## måndag 20 december 2010

### How to Kill a Sky Dragon by Mathematics

Our new book Slaying the Sky Dragon: Death of the Greenhouse Gas Theory is topping Amazon eBook lists. The paperback version will appear after Christmas along with radio and TV presentations.

The message of the book is that the so-called atmospheric
Greenhouse Gas Effect GGE, presented by IPCC as the scientific basis of CO2 alarmism, lacks sound mathematical and physical rationale.

My role in the team of authors is to shoot with the weapon of mathematics at the heart of climate science consisting of the two chambers
• blackbody radiation: transfer of heat energy by electromagnetic waves
• thermodynamics: interplay of heat energy and kinetic/potential energy under gravitation.
GGE is claimed to result from a small change of the atmospheric trace gas CO2 (from 0.028% to 0.056%) capable of changing the heat transfer between the Earth Surface ES and the Top Of the Atmosphere TOA and causing warming of ES of 2 - 4.5 C.

GGE thus concerns substantial change of ES temperature under a very small perturbation of the radiative transfer properties of the atmosphere connecting ES with TOA. GGE as
a mathematical/physical mechanism is thus unstable, in the sense that a small cause gives a big effect: a small change of an atmospheric trace gas can change global climate.

To change something small into something substantial, it is necessary to multiply the small with something big. To this end GGE has invented the concept of "backradiation" with ES emitting 390 W/m2 out of which 340 W/m2 is received from TOA as re-emitted radiation from ES, with 340 W/m2 = 100% of gross (total) incoming radiation from the Sun.

"Backradiation" thus gives GGE a major energy flow of 340 W/m2 to operate on, namely a circulating flow of energy (equal to gross incoming energy) transferring energy from ES to TOA and back again. GGE now says that a trace gas changing the radiative properties of the atmosphere by say 1% operating on the circulation of 340 W/m2 can give rise to a change of 3.4 W/m2 which by Stefan-Boltzmann's radiation law can be connected to about 1 C of global warming. This gives the basic axiom of IPCC CO2 alarmism of a climate sensitivity of 1 C upon doubling of atmospheric CO2, which then is inflated to 2 - 4.5 C by imagined feedbacks of factors 2 - 5.

The basic killer shot of my contribution to the book, is a mathematical analysis of blackbody radiation showing that "backradiation" is unphysical, because it corresponds to an unstable process which cannot be realized. The result is that the radiative transfer of heat energy between ES and TOA consists of a net transfer of about 120 W/m2, about 1/3 of the fictitious
circulating flow of 340 W/m2. This reduces the basic climate sensitivity to less than 0.3 C,
which cannot be used to create alarm, because feedback factors of size 10 lack any scientific rationale.

It thus appears to be possible to kill the Sky Dragon by one shot (my blackbody article). If that does not turn out to be enough, depending on the audience, another shot can be launched at an unprotected flank of the Dragon by recalling the fact that climate results from a combination of thermodynamics under gravitation and radiation, and that GGE is essentially based on radiation alone (my thermodynamics article). The second shot says that not only the magnitude of climate sensitivity is unclear but also its sign: It is conceivable that more CO2 can cause some (small) cooling.

I believe that the above shots can be effective in coming TV and radio presentations, because convincing mathematics is hard to deny, for both alarmists and skeptics.

But even if the Sky Dragon is afraid of mathematics, because alarmistic Dragons have limited intellectual capacity, what the Dragon fears the most is, yes cold weather, and the record lows now hitting Europe is turning the Dragon into a freezing lame duck which will not likely survive the winter. And what we have seen is only the beginning according to one of the slayers, Piers Corbyn.

An analogy in economics presents itself: Imagine a national economy with a large scale circulation of money from high taxes and large government subsidies of the order of trillions
of dollars, and imagine a broker charging the tiny percentage say 0.0o1%, with a net profit
of billions of dollars. Nice, right? But what about the stability of an economy with unlimited circulation of money, of fictitious money without any real value? Any clue?

#### 8 kommentarer:

1. Looks to me like it is a "stable" process: large change in input (from 0.028% to 0.056% is a factor 2) and small change in output (+4.5 C is a small relative change).

2. You are right: A change of 0.028% may in a stable fashion change the atmospheric radiative properties by say 0.028% with an upper estimate
of say 1%. The key question is what radiative flux this 1% (or maybe rather 0.028%) is supposed to multiply: If you assume a recirculating heat energy of 340 W/m2, then you get 3.4 W/m2, which by Stefan Boltzmann can be associated with 1 C warming. If you assume 3400 W/m2 recirculation, the you get 34 C and 10 C warming. But heat energy is not recirculating by"backradiation" and the net heat transfer is rather around 120 W/m2 corresponding to 0.3 C (or less with 0.028% instead of 1%) Do you get the essence of the argument?

3. No, I would need to know a lot more to draw any conclusions (and I'm not really interested).

4. Why are you commenting if you are not interested?

5. I can only comment on the math (and maybe some physics) but not on the rest.

6. Still I don't understand why you comment if you are not interested.

7. A pure mathematician or hindu can claim not to be interested in the world,
but can you?

8. I think my killer shot would be the following:

The net heat flow is always from higher temperature to lower temperature. Since energy is conserved, this means that the natural tendency of any (real) heat transfer process is to make temperature differences between different parts of the system as small as possible.

However, the greenhouse effect supposedly makes these differences larger. Some people ignore the fact that the canonical version of the greenhouse effect predicts a cooling of the upper parts of the atmosphere. Instead they invent new theories to remedy this inconvenience. But why is the cooling necessary? The answer is the following:

Suppose that the GE merely "heats the atmosphere as a whole" (with lapse rate determined by gravity). Higher temperature means more radiation which in turn means more GE and so on, hence you get a runaway effect, the temperature will reach infinity. The cooling of some part of the system is simply necessary to avoid the runaway effect.

When scientists understand this, the greenhouse effect will be dead.