A highly authoritative critic of the "consensus" view of global warming, Roy W. Spencer, wrote a marvelous summary with criticisms which can be used as a reference for evaluation. I find that the authoritative critics take the right position without getting to the source of the errors with basic and accurate enough evaluation. In part, they are too sheepish, not wanting to create too much of a stir in the rattlesnake den of climate change agitators, where scientists lose their jobs or funding for opposing the status quo. But also, specialists get into mind ruts where they close off avenues of thought not knowing how much weight to place on different elements of the problem. This always occurs at the boundaries of knowledge. An external viewpoint is freer from the mind ruts and from the intimidating forces.

The modeling starts with the claim that if the amount of carbon dioxide in the atmosphere were doubled, there would be a little more than 0.6°C of surface warming (stated here). I show with my simple estimates that it would be 0.026°C. So the discrepancy is a factor of 23. Could I be off that much? Not hardly. Modelers use "energy budgets" which sometimes show as much radiation leaving the earth as striking the earth, which is absurd. A person's skin would be fried lying in bed, if normal temperature matter were giving off as much radiation as the sun's radiation striking the earth.

But I say this only to clarify the next point. As Spencer then points out, the 0.6+°C increase would not in itself be significant. Only "positive feedback" could make it relevant. Positive feedback means that some other factor amplifies the temperature increase. The claimed cause of this is that increased heat causes more water to evaporate, while water vapor is a strong greenhouse gas. Modelers claim that positive feedback through water vapor increases the humanly caused effect from 0.6°C to 3-6°C, when the amount of carbon dioxide in the atmosphere is doubled.

If there really were such feedback, it would cause thermal runaway. The temperature increase due to feedback would create a second cycle of feedback, and it would be greater than the first; and then it would trigger a third cycle greater than the second; and this would continue infinitely. You can't stop the feedback after the first cycle. If there were some force stopping it after the first cycle, then that force would be stopping the first cycle also. If you said moisture runs out after the first cycle, there is nothing magical about the first cycle that limits the moisture to it. Evaporation isn't some flash-in-the-pan which only responds to a 0.6°C temperature increase caused by humans.

Another error in the concept of feedback is that it is only applied to human input. Nature creates far more variation than 0.6°C because of random, seasonal and yearly variation.

Of course, modelers are averaging the human influence across a wide domain of several years. But nature produces long term variations also. Why are some years are said to be the hottest ever? Why not every year? Because nature varies a lot.

Another problem with modeling based on feedback is that neither water vapor, carbon dioxide nor any other so-called greenhouse gas can cause global warming, because so little is required to absorb the infrared radiation available that it does whatever it is going to do at a very small concentration and a very short distance. More only shortens the distance; it does not increase the heat. Carbon dioxide absorbs all radiation available to it in about 10 meters. Doubling it would shorten the distance to 5 meters. Water vapor would absorb all radiation available to it in less than a meter. Shortening the distance some more would be of no relevance.

Supposedly, humans already caused a 30% increase in carbon dioxide in the atmosphere (based on discredited ice core measurements), and the result is a 0.6°C temperature increase. Why wasn't it multiplied by a factor or 5-10 due to positive feedback through water vapor? The modelers didn't seem to apply their theory of feedback to it.

Addendum

I'm told that the reason why thermal runaway doesn't occur is because the initial increase in temperature causes an increase in radiation escaping into space. In other words, negative feedback stops the process after the first cycle.

All of this logic is extremely incredible. There is no real difference between the first cycle, second cycle or any other cycle. If a 0.6°C temperature increase is multiplied when humans are the cause, then it is multiplied when nature is the cause. There is nothing to distinguish between the first one degree increase caused by humans and the next five degrees, or the first 33°C which nature supposedly heats the atmosphere. To say that a 0.6°C increase by humans does something different (triggers a 3-6°C increase through feedback) which no other temperature increase does is to say nature creates a fixed system which is thrown into aberration by the most minute effects caused by humans. There is no such fixed system, as explained on the page titled Logic Error.

Summary by Roy W. Spencer
Modeling Useless for Predicting — Pielke