Updated with a new first section (of three posted today, February 16):
Problems with the radiative transfer modeling in the IPCC models.

Since today is the day the Kyoto Protocol goes into effect, it is as good a time as any for me to explain why I think the fundamental thought experiment underlaying the AGW theory is both simplistic and wrong.

It may amuse some, confuse some, and, if I am lucky, convince some that I am right.

First though consider three simple "thought" experiments:

1. A an object travels at three time the speed of light.

2. One is instantaneously transported to the moon.

3. The carbon dioxide content of the atmosphere is instantaneously doubled.

All three experiments are fantasy since they can't happen in the real world. In other words, just because something can be imagined, it doesn't mean that it can actually happen. For most everyone, it seems, the third "thought" experiment appears to be true and is accepted without question. It is my purpose here to show why it is not a valid thought experiment. It is a thought experiment that violates several laws of physics.

The doubling thought experiment proceeds as follows:

1. A radiation field is calculated for the present day atmosphere with the present day temperature and temperature lapse rate and present day concentration of carbon dioxide.

2. Next the level of carbon dioxide is instantaneously doubled.

3. A radiation field is then calculated for the doubled concentration yet the atmosphere maintains its present temperature and temperature lapse rate.

4. Finally the difference in the radiation fields calculated for the two concentrations is used to calculate the radiative forcing of climate. It equals roughly 3.5 W/m2 at the top of the troposphere.

This thought experiment is accepted without question and forms the basis of about 10,000 papers in the peer reviewed literature.

This thought experiment cannot happen in reality for the following reasons:

1. In the first place, nothing can happen instantaneously. It is a violation of the theory of relativity since it would require 600 Gt of carbon dioxide be transported from the surface to an average of 5 kilometers in the atmosphere.

2. If we assume by "instantaneous", they mean at the speed of light, then when the 600 Gt of material suddenly stops, it will be converted to heat and light amounting to about 57,000 W/m2. This power release is sufficient to extinguish life on Earth and perhaps blow part of the atmosphere into space. The release of the braking energy would indeed be an energetic and explosive event.

3.Even one managed to do the doubling with a few days (so as to lessen the effects of the release of the braking energy), ordinary weather and seasonal variations would make it impossible to hold the temperature invariant. The before and after atmospheres would be quite different in many ways.

4. Not only is the instantaneous doubled concentration atmosphere with an unchanged tropospheric temperature impossible to construct, it is also inherently unstable since the temperature and radiation fields are widely discordant. It could not be maintained in this state for even an instant unless one is invoking magic. Yet a fundamental assumption of the AGW theory is that the very transient 3.5 W/m2 forcing they calculate will remain invariant for decades until a new temperature equilibrium is reached. It won't happen.

5. Finally the difference in radiation fields postulated above assumes that only the difference in the carbon dioxide bands occurs and the continuum radiation remains invariant. This assumption implies that the continuum region of the spectrum is a perfect insulator and further implies that a perpetual motion machine could exist. In the real world, perturbations in one part of the spectrum will cause re-adjustments in the rest of the spectrum. The IPCC thought experiment neglects these re-adjustments and thus overestimates the radiative forcing. Any added absorption in the carbon dioxide absorption bands will be partially offset by increased emission in the continuum or windows of the spectrum. Calculated properly, the 3.5 W/m2 forcing becomes about 1.3 W/m2.

These are just some of the problems with the IPCC "thought" experiment, which in reality is simply a fantasy experiment. It is ridiculous to just make cavalier claims of an instantaneously doubling of carbon dioxide without examining whether such changes are physically possible.

The implications of the above discussion are as follows:

1. The IPCC overestimates the warming by a factor of about three.

2. There are roughly 10,000 peer reviewed climate papers based upon a faulty thought experiment that reach incorrect conclusions and should be withdrawn by their authors.

3. The correct forcing is smaller than the IPCC forcing by the equivalent of 30 Kyoto Protocols.

I suppose I will receive considerable flak about these comments. In the past when I have brought up this topic, people have refused to discuss it and in one case, I was told "it is a not a topic for discussion". Nonetheless, it seems pretty evident to me that the entire AGW hypothesis is based on a carelessly constructed thought experiment and the resulting radiative forcing number has no physical significance. Real climate science should rely on real physics, not magic.

The bottom line: Basically to believe the 3.5 W/m2 figure, one has to believe that a highly unstable atmosphere can be created instantaneously without expending any energy and with massive flows of matter having zero effect on atmospheric temperature. One further has to believe that a perturbation in one part of the spectrum can be made with no effects on the rest of the spectrum.

