Before posting any more remarks on global warming in the comments of this forum I want something that I can link back to that states my own position and why I believe it. The following is a rather long (sorry) rewrite of something from a while ago. Basically, AGW is real in that man's actions will produce an increase in temperature that will be measurable and perhaps even noticeable, but the increase will be far less than predicted by the IPCC. Therefore, I am a Luke-Warmer :-)

My apologies if this reads like some sort of tutorial. That wasn't intended. I just don't know any other way to write it. I'm no climatologist; following the debate is a hobby.

I am a back-of-a-fag-packet calculation kind of guy. The following oversimplifies greatly, but if my basic reality check numbers are out of kilter with the mega-models, I begin to question which of the two is wrong. And that is where I am now. The mega-models predict between 2 and 4.5 degrees C warming, with a best estimate of 3 degrees. My climate-for-dummies reality check is half that at best.

From the Arrhenius equation we know the radiative forcing from a doubling of CO2 fairly well. It is ΔF = 5.3 ln(C_t/C_o) = 5.3 ln(2) = 3.7 watts/m^2. The 6 trillion dollar question is instead, what will be the response of the earth to this forcing in terms of temperature? To express this you often see:

where lambda, λ, is the climate sensitivity of the earth to a unit forcing of 1 w/m^2. It has units of °C/w/m^2. It incorporates possible feedback effects due to, for example, increased atmospheric water vapor content.

Despite the millions spent on research and despite what the IPCC says about a consensus, the value of λ is an open question. Nobody really knows what it is, or how much it is time-scale dependent (it almost certainly is to a degree). The estimates are all over the map, from less than 0.1 to well over 1. As a consequence there is an order of magnitude difference in temperature projections.

As a starting point, you can use standard Stefan Boltzmann black body physics (or actually "gray body", considering albedo) to derive a climate sensitivity of 0.3 °C/w/m^2. From this, the temperature response to 2xCO2 is ΔT = λ ΔF = 0.3 * 3.7 = 1.1 °C. This assumes equilibrium (no lag) and ignores all feedback effects. It also ignores other possible anthropogenic influences (which generally cancel out). The clearest explanation I've seen of this derivation is here, by Israeli physicist Nir Shaviv.

Now, recognizing that feedback is not yet considered, at this point we are at a level approaching scientific law. Really. It is mostly from first principles. Up to here, the skeptics and the IPCC agree. Only a few six sigma nut-case deniers dispute it. General comment: I reserve the term "denier" for those that refute even the simplest of observations to the point of absurdity. And I use the term "skeptic" in an honorable sense: to question consensus (especially new consensus) is a requirement of good science. (and oh, Dr. Heidi Cullen can kiss my....)

The next six gazillion dollar question is then, how big are the feedback effects?

The basic mechanism is not particularly in dispute. Predominantly, it is from additional water vapor. CO2 initially warms the troposphere by the greenhouse effect, which through increased evaporation creates more water vapor in the atmosphere. Water vapor is itself a greenhouse gas (the biggest one) so this begets yet higher temperatures, which begets more water vapor, etc. In this way a feedback loop is created. It is generally accepted that the feedback is positive in sign. How long this can go on is, to my knowledge, unknown. But still: do other feedbacks act in the opposite direction? Is the net feedback even positive? There is some evidence that it is not.

We can also make empirical based estimates of λ in which we try to find an isolated forcing (e.g., Mount Pinatubo) and observe the earth's actual response to that forcing. The standard example is derived from the ice core records of CO2 and T during the last glacial cycle (I forget the source; I think it was a Hansen paper). After accounting for albedo change, over the millennia there was a net forcing of ~7 w/m^2 and a temperature response of ~5 °C. This gives a sensitivity of 0.7 and a 2xCO2 temperature increase of about 3 °C.

The trouble is, I can cite numerous papers where empirical estimates of λ are far lower, generally around 0.1 to 0.2 °C/w/m^2. Such estimates imply negative feedback, actually, since they are less than the Stefan Boltzmann value. They include an analysis of the Pinatubo eruption [PDF] from satellite measurements. Another is based simply on the observed warming seen during the last century with respect to the known forcing by CO2 [λ = ~0.6 °C/~1.6 w/m^2 = 0.38]. There have been many others (such as Idso, 1998, PDF), and some more recent. I can see no particular reason why these estimates are ignored by the AGW crowd. There may be valid criticisms for the individual approaches but when realistically accounted for, the numbers don't change all that much!

Regardless, let's look at the feedback gain implied by the IPCC estimates and ask if these are reasonable. The lastest IPCC AR4 estimate for a 2xCO2 world is a temperature increase of 2 to 4.5 °C. Using a simple ratio with respect to the Stefan Boltzmann value of 1.1 °C, the implied feedback gain is somewhere between 1.8 and 4 -- i.e, up to 400% But let's take it a small step further.

In math terms, we have a gain, g, produced by a feedback, f as follows:

Defined this way a feedback of 50% (0.5) produces a gain of 2, or two times the strength of the original forcing. The above can also be expressed in series form, which for me more is intuitive when thinking about feedback loops. For example, with f = 0.5 each term in the following series is reduced by half:

For f = 1 the series no longer converges to a number. For f > 1 the series is unstable and runs-away into cataclysmic Goregasms. For the heck of it, here's a chart of various feedback terms:

As a first approximation, gain and feedback are related to the climate sensitivity by λ_f = g λ, where in this case λ is the Stefan Boltzmann sensitivity (no feedback) and λ_f is the climate sensitivity including feedback. Given the IPCC temperature estimates we can now work backwards and find the gain and feedbacks implicit within the IPCC models (Table 1).

It can be seen that their mid- and high-end estimates imply a feedback factor that gets closer and closer to 1, and that feedback gains of 180 to 400% are required.

From all this I have two basic problems. The first problem is the dependence on feedback gains that are far greater than the original forcing strength. For me, this is simply non-intuitive, probably unphysical, and violates my idea of a basic reality check. I can imagine a maximum feedback gain of, say, 1.5 times the original forcing, but no more. My estimate for 2xCO2 is therefore between about 0.7 and 1.7 °C. I am not alone in this. Many engineers knowledgeable in circuit design and signal processing (they deal with feedback loops all the time) are simply gobsmacked when they learn of this in reference to global warming.

The second related problem is that the IPCC's numbers imply an earth that is just short of unstable and dangerously close to run-away conditions. All I know about earth science says this cannot be true.

Lastly I want to point out that the IPCC position, especially after the recent demise of the hockey stick, is almost entirely dependent upon the mega-models. They provide no theory based on first principles to document their feedback and related predictions. No, it is all based on models with multiple tweaking parameters.

QED? lol.

P.S. - I'll get into why the models have problems another day.
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Get your facts first, and then you can distort them as much as you please --Mark Twain

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Get your facts first, and then you can distort them as much as you please --Mark Twain