only resolution of this whole subject is to measure the claimed temperature increase of the past and assume something similar will happen in the future. (See above)

I give explanations and logic for a miniscule effect (see Crunching the Numbers), while alarmists do not explain why the heat would be significant. But regardless of the numbers, there is no explanation of how the supposed temperature increase at the top of the troposphere, which is very cold, can produce heat at ground level.

Getting back to the image above, notice that the slope of the absorption spectrum used by alarmists is about 45 degrees of angle. This leaves a lot of space for change. But the actual absorption spectrum for CO2 is nothing resembling this. The edges are sharp. The actual absorption spectrum for CO2 is bounded by the wavelengths 14 to 16 microns. In the above image, the relevant band is shown as 13 to 17.5 microns. CO2 cannot absorb at such wavelengths. The wavelength of absorption is determined by the energy state of the molecules, while increasing the amount of CO2 does not change the energy state.

So where do these 45 degree angles come from? This graph is based upon measurements high in the atmosphere by the Air Force during WW-II. The atmosphere doesn't represent anything close to an absorption spectrum for a single gas such as CO2. After radiation goes through several kilometers of atmosphere it is influence by a large number of unknown factors including scattering and absorption by any number of unknown substances. This means that the angled slopes on the curve are not caused by CO2 but other things. So the entire rationale for absorption on the edges of the absorption spectrum is not valid.

This graph is not a properly scaled representation of anything. It's designed to catch the eye of the unwary, much like the fake hockey stick graph. Oddly, they multiplied the CO2 level by a factor of four, where the usual question is what happens upon doubling of CO2. Then the lines across the graph for 1X and 4X have no meaning. They don't intersect with anything relevant on the graph.

The 1X line is arbitrarily placed at one absorption unit, and the 4X line is placed at the 0.5 absorption units, while the peak is at 10,000 absorption units. So how do they know that the increase will widen the effective absorption by almost one micron of wavelength? There is nothing on the graph or anywhere in science which will tell them that.