This section is the oldest discussion of this topic

The IPCC definition of radiative forcing states it is calculated "after allowing the stratospheric temperatures to re-adjust to radiative equilibrium, but with surface and tropospheric temperature and state held fixed at the unperturbed values". In this approach to calculating radiative forcing, the tropospheric temperatures are identical with 290 ppm carbon dioxide and 580 ppm carbon dioxide (a doubling). With 290 ppm, the temperature and radiation are self-consistent and in equilibrium. With 580 ppm, the temperature and radiation are far from being self-consistent and are far from being in equilibrium. We refer to the IPCC approach as an instantaneous forcing.

The instantaneous forcing number is an easy number to calculate, but it is conceptually wrong to use it to calculate an equilibrium response. The problems with this approach are as follows:

1. Although a thought experiment can be conceived in which you have an atmosphere with current temperatures and doubled carbon dioxide, in reality such an atmosphere could NEVER be achieved since it is far from being in equilibrium. An analogy would be a calculation for how long it takes to walk to the moon. Although detailed mathematical calculations could be made taking into account speed of walking, meal times, sleep time, and so forth, the calculations would be meaningless since physically the walk could never be made. Similarly the IPCC proposed doubled carbon dioxide atmosphere with present temperatures can NEVER be created in the real world.

2. As a consequence of the above, the associated radiative field can never occur in reality.

3. As a consequence, the associated radiative field is a fiction and the IPCC radiative forcing calculated by subtracting the present radiative field from the fictional doubled radiative field is also a fiction. The IPCC radiative forcing can never occur in the real world.

The IPCC instantaneous carbon dioxide doubling forcing is a flawed thought experiment giving rise to high numerical values that cannot occur. In the IPCC thought experiment, the outgoing longwave (thermal) radiation is reduced by about 3.5 W/m². All the changes in the radiation occur in the bands where the carbon dioxide absorption occurs. The continuum radiation outside the absorption is assumed to be invariant and unchanged because the temperature filed is assumed to invariant and unchanged (see figure at the end of this essay). The IPCC approach essentially says that once a photon is absorbed and converted to heat, the energy remains in the system. It is tantamount to claiming carbon dioxide is a perfect insulator.

The problem with the IPCC approach is that the continuum radiation is invariant. In reality it cannot be invariant; rather, the radiation will decrease in the carbon dioxide bands and increase outside the bands due to thermalization and re-emission. In other words, there will be a re-adjustment of the tropospheric temperature that is not accounted for in the standard instantaneous doubling approach. Correct calculations reduce the 3.5 W/m² flux decrease to 3.5 e^-1 W/m² or 1.3 W/m². The latter number is the number that should be used to calculate the equilibrium response to a doubling of carbon dioxide.

The equilibrium forcing should be used to calculate the equilibrium response. The IPCC instantaneous forcing number is inappropriate.

Similar conclusions to ours are reached by Peter Dietze, who concludes the radiative forcing is about 1.4 to 1.9 W/m².

The figure below shows the radiation field and how it is perturbed according to the IPCC approach. Note that there is no change in the continuum radiation.

Addendum added in December 25, 2004.

Apparently the above criticism of the radiative effects of a carbon dioxide doubling were not clear enough, so we are adding a few more comments.

First of all, a thought experiment MUST obey ALL the laws of nature and not just some of them, just like a real experiment. A thought experiment is conducted because to do it in reality would be difficult for a variety of reasons, such as time constraints, size constraints, cost constraints, etc.

In the case of the instantaneous doubling of carbon dioxide, there are several problems with this simplistic thought experiment. For example, what does the word “instantaneous” mean? Is it the speed of light? If so, then we have an experiment where 600 gigatons of carbon dioxide enters the atmosphere and is suddenly stopped. The resulting release of heat would be enormous and would end all life on the surface of the Earth. So an instantaneous doubling is impossible, and the thought experiment is fantasy.

Secondly, an atmosphere with the present temperature structure and a doubled carbon dioxide is far from equilibrium. It could not be constructed instantaneously or any other way. Again the thought experiment is fantasy.

Thirdly, in the thought experiment, the radiation in the continuum outside the carbon dioxide absorption bands is held fixed. Again, it is impossible and the implications of saying it does happen is that one is stating that a perfect insulator exists. With a perfect insulator (as with a perfect conductor), it becomes possible to construct a perpetual motion machine. It seems the IPCC has endorsed the existence of perpetual motion machines as de facto result of their faulty thought experiment.

The reality is that the thought experiment proposed by the IPCC is a fantasy and radiative forcing numbers they use in all their calculations in all their climate models are fictions. As explained above, the transient radiative forcing should not be used to calculate the equilibrium response of the climate system. The equilibrium radiative forcing is much smaller and its use would mean the global warming scare would disappear